Journal of theoretical Biology

The effect of metapopulation dynamics on the survival and spread of a novel, conspicuous prey.

Publication Date: 2010 Aug 27 PMID: 20804773
Authors: Lee, T. J. - Speed, M. P.
Journal: J Theor Biol

Animals that deploy chemical defences against predators often signal their unprofitability using bright colouration. This pairing of toxicity and conspicuous patterning is known as aposematism. Explaining the evolution and spread of aposematic traits in previously cryptic species has been the focus of much empirical and theoretical work over the last two decades. Existing research concerning the initial evolution of aposematism does not however properly consider that many aposematic species (such as members of the hymenoptera, the lepidoptera, and amphibia) are highly mobile. We argue in this paper that the evolution of aposematic displays is therefore often best understood within a metapopulation framework, hence in this paper we present the first explicit metapopulation model of the evolution of aposematism. Our most general finding is that migration tends to reduce the probability that an aposematic prey can increase from rarity and spread across a large population. Hence, the best case scenarios for the spread of aposematism required fixation of the aposematic form in one or more isolated sub-habitats prior to some event which subsequently enabled migration. We observed that changes in frequency of new aposematic forms within source habitats are likely to be nonmonotonic. First, aposematic prey tend to decline in frequency as they migrate outwards from the source habitat to neighbouring sink habitats, but subsequently they increase in relative abundance in the source, as the descendents of earlier migrants migrate back from newly converted sub-populations. This pattern of initial loss and subsequent gain between new source and neighbouring sink habitats is then repeated as the aposematic form spreads via a moving cline.

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Simple model of recovery dynamics after mass extinction.

Publication Date: 2010 Aug 27 PMID: 20804772
Authors: Sole, R. V. - Saldana, J. - Montoya, J. M. - Erwin, D. H.
Journal: J Theor Biol

Biotic recoveries following mass extinctions are characterized by a complex set of dynamics, including the rebuilding of whole ecologies from low-diversity assemblages of survivors and opportunistic species. Three broad classes of diversity dynamics during recovery have been suggested: an immediate linear response, a logistic recovery, and a simple positive feedback pattern of species interaction. Here we present a simple model of recovery which generates these three scenarios via differences in the extent of species interactions, thus capturing the dynamical logic of the recovery pattern. The model results indicate that the lag time to biotic recovery increases significantly as biotic interactions become more important in the recovery process.

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Formulas for intrinsic noise evaluation in oscillatory genetic networks.

Publication Date: 2010 Aug 25 PMID: 20800602
Authors: Ito, Y. - Uchida, K.
Journal: J Theor Biol

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; First, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; We also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.

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A two level mutation-selection model of cultural evolution and diversity.

Publication Date: 2010 Aug 25 PMID: 20800601
Authors: Salazar-Ciudad, I.
Journal: J Theor Biol

Cultural evolution is a complex process that can happen at several levels. At the level of individuals in a population, each human bears a set of cultural traits that he or she can transmit to its offspring (vertical transmission) or to other members of his or her society (horizontal transmission). The relative frequency of a cultural trait in a population or society can thus increase or decrease with the relative reproductive success of its bearers (individual's level) or the relative success of transmission ( called the idea's level). This article presents a mathematical model on the interplay between these two levels. The first aim of this article is to explore when cultural evolution is driven by the idea's level, when it is driven by the individuals level and when it is driven by both. These three possibilities are explored in relation to: a) the amount of interchange of cultural traits between individuals, b) the selective pressure acting on individuals, c) the rate of production of new cultural traits, d) the individual's capacity to remember cultural traits and to the population size. The aim is to explore the conditions in which cultural evolution does not lead to a better adaptation of individuals to the environment. This is to contrast the spread of fitness-enhancing ideas, which make individual bearers better adapted to the environment, to the spread of "selfish" ideas, which spread well simply because they are easy to remember but do not help their individual bearers (and may even hurt them). At the same time this article explores in which conditions the adaptation of individuals is maximal. The second aim is to explore how these factors affect cultural diversity, or the amount of different cultural traits in a population. This study suggests that a larger interchange of cultural traits between populations could lead to cultural evolution not improving the adaptation of individuals to their environment and to a decrease of cultural diversity.

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Pollinator coupling can induce synchronized flowering in different plant species.

Publication Date: 2010 Aug 25 PMID: 20800600
Authors: Tachiki, Y. - Iwasa, Y. - Satake, A.
Journal: J Theor Biol

Synchronous and intermittent plant reproduction has been identified widely in diverse biomes. While synchronous flowering is normally observed within the same species, different species also flower in synchrony. A well-known example of interspecific synchrony is "general flowering" in tropical rain forests of Southeast Asia. Environmental factors, such as low temperature and drought, have been considered as major trigger of general flowering. However, environmental cues are not enough to explain general flowering because some trees do not flower even when they encounter favorable environmental cues. We propose alternative explanation of general flowering; "pollinator coupling". When species flower synchronously, the elevated pollen and nectar resource may attract increased numbers of generalist pollinators, with a concomitant enhancement of pollination success (facilitation). However, under these circumstances, plants of different species may compete with one another for limited pollinator services, resulting in declines in pollination success for individual species (competition). Here, we present a model describing resource dynamics of individual trees serviced by generalist pollinators. We analyze combinations of conditions under which plants reproduce intermittently with synchronization within species, and/or (sometimes) between different species. We show that plants synchronize flowering when the number of pollinators attracted to an area increases at an accelerating rate with increasing numbers of flowers. In this case, facilitation of flowering by different species exceeds the negative influence of interspecific plant competition. We demonstrate mathematically that co-flowering of different species occurs under a much narrower range of circumstances than intraspecific co-flowering.

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Enhancer and competitive allosteric modulation model for G-protein coupled receptors.

Publication Date: 2010 Aug 25 PMID: 20800599
Authors: Pietra, D. - Borghini, A. - Cristina Breschi, M. - Maria Bianucci, A.
Journal: J Theor Biol

A new mathematical model, referred to as Enhancer and Competitive Allosteric Modulator (ECAM) model, developed with the aim of quantitatively describing the interaction of an allosteric modulator with both enhancer and competitive properties towards G-protein coupled receptors is described here. Model simulations for equilibrium (displacement-like, saturation-like), and kinetic (association, dissociation) binding experiments were performed. The results showed the ability of the model to interpret a number of possible ligand-receptor binding behaviors. In particular, the binding properties of PD81723, an enhancer and competitive allosteric modulator for the adenosine A(1) receptor, were experimentally evaluated by radioligand binding assays and interpreted by the ECAM model. The results also offer a theoretical background enabling the design and optimization of compounds endowed with allosteric enhancer, competitive, agonist, antagonist, inverse agonist properties.

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Optimal seasonal schedules and the relative dominance of heteromorphic and isomorphic life cycles in macroalgae.

Publication Date: 2010 Aug 21 PMID: 20732332
Authors: Bessho, K. - Iwasa, Y.
Journal: J Theor Biol

Marine macroalgae (seaweed) show diverse life cycles. Species with a heteromorphic life cycle have a large multicellular algal body in one generation but have a very small body in the second generation of the same year. In contrast, the diploid and haploid life forms of isomorphic species have similar morphology, and these species often have more than two generations in a year. Here, we first study the optimal life cycle schedule of marine macroalgae when daily mortality changes seasonally, and then we discuss the conditions for coexistence and relative dominance of different life cycles. According to the optimal life cycle schedule, heteromorphic species tend to have a generation with a large algal body when mortality is low, and a microscopic-sized generation when mortality is high. In contrast, isomorphic species tend to mature when body size reaches a threshold value that is the same for different generations. We then examine the coexistence of the two life cycles when growth rate decreases with biomass. The model predicts that (1) at high latitudes (i.e., in strongly seasonal environments), heteromorphic species are likely to dominate over isomorphic species, and (2) species with a heteromorphic life cycle should dominate in the supratidal and upper intertidal zones where macroalgae tend to suffer high mortality, and also in the subtidal zone, where mortality is low, whereas isomorphic species are likely to be more successful when mortality is intermediate. These predictions are consistent with the observed distribution patterns of the two life cycles in macroalgae.

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On the generality of stability-complexity relationships in Lotka-Volterra ecosystems.

Publication Date: 2010 Aug 20 PMID: 20728456
Authors: Townsend, S. E. - Haydon, D. T. - Matthews, L.
Journal: J Theor Biol

Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought.

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Optimal risk management of human alveolar echinococcosis with vermifuge.

Publication Date: 2010 Aug 20 PMID: 20728455
Authors: Kato, N. - Kotani, K. - Ueno, S. - Matsuda, H.
Journal: J Theor Biol

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.

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Long-tail behavior in locomotion of Caenorhabditis elegans.

Publication Date: 2010 Aug 20 PMID: 20728454
Authors: Ohkubo, J. - Yoshida, K. - Iino, Y. - Masuda, N.
Journal: J Theor Biol

The locomotion of Caenorhabditis elegans exhibits complex patterns. In particular, the worm combines mildly curved runs and sharp turns to steer its course. Both runs and sharp turns of various types are important components of taxis behavior. The statistics of sharp turns have been intensively studied. However, there have been few studies on runs, except for those on klinotaxis (also called weathervane mechanism), in which the worm gradually curves toward the direction with a high concentration of chemicals; this phenomenon was discovered recently. We analyzed the data of runs by excluding sharp turns. We show that the curving rate obeys long-tail distributions, which implies that large curving rates are relatively frequent. This result holds true for locomotion in environments both with and without a gradient of NaCl concentration; it is independent of klinotaxis. We propose a phenomenological computational model on the basis of a random walk with multiplicative noise. The assumption of multiplicative noise posits that the fluctuation of the force is proportional to the force exerted. The model reproduces the long-tail property present in the experimental data.

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Genome analyses and modelling the relationships between coding density, recombination rate and chromosome length.

Publication Date: 2010 Aug 20 PMID: 20728453
Authors: Mackiewicz, D. - Zawierta, M. - Waga, W. - Cebrat, S.
Journal: J Theor Biol

In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been observed that the recombination events are distributed unevenly along the chromosomes. We have found that many of such recombination properties can be predicted by computer simulations of population evolution based on the Monte Carlo methods. For example, these simulations have shown that the probability of acceptance of the recombination events by selection is higher at the ends of chromosomes and lower in their middle parts. The regions of high coding density are more prone to enter the strategy of haplotype complementation and to form clusters of genes, which are "recombination deserts". The phenomenon of switching in-between the purifying selection and haplotype complementation has a phase transition character, and many relations between the effective population size, coding density, chromosome size and recombination frequency are those of the power law type.

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A novel efficient dynamic programming algorithm for haplotype block partitioning.

Publication Date: 2010 Aug 20 PMID: 20728452
Authors: Zahiri, J. - Mahdevar, G. - Nowzari-Dalini, A. - Ahrabian, H. - Sadeghi, M.
Journal: J Theor Biol

In this paper, a new efficient algorithm is presented for haplotype block partitioning based on haplotype diversity. In this algorithm, finding the largest meaningful block that satisfies the diversity condition is the main goal as an optimization problem. The algorithm can be performed in polynomial time complexity with regard to the number of haplotypes and SNPs. We apply our algorithm on three biological data sets from chromosome 21 in three different population data sets from HapMap data bulk; the obtained results show the efficiency and better performance of our algorithm in comparison with three other well known methods.

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Semantic and layered protein function prediction from PPI networks.

Publication Date: 2010 Aug 17 PMID: 20723548
Authors: Zhu, W. - Hou, J. - Phoebe Chen, Y. P.
Journal: J Theor Biol

BACKGROUND: The past few years have seen a rapid development in novel high-throughput technologies that have created large-scale data on protein-protein interactions (PPI) across human and most model species. This data is commonly represented as networks, with nodes representing proteins and edges representing the PPIs. A fundamental challenge to bioinformatics is how to interpret this wealth of data to elucidate the interaction of patterns and the biological characteristics of the proteins. One significant purpose of this interpretation is to predict unknown protein functions. Although many approaches have been proposed in recent years, the challenge still remains how to reasonably and precisely measure the functional similarities between proteins to improve the prediction effectiveness. RESULTS: We used a Semantic and Layered Protein Function Prediction (SLPFP) framework to more effectively predict unknown protein functions at different functional levels. The framework relies on a new protein similarity measurement and a clustering-based protein function prediction algorithm. The new protein similarity measurement incorporates the topological structure of the PPI network, as well as the protein's semantic information in terms of known protein functions at different functional layers. Experiments on real PPI datasets were conducted to evaluate the effectiveness of the proposed framework in predicting unknown protein functions. CONCLUSION: The proposed framework has a higher prediction accuracy compared with other similar approaches. The prediction results are stable even for a large number of proteins. Furthermore, the framework is able to predict unknown functions at different functional layers within the Munich Information Center for Protein Sequence (MIPS) hierarchical functional scheme. The experimental results demonstrated that the new protein similarity measurement reflects more reasonably and precisely relationships between proteins.

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Stochastic amplification in an epidemic model with seasonal forcing.

Publication Date: 2010 Aug 17 PMID: 20723547
Authors: Black, A. J. - McKane, A. J.
Journal: J Theor Biol

We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a continuous time Markov process, which is decomposed into a deterministic dynamics together with stochastic corrections, by using an expansion in inverse system size. The forcing induces a limit cycle in the deterministic dynamics, and a complete analysis of the fluctuations about this time-dependent solution is given. This analysis is applied when the limit cycle is annual, and after a period doubling when it is biennial. The comprehensive nature of our approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in whooping cough and measles epidemics.

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Non-local models for the formation of hepatocyte-stellate cell aggregates.

Publication Date: 2010 Aug 13 PMID: 20709085
Authors: Green, J. E. - Waters, S. L. - Whiteley, J. P. - Edelstein-Keshet, L. - Shakesheff, K. M. - Byrne, H. M.
Journal: J Theor Biol

Liver cell aggregates may be grown in vitro by co-culturing hepatocytes with stellate cells. This method results in more rapid aggregation than hepatocyte-only culture, and appears to enhance cell viability and the expression of markers of liver-specific functions. We consider the early stages of aggregate formation, and develop a new mathematical model to investigate two alternative hypotheses (based on evidence in the experimental literature) for the role of stellate cells in promoting aggregate formation. Under Hypothesis 1, each population produces a chemical signal which affects the other, and enhanced aggregation is due to chemotaxis. Hypothesis 2 asserts that the interaction between the two cell types is by direct physical contact: the stellates extend long cellular processes which pull the hepatocytes into the aggregates. Under both hypotheses, hepatocytes are attracted to a chemical they themselves produce, and the cells can experience repulsive forces due to overcrowding. We formulate non-local (integro-partial differential) equations to describe the densities of cells, which are coupled to reaction-diffusion equations for the chemical concentrations. The behaviour of the model under each hypothesis is studied using a combination of linear stability analysis and numerical simulations. Our results show how the initial rate of aggregation depends upon the cell seeding ratio, and how the distribution of cells within aggregates depends on the relative strengths of attraction and repulsion between the cell types. Guided by our results, we suggest experiments which could be performed to distinguish between the two hypotheses.

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Cooperation enhanced by the 'survival of the fittest' rule in prisoner's dilemma games on complex networks.

Publication Date: 2010 Aug 12 PMID: 20708630
Authors: Zhang, J. - Zhang, C. - Chu, T.
Journal: J Theor Biol

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection, whereby we introduce a model of strategy evolution taking place on evolving networks based on Darwinian 'survival of the fittest' rule. In the present work, players whose payoffs are below a certain threshold will be deleted and the same number of new nodes will be added to the network to maintain the constant system size. Furthermore, the networking effect is also studied via implementing simulations on four typical network structures. Numerical results show that cooperators can obtain the biggest boost if the elimination threshold is fine-tuned. Notably, this coevolutionary rule drives the initial networks to evolve into statistically stationary states with a broad-scale degree distribution. Our results may provide many more insights for understanding the coevolution of strategy and network topology under the mechanism of nature selection whereby superior individuals will prosper and inferior ones be eliminated.

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Tree-grass co-existence in savanna: Interactions of rain and fire.

Publication Date: 2010 Aug 12 PMID: 20708629
Authors: Accatino, F. - De Michele, C. - Vezzoli, R. - Donzelli, D. - Scholes, R. J.
Journal: J Theor Biol

The mechanisms permitting the co-existence of tree and grass in savannas have been a source of contention for many years. The two main classes of explanations involve either competition for resources, or differential sensitivity to disturbances. Published models focus principally on one or the other of these mechanisms. Here we introduce a simple ecohydrologic model of savanna vegetation involving both competition for water, and differential sensitivity of trees and grasses to fire disturbances. We show how the co-existence of trees and grasses in savannas can be simultaneously controlled by rainfall and fire, and how the relative importance of the two factors distinguishes between dry and moist savannas. The stability map allows to predict the changes in vegetation structure along gradients of rainfall and fire disturbances realistically, and to clarify the distinction between climate- and disturbance-dependent ecosystems.

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Allometry and catastrophic regime shifts in food chains.

Publication Date: 2010 Aug 12 PMID: 20708628
Authors: Suzuki, K. - Ikegami, T.
Journal: J Theor Biol

Population dynamics can reflect the body mass distribution of species because there is an allometric relationship between the average body mass of species and its metabolic timescale. Since predators are generally larger than their prey, a hierarchical structure from fast timescales to slow timescales can be a general structure in food webs. In this paper, we show that the change of the metabolic timescale ratio can cause catastrophic shifts. Then, we investigate a two-dimensional parameter space with the timescale ratio and the carrying capacity of basal species, and reveal that the timescale ratio characterizes the response of the system to environmental variation. Finally, in a bistable regime, we try to clarify the relationship between the trophic position of a species and the extent to which the species induces attractor switching. We saw that, in a 4-species food chain, top predators and second consumers induce attractor switching easily compared to first consumers and basal species.

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A study of entropy/clarity of genetic sequences using metric spaces and fuzzy sets.

Publication Date: 2010 Aug 11 PMID: 20708019
Authors: Georgiou, D. N. - Karakasidis, T. E. - Nieto, J. J. - Torres, A.
Journal: J Theor Biol

The study of genetic sequences is of great importance in biology and medicine. Sequence analysis and taxonomy are two major fields of application of bioinformatics. In the present paper we extend the notion of entropy and clarity to the use of different metrics and apply them in the case of the Fuzzy Polynuclotide Space (FPS). Applications of these notions on selected polynucleotides and complete genomes both in the I(12xk) space, but also using their representation in FPS are presented. Our results show that the values of fuzzy entropy/clarity are indicative of the degree of complexity necessary for the description of the polynucleotides in the FPS, although in the latter case the interpretation is slightly different than in the case of the I(12xk) hypercube. Fuzzy entropy/clarity along with the use of appropriate metrics can contribute to sequence analysis and taxonomy.

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Replicator dynamics of reward & reputation in public goods games.

Publication Date: 2010 Aug 11 PMID: 20708018
Authors: Hauert, C.
Journal: J Theor Biol

Public goods games have become the mathematical metaphor for game theoretical investigations of cooperative behavior in groups of interacting individuals. Cooperation is a conundrum because cooperators make a sacrifice to benefit others at some cost to themselves. Exploiters or defectors reap the benefits and forgo costs. Despite the fact that groups of cooperators outperform groups of defectors, Darwinian selection or utilitarian principles based on rational choice should favor defectors. In order to overcome this social dilemma, much effort has been expended for investigations pertaining to punishment and sanctioning measures against defectors. Interestingly, the complementary approach to create positive incentives and to reward cooperation has received considerably less attention-despite being heavily advocated in education and social sciences for increasing productivity or preventing conflicts. Here we show that rewards can indeed stimulate cooperation in interaction groups of arbitrary size but, in contrast to punishment, fail to stabilize it. In both cases, however, reputation is essential. The combination of reward and reputation result in complex dynamics dominated by unpredictable oscillations.

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Spatio-temporal calcium dynamics in pacemaking units of the interstitial cells of Cajal.

Publication Date: 2010 Aug 10 PMID: 20705074
Authors: Means, S. A. - Sneyd, J.
Journal: J Theor Biol

The interstitial cells of Cajal (ICC) are responsible for producing pacemaking signals that stimulate rhythmic contractions in the gastro-intestinal system. The pacemaking signals are generated by membrane depolarizations, which are in turn linked to the integrated transport of calcium between the endoplasmic reticulum (ER), through inositol-trisphosphate receptor (IP(3)R) release, and mitochondria, through the uniporter. A non-specific cation channel (NSCC) is associated with the membrane depolarizations, and is inhibited by intracellular calcium. One theory proposes that the integrated calcium transport occurs within specific regions of the ICC called "pacemaker units," and results in localized calcium concentration reductions within these units, which in turn activate the NSCC and depolarize the membrane. We have constructed a model of the spatio-temporal calcium dynamics within an ICC pacemaker unit to determine under what conditions the local calcium concentrations may reduce below baseline. We obtain reductions of calcium concentrations below baseline but only under certain conditions. Without strong and persistent stimulation of the IP(3)R, reductions of calcium below baseline occur only with a non-physiological, time-dependent uniporter. Alternatively, sufficient IP(3)R release leads to reductions of calcium below baseline, due to depletion of the ER calcium store over the time scale of seconds, although these reductions require strong mitochondrial and ER calcium uptake.

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Leaky vessels as a potential source of stromal acidification in tumours.

Publication Date: 2010 Aug 10 PMID: 20699102
Authors: Martin, N. K. - Gaffney, E. A. - Gatenby, R. A. - Maini, P. K.
Journal: J Theor Biol

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to the breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than as seen in the window chamber, indicating that although vessel leakiness might be acting as a source of acid, it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption.

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2D-MH: A web-server for generating graphic representation of protein sequences based on the physicochemical properties of their constituent amino acids.

Publication Date: 2010 Aug 7 PMID: 20696175
Authors: Wu, Z. C. - Xiao, X. - Chou, K. C.
Journal: J Theor Biol

Introduction of graphic representation for biological sequences can provide intuitive overall pictures as well as useful insights for performing large-scale analysis. Here, a new two-dimensional graph, called "2D-MH", is proposed to represent protein sequences. It is formed by incorporating the information of the side-chain mass of each of the constituent amino acids and its hydrophobicity. The graphic curve thus generated is featured by (1) an one-to-one correspondence relation without circuit or degeneracy, (2) better reflecting the innate structure of the protein sequence, (3) clear visibility in displaying the similarity of protein sequences, (4) more sensitive for the mutation sites important for drug targeting, and (5) being able to be used as a metric for the "evolutionary distance" of a protein from one species to the other. It is anticipated that the presented graphic method may become a useful vehicle for large-scale analysis of the avalanche of protein sequences generated in the post-genomic age. As a web-server, 2D-MH is freely accessible at http://icpr.jci.jx.cn/bioinfo/pplot/2D-MH, by which one can easily generate the two-dimensional graphs for any number of protein sequences and compare the evolutionary distances between them.

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Models for gibberellic acid transport and enzyme production and transport in the aleurone layer of barley.

Publication Date: 2010 Aug 7 PMID: 20696174
Authors: O'Brien, R. - Fowkes, N. - Bassom, A. P.
Journal: J Theor Biol

Gibberellins are growth hormones produced in the embryo of grain released during germination. They promote growth through the production of enzymes in the aleurone layer surrounding the endosperm. These enzymes then diffuse into the endosperm and produce the sugars required by the growing acrospire. Here we model the transport of gibberellins into and along the aleurone layer, the consequent production of enzymes, and their transport into the endosperm. Simple approximate solutions of the governing equations are obtained which suggest that the enzymes are released immediately behind a gibberellin front which travels with almost constant speed along the aleurone layer. The model also suggests that this propagation speed is determined primarily by conditions near the scutellum-aleurone junction, which may enable the embryo to actively control the germination process.

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Hydrodynamic interaction of two unsteady model microorganisms.

Publication Date: 2010 Aug 7 PMID: 20696173
Authors: Giacche, D. - Ishikawa, T.
Journal: J Theor Biol

The study of pair-wise interactions between swimming microorganisms is fundamental to the understanding of the rheological and transport properties of semi-dilute suspensions. In this paper, the hydrodynamic interaction of two ciliated microorganisms is investigated numerically using a boundary-element method, and the microorganisms are modeled as spherical squirmers that swim by time-dependent surface deformations. The results show that the inclusion of the unsteady terms in the ciliary propulsion model has a large impact on the trajectories of the interacting cells, and causes a significant change in scattering angles with potential important consequences on the diffusion properties of semi-dilute suspensions. Furthermore, the analysis of the shear stress acting on the surface of the microorganisms revealed that the duration and the intensity of the near-field interaction are significantly modified by the presence of unsteadiness. This observation may account for the hydrodynamic nature of randomness in some biological reactions, and supersedes the distinction between intrinsic randomness and hydrodynamic interactions, adding a further element to the understanding and modeling of interacting microorganisms.

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The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks.

Publication Date: 2010 Aug 7 PMID: 20696172
Authors: Greenbury, S. F. - Johnston, I. G. - Smith, M. A. - Doye, J. P. - Louis, A. A.
Journal: J Theor Biol

We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SF(in) topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SF(both) and SF(out) topologies. The functionality of the SF(out) topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SF(out) and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SF(out) topologies are also more robust to mutations than ER networks. Furthermore, the SF(out) topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.

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Herbivore-induced coexistence of competing plant species.

Publication Date: 2010 Aug 6 PMID: 20692270
Authors: Ishii, R. - Crawley, M. J.
Journal: J Theor Biol

We study a series of spatially implicit lottery models in which two competing plant species, with and without defensive traits, are grazed by a herbivore in a homogeneous habitat. One species (palatable) has no defensive traits, while the other (defended) has defensive traits but suffers reduced reproduction as the result of an assumed trade-off. Not surprisingly, coexistence of these plants cannot occur when the herbivore density is very low (the palatable plant always wins) or very high (the defended plant wins). At intermediate densities, however, herbivory can mediate plant coexistence, even in a homogeneous environment. If the herbivore eats several plants per bite, and its forage-selection depends on the average palatability of the plants it eats, then palatable species in the immediate neighbourhood of defended plants may be more likely to persist (associational resistance) even at higher grazing pressure. If the herbivore shows a positive numerical response to the average palatability of the habitat as a whole, then both plant populations are stabilized and coexistence is promoted, because both species obtain a minority advantage through the negative feedback caused by herbivory. If the herbivore exhibits both of these traits, the system may have at most two non-trivial equilibria, one of which is stable and the other unstable. This means that coexistence in such a system is vulnerable to large fluctuations in herbivore density and identity, and this has implications for conservation in systems where large herbivores are managed to promote plant diversity.

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SecretP: Identifying bacterial secreted proteins by fusing new features into Chou's pseudo-amino acid composition.

Publication Date: 2010 Aug 5 PMID: 20691704
Authors: Yu, L. - Guo, Y. - Li, Y. - Li, G. - Li, M. - Luo, J. - Xiong, W. - Qin, W.
Journal: J Theor Biol

Protein secretion plays an important role in bacterial lifestyles. Secreted proteins are crucial for bacterial pathogenesis by making bacteria interact with their environments, particularly delivering pathogenic and symbiotic bacteria into their eukaryotic hosts. Therefore, identification of bacterial secreted proteins becomes an important process for the study of various diseases and the corresponding drugs. In this paper, fusing several new features into Chou's pseudo-amino acid composition (PseAAC), two support vector machine (SVM)-based ternary classifiers are developed to predict secreted proteins of Gram-negative and Gram-positive bacteria. For the two types of bacteria, the high accuracy of 94.03% and 94.36% are obtained in distinguishing classically secreted, non-classically secreted and non-secreted proteins by our method. In order to compare the practical ability of our method in identifying bacterial secreted proteins with those of six published methods, proteins in Escherichia coli and Bacillus subtilis are collected to construct the test sets of Gram-negative and Gram-positive bacteria, and the prediction results of our method are comparable to those of existing methods. When performed on two public independent data sets for predicting NCSPs, it also yields satisfactory results for Gram-negative bacterial proteins. The prediction server SecretP can be accessed at http://cic.scu.edu.cn/bioinformatics/secretPV2/index.htm.

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Using underdominance to bi-stably transform local populations.

Publication Date: 2010 Aug 5 PMID: 20691703
Authors: Altrock, P. M. - Traulsen, A. - Reeves, R. G. - Reed, F. A.
Journal: J Theor Biol

Underdominance refers to natural selection against individuals with a heterozygous genotype. Here, we analyze a single-locus underdominant system of two large local populations that exchange individuals at a certain migration rate. The system can be characterized by fixed points in the joint allele frequency space. We address the conditions under which underdominance can be applied to transform a local population that is receiving wildtype immigrants from another population. In a single population, underdominance has the benefit of complete removal of genetically modified alleles (reversibility) and coexistence is not stable. The two population system that exchanges migrants can result in internal stable states, where coexistence is maintained, but with additional release of wildtype individuals the system can be reversed to a fully wildtype state. This property is critically controlled by the migration rate. We approximate the critical minimum frequency required to result in a stable population transformation. We also concentrate on the destabilizing effects of fitness and migration rate asymmetry. Practical implications of our results are discussed in the context of utilizing underdominance to genetically modify wild populations. This is of importance especially for genetic pest management strategies, where locally stable and potentially reversible transformations of populations of disease vector species are of interest.

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Invasions with density-dependent ecological parameters.

Publication Date: 2010 Aug 4 PMID: 20691194
Authors: Balasuriya, S.
Journal: J Theor Biol

The speed and the minimum carrying capacity needed for a successful population expansion into new territory are addressed using a reaction-diffusion model. The model is able to encapsulate a rich collection of ecological behaviours, including the Allee effect, resource depletion due to consumption, dispersal adaptation due to population pressure, biological control agents, and a range of breeding suppression mechanisms such as embryonic diapause, delayed development and sperm storage. It is shown how many of these phenomena can be characterised as density-dependence in a few fundamental ecological parameters. With the help of a powerful mathematical technique recently developed by Balasuriya and Gottwald (J. Math. Biol. 61, pp. 377-399, 2010), explicit formulae for the effect on the speed and minimum carrying capacity are obtained.

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Classification studies based on a spectral representation of DNA.

Publication Date: 2010 Aug 4 PMID: 20691193
Authors: Bielinska-Wa, Z. D - Subramaniam, S.
Journal: J Theor Biol

The aim of this paper is to provide a new tool to classify the nucleic acid sequences. The profiles based on the values characterizing DNA sequences (descriptors derived from recently introduced graphical representation) are used as a basis of classification schemes related to different aspects of similarity of the sequences. New multicomponent similarity measures based on these descriptors have been defined. Each component of the new measures can be analyzed separately. The new measures are consistent with the standard ones but they contain more detailed information. In particular, it has been shown that within the new approach one can define a quantity which converges to the standard similarity measure. An application of the multicomponent similarity measure to families of histone sequences demonstrates the power and efficiency of the method.

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Defence, intrusion and the evolutionary stability of territoriality.

Publication Date: 2010 Aug 3 PMID: 20688084
Authors: Hinsch, M. - Komdeur, J.
Journal: J Theor Biol

Territorial behaviour can only be adaptive if its costs are outweighed by its benefits. Territorial individuals incur costs by defending their territories against intruders. Usually these intruders are assumed to be non-territorial floaters attempting to take over the whole territory or neighbours trying to extend the borders of their own territory. We instead investigate how costs and benefits of territorial behaviour are affected by neighbours which invade to steal resources on a territory. We show analytically that in the absence of defence intrusion into neighbouring territories always pays and that even if territories are defended intrusion levels can still be high. Using a more detailed simulation model we find that territory defence usually disappears from the population even if owners have a strong advantage over intruders in terms of fighting costs or foraging efficiency. Defence and thus territoriality can only be evolutionarily stable if fighting costs for the intruder relative to the productivity of the territory are very high or if crossing the borders between territories carries additional costs. Our results show that stealing of resources by neighbours can have a considerable effect on the evolutionary stability of territory defence and thus territoriality itself. A more mechanistic model of territorial behaviour is needed to incorporate these kinds of mechanisms into a general theory on the evolution of territoriality.

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The option to leave: Conditional dissociation in the evolution of cooperation.

Publication Date: 2010 Aug 5 PMID: 20688083
Authors: Izquierdo, S. S. - Izquierdo, L. R. - Vega-Redondo, F.
Journal: J Theor Biol

Conditional dissociation, i.e. the option to leave an interacting partner in response to his behaviour, is a mechanism that has been shown to promote cooperation in several settings, but the fundamental features that make conditional dissociation work in this way are not yet fully understood. This paper identifies some of the key conditions that make conditional dissociation lead to high levels of cooperation, explains how this mechanism can support the evolutionary coexistence of cooperative and non-cooperative behaviour typically observed in nature, and provides an analytical formula to estimate the expected degree of cooperation thus achieved. Our model involves a population of individuals who are paired to play an iterated prisoner's dilemma. All individuals share the same capacity to react to the action previously chosen by their partner and, without any other a priori constraint or exclusion, they may use any behavioural rule that is compatible with this capacity. The dynamic evolution of the population eventually enters either a non-cooperative or a partially cooperative regime, depending mainly on the expected lifetime of individuals. Whenever the partially cooperative regime materializes, the cornerstone of its long-run stability is the coexistence of defectors and "Out-for-Tat" strategists, the latter being those who start cooperating and respond to defection by merely leaving. We find, therefore, that conditional dissociation is the essential disciplinary device supporting cooperation, whilst other conditional strategies (such as Tit-for-Tat) remain present only in small population shares. These conclusions are obtained both by extensive numerical simulations and through analytical mean-field methods that approximate the stochastic simulation dynamics and deliver accurate predictions for general parameter configurations.

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New method for comparing DNA primary sequences based on a discrimination measure.

Publication Date: 2010 Aug 3 PMID: 20688082
Authors: Feng, J. - Hu, Y. - Wan, P. - Zhang, A. - Zhao, W.
Journal: J Theor Biol

We introduce a new approach to compare DNA primary sequences. The core of our method is a new measure of pairwise distances among sequences. Using the primitive discrimination substrings of sequence S and Q, a discrimination measure DM(S, Q) is defined for the similarity analysis of them. The proposed method does not require multiple alignments and is fully automatic. To illustrate its utility, we construct phylogenetic trees on two independent data sets. The results indicate that the method is efficient and powerful.

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A stochastic model of neuronal growth cone guidance regulated by multiple sensors.

Publication Date: 2010 Aug 3 PMID: 20688081
Authors: Kobayashi, T. - Terajima, K. - Nozumi, M. - Igarashi, M. - Akazawa, K.
Journal: J Theor Biol

Neuronal growth cones migrate directionally under the control of axon guidance molecules, thereby forming synapses in the developing brain. The signal transduction system by which a growth cone detects surrounding guidance molecules, analyzes the detected signals, and then determines the overall behavior remains undetermined. In this study, we describe a novel stochastic model of this behavior that utilizes multiple sensors on filopodia to respond to guidance molecules. Overall growth cone behavior is determined by using only the concentration gradients of guidance molecules in the immediate vicinity of each sensor. The detected signal at each sensor, which is treated as a vector quantity, is sent to the growth cone center and then integrated to determine axonal growth in the next step by means of a simple vector operation. We compared the results of computer simulations of axonal growth with observations of actual axonal growth from co-culture experiments using olfactory bulb and septum. The probabilistic distributions of axonal growth generated by the computer simulation were consistent with those obtained from the culture experiments, indicating that our model accurately simulates growth cone behavior. We believe that this model will be useful for elucidating the as yet unknown mechanisms responsible for axonal growth in vivo.

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Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network.

Publication Date: 2010 Aug 5 PMID: 20688080
Authors: Ang, J. - Bagh, S. - Ingalls, B. P. - McMillen, D. R.
Journal: J Theor Biol

It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, "perfect" adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, "constructed" using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.

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A mathematical and computational approach for integrating the major sources of cell population heterogeneity.

Publication Date: 2010 Sep 7 PMID: 20685607
Authors: Stamatakis, M. - Zygourakis, K.
Journal: J Theor Biol

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.

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A mathematical model of intercellular signaling during epithelial wound healing.

Publication Date: 2010 Sep 7 PMID: 20685318
Authors: Posta, F. - Chou, T.
Journal: J Theor Biol

Recent experiments monitoring the healing process of wounded epithelial monolayers have demonstrated the necessity of MAPK activation for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK "wave" that originates immediately after injury, propagates deep into the cell sheet, away from the edge, and then rebounds back to the wound interface. After this initial MAPK activity has largely disappeared, a second MAPK front propagates slowly from the wound interface and also continues into the cell sheet, maintaining a sustained level of MAPK activity throughout the cell sheet. It has been suggested that the first wave is initiated by Reactive Oxygen Species (ROS) generated at the time of injury. In this work, we develop a minimal mathematical model that reproduces the observed behavior. The main ingredients of our model are a competition between ligand (e.g., Epithelial Growth Factor) and ROS for the activation of Epithelial Growth Factor Receptor, and a feedback loop between receptor occupancy and MAPK activation. We explore the mathematical properties of the model and look for traveling wave solutions consistent with the experimentally observed MAPK activity patterns.

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A multiscale, spatially distributed model of asthmatic airway hyper-responsiveness.

Publication Date: 2010 Aug 3 PMID: 20678506
Authors: Politi, A. Z. - Donovan, G. M. - Tawhai, M. H. - Sanderson, M. J. - Lauzon, A. M. - Bates, J. H. - Sneyd, J.
Journal: J Theor Biol

We present a multiscale, spatially distributed model of lung and airway behaviour with the goal of furthering the understanding of airway hyper-responsiveness and asthma. The model provides an initial computational framework for linking events at the cellular and molecular levels, such as Ca(2+) and crossbridge dynamics, to events at the level of the entire organ. At the organ level, parenchymal tissue is modelled using a continuum approach as a compressible, hyperelastic material in three dimensions, with expansion and recoil of lung tissue due to tidal breathing. The governing equations of finite elasticity deformation are solved using a finite element method. The airway tree is embedded in this tissue, where each airway is modelled with its own airway wall, smooth muscle and surrounding parenchyma. The tissue model is then linked to models of the crossbridge mechanics and their control by Ca(2+) dynamics, thus providing a link to molecular and cellular mechanisms in airway smooth muscle cells. By incorporating and coupling the models at these scales, we obtain a detailed, computational multiscale model incorporating important physiological phenomena associated with asthma.

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A large population parental care game: Polymorphisms and feedback between patterns of care and the operational sex ratio.

Publication Date: 2010 Aug 4 PMID: 20678504
Authors: Ramsey, D. M.
Journal: J Theor Biol

This article presents a game theoretic model of parental care which models the feedback between patterns of care and the operational sex ratio. It is assumed here that males can be in one of two states: searching for a mate or breeding (including caring for their offspring). Females can be in one of three states: receptive (searching), non-receptive or breeding. However, these sets of states can be adapted to the physiology of a particular species. The length of time that an individual remains in the breeding state depends on the level of care an individual gives. When in the searching state, individuals find partners at a rate dependent on the proportion of members of the opposite sex searching. These rates are defined to satisfy the Fisher condition that the total number of offspring of males equals the total number of offspring of females. The operational sex ratio is not defined exogenously, but can be derived from the adult sex ratio and the pattern of parental care. Pure strategy profiles and the so-called single sex stable polymorphisms, in which behaviour is varied within one sex, are derived analytically. The difference between mixed evolutionarily stable strategies and stable polymorphisms within this framework is highlighted. The effects of various physiological and demographic parameters on patterns of care are considered.

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A theory of leadership in human cooperative groups.

Publication Date: 2010 Aug 21 PMID: 20665973
Authors: Hooper, P. L. - Kaplan, H. S. - Boone, J. L.
Journal: J Theor Biol

Two types of models aim to account the origins of rank differentiation and social hierarchy in human societies. Conflict models suggest that the formation of social hierarchies is synonymous with the establishment of relationships of coercive social dominance and exploitation. Voluntary or 'integrative' models, on the other hand, suggest that rank differentiation--the differentiation of leader from follower, ruler from ruled, or state from subject--may sometimes be preferred over more egalitarian social arrangements as a solution to the challenges of life in social groups, such as conflict over resources, coordination failures, and free-riding in cooperative relationships. Little formal theoretical work, however, has established whether and under what conditions individuals would indeed prefer the establishment of more hierarchical relationships over more egalitarian alternatives. This paper provides an evolutionary game theoretical model for the acceptance of leadership in cooperative groups. We propose that the effort of a leader can reduce the likelihood that cooperation fails due to free-riding or coordination errors, and that under some circumstances, individuals would prefer to cooperate in a group under the supervision of a leader who receives a share of the group's productivity than to work in an unsupervised group. We suggest, in particular, that this becomes an optimal solution for individual decision makers when the number of group members required for collective action exceeds the maximum group size at which leaderless cooperation is viable.

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A simple feature representation vector for phylogenetic analysis of DNA sequences.

Publication Date: 2010 Aug 21 PMID: 20665972
Authors: Ding, S. - Dai, Q. - Liu, H. - Wang, T.
Journal: J Theor Biol

In this study, a simple 4k-dimension feature representation vector is proposed to reconstruct phylogenetic trees, where k is the length of a word. The vector is composed of elements which characterize the relative difference of biological sequence from sequence generated by an independent random process. In addition, the variance of a vector which is obtained by averaging every column of feature representation matrix is employed to determine appropriate word length. In our experiments, reliable results can always be generated when word length is < 7 which appears to be of lower computational complexity. Phylogenetic trees of 24 transferrins and 48 Hepatitis E viruses reconstructed at word length 6 are in good agreements with previous study, it shows that our method is efficient and powerful.

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Coexistence and invasibility in a two-species competition model with habitat-preference.

Publication Date: 2010 Aug 21 PMID: 20665971
Authors: Pigolotti, S. - Cencini, M.
Journal: J Theor Biol

The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference--generating spatial niches--strongly stabilizes the coexistence of the two species. Eliminating habitat preference--neutral dynamics--the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.

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A plausible explanation for heart rates in mammals.

Publication Date: 2010 Aug 21 PMID: 20665970
Authors: Flores, J. - Corvera Poire, E. - del Rio, J. A. - Lopez de Haro, M.
Journal: J Theor Biol

We consider a simple model to give a plausible mechanical explanation of what are the actual resting heart rates of mammals optimized for. We study what is the optimal frequency for a viscoelastic fluid circulating in a pulsatile way through a network of tubes and conclude that the heart rate is not optimized to transport blood through the whole net. Rather, actual resting heart rates of mammals happen at frequencies that optimize flow in vessels of radii that correspond to large arteries, which bring oxygenated blood rapidly far away from the heart, towards head and limbs. Our results for the optimal frequencies, obtained using observed radii of femoral arteries in mammals, agree best with the heart rates observed. We find a theoretical allometric relation between optimal flow frequency and radius: nu approximately R(-1). This one, agrees with the exponent obtained when plotting observed heart rates versus radii of both, femoral arteries and carotids in mammals of different sizes, from mice to horses.

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Signal transduction and amplification in a circadian oscillator: interaction between two colored noises.

Publication Date: 2010 Aug 21 PMID: 20665968
Authors: Jian-Cheng, S.
Journal: J Theor Biol

The signal transduction and amplification in a Neurospora circadian clock system is studied by using the mechanism of internal signal stochastic resonance (ISSR). Two cases have been investigated: the case of no correlations between multiplicative and additive colored noises and the case of correlations between two noises. The results show that, in both cases, the noise-induced circadian oscillations can be transduced with the phenomenon of internal signal stochastic resonance (ISSR). However, the correlation time and intensity of an additive colored noise play different roles for the ISSR, driven by multiplicative colored noise, while the correlation time and intensity of multiplicative colored noise hardly influence the ISSR driven by additive colored noise. In addition, the ISSR can be amplified or suppressed at an appropriate range of the correlation intensity between two colored noises. The fundamental frequency of noise-induced circadian oscillations is hardly shifted with the increment of the intensity and correlation time of colored noises, which implies that the Neurospora system could be resistant to colored noises, exhibit strong vitality and sustain intrinsic circadian rhythms.

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On the dynamics of the growth plate in primary ossification.

Publication Date: 2010 Aug 21 PMID: 20665967
Authors: Fasano, A. - Herrero, M. A. - Lopez, J. M. - Medina, E.
Journal: J Theor Biol

In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP). These are known to be major agents in the dynamics of the so-called growth plate, where transition from pristine cartilage to advancing bone takes place. Our model consists in a steady-state linear approximation to a reaction-diffusion system where only diffusion and absorption mechanisms are retained. Estimates on some system parameters are given, on the basis of the knowledge of a few measurable quantities. This allows for explicitly solving our model, whereupon a discussion on robustness and regulatory properties thereof is provided. In particular, we show that the size of the Proliferative Zone in the growth plate is rather insensitive to variations in the flux coefficients for Ihh and PTHrP at their boundaries. Besides, we also show that the model is also insensitive to large changes in the (comparatively small) critical value of the PTHrP concentration which marks the transition form Proliferative to Hyperthropic Regions within the Growth Plate. These results hold irrespective of the particular diffusivities selected for Ihh and PTHrP.

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Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model.

Publication Date: 2010 Aug 21 PMID: 20665966
Authors: Drysdale, P. M. - Huber, J. P. - Robinson, P. A. - Aquino, K. M.
Journal: J Theor Biol

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.

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Quantitative analysis of morphological alterations in Plasmodium falciparum infected red blood cells through theoretical interpretation of spectral measurements.

Publication Date: 2010 Aug 21 PMID: 20665965
Authors: Serebrennikova, Y. M. - Patel, J. - Milhous, W. K. - Garcia-Rubio, L. H.
Journal: J Theor Biol

Spectroscopic analysis can provide valuable insights into morphological and biochemical cellular transformations caused by diseases. However, traditional spectroscopic methods and the corresponding spectral interpretation approaches have been challenged by the complexities of the cell shape, orientation, and internal structure. Here we present an elegant spectral interpretation model that enables accurate quantitative analysis of the UV-visible spectra of red blood cells (RBCs) parasitized by the lethal human malaria parasite, Plasmodium falciparum. The model is based on the modified Mie theory (MMT) approach that incorporates the effects of the nonsphericity and orientation and multilayered cell structure to account for complex composition of the infected RBCs (IRBCs). We determine the structure and composition of the IRBCs and address unresolved matters over the alterations induced by the intraerythrocytic development of P. falciparum. The results indicate deformation and swelling of the IRBCs during the trophozoite stage of P. falciparum that is followed by substantial shrinkage during the schizont stages. We determine that up to 90% depletion of hemoglobin from the RBC cytosol does not lead to a net loss of iron from the infected cells. We quantitatively follow the morphological changes in the parasites during the intraerythrocytic development by applying the interpretation model to the UV-visible spectroscopic measurements of the IRBCs. We expect this method of quantitative spectroscopic characterization of the diseased cells to have practical clinical utility for rapid diagnosis, therapeutic monitoring, and drug susceptibility testing.

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Local adaptation and the evolution of species' ranges under climate change.

Publication Date: 2010 Oct 7 PMID: 20654630
Authors: Atkins, K. E. - Travis, J. M.
Journal: J Theor Biol

The potential impact of climate change on biodiversity is well documented. A well developed range of statistical methods currently exists that projects the possible future habitat of a species directly from the current climate and a species distribution. However, studies incorporating ecological and evolutionary processes remain limited. Here, we focus on the potential role that local adaptation to climate may play in driving the range dynamics of sessile organisms. Incorporating environmental adaptation into a stochastic simulation yields several new insights. Counter-intuitively, our simulation results suggest that species with broader ranges are not necessarily more robust to climate change. Instead, species with broader ranges can be more susceptible to extinction as locally adapted genotypes are often blocked from range shifting by the presence of cooler adapted genotypes that persist even when their optimum climate has left them behind. Interestingly, our results also suggest that it will not always be the cold-adapted phenotypes that drive polewards range expansion. Instead, range shifts may be driven by phenotypes conferring adaptation to conditions prevalent towards the centre of a species' equilibrium distribution. This may have important consequences for the conservation method termed predictive provenancing. These initial results highlight the potential importance of local adaptation in determining how species will respond to climate change and we argue that this is an area requiring urgent theoretical and empirical attention.

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Biologically meaningful update rules increase the critical connectivity of generalized Kauffman networks.

Publication Date: 2010 Oct 7 PMID: 20654629
Authors: Wittmann, D. M. - Marr, C. - Theis, F. J.
Journal: J Theor Biol

We generalize random Boolean networks by softening the hard binary discretization into multiple discrete states. These multistate networks are generic models of gene regulatory networks, where each gene is known to assume a finite number of functionally different expression levels. We analytically determine the critical connectivity that separates the biologically unfavorable frozen and chaotic regimes. This connectivity is inversely proportional to a parameter which measures the heterogeneity of the update rules. Interestingly, the latter does not necessarily increase with the mean number of discrete states per node. Still, allowing for multiple states decreases the critical connectivity as compared to random Boolean networks, and thus leads to biologically unrealistic situations. Therefore, we study two approaches to increase the critical connectivity. First, we demonstrate that each network can be kept in its frozen regime by sufficiently biasing the update rules. Second, we restrict the randomly chosen update rules to a subclass of biologically more meaningful functions. These functions are characterized based on a thermodynamic model of gene regulation. We analytically show that their usage indeed increases the critical connectivity. From a general point of view, our thermodynamic considerations link discrete and continuous models of gene regulatory networks.

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Calsequestrin mediates changes in spontaneous calcium release profiles.

Publication Date: 2010 Aug 7 PMID: 20648970
Authors: Tania, N. - Keener, J. P.
Journal: J Theor Biol

Calsequestrin (CSQ) is the primary calcium buffer within the sarcoplasmic reticulum (SR) of cardiac cells. It has also been identified as a regulator of Ryanodine receptor (RyR) calcium release channels by serving as a SR luminal sensor. When calsequestrin is free and unbound to calcium, it can bind to RyR and desensitize the channel from cytoplasmic calcium activation. In this paper, we study the role of CSQ as a buffer and RyR luminal sensor using a mechanistic model of RyR-CSQ interaction. By using various asymptotic approximations and mean first exit time calculation, we derive a minimal model of a calcium release unit which includes CSQ dependence. Using this model, we then analyze the effect of changing CSQ expression on the calcium release profile and the rate of spontaneous calcium release. We show that because of its buffering capability, increasing CSQ increases the spark duration and size. However, because of luminal sensing effects, increasing CSQ depresses the basal spark rate and increases the critical SR level for calcium release termination. Finally, we show that with increased bulk cytoplasmic calcium concentration, the CRU model exhibits deterministic oscillations.

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Investigating the link between epithelial-mesenchymal transition and the cancer stem cell phenotype: A mathematical approach.

Publication Date: 2010 Aug 7 PMID: 20648969
Authors: Turner, C. - Kohandel, M.
Journal: J Theor Biol

Under the cancer stem cell (CSC) hypothesis, sustained metastatic growth requires the dissemination of a CSC from the primary tumour followed by its re-establishment in a secondary site. The epithelial-mesenchymal transition (EMT), a differentiation process crucial to normal development, has been implicated in conferring metastatic ability on carcinomas. Balancing these two concepts has led researchers to investigate a possible link between EMT and the CSC phenotype-indeed, recent evidence indicates that, following induction of EMT in human breast cancer and related cell lines, stem cell activity increased, as judged by the presence of cells displaying the CD44(high)/CD24(low) phenotype and an increase in the ability of cells to form mammospheres. We mathematically investigate the nature of this increase in stem cell activity. A stochastic model is used when small number of cells are under consideration, namely in simulating the mammosphere assay, while a related continuous model is used to probe the dynamics of larger cell populations. Two scenarios of EMT-mediated CSC enrichment are considered. In the first, differentiated cells re-acquire a CSC phenotype-this model implicates fully mature cells as key subjects of de-differentiation and entails a delay period of several days before de-differentiation occurs. In the second, pre-existing CSCs experience accelerated division and increased proportion of self-renewing divisions; a lack of perfect CSC biomarkers and cell sorting techniques requires that this model be considered, further emphasizing the need for better characterization of the mammary (cancer) stem cell hierarchy. Additionally, we suggest the utility of comparing mammosphere data to computational mammosphere simulations in elucidating the growth characteristics of mammary (cancer) stem cells.

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Evolution of the rate of biological aging using a phenotype based computational model.

Publication Date: 2010 Oct 7 PMID: 20643151
Authors: Kittas, A.
Journal: J Theor Biol

In this work I introduce a simple model to study how natural selection acts upon aging, which focuses on the viability of each individual. It is able to reproduce the Gompertz law of mortality and can make predictions about the relation between the level of mutation rates (beneficial/deleterious/neutral), age at reproductive maturity and the degree of biological aging. With no mutations, a population with low age at reproductive maturity R stabilizes at higher density values, while with mutations it reaches its maximum density, because even for large pre-reproductive periods each individual evolves to survive to maturity. Species with very short pre-reproductive periods can only tolerate a small number of detrimental mutations. The probabilities of detrimental (P(d)) or beneficial (P(b)) mutations are demonstrated to greatly affect the process. High absolute values produce peaks in the viability of the population over time. Mutations combined with low selection pressure move the system towards weaker phenotypes. For low values in the ratio P(d)/P(b), the speed at which aging occurs is almost independent of R, while higher values favor significantly species with high R. The value of R is critical to whether the population survives or dies out. The aging rate is controlled by P(d) and P(b) and the amount of the viability of each individual is modified, with neutral mutations allowing the system more "room" to evolve. The process of aging in this simple model is revealed to be fairly complex, yielding a rich variety of results.

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Expanding importance of mRNA expression in understanding stress and stress responses.

Publication Date: 2010 Oct 7 PMID: 20643149
Authors: Couee, I. - Bringel, F.
Journal: J Theor Biol

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Density-dependent dispersal and relative dispersal affect the stability of predator-prey metacommunities.

Publication Date: 2010 Oct 7 PMID: 20638390
Authors: Hauzy, C. - Gauduchon, M. - Hulot, F. D. - Loreau, M.
Journal: J Theor Biol

Although density-dependent dispersal and relative dispersal (the difference in dispersal rates between species) have been documented in natural systems, their effects on the stability of metacommunities are poorly understood. Here we investigate the effects of intra- and interspecific density-dependent dispersal on the regional stability in a predator-prey metacommunity model. We show that, when the dynamics of the populations reach equilibrium, the stability of the metacommunity is not affected by density-dependent dispersal. However, the regional stability, measured as the regional variability or the persistence, can be modified by density-dependent dispersal when local populations fluctuate over time. Moreover these effects depend on the relative dispersal of the predator and the prey. Regional stability is modified through changes in spatial synchrony. Interspecific density-dependent dispersal always desynchronizses local dynamics, whereas intraspecific density-dependent dispersal may either synchronize or desynchronize it depending on dispersal rates. Moreover, intra- and interspecific density-dependent dispersal strengthen the top-down control of the prey by the predator at intermediate dispersal rates. As a consequence the regional stability of the metacommunity is increased at intermediate dispersal rates. Our results show that density-dependent dispersal and relative dispersal of species are keys to understanding the response of ecosystems to fragmentation.

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Wright-Fisher model of social insects with haploid males and diploid females.

Publication Date: 2010 Oct 7 PMID: 20633564
Authors: Tyvand, P. A. - Thorvaldsen, S.
Journal: J Theor Biol

An inhomogeneous discrete Markov model is formulated for sexual random mating in finite populations of haploid male and diploid female individuals. This is a Wright-Fisher type of model for social insects. The generations are non-overlapping and of given finite sizes. Bottlenecks are included, allowing different sizes to change from generation to generation. Mutations and selection are included in this exact model for the stochastic process. Computations of the exact Markov model are presented, focussing on the sexually asymmetric genetic drift caused by haplodiploidy.

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Positive interactions and the emergence of community structure in metacommunities.

Publication Date: 2010 Oct 7 PMID: 20627108
Authors: Filotas, E. - Grant, M. - Parrott, L. - Rikvold, P. A.
Journal: J Theor Biol

The significant role of space in maintaining species coexistence and determining community structure and function is well established. However, community ecology studies have mainly focused on simple competition and predation systems, and the relative impact of positive interspecific interactions in shaping communities in a spatial context is not well understood. Here we employ a spatially explicit metacommunity model to investigate the effect of local dispersal on the structure and function of communities in which species are linked through an interaction web comprising mutualism, competition and exploitation. Our results show that function, diversity and interspecific interactions of locally linked communities undergo a phase transition with changes in the rate of species dispersal. We find that low spatial interconnectedness favors the spontaneous emergence of strongly mutualistic communities which are more stable but less productive and diverse. On the other hand, high spatial interconnectedness promotes local biodiversity at the expense of local stability and supports communities with a wide range of interspecific interactions. We argue that investigations of the relationship between spatial processes and the self-organization of complex interaction webs are critical to understanding the geographic structure of interactions in real landscapes.

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Balancing organization and flexibility in foraging dynamics.

Publication Date: 2010 Oct 7 PMID: 20627107
Authors: Tabone, M. - Ermentrout, B. - Doiron, B.
Journal: J Theor Biol

Proper pattern organization and reorganization are central problems facing many biological networks which thrive in fluctuating environments. However, in many cases the mechanisms that organize system activity oppose those that support behavioral flexibility. Thus, a balance between pattern organization and pattern flexibility is critically important for overall biological fitness. We study this balance in the foraging strategies of ant colonies exploiting food in dynamic environments. We present discrete time and space simulations of colony activity that uses a pheromone-based recruitment strategy biasing foraging towards a food source. After food relocation, the pheromone must evaporate sufficiently before foraging can shift colony attention to a new food source. The amount of food consumed within the dynamic environment depends non-monotonically on the pheromone evaporation time constant-with maximal consumption occurring at a time constant which balances trail formation and trail flexibility. A deterministic, 'mean field' model of pheromone and foragers on trails mimics our colony simulations. This reduced framework captures the essence of the flexibility-organization balance, and relates optimal pheromone evaporation to the timescale of the dynamic environment. We expect that the principles exposed in our study will generalize and motivate novel analysis across a broad range systems biology.

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A duplex DNA model with regular inter-base-pair hydrogen bonds.

Publication Date: 2010 Oct 7 PMID: 20621103
Authors: Li, X. Q. - Fan, P.
Journal: J Theor Biol

It is well known that base-pair stacking is the main factor in stabilizing DNA duplex and plays an important role in determining DNA sequence-dependence. What is the dominant force in base-pair stacking? This fundamental biological question remains a challenging problem. Here, based on recent studies about the non-planarity of amino groups on DNA bases, we propose a new duplex DNA model, in which all base amino groups are non-planar and participate in forming regular inter-base-pair hydrogen bonds (IBP H-bonds). This model implies that IBP H-bonds are the dominant force stabilizing base-pair stacking and play a crucial role in determining the geometry and physical properties of sequence-dependent twisted stacking between adjacent base pairs. The model presents a new insight into the link, through regular IBP H-bonds, between base-sequence, fine structure and physical properties at dinucleotide step level, and provides an attractively concise, uniform and quantitative interpretation for various experimentally observed DNA sequence-dependent properties in terms of regular IBP H-bonds. It would provide a new approach to understanding the dynamics and underlying mechanisms of DNA sequence-dependent biological processes, sequence-structure-property relationships, DNA strand separation during replication and transcriptions, etc.

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Feedback-control induced pattern formation in cardiac myocytes: a mathematical modeling study.

Publication Date: 2010 Oct 7 PMID: 20620154
Authors: Gaeta, S. A. - Krogh-Madsen, T. - Christini, D. J.
Journal: J Theor Biol

Cardiac alternans is a dangerous rhythm disturbance of the heart, in which rapid stimulation elicits a beat-to-beat alternation in the action potential duration (APD) and calcium (Ca) transient amplitude of individual myocytes. Recently, "subcellular alternans", in which the Ca transients of adjacent regions within individual myocytes alternate out-of-phase, has been observed. A previous theoretical study suggested that subcellular alternans may result during static pacing from a Turing-type symmetry breaking instability, but this was only predicted in a subset of cardiac myocytes (with negative Ca to voltage (Ca-->V(m)) coupling) and has never been directly verified experimentally. A recent experimental study, however, showed that subcellular alternans is dynamically induced in the remaining subset of myocytes during pacing with a simple feedback control algorithm ("alternans control"). Here we show that alternans control pacing changes the effective coupling between the APD and the Ca transient (V(m)-->Ca coupling), such that subcellular alternans is predicted to occur by a Turing instability in cells with positive Ca-->V(m) coupling. In addition to strengthening the understanding of the proposed mechanism for subcellular alternans formation, this work (in concert with previous theoretical and experimental results) illuminates subcellular alternans as a striking example of a biological Turing instability in which the diffusing morphogens can be clearly identified.

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With whom is the gene in conflict in offspring production? Synthesis of the theories of intragenomic and parent-offspring conflict.

Publication Date: 2010 Oct 7 PMID: 20620153
Authors: Sakai, S.
Journal: J Theor Biol

In offspring production, with whom are the maternally derived (madumnal), paternally derived (padumnal), and maternal genes in conflict? I developed a model, in which those genes independently regulate resource absorption of developing offspring, and offspring with a high realized resource absorption rate may become large, but may suffer abortion due to overgrowth. I analyzed two cases: maternal control is weak (maternal genes cannot completely inhibit the resource demand by the madumnal or the padumnal genes) and is strong (maternal genes can completely inhibit it). I found that, under weak maternal control, the maternal genes inhibit resource absorption, but the madumnal and padumnal genes enhance it if the abortion cost of overgrowth is low. The maternal and madumnal genes inhibit resource absorption, but the padumnal genes enhance it if the cost is high. Under strong maternal control, the maternal genes inhibit resource absorption, but the madumnal and padumnal genes enhance it irrespective of the degree of abortion cost. I also found that the effects of offspring abortion on an ESS size and number of offspring when independent are large under weak maternal control, but are moderated under strong maternal control.

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The dilution effect of the domestic animal population on the transmission of P. vivax malaria.

Publication Date: 2010 Sep 21 PMID: 20619273
Authors: Nah, K. - Kim, Y. - Lee, J. M.
Journal: J Theor Biol

The diversion of disease carrying insect from humans to animals may reduce transmission of diseases such as malaria. The use of animals to mitigate mosquito bites on human is called 'zooprophylaxis'. We introduce a mathematical model for Plasmodium vivax malaria transmission with two bloodmeal hosts (humans and domestic animals) to study the effect of zooprophylaxis. After computing the basic reproduction number from the proposed model, we explore how perturbations in the parameters, sensitive to the effects of control measures, affect its value. Zooprophylaxis is shown to determine whether a basic reproduction becomes bigger than an outbreak threshold value or not. Sensitivity analysis shows that increasing the relative animal population size works better in P. vivax malaria control than decreasing the mosquito population when the relative animal population size is larger than a threshold value.

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Correlated fluctuations carry signatures of gene regulatory network dynamics.

Publication Date: 2010 Oct 7 PMID: 20619272
Authors: Pakka, V. H. - Prugel-Bennett, A. - Dasmahapatra, S.
Journal: J Theor Biol

The dynamics of transcriptional control involve small numbers of molecules and result in significant fluctuations in protein and mRNA concentrations. The correlations between these intrinsic fluctuations then offer, via the fluctuation dissipation relation, the possibility of capturing the system's response to external perturbations, and hence the nature of the regulatory activity itself. We show that for simple regulatory networks of activators and repressors, the correlated fluctuations between molecular species show distinct characteristics for changes in regulatory mechanism and for changes to the topology of causal influence. Here, we do a stochastic analysis and derive time-dependent correlation functions between molecular species of regulatory networks and present analytical and numerical results on peaks and delays in correlations between proteins within networks. Upon using these values of peaks and delays as a two-dimensional feature space, we find that different regulatory mechanisms separate into distinct clusters. This indicates that experimentally observable pairwise correlations can distinguish between gene regulatory networks.

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Invasion and expansion of cooperators in lattice populations: prisoner's dilemma vs. snowdrift games.

Publication Date: 2010 Oct 7 PMID: 20619271
Authors: Fu, F. - Nowak, M. A. - Hauert, C.
Journal: J Theor Biol

The evolution of cooperation is an enduring conundrum in biology and the social sciences. Two social dilemmas, the prisoner's dilemma and the snowdrift game have emerged as the most promising mathematical metaphors to study cooperation. Spatial structure with limited local interactions has long been identified as a potent promoter of cooperation in the prisoner's dilemma but in the spatial snowdrift game, space may actually enhance or inhibit cooperation. Here we investigate and link the microscopic interaction between individuals to the characteristics of the emerging macroscopic patterns generated by the spatial invasion process of cooperators in a world of defectors. In our simulations, individuals are located on a square lattice with Moore neighborhood and update their strategies by probabilistically imitating the strategies of better performing neighbors. Under sufficiently benign conditions, cooperators can survive in both games. After rapid local equilibration, cooperators expand quadratically until global saturation is reached. Under favorable conditions, cooperators expand as a large contiguous cluster in both games with minor differences concerning the shape of embedded defectors. Under less favorable conditions, however, distinct differences arise. In the prisoner's dilemma, cooperators break up into isolated, compact clusters. The compact clustering reduces exploitation and leads to positive assortment, such that cooperators interact more frequently with other cooperators than with defectors. In contrast, in the snowdrift game, cooperators form small, dendritic clusters, which results in negative assortment and cooperators interact more frequently with defectors than with other cooperators. In order to characterize and quantify the emerging spatial patterns, we introduce a measure for the cluster shape and demonstrate that the macroscopic patterns can be used to determine the characteristics of the underlying microscopic interactions.

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Quantitative prediction of the thermal motion and intrinsic disorder of protein cofactors in crystalline state: a case study on halide anions.

Publication Date: 2010 Sep 21 PMID: 20619270
Authors: Ren, Y. - Chen, X. - Li, X. - Lai, H. - Wang, Q. - Zhou, P. - Chen, G.
Journal: J Theor Biol

The thermal motion and intrinsic disorder of protein cofactors are highly correlated with their biological functions and can be at least in part measured by atomic temperature factor or B-factor. However, this crystallographic parameter, which actually shares the equal importance with the atomic coordinate in describing the complete profile of crystal structures, has long been underappreciated in the field of biology. In the present study, we attempt to put the first step towards the quantitative prediction of the B-factor values of halide anions, which were recently found to play a fundamental role in conferring stability and specificity to the architecture of proteins and their complexes with nucleic acids and small ligands. In this procedure, the local nonbonding landscapes of halide anions bound in proteins are characterized by electrostatic and dispersion potentials, and then the resulting descriptors of the characterization are statistically correlated with experimentally measured B-factors by using both linear and nonlinear machine learning approaches. From the modeling results and the comparison of these results to those obtained previously for predicting protein B-factors, we demonstrate that the dynamic behavior of halide anions in protein crystals is primarily governed by the local features of nonbonding potential landscapes and, owing to the non-ignorable noise existing in experimental data, the relationship between the B-factor values and the local nonbonding landscapes can only be modeled at a moderate level of accuracy even using the complicated nonlinear methods. These findings are consistent well with that concluding from previous studies of protein B-factors.

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Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory.

Publication Date: 2010 Sep 21 PMID: 20609368
Authors: Tounsi, A. - Heireche, H. - Benhassaini, H. - Missouri, M.
Journal: J Theor Biol

Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. A remarkable controversy has occurred in the literature, regarding the length dependence of flexural rigidity of microtubules predicted by the classical elastic beam model. In this study, a higher order shear deformable beam model for microtubules is employed to study unexplained length-dependent flexural rigidity and Young's modulus of microtubules reported in the literature. The formulation allows for warping of the cross-section of the microtubule and eliminates the need for using arbitrary shear correction coefficients as in other theories. It is showed that vibration frequencies predicted by the present parabolic shear deformation theory (PSDT) are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is confirmed that transverse shearing and the warping of the cross-section of microtubules are mainly responsible for the length-dependent flexural rigidity of an isolated microtubule reported in the literature, which cannot be explained by the widely used Euler-Bernoulli beam model. Indeed, the length-dependent flexural rigidity predicted by the present model is found to be in qualitative agreement with the existing experimental data (Kurachi et al., 1995; Pampaloni et al., 2006). These results recommend that the parabolic shear deformation-beam theory offers a unified simple 1D model, which can capture the length dependence of flexural rigidity and be applied to various static and dynamic problems of microtubule mechanics.

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The level of cytosine is usually much higher than the level of guanine in two-fold degenerated sites from third codon positions of genes from Simplex- and Varicelloviruses with G+C higher than 50%.

Publication Date: 2010 Sep 7 PMID: 20600145
Authors: Khrustalev, V. V. - Barkovsky, E. V.
Journal: J Theor Biol

We studied usage of cytosine and guanine in 914 genes from completely sequenced genomes of five Simplex- and seven Varicelloviruses. In genes with total GC-content higher than 50% usage of cytosine is usually higher than usage of guanine (an average difference for genes with G+C higher than 70% reaches 4.0%). This difference is caused mostly by the elevated usage of cytosine in two-fold degenerated sites situated in third codon positions relatively to the usage of guanine in two-fold degenerated sites situated in third codon positions (an average difference for genes with G+C higher than 70% is equal to 28.2%). The usage of amino acids that are encoded by codons containing cytosine in two-fold degenerated sites situated in third codon positions (AA2TC) is much higher than the usage of amino acids encoded by codons containing guanine in two-fold degenerated sites situated in third codon positions (AA2AG). The usage of AA2AG declines much more steeply with the growth of GC-content than the usage of AA2TC. This effect is the consequence of the nature of genetic code and of the negative selection. In GC-rich genes the usage of cytosine in four-fold degenerated sites is only a little (but significantly) higher than the usage of guanine (in genes with G+C higher than 70% an average difference is equal to 4.3%). This difference may be caused by transcription-associated mutational pressure.

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A mechanism accounting for independence on starting length of tension increase in ramp stretches of active skeletal muscle at short half-sarcomere lengths.

Publication Date: 2010 Sep 7 PMID: 20600144
Authors: Till, O. - Siebert, T. - Blickhan, R.
Journal: J Theor Biol

Based on previous experimental results of independence on starting length of the tension gradient in constant-velocity stretches of active skeletal muscle at muscle lengths including the ascending limb and the plateau of the tension-length relation, a possible physiological mechanism determining the tension increase in lengthening active muscle is discussed. Considering the sliding filament theory, it is suggested that the tension-length relation of a half-sarcomere in lengthening contractions is different from that in isometric contractions. The assumed mechanism predicts, among others, that the thick filament retains its shortened length in lengthening contractions starting from a half-sarcomere length where this filament is compressed. An example model is implemented and checked with simulations.

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In silico analysis of antibody triggering biofilm associated protein in Acinetobacter baumannii.

Publication Date: 2010 Sep 21 PMID: 20600143
Authors: Rahbar, M. R. - Rasooli, I. - Mousavi Gargari, S. L. - Amani, J. - Fattahian, Y.
Journal: J Theor Biol

Acinetobacter baumannii surface protein, commonly known as biofilm associated protein (Bap), is involved in biofilm formation. A high propensity among the clinical isolates to form biofilm and a significant association of biofilms with multiple drug resistance has been demonstrated. Production of antibodies can be used for inhibition of biofilm and control of the diseases caused by A. baumannii. Large molecular mass of Bap justifies an approach to identifying A. baumannii effective antigens. It has a core domain of seven repeat modules A-G. With the large number of available biofilm gene sequences, bioinformatic tools are needed to identify the genes encoding the antigens. Proteins containing these tandem repeats of Bap domains have high propensities to attach to each other to form biofilm. We hypothesized that conserved and functional domains of tandem repeat could be identified with a search and alignment of the repeats for evaluation of antigenic determinants. Here we demonstrate the results of bioinformatics screening and gene scan of the gene sequence database of homolog sequences to identify conserved domains. Higher scoring hits were found in repeat modules mostly D, B, C and A, respectively. Upon the analysis four regions of highly structural and functional conserved regions from Bap sequence of A. baumannii were selected. 3D structure, antigenicity and solubility predictions revealed that these regions were appropriate candidates for antibody production.

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A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs.

Publication Date: 2010 Sep 7 PMID: 20600142
Authors: Kim, B. N. - Gordillo, L. F. - Kim, Y.
Journal: J Theor Biol

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.

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Depressing synapse as a detector of frequency change.

Publication Date: 2010 Oct 7 PMID: 20600141
Authors: Jedrzejewska-Szmek, J. - Zygierewicz, J.
Journal: J Theor Biol

In this article we discuss the short-term synaptic depression using a mathematical model. We derive the model of synaptic depression caused by the depletion of synaptic vesicles for the case of infinitely short stimulation time and show that the analytical formulas for the postsynaptic potential (PSP) and kinetic functions take simple closed form. A solution in this form allows an analysis of the characteristics of depression as a function of the models parameters and the derivation of analytic formulas for measures of short time synaptic depression commonly used in experimental studies. Those formulas are used to validate the model by fitting it to two types of synapses described in the literature. Given the fitted parameters we discuss the behavior of the synapse in situations involving frequency change. We also indicate a possible role of depressing synapses in information processing as not only a filter of high frequency input but as a detector of the return from high frequency stimulation to the stimulation within frequency band specific for a given synapse.

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Quasi-stationary and ratio of expectations distributions: a comparative study.

Publication Date: 2010 Sep 21 PMID: 20600140
Authors: Artalejo, J. R. - Lopez-Herrero, M. J.
Journal: J Theor Biol

Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach (Darroch and Seneta, 1965, 1967) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.

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A Markov chain description of the stepwise mutation model: local and global behaviour of the allele process.

Publication Date: 2010 Sep 21 PMID: 20600139
Authors: Caliebe, A. - Jochens, A. - Krawczak, M. - Rosler, U.
Journal: J Theor Biol

The stepwise mutation model (SMM) is a simple, widely used model to describe the evolutionary behaviour of microsatellites. We apply a Markov chain description of the SMM and derive the marginal and joint properties of this process. In addition to the standard SMM, we also consider the normalised allele process. In contrast to the standard process, the normalised process converges to a stationary distribution. We show that the marginal stationary distribution is unimodal. The standard and normalised processes capture the global and the local behaviour of the SMM, respectively.

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A theoretical interpretation of length-biomass allometry of predominantly bidimensional seaweeds.

Publication Date: 2010 Sep 21 PMID: 20600138
Authors: Majumdar, P. - Roy, S.
Journal: J Theor Biol

Experimental studies on bidimensional seaweeds revealed a scaling exponent of 0.472 for their length-biomass allometry. This was significantly higher than the value 0.25, which was proposed earlier as universal for all primary producers, based on the data for unicellular microalgae and vascular plants. Later, an exponent of 0.5 was theoretically derived, which agreed, to some extent, with experimental findings. Here, it is shown that there exists a power-law relation between the two perpendicular length parameters along the directions of growth of a bidimensional organism. The length-biomass allometric parameters can be expressed in terms of this power index. A relation between the allometric scaling exponent and allometric constant, involving the mass per unit area, has been obtained analytically. A method is proposed to determine the power index experimentally. Some mathematical expressions, relating mass, length and other parameters, have been formulated and these would be useful for experimental purposes in allometric studies. Analyzing images from an experimental study, a lot of parameters, regarding flat seaweeds, have been determined by analytical and numerical techniques.

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Adaptive foraging does not always lead to more complex food webs.

Publication Date: 2010 Sep 21 PMID: 20600137
Authors: Berec, L. - Eisner, J. - Krivan, V.
Journal: J Theor Biol

Recent modeling studies exploring the effect of consumers' adaptivity in diet composition on food web complexity invariably suggest that adaptivity in foraging decisions of consumers makes food webs more complex. That is, it allows for survival of a higher number of species when compared with non-adaptive food webs. Population-dynamical models in these studies share two features: parameters are chosen uniformly for all species, i.e. they are species-independent, and adaptive foraging is described by the search image model. In this article, we relax both these assumptions. Specifically, we allow parameters to vary among the species and consider the diet choice model as an alternative model of adaptive foraging. Our analysis leads to three important predictions. First, for species-independent parameter values for which the search image model demonstrates a significant effect of adaptive foraging on food web complexity, the diet choice model produces no such effect. Second, the effect of adaptive foraging through the search image model attenuates when parameter values cease to be species-independent. Finally, for the diet choice model we observe no (significant) effect of adaptive foraging on food web complexity. All these observations suggest that adaptive foraging does not always lead to more complex food webs. As a corollary, future studies of food web dynamics should pay careful attention to the choice of type of adaptive foraging model as well as of parameter values.

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Silk elasticity as a potential constraint on spider body size.

Publication Date: 2010 Oct 7 PMID: 20600136
Authors: Rodriguez-Girones, M. A. - Corcobado, G. - Moya-Larano, J.
Journal: J Theor Biol

Silk is known for its strength and extensibility and has played a key role in the radiation of spiders. Individual spiders use different glands to produce silk types with unique sets of proteins. Most research has studied the properties of major ampullate and capture spiral silks and their ecological implications, while little is known about minor ampullate silk, the type used by those spider species studied to date for bridging displacements. A biomechanical model parameterised with available data shows that the minimum radius of silk filaments required for efficient bridging grows with the square root of the spider's body mass, faster than the radius of minor ampullate silk filaments actually produced by spiders. Because the morphology of spiders adapted to walking along or under silk threads is ill suited for moving on a solid surface, for these species there is a negative relationship between body mass and displacement ability. As it stands, the model suggests that spiders that use silk for their displacements are prevented from attaining a large body size if they must track their resources in space. In particular, silk elasticity would favour sexual size dimorphism because males that must use bridging lines to search for females cannot grow large.

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Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling.

Publication Date: 2010 Sep 21 PMID: 20600134
Authors: Baltcheva, I. - Codarri, L. - Pantaleo, G. - Le Boudec, J. Y.
Journal: J Theor Biol

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

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Nutrient flows between ecosystems can destabilize simple food chains.

Publication Date: 2010 Sep 7 PMID: 20600133
Authors: Marleau, J. N. - Guichard, F. - Mallard, F. - Loreau, M.
Journal: J Theor Biol

Dispersal of organisms has large effects on the dynamics and stability of populations and communities. However, current metacommunity theory largely ignores how the flows of limiting nutrients across ecosystems can influence communities. We studied a meta-ecosystem model where two autotroph-consumer communities are spatially coupled through the diffusion of the limiting nutrient. We analyzed regional and local stability, as well as spatial and temporal synchrony to elucidate the impacts of nutrient recycling and diffusion on trophic dynamics. We show that nutrient diffusion is capable of inducing asynchronous local destabilization of biotic compartments through a diffusion-induced spatiotemporal bifurcation. Nutrient recycling interacts with nutrient diffusion and influences the susceptibility of the meta-ecosystem to diffusion-induced instabilities. This interaction between nutrient recycling and transport is further shown to depend on ecosystem enrichment. It more generally emphasizes the importance of meta-ecosystem theory for predicting species persistence and distribution in managed ecosystems.

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Competition and species coexistence in a metapopulation model: can fast asymmetric migration reverse the outcome of competition in a homogeneous environment?

Publication Date: 2010 Sep 21 PMID: 20600132
Authors: Ngoc, D. N. - de la Parra, R. B. - Zavala, M. A. - Auger, P.
Journal: J Theor Biol

We investigate whether asymmetric fast migration can modify the predictions of classical competition theory and, in particular revert species dominance. We consider a model of two species competing for an implicit resource on a habitat divided into two patches. Both patches are connected through constant migration rates and in each patch local dynamics are driven by a Lotka-Volterra competition system. Local competition is asymmetric with the same superior competitor in both patches. Migration is asymmetric, species dependent and fast in comparison to local competitive interactions. The species and patches are taken to be otherwise similar: in both patches we assume the same carrying capacities for both species, and the same growth rates and pair-wise competition coefficients for each species. We show that global dynamics can be described by a classical Lotka-Volterra competition model. We found that by modifying the ratio of intraspecific migration rates for both species all possible combinations of global species relative dominance can be achieved. We find specific conditions for which the local superior competitor is globally excluded. This is to our knowledge the first study showing that fast asymmetric migration can lead to inferior competitor dominance in a homogeneous environment. We conclude that disparity of temporal scales between migration and local dynamics may have important consequences for the maintenance of biodiversity in spatially structured populations.

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The correlation of gene expression and co-regulated gene patterns in characteristic KEGG pathways.

Publication Date: 2010 Sep 21 PMID: 20599549
Authors: Hua, L. - Li, D. G. - Lin, H. - Li, L. - Li, X. - Liu, Z. C.
Journal: J Theor Biol

There is great interest in chromosome- and pathway-based techniques for genomics data analysis in the current work in order to understand the mechanism of disease. However, there are few studies addressing the abilities of machine learning methods in incorporating pathway information for analyzing microarray data. In this paper, we identified the characteristic pathways by combining the classification error rates of out-of-bag (OOB) in random forests with pathways information. At each characteristic pathway, the correlation of gene expression was studied and the co-regulated gene patterns in different biological conditions were mined by Mining Attribute Profile (MAP) algorithm. The discovered co-regulated gene patterns were clustered by the average-linkage hierarchical clustering technique. The results showed that the expression of genes at the same characteristic pathway were approximate. Furthermore, two characteristic pathways were discovered to present co-regulated gene patterns in which one contained 108 patterns and the other contained one pattern. The results of cluster analysis showed that the smallest similarity coefficient of clusters was more than 0.623, which indicated that the co-regulated patterns in different biological conditions were more approximate at the same characteristic pathway. The methods discussed in this paper can provide additional insight into the study of microarray data.

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The evolution of gynodioecy on a lattice.

Publication Date: 2010 Sep 21 PMID: 20599548
Authors: Preece, T. - Mao, Y.
Journal: J Theor Biol

Gynodioecy is a breeding system in plants where populations consist of hermaphrodites and females. The females result from a genetic mutation which impairs pollen production in hermaphrodite plants. Most previous models for the evolution of gynodioecy do not take into account any spatial detail, which might be expected to play an important role in populations with short range interactions caused by poor or no locomotion. In this article we present a generalised mean-field analysis (which ignores any spatial detail), together with stochastic spatial simulations, to investigate the spatial effect on the evolution of gynodioecy. We show that, in a population of hermaphrodites where male sterility is caused by a dominant allele in a nuclear gene, mean-field calculations greatly underestimate the reproductive advantage females require to become viable under spatial constraints. This suggests that gynodioecy is less likely to evolve in plants with more localised pollination and seed setting. This may have implications for the evolution of dioecy, a breeding system in plants where the population consists of males and females, as gynodioecy is thought to be a route to dioecy. Our results also demonstrate that a lower frequency of females should be expected for gynodioecious populations when interactions are local. This is relevant when comparing the results of breeding experiments with observations of female frequency in the wild.

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Tumour suppression by immune system through stochastic oscillations.

Publication Date: 2010 Aug 7 PMID: 20580640
Authors: Caravagna, G. - d'Onofrio, A. - Milazzo, P. - Barbuti, R.
Journal: J Theor Biol

The well-known Kirschner-Panetta model for tumour-immune System interplay [Kirschner, D., Panetta, J.C., 1998. Modelling immunotherapy of the tumour-immune interaction. J. Math. Biol. 37 (3), 235-252] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid-stochastic version of that model. In this new framework, we show that in reality the model is also able to reproduce the suppression, through stochastic extinction after the first spike of an oscillation.

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Phenotypic differences in viral immune escape explained by linking within-host dynamics to host-population immunity.

Publication Date: 2010 Aug 21 PMID: 20570681
Authors: Pepin, K. M. - Volkov, I. - Banavar, J. R. - Wilke, C. O. - Grenfell, B. T.
Journal: J Theor Biol

Viruses that do not cause life-long immunity persist by evolving rapidly in response to prevailing host immunity. The immune-escape mutants emerge frequently, displacing or co-circulating with native strains even though mutations conferring immune evasion are often detrimental to viral replication. The epidemiological dynamics of immune-escape in acute-infection viruses with high transmissibility have been interpreted mainly through immunity dynamics at the host population level, despite the fact that immune-escape evolution involves dynamical processes that feedback across the within- and between-host scales. To address this gap, we use a nested model of within- and between-host infection dynamics to examine how the interaction of viral replication rate and cross-immunity imprint host population immunity, which in turn determines viral immune escape. Our explicit consideration of direct and immune-mediated competitive interactions between strains within-hosts revealed three insights pertaining to risk and control of viral immune-escape: (1) replication rate and immune-stimulation deficiencies (i.e., original antigenic sin) act synergistically to increase immune escape, (2) immune-escape mutants with replication deficiencies relative to their wildtype progenitor are most successful under moderate cross-immunity and frequent re-infections, and (3) the immunity profile along short host-transmission chains (local host-network structure) is a key determinant of immune escape.

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A neural network approach for the prediction of in vitro culture parameters for maximum biomass yields in hairy root cultures.

Publication Date: 2010 Aug 21 PMID: 20561985
Authors: Prakash, O. - Mehrotra, S. - Krishna, A. - Mishra, B. N.
Journal: J Theor Biol

The present study deals with ANN based prediction of culture parameters in terms of inoculum density, pH and volume of growth medium per culture vessel and sucrose content of the growth medium for Glycyrrhiza hairy root cultures. This kind of study could be a model system in exploitation of hairy root cultures for commercial production of pharmaceutical compounds using large bioreactors. The study is aimed to evaluate the efficiency of regression neural network and back propagation neural network for the prediction of optimal culture conditions for maximum hairy root biomass yield. The training data for regression and back propagation networks were primed on the basis of function approximation, where final biomass fresh weight (f(wt)) was considered as a function of culture parameters. On this basis the variables in culture conditions were described in the form of equations which are for inoculum density: y=0.02x+0.04, for pH of growth medium: y=x+2.8, for sucrose content in medium: y=9.9464x+(-9.7143) and for culture medium per culture vessel: y=10x. The fresh weight values obtained from training data were considered as target values and further compared with predicted fresh weight values. The empirical data were used as testing data and further compared with values predicted from trained networks. Standard MATLAB inbuilt generalized regression network with radial basis function radbas as transfer function in layer one and purelin in layer two and back propagation having purelin as transfer function in output layer and logsig in hidden layer were used. Although in comparative assessment both the networks were found efficient for prediction of optimal culture conditions for high biomass production, more accuracy in results was seen with regression network.

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Impact of protein binding on receptor occupancy: a two-compartment model.

Publication Date: 2010 Aug 21 PMID: 20561976
Authors: Peletier, L. A. - Benson, N. - van der Graaf, P. H.
Journal: J Theor Biol

In this paper we analyse the impact of protein-, lipid- and receptor-binding on receptor occupancy in a two-compartment system, with proteins in both compartments and lipids and receptors in the peripheral compartment only. We do this for two manners of drug administration: a bolus administration and a constant rate infusion, both into the central compartment. We derive explicit approximations for the time-curves of the different compounds valid for a wide range of realistic values of rate constants and initial concentrations of proteins, lipids, receptors and the drug. These approximations are used to obtain both qualitative and quantitative insight into such critical properties as the distribution of the drug over the two compartments, the maximum receptor occupancy and the area under the drug-receptor complex curve. In particular we focus on assessing the impact of the dissociation constants, K(P), K(L) and K(R) of the drug with, respectively, the proteins, the lipids and the receptors, the permeability and the surface area of the membrane between compartments, and the rate the drug is eliminated from the system.

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A spatially explicit model for tropical tree diversity patterns.

Publication Date: 2010 Aug 21 PMID: 20561975
Authors: Horvat, S. - Derzsi, A. - Neda, Z. - Balog, A.
Journal: J Theor Biol

A simple two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. The parameters of the model characterize the speciation- and global-dispersion rates. Monte Carlo type computer simulations are performed on the model, investigating species abundances and the spatial distribution of individuals and species. Simulation results are critically compared with the experimental data obtained from a tree census on a 50 hectare area of the Barro Colorado Island (BCI), Panama. Fitting to only two observable quantities from the BCI data (total species number and the slope of the log-log species-area curve at the maximal area), it is possible to reproduce the full species-area curve, the relative species abundance distribution, and a more realistic spatial distribution of species.

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Species, clusters and the 'Tree of life': a graph-theoretic perspective.

Publication Date: 2010 Aug 21 PMID: 20561974
Authors: Dress, A. - Moulton, V. - Steel, M. - Wu, T.
Journal: J Theor Biol

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life'. In this paper we use an approach based on discrete mathematics to address a basic question: could one delineate this hierarchical structure in nature purely by reference to the 'genealogy' of present-day individuals, which describes how they are related with one another by ancestry through a continuous line of descent? We describe several mathematically precise ways by which one can naturally define collections of subsets of present day individuals so that these subsets are nested (and so form a tree) based purely on the directed graph that describes the ancestry of these individuals. We also explore the relationship between these and related clustering constructions.

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Mathematical modelling of carbohydrate degradation by human colonic microbiota.

Publication Date: 2010 Sep 7 PMID: 20561534
Authors: Munoz-Tamayo, R. - Laroche, B. - Walter, E. - Dore, J. - Leclerc, M.
Journal: J Theor Biol

The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insight into its dynamics. In this context, this paper presents the development of a mathematical model of carbohydrate degradation. Our aim was to provide an in silico approach to contribute to a better understanding of the fermentation patterns in such an ecosystem. Our mathematical model is knowledge-based, derived by writing down mass-balance equations. It incorporates physiology of the intestine, metabolic reactions and transport phenomena. The model was used to study various nutritional scenarios and to assess the role of the mucus on the system behavior. Model simulations provided an adequate qualitative representation of the human colon. Our model is complementary to experimental studies on human colonic fermentation, which, of course, is not meant to replace. It may be helpful to gain insight on questions that are still difficult to elucidate by experimentation and suggest future experiments.

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Quantal basis of vesicle growth and information content, a unified approach.

Publication Date: 2010 Sep 7 PMID: 20561533
Authors: Nitzany, E. - Hammel, I. - Meilijson, I.
Journal: J Theor Biol

Secretory vesicles express a periodic multimodal size distribution. The successive modes are integral multiples of the smallest mode (G(1)). The vesicle content ranges from macromolecules (proteins, mucopolysaccharides and hormones) to low molecular weight molecules (neurotransmitters). A steady-state model has been developed to emulate a mechanism for the introduction of vesicles of monomer size, which grow by a unit addition mechanism, G(1)+G(n)-->G(n+1) which, at a later stage are eliminated from the system. We describe a model of growth and elimination transition rates which adequately illustrates the distributions of vesicle population size at steady-state and upon elimination. Consequently, prediction of normal behavior and pathological perturbations is feasible. Careful analysis of spontaneous secretion, as compared to short burst-induced secretion, suggests that the basic character-code for reliable communication should be within a range of only 8-10 vesicles' burst which may serve as a yes/no message.

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High performance set of PseAAC and sequence based descriptors for protein classification.

Publication Date: 2010 Sep 7 PMID: 20558184
Authors: Nanni, L. - Brahnam, S. - Lumini, A.
Journal: J Theor Biol

The study of reliable automatic systems for protein classification is important for several domains, including finding novel drugs and vaccines. The last decade has seen a number of advances in the development of reliable systems for classifying proteins. Of particular interest has been the exploration of new methods for extracting features from a protein that enhance classification for a given problem. Most methods developed to date, however, have been evaluated in only one or two application areas. Methods have not been explored that generalize well across a number of application areas and datasets. The aim of this study is to find a general method, or an ensemble of methods, that works well on different protein classification datasets and problems. Towards this end, we evaluate several feature extraction approaches for representing proteins starting from their amino acid sequence as well as different feature descriptor combinations using an ensemble of classifiers (support vector machines). In our experiments, more than ten different protein descriptors are compared using nine different datasets. We develop our system using a blind testing protocol, where the parameters of the system are optimized using one dataset and then validated using the other datasets (and so on for each dataset). Although different stand-alone classifiers work well on some datasets and not on others, we have discovered that fusion among different methods obtains a good performance across all the tested datasets, especially when using the weighted sum rule. Included in our feature descriptor combinations is the introduction of two new descriptors, one based on wavelets and the other based on amino acid groups. Using our system, both outperform their standard implementations. We also consider as a baseline the simple amino acid composition (AC) and dipeptide composition (2G), since they have been widely used for protein classification. Our proposed method outperforms AC and 2G.

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Theoretical results for chemotactic response and drift of E. coli in a weak attractant gradient.

Publication Date: 2010 Sep 7 PMID: 20558183
Authors: Reneaux, M. - Gopalakrishnan, M.
Journal: J Theor Biol

The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of runs in the direction of the source. When there is a spatial gradient in the attractant concentration, this bias produces a drift velocity directed towards its source, whereas in a uniform concentration, E. coli adapts, almost perfectly in case of methyl aspartate. Recently, microfluidic experiments have measured the drift velocity of E. coli in precisely controlled attractant gradients, but no general theoretical expression for the same exists. With this motivation, we study an analytically soluble model here, based on the Barkai-Leibler model, originally introduced to explain the perfect adaptation. Rigorous mathematical expressions are obtained for the chemotactic response function and the drift velocity in the limit of weak gradients and under the assumption of completely random tumbles. The theoretical predictions compare favorably with experimental results, especially at high concentrations. We further show that the signal transduction network weakens the dependence of the drift on concentration, thus enhancing the range of sensitivity.

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The evolution of associative learning: A factor in the Cambrian explosion.

Publication Date: 2010 Sep 7 PMID: 20558182
Authors: Ginsburg, S. - Jablonka, E.
Journal: J Theor Biol

The Cambrian explosion is probably the most spectacular diversification in evolutionary history, and understanding it has been a challenge for biologists since the time of Darwin. We propose that one of the key factors that drove this great diversification was associative learning. Although the evolutionary emergence of associative learning required only small modifications in already existing memory mechanisms and may have occurred in parallel in several groups, once this type of learning appeared on the evolutionary scene, it led to extreme diversifying selection at the ecological level: it enabled animals to exploit new niches, promoted new types of relations and arms races, and led to adaptive responses that became fixed through genetic accommodation processes. This learning-based diversification was accompanied by neurohormonal stress, which led to an ongoing destabilization and re-patterning of the epigenome, which, in turn, enabled further morphological, physiological, and behavioral diversification. Our hypothesis combines several previous ideas about the dynamics of the Cambrian explosion and provides a unifying framework that includes both ecological and genomic factors. We conclude by suggesting research directions that would clarify the timing and manner in which associative learning evolved, and the effects it had on the evolution of nervous systems, genomes, and animal morphology.

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Possible origin of life between mica sheets.

Publication Date: 2010 Sep 7 PMID: 20558181
Authors: Hansma, H. G.
Journal: J Theor Biol

The mica hypothesis is a new hypothesis about how life might have originated. The mica hypothesis provides simple solutions to many basic questions about the origins of life. In the mica hypothesis, the spaces between mica sheets functioned as the earliest cells. These 'cells' between mica sheets are filled with potassium ions, and they provide an environment in which: polymer entropy is low; cyclic wetting and drying can occur; molecules can evolve in isolated spaces and also migrate and ligate to form larger molecules. The mica hypothesis also proposes that mechanical energy (work) is a major energy source that could have been used on many length scales to form covalent bonds, to alter polymer conformations, and to bleb daughter cells off protocells. The mica hypothesis is consistent with many other origins hypotheses, including the RNA, lipid, and metabolic 'worlds'. Therefore the mica hypothesis has the potential to unify origins hypotheses, such that different molecular components and systems could simultaneously evolve in the spaces between mica sheets.

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Evolution of cytoplasmic sex ratio distorters: Effect of paternal transmission.

Publication Date: 2010 Sep 7 PMID: 20558180
Authors: Yamauchi, A. - Telschow, A. - Kobayashi, Y.
Journal: J Theor Biol

Eukaryotic organisms carry various genetic factors the so-called cytoplasmic genetic elements (CGEs), in their cytoplasm. Numerous examples are known in which CGEs possess the ability to control sex determination of their host organisms and cause sex ratio distortion (SRD). In general, CGEs are inherited maternally from female hosts, via egg cytoplasm to offspring. Thus, the elements tend to evolve abilities to avoid entrance into "dead-end" males. Previous theoretical studies have revealed that, as long as maternal transmission is perfect, CGEs evolve the highest levels of ability to cause SRD. However, it is recently reported that some CGEs transmit from male to offspring through infection to female in mating. This raises the question of how such a paternal contribution alters selective forces and SRD evolution. In the present study, the evolutionary process of SRD ability of CGEs was analyzed theoretically. The main finding is that paternal transmission results in evolution towards intermediate levels of SRD. Further, coexistence was observed of different CGEs inducing different levels of SRD. These results point to the importance of paternal transmission in the evolution of CGEs.

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Dynamical behavior of a hepatitis B virus transmission model with vaccination.

Publication Date: 2010 Aug 21 PMID: 20553944
Authors: Pang, J. - Cui, J. A. - Zhou, X.
Journal: J Theor Biol

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R(0)< or =1, and a globally asymptotically stable endemic equilibrium when R(0)>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.

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Analyzing steady states of dynamics of bio-molecules from the structure of regulatory networks.

Publication Date: 2010 Sep 21 PMID: 20553943
Authors: Mochizuki, A. - Saito, D.
Journal: J Theor Biol

Regulatory relations between biological molecules constitute complex network systems and realize diverse biological functions through the dynamics of molecular activities. However, we currently have very little understanding of the relationship between the structure of a regulatory network and its dynamical properties. In this paper we introduce a new method, named "linkage logic" to analyze the dynamics of network systems. By this method, we can restrict possible steady states of a given complex network system from the knowledge of regulatory linkages alone. The regulatory linkage simply specifies the list of variables that affect the dynamics of each variable. We formalize two aspects of the linkage logic: the "Principle of Compatibility" determines the upper limit of the diversity of possible steady states of the dynamics realized by a given network; the "Principle of Dependency" determines the possible combinations of states of the system. By combining these two aspects, (i) for a given network, we can identify a cluster of nodes that gives an alternative representation of the steady states of the whole system, (ii) we can reduce a given complex network into a simpler one without loss of the ability to generate the diversity of steady states, (iii) we can examine the consistency between the structure of network and observed set of steady states, and (iv) sometimes we can predict unknown states or unknown regulations from an observed set of steady states alone. We illustrate the method by several applications to an experimentally determined regulatory network for biological functions.

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A mathematical model of pregnancy recognition in mammals.

Publication Date: 2010 Sep 7 PMID: 20553942
Authors: Shorten, P. R. - Peterson, A. J. - O'Connell, A. R. - Juengel, J. L. - McNatty, K. P. - Soboleva, T. K.
Journal: J Theor Biol

In this paper we develop a mathematical model of the luteal phase of the reproductive cycle in mammals with the aim to generate a systems understanding of pregnancy recognition. Pregnancy recognition is initiated by the production of interferon tau (IFNtau) by the growing conceptus. This ensures that the maternal corpus luteum (CL) remains viable to secrete progesterone, which is critical for providing a uterine microenvironment suitable for embryonic growth. Our mathematical model describes the interactions among the CL, the reproductive hormones and the hormone receptors in the uterus. It also characterises the complex interactions amongst the uterine oestrogen, progesterone and oxytocin receptors that control the sensitivity of the uterus to oestrogen, progesterone and oxytocin, respectively. The model is represented by a dynamical system and exhibits qualitative features consistent with the known experimental results in sheep. A key factor identified was a time-dependent threshold for the IFNtau signal below which the presence of the embryo might not be recognised and thus pregnancy would likely fail. Furthermore, the model indicated that if the IFNtau signal is later than around day 13 of the cycle, then pregnancy will not be recognised irrespective of the IFNtau concentration. The thresholds in the concentration and time of the IFNtau signal is a screening mechanism whereby only embryos of sufficient quality are able to prevent luteolysis (i.e. regression of the CL). The effect of progesterone secretion rate from the CL on pregnancy recognition was investigated. The model suggests that if the secretion rate is low then the initiation of the IFNtau signal is delayed, which in turn compromises the likelihood of a pregnancy being recognised by the CL. Furthermore, pregnancy recognition does not occur below a critical threshold in the progesterone secretion rate. In summary, the model can be used to identify the most favourable conditions for pregnancy recognition.

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Glucose induced fractal colony pattern of Bacillus thuringiensis.

Publication Date: 2010 Aug 7 PMID: 20553734
Authors: Roy, M. K. - Banerjee, P. - Sengupta, T. K. - Dattagupta, S.
Journal: J Theor Biol

Growing colonies of bacteria on the surface of thin agar plates exhibit fractal patterns as a result of nonlinear response to environmental conditions, such as nutrients, solidity of the agar medium and temperature. Here, we examine the effect of glucose on pattern formation by growing colonies of Bacillus thuringiensis isolate KPWP1. We also present the theoretical modeling of the colony growth of KPWP1 and the associated spatio-temporal patterns. Our experimental results are in excellent agreement with simulations based on a reaction-diffusion model that describes diffusion-limited aggregation and branching, in which individual cells move actively in the periphery, but become immotile in the inner regions of the growing colony. We obtain the Hausdorff fractal dimension of the colony patterns: D(H.Expt)=1.1969 and D(H, R.D.=)1.1965, for experiment and reaction-diffusion model, respectively. Results of our experiments and modeling clearly show how glucose at higher concentration can prove to be inhibitory for motility of growing colonies of B. thuringiensis cells on semisolid support and be responsible for changes in the growth pattern.

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Understanding inhibition of viral proteins on type I IFN signaling pathways with modeling and optimization.

Publication Date: 2010 Aug 21 PMID: 20553733
Authors: Zou, X. - Xiang, X. - Chen, Y. - Peng, T. - Luo, X. - Pan, Z.
Journal: J Theor Biol

The interferon system provides a powerful and universal intracellular defense mechanism against viruses. As one part of their survival strategies, many viruses have evolved mechanisms to counteract the host type I interferon (IFN-alpha/beta) responses. In this study, we attempt to investigate virus- and double-strand RNA (dsRNA)-triggered type I IFN signaling pathways and understand the inhibition of IFN-alpha/beta induction by viral proteins using mathematical modeling and quantitative analysis. Based on available literature and our experimental data, we develop a mathematical model of virus- and dsRNA-triggered signaling pathways leading to type I IFN gene expression during the primary response, and use the genetic algorithm to optimize all rate constants in the model. The consistency between numerical simulation results and biological experimental data demonstrates that our model is reasonable. Further, we use the model to predict the following phenomena: (1) the dose-dependent inhibition by classical swine fever virus (CSFV) N(pro) or E(rns) protein is observed at a low dose and can reach a saturation above a certain dose, not an increase; (2) E(rns) and N(pro) have no synergic inhibitory effects on IFN-beta induction; (3) the different characters in an important transcription factor, phosphorylated IRF3 (IRF3p), are exhibited because N(pro) or E(rns) counteracted dsRNA- and virus-triggered IFN-beta induction by targeting the different molecules in the signaling pathways and (4) N(pro) inhibits the IFN-beta expression not only by interacting with IFR3 but also by affecting its complex with MITA. Our approaches help to gain insight into system properties and rational therapy design, as well as to generate hypotheses for further research.

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A classification-based prediction model of messenger RNA polyadenylation sites.

Publication Date: 2010 Aug 7 PMID: 20546757
Authors: Ji, G. - Wu, X. - Shen, Y. - Huang, J. - Quinn Li, Q.
Journal: J Theor Biol

Messenger RNA polyadenylation is one of the essential processing steps during eukaryotic gene expression. The site of polyadenylation [(poly(A) site] marks the end of a transcript, which is also the end of a gene. A computation program that is able to recognize poly(A) sites would not only prove useful for genome annotation in finding genes ends, but also for predicting alternative poly(A) sites. Features that define the poly(A) sites can now be extracted from the poly(A) site datasets to build such predictive models. Using methods, including K-gram pattern, Z-curve, position-specific scoring matrix and first-order inhomogeneous Markov sub-model, numerous features were generated and placed in an original feature space. To select the most useful features, attribute selection algorithms, such as information gain and entropy, were employed. A training model was then built based on the Bayesian network to determine a subset of the optimal features. Test models corresponding to the training models were built to predict poly(A) sites in Arabidopsis and rice. Thus, a prediction model, termed Poly(A) site classifier, or PAC, was constructed. The uniqueness of the model lies in its structure in that each sub-model can be replaced or expanded, while feature generation, selection and classification are all independent processes. Its modular design makes it easily adaptable to different species or datasets. The algorithm's high specificity and sensitivity were demonstrated by testing several datasets and, at the best combinations, they both reached 95%. The software package may be used for genome annotation and optimizing transgene structure.

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Study of proteome maps using partial ordering.

Publication Date: 2010 Sep 7 PMID: 20542044
Authors: Randic, M. - Novic, M. - Vracko, M. - Plavsic, D.
Journal: J Theor Biol

This paper describes numerical characterization of proteome maps based on partial ordering of protein spots with respect to the mass and the charge. The partial ordering diagram is embedded directly over the 2D map and the corresponding adjacency matrix is constructed. The adjacency matrix is augmented by including the information on the abundance of proteins in a gel as suitably scaled diagonal entries of the matrix. The approach is illustrated on proteome maps of Anderson et al. (1996) based on experimental results from liver cells of rats exposed to four peroxisome proliferators. We used the leading eigenvectors of the adjacency matrices as maps descriptors in order to determine the degree of similarity between proteome maps.

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Comparing strategies to preserve evolutionary diversity.

Publication Date: 2010 Sep 7 PMID: 20542043
Authors: Magnuson-Ford, K. - Mooers, A. - Rioux Paquette, S. - Steel, M.
Journal: J Theor Biol

The likely future extinction of various species will result in a decline of two quantities: species richness and phylogenetic diversity (PD, or 'evolutionary history'). Under a simple stochastic model of extinction, we can estimate the expected loss of these quantities under two conservation strategies: An 'egalitarian' approach, which reduces the extinction risk of all species, and a 'targeted' approach that concentrates conservation effort on the most endangered taxa. For two such strategies that are constrained to experience the same expected loss of species richness, we ask which strategy results in a greater expected loss of PD. Using mathematical analysis and simulation, we describe how the strategy (egalitarian versus targeted) that minimizes the expected loss of PD depends on the distribution of endangered status across the tips of the tree, and the interaction of this status with the branch lengths. For a particular data set consisting of a phylogenetic tree of 62 lemur species, with extinction risks estimated from the IUCN 'Red List', we show that both strategies are virtually equivalent, though randomizing these extinction risks across the tip taxa can cause either strategy to outperform the other. In the second part of the paper, we describe an algorithm to determine how extreme the loss of PD for a given decline in species richness can be. We illustrate the use of this algorithm on the lemur tree.

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A two-sex demographic model with single-dependent divorce rate.

Publication Date: 2010 Aug 21 PMID: 20542042
Authors: Maxin, D. - Berec, L.
Journal: J Theor Biol

Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.

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Computational experiments reveal plausible mechanisms for changing patterns of hepatic zonation of xenobiotic clearance and hepatotoxicity.

Publication Date: 2010 Aug 21 PMID: 20541559
Authors: Sheikh-Bahaei, S. - Maher, J. J. - Anthony Hunt, C.
Journal: J Theor Biol

No concrete, causal, mechanistic theory is available to explain how different hepatic zonation patterns of P450 isozyme levels and hepatotoxicity emerge following dosing with different compounds. We used the synthetic method of modeling and simulation to discover, explore, and experimentally challenge concrete mechanisms that show how and why biomimetic zonation patterns can emerge and change within agent-based analogues, expecting that those mechanisms may have counterparts in rats. Mobile objects map to compounds. One analogue represents a cross-section through a lobule. It is comprised of 460 identical, quasi-autonomous functional units called sinusoidal segments (SSs). SSs detect and respond to compound-generated response signals and the local level of an endogenous gradient. Each SS adapts by using those signals to adjust (or not) the probability that it will clear a detected compound during the next simulation cycle. The adjustment decision is based on the value of a biomimetic algorithm that is based on an assumed, evolution imposed, genetic mandate that normal hepatocytes resist increasing the cost of their actions. The algorithm estimates the long-term, discounted cost to a given SS of continuing to use its current clearance effort. Upon compound exposure, lobular analogues developed a variety of clearance and hepatotoxicity patterns that were strikingly similar to those reported in the literature. A degree of quantitative validation was achieved against data on hepatic zonation of CYP1A2 mRNA expression caused by three different doses of TCDD (2,3,7,8-tetracholorodibenzo-p-dioxone).

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The dynamics of plant disease models with continuous and impulsive cultural control strategies.

Publication Date: 2010 Sep 7 PMID: 20540953
Authors: Meng, X. - Li, Z.
Journal: J Theor Biol

Plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are proposed and investigated. This novel theoretical framework could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Firstly, continuous replanting of healthy plants and removing of infected plants is taken. The existence and stability of disease-free equilibrium and positive equilibrium are studied and continuous cultural control strategy is given. Secondly, plant disease model with impulsive replanting of healthy plants and removing of infected plants is also considered. Using Floquet's theorem and small amplitude perturbation, the sufficient conditions under which the infected plant free periodic solution is locally stable are obtained. Moreover, permanence of the system is investigated. Under certain parameter spaces, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. The modeling methods and analytical analysis presented can serve as an integrating measure to identify and design appropriate plant disease control strategies.

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Anti-social punishment can prevent the co-evolution of punishment and cooperation.

Publication Date: 2010 Aug 21 PMID: 20540952
Authors: Rand, D. G. - Armao, J. J. 4th - Nakamaru, M. - Ohtsuki, H.
Journal: J Theor Biol

The evolution of cooperation is one of the great puzzles in evolutionary biology. Punishment has been suggested as one solution to this problem. Here punishment is generally defined as incurring a cost to inflict harm on a wrong-doer. In the presence of punishers, cooperators can gain higher payoffs than non-cooperators. Therefore cooperation may evolve as long as punishment is prevalent in the population. Theoretical models have revealed that spatial structure can favor the co-evolution of punishment and cooperation, by allowing individuals to only play and compete with those in their immediate neighborhood. However, those models have usually assumed that punishment is always targeted at non-cooperators. In light of recent empirical evidence of punishment targeted at cooperators, we relax this assumption and study the effect of so-called 'anti-social punishment'. We find that evolution can favor anti-social punishment, and that when anti-social punishment is possible costly punishment no longer promotes cooperation. As there is no reason to assume that cooperators cannot be the target of punishment during evolution, our results demonstrate serious restrictions on the ability of costly punishment to allow the evolution of cooperation in spatially structured populations. Our results also help to make sense of the empirical observation that defectors will sometimes pay to punish cooperators.

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Molecular modeling of BAD complex resided in a mitochondrion integrating glycolysis and apoptosis.

Publication Date: 2010 Sep 21 PMID: 20540951
Authors: Yang, J. - Li, J. H. - Wang, J. - Zhang, C. Y.
Journal: J Theor Biol

BAD (Bcl-2 antagonist of cell death) and GK (glucokinase) reside in a mitochondrial complex together with PKA and PP1 catalytic units (PKAc and PP1c) and WAVE-1 that integrates glycolysis and apoptosis. Our research results reveal that BAD is phosphorylated and inactivated on Ser 75 in a BAD-Bcl-xL complex by PKA (targeted to mitochondria through association with WAVE1), resulting in the dissociation of BAD and its binding to GK. Moreover, GK can interact with PP1c and also distinguish WAVE1. On the other hand, BAD is dephosphorylated and activated on Ser75 by PP1c, leading to the separation of PKAc and its binding to the regulatory (R) subunit of PKA which by the dimerization domain of its R subunit connects with WAVE1 linked with GK of the complex. This may be the reason of the complex existing in liver mitochondria, regardless of phosphorylated and dephosphorylated BAD. Additionally, GK like PKA may also prevent Bcl-xL from rebinding to BAD by phosphorylating BAD at Ser 118. The BAD complex model reveals that BAD and GK play key roles because of BAD as a substrate for the PKA-PP1 pair and by BH3 domain directly interacting with GK. This is helpful for our development and research of the molecular mechanism of BAD integrating glycolysis and apoptosis.

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An analysis of the orientation of an orb-web spider.

Publication Date: 2010 Aug 21 PMID: 20538009
Authors: Maciejewski, W.
Journal: J Theor Biol

In nature, orb-web spinning spiders are often observed residing on the hub of their web, facing down. An explanation of this phenomenon has only recently appeared in the literature [Zschokke, S., Nakata, K., 2010. Spider orientation and hub position in orb webs. Naturwissenschaften 97, 43-52, doi:10.1007/s00114-009-0609-7], although a similar explanation is implicit in Masters and Moffat [1983. A functional explanation of top-bottom asymmetry in vertical orbwebs. Animal Behaviour 31, 351-391, doi:10.1016/S0003-3472(83)80010-4] and ap Rhisiart and Vollrath [1994. Design features of the orb web of the spider, Araneus diadematus. Behavioural Ecology 5, 280-287]. In the present article a mathematical description of the region a spider can reach in a fixed amount of time, based on the velocity, turning rate, and initial orientation of a spider, is proposed. Maximizing the amount of prey caught on the web in the long term corresponds to maximizing the area of the region. The orientation that maximizes this area is shown to be downwards. The paper concludes with a conjectured explanation for the vertical asymmetry of orb-webs.

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A bioenergetic model of the mitochondrial population undergoing permeability transition.

Publication Date: 2010 Aug 21 PMID: 20538008
Authors: Bazil, J. N. - Buzzard, G. T. - Rundell, A. E.
Journal: J Theor Biol

Mitochondrial permeability transition (MPT) is a highly regulated complex phenomenon that is a type of ischemia/reperfusion injury that can lead to cell death and ultimately organ dysfunction. A novel population transition and detailed permeability transition pore regulation model were integrated with an existing bioenergetics model to describe MPT induction under a variety of conditions. The framework of the MPT induction model includes the potential states of the mitochondria (aggregated, orthodox and post-transition), their transitions from one state to another as well as their interaction with the extra-mitochondrial environment. The model encodes the three basic necessary conditions for MPT: a high calcium load, alkaline matrix pH and circumstances which favor de-energization. The MPT induction model was able to reproduce the expected bioenergetic trends observed in a population of mitochondria subjected to conditions that favor MPT. The model was corroborated and used to predict that MPT in an acidic environment is mitigated by an increase in activity of the mitochondrial potassium/hydrogen exchanger. The model was also used to present the beneficial impact of reducing the duration mitochondria spend in the orthodox state on preserving the extra-mitochondrial ATP levels. The model serves as a tool for investigators to use to understand the MPT induction phenomenon, explore alternative hypotheses for PTP regulation, as well as identify endogenous pharmacological targets and evaluate potential therapeutics for MPT mitigation.

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An advanced discrete state-discrete event multiscale simulation model of the response of a solid tumor to chemotherapy: Mimicking a clinical study.

Publication Date: 2010 Sep 7 PMID: 20515697
Authors: Stamatakos, G. S. - Kolokotroni, E. A. - Dionysiou, D. D. - Georgiadi, E. C. h. - Desmedt, C.
Journal: J Theor Biol

In this paper an advanced, clinically oriented multiscale cancer model of breast tumor response to chemotherapy is presented. The paradigm of early breast cancer treated by epirubicin according to a branch of an actual clinical trial (the Trial of Principle, TOP trial) has been addressed. The model, stemming from previous work of the In Silico Oncology Group, National Technical University of Athens, is characterized by several crucial new features, such as the explicit distinction of proliferating cells into stem cells of infinite mitotic potential and cells of limited proliferative capacity, an advanced generic cytokinetic model and an improved tumor constitution initialization technique. A sensitivity analysis regarding critical parameters of the model has revealed their effect on the behavior of the biological system. The favorable outcome of an initial step towards the clinical adaptation and validation of the simulation model, based on the use of anonymized data from the TOP clinical trial, is presented and discussed. Two real clinical cases from the TOP trial with variable molecular profile have been simulated. A realistic time course of the tumor diameter and a reduction in tumor size in agreement with the clinical data has been achieved for both cases by selection of reasonable model parameter values, thus demonstrating a possible adaptation process of the model to real clinical trial data. Available imaging, histological, molecular and treatment data are exploited by the model in order to strengthen patient individualization modeling. The expected use of the model following thorough clinical adaptation, optimization and validation is to simulate either several candidate treatment schemes for a particular patient and support the selection of the optimal one or to simulate the expected extent of tumor shrinkage for a given time instant and decide on the adequacy or not of the simulated scheme.

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Development of a stochastic model for the efficacy of NRTIs using known mechanisms of action.

Publication Date: 2010 Aug 21 PMID: 20510251
Authors: Khalili, S. - Monaco, J. M. - Armaou, A.
Journal: J Theor Biol

We analyze the mechanisms by which nucleoside-analogue reverse transcriptase inhibitors, the most common class of drugs used in the treatment of HIV-1, exert their antiviral effects. We then seek to identify ways in which those known mechanisms can be employed to generate mathematical models for drug efficacy in terms of measurable physical values. We demonstrate that the probability a NRTI instead of a natural nucleotide is included can be expressed in terms of intracellular drug concentrations, natural nucleotide concentrations, and relevant rate constants derived from reverse transcriptase's mechanism of nucleotide addition. In order to determine the ultimate effect, the resistance of the NRTI to removal from the genome must be considered, which is achieved via stochastic modeling. We employ this model to determine the relationship between efficacy and drug concentration, as well as other drug characteristics like half life. We also investigate the effect of drug administration time on the overall efficacy. The model is employed for four different drugs and a sensitivity analysis on mutation and resistance is performed.

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A mathematical modelling framework for understanding chemorepulsive signal transduction in Dictyostelium.

Publication Date: 2010 Sep 7 PMID: 20510250
Authors: Alam-Nazki, A. - Krishnan, J.
Journal: J Theor Biol

Chemorepulsion is the process by which an organism or a cell moves in the direction of decreasing chemical concentration. While a few experimental studies have been performed, no mathematical models exist for this process. In this paper we have modelled gradient sensing, the first subprocess of chemorepulsion, in Dictyostelium discoideum-a well characterized model eukaryotic system. We take the first steps towards achieving a comprehensive mechanistic understanding of chemorepulsion in this system. We have used, as a basis, the biochemical network of the Keizer-Gunnink et al. (2007) to develop the mathematical modelling framework. This network describes the underlying pathways of chemorepellent gradient sensing in D. discoideum. Working within this modelling framework we address whether the postulated interactions of the pathways and species in this network can lead to a chemorepulsive response. We also analyse the possible role of additional regulatory effects (such as additional receptor regulation of enzymes in this network) and if this is necessary to achieve this behaviour. Thus we have investigated the receptor regulation of important enzymes and feedback effects in the network. This modelling framework generates important insights into and testable predictions regarding the role of key components and feedback loops in regulating chemorepulsive gradient sensing, and what factors might be important for generating a chemorepulsive response; it serves as a first step towards a comprehensive mechanistic understanding of this process.

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TNF and IL-10 are major factors in modulation of the phagocytic cell environment in lung and lymph node in tuberculosis: a next-generation two-compartmental model.

Publication Date: 2010 Aug 21 PMID: 20510249
Authors: Marino, S. - Myers, A. - Flynn, J. L. - Kirschner, D. E.
Journal: J Theor Biol

Tuberculosis (TB) is one of the earliest recorded human diseases and still one of the deadliest worldwide. Its causative agent is the bacteria Mycobacterium tuberculosis (Mtb). Cytokine-mediated macrophage activation is a necessary step in control of bacterial growth, and early immunologic events in lymph node and lung are crucial to the outcome of infection, although the factors that influence these environments and the immune response are poorly understood. Our goal is to build the next-generation two-compartmental model of the immune response to provide a gateway to more spatial and mechanistic investigations of M. tuberculosis infection in the LN and lung. Crucial immune factors emerge that affect macrophage populations and inflammation, namely TNF-dependent recruitment and apoptosis, and IL-10 levels. Surprisingly, bacterial load plays a less important role than TNF in increasing the population of infected macrophages and inflammation. Using a mathematical model, it is possible to distinguish the effects of pro-inflammatory (TNF) and anti-inflammatory (IL-10) cytokines on the spectrum of phagocyte populations (macrophages and dendritic cells) in the lung and lymph node. Our results suggest that TNF is a major mediator of recruitment of phagocytes to the lungs. In contrast, IL-10 plays a role in balancing the dominant macrophage phenotype in LN and lung.

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The implications of gene heterozygosity for protein folding and protein turnover.

Publication Date: 2010 Aug 21 PMID: 20493885
Authors: Ginn, B. R.
Journal: J Theor Biol

The offspring of closely related parents often suffer from inbreeding depression, sometimes resulting in a slower growth rate for inbred offspring relative to non-inbred offspring. Previous research has shown that some of the slower growth rate of inbred organisms can be attributed to the inbred organisms' increased levels of protein turnover. This paper attempts to show that the higher levels of protein turnover among inbred organisms can be attributed to accumulations of misfolded and aggregated proteins that require degradation by the inbred organisms' protein quality control systems. The accumulation of misfolded and aggregated proteins within inbred organisms are the result of more negative free energies of folding for proteins encoded at homozygous gene loci and higher concentrations of potentially aggregating non-native protein species within the cell. The theory presented here makes several quantitative predictions that suggest a connection between protein misfolding/aggregation and polyploidy that can be tested by future research.

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Error threshold in RNA quasispecies models with complementation.

Publication Date: 2010 Aug 7 PMID: 20493884
Authors: Sardanyes, J. - Elena, S. F.
Journal: J Theor Biol

A general assumption of quasispecies models of replicons dynamics is that the fitness of a genotype is entirely determined by its sequence. However, a more biologically plausible situation is that fitness depends on the proteins that catalyze metabolic reactions, including replication. In a stirred population of replicons, such as viruses replicating and accumulating within the same cell, the association between a given genome and the proteins it encodes is not tight as it can be replicated by proteins translated from other genomes. We have investigated how this complementation phenomenon affects the error threshold in simple quasispecies mean field models. We first studied a model in which the master and the mutant genomes code for wild-type and mutant replicases, respectively. We assume that the mutant replicase has a reduced activity and that the wild-type replicase does not have increased affinity for the master genome. The whole pool of replicases can bind and replicate both genomes. We then analyze a different model considering a more extreme case of mutant genomes, the defective interfering particles (DIPs) described in many cases of viral infection. DIPs, with a higher replication rate owed to their shorter genomes, do not code for replicase, but they are able of using the replicase translated from the master genome. Our models allow to study how the probability of interaction between the genomes and the whole pool of replicases affects the error threshold. In both systems we characterize the scenario of coexistence between master and mutant genomes, providing the critical values of mutation rate, mu(c), and the critical interaction rate between master genomes and replicases, gamma(c), at which the quasispecies enters into error catastrophe, a situation in which the mutant genomes dominate the population. In both cases, we showed that the error-threshold transition is given by transcritical-like bifurcations, suggesting a continuous phase transition. We have also found that the region in the parameter space (mu,gamma) in which the master sequence survives is reduced when DIPs are introduced into the system.

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Pavlovian Prisoner's Dilemma-Analytical results, the quasi-regular phase and spatio-temporal patterns.

Publication Date: 2010 Aug 7 PMID: 20493883
Authors: Pereira, M. A. - Martinez, A. S.
Journal: J Theor Biol

The Prisoner's Dilemma (PD) game is applied in several research fields due to the emergence of cooperation among selfish players. In this work the PD is studied in a one-dimensional lattice, where each cell represents a player, which in turn can interact with the neighbors playing the PD (cooperate or defect). The update of states adopts the Pavlovian Evolutionary Strategy (PES) or Darwinian Evolutionary Strategy (DES). Adopting PES, if a player receives a positive payoff greater than his/her aspiration level, he/she keeps the current state, and switches otherwise. Adopting DES, player compares his/her payoff with payoff of opponents. If it is not the highest, he/she copies the state of fittest player, switching the state if it is different of his/her current state. The critical temptation values obtained analytically are reported, and the cluster patterns that emerge from the interactions among the players are shown. Also we defined analytical functions that calculate the maximum/minimum size of defective/cooperative clusters. Also, the parameter space is explored with exhaustive computational simulations, which confirm the analytical results and reinforce that Pavlovian strategy foments cooperation among players. In steady state, system can reach the cooperative or quasi-regular phases, when adopting the PES, and cooperative, defective or chaotic phases, adopting the DES. The new quasi-regular phase occurs when several players switch their states in each round, but the proportion of cooperators does not show significant variation. Additionally, the present work shows that the lowest temptation level (T=1) may be considered a trivial case only for the particular case where the players interact with only one neighbor, otherwise system presents the same features that for higher temptation values.

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Water: a medium where dissipative structures are produced by a coherent dynamics.

Publication Date: 2010 Aug 21 PMID: 20493195
Authors: Marchettini, N. - Del Giudice, E. - Voeikov, V. - Tiezzi, E.
Journal: J Theor Biol

The Belousov-Zhabotinsky phenomenon is analyzed in a framework where the dynamics of dissipative structures outlined by Prigogine is implemented through the collective dynamics produced in liquid water by Quantum Electrodynamics, which has received recently some experimental support. A mechanism allowing the appearance of self-produced oscillations is suggested.

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The effect of intracellular calcium oscillations on fluid secretion in airway epithelium.

Publication Date: 2010 Aug 7 PMID: 20488194
Authors: Warren, N. J. - Tawhai, M. H. - Crampin, E. J.
Journal: J Theor Biol

Airway epithelium has been shown to elicit fluid secretion after a rise in intracellular calcium. This rise in intracellular calcium has been shown to display complex oscillations in many species after the binding of particular agonists to extracellular receptors. Fluid secreted by the airway epithelium is used to maintain the depth of the periciliary liquid (PCL) above the apical membrane of the epithelial cells lining the bronchial airways. Previous mathematical models have been published which separately consider the electrophysiology involved in regulating periciliary liquid depth, and the transmission of intracellular calcium waves in airway epithelial tissue. In this paper we present a mathematical model that combines these previous models and allows the effect of oscillations in intracellular calcium on fluid secretion by airway epithelial cells to be investigated. We show that an oscillatory calcium response produces different fluid secretion properties to that elicited by a tonic rise in intracellular calcium. These differences are shown to be due to saturation of the Ca(2+) activated ion channels.

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Upstream reciprocity in heterogeneous networks.

Publication Date: 2010 Aug 7 PMID: 20478314
Authors: Iwagami, A. - Masuda, N.
Journal: J Theor Biol

Many mechanisms for the emergence and maintenance of altruistic behavior in social dilemma situations have been proposed. Indirect reciprocity is one such mechanism, where other-regarding actions of a player are eventually rewarded by other players with whom the original player has not interacted. The upstream reciprocity (also called generalized indirect reciprocity) is a type of indirect reciprocity and represents the concept that those helped by somebody will help other unspecified players. In spite of the evidence for the enhancement of helping behavior by upstream reciprocity in rats and humans, theoretical support for this mechanism is not strong. In the present study, we numerically investigate upstream reciprocity in heterogeneous contact networks, in which the players generally have different number of neighbors. We show that heterogeneous networks considerably enhance cooperation in a game of upstream reciprocity. In heterogeneous networks, the most generous strategy, by which a player helps a neighbor on being helped and in addition initiates helping behavior, first occupies hubs in a network and then disseminates to other players. The scenario to achieve enhanced altruism resembles that seen in the case of the Prisoner's Dilemma game in heterogeneous networks.

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Structural analysis of metabolic networks based on flux centrality.

Publication Date: 2010 Aug 7 PMID: 20471988
Authors: Koschutzki, D. - Junker, B. H. - Schwender, J. - Schreiber, F.
Journal: J Theor Biol

Metabolic reactions are fundamental to living organisms, and a large number of reactions simultaneously occur at a given time in living cells transforming diverse metabolites into each other. There has been an ongoing debate on how to classify metabolites with respect to their importance for metabolic performance, usually based on the analysis of topological properties of genome scale metabolic networks. However, none of these studies have accounted quantitatively for flux in metabolic networks, thus lacking an important component of a cell's biochemistry. We therefore analyzed a genome scale metabolic network of Escherichia coli by comparing growth under 19 different growth conditions, using flux balance analysis and weighted network centrality investigation. With this novel concept of flux centrality we generated metabolite rankings for each particular growth condition. In contrast to the results of conventional analysis of genome scale metabolic networks, different metabolites were top-ranking dependent on the growth condition. At the same time, several metabolites were consistently among the high ranking ones. Those are associated with pathways that have been described by biochemists as the most central part of metabolism, such as glycolysis, tricarboxylic acid cycle and pentose phosphate pathway. The values for the average path length of the analyzed metabolite networks were between 10.5 and 12.6, supporting recent findings that the metabolic network of E. coli is not a small-world network.

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Langevin dynamics simulations reveal biologically relevant folds arising from the incorporation of a torsional potential.

Publication Date: 2010 Aug 7 PMID: 20471987
Authors: Anjukandi, P. - Pereira, G. G. - Williams, M. A.
Journal: J Theor Biol

The conformational behaviour of polymer chains has been examined using Langevin dynamics simulation techniques. Polymer chains were modelled as "beads" undergoing Brownian motion in a defined potential that accounted for stretching, bending and solvation energies. As expected, the competition between chain stiffness and solvent interactions was found to yield standard swollen or collapsed configurations in good or poor solvents, respectively. However, when a torsional term was introduced into the model, additional biologically relevant conformations such as helices, sheets, turns and hairpins naturally arose.

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Effect of retentive markers on the dynamics of settlement: The case of arthropod silk.

Publication Date: 2010 Aug 7 PMID: 20471986
Authors: Astudillo Fernandez, A. - Mailleux, A. C. - Saffre, F. - Krafft, B. - Deneubourg, J. L.
Journal: J Theor Biol

During a settlement decision, the presence of conspecifics is crucial to species subject to Allee effects, for which the number of founders affects the subsequent growth of the colony. Marking the area (physically or chemically) conveys information about the number of conspecifics present in a new patch. Here, we study how an individual affinity for the marker affects the dynamics of a foundation process. A generic population model is presented, in which marking and affinity for the marker are at stake. Our results show that population size thresholds can appear, below which settlement is not possible. This model is then used to study the dynamics of migration and aggregation in a set of interconnected populations. We show that affinity for the marker can induce asymmetries in the population distribution. Anelosimus eximius is a social spider subject to Allee effects, for which silk potentially acts as a marker. We test our predictions with field experiments involving two populations of A. eximius in a Y-shaped setup. The agreement between our experimental and theoretical results strongly supports the validity of the model. This allows us to use the model to estimate a realistic set of parameters of biological significance to this social spider.

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A simple method to analyze the similarity of biological sequences based on the fuzzy theory.

Publication Date: 2010 Aug 7 PMID: 20471985
Authors: Huang, W. - Zhang, J. - Wang, Y. - Huang, D.
Journal: J Theor Biol

In this paper, we propose a simple method to analyze the similarity of biological sequences. By taking the average contents of biological sequences and their information entropies as the variables, the fuzzy method is used to cluster them. From the results of application, it finds that the method is relatively easy and rapid. Unlike other methods such as the graphical representation methods, which is usually very complex to compute some invariants of matric derived from graphical representation, our method pays more attention to the information of biological sequences themselves. Especially with the help of the software (SPSS), it seems to be very convenient. Therefore, it may be used to study the new biological sequences such as their evolution relationship and structures.

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Stochastic competitive exclusion in the maintenance of the naive T cell repertoire.

Publication Date: 2010 Aug 7 PMID: 20471403
Authors: Stirk, E. R. - Lythe, G. - van den Berg, H. A. - Molina-Paris, C.
Journal: J Theor Biol

Recognition of antigens by the adaptive immune system relies on a highly diverse T cell receptor repertoire. The mechanism that maintains this diversity is based on competition for survival stimuli; these stimuli depend upon weak recognition of self-antigens by the T cell antigen receptor. We study the dynamics of diversity maintenance as a stochastic competition process between a pair of T cell clonotypes that are similar in terms of the self-antigens they recognise. We formulate a bivariate continuous-time Markov process for the numbers of T cells belonging to the two clonotypes. We prove that the ultimate fate of both clonotypes is extinction and provide a bound on mean extinction times. We focus on the case where the two clonotypes exhibit negligible competition with other T cell clonotypes in the repertoire, since this case provides an upper bound on the mean extinction times. As the two clonotypes become more similar in terms of the self-antigens they recognise, one clonotype quickly becomes extinct in a process resembling classical competitive exclusion. We study the limiting probability distribution for the bivariate process, conditioned on non-extinction of both clonotypes. Finally, we derive deterministic equations for the number of cells belonging to each clonotype as well as a linear Fokker-Planck equation for the fluctuations about the deterministic stable steady state.

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Variable valuations and voluntarism under group selection: An evolutionary public goods game.

Publication Date: 2010 Aug 7 PMID: 20470784
Authors: Crowley, P. H. - Hwan Baik, K.
Journal: J Theor Biol

In biological systems, as in human society, competing social groups may depend heavily on a small number of volunteers to advance the group's prospects. This phenomenon can be understood as the solution to an evolutionary public goods game, in which a beneficent individual or a small number of individuals may place the highest value on group success and contribute the most to achieving it while profiting very little. Here we demonstrate that this type of solution, recently recognized in the social sciences, is evolutionarily stable and evolves in evolutionary simulations sensitive to alternative ways of gaining fitness beyond the present social group. The public goods mechanism may help explain biological voluntarism in cases like predator inspection and foraging on behalf of non-relatives and may determine the extent of commitment to group welfare at different intensities of group selection.

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Dipteran insect flight dynamics. Part 2: Lateral-directional motion about hover.

Publication Date: 2010 Aug 7 PMID: 20470783
Authors: Faruque, I. - Sean Humbert, J.
Journal: J Theor Biol

The purpose of this study is to determine computationally tractable models describing the lateral-directional motion of a Drosophila-like dipteran insect, which may then be used to estimate the requirements for flight control and stabilization. This study continues the work begun in Faruque and Humbert (2010) to extend the quasi-steady aerodynamics model via inclusion of perturbations from the hover state. The aerodynamics model is considered as forcing upon rigid body dynamics, and frequency-based system identification tools used to derive the models. The analysis indicates two stable real poles, and two very lightly damped and nearly unstable complex poles describing a decoupling of roll/sideslip oscillatory motion from a first order subsidence yaw behavior. The results are presented with uncertainty variation for both a smaller male and larger female phenotype.

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Modeling the physiological glucose-insulin dynamic system on diabetics.

Publication Date: 2010 Aug 7 PMID: 20466007
Authors: Chen, C. L. - Tsai, H. W. - Wong, S. S.
Journal: J Theor Biol

A novel mathematical model is presented to describe the dynamic behavior of plasma glucose and insulin on diabetic subjects. Though various models have been proposed to simulate the short-term (a variety of intravenous glucose or insulin injection) glucose-insulin dynamics, it is intended to construct a modified delay differential equations (DDEs) model based on the human glucose-insulin metabolic system. Five specific adjustable parameters inside the model are defined as the factors of the major physiological functions. Then several clinical data sets (56 subjects) which includes the information of food ingestion and exogenous insulin injection are verified and the model could practically reflect the dynamics and oscillation behavior on diabetic subjects by varying the adjustable parameters. Moreover, the corresponding parameters are fairly helpful to identify the patient's conditions of major physiological functions. This generic glucose-insulin dynamic model can be expected to develop such advanced therapy strategies for diabetics in the future.

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Modeling anti-tumor Th1 and Th2 immunity in the rejection of melanoma.

Publication Date: 2010 Aug 7 PMID: 20450922
Authors: Eftimie, R. - Bramson, J. L. - Earn, D. J.
Journal: J Theor Biol

Recent experiments indicate that CD4(+) Th2 cells can reject skin tumors in mice, while CD4(+) Th1 cells cannot (Mattes et al., 2003; Zhang et al., 2009). These results are surprising because CD4(+) Th1 cells are typically considered to be capable of tumor rejection. We used mathematical models to investigate this unexpected outcome. We found that neither CD4(+) Th1 nor CD4(+) Th2 cells could eliminate the cancer cells when acting alone, but that tumor elimination could be induced by recruitment of eosinophils by the Th2 cells. These recruited eosinophils had unexpected indirect effects on the decay rate of type 2 cytokines and the rate at which Th2 cells are inactivated through interactions with cancer cells. Strikingly, the presence of eosinophils impacted tumor growth more significantly than the release of tumor-suppressing cytokines such as IFN-gamma and TNF-alpha. Our simulations suggest that novel strategies to enhance eosinophil recruitment into skin tumors may improve cancer immunotherapies.

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A disequilibrium model for detecting genetic mutations for cancer.

Publication Date: 2010 Aug 7 PMID: 20450921
Authors: Li, Y. - Ma, C. - Wang, Z. - Chen, G. - Ahn, K. - Lazarus, P. - Wu, R.
Journal: J Theor Biol

It has been recognized that genetic mutations in specific nucleotides may give rise to cancer via the alteration of signaling pathways. Thus, the detection of those cancer-causing mutations has received considerable interest in cancer genetic research. Here, we propose a statistical model for characterizing genes that lead to cancer through point mutations using genome-wide single nucleotide polymorphism (SNP) data. The basic idea of the model is that mutated genes may be in high association with their nearby SNPs because of evolutionary forces. By genotyping SNPs in both normal and cancer cells, we formulate a polynomial likelihood to estimate the population genetic parameters related to cancer, such as allele frequencies of cancer-causing alleles, mutation rates of alleles derived from maternal or paternal parents, and zygotic linkage disequilibria between different loci after the mutation occurs. We implement the EM algorithm to estimate some of these parameters because of the missing information in the likelihood construction. The model allows the elegant tests of the significant associations between mutated cancer genes and genome-wide SNPs, thus providing a way for predicting the occurrence and formation of cancer with genetic information. The model, validated through computer simulation, may help cancer geneticists design efficient experiments and formulate hypotheses for cancer gene identification.

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Renormalization group approach to power-law modeling of complex metabolic networks.

Publication Date: 2010 Aug 7 PMID: 20447410
Authors: Hernandez-Bermejo, B.
Journal: J Theor Biol

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations.

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A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis.

Publication Date: 2010 Aug 7 PMID: 20447409
Authors: Goktepe, S. - Abilez, O. J. - Parker, K. K. - Kuhl, E.
Journal: J Theor Biol

We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In response to chronic volume-overload, an increased diastolic wall strain leads to the addition of sarcomeres in series, resulting in a relative increase in cardiomyocyte length, associated with eccentric hypertrophy and ventricular dilation. In response to chronic pressure-overload, an increased systolic wall stress leads to the addition of sacromeres in parallel, resulting in a relative increase in myocyte cross sectional area, associated with concentric hypertrophy and ventricular wall thickening. The continuum equations for both forms of maladaptive growth are discretized in space using a nonlinear finite element approach, and discretized in time using the implicit Euler backward scheme. We explore a generic bi-ventricular heart model in response to volume- and pressure-overload to demonstrate how local changes in cellular morphology translate into global alterations in cardiac form and function.

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Stochastic modelling of the eukaryotic heat shock response.

Publication Date: 2010 Aug 7 PMID: 20438739
Authors: Mizera, A. - Gambin, B.
Journal: J Theor Biol

The heat shock response (HSR) is a highly evolutionarily conserved defence mechanism allowing the cell to promptly react to elevated temperature conditions and other forms of stress. It has been subject to intense research for at least two main reasons. First, it is considered a promising candidate for deciphering the engineering principles underlying regulatory networks. Second, heat shock proteins (main actors of the HSR) play crucial role in many fundamental cellular processes. Therefore, profound understanding of the heat shock response would have far-reaching ramifications for the cell biology. Recently, a new deterministic model of the eukaryotic heat shock response has been proposed in the literature. It is very attractive since it consists of only the minimum number of components required by any functional regulatory network, while yet being capable of biological validation. However, it admits small molecule populations of some of the considered metabolites. In this paper a stochastic model corresponding to the deterministic one is constructed and the outcomes of these two models are confronted. The aim with this comparison is to show that, in the case of the heat shock response, the approximation of a discrete system with a continuous model is a reasonable approach. This is not always the truth, especially when the numbers of molecules of the considered species are small. By making the effort of performing and analysing 1000 stochastic simulations, we investigate the range of behaviour the stochastic model is likely to exhibit. We demonstrate that the obtained results agree well with the dynamics displayed by the continuous model, which strengthens the trust in the deterministic description. A proof of the existence and uniqueness of the stationary distribution of the Markov chain underlying the stochastic model is given. Moreover, the obtained view of the stochastic dynamics and the performed comparison to the outcome of the continuous formulation provide more insight into the dynamics of the heat shock response mechanism.

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Organising metabolic networks: Cycles in flux distributions.

Publication Date: 2010 Aug 7 PMID: 20435049
Authors: Kritz, M. V. - Trindade Dos Santos, M. - Urrutia, S. - Schwartz, J. M.
Journal: J Theor Biol

Metabolic networks are among the most widely studied biological systems. The topology and interconnections of metabolic reactions have been well described for many species. This is, however, not sufficient to understand how their activity is regulated in living organisms. These descriptions depict a static set of possible chains of reactions, with no information about the dynamic activity of reaction fluxes. Cyclic structures are thought to play a central role in the homeostasis of biological systems and in their resilience to a changing environment. In this work, we present a methodology to help investigating dynamic fluxes associated to biochemical reactions in metabolic networks. We introduce an algorithm for partitioning fluxes between cyclic and acyclic sub-networks, adapted from an algorithm initially developed to study fluxes in trophic networks. Using this algorithm, we analyse three metabolic systems: the central metabolism of wild type and a deletion mutant of Escherichia coli, erythrocyte metabolism and the central metabolism of the bacterium Methylobacterium extorquens. This methodology unveils the role of cycles in driving and maintaining metabolic fluxes under perturbations in these examples, and may be used to further investigate and understand the organisational invariance of biological systems.

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Bifurcations and chaos in the MAPK signaling cascade.

Publication Date: 2010 Aug 7 PMID: 20435047
Authors: Zumsande, M. - Gross, T.
Journal: J Theor Biol

The mitogen-activated protein kinase (MAPK) cascade is an important signaling cascade in eukaryotes. We use the approach of generalized modeling to analyze the dynamics of the MAPK cascade and identify key mechanisms of instability. Furthermore, we report sustained multi-mode oscillations and potentially chaotic behavior caused by a sequestration-based feedback mechanism. Finally, we investigate the interplay between sequestration and external feedback loops. Our analysis thereby confirms, extends and generalizes previous results obtained by conventional modeling and points out the diversity of dynamics that sequestration can bring about.

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Asymmetrical over-infection as a process of plant virus emergence.

Publication Date: 2010 Aug 7 PMID: 20435046
Authors: Fabre, F. - Chadoeuf, J. - Costa, C. - Lecoq, H. - Desbiez, C.
Journal: J Theor Biol

Disentangling the role of epidemiological factors in plant pathogen emergences is a prerequisite to identify the most likely future invaders. An example of emergence was recently observed in France: in 10 years, "classic" (CL) strains of Watermelon mosaic virus (WMV) were displaced at a regional scale by newly introduced "emerging" (EM) strains. Here we analyse a 3 years dataset describing the co-dynamics of CL and EM strains at field scale using state-space models estimating jointly: (i) probabilities of primary and secondary infection and (ii) probabilities of over-infecting with a CL [EM] strain a plant already infected with an EM [CL] strain. Results especially indicate that it is more than 3 times less probable for a CL strain to over-infect an EM infected plant than for an EM strain to over-infect a CL infected plant. To investigate if these asymmetric interactions can explain the CL/EM shift observed at regional scale, an exploratory model describing WMV epidemiology over several years in a landscape composed of a reservoir and a cultivated compartment is introduced. In most simulations a shift is observed and both strains do coexist in the landscape, reaching an equilibrium that depends on the probabilities of over-infection.

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Modeling continuous cultures of microalgae colimited by nitrogen and phosphorus.

Publication Date: 2010 Aug 7 PMID: 20433853
Authors: Bougaran, G. - Bernard, O. - Sciandra, A.
Journal: J Theor Biol

It is well documented that the combination of low nitrogen and phosphorus resources can lead to situations where colimitation of phytoplankton growth arises, yet the underlying mechanisms are not fully understood. Here, we propose a Droop-based model built on the idea that colimitation by nitrogen and phosphorus arises from the uptake of nitrogen. Indeed, since N-porters are active systems, they require energy that could be related to the phosphorus status of the cell. Therefore, we assumed that N uptake is enhanced by the P quota. Our model also accounts for the biological observations that uptake of a nutrient can be down-regulated by its own internal quota, and succeeds in describing the strong contrast for the non-limiting quotas under N-limited and P-limited conditions that was observed on continuous cultures with Selenastrum minutum and with Isochrysis affinis galbana. Our analysis suggests that, regarding the colimitation concept, N and P would be better considered as biochemically dependent rather than biochemically independent nutrients.

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The influence of viral infection on a plankton ecosystem undergoing nutrient enrichment.

Publication Date: 2010 Aug 7 PMID: 20433852
Authors: Rhodes, C. J. - Martin, A. P.
Journal: J Theor Biol

It is increasingly recognised that viruses are a significant active component of oceanic plankton ecosystems. They play an important role in biogeochemical cycles as well as being implicated in observed patterns of species abundance and diversity. The influence of viral infection in plankton ecosystems is not fully understood. Here we use a number of well-founded mathematical models to investigate the interplay of the ecological and epidemiological interactions of plankton and viruses in the sea. Of particular interest is the role of nutrient on the population dynamics. Nutrient forcing has been suggested as a means of absorbing excess anthropogenic atmospheric carbon dioxide by stimulating increased phytoplankton primary productivity. Here we show that enriching nutrient levels in the sea may decrease the amount of infected phytoplankton species thereby additionally enhancing the efficiency of the biological pump, a means by which carbon is transferred from the atmosphere to the deep ocean.

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