Journal of theoretical Biology

Egalitarian motive in punishing defectors.

Publication Date: 2010 Mar 4 PMID: 20211635
Authors: Scheuring, I.
Journal: J Theor Biol

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Statistical methods for estimating complexity from competition experiments between two populations.

Publication Date: 2010 Mar 4 PMID: 20211634
Authors: Montgomery-Smith, S. J. - Schmidt, F. J.
Journal: J Theor Biol

Often a screening or selection experiment targets a cell or tissue, which presents many possible molecular targets and identifies a correspondingly large number of ligands. We describe a statistical method to extract an estimate of the complexity or richness of the set of molecular targets from competition experiments between distinguishable ligands, including aptamers derived from combinatorial experiments (SELEX or phage display). In simulations, the nonparametric statistic provides a robust estimate of complexity from a 100x100 matrix of competition experiments, which is clearly feasible in high-throughput format. The statistic and method are potentially applicable to other ligand binding situations.

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The role played by exons in genomic DNA sequence correlations.

Publication Date: 2010 Mar 4 PMID: 20211633
Authors: Carlos de Oliveira Guerra, J. - Licinio, P.
Journal: J Theor Biol

The codon structure inside exons imposes a strong modulation with period-3 for genomic composition correlations. A new formalism for calculating nucleotide correlations along DNA sequences in terms of an irreducible set of six correlation functions is presented. New procedures to extract the corresponding period-3 modulations are also developed. These modulations are seen to be stronger for the irreducible self-correlation C(xx)(k), which accounts only for the binding strength of dinucleotides (z stands for adenine or thymine minus cytosine or guanine concentrations). We investigate and model the relationship between exon distribution and genomic period-3 correlations for the D. melanogaster genome.

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On a phenomenological model for fatigue effects in skeletal muscles.

Publication Date: 2010 Mar 4 PMID: 20211632
Authors: Bol, M.
Journal: J Theor Biol

This work deals with the development and implementation of a new fatigue model for simulating fatigue effects in skeletal muscles. Basic idea of this modelling strategy is an approach that divides the fibres of a muscle into three groups: fibres in the active state, those that are already fatigued and fibres in the resting state. All fibres are able to switch between the different groups by defining adequate rates. In this way a continuous transfer of fibres between those three states has been described. Rooted on an incompressible, hyperelastic constitutive law with transversely isotropic characteristics the fatigue model has been implemented in the framework of the finite element method. Numerical examples are given in order to illustrate the ability of this model. Further, we validate the model by fatigue experiments of the rat soleus muscle. In doing so, it proves that the model is able to predict physiological observations and mechanical test results.

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An enzymatic model of the growth hormone-releasing hormone oscillator incorporating neuronal synchronization.

Publication Date: 2010 Mar 4 PMID: 20211631
Authors: Roy Caplan, S. - Tannenbaum, G. S. - Johnstone, R. M.
Journal: J Theor Biol

Models of growth hormone (GH) rhythmogenesis which we and others have presented suggest that the GH pulses in the circulation are generated by a GH-releasing hormone (GHRH) oscillator with a 1 hour periodicity. Here we examine the possibility that this is an intrinsic neuronal rhythm resulting from enzymatic reactions occurring in the axon terminals. A "Baselator" feedback reaction sequence can generate an hourly chemical burst of a primer (presumably a low molecular weight peptide) regulating Ca(2+)-triggered exocytosis of GHRH-loaded vesicles. Accordingly we propose that the priming species is largely immobilized by binding within the terminals. Free unbound primer is able to diffuse and is alternately phosphorylated and dephosphorylated by a kinase and a phosphatase (or undergoes a similar pair of complementary reactions). Under appropriate conditions involving feedback control of one or other of the enzymes the levels of both unreacted and reacted free primer peak sharply at hourly intervals. It is self-evident that synchronization between the packed terminals of the GHRH neurons at the median eminence is necessary to generate highly ordered in vivo pulses of GH release. Gap junctions provide a means of interterminal communication for the primer. Simulations of clusters of 4 adjacent axon terminals in a linear array were performed to assess whether and when synchrony can occur. With gap junctions closed the axons were set to be 90 degrees out of phase, i.e. their chemical bursts were separated by 15 minutes. Opening the gap junctions, assuming either that only the unphosphorylated species permeates, or that both species permeate, resulted in rapid overall synchronization. The oscillatory systems undergo mutual entrainment and all peaks appeared simultaneously at an intermediate hourly interval. This result was independent of the mode of chemical feedback, whether positive or negative. Closing the gap junctions led to a gradual, but not immediate, loss of synchrony.

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A general multi-strain model with environmental transmission: Invasion conditions for the disease-free and endemic states.

Publication Date: 2010 Mar 4 PMID: 20211630
Authors: Breban, R. - Drake, J. M. - Rohani, P.
Journal: J Theor Biol

Although many infectious diseases of humans and wildlife are transmitted via an environmental reservoir, the theory of environmental transmission remains poorly elaborated. Here we introduce an SIR-type multi-strain disease transmission model with perfect cross immunity where environmental transmission is broadly defined by three axioms. We establish the conditions under which a multi-strain endemic state is invaded by another strain which is both directly and environmentally transmitted. EWe discuss explicit forms for environmental transmission terms and apply our newly derived invasion conditions to a two-strain system. Then, we consider the case of two strains with matching basic reproduction numbers (i.e., R(0)), one directly transmitted only and the other both directly and environmentally transmitted, invading each other's endemic state. EWe find that the strain which is Eonly directly transmitted can invade the endemic state of the strain with mixed transmission. However, the endemic state of the first strain is neutrally stable to invasion by the second strain. EThus, our results suggest that environmental transmission makes the endemic state less resistant to invasion.

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Modelling the unpredictability of future biodiversity in ecological networks.

Publication Date: 2010 Mar 4 PMID: 20211629
Authors: Ingram, T. - Steel, M.
Journal: J Theor Biol

We consider the question of how accurately we can hope to predict future biodiversity in a world in which many interacting species are at risk of extinction. Simple models assuming that species' extinctions occur independently are easily analysed, but do not account for the fact that many species depend on or otherwise interact with each other. In this paper we evaluate the effect of explicitly incorporating ecological dependencies on the predictive ability of models of extinction. In particular, we compare a model in which species' extinction rates increase because of the extinction of their prey to a model in which the same average rate increase takes place, but in which extinctions occur independently from species to species. One might expect that including this ecological information would make the prediction of future biodiversity more accurate, but instead we find that accounting for food web dependencies reveals greater uncertainty. The expected loss of biodiversity over time is similar between the two models, but the variance in future biodiversity is considerably higher in the model that includes species interactions. This increased uncertainty is because of the non-independence of species - the tendency of two species to respond similarly to the loss of a species on which both depend. We use simulations to show that this increase in variance is robust to many variations of the model, and that its magnitude should be largest in food webs that are highly dependent on a few basal species. Our results should hold whenever ecological dependencies cause most species' extinction risks to covary positively, and illustrate how more information does not necessarily improve our ability to predict future biodiversity loss.

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Swarming in homogeneous environments: A social interaction based framework.

Publication Date: 2010 Mar 5 PMID: 20211189
Authors: Li, X. - Xiao, J.
Journal: J Theor Biol

A great variety of biological groups form a self-organized swarming motion at some point during their life spans, which has two prominent collective features: common velocity and constant spacings among members. In this paper, we present a general individual-based motion framework to explain such collective motion of swarms in homogeneous environments. The motion framework utilizes the concept of social interactions that has been widely accepted throughout the literature. We assume that during the motion of the swarm, each member senses and interacts with its neighbors via virtual Attraction/Alignment/Repulsion (A/A/R) forces, while perceiving and following the gradient force of the environment. During the swarm's motion, the neighborhood and the interaction relations among members may dynamically change. To explicitly consider the effect of such dynamic change on the emergence of swarm's collective behavior, we use an algebraic graph to model the topology of the interaction and the neighborhood relations of the group. By using mathematical tools of nonsmooth analysis theory and Lyapunov stability theory, we analytically prove that if the A/A/R forces have limited ranges, and the attraction/repulsion forces are balanced at a certain range, the proposed framework leads to a parallel type of collective motion of the swarm. We mathematically show that the velocities of all swarm members asymptotically converge to a common value and the spacings among neighbors remain unchanging. In addition to the mathematical analysis, a few sets of simulation results are included to demonstrate the presented framework. The contributions of this paper are twofold: First, unlike most works in the literature that mainly use computer simulations to study the swarming phenomena, this paper provides an analytical methodology to investigate how the collective group behavior is self-organized by individual motions. Second, the presented motion framework works over a general range of A/A/R interactions. In other words, we analytically prove that the commonly used A/A/R model can lead to a collective motion of the swarm. In addition, we show that the alternative model in the literature that uses only attraction/repulsion(A/R) interactions is in fact a special case of the A/A/R model.

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Towards multi-scale modeling of muscle fibers with sarcomere non-uniformities.

Publication Date: 2010 Mar 6 PMID: 20206638
Authors: Givli, S.
Journal: J Theor Biol

A theoretical framework for studying the collective behavior of a large ensemble of half sarcomeres in a myofibril is presented. The approach is based on transforming the large system of discrete elements (half-sarcomeres) into a continuum for which macro-behavior is dictated by micro-properties. Specifically, we consider statistical properties of the ensemble rather than solving for each degree of freedom. This enables a reasonable computational effort and provides important insights. We demonstrate that such a multi-scale approach is indispensable for studying quantitatively the role of sarcomere non-uniformities in muscle mechanics. Specifically, we illustrate that adopting a model with a non-physiological number of sarcomeres can lead to a non-realistic behavior and therefore to erroneous interpretation. Further, we demonstrate that the new modeling approach provides a suitable platform for addressing controversial phenomena, such as residual enhanced tension, creep, length redistribution, and damage due to eccentric contraction.

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Quantification of the effects of vasomotion on mass transport to tissue from axisymmetric blood vessels.

Publication Date: 2010 Mar 3 PMID: 20206637
Authors: Hapuarachchi, T. - Park, C. S. - Payne, S.
Journal: J Theor Biol

The process known as vasomotion, rhythmic oscillations in vessel diameter, has been proposed to act as a protective mechanism for tissue under conditions of reduced perfusion, since it is frequently only observed experimentally when perfusion levels are reduced. This could be due to a resultant increase in oxygen transport from the vasculature to the surrounding tissue, either directly or indirectly. It is thus potentially of significant clinical interest as a warning signal for ischemia. However, there has been little analysis performed to quantify the effects of vessel wall movement on time-averaged mass transport. We thus present a detailed analysis of such mass transport for an axisymmetric vessel with a periodically oscillating wall, by solving the non-linear mass transport equation, and quantify the differences between the time-averaged mass transport under conditions of no oscillation (i.e. the steady-state) and varying wall oscillation amplitude. The results show that if the vessel wall alone is oscillated, with an invariant wall concentration, the time-averaged mass transport is reduced relative to the steady-state, but if the vessel wall concentration is also oscillated, then mass transport is increased, although this is generally only true when these oscillate in phase with each other. The influence of Peclet number and the non-dimensional rate of consumption of oxygen in tissue, as well as the amplitude of oscillations, are fully characterised. We conclude by considering the likely implications of these results in the context of oxygen transport to tissue.

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Sperm competition games: Sperm size (mass) and number under raffle and displacement, and the evolution of P(2).

Publication Date: 2010 Mar 2 PMID: 20206187
Authors: Parker, G. A. - Immler, S. - Pitnick, S. - Birkhead, T. R.
Journal: J Theor Biol

We examine models for evolution of sperm size (i.e. mass m) and number (s) under three mechanisms of sperm competition at low 'risk' levels: (i) raffle with no constraint on space available for competing sperm, (ii) direct displacement mainly by seminal fluid, and (iii) direct displacement mainly by sperm mass. Increasing sperm mass increases a sperm's 'competitive weight' against rival sperm through a diminishing returns function, r(m). ESS total ejaculate expenditure (the product m(*)s(*)) increases in all three models with sperm competition risk, q. If r(m), or ratio r'(m)/r(m), is independent of ESS sperm numbers, ESS sperm mass remains constant, and the sperm mass/number ratio (m(*)/s(*)) therefore decreases with risk. Dependency of sperm mass on risk can arise if r(m) depends on competing sperm density (sperm number / space available for sperm competition). Such dependencies generate complex relationships between sperm mass and number with risk, depending both on the mechanism and how sperm density affects r(m). While numbers always increase with risk, mass can either increase or decrease, but m(*)/s(*) typically decreases with risk unless sperm density strongly influences r(m). Where there is no extrinsic loading due to mating order, ESS paternity of the second (i.e. last) male to mate (P(2)) under displacement always exceeds 0.5, and increases with risk (in the raffle P(2) = 0.5). Caution is needed when seeking evidence for a sperm size-number trade-off. Although size and number trade-off independently against effort spent on acquiring matings, their product, m(*)s(*), is invariant or fixed at a given risk level, effectively generating a size-number trade-off. However, unless controlled for the effects of risk, the relation between m(*) and s(*) can be either positive or negative (a positive relation is usually taken as evidence against a size-number trade-off).

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Helix-helix interactions and their impact on protein motifs and assemblies.

Publication Date: 2010 Mar 2 PMID: 20202472
Authors: Kurochkina, N.
Journal: J Theor Biol

Protein secondary structure elements are arranged in distinct structural motifs such as four-alpha-helix bundle, 8alpha/8beta TIM-barrel, Rossmann dinucleotide binding fold, assembly of a helical rod. Each structural motif is characterized by a particular type of helix-helix interactions. A unique pattern of contacts is formed by interacting helices of the structural motif. In each type of fold, edges of the helix surface, which participate in the formation of helix-helix contacts with preceding and following helices, differ. This work shows that circular arrangements of the four, eight, and sixteen alpha-helices, which are found in the four-alpha-helical motif, TIM-barrel 8alpha/8beta fold, and helical rod of 16.3 helices per turn correspondingly, can be associated with the mutual positioning of the edges of the helix surfaces. Edges (i, i+1)-(i+1, i+2) of the helix surface are central for the interhelical contacts in a four-alpha-helix bundle. Edges (i, i+1)-(i+2, i+3) are involved in the assembly of four-alpha-helix subunits into helical rod of a tobacco mosaic virus and a three-helix fragment of a Rossmann fold. In 8alpha/8beta TIM-barrel fold, edges (i, i+1)-(i+5, i+6) are involved in the octagon arrangement. Approximation of a cross section of each motif with a polygon (n-gon, n=4, 8, 16) shows that a good correlation exists between polygon interior angles and angles formed by the edges of helix surfaces.

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New syntax to describe local continuous structure-sequence information for recognizing new pre-miRNAs.

Publication Date: 2010 Mar 2 PMID: 20202471
Authors: Wang, M. - Song, X. - Han, P. - Li, W. - Jiang, B.
Journal: J Theor Biol

As an important complement to experimental identification of pre-miRNA, computational prediction methods are attracting more and more attention. Features extracted from pre-miRNA are the key to computational prediction. Among the features, local continuous structure-sequence information is usually employed by existing computational methods. As more and more species-specific miRNAs have been identified, a new syntax is required to describe pre-miRNA local continuous structure-sequence features. Therefore, we proposed here the use of couplet syntax to describe pre-miRNA intrinsic features. When tested on a dataset from miRBase12.0 with the use of features extracted by couplet syntax, the SVM classifier achieves a sensitivity of 81.98% and specificity of 87.16% on a human test set and a sensitivity of 86.71% on all other species. The obtained results indicate that the proposed couplet syntax can describe the intrinsic features of pre-miRNA better than traditional methods. By means of describing pre-miRNA secondary structure more precisely and masking frequently mutated nucleotides, couplet syntax provides a powerful feature-describing method that can be applied to many computational prediction methods.

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Cellular signaling identifiability analysis: A case study.

Publication Date: 2010 Feb 24 PMID: 20188743
Authors: Roper, R. T. - Pia Saccomani, M. - Vicini, P.
Journal: J Theor Biol

Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling-the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology.

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Target size and optimal life history when individual growth and energy budget are stochastic.

Publication Date: 2010 Feb 23 PMID: 20184902
Authors: Filin, I.
Journal: J Theor Biol

I extend my previous work on life history optimization when body mass is divided into reserves and structure components. Two important innovations are: (1) effect of finite target size on optimal structural growth; (2) incorporating reproduction in the optimization objective. I derive optimal growth trajectories and life histories, given that the individual is subject to both starvation mortality and exogenous hazards (e.g., predation). Because of overhead costs in building structural mass, it is optimal to stop structural growth close to the target size, and to proceed only by accumulating reserves. Higher overhead costs cause earlier cessation of structural growth and smaller final structures. Semelparous reproduction also promotes early cessation of structural growth, compared to when only survival to target size is maximized. In contrast, iteroparous reproduction can prolong structural growth, resulting in larger final structures than in either the survival or the semelparous scenarios. Increasing the noise in individual growth lowers final structural mass at small target sizes, but the effect is reversed for large target sizes. My results provide predictions for comparative studies. I outline important consequences of my results to additional important evolutionary questions: evolution of sexual dimorphism, optimization of clutch size and evolution of progeny and adult sizes.

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Endemic disease, awareness, and local behavioural response.

Publication Date: 2010 Feb 23 PMID: 20184901
Authors: Funk, S. - Gilad, E. - Jansen, V. A.
Journal: J Theor Biol

The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.

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Phospholipid demixing and the birth of a lipid droplet.

Publication Date: 2010 Feb 23 PMID: 20184900
Authors: Zanghellini, J. - Wodlei, F. - von Grunberg, H. H.
Journal: J Theor Biol

The biogenesis of lipid droplets (LD) in the yeast Saccharomyces cerevisiae was theoretically investigated on basis of a biophysical model. In accordance with the prevailing model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LD that bud-off when a critical size is reached. Mathematically, LD were modeled as spherical protuberances in an otherwise planar ER membrane. We estimated the local phospholipid composition, and calculated the change in elastic free energy of the membrane caused by nascent LD. Based on this model calculation, we found a gradual demixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. During demixing, the phospholipid monolayer was able to gain energy during LD growth, which suggested that the formation of curved interfaces was supported by or even driven by lipid demixing. In addition, we show that demixing is thermodynamically necessary as LD cannot bud-off otherwise. In the case of Saccharomyces cerevisiae our model predicts a LD bud-off diameter of about 12nm. This diameter is far below the experimentally determined size of typical yeast LD. Thus, we concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. Small LD are produced from the ER, which subsequently ripe within the cytosol through a series of fusions.

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Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach.

Publication Date: 2010 Feb 21 PMID: 20178805
Authors: Raghib, M. - Levin, S. A. - Kevrekidis, I. G.
Journal: J Theor Biol

We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of 'naive' and 'informed' individuals. The method is based on projecting the particle configuration onto a single 'meta-particle' that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model.

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Quantitative physiologically based modeling of subjective fatigue during sleep deprivation.

Publication Date: 2010 Feb 19 PMID: 20176034
Authors: Fulcher, B. D. - Phillips, A. J. - Robinson, P. A.
Journal: J Theor Biol

A quantitative physiologically based model of the sleep-wake switch is used to predict variations in subjective fatigue-related measures during total sleep deprivation. The model includes the mutual inhibition of the sleep-active neurons in the hypothalamic ventrolateral preoptic area (VLPO) and the wake-active monoaminergic brainstem populations (MA), as well as circadian and homeostatic drives. We simulate sleep deprivation by introducing a drive to the MA, which we call wake effort, to maintain the system in a wakeful state. Physiologically this drive is proposed to be afferent from the cortex or the orexin group of the lateral hypothalamus. It is hypothesized that the need to exert this effort to maintain wakefulness at high homeostatic sleep pressure correlates with subjective fatigue levels. The model's output indeed exhibits good agreement with existing clinical time series of subjective fatigue-related measures, supporting this hypothesis. Subjective fatigue, adrenaline, and body temperature variations during two 72h sleep deprivation protocols are reproduced by the model. By distinguishing a motivation-dependent orexinergic contribution to the wake-effort drive, the model can be extended to interpret variation in performance levels during sleep deprivation in a way that is qualitatively consistent with existing, clinically derived results. The example of sleep deprivation thus demonstrates the ability of physiologically based sleep modeling to predict psychological measures from the underlying physiological interactions that produce them.

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A mathematical modelling framework for elucidating the role of feedback control in translation termination.

Publication Date: 2010 Feb 20 PMID: 20176033
Authors: de Silva, E. - Krishnan, J. - Betney, R. - Stansfield, I.
Journal: J Theor Biol

Translation is the final stage of gene expression where messenger RNA is used as a template for protein polymerization from appropriate amino acids. Release of the completed protein requires a release factor protein acting at the termination/stop codon to liberate it. In this paper we focus on a complex feedback control mechanism involved in the translation and synthesis of release factor proteins, which has been observed in different systems. These release factor proteins are involved in the termination stage of their own translation. Further, mutations in the release factor gene can result in a premature stop codon. In this case translation can result either in early termination and the production of a truncated protein or readthrough of the premature stop codon and production of the complete release factor protein. Thus during translation of the release factor mRNA containing a premature stop codon, the full length protein negatively regulates its production by its action on a premature stop codon, while positively regulating its production by its action on the regular stop codon. This paper develops a mathematical modelling framework to investigate this complex feedback control system involved in translation. A series of models is established to carefully investigate the role of individual mechanisms and how they work together. The steady state and dynamic behaviour of the resulting models are examined both analytically and numerically.

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Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer.

Publication Date: 2010 Feb 20 PMID: 20176032
Authors: Hirata, Y. - Bruchovsky, N. - Aihara, K.
Journal: J Theor Biol

We propose a mathematical model that quantitatively reproduces the dynamics of the serum prostate-specific antigen (PSA) level under intermittent androgen suppression (IAS) for prostate cancer. Taking into account the biological knowledge that there are reversible and irreversible changes in a malignant cell, we constructed a piecewise-linear dynamical model where the testosterone dynamics are modelled with rapid shifts between two levels, namely the normal and castrate concentrations of the male hormone. The validity of the model was supported by patient data obtained from a clinical trial of IAS. It accurately reproduced the kinetics of the therapeutic reduction of PSA and predicted the future nadir level correctly. The coexistence of reversible and irreversible changes within the malignant cell provided the best explanation of early progression to androgen independence. Finally, since the model identified patients for whom IAS was effective, it potentially offers a novel approach to individualized therapy requiring the input of time sequence values of PSA only.

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A cell kinetics model for prostate cancer and its application to clinical data and individual patients.

Publication Date: 2010 Feb 20 PMID: 20176031
Authors: Dimonte, G.
Journal: J Theor Biol

A cell kinetics model is developed to describe the evolution of prostate cancer (PC) from diagnosis to PC specific death. Such a model can be used to estimate an individual's eventual outcome and thus to inform decisions about therapy. To describe the observed clinical progression, the model must postulate three PC cell populations that are (1) local to the prostate and sensitive to hormones, (2) regional and hormone sensitive, and (3) systemic and hormone resistant. A set of coupled first-order differential equations describes the exponential growth of a PC tumor as well as its transformation from a local to systemic disease. The time dependence of the solutions is scaled to the doubling time of the prostate specific antigen (PSADT) because it characterizes the tumor growth for the individual. The conversion from local to systemic cell populations is described with a parameter alpha that can be associated with the Gleason score. The model also has three critical cell populations that describe (1) the initiation of the non-local populations, (2) the saturation level of the local tumor, and (3) the cell count likely to cause PC specific death. These parameters are calibrated by reproducing published PC clinical data and survival tables. The model is then applied to individuals with complete PC diagnostic data in order to calculate the progression to PC specific death. One man has early stage PC as described in the 'vignette' patient of Walsh et al. (2007. N. Engl. J. Med. 357, 2696-2705). The second man has a more serious condition and has undergone both local and systemic treatments. Unfortunately, I am that patient.

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The effect of correlations on the population dynamics of lymphocytes.

Publication Date: 2010 Feb 19 PMID: 20171973
Authors: Wellard, C. - Markham, J. - Hawkins, E. D. - Hodgkin, P. D.
Journal: J Theor Biol

Recent studies of the population dynamics of a system of lymphocytes in an in vitro immune response have reported strong correlations in cell division times, both between parents and their progeny, and between those of sibling cells. The data also show a high level of correlation in the ultimate number of divisions achieved by cells within the same clone. Such correlations are often ignored in mathematical models of cell dynamics as they violate a standard assumption in the theory of branching processes, that of the statistical independence of cells. In this article we present a model in which these correlations can be incorporated, and have used this model to study the effect of these correlations on the population dynamics of a system of cells. We found that correlation in the division times between parents and their progeny can alter the mean population size of clones within the system, while all of the correlations can affect the variance in the sizes of different clones. The model was then applied to experimental data obtained from time-lapse video microscopy of a system of CpG stimulated B lymphocytes and it was found that inclusion of the correct correlation structure is necessary to accurately reproduce the observed population dynamics. We conclude that correlations in the dynamics of cells within an ensemble will affect the population dynamics of the system, and the effects will become more pronounced as the number of divisions increases.

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Effects of life history variation on vertical transfer of toxicants in marine mammals.

Publication Date: 2010 Feb 18 PMID: 20171232
Authors: Noonburg, E. G. - Nisbet, R. M. - Klanjscek, T.
Journal: J Theor Biol

Toxicant bioaccumulation poses a risk to many marine mammal populations. Although individual-level toxicology has been the subject of considerable research in several species, we lack a theoretical framework to generalize the results across environments and life histories. Here we formulate a dynamic energy budget model to predict the effects of intra- and interspecific life history variation on toxicant dynamics in marine mammals. Dynamic energy budget theory attempts to describe the most general processes of energy acquisition and utilization in heterotrophs. We tailor the basic model to represent the marine mammal reproductive cycle, and we add a model of toxicant uptake and partitioning to describe vertical transfer of toxicants from mother to offspring during gestation and lactation. We first show that the model predictions are consistent with qualitative patterns reported in empirical studies and previous species-specific modeling studies. Next, we use this model to examine the dependence of offspring toxicant load on birth order, food density, and interspecific life history variation.

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Optimal cytoplasmatic density and flux balance model under macromolecular crowding effects.

Publication Date: 2010 Feb 18 PMID: 20171231
Authors: Vazquez, A.
Journal: J Theor Biol

Macromolecules occupy between 34% and 44% of the cell cytoplasm, about half the maximum packing density of spheres in three dimension. Yet, there is no clear understanding of what is special about this value. To address this fundamental question we investigate the effect of macromolecular crowding on cell metabolism. We develop a cell scale flux balance model capturing the main features of cell metabolism at different nutrient uptakes and macromolecular densities. Using this model we show there are two metabolic regimes at low and high nutrient uptakes. The latter regime is characterized by an optimal cytoplasmatic density where the increase of reaction rates by confinement and the decrease by diffusion slow-down balance. More important, the predicted optimal density is in the range of the experimentally determined density of Escherichia coli.

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Reverse-engineering of biochemical reaction networks from spatio-temporal correlations of fluorescence fluctuations.

Publication Date: 2010 Feb 18 PMID: 20171230
Authors: Tanaka, N. - Papoian, G. A.
Journal: J Theor Biol

Recent developments of fluorescence labeling and highly advanced microscopy techniques have enabled observations of activities of biosignaling molecules in living cells. The high spatial and temporal resolutions of these video microscopy experiments allow detection of fluorescence fluctuations at the timescales approaching those of enzymatic reactions. Such fluorescence fluctuation patterns may contain information about the complex reaction-diffusion system driving the dynamics of the labeled molecule. Here, we have developed a method of identifying the reaction-diffusion system of fluorescently labeled signaling molecules in the cell, by combining spatio-temporal correlation function analysis of fluctuating fluorescent patterns, stochastic reaction-diffusion simulations, and an iterative system identification technique using a simulated annealing algorithm. In this report, we discuss the validity and usability of spatio-temporal correlation functions in characterizing the reaction-diffusion dynamics of biomolecules, and demonstrate application of our reaction-diffusion system identification method to a simple conceptual model for small GTPase activation.

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A kinematic model coupling stress fiber dynamics with JNK activation in response to matrix stretching.

Publication Date: 2010 Feb 18 PMID: 20171229
Authors: Kaunas, R. - Huang, Z. - Hahn, J.
Journal: J Theor Biol

The role of the actin cytoskeleton in regulating mechanotransduction in response to external forces is complex and incompletely understood. Here, we develop a mathematical model coupling the dynamic disassembly and reassembly of actin stress fibers and associated focal adhesions to the activation of c-jun N-terminal kinase (JNK) in cells attached to deformable matrices. The model is based on the assumptions that stress fibers are pre-extended to a preferred level under static conditions and that perturbations from this preferred level destabilize the stress fibers. The subsequent reassembly of fibers upregulates the rate of JNK activation as a result of the formation of new integrin bonds within the associated focal adhesions. Numerical solutions of the model equations predict that different patterns of matrix stretch result in distinct temporal patterns in JNK activation that compare well with published experimental results. In the case of cyclic uniaxial stretching, stretch-induced JNK activation slowly subsides as stress fibers gradually reorient perpendicular to the stretch direction. In contrast, JNK activation is chronically elevated in response to cyclic equibiaxial stretch. A step change in either uniaxial or equibiaxial stretch results in a short, transient upregulation in JNK that quickly returns to the basal level as overly stretched stress fibers disassemble and are replaced by fibers assembled at the preferred level of stretch. In summary, the model describes a mechanism by which the dynamic properties of the actin cytoskeleton allow cells to adapt to applied forces through turnover and reorganization to modulate intracellular signaling.

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A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference.

Publication Date: 2010 Feb 17 PMID: 20170665
Authors: Ogunnaike, B. A. - Gelmi, C. A. - Edwards, J. S.
Journal: J Theor Biol

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.

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Dipteran insect flight dynamics. Part 1 Longitudinal motion about hover.

Publication Date: 2010 Feb 17 PMID: 20170664
Authors: Faruque, I. - Sean Humbert, J.
Journal: J Theor Biol

This paper presents a reduced-order model of longitudinal hovering flight dynamics for dipteran insects. The quasi-steady wing aerodynamics model is extended by including perturbation states from equilibrium and paired with rigid body equations of motion to create a nonlinear simulation of a Drosophila-like insect. Frequency-based system identification tools are used to identify the transfer functions from biologically inspired control inputs to rigid body states. Stability derivatives and a state space linear system describing the dynamics are also identified. The vehicle control requirements are quantified with respect to traditional human pilot handling qualities specification. The heave dynamics are found to be decoupled from the pitch/fore/aft dynamics. The haltere-on system revealed a stabilized system with a slow (heave) and fast subsidence mode, and a stable oscillatory mode. The haltere-off (bare airframe) system revealed a slow (heave) and fast subsidence mode and an unstable oscillatory mode, a modal structure in agreement with CFD studies. The analysis indicates that passive aerodynamic mechanisms contribute to stability, which may help explain how insects are able to achieve stable locomotion on a very small computational budget.

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A computational model of cerebral cortex folding.

Publication Date: 2010 Feb 15 PMID: 20167224
Authors: Nie, J. - Guo, L. - Li, G. - Faraco, C. - Stephen Miller, L. - Liu, T.
Journal: J Theor Biol

The geometric complexity and variability of the human cerebral cortex have long intrigued the scientific community. As a result, quantitative description of cortical folding patterns and the understanding of underlying folding mechanisms have emerged as important research goals. This paper presents a computational 3D geometric model of cerebral cortex folding initialized by MRI data of a human fetal brain and deformed under the governance of a partial differential equation modeling cortical growth. By applying different simulation parameters, our model is able to generate folding convolutions and shape dynamics of the cerebral cortex. The simulations of this 3D geometric model provide computational experimental support to the following hypotheses: (1) Mechanical constraints of the skull regulate the cortical folding process. (2) The cortical folding pattern is dependent on the global cell growth rate of the whole cortex. (3) The cortical folding pattern is dependent on relative rates of cell growth in different cortical areas. (4) The cortical folding pattern is dependent on the initial geometry of the cortex.

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Evolutionary game theory meets social science: Is there a unifying rule for human cooperation?

Publication Date: 2010 Feb 16 PMID: 20167223
Authors: Rosas, A.
Journal: J Theor Biol

Evolutionary game theory has shown that human cooperation thrives in different types of social interactions with a PD structure. Models treat the cooperative strategies within the different frameworks as discrete entities and sometimes even as contenders. Whereas strong reciprocity was acclaimed as superior to classic reciprocity for its ability to defeat defectors in public goods games, recent experiments and simulations show that costly punishment fails to promote cooperation in the IR and DR games, where classic reciprocity succeeds. My aim is to show that cooperative strategies across frameworks are capable of a unified treatment, for they are governed by a common underlying rule or norm. An analysis of the reputation and action rules that govern some representative cooperative strategies both in models and in economic experiments confirms that the different frameworks share a conditional action rule and several reputation rules. The common conditional rule contains an option between costly punishment and withholding benefits that provides alternative enforcement methods against defectors. Depending on the framework, individuals can switch to the appropriate strategy and method of enforcement. The stability of human cooperation looks more promising if one mechanism controls successful strategies across frameworks.

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Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model.

Publication Date: 2010 Feb 16 PMID: 20167222
Authors: Shen, H. S.
Journal: J Theor Biol

This paper presents an investigation on the buckling and postbuckling of microtubules (MTs) subjected to a uniform external radial pressure in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on higher order shear deformation shell theory with a von Karman-Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The small scale parameter e(0)a is estimated by matching the buckling pressure of MTs measured from the experiments with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling pressure and postbuckling behavior of MTs are very sensitive to the small scale parameter e(0)a. The results reveal that the 13_3 microtubule has a stable postbuckling path, whereas the 13_2 microtubule has an unstable postbuckling behavior due to the presence of skew angles.

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Exact analytic solutions for a global equation of plant cell growth.

Publication Date: 2010 Feb 16 PMID: 20167221
Authors: Pietruszka, M.
Journal: J Theor Biol

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties-in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, variantexp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative.

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CAMBIUM, a process-based model of daily xylem development in Eucalyptus.

Publication Date: 2010 Feb 16 PMID: 20167220
Authors: Drew, D. M. - Downes, G. M. - Battaglia, M.
Journal: J Theor Biol

In hardwoods such as Eucalyptus spp., xylem (wood) is a heterogeneous tissue consisting of multiple cell types. As such, xylem development involves multiple complex interactions. To describe and understand xylem development, and ultimately predict the resultant wood properties, a process-based approach to modelling wood property variation is potentially very useful. In this paper, a new model (CAMBIUM), which incorporates concepts of these processes, is described. CAMBIUM predicts how wood density and fibre and vessel anatomical properties vary from pith-to-bark at a daily time step as a function of changing environmental conditions and a set of simulated physiological processes. Simulations from an existing process-based model of stand development (CABALA) are used as inputs. A key feature of CAMBIUM is a model of the interaction between different xylem cell types. Some weaknesses were identified in the ability of the model to simulate vessel spatial patterns and frequencies, emphasizing the complexities inherent in this aspect of angiosperm wood formation. The model was, however, able to provide realistic estimates of short-term variation and temporal ranges in eucalypt fibre diameter and secondary wall development and wood density.

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Essential molecular functions associated with the circular code evolution.

Publication Date: 2010 Feb 11 PMID: 20153338
Authors: Ahmed, A. - Frey, G. - Michel, C. J.
Journal: J Theor Biol

A circular code is a set of trinucleotides allowing the reading frames in genes to be retrieved locally, i.e. anywhere in genes and in particular without start codons, and automatically with a window of few nucleotides. In 1996, a common circular code, called X, was identified in large populations of eukaryotic and prokaryotic genes. Hence, it is believed to be an ancestral structural property of genes. A new computational approach based on comparative genomics is developed to identify essential molecular functions associated with circular codes. It is based on a quantitative and sensitive statistical method (FPTF) to identify three permuted trinucleotide sets in the three frames of genes, a flower automaton algorithm to determine if a trinucleotide set is a circular code or not, and an integrated Gene Ontology and Taxonomy (iGOT) database. By carrying out automatic circular code analyses on a huge number of gene populations where each population is associated with a particular molecular function, it identifies 266 gene populations having circular codes close to X. Surprisingly, their molecular functions include 98% of those covered by the essential genes of the DEG database (database of essential genes). Furthermore, three trinucleotides GTG, AAG and GCG, replacing three trinucleotides of the code X and called "evolutionary" trinucleotides, significantly occur in these 266 gene populations. Finally, a new method developed to analyse and quantify the stability of a set of trinucleotides demonstrates that these evolutionary trinucleotides are associated with a significant increase of the stability of the common circular code X. Indeed, its stability increases from the 1502th rank to the 16th rank after the replacement of the three evolutionary trinucleotides among 9920 possible trinucleotides replacement sets.

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Dynamical phase coexistence: A simple solution to the "savanna problem"

Publication Date: 2010 Feb 11 PMID: 20153337
Authors: Vazquez, F. - Lopez, C. - Calabrese, J. M. - Munoz, M. A.
Journal: J Theor Biol

We introduce the concept of dynamical phase coexistence to provide a simple solution for a long-standing problem in theoretical ecology, the so-called "savanna problem". The challenge is to understand why in savanna ecosystems trees and grasses coexist in a robust way with large spatiotemporal variability. We propose a simple model, a variant of the contact process (CP), which includes two key extra features: varying external (environmental/rainfall) conditions and tree age. The system fluctuates locally between a woodland and a grassland phase, corresponding to the active and absorbing phases of the underlying pure contact process. This leads to a highly variable stable phase characterized by patches of the woodland and grassland phases coexisting dynamically. We show that the mean time to tree extinction under this model increases as a power-law of system size and can be of the order of 10,000,000 years in even moderately sized savannas. Finally, we demonstrate that while local interactions among trees may influence tree spatial distribution and the order of the transition between woodland and grassland phases, they do not affect dynamical coexistence. We expect dynamical coexistence to be relevant in other contexts in physics, biology or the social sciences.

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Mathematical study of feedback control roles and relevance in stress erythropoiesis.

Publication Date: 2010 Apr 7 PMID: 20043921
Authors: Crauste, F. - Demin, I. - Gandrillon, O. - Volpert, V.
Journal: J Theor Biol

This work is devoted to mathematical modelling of erythropoiesis. We propose a new multi-scale model, in which we bring together erythroid progenitor dynamics and intracellular regulatory network that determines erythroid cell fate. All erythroid progenitors are divided into several sub-populations according to their maturity. Two intracellular proteins, Erk and Fas, are supposed to be determinant for regulation of self-renewal, differentiation and apoptosis. We consider two growth factors, erythropoietin and glucocorticoids, and describe their dynamics. Several feedback controls are introduced in the model. We carry out computer simulations of anaemia and compare the obtained results with available experimental data on induced anaemia in mice. The main objective of this work is to evaluate the roles of the feedback controls in order to provide more insights into the regulation of erythropoiesis. Feedback by Epo on apoptosis is shown to be determinant in the early stages of the response to anaemia, whereas regulation through intracellular regulatory network, based on Erk and Fas, appears to operate on a long-term scale.

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Prediction of the parallel/antiparallel orientation of beta-strands using amino acid pairing preferences and support vector machines.

Publication Date: 2010 Apr 7 PMID: 20035768
Authors: Zhang, N. - Duan, G. - Gao, S. - Ruan, J. - Zhang, T.
Journal: J Theor Biol

In principle, structural information of protein sequences with no detectable homology to a protein of known structure could be obtained by predicting the arrangement of their secondary structural elements. Although some ab initio methods for protein structure prediction have been reported, the long-range interactions required to accurately predict tertiary structures of beta-sheet containing proteins are still difficult to simulate. To remedy this problem and facilitate de novo prediction of beta-sheet containing protein structures, we developed a support vector machine (SVM) approach that classified parallel and antiparallel orientation of beta-strands by using the information of interstrand amino acid pairing preferences. Based on a second-order statistics on the relative frequencies of each possible interstrand amino acid pair, we defined an average amino acid pairing encoding matrix (APEM) for encoding beta-strands as input in the prediction model. As a result, a prediction accuracy of 86.89% and a Matthew's correlation coefficient value of 0.71 have been achieved through 7-fold cross-validation on a non-redundant protein dataset from PISCES. Although several issues still remain to be studied, the method presented here to some extent could indicate the important contribution of the amino acid pairs to the beta-strand orientation, and provide a possible way to further be combined with other algorithms making a full 'identification' of beta-strands.

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The basic reproductive ratio of life.

Publication Date: 2010 Apr 7 PMID: 20034501
Authors: Manapat, M. L. - Chen, I. A. - Nowak, M. A.
Journal: J Theor Biol

Template-directed polymerization of nucleotides is believed to be a pathway for the replication of genetic material in the earliest cells. We assume that activated monomers are produced by prebiotic chemistry. These monomers can undergo spontaneous polymerization, a system that we call "prelife." Adding template-directed polymerization changes the equilibrium structure of prelife if the rate constants meet certain criteria. In particular, if the basic reproductive ratio of sequences of a certain length exceeds one, then those sequences can attain high abundance. Furthermore, if many sequences replicate, then the longest sequences can reach high abundance even if the basic reproductive ratios of all sequences are less than one. We call this phenomenon "subcritical life." Subcritical life suggests that sequences long enough to be ribozymes can become abundant even if replication is relatively inefficient. Our work on the evolution of replication has interesting parallels to infection dynamics. Life (replication) can be seen as an infection of prelife.

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Interpreting the effect of vaccination on steady state infection in animals challenged with Simian immunodeficiency virus.

Publication Date: 2010 Apr 7 PMID: 20034499
Authors: Sergeev, R. A. - Batorsky, R. E. - Coffin, J. M. - Rouzine, I. M.
Journal: J Theor Biol

A representative vaccinated macaque challenged with SIVmac251 establishes a persistent infection with a lower virus load, higher CTL frequencies, and much higher helper cell frequencies, than a representative control animal. The reasons for the difference are not fully understood. Here we interpret this effect using a mathematical model we developed recently to explain results of various experiments on virus and CTL dynamics in SIV-infected macaques and HIV-infected humans. The model includes two types of cytotoxic lymphocytes (CTLs) regulated by antigen-activated helper cells and directly by infected cells, respectively, and predicts the existence of two steady states with different viremia, helper cell and CTL levels. Depending on the initial level of CTL memory cells and helper cells, a representative animal ends up in either the high-virus state or the low-virus state, which accounts for the observed differences between the two animal groups. Viremia in the low-virus state is proportional to the antigen sensitivity threshold of helper cells. Estimating the infectivity ratio of activated and resting CD4 T cells at 200-300, the correct range for the critical memory cell percentage and the viremia peak suppression is predicted. However, the model does not explain why viremia in the "low-virus state" is surprisingly high , relative to vaccinated animals infected with SHIV, and broadly distributed among challenged animals. We conclude that the model needs an update explaining extremely low sensitivity of uninfected helper cells to antigen in vaccinated animals.

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Selection for fitness at the individual or population levels: modelling effects of genetic modifications in microalgae on productivity and environmental safety.

Publication Date: 2010 Apr 7 PMID: 20034498
Authors: Flynn, K. J. - Greenwell, H. C. - Lovitt, R. W. - Shields, R. J.
Journal: J Theor Biol

A mechanistic model of microalgae is used to explore the implications of modifying microalgal chlorophyll content and photosynthetic efficiency with an aim to optimising commercial biomass production. The models show the potential for a 10 fold increase in microalgae productivity in genetically modified versus unmodified configurations, while also enabling the use of bioreactors of greater optical depth operating at lower dilution rates. Analysis suggests that natural selection of a trait benefiting the individual (high Chl:C(max), i.e., high antennae size) conflicts with artificial selection of a trait (low Chl:C(max)) of most benefit to production at the population level. The implication is that GM strains rather than strains selected from nature will be most beneficial for commercial algal biofuels production. Further, escaped GM algae populations may, depending on the specific nature of the modification, be quickly out-competed by the natural forms because individually a high Chl:C is beneficial in low light environments. However, it remains possible that changes in biochemical composition associated with genetic modification of photosystem competence, or with other selection processes to enhance commercial gain, may adversely affect the value of such organisms as prey for zooplankton, leading to the unwanted generation of future harmful algae.

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New method for global alignment of 2 DNA sequences by the tree data structure.

Publication Date: 2010 Mar 21 PMID: 20025888
Authors: Qi, Z. H. - Qi, X. Q. - Liu, C. C.
Journal: J Theor Biol

We introduce a new approach to investigate problem of DNA sequence alignment. The method consists of three parts: (i) simple alignment algorithm, (ii) extension algorithm for largest common substring, (iii) graphical simple alignment tree (GSA tree). The approach firstly obtains a graphical representation of scores of DNA sequences by the scoring equation R(0)*R-S(0)*S-T(0)*(a+bk). Then a GSA tree is constructed to facilitate solving the problem for global alignment of 2 DNA sequences. Finally we give several practical examples to illustrate the utility and practicality of the approach.

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Consequential classes of resources: Subtle global bifurcation with dramatic ecological consequences in a simple population model.

Publication Date: 2010 Mar 21 PMID: 20018195
Authors: Vandermeer, J. - King, A.
Journal: J Theor Biol

Numerous situations exist in which a consumer uses two different kinds of resources, one fixed, the other renewable, e.g., nesting resources and food resources. With an elementary modification of the basic Lotka-Volterra consumer resource equations, we investigate the population dynamics of a consumer dependent on two resources, one fixed, the other renewable. Emerging from this structure is a situation of alternative attractors that remain qualitatively robust over a significant range of parameter values. However, a dramatic change in basins of attraction is induced by very small changes in parameters due to a global bifurcation. Noteworthy is the fact that the qualitative nature of the alternative equilibria remains constant but the dramatic change in the basins does not arise from subtle differences in initial conditions. Rather, there is a major restructuring of the vector field such that a permanent change involving large sets of initial conditions results from very small changes in parameters.

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Modeling growth and telomere dynamics in Saccharomyces cerevisiae.

Publication Date: 2010 Apr 7 PMID: 20018194
Authors: Olofsson, P. - Bertuch, A. A.
Journal: J Theor Biol

A general branching process is proposed to model a population of cells of the yeast Saccharomyces cerevisiae following loss of telomerase. Previously published experimental data indicate that a population of telomerase-deficient cells regain exponential growth after a period of slowing due to critical telomere shortening. The explanation for this phenomenon is that some cells engage telomerase-independent pathways to maintain telomeres that allow them to become "survivors." Our model takes into account random variation in individual cell cycle times, telomere length, finite replicative lifespan of mother cells, and survivorship. We identify and estimate crucial parameters such as the probability of an individual cell becoming a survivor, and compare our model predictions to experimental data.

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A diffusion process to model generalized von Bertalanffy growth patterns: fitting to real data.

Publication Date: 2010 Mar 7 PMID: 20018193
Authors: Roman-Roman, P. - Romero, D. - Torres-Ruiz, F.
Journal: J Theor Biol

The von Bertalanffy growth curve has been commonly used for modeling animal growth (particularly fish). Both deterministic and stochastic models exist in association with this curve, the latter allowing for the inclusion of fluctuations or disturbances that might exist in the system under consideration which are not always quantifiable or may even be unknown. This curve is mainly used for modeling the length variable whereas a generalized version, including a new parameter b > or = 1, allows for modeling both length and weight for some animal species in both isometric (b = 3) and allometric (b not = 3) situations. In this paper a stochastic model related to the generalized von Bertalanffy growth curve is proposed. This model allows to investigate the time evolution of growth variables associated both with individual behaviors and mean population behavior. Also, with the purpose of fitting the above-mentioned model to real data and so be able to forecast and analyze particular characteristics, we study the maximum likelihood estimation of the parameters of the model. In addition, and regarding the numerical problems posed by solving the likelihood equations, a strategy is developed for obtaining initial solutions for the usual numerical procedures. Such strategy is validated by means of simulated examples. Finally, an application to real data of mean weight of swordfish is presented.

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Glucose transport from mother to fetus--a theoretical study.

Publication Date: 2010 Apr 7 PMID: 20006624
Authors: Barta, E. - Drugan, A.
Journal: J Theor Biol

The factors that affect and govern the glucose transfer from maternal blood to the fetus are not completely deciphered. We present a steady state, one dimensional mathematical simulation which integrates the main mechanisms that have been shown to exist: metabolic consumption of the placenta, simple and facilitated diffusion via the two membranes of the microvillous and simple diffusion within the placenta. The model uses all available physiologic data we could collect. Numerical results indicate that the most crucial factor in determining the fetal glucose concentration is the facilitated diffusion process at the basal membrane or, more specifically: the permeability of the basal membrane and the density of the transporter GLUT1 on its faces. The gradient between the maternal and the fetal glucose concentration is important as is the metabolic consumption of the placenta. The diffusion within the placenta and the conditions that prevail at the apical microvillous plasma membrane are much less significant. Intrasyncytial concentration of glucose is close to that of maternal blood. The adjustment of the fetal glucose concentration to abrupt changes of its surrounding is estimated to be quite rapid hence for all practical purposes this steady state model can serve as a reasonable approximation. Parameters that await experimental determination are identified.

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On the role of diffusible binding partners in modulating the transport and concentration of proteins in tissues.

Publication Date: 2010 Mar 7 PMID: 20005880
Authors: Zhang, L. - Gardiner, B. S. - Smith, D. W. - Pivonka, P. - Grodzinsky, A. J.
Journal: J Theor Biol

Here a reactive-diffusion transport model is used to demonstrate two previously undescribed functional roles for diffusible binding partners in the transport of molecules into tissues. The uptake of the insulin-like growth (IGF) and its binding partner the IGF binding protein (IGFBP3) into cartilage is used a specific tissue example to demonstrate a general principal. First, we show that reversible binding between free protein (IGF) and its diffusible binding partner (free IGFBPs) increases the rate of protein uptake into the tissue. Second, selective degradation of the binding partner can increase the transient and steady state free protein in tissues, well above the concentration at the source boundary, with the maximum free concentration occurring distant from the source boundary, deep within the tissue. This finding is very much at odds with expectations based on a traditional diffusion analysis. In cartilage, using realistic parameters, these new mechanisms raise the free IGF concentration by an order of magnitude deep within the tissue. As the increase in free protein is 'tunable' by cells, our analyses are postulated to demonstrate a general regulatory principle that may operate in any tissues throughout the body.

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A model for Ca2+ waves in networks of glial cells incorporating both intercellular and extracellular communication pathways.

Publication Date: 2010 Mar 7 PMID: 20005235
Authors: Edwards, J. R. - Gibson, W. G.
Journal: J Theor Biol

Networks of glial cells, and in particular astrocytes, are capable of sustaining calcium (Ca(2+)) waves both in vivo and in vitro. Experimentally, it has been shown that there are two separate modes of communication: the first by the passage of an agent (inositol 1,4,5-triphosphate, IP(3)) through gap junctions (GJs) joining cells; the second by the diffusion of an extracellular agent (adenosine triphosphate, ATP) that binds to receptors on the cells. In both cases, the outcome is the release of Ca(2+) from internal stores in the glial cells. These two modes of communication are not mutually exclusive, but probably work in conjunction in many cases. We present a model of a two-dimensional network of glial cells that incorporates regenerative intercellular (GJ) and extracellular (ATP) pathways. In the extreme cases of only one type of pathway, the results are in agreement with previous models. Adding an extracellular pathway to the GJ model increased the extent and duration of the Ca(2+) wave, but did not significantly change the speed of propagation. Conversely, adding GJs to the extracellular model did increase the wave speed. The model was modified to apply to the retina by extending it to include both astrocytes and Muller cells, with GJs the dominant coupling between astrocytes and ATP responsible for most of the remaining communication. It was found that both pathways are necessary to account for experimental results.

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Cycling expression and cooperative operator interaction in the trp operon of Escherichia coli.

Publication Date: 2010 Apr 7 PMID: 20004672
Authors: Hernandez-Valdez, A. - Santillan, M. - Zeron, E. S.
Journal: J Theor Biol

Oscillatory behaviour in the tryptophan operon of an Escherichia coli mutant strain lacking the enzyme-inhibition regulatory mechanism has been observed by Bliss et al. but not confirmed by others. This behaviour could be important from the standpoint of synthetic biology, whose goals include the engineering of intracellular genetic oscillators. This work is devoted to investigating, from a mathematical modelling point of view, the possibility that the trp operon of the E. coli inhibition-free strain expresses cyclically. For that we extend a previously introduced model for the regulatory pathway of the tryptophan operon in Escherichia coli to account for the observed multiplicity and cooperativity of repressor binding sites. Thereafter we investigate the model dynamics using deterministic numeric solutions, stochastic simulations, and analytic studies. Our results suggest that a quasi-periodic behaviour could be observed in the trp operon expression level of single bacteria.

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Anomalies in the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae.

Publication Date: 2010 Apr 7 PMID: 20004671
Authors: Tugrul, M. - Kabakcioglu, A.
Journal: J Theor Biol

We investigate the structural and dynamical properties of the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae and compare it with two "unbiased" ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first-by construction-exactly and the second approximately), degree-degree correlations and the k-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications in the network's degree distributions. We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behavior, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network.

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Evolution of resistance to anti-cancer therapy during general dosing schedules.

Publication Date: 2010 Mar 21 PMID: 20004211
Authors: Foo, J. - Michor, F.
Journal: J Theor Biol

Anti-cancer drugs targeted to specific oncogenic pathways have shown promising therapeutic results in the past few years; however, drug resistance remains an important obstacle for these therapies. Resistance to these drugs can emerge due to a variety of reasons including genetic or epigenetic changes which alter the binding site of the drug target, cellular metabolism or export mechanisms. Obtaining a better understanding of the evolution of resistant populations during therapy may enable the design of more effective therapeutic regimens which prevent or delay progression of disease due to resistance. In this paper, we use stochastic mathematical models to study the evolutionary dynamics of resistance under time-varying dosing schedules and pharmacokinetic effects. The populations of sensitive and resistant cells are modeled as multi-type non-homogeneous birth-death processes in which the drug concentration affects the birth and death rates of both the sensitive and resistant cell populations in continuous time. This flexible model allows us to consider the effects of generalized treatment strategies as well as detailed pharmacokinetic phenomena such as drug elimination and accumulation over multiple doses. We develop estimates for the probability of developing resistance and moments of the size of the resistant cell population. With these estimates, we optimize treatment schedules over a subspace of tolerated schedules to minimize the risk of disease progression due to resistance as well as locate ideal schedules for controlling the population size of resistant clones in situations where resistance is inevitable. Our methodology can be used to describe dynamics of resistance arising due to a single (epi)genetic alteration in any tumor type.

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Estimating trees from filtered data: identifiability of models for morphological phylogenetics.

Publication Date: 2010 Mar 7 PMID: 20004210
Authors: Allman, E. S. - Holder, M. T. - Rhodes, J. A.
Journal: J Theor Biol

As an alternative to parsimony analyses, stochastic models have been proposed (Lewis, 2001; Nylander et al., 2004) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A key feature of these models is that they account for ascertainment bias, in that only varying, or parsimony-informative characters are observed. However, statistical consistency of such model-based inference requires that the model parameters be identifiable from the joint distribution they entail, and this issue has not been addressed. Here we prove that parameters for several such models, with finite state spaces of arbitrary size, are identifiable, provided the tree has at least eight leaves. If the tree topology is already known, then seven leaves suffice for identifiability of the numerical parameters. The method of proof involves first inferring a full distribution of both parsimony-informative and non-informative pattern joint probabilities from the parsimony-informative ones, using phylogenetic invariants. The failure of identifiability of the tree parameter for four-taxon trees is also investigated.

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Fixation probabilities of random mutants under frequency dependent selection.

Publication Date: 2010 Mar 21 PMID: 19995564
Authors: Huang, W. - Traulsen, A.
Journal: J Theor Biol

Evolutionary game dynamics describes frequency dependent selection in asexual, haploid populations. It typically considers predefined strategies and fixed payoff matrices. Mutations occur between these known types only. Here, we consider a situation in which a mutation has produced an entirely new type which is characterized by a random payoff matrix that does not change during the fixation or extinction of the mutant. Based on the probability distribution underlying the payoff values, we address the fixation probability of the new mutant. It turns out that for weak selection, only the first moments of the distribution matter. For strong selection, the probability that a new payoff entry is larger than the wild type's payoff against itself is the crucial quantity.

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Theoretical blood glucose control in hyper- and hypoglycemic and exercise scenarios by means of an H(infinity) algorithm.

Publication Date: 2010 Mar 7 PMID: 19962391
Authors: Quiroz, G. - Femat, R.
Journal: J Theor Biol

Artificial Endocrine Pancreas (AEP) is one of the most optimistic approaches in Type 1 Diabetes Mellitus (T1DM) treatment due to the novel technological advances in continuous glucose monitoring, exogenous insulin delivery, and their proofs in clinical assessments. The main goal of AEP is to replace the pancreatic insulin secretion in the blood glucose regulation loop by means of an automatic exogenous insulin infusion. The joint element between glucose sensing and insulin delivering actions is an automatic algorithm-based decision. In this contribution, there is an H(infinity) control algorithm to compute the insulin infusion rate during hyperglycemia, exercise and nocturnal hypoglycemia. In order to mimic the insulin release pattern of a healthy pancreas, a frequency restriction in the insulin infusion pattern generated by controller was considered in the design. The inclusion of mathematical models of relations between glucose and chosen biosignals in the control loop generates an adequate insulin infusion pattern to compensate blood glucose variations during each metabolic scenario. The proposed automatic algorithm for decision shows good performance in controlling glycemia in metabolic scenarios, avoiding long-term hyperglycemia as well as glycemic disturbances during exercise and nocturnal hypoglycemia, guaranteeing insulin infusion with a delivery pattern closer to that generated by a healthy pancreas.

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The competition of assessment rules for indirect reciprocity.

Publication Date: 2010 Mar 7 PMID: 19962390
Authors: Uchida, S. - Sigmund, K.
Journal: J Theor Biol

Indirect reciprocity is one of the basic mechanisms to sustain mutual cooperation. Beneficial acts are returned, not by the recipient, but by third parties. Indirect reciprocity is based on reputation and status: it pays to provide help because this makes one more likely to receive help in turn. The mechanism depends on knowing the past behavior of other players, and assessing that behavior. There are many different systems of assessing other individuals, which can be interpreted as rudimentary moral systems (i.e. views on what is 'good' or 'bad'). In this paper, we describe the competition of some of the leading assessment rules called SUGDEN and KANDORI by analytic methods. We show that the sterner rule KANDORI has a slight advantage in the sense that KANDORI-players have more chance to earn higher payoff than SUGDEN-players in the presence of unconditional altruists. On the other hand, we see that the unconditional altruists are eliminated in the long run and that stable polymorphisms of KANDORI and SUGDEN can subsist, but that a moral consensus is realized even in those polymorphic states: all players' images are the same in each observer's eyes.

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Closure to efficient causation, computability and artificial life.

Publication Date: 2010 Mar 7 PMID: 19962389
Authors: Cardenas, M. L. - Letelier, J. C. - Gutierrez, C. - Cornish-Bowden, A. - Soto-Andrade, J.
Journal: J Theor Biol

The major insight in Robert Rosen's view of a living organism as an (M,R)-system was the realization that an organism must be "closed to efficient causation", which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.

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Information content based model for the topological properties of the gene regulatory network of Escherichia coli.

Publication Date: 2010 Apr 7 PMID: 19962388
Authors: Malkoc, B. - Balcan, D. - Erzan, A.
Journal: J Theor Biol

Gene regulatory networks (GRN) are being studied with increasingly precise quantitative tools and can provide a testing ground for ideas regarding the emergence and evolution of complex biological networks. We analyze the global statistical properties of the transcriptional regulatory network of the prokaryote Escherichia coli, identifying each operon with a node of the network. We propose a null model for this network using the content-based approach applied earlier to the eukaryote Saccharomyces cerevisiae (Balcan et al., 2007). Random sequences that represent promoter regions and binding sequences are associated with the nodes. The length distributions of these sequences are extracted from the relevant databases. The network is constructed by testing for the occurrence of binding sequences within the promoter regions. The ensemble of emergent networks yields an exponentially decaying in-degree distribution and a putative power law dependence for the out-degree distribution with a flat tail, in agreement with the data. The clustering coefficient, degree-degree correlation, rich club coefficient and k-core visualization all agree qualitatively with the empirical network to an extent not yet achieved by any other computational model, to our knowledge. The significant statistical differences can point the way to further research into non-adaptive and adaptive processes in the evolution of the E. coli GRN.

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Which coordinate system for modelling path integration?

Publication Date: 2010 Mar 21 PMID: 19962387
Authors: Vickerstaff, R. J. - Cheung, A.
Journal: J Theor Biol

Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justifications and supporting data. Despite the importance of the phenomenon, consensus and unifying principles appear lacking. A fundamental issue is the neural representation of space needed for biological path integration. This paper presents a scheme to classify path integration systems on the basis of the way the home vector records and updates the spatial relationship between the animal and its home location. Four extended classes of coordinate systems are used to unify and review both canonical and neural network models of path integration, from the arthropod and mammalian literature. This scheme demonstrates analytical equivalence between models which may otherwise appear unrelated, and distinguishes between models which may superficially appear similar. A thorough analysis is carried out of the equational forms of important facets of path integration including updating, steering, searching and systematic errors, using each of the four coordinate systems. The type of available directional cue, namely allothetic or idiothetic, is also considered. It is shown that on balance, the class of home vectors which includes the geocentric Cartesian coordinate system, appears to be the most robust for biological systems. A key conclusion is that deducing computational structure from behavioural data alone will be difficult or impossible, at least in the absence of an analysis of random errors. Consequently it is likely that further theoretical insights into path integration will require an in-depth study of the effect of noise on the four classes of home vectors.

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A two-sex life history model of handicap signaling.

Publication Date: 2010 Mar 21 PMID: 19962386
Authors: Cyrus Chu, C. Y.
Journal: J Theor Biol

The males of many species (such as peacocks) develop excessively large traits, which appear to interfere with their agility and hence survival probability. Moreover, it is also observed that females seem to prefer mating males with such clumsy traits. Zahavi (1975) proposed a handicap theory to explain this phenomenon, suggesting that this trait/preference interaction is a way in which strong males can signal their viability by yielding a handicap in terms of a clumsy trait size. This paper presents a two-sex model of selfish genes that generates this particular male-female interaction, and characterizes the conditions behind a handicap equilibrium. We first show the female dominance result of Bateman (1948) in this two-sex model, and then specify the relevant equilibrium conditions, including the incentive compatibility condition for females, the individual rationality condition for males, and the stability condition of population composition. Identifying these conditions helps us understand the various features of the searching/signaling of sex selection in evolution.

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Using the concept of Chou's pseudo amino acid composition for risk type prediction of human papillomaviruses.

Publication Date: 2010 Mar 21 PMID: 19961864
Authors: Esmaeili, M. - Mohabatkar, H. - Mohsenzadeh, S.
Journal: J Theor Biol

High-risk types of human papillomaviruses (HPVs) are the etiological agents in nearly all cases (99.7%) of cervical cancer, and the HPV E6 protein is one of the two viral oncoproteins which is expressed in virtually all HPV-positive cancers. Therefore, classifying the risk type of HPVs is very useful and necessary for diagnosis and remedy of cervical cancer. To predict and to classify the risk types of HPV by bioinformatics analysis, 96 E6 protein sequences from available databases were obtained. To investigate the risk type of these sequences, PseAAC server, ROC curves and statistical analysis were applied. Our classification was based on some characters of HPV E6 proteins, such as hydrophobicity, hydrophilicity, side chain mass, PK of the alpha-COOH group, PK of the alpha-NH3(+) group and PI at 25 degrees C. Risk type of 4 unknown HPV types and 25 non-reported HPV types were also predicted. These results show that bioinformatics based theoretical approaches can direct and simplify experimental studies.

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Base pair stacking in nucleosome DNA and bendability sequence pattern.

Publication Date: 2010 Apr 7 PMID: 19961863
Authors: Trifonov, E. N.
Journal: J Theor Biol

DNA deformation in the nucleosome involves partial unstacking between bases and base pairs. By adjusting orientations of different base-pair stacks relative to the histone octamer surface, the optimal set of stacks and their positions is derived, resulting in a sequence pattern, theoretically best suitable for nucleosome DNA. The sequence is very much consistent with available experimental data, thus, suggesting a common eukaryotic nucleosome DNA bendability sequence pattern based exclusively on the very basics of DNA.

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Effects of extinction on food web structures on an evolutionary time scale.

Publication Date: 2010 Mar 21 PMID: 19961862
Authors: Hironaga, R. - Yamamura, N.
Journal: J Theor Biol

Extinction affected food web structure in paleoecosystems. Recent theoretical studies that examined the effects of extinction intensity on food web structure on ecological time scales have considered extinction to involve episodic events, with pre-extinction food webs becoming established without dynamics. However, in terms of the paleontological time scale, food web structures are generated from feedback with repeated extinctions, because extinction frequency is affected by food web structure, and food web structure itself is a product of previous extinctions. We constructed a simulation model of changes in tri-trophic-level food webs to examine how continual extinction events affect food webs on an evolutionary time scale. We showed that under high extinction intensity (1) species diversity, especially that of consumer species, decreased; (2) the total population density at each trophic level decreased, while the densities of individual species increased; and (3) the trophic link density of the food web increased. In contrast to previous models, our results were based on an assumption of long-term food web development and are able to explain overall trends posited by empirical investigations based on fossil records.

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Optimal number of regulatory T cells.

Publication Date: 2010 Mar 21 PMID: 19961861
Authors: Saeki, K. - Iwasa, Y.
Journal: J Theor Biol

The adaptive immune system of a vertebrate may attack its own body, causing autoimmune diseases. Regulatory T cells suppress the activity of the autoreactive effector T cells, but they also interrupt normal immune reactions against foreign antigens. In this paper, we discuss the optimal number of regulatory T cells that should be produced. We make the assumptions that some self-reactive immature T cells may fail to interact with their target antigens during the limited training period and later become effector T cells causing autoimmunity, and that regulatory T cells exist that recognize self-antigens. When a regulatory T cell is stimulated by its target self-antigen on an antigen-presenting cell (APC), it stays there and suppresses the activation of other naive T cells on the same APC. Analysis of the benefit and the harm of having regulatory T cells suggests that the optimal number of regulatory T cells depends on the number of self-antigens, the severity of the autoimmunity, the abundance of pathogenic foreign antigens, and the spatial distribution of self-antigens in the body. For multiple types of self-antigen, we discuss the optimal number of regulatory T cells when the self-antigens are localized in different parts of the body and when they are co-localized. We also examine the separate regulation of the abundances of regulatory T cells for different self-antigens, comparing it with the situation in which they are constrained to be equal.

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Modelling conjugation with stochastic differential equations.

Publication Date: 2010 Mar 7 PMID: 19941872
Authors: Philipsen, K. R. - Christiansen, L. E. - Hasman, H. - Madsen, H.
Journal: J Theor Biol

Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.

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Reproductive skew theory unified: the general bordered tug-of-war model.

Publication Date: 2010 Mar 7 PMID: 19932705
Authors: Shen, S. F. - Kern Reeve, H.
Journal: J Theor Biol

Reproductive skew has been identified as a major dimension along which animal societies vary. Two major kinds of reproductive skew models are transactional models, which explain the distribution of reproduction within animal societies as the result of reproductive payments exchanged among group members with differential leverage, and tug-of-war models, in which the reproductive shares are determined by costly 'tugs-of-war'. These two models have recently been synthesized to yield the mutual-pay, bordered tug-of-war model. In this paper, we extend the latter, show its evolutionary stability, and demonstrate that the generalized model yields four sub-models, namely the mutual-pay, alpha-pay, beta-pay, and pure tug-of-war. The alpha-pay sub-model turns out to closely resemble the original "concessions" transactional skew model, and the beta-pay sub-model turns out to have properties similar to the "restraint" transactional skew model. Thus, the general model unifies the four major models of reproductive skew and is rich in its predictions, as each sub-model exhibits different qualitative and quantitative relationships between reproductive skew or intra-group conflict and the ecological and genetic factors that determine skew and conflict. The conditions favoring transitions among these sub-models also are precisely predicted by the general model. The general model accommodates data from acorn woodpeckers and primitively eusocial bees potentially can account for many of the highly varied empirical findings on reproductive skew. We suggest further research that focuses on (1) determining which model is suitable for certain species and (2) understanding why and how various social animals resolve their breeding conflict by different conflict resolution mechanisms.

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Stability of choice in the honey bee nest-site selection process.

Publication Date: 2010 Mar 7 PMID: 19932704
Authors: Nevai, A. L. - Passino, K. M. - Srinivasan, P.
Journal: J Theor Biol

We introduce a pair of compartment models for the honey bee nest-site selection process that lend themselves to analytic methods. The first model represents a swarm of bees deciding whether a site is viable, and the second characterizes its ability to select between two viable sites. We find that the one-site assessment process has two equilibrium states: a disinterested equilibrium (DE) in which the bees show no interest in the site and an interested equilibrium (IE) in which bees show interest. In analogy with epidemic models, we define basic and absolute recruitment numbers (R(0) and B(0)) as measures of the swarm's sensitivity to dancing by a single bee. If R(0) is less than one then the DE is locally stable, and if B(0) is less than one then it is globally stable. If R(0) is greater than one then the DE is unstable and the IE is stable under realistic conditions. In addition, there exists a critical site quality threshold Q(*) above which the site can attract some interest (at equilibrium) and below which it cannot. We also find the existence of a second critical site quality threshold Q(**) above which the site can attract a quorum (at equilibrium) and below which it cannot. The two-site discrimination process, in which we examine a swarm's ability to simultaneously consider two sites differing in both site quality and discovery time, has a stable DE if and only if both sites' individual basic recruitment numbers are less than one. Numerical experiments are performed to study the influences of site quality on quorum time and the outcome of competition between a lower quality site discovered first and a higher quality site discovered second.

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Cooperative differentiation through clustering in multicellular populations.

Publication Date: 2010 Mar 21 PMID: 19932703
Authors: Koseska, A. - Ullner, E. - Volkov, E. - Kurths, J. - Garcia-Ojalvo, J.
Journal: J Theor Biol

The coordinated development of multicellular organisms is driven by intercellular communication. Differentiation into diverse cell types is usually associated with the existence of distinct attractors of gene regulatory networks, but how these attractors emerge from cell-cell coupling is still an open question. In order to understand and characterize the mechanisms through which coexisting attractors arise in multicellular systems, here we systematically investigate the dynamical behavior of a population of synthetic genetic oscillators coupled by chemical means. Using bifurcation analysis and numerical simulations, we identify various attractors and attempt to deduce from these findings a way to predict the organized collective behavior of growing populations. Our results show that dynamical clustering is a generic property of multicellular systems. We argue that such clustering might provide a basis for functional differentiation and variability in biological systems.

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Degeneracy: a design principle for achieving robustness and evolvability.

Publication Date: 2010 Mar 7 PMID: 19925810
Authors: Whitacre, J. - Bender, A.
Journal: J Theor Biol

Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.

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The evolution of tumor metastases during clonal expansion.

Publication Date: 2010 Mar 7 PMID: 19917298
Authors: Haeno, H. - Michor, F.
Journal: J Theor Biol

Cancer is a leading cause of morbidity and mortality in many countries. Solid tumors generally initiate at one particular site called the primary tumor, but eventually disseminate and form new colonies in other organs. The development of such metastases greatly diminishes the potential for a cure of patients and is thought to represent the final stage of the multi-stage progression of human cancer. The concept of early metastatic dissemination, however, postulates that cancer cell spread might arise early during the development of a tumor. It is important to know whether metastases are present at diagnosis since this determines treatment strategies and outcome. In this paper, we design a stochastic mathematical model of the evolution of tumor metastases in an expanding cancer cell population. We calculate the probability of metastasis at a given time during tumor evolution, the expected number of metastatic sites, and the total number of cancer cells as well as metastasized cells. Furthermore, we investigate the effect of drug administration and tumor resection on these quantities and predict the survival time of cancer patients. The model presented in this paper allows us to determine the probability and number of metastases at diagnosis and to identify the optimum treatment strategy to maximally prolong survival of cancer patients.

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Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity.

Publication Date: 2010 Mar 21 PMID: 19914259
Authors: Chiyaka, C. - Mukandavire, Z. - Das, P. - Nyabadza, F. - Hove-Musekwa, S. D. - Mwambi, H.
Journal: J Theor Biol

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

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A stochastic dispersal-limited trait-based model of community dynamics.

Publication Date: 2010 Feb 21 PMID: 19913559
Authors: Jabot, F.
Journal: J Theor Biol

I present a model of stochastic community dynamics in which death occurs randomly in the community, propagules disperse randomly from a regional pool, and recruitment of new individuals of a species is proportional to the species local abundance multiplied by its local competitive ability. The competitive ability of a species is assumed to be determined by a function of one trait of the species, and I call this function the environmental filtering function. I show that information on local species abundances in a network of plots, together with trait data for each species, enables the inference of both the immigration rate and the environmental filtering function in each plot. I further study how the diversity patterns produced by this model deviate from the neutral predictions, and how this deviation depends on the characteristics of the environmental filtering function. I show that this inference framework is more powerful at detecting trait-based environmental filtering than existing statistical approaches based on trait distributions, and discuss how the predictions of this model could be used to assess environmental heterogeneity in a plot, to detect functionally meaningful trade-offs among species traits, and to test the assumption that there exists a simple relationship between species traits and local competitive ability.

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Model with two types of CTL regulation and experiments on CTL dynamics.

Publication Date: 2010 Apr 7 PMID: 19913558
Authors: Sergeev, R. A. - Batorsky, R. E. - Rouzine, I. M.
Journal: J Theor Biol

Recently, we developed a mathematical model of interaction between the HIV and the immune system to match various dynamic experiments carried out in HIV-infected humans and SIV-infected macaques. The model includes helper cell-dependent and helper cell-independent cytotoxic lymphocytes (CTLs) and predicts two stable steady states, a state with a high virus load and few helper cells, and another state with a low virus load and many helper cells. Here we upgrade the model to take into account recent reports on the link between the activation status of infected cells and their ability to produce virus, the effect of helper cells at the time of priming on CTL differentiation, and virus dynamics in unvaccinated macaques with a broad genetic background acutely infected with SIVmac251. We also discuss in detail the experimental justification of the CTL block and the robustness of model predictions with respect to the hypothesis of two CTL subtypes.

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Fractal analysis of vascular networks: insights from morphogenesis.

Publication Date: 2010 Feb 21 PMID: 19913557
Authors: Lorthois, S. - Cassot, F.
Journal: J Theor Biol

Considering their extremely complicated and hierarchical structure, a long standing question in vascular physio-pathology is how to characterize blood vessels patterns, including which parameters to use. Another question is how to define a pertinent taxonomy, with applications to normal development and to diagnosis and/or staging of diseases. To address these issues, fractal analysis has been applied by previous investigators to a large variety of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the results obtained on healthy vascular networks first shows that no consensus has emerged about whether normal networks must be considered as fractals or not. Based on a review of previous theoretical work on vascular morphogenesis, we argue that these divergences are the signature of a two-step morphogenesis process, where vascular networks form via progressive penetration of arterial and venous quasi-fractal arborescences into a pre-existing homogeneous capillary mesh. Adopting this perspective, we study the multi-scale behavior of generic patterns (model structures constructed as the superposition of homogeneous meshes and quasi-fractal trees) and of healthy intracortical networks in order to determine the artifactual and true components of their multi-scale behavior. We demonstrate that, at least in the brain, healthy vascular structures are a superposition of two components: at low scale, a mesh-like capillary component which becomes homogeneous and space-filling over a cut-off length of order of its characteristic length; at larger scale, quasi-fractal branched (tree-like) structures. Such complex structures are consistent with all previous studies on the multi-scale behavior of vascular structures at different scales, resolving the apparent contradiction about their fractal nature. Consequences regarding the way fractal analysis of vascular networks should be conducted to provide meaningful results are presented. Finally, consequences for vascular morphogenesis or hemodynamics are discussed, as well as implications in case of pathological conditions, such as cancer.

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The Burrows-Wheeler similarity distribution between biological sequences based on Burrows-Wheeler transform.

Publication Date: 2010 Feb 21 PMID: 19903487
Authors: Yang, L. - Zhang, X. - Wang, T.
Journal: J Theor Biol

This work aims at the similarity of biological sequences. Based on the Burrows-Wheeler transform, a definition of Burrows-Wheeler similarity distribution of two sequences is proposed to compare two sequences. Some distance measures are naturally followed by the distribution. The expectation and entropy of the similarity distribution are used to construct phylogenetic trees on two independent data sets. The result demonstrates that the method is efficient and powerful.

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Predict potential drug targets from the ion channel proteins based on SVM.

Publication Date: 2010 Feb 21 PMID: 19903486
Authors: Huang, C. - Zhang, R. - Chen, Z. - Jiang, Y. - Shang, Z. - Sun, P. - Zhang, X. - Li, X.
Journal: J Theor Biol

The identification of molecular targets is a critical step in the drug discovery and development process. Ion channel proteins represent highly attractive drug targets implicated in a diverse range of disorders, in particular in the cardiovascular and central nervous systems. Due to the limits of experimental technique and low-throughput nature of patch-clamp electrophysiology, they remain a target class waiting to be exploited. In our study, we combined three types of protein features, primary sequence, secondary structure and subcellular localization to predict potential drug targets from ion channel proteins applying classical support vector machine (SVM) method. In addition, our prediction comprised two stages. In stage 1, we predicted ion channel target proteins based on whole-genome target protein characteristics. Firstly, we performed feature selection by Mann-Whitney U test, then made predictions to identify potential ion channel targets by SVM and designed a new evaluating indicator Q to prioritize results. In stage 2, we made a prediction based on known ion channel target protein characteristics. Genetic algorithm was used to select features and SVM was used to predict ion channel targets. Then, we integrated results of two stages, and found that five ion channel proteins appeared in both prediction results including CGMP-gated cation channel beta subunit and Gamma-aminobutyric acid receptor subunit alpha-5, etc., and four of which were relative to some nerve diseases. It suggests that these five proteins are potential targets for drug discovery and our prediction strategies are effective.

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The impact of non-lethal synergists on the population and evolutionary dynamics of host-pathogen interactions.

Publication Date: 2010 Feb 21 PMID: 19900467
Authors: Bonsall, M. B.
Journal: J Theor Biol

Multiple pathogenic infections can influence disease transmission and virulence, and have important consequences for understanding the community ecology and epidemiology of host-pathogen interactions. Here the population and evolutionary dynamics of a host-pathogen interaction with free-living stages are explored in the presence of a non-lethal synergist that hosts must tolerate. Through the coupled effects on pathogen transmission, host mass gain and allometry it is shown how investing in tolerance to a non-lethal synergist can lead to a broad range of different population dynamics. The effects of the synergist on pathogen fitness are explored through a series of life-history trait trade-offs. Coupling trade-offs between pathogen yield and pathogen speed of kill and the presence of a synergist favour parasites that have faster speeds of kill. This evolutionary change in pathogen characteristics is predicted to lead to stable population dynamics. Evolutionary analysis of tolerance of the synergist (strength of synergy) and lethal pathogen yield show that decreasing tolerance allows alternative pathogen strategies to invade and replace extant strategies. This evolutionary change is likely to destabilize the host-pathogen interaction leading to population cycles. Correlated trait effects between speed of kill and tolerance (strength of synergy) show how these traits can interact to affect the potential for the coexistence of multiple pathogen strategies. Understanding the consequences of these evolutionary relationships is important for the both the evolutionary and population dynamics of host-pathogen interactions.

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Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission.

Publication Date: 2010 Feb 21 PMID: 19900466
Authors: Mbah, M. L. - Gilligan, C. A.
Journal: J Theor Biol

There is growing interest in incorporating economic factors into epidemiological models in order to identify optimal strategies for disease control when resources are limited. In this paper we consider how to optimize the control of a pathogen that is capable of infecting multiple hosts with different rates of transmission within and between species. Our objective is to find control strategies that maximize the discounted number of healthy individuals. We consider two classes of host-pathogen system, comprising two host species and a common pathogen, one with asymmetrical and the other with symmetrical transmission rates, applicable to a wide range of SI (susceptible-infected) epidemics of plant and animal pathogens. We motivate the analyses with an example of sudden oak death in California coastal forests, caused by Phytophthora ramorum, in communities dominated by bay laurel (Umbellularia californica) and tanoak (Lithocarpus densiflorus). We show for the asymmetric case that it is optimal to give priority in treating disease to the more infectious species, and to treat the other species only when there are resources left over. For the symmetric case, we show that although a switching strategy is an optimum, in which preference is first given to the species with the lower level of susceptibles and then to the species with the higher level of susceptibles, a simpler strategy that favors treatment of infected hosts for the more susceptible species is a robust alternative for practical application when the optimal switching time is unknown. Finally, since transmission rates are notoriously difficult to estimate, we analyze the robustness of the strategies when the true state with respect to symmetry or otherwise is unknown but one or other is assumed.

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Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer.

Publication Date: 2010 Mar 7 PMID: 19896955
Authors: Ryabov, A. B. - Rudolf, L. - Blasius, B.
Journal: J Theor Biol

The vertical distribution of phytoplankton is of fundamental importance for the dynamics and structure of aquatic communities. Here, using an advection-reaction-diffusion model, we investigate the distribution and competition of phytoplankton species in a water column, in which inverse resource gradients of light and a nutrient can limit growth of the biomass. This problem poses a challenge for ecologists, as the location of a production layer is not fixed, but rather depends on many internal parameters and environmental factors. In particular, we study the influence of an upper mixed layer (UML) in this system and show that it leads to a variety of dynamic effects: (i) Our model predicts alternative density profiles with a maximum of biomass either within or below the UML, thereby the system may be bistable or the relaxation from an unstable state may require a long-lasting transition. (ii) Reduced mixing in the deep layer can induce oscillations of the biomass; we show that a UML can sustain these oscillations even if the diffusivity is less than the critical mixing for a sinking phytoplankton population. (iii) A UML can strongly modify the outcome of competition between different phytoplankton species, yielding bistability both in the spatial distribution and in the species composition. (iv) A light limited species can obtain a competitive advantage if the diffusivity in the deep layers is reduced below a critical value. This yields a subtle competitive exclusion effect, where the oscillatory states in the deep layers are displaced by steady solutions in the UML. Finally, we present a novel graphical approach for deducing the competition outcome and for the analysis of the role of a UML in aquatic systems.

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A mixed two-stage method for detecting interactions in genomewide association studies.

Publication Date: 2010 Feb 21 PMID: 19896954
Authors: Zuo, Y. - Kang, G.
Journal: J Theor Biol

Genomewide association studies (GWAS) are being conducted to unravel the genetic etiology of complex diseases, in which complex epistasis may play an important role. One-stage method in which interactions are tested using all samples at one time may be computationally problematic, may have low power as the number of markers tested increases and may not be cost-efficient. A common two-stage method may be a reasonable and powerful approach for detecting interacting genes using all samples in both two stages. In this study, we introduce an alternative two-stage method, in which some promising markers are selected using a proportion of samples in the first stage and interactions are then tested using the remaining samples in the second stage. This two-stage method is called mixed two-stage method. We then investigate the power of both one-stage method and mixed two-stage method to detect interacting disease loci for a range of two-locus epistatic models in a case-control study design. Our results suggest that mixed two-stage method may be more powerful than one-stage method if we choose about 30% of samples for single-locus tests in the first stage, and identify less than and equal to 1% of markers for follow-up interaction tests. In addition, we compare both two-stage methods and find that our two-stage method will lose power because we only use part of samples in both two stages.

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Modeling the vestibular evoked myogenic potential.

Publication Date: 2010 Mar 7 PMID: 19896953
Authors: Lutkenhoner, B. - Stoll, W. - Basel, T.
Journal: J Theor Biol

Measuring the vestibular evoked myogenic potential (VEMP) promises to become a routine method for assessing vestibular function, although the technique is not yet standardized. To overcome the problem that the VEMP amplitude depends not only on the inhibition triggered by the acoustic stimulation of the vestibular end organs in the inner ear, but also on the tone of the muscle from which the potential is recorded, the VEMP is often normalized by dividing through a measure of the electromyogram (EMG) activity. The underlying idea is that VEMP amplitude and EMG activity are proportional. But this would imply that the muscle tone is irrelevant for a successful VEMP recording, contradicting experimental evidence. Here, an analytical model is presented that allows to resolve the contradiction. The EMG is modeled as the sum of motor unit action potentials (MUAPs). A brief inhibition can be characterized by its equivalent rectangular duration (ERD), irrespective of the actual time course of the inhibition. The VEMP resembles a polarity-inverted MUAP under such circumstances. Its amplitude is proportional to both the ERD and the MUAP rate. The EMG activity, by contrast, is proportional to the square root of the MUAP rate. Thus, the normalized VEMP still depends on the muscle tone. To avoid confounding effects of the muscle tone, the standard deviation of the EMG could be considered. But the inhibition effect on the standard deviation is small so that the measuring time would have to be much longer than usual today.

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A quantitative theoretical model for the development of malignancy in ductal carcinoma in situ.

Publication Date: 2010 Feb 21 PMID: 19887072
Authors: Silva, A. S. - Gatenby, R. A. - Gillies, R. J. - Yunes, J. A.
Journal: J Theor Biol

Mathematical models and clinical observations have demonstrated that microenvironmental hypoxia and acidosis are important selection factors during the later stages of the somatic evolution of breast cancer. The consequent promotion of constitutive upregulation of glycolysis and resistance to acid-induced cellular toxicity is hypothesized to be critical for the ability of cancer cells to invade host tissue. In this work we developed a 3D fixed lattice cellular automata model to study the role of these two phenotypes in determining morphology and the potential for invasion of ductal carcinoma in situ (DCIS), which in this work is defined as the erosion of a healthy epithelial cell layer and direct contact with the basement membrane. The model was conceived as a 40-cell wide epithelial duct surrounded by blood vessels and composed of a basement membrane and one internal layer of epithelial cells. Our results show that an increment in the order of 8-fold in glucose metabolism and an increase in acid resistance corresponding to pH thresholds of approximately 6.8 and 6.45 for quiescence and death, respectively, are required for the tumor to breach through the layer of healthy epithelial cells and reach the basement membrane as a first step for invasion. Our model also suggests correlations between classic morphologies and different values of hyperglycolytic and acid-resistant phenotypes, indicating that immunohistochemistry studies targeting these genes may improve the predictive power of morphological analyses of biopsies.

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Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage.

Publication Date: 2010 Feb 21 PMID: 19883664
Authors: Callender, H. L. - Horn, M. A. - DeCamp, D. L. - Sternweis, P. C. - Alex Brown, H.
Journal: J Theor Biol

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y(6) receptors activated by the ubiquitous signaling nucleotide uridine 5'-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5'-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

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Elastic energy storage in an unmineralized collagen type I molecular model with explicit solvation and water infiltration.

Publication Date: 2010 Feb 21 PMID: 19878687
Authors: Kwansa, A. L. - Freeman, J. W.
Journal: J Theor Biol

Collagen type I is a structural protein that provides tensile strength to tendons and ligaments. Type I collagen molecules form collagen fibers, which are viscoelastic and can therefore store energy elastically via molecular elongation and dissipate viscous energy through molecular rearrangement and fibrillar slippage. The ability to store elastic energy is important for the resiliency of tendons and ligaments, which must be able to deform and revert to their initial lengths with changes in load. In an earlier paper by one of the present authors, molecular modeling was used to investigate the role of mineralization upon elastic energy storage in collagen type I. Their collagen model showed a similar trend to their experimental data but with an over-estimation of elastic energy storage. Their simulations were conducted in vacuum and employed a distance-dependent dielectric function. In this study, we performed a re-evaluation of Freeman and Silver's model data incorporating the effects of explicit solvation and water infiltration, in order to determine whether the model data could be improved with a more accurate representation of the solvent and osmotic effects. We observed an average decrease in the model's elastic energy storage of 45.1%+/-6.9% in closer proximity to Freeman and Silver's experimental data. This suggests that although the distance-dependent dielectric implicit solvation approach was favored for its increased speed and decreased computational requirements, an explicit representation of water may be necessary to more accurately model solvent interactions in this particular system. In this paper, we discuss the collagen model described by Freeman and Silver, the present model building approach, the application of the present model to that of Freeman and Silver, and additional assumptions and limitations.

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Modeling the role of IL-2 in the interplay between CD4+ helper and regulatory T cells: assessing general dynamical properties.

Publication Date: 2010 Feb 21 PMID: 19878686
Authors: Garcia-Martinez, K. - Leon, K.
Journal: J Theor Biol

Mathematical models accounting for well-known evidences relating to the dynamics of interleukin 2, helper and regulatory T cells are presented. These models extend an existent model (the so-called cross-regulation model of immunity), by assuming IL-2 as the growth factor produced by helper cells, but used by both helper and regulatory cells to proliferate and survive. Two model variants, motivated by current literature, are explored. The first variant assumes that regulatory cells suppress helper cells by limiting IL-2 production and consuming the available IL-2; i.e. they just trigger competition for IL-2. The second model variant adds to the latter competitive mechanism the direct inhibition of helper cells activation by regulatory cells. The extended models retain key dynamical features of the cross-regulation model. But such reasonable behavior depends on parameter constraints, which happen to be realistic and lead to interesting biological discussions. Furthermore, the introduction of IL-2 in these models breaks the local/specific character of interactions, providing new properties to them. In the extended models, but not in the cross-regulation model, the response triggered by an antigen affects the response to other antigens in the same lymph node. The first model variant predicts an unrealistic coupling of the immune reactions to all the antigens in the lymph node. In contrast, the second model variant allows the coexistent of concomitant tolerant and immune responses to different antigens. The IL-2 derived from an ongoing immune reaction reinforces tolerance to other antigens in the same lymph node. Overall the models introduced here are useful extensions of the cross-regulation formalism. In particular, they might allow future studies of the effect of different IL-2 modulation therapies on CD4+ T cell dynamics.

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The expression of the skeletal muscle force-length relationship in vivo: a simulation study.

Publication Date: 2010 Feb 21 PMID: 19878685
Authors: Winter, S. L. - Challis, J. H.
Journal: J Theor Biol

The force-length relationship is one of the most important mechanical characteristics of skeletal muscle in humans and animals. For a physiologically realistic joint range of motion and therefore range of muscle fibre lengths only part of the force-length curve may be used in vivo, i.e. only a section of the force-length curve is expressed. A generalised model of a mono-articular muscle-tendon complex was used to examine the effect of various muscle architecture parameters on the expressed section of the force-length relationship for a 90 degrees joint range of motion. The parameters investigated were: the ratio of tendon resting length to muscle fibre optimum length (L(TR):L(F.OPT)) (varied from 0.5 to 11.5), the ratio of muscle fibre optimum length to average moment arm (L(F.OPT):r) (varied from 0.5 to 5), the normalised tendon strain at maximum isometric force (c) (varied from 0 to 0.08), the muscle fibre pennation angle (theta) (varied from 0 degrees to 45 degrees) and the joint angle at which the optimum muscle fibre length occurred (phi). The range of values chosen for each parameter was based on values reported in the literature for five human mono-articular muscles with different functional roles. The ratios L(TR):L(F.OPT) and L(F.OPT):r were important in determining the amount of variability in the expressed section of the force-length relationship. The modelled muscle operated over only one limb at intermediate values of these two ratios (L(TR):L(F.OPT)=5; L(F.OPT):r=3), whether this was the ascending or descending limb was determined by the precise values of the other parameters. It was concluded that inter-individual variability in the expressed section of the force-length relationship is possible, particularly for muscles with intermediate values of L(TR):L(F.OPT) and L(F.OPT):r such as the brachialis and vastus lateralis. Understanding the potential for inter-individual variability in the expressed section is important when using muscle models to simulate movement.

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Successional state dynamics: a novel approach to modeling nonequilibrium foodweb dynamics.

Publication Date: 2010 Feb 21 PMID: 19861131
Authors: Klausmeier, C. A.
Journal: J Theor Biol

Communities and ecosystems are often far from equilibrium, but our understanding of nonequilibrium dynamics has been hampered by a paucity of analytical tools. Here I describe a novel approach to modeling seasonally forced food webs, called "successional state dynamics" (SSD). It is applicable to communities where species dynamics are fast relative to the external forcing, such as plankton and other microbes, diseases, and some insect communities. The approach treats succession as a series of state transitions driven by both the internal dynamics of species interactions and external forcing. First, I motivate the approach with numerical solutions of a seasonally forced predator-prey model. Second, I describe how to set up and analyze an SSD model. Finally, I apply the techniques to three additional models of two-species interactions: resource competition (r-K selection), facilitation, and flip-flop competition (where the competitive hierarchy alternates over time). This approach allows easy and thorough exploration of how dynamics depend on the environmental forcing regime, and uncovers unexpected phenomena such as multiple stable annual trajectories and year-to-year irregularity in successional trajectories (chaos).

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Identifying translation initiation sites in prokaryotes using support vector machine.

Publication Date: 2010 Feb 21 PMID: 19840808
Authors: Gao, T. - Yang, Z. - Wang, Y. - Jing, L.
Journal: J Theor Biol

MOTIVATION: Gene identification in genomes has been a fundamental and long-standing task in bioinformatics and computational biology. Many computational methods have been developed to predict genes in prokaryote genomes by identifying translation initiation site (TIS) in transcript data. However, the pseudo-TISs at the genome level make these methods suffer from a high number of false positive predictions. In addition, most of the existing tools use an unsupervised learning framework, whose predictive accuracy may depend on the choice of specific organism. RESULTS: In this paper, we present a supervised learning method, support vector machine (SVM), to identify translation initiation site at the genome level. The features are extracted from the sequence data by modeling the sequence segment around predicted TISs as a position specific weight matrix (PSWM). We train the parameters of our SVM through well constructed positive and negative TIS datasets. Then we apply the method to recognize translation initiation sites in E. coli, B. subtilis, and validate our method on two GC-rich bacteria genomes: Pseudomonas aeruginosa and Burkholderia pseudomallei K96243. We show that translation initiation sites can be recognized accurately at the genome level by our method, irrespective of their GC content. Furthermore, we compare our method with four existing methods and demonstrate that our method outperform these methods by obtaining better performance in all the four organisms.

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Accounting for mating pair formation in plasmid population dynamics.

Publication Date: 2010 Feb 21 PMID: 19835890
Authors: Zhong, X. - Krol, J. E. - Top, E. M. - Krone, S. M.
Journal: J Theor Biol

Plasmids are important vehicles for horizontal gene transfer and rapid adaptation in bacteria, including the spread of antibiotic resistance genes. Conjugative transfer of a plasmid from a plasmid-bearing to a plasmid-free bacterial cell requires contact and attachment of the cells followed by plasmid DNA transfer prior to detachment. We introduce a system of differential equations for plasmid transfer in well-mixed populations that accounts for attachment, DNA transfer, and detachment dynamics. These equations offer advantages over classical mass-action models that combine these three processes into a single "bulk" conjugation rate. By decomposing the process of plasmid transfer into its constituent parts, this new model provides a framework that facilitates meaningful comparisons of plasmid transfer rates in surface and liquid environments. The model also allows one to account for experimental and environmental effects such as mixing intensity. To test the adequacy of the model and further explore the effects of mixing on plasmid transfer, we performed batch culture experiments using three different plasmids and a range of different mixing intensities. The results show that plasmid transfer is optimized at low to moderate shaking speeds and that vigorous shaking negatively affects plasmid transfer. Using reasonable assumptions on attachment and detachment rates, the mathematical model predicts the same behavior.

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Effect of lethality on the extinction and on the error threshold of quasispecies.

Publication Date: 2010 Feb 21 PMID: 19833133
Authors: Tejero, H. - Marin, A. - Montero, F.
Journal: J Theor Biol

In this paper the effect of lethality on error threshold and extinction has been studied in a population of error-prone self-replicating molecules. For given lethality and a simple fitness landscape, three dynamic regimes can be obtained: quasispecies, error catastrophe, and extinction. Using a simple model in which molecules are classified as master, lethal and non-lethal mutants, it is possible to obtain the mutation rates of the transitions between the three regimes analytically. The numerical resolution of the extended model, in which molecules are classified depending on their Hamming distance to the master sequence, confirms the results obtained in the simple model and shows how an error catastrophe regime changes when lethality is taken in account.

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Viruses are essential agents within the roots and stem of the tree of life.

Publication Date: 2010 Feb 21 PMID: 19833132
Authors: Villarreal, L. P. - Witzany, G.
Journal: J Theor Biol

In contrast with former definitions of life limited to membrane-bound cellular life forms which feed, grow, metabolise and replicate (i) a role of viruses as genetic symbionts, (ii) along with peripheral phenomena such as cryptobiosis and (iii) the horizontal nature of genetic information acquisition and processing broaden our view of the tree of life. Some researchers insist on the traditional textbook conviction of what is part of the community of life. In a recent review [Moreira, D., Lopez-Garcia, P., 2009. Ten reasons to exclude viruses from the tree of life. Nat. Rev. Microbiol. 7, 306-311.] they assemble four main arguments which should exclude viruses from the tree of life because of their inability to self-sustain and self-replicate, their polyphyly, the cellular origin of their cell-like genes and the volatility of their genomes. In this article we will show that these features are not coherent with current knowledge about viruses but that viral agents play key roles within the roots and stem of the tree of life.

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Mate choice and optimal search behavior: fitness returns under the fixed sample and sequential search strategies.

Publication Date: 2010 Feb 21 PMID: 19825377
Authors: Wiegmann, D. D. - Seubert, S. M. - Wade, G. A.
Journal: J Theor Biol

The behavior of a female in search of a mate determines the likelihood that she encounters a high-quality male in the search process. The fixed sample (best-of-n) search strategy and the sequential search (fixed threshold) strategy are two prominent models of search behavior. The sequential search strategy dominates the former strategy--yields an equal or higher expected net fitness return to searchers--when search costs are nontrivial and the distribution of quality among prospective mates is uniform or truncated normal. In this paper our objective is to determine whether there are any search costs or distributions of male quality for which the sequential search strategy is inferior to the fixed sample search strategy. The two search strategies are derived under general conditions in which females evaluate encountered males by inspection of an indicator character that has some functional relationship to male quality. The solutions are identical to the original models when the inspected male attribute is itself male quality. The sequential search strategy is shown to dominate the fixed sample search strategy for all search costs and distributions of male quality. Low search costs have been implicated to explain empirical observations that are consistent with the use of a fixed sample search strategy, but under conditions in which the original models were derived there is no search cost or distribution of male quality that favors the fixed sample search strategy. Plausible alternative explanations for the apparent use of this search strategy are discussed.

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Background evolution in camouflage systems: a predator-prey/pollinator-flower game.

Publication Date: 2010 Feb 21 PMID: 19747925
Authors: Abbott, K. R.
Journal: J Theor Biol

A common predator or anti-predator strategy involves camouflage based on background matching. In some systems, the background is an organism whose fitness is affected by the predator-prey interaction. In these cases, the phenotype of the background species may evolve to affect the degree of background matching in the predator-prey interaction. For example, some flower species (the background) are inhabited by camouflaged ambush predators that attack visiting pollinators. These flowers have a fitness interest in the outcome of the predator-prey interaction because flowers depend on pollinator visitations for reproduction. Therefore, floral colour might evolve relative to predator colour so as to influence the detectability of resident predators. I have created a three-player game, based on Signal Detection Theory, to model the co-evolution of predator and prey/pollinator behavioural strategies with floral colour. This model makes two general predictions: (1) Constraints on predator distributions favour the evolution of flowers that match the predators' colour because they prevent predators from overexploiting these flowers; (2) factors that produce less discriminating pollinators also favour the evolution of flowers that match the predators' colour because these pollinators are willing to land on these flowers even if the safety of the flower is in doubt.

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