Journal of theoretical Biology

The limitations of scaling laws in the prediction of performance in endurance events.

Publication Date: 2012 Jan 26 PMID: 22300800
Authors: Garcia-Manso, J. M. - Martin-Gonzalez, J. M. - Vaamonde, D. - Da Silva-Grigoletto, M. E.
Journal: J Theor Biol

In the twentieth century, scientists have examined running speed over various distances, analyzing world records and studying the ability of an athlete to sustain a given speed. Assuming that running speed expresses the response of a non-linear multisystemic behavior, the relationship between these two variables (distance vs. velocity) can therefore be evaluated by applying scaling laws that fulfill the key principles of specificity and individuality of each athlete, yet responding to bioenergetic and functional patterns that are well-known to sports physiology. Since speed loss as distance increases exhibits fractal behavior, with small changes in the speed-reduction curve due to the effect of fatigue, it must be recognized that no universal scaling law can account, with acceptable precision, for the effect exerted by fatigue on potential speed at any given moment in a race. Power laws using a range of scaling exponents provide technical staff and athletes with a reliable, non-invasive tool for planning of training schedules, predicting athletes' performances over various distances and comparing the performance of specialists in different track events. The equations for the scaling laws for the distances investigated here were: V(1500)=15.00xD(-0.10) (R(2)=0.99); V(3000)=12.76xD(-0.08) (R(2)=0.99); V(5000)=11.55xD(-0.07) (R(2)=0.99); V(10,000)=11.59xD(-0.07) (R(2)=0.99); V(21,095)=10.78xD(-0.06) (R(2)=0.97); V(42,175)=10.27xD(-0.057) (R(2)=0.99).

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Impact of endothelium roughness on blood flow.

Publication Date: 2012 Jan 26 PMID: 22300799
Authors: Park, S. - Intaglietta, M. - Tartakovsky, D. M.
Journal: J Theor Biol

Cell free layer (CFL), a plasma layer bounded by the red blood cell (RBC) core and the endothelium, plays an important physiological role. Its width affects the effective blood viscosity as well as the scavenging and production of nitric oxide (NO). Measurements of the CFL and its spatio-temporal variability are highly uncertain, exhibiting random fluctuations. Yet traditional models of blood flow and NO scavenging treat the CFL's bounding surfaces as deterministic and smooth. We investigate the effects of the endothelium roughness and uncertain (random) spatial variability on blood flow and the estimates of effective blood viscosity.

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Economic analysis of the use of facemasks during pandemic (H1N1) 2009.

Publication Date: 2012 Jan 28 PMID: 22300798
Authors: Tracht, S. M. - Del Valle, S. Y. - Edwards, B. K.
Journal: J Theor Biol

A large-scale pandemic could cause severe health, social, and economic impacts. The recent 2009 H1N1 pandemic confirmed the need for mitigation strategies that are cost-effective and easy to implement. Typically, in the early stages of a pandemic, as seen with pandemic (H1N1) 2009, vaccines and antivirals may be limited or non-existent, resulting in the need for non-pharmaceutical strategies to reduce the spread of disease and the economic impact. We construct and analyze a mathematical model for a population comprised of three different age groups and assume that some individuals wear facemasks. We then quantify the impact facemasks could have had on the spread of pandemic (H1N1) 2009 and examine their cost effectiveness. Our analyses show that an unmitigated pandemic could result in losses of nearly $832billion in the United States during the length of the pandemic. Based on present value of future earnings, hospital costs, and lost income estimates due to illness, this study estimates that the use of facemasks by 10%, 25%, and 50% of the population could reduce economic losses by $478billion, $570billion, and $573billion, respectively. The results show that facemasks can significantly reduce the number of influenza cases as well as the economic losses due to a pandemic.

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A heuristic approach to RNA-RNA interaction prediction.

Publication Date: 2012 Jan 26 PMID: 22300797
Authors: Montaseri, S. - Charkari, N. M. - Mirakabad, F. Z.
Journal: J Theor Biol

RNA-RNA interaction is used in many biological processes such as gene expression regulation. In this process, an RNA molecule prohibits the translation of another RNA molecule by establishing stable interactions with it. In this regard, some algorithms have been formed to predict the structure of the interaction between two RNA molecules. One common pitfall in the most algorithms is their high computational time. In this paper, we introduce a novel algorithm called TIRNA to accurately predict the secondary structure between two RNA molecules based on minimum free energy (MFE). The algorithm is stand on a heuristic approach which employs some dot matrices for finding the secondary structure of each RNA and between two RNAs. The proposed algorithm has been performed on some standard datasets such as CopA-CopT, R1inv-R2inv, Tar-Tar(), DIS-DIS and IncRNA(54)-RepZ in the Escherichia coli bacteria. The time and space complexity of the algorithm are 0(k(2)logk(2)) and 0(k(2)), respectively, where k indicates the sum of the length of two RNAs. The experimental results show the high validity and efficiency of the TIRNA.

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Colored petri nets to model gene mutation and amino acids classification.

Publication Date: 2012 Jan 26 PMID: 22289261
Authors: Yang, J. - Gao, R. - Meng, M. Q. - Tarn, T. J.
Journal: J Theor Biol

The genetic code is the triplet code based on the three-letter codons, which determines the specific amino acid sequences in proteins synthesis. Choosing an appropriate model for processing these codons is a useful method to study genetic processes in Molecular Biology. As an effective modeling tool of discrete event dynamic systems (DEDS), colored petri net (CPN) has been used for modeling several biological systems, such as metabolic pathways and genetic regulatory networks. According to the genetic code table, CPN is employed to model the process of genetic information transmission. In this paper, we propose a CPN model of amino acids classification, and further present the improved CPN model. Based on the model mentioned above, we give another CPN model to classify the type of gene mutations via contrasting the bases of DNA strands and the codons of amino acids along the polypeptide chain. This model is helpful in determining whether a certain gene mutation will cause the changes of the structures and functions of protein molecules. The effectiveness and accuracy of the presented model are illustrated by the examples in this paper.

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The core control system of intracellular iron homeostasis: A mathematical model.

Publication Date: 2012 Jan 23 PMID: 22286016
Authors: Chifman, J. - Kniss, A. - Neupane, P. - Williams, I. - Leung, B. - Deng, Z. - Mendes, P. - Hower, V. - Torti, F. M. - Akman, S. A. - Torti, S. V. - Laubenbacher, R.
Journal: J Theor Biol

Iron is a metal essential for cellular metabolism. However, excess iron available for reactions contributes to the formation of dangerous reactive oxygen species, such as the hydroxyl radical, via the Fenton reaction. Therefore, intracellular iron levels are tightly constrained by a control system of proteins. This paper contains a mathematical model, in the form of a system of five ordinary differential equations, of the core of this control system, including the labile iron pool as well as proteins that regulate uptake, storage, and export and are connected through negative feedback loops. The model is validated using data from an overexpression experiment with cultured human breast epithelial cells. The parameters in the mathematical model are not known for this particular cell culture system, so the analysis of the model was done for a generic choice of parameters. Through a mixture of analytical arguments and extensive simulations it is shown that for any choice of parameters the model reaches a unique stable steady state, thereby ruling out oscillatory behavior. It is shown furthermore that the model parameters are identifiable through suitable experiments.

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A compartmentalization model of hepatitis C virus replication: An appropriate distribution of HCV RNA for the effective replication.

Publication Date: 2012 Jan 23 PMID: 22286015
Authors: Nakabayashi, J.
Journal: J Theor Biol

Hepatitis C virus (HCV) infection is a major cause of liver disease. Ten to twenty percent of chronic hepatitis C will develop complications of chronic liver diseases such as liver cirrhosis and hepatocellular carcinoma. The culture system of HCV is established by the specific combination between HCV strain and a host cell. Some chimeras substituting core to NS2 into the analogous region of JFH1 strain fail to effectively replicate. Core to NS2 of HCV gene mainly encodes the structural protein of HCV virion and contributes to the virion assembly, while other regions mainly contribute to the genome replication. The balance between the virion assembly and the genome replication of chimera may differ from that of reference strain. We construct a mathematical model of the whole replication process of HCV in single infected cell. It is revealed by this model that there are two replication patterns of HCV, explosive and arrested replication. In the explosive replication, HCV can continue to exponentially reproduce its progeny. The explosive replication is caused by the effect of the positive feedback in the replication cycle. On the other hand, in the arrested replication, the replication is stalled after sufficiently long time has passed from the infection because of the depletion of the genome RNA of HCV. To avoid the arrest of replication, HCV RNA must be appropriately distributed to three distinct functions as a template for the genome replication, as a template for the translation of viral proteins and as a component of the viral particle. When the genome replication and the translation of viral proteins precede to the virion assembly, HCV can effectively replicate by explosive replication. It is suggested that some chimeras of HCV fail to effectively replicate because of the inappropriate distribution of HCV RNA to these functions.

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Effects of anti-predator defence through toxin sequestration on use of alternative food microhabitats by small herbivores.

Publication Date: 2012 Jan 24 PMID: 22285787
Authors: Higginson, A. D. - Speed, M. P. - Ruxton, G. D.
Journal: J Theor Biol

Many invertebrate herbivores sequester plant toxins from their food, and the availability of toxins and the costs and benefits of sequestering toxins may influence food patch choice. In many plants, young leaves contain higher concentrations of toxins than old leaves and so can be preferred by sequestering herbivores, even if herbivores are more readily detected by predators when on them. We modelled patch use and sequestration strategies for the growth period of herbivores, assuming that the effectiveness of a toxin against predators is positively related to its cost of sequestration and that high-reward patches have higher predation risk. We show that the empirically commonly-observed strategy of moving from a low-reward patch to a high-reward patch can be optimal in a range of circumstances, but especially those that are common in nature. Body size when herbivores are predicted to switch increases with increasing size of maturation under most conditions, whilst use of the high-reward patch increases. Our predictions about how the proportion of time spent in the high-reward patch changes with the distribution and potency of toxins indicate a reason for plant toxins to be relatively mild. We provide further testable predictions about the role of the plant's defence strategy and herbivore behaviour in tritrophic interactions.

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Modulation of T cell activation by localized K(+) accumulation at the immunological synapse-A mathematical model.

Publication Date: 2012 Jan 23 PMID: 22285786
Authors: Martin, G. V. - Yun, Y. H. - Conforti, L.
Journal: J Theor Biol

The response of T cells to antigens (T cell activation) is marked by an increase in intracellular Ca(2+) levels. Voltage-gated and Ca(2+)-dependent K(+) channels control the membrane potential of human T cells and regulate Ca(2+)influx. This regulation is dependent on proper accumulation of K(+) channels at the immunological synapse (IS) a signaling zone that forms between a T cell and antigen presenting cell. It is believed that the IS provides a site for regulation of the activation response and that K(+) channel inhibition occurs at the IS, but the underlying mechanisms are unknown. A mathematical model was developed to test whether K(+) efflux through K(+) channels leads to an accumulation of K(+) in the IS cleft, ultimately reducing K(+) channel function and intracellular Ca(2+) concentration ([Ca(2+)](i)). Simulations were conducted in models of resting and activated T cell subsets, which express different levels of K(+) channels, by varying the K(+) diffusion constant and the spatial localization of K(+) channels at the IS. K(+) accumulation in the IS cleft was calculated to increase K(+) concentration ([K(+)]) from its normal value of 5.0mM to 5.2-10.0mM. Including K(+) accumulation in the model of the IS reduced calculated K(+) current by 1-12% and consequently, reduced calculated [Ca(2+)](i) by 1-28%. Significant reductions in K(+) current and [Ca(2+)](i) only occurred in activated T cell simulations when most K(+) channels were centrally clustered at the IS. The results presented show that the localization of K(+) channels at the IS can produce a rise in [K(+)] in the IS cleft and lead to a substantial decrease in K(+) currents and [Ca(2+)](i) in activated T cells thus providing a feedback inhibitory mechanism during T cell activation.

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Front dynamics in a two-species competition model driven by Levy flights.

Publication Date: 2012 Jan 23 PMID: 22285785
Authors: Hanert, E.
Journal: J Theor Biol

A number of recent studies suggest that many biological species follow a Levy random walk in their search for food. Such a strategy has been shown to be more efficient than classical Brownian motion when resources are scarce. However, current diffusion-reaction models used to describe many ecological systems do not account for the superdiffusive spread of populations due to Levy flights. We have developed a model to simulate the spatial spread of two species competing for the same resources and driven by Levy flights. The model is based on the Lotka-Volterra equations and has been obtained by replacing the second-order diffusion operator by a fractional-order one. Consistent with previous known results, theoretical developments and numerical simulations show that fractional-order diffusion leads to an exponential acceleration of the population fronts and a power-law decay of the fronts' leading tail. Depending on the skewness of the fractional derivative, we derive catch-up conditions for different types of fronts. Our results indicate that second-order diffusion-reaction models are not well-suited to simulate the spatial spread of biological species that follow a Levy random walk as they are inclined to underestimate the speed at which these species propagate.

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Cargo distributions differentiate pathological axonal transport impairments.

Publication Date: 2012 Jan 25 PMID: 22285784
Authors: Mitchell, C. S. - Lee, R. H.
Journal: J Theor Biol

Axonal transport is an essential process in neurons, analogous to shipping goods, by which energetic and cellular building supplies are carried downstream (anterogradely) and wastes are carried upstream (retrogradely) by molecular motors, which act as cargo porters. Impairments in axonal transport have been linked to devastating and often lethal neurodegenerative diseases, such as Amyotrophic Lateral Sclerosis, Huntington's, and Alzheimer's. Axonal transport impairment types include a decrease in available motors for cargo transport (motor depletion), the presence of defective or non-functional motors (motor dilution), and the presence of increased or larger cargos (protein aggregation). An impediment to potential treatment identification has been the inability to determine what type(s) of axonal transport impairment candidates that could be present in a given disease. In this study, we utilize a computational model and common axonal transport experimental metrics to reveal the axonal transport impairment general characteristics or "signatures" that result from three general defect types of motor depletion, motor dilution, and protein aggregation. Our results not only provide a means to discern these general impairments types, they also reveal key dynamic and emergent features of axonal transport, which potentially underlie multiple impairment types. The identified characteristics, as well as the analytical method, can be used to help elucidate the axonal transport impairments observed in experimental and clinical data. For example, using the model-predicted defect signatures, we identify the defect candidates, which are most likely to be responsible for the axonal transport impairments in the G93A SOD1 mouse model of ALS.

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Mathematical modeling of monoclonal conversion in the colonic crypt.

Publication Date: 2012 Jan 23 PMID: 22285553
Authors: Fletcher, A. G. - Breward, C. J. - Jonathan Chapman, S.
Journal: J Theor Biol

A novel spatial multiscale model of a colonic crypt is described, which couples the cell cycle (including cell division) with the mechanics of cell movement. The model is used to investigate the process of monoclonal conversion under two hypotheses concerning stem cell behavior. Under the first hypothesis, 'stem-ness' is an intrinsic cell property, and the stem cell population is maintained through asymmetric division. Under the second hypothesis, the proliferative behavior of each cell is governed by its microenvironment through a biochemical signalling cue, and all cell division is symmetric. Under each hypothesis, the model is used to run virtual experiments, in which a harmless labeling mutation is bestowed upon a single cell in the crypt and the mutant clonal population is tracked over time to check if and when the crypt becomes monoclonal. It is shown that under the first hypothesis, a stable structured cell population is not possible without some form of population-dependent feedback; in contrast, under the second hypothesis, a stable crypt architecture arises naturally. Through comparison with an existing spatial crypt model and a non-spatial stochastic population model, it is shown that the spatial structure of the crypt has a significant effect on the time scale over which a crypt becomes monoclonal.

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Turbulent particle transport in streams: Can exponential settling be reconciled with fluid mechanics?

Publication Date: 2012 Jan 21 PMID: 22281520
Authors: McNair, J. N. - Newbold, J. D.
Journal: J Theor Biol

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances.

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Evolving cooperation.

Publication Date: 2012 Jan 21 PMID: 22281519
Authors: Nowak, M. A.
Journal: J Theor Biol

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Self-organized spatial pattern determines biodiversity in spatial competition.

Publication Date: 2012 Jan 20 PMID: 22281518
Authors: Vandermeer, J. - Yitbarek, S.
Journal: J Theor Biol

In a simple cellular automata model it is shown that self-organization of spatial pattern in a community of strong competitors may generate a previously unrecognized mechanism of species richness determination. Employing some well-known general properties of interspecific competition, we elaborate a theoretical framework that generates both spatial mosaics and spiral waves within the same conceptual framework, dependent on the covariance of competition. We demonstrate that the qualitative nature of the spatial pattern depends on the "balance" of competition and that the number of species retained in the community depends on this spatial patterning.

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Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China.

Publication Date: 2012 Jan 20 PMID: 22273729
Authors: Hou, Q. - Jin, Z. - Ruan, S.
Journal: J Theor Biol

Rabies is a major public health problem in some developing countries including China. One of the reasons is that there is a very large number of dogs, both domestic and stray, especially in Guangdong Province which has the third most rabies cases (after Guangxi and Hunan) among the 31 provinces, autonomous regions and municipalities in Mainland China, and at least 18.2% of the human rabies cases are caused by stray dogs. In this paper, based on the reported data and characteristics of the rabies infection in Guangdong Province, we propose a mathematical model for the dog-human transmission of rabies. We first determine the basic reproduction number R(0) and discuss the stability of the disease-free equilibrium and persistence of the disease. By carrying out sensitivity analysis of the basic reproduction number in terms of some parameters, we find that the domestic dog vaccination rate, the recruitment rate of domestic dogs, and the quantity of stray dogs play important roles in the transmission of rabies. This study suggests that rabies control and prevention strategies should include public education and awareness about rabies, increase of the domestic dog vaccination rate and reduction of the stray dog population.

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Publication Date: 2012 Jan 20 PMID: 22269802
Authors: Andersen, M. S. - Rasmussen, J. - Damsgaard, M.
Journal: J Theor Biol

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Evolutionary dynamics in finite populations can explain the full range of cooperative behaviors observed in the centipede game.

Publication Date: 2012 Jan 14 PMID: 22266662
Authors: Rand, D. G. - Nowak, M. A.
Journal: J Theor Biol

Classical economic models make behavioral predictions based on the assumption that people are fully rational and care only about maximizing their own payoffs. Although this approach successfully explains human behavior in many situations, there is a wealth of experimental evidence demonstrating conditions where people deviate from the predictions of these models. One setting that has received particular attention is offered by fixed length repeated games. Iterating a social dilemma can promote cooperation through direct reciprocity, even if it is common knowledge that all players are rational and self-interested. However, this is not the case if the length of the game is known to the players. In the final round, a rational player will defect, because there is no future to be concerned with. But if you know the other player will defect in the last round, then you should defect in the second to last round, and so on. This logic of backwards induction leads to immediate defection as the only rational (sub-game perfect Nash equilibrium) strategy. When people actually play such games, however, immediate defection is rare. Here we use evolutionary dynamics in finite populations to study the centipede game, which is designed to explore this issue of backwards induction. We make the following observation: since full cooperation can risk-dominate immediate defection in the centipede game, stochastic evolutionary dynamics can favor both delayed defection and even full cooperation. Furthermore, our evolutionary model can quantitatively reproduce human behavior from two experiments by fitting a single free parameter, which is the product of population size and selection intensity. Thus we provide evidence that people's cooperative behavior in fixed length games, which is often called 'irrational', may in fact be the favored outcome of natural selection.

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Exact analysis of intrinsic qualitative features of phosphorelays using mathematical models.

Publication Date: 2012 Jan 13 PMID: 22266661
Authors: Knudsen, M. - Feliu, E. - Wiuf, C.
Journal: J Theor Biol

Phosphorelays are a class of signaling mechanisms used by cells to respond to changes in their environment. Phosphorelays (of which two-component systems constitute a special case) are particularly abundant in prokaryotes and have been shown to be involved in many fundamental processes such as stress response, osmotic regulation, virulence, and chemotaxis. We develop a general model of phosphorelays extending existing models of phosphorelays and two-component systems. We analyze the model analytically under the assumption of mass-action kinetics and prove that a phosphorelay has a unique stable steady-state. Furthermore, we derive explicit functions relating stimulus to the response in any layer of a phosphorelay and show that a limited degree of ultrasensitivity in the bottom layer of a phosphorelay is an intrinsic feature which does not depend on any reaction rates or substrate amounts. On the other hand, we show how adjusting reaction rates and substrate amounts may lead to higher degrees of ultrasensitivity in intermediate layers. The explicit formulas also enable us to prove how the response changes with alterations in stimulus, kinetic parameters, and substrate amounts. Aside from providing biological insight, the formulas may also be used to replace the time-consuming simulations in numerical analyses.

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Sonication-induced unfolding proteins.

Publication Date: 2012 Jan 12 PMID: 22266660
Authors: Stepanskiy, L. G.
Journal: J Theor Biol

The methodology of predicting sonication-induced unfolding proteins (SUP) is presented in this study. The methodology bases on: (a) simulation of SUP by the excessive deviations of protein domains in regime of damped forced vibrations caused by critical level of involved acoustic energy, which is associated with temperature rise and acoustic pressure; (b) simulation of stochasticity of SUP by failures in jobs service in the queueing system with Markovian fluxes. The assessments of probability of SUP accounting the complex of parameters of pulsed ultrasound, biophysical properties of tissue and macromolecular crowding of insonated zone of tissue are considered.

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Non-random spatial coupling induces desynchronization, chaos and multistability in a predator-prey-resource system.

Publication Date: 2012 Jan 18 PMID: 22266124
Authors: Suzuki, K. - Yoshida, T.
Journal: J Theor Biol

The metacommunity perspective has attracted much attention recently, but the understanding of how dispersal between local communities alters their ecological dynamics is still limited, especially regarding the effect of non-random, unequal dispersal of organisms. This is a study of a three-trophic-level (predator-prey-resource) system that is connected by different manners of dispersal. The model is based on a well-studied experimental system cultured in chemostats (continuous flow-through culture), which consists of rotifer predator, algal prey and nutrient. In the model, nutrient dispersal can give rise to multistability when the two systems are connected by nutrient dispersal, whereas three-trophic-level systems tend to show a rich dynamical behavior, e.g. antisynchronous or asynchronous oscillations including chaos. Although the existence of multistability was already known in two-trophic-level (predator-prey) systems, it was confined to a small range of dispersal rate. In contrast, the multistability in the three-trophic-level system is found in a broader range of dispersal rate. The results suggest that, in three-trophic-level systems, the dispersal of nutrient not only alters population dynamics of local systems but can also cause regime shifts such as a transition to different oscillation phases.

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Aerodynamic effects of corrugation and deformation in flapping wings of hovering hoverflies.

Publication Date: 2012 Jan 12 PMID: 22266123
Authors: Du, G. - Sun, M.
Journal: J Theor Biol

We investigated the aerodynamic effects of wing deformation and corrugation of a three-dimensional model hoverfly wing at a hovering condition by solving the Navier-Stokes equations on a dynamically deforming grid. Various corrugated wing models were tested. Insight into whether or not there existed significant aerodynamic coupling between wing deformation (camber and twist) and wing corrugation was obtained by comparing aerodynamic forces of four cases: a smooth-plate wing in flapping motion without deformation (i.e. a rigid flat-plate wing in flapping motion); a smooth-plate wing in flapping motion with deformation; a corrugated wing in flapping motion without deformation (i.e. a rigid corrugated wing in flapping motion); a corrugated wing in flapping motion with deformation. There was little aerodynamic coupling between wing deformation and corrugation: the aerodynamic effect of wing deformation and corrugation acting together was approximately a superposition of those of deformation and corrugation acting separately. When acting alone, the effect of wing deformation was to increase the lift by 9.7% and decrease the torque (or aerodynamic power) by 5.2%, and that of wing corrugation was to decrease the lift by 6.5% and increase the torque by 2.2%. But when acting together, the wing deformation and corrugation only increased the lift by approximately 3% and decreased the torque by approximately 3%. That is, the combined aerodynamic effect of deformation and corrugation is rather small. Thus, wing corrugation is mainly for structural, not aerodynamic, purpose, and in computing or measuring the aerodynamic forces, using a rigid flat-plate wing to model the corrugated deforming wing at hovering condition can be a good approximation.

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On delayed discrete evolutionary dynamics.

Publication Date: 2012 Jan 18 PMID: 22266122
Authors: Iijima, R.
Journal: J Theor Biol

We examine the asymptotic stability of equilibria where individuals react to delayed information and the delays are heterogeneously distributed. For symmetric games with binary actions, we derive conditions under which the stability/instability of equilibria does not depend on the delay distribution. As a corollary, we show that a unique mixed evolutionarily stable state in games in well-mixed populations is asymptotically stable under a class of delayed replicator dynamics, for any lag distribution.

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Size matters: Influence of stochasticity on the self-maintenance of a simple model of metabolic closure.

Publication Date: 2012 Jan 18 PMID: 22266121
Authors: Piedrafita, G. - Cornish-Bowden, A. - Moran, F. - Montero, F.
Journal: J Theor Biol

A fundamental landmark in the emergence and maintenance of the first proto-biological systems must have been the formation of a "closed" metabolic organization, and this paper describes a stochastic analysis of a simple model of a system that is closed to efficient causation. Although it shows an absorbing barrier corresponding to the trivial solution that implies collapse and extinction, for certain values of the kinetic parameters it can also show a "coexistence state" in which there are non-null populations of its intermediates, which corresponds approximately to a non-trivial deterministic stable steady state. Depending on the initial conditions, fluctuations can drive the system either to the self-maintaining regime or to extinction, with different probabilities. Different lines of equal probability have been obtained and compared with the deterministic results, and the average time for reaching these states (characteristic time) has been estimated. The system shows strong dependence on volume size, and there is a critical volume below which it collapses very rapidly. The characteristic time is also affected by the volume, with faster responses for lower system volumes. All these results are discussed in the context of the origin of living organization.

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Influence of temporary migration on the transmission of infectious diseases in a migrants' home village.

Publication Date: 2012 Jan 13 PMID: 22266046
Authors: Wang, L. - Wang, X.
Journal: J Theor Biol

The number of temporary migrant workers from rural areas to urban areas in emerging market economies like China has increased dramatically since the early 1980s. Temporary migrant workers have been labeled as the major driving force for the rising incidence of infectious diseases in cities. However, it has not been well recognized that temporary migration indeed may have tremendous impacts on the spread of infectious diseases in migrants' home villages. In this paper, by proposing a delay differential equation model, we provide a framework to study the influence of temporary migration on the transmission of infectious diseases in a migrant workers' home village. The model is shown to admit a unique positive equilibrium which is locally asymptotically stable and is globally asymptotically stable under certain conditions. This implies that the disease always persists at a constant level. Considering tuberculosis as an example, we explore various disease prevention and control strategies numerically to demonstrate how migration related parameters affect the early outbreak of the disease. We find that a single control strategy, such as reducing the migration time period alone, has little effect on reducing the disease endemic level. For disease prevention and control, temporary migrant workers should be identified as the top target group, and a combination of several prevention strategies should be implemented.

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Swimming capability of the remopleuridid trilobite Hypodicranotus striatus: Hydrodynamic functions of the exoskeleton and the long, forked hypostome.

Publication Date: 2012 Jan 12 PMID: 22261264
Authors: Shiino, Y. - Kuwazuru, O. - Suzuki, Y. - Ono, S.
Journal: J Theor Biol

The sophisticated hydrodynamic performance achieved by the exoskeleton and the long, forked hypostome of the remopleuridid trilobite Hypodicranotus striatus was demonstrated using image-based modelling and computational fluid dynamics simulation techniques. To understand the function of the long, forked hypostome, we examined two types of exoskeletal models, one with and one without the hypostome. We simulated the flow structures around the exoskeletal models under several ambient flow velocities to evaluate the shapes of the streamlines, the values of the drag and lift forces and the relevant coefficients acting on the models. The simulation results showed that the long, forked hypostome prevents the formation of a ventral vortex; thus, it stabilises the flow structure under all of the ambient velocities tested. Moreover, the hypostome functions to create positive lift, with stable lift coefficients observed under a wide range of velocities, and to reduce the drag coefficient as velocity increases. These results imply that the hypostome can reduce viscous drag with a modest lift force, which is an essential requirement for actively swimming animals. We conclude that the long, forked hypostome evolved to provide an active and stable swimming system, and we therefore hypothesise that Hypodicranotus exoskeletal morphology resulted from the adaptation to be a high-performance swimmer.

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HIV transmissions by stage in dynamic sexual partnerships.

Publication Date: 2012 Jan 12 PMID: 22261263
Authors: Kim, J. H. - Koopman, J. S.
Journal: J Theor Biol

Most models assessing relative transmissions during different progressive stages of human immunodeficiency virus (HIV) infection assume that infections are transmitted through instantaneous sexual contacts. In reality, however, HIV will often be transmitted through repeated sex acts during partnerships that form and dissolve at varying rates. We sought to understand how dynamic sexual partnerships would influence transmissions during different progression stages of HIV infection: primary HIV infection (PHI) and chronic stage. Using a system of ordinary differential equations with a pair approximation technique, we constructed a model of HIV transmission in a homogeneous population in which sexual partnerships form and dissolve. We derived analytical expressions for useful epidemiological quantities such as basic reproduction number and also did simulation runs of the model. Partnership dynamics strongly influence transmissions during progressive stages of HIV infection. The fraction of transmissions during PHI has a U-shaped relationship with respect to the rate of partnership change, where the minimum and maximum occur given partnerships of about 100 days and fixed partnerships, respectively. Models that assume instantaneous contacts may overestimate transmissions during PHI for real, dynamic sexual partnerships with varying (non-zero) durations.

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Improved haplotype assembly using Xor genotypes.

Publication Date: 2012 Jan 12 PMID: 22251889
Authors: Mousavi, S. R.
Journal: J Theor Biol

Given a set of aligned fragments, haplotype assembly is the problem of finding the haplotypes from which the fragments have been read. The problem is important because haplotypes contain SNP information, which is essential to many genomic analyses such as the analysis of potential association between certain diseases and genetic variations. The current state-of-the-art haplotype assembly algorithm, HapSAT, does not exploit genotype information and only receives a read matrix as input. However, the imminent importance of haplotypes and inexpensiveness of genotype information motivate for exploiting genotype information to obtain more accurate haplotypes. In this paper, an improved haplotype assembly method, xGenHapSAT, is proposed, which exploits xor genotype information for more accurate haplotype assembly. Xor genotype information is even less expensive than full genotype information, e.g., using the Denaturing High-Performance Liquid Chromatography (DHPLC) technique. It is shown that using this inexpensively obtainable information significantly improves the accuracy of the assembled haplotypes. In addition, a new, more efficient, Max-2-SAT formulation is adopted in xGenHapSAT, which, on average, increases the speed of the algorithm. Moreover, the proposed xGenHapSAT method replaces the current state-of-the-art haplotype assembly method based on genotype information. Finally, our state-of-the-art haplotype assembly software, HapSoft, which includes both xGenHapSAT and HapSAT, is made freely available for research purposes.

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A 3D-geometric model for the deformation of a transversally loaded muscle.

Publication Date: 2012 Jan 12 PMID: 22251888
Authors: Siebert, T. - Gunther, M. - Blickhan, R.
Journal: J Theor Biol

Very recent measurements provided data on the ratio between the change in length of the active fibres and the lifting height of a mass compressing the muscle belly transversally to the direction of fibre contraction. In this study, we present additional data of the change in the third (unloaded) muscle dimension, extracted from the same contraction experiments. Using this data set for validation, we verify whether body models of two different geometries, cylindrical or ellipsoidal, can explain the three-dimensional deformation of a contracting muscle, when volume constancy is required as a constraint. Presetting the contractile length change and using this constraint, an additional equation is needed for model predictions. To that, we minimise the sum of the squared and weighted circumference length changes. With a specific set of the three penalty weights, it turns out that the ellipsoid model can explain the three-dimensional deformation. The set of penalty weights can also be interpreted as an anisotropic stiffness distribution of the connective tissue of the muscle belly. In various loading situations, our ellipsoidal model may help to predict the corresponding deformation scenarios or to calculate the stiffness distribution from measured load and deformation data.

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Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage.

Publication Date: 2012 Jan 11 PMID: 22245622
Authors: Fischer, S. - Kurbatova, P. - Bessonov, N. - Gandrillon, O. - Volpert, V. - Crauste, F.
Journal: J Theor Biol

The production and regulation of red blood cells, erythropoiesis, occurs in the bone marrow where erythroid cells proliferate and differentiate within particular structures, called erythroblastic islands. A typical structure of these islands consists of a macrophage (white cell) surrounded by immature erythroid cells (progenitors), with more mature cells on the periphery of the island, ready to leave the bone marrow and enter the bloodstream. A hybrid model, coupling a continuous model (ordinary differential equations) describing intracellular regulation through competition of two key proteins, to a discrete spatial model describing cell-cell interactions, with growth factor diffusion in the medium described by a continuous model (partial differential equations), is proposed to investigate the role of the central macrophage in normal erythropoiesis. Intracellular competition of the two proteins leads the erythroid cell to either proliferation, differentiation, or death by apoptosis. This approach allows considering spatial aspects of erythropoiesis, involved for instance in the occurrence of cellular interactions or the access to external factors, as well as dynamics of intracellular and extracellular scales of this complex cellular process, accounting for stochasticity in cell cycle durations and orientation of the mitotic spindle. The analysis of the model shows a strong effect of the central macrophage on the stability of an erythroblastic island, when assuming the macrophage releases pro-survival cytokines. Even though it is not clear whether or not erythroblastic island stability must be required, investigation of the model concludes that stability improves responsiveness of the model, hence stressing out the potential relevance of the central macrophage in normal erythropoiesis.

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Evolutionary dynamics of collective action when individual fitness derives from group decisions taken in the past.

Publication Date: 2012 Jan 8 PMID: 22245522
Authors: Moreira, J. A. - Pinheiro, F. L. - Nunes, A. - Pacheco, J. M.
Journal: J Theor Biol

Many actions take some time to have an impact - their effects only appear at some point in the future. Such time lags turn out to be ubiquitous among living organisms. Here we study the impact of time lags in the evolutionary dynamics of cooperative collective action. We consider a population in which individuals interact via a N-Person Stag Hunt dilemma and must opt to cooperate or defect. In the absence of any delay, the replicator dynamics reveals the existence of regimes in which two internal fixed points appear simultaneously. We show that the presence of time delay in the fitness of individuals leads to a delayed replicator equation exhibiting new evolutionary profiles, each profile being separated by critical values of the delay that we determine explicitly. When we break the symmetry in the time lags, we show that, generally, defectors take more advantage from delay than cooperators. Finally, when we take into consideration, approximately, effects associated with the finite population size, we find that counter-intuitive evolutionary outcomes may occur, resulting from the interplay between delay and the basins of attraction in the neighborhood of the internal fixed-points, and which may lead to full cooperation in conditions under which the outcome would be Full Defection in infinite populations.

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An overlapping genetic code for frameshifted overlapping genes in Drosophila mitochondria: Antisense antitermination tRNAs UAR insert serine.

Publication Date: 2012 Jan 8 PMID: 22244915
Authors: Seligmann, H.
Journal: J Theor Biol

Mitochondrial Drosophila genomes possess at least one antisense antiterminator (suppressor) tRNA matching stop codons UAR: antitermination might enable translation after ribosomal frameshift. Proteins translated from samestrand frameshifted and antisense sequences match 26 Genbank proteins (16 are samestrand). Natural frameshifted sequences match more Genbank proteins than after randomizing synonymous codons, suggesting optimization for overlap coding, but some genes avoid overlap coding. Alignments reassign serine to UAR: translational activity by antitermination tRNAs defines a new, presumably stopless overlapping genetic code. Cloverleaf formation by antisense suppressor tRNAs UAA and UAG coevolve with overlapping samestrand and antisense genes, respectively. Coevolution between suppressor tRNAs and sense as well as antisense overlapping genes increases with relative abundances of corresponding sense and antisense (m)RNAs, strong functional evidence for this parallel coding system. Antisense tRNA abundances converge with computed adaptations of antisense tRNAs for translation. Some short frameshifted coding regions are apparently programmed frameshifts putatively producing altered forms of the known main frame protein; most overlapping genes apparently code for unknown proteins. Overlap coding increases gene density without increasing genome size, but decreases with genome size. Parallel genetic systems coded by an additional mitochondrial genetic code in Drosophila confirm similar phenomena in primate mitochondria.

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Numericalization of the self adaptive spectral rotation method for coding region prediction.

Publication Date: 2012 Mar 7 PMID: 22178641
Authors: Chen, B. - Ji, P.
Journal: J Theor Biol

Recently, for identifying protein coding regions in new sequences from unknown organisms without training sets, a Self Adaptive Spectral Rotation (SASR) method has been developed to visualize the Triplet Periodicity (TP) property, which is a simple and universal coding related property. The rough locations of coding regions can be visually revealed by the SASR method, without any training. However, the method does not numerically discriminate the locations of coding regions. Based on the SASR method, we develop a new approach, named the T-Z-T analysis, to provide numerical results of coding region prediction. This approach adopts a t-test segmentation to separate coding and non-coding regions in the SASR's output and further uses a z-test filter to recognize region patterns. After that, another t-test segmentation is conducted to break down adjacent coding regions by detecting the frame shifts. Since it is based on the graphic output of the SASR, this approach does not require any training. Meanwhile, this approach is more stable, because it is not sensitive to errors in the input DNA sequence. Such advantages make it suitable for coding region prediction in the early stage, when there is insufficient training set, and even the input data are inaccurate.

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Specialized nursery pollination mutualisms as evolutionary traps stabilized by antagonistic traits.

Publication Date: 2012 Mar 7 PMID: 22178640
Authors: Louca, S. - Ibanez, S. - Piau, D. - Despres, L.
Journal: J Theor Biol

We examine the conditions for the transition from antagonism to mutualism between plants and their specialists nursery pollinators in a reference case which is the Trollius europaeus-Chiastocheta interaction. The mechanistic model we developed shows that a specialization of T. europaeus on Chiastocheta could be the result of an attempt to escape over-exploitation by closing its flower. The pressure for such an escape increases with the parasite's frequency and its pollination efficiency but decreases in the presence of alternative pollinators. The resulting specialization is a priori an unstable one, leading either to strong evolutionary oscillations, or to evolutionary suicide due to over-exploitation of the plants. It becomes stable if the plants develop a defense mechanism to regulate their parasite's population size and limit seed-exploitation. The development of a counter-measure by the latter can destabilize the mutualism depending on the costs linked to such a trait. On the other hand, we find that a specialization on a purely mutualistic basis would require a preexisting high diversity of flower-opening within the population.

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Toward an evolutionary containment of evolving pathogen-receptors by using an ensemble of multiple mutant ligands: From the viewpoint of fitness landscape in sequence space.

Publication Date: 2012 Mar 7 PMID: 22172531
Authors: Aita, T. - Husimi, Y.
Journal: J Theor Biol

It is known that even if a ligand peptide is designed to bind to a target receptor on the surface of a pathogen such as viruses, bacteria or cancer cells, it is likely that some receptors are subject to random mutation and thus the ligand has a reduced ability to bind to these receptors. This issue is known as drug-resistant or escape mutants. In this paper, we present an idea to inhibit the evolving receptors by using an ensemble of all possible single- or double-point mutant sequences of the ligand peptide. Several mutant ligands in the ensemble are expected to bind to the mutant receptors, and then the ensemble may create a defensive wall surrounding the target receptors in receptor-sequence space. We examined the effectiveness of this "evolutionary containment" of the evolving receptors through eight peptide-protein complex systems, which were retrieved from the Protein Data Bank (PDB). As a result, we obtained a suggestion that the original (or parent) ligand sequence should be designed to have as high fitness as possible but to be not local optima, in order to maximize the rate of the evolutionary containment. This may be a strategy of the drug-design against evolving pathogens.

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A novel coding method for gene mutation correction during protein translation process.

Publication Date: 2012 Mar 7 PMID: 22172530
Authors: Zhang, L. - Tian, F. - Wang, S. - Liu, X.
Journal: J Theor Biol

In gene expression, gene mutations often lead to negative effect of protein translation in prokaryotic organisms. With consideration of the influences produced by gene mutation, a novel method based on error-correction coding theory is proposed for modeling and detection of translation initiation in this paper. In the proposed method, combined with a one-dimensional codebook from block coding, a decoding method based on the minimum hamming distance is designed for analysis of translation efficiency. The results show that the proposed method can recognize the biologically significant regions such as Shine-Dalgarno region within the mRNA leader sequences effectively. Also, a global analysis of single base and multiple bases mutations of the Shine-Dalgarno sequences are established. Compared with other published experimental methods for mutation analysis, the translation initiation can not be disturbed by multiple bases mutations using the proposed method, which shows the effectiveness of this method in improving the translation efficiency and its biological relevance for genetic regulatory system.

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Evolution of ape and human mating systems.

Publication Date: 2012 Mar 7 PMID: 22155135
Authors: Nakahashi, W. - Horiuchi, S.
Journal: J Theor Biol

Humans (Homo sapiens) generally form multiple-male-multiple-female groups that include multiple family units. This social structure is maintained because dominant males do not monopolize females and, thus, allow subordinate males to mate, and human females are not generally promiscuous. Although apes show great variation in mating systems, the human-type mating system is unique among primates. The mating systems of apes and humans have evolved in response to their adaptation to different ecological conditions. We created and analyzed a mathematical model to investigate the conditions for each type of mating system to evolve. We focused on the mating strategy of alpha males and the mating and grouping strategies of females. We defined the human-type mating system as one with multiple-male-multiple-female groups in which alpha males do not monopolize females and females are not promiscuous. We demonstrated that the human-type mating system could evolve when a large group is advantageous and the cost of female promiscuity is great. Moreover, the human- and Pan-type mating systems can be bistable. Our results shed light on the origin of the human family.

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The influence of assortativity on the robustness of signal-integration logic in gene regulatory networks.

Publication Date: 2012 Mar 7 PMID: 22155134
Authors: Pechenick, D. A. - Payne, J. L. - Moore, J. H.
Journal: J Theor Biol

Gene regulatory networks (GRNs) drive the cellular processes that sustain life. To do so reliably, GRNs must be robust to perturbations, such as gene deletion and the addition or removal of regulatory interactions. GRNs must also be robust to genetic changes in regulatory regions that define the logic of signal-integration, as these changes can affect how specific combinations of regulatory signals are mapped to particular gene expression states. Previous theoretical analyses have demonstrated that the robustness of a GRN is influenced by its underlying topological properties, such as degree distribution and modularity. Another important topological property is assortativity, which measures the propensity with which nodes of similar connectivity are connected to one another. How assortativity influences the robustness of the signal-integration logic of GRNs remains an open question. Here, we use computational models of GRNs to investigate this relationship. We separately consider each of the three dynamical regimes of this model for a variety of degree distributions. We find that in the chaotic regime, robustness exhibits a pronounced increase as assortativity becomes more positive, while in the critical and ordered regimes, robustness is generally less sensitive to changes in assortativity. We attribute the increased robustness to a decrease in the duration of the gene expression pattern, which is caused by a reduction in the average size of a GRN's in-components. This study provides the first direct evidence that assortativity influences the robustness of the signal-integration logic of computational models of GRNs, illuminates a mechanistic explanation for this influence, and furthers our understanding of the relationship between topology and robustness in complex biological systems.

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The apparent hysteresis in hormone-agonist relationships.

Publication Date: 2012 Mar 7 PMID: 22154846
Authors: Pruett, W. A. - Hester, R. L. - Coleman, T. G.
Journal: J Theor Biol

It has been noted in multiple studies that the calcium-PTH axis, among others, is subject to an apparent hysteresis. We sought to explain a major component of the observed phenomenon by constructing a simple mathematical model of a hormone and secretagogue system with concentration dependent secretion and containing two delays. We constructed profiles of the hormone-agonist axis in this model via four types of protocols, three of which emulating experiments from the literature, and observed a delay- and load-dependent hysteresis that is an expected mathematical artifact of the system described. In particular, the delay associated with correction allows for over-secretion of the hormone influencing the corrective mechanism; thus rate dependence is an artifact of the corrective mechanism, not a sensitivity of the gland to the magnitude of change. From these observations, the detected hysteresis is due to delays inherent in the systems being studied, not in the secretory mechanism.

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Threshold dynamics for periodically forced ecological systems: The control of population invasion and exclusion.

Publication Date: 2012 Feb 21 PMID: 22146345
Authors: Greenman, J. V. - Pasour, V. B.
Journal: J Theor Biol

Ecosystems are under increasing threat as a result of anthropogenic activity, through pollution, unregulated harvesting, habitat destruction and the inadvertent spread of pathogens and vertebrate and non-vertebrate species through global transportation links. Many of the necessary interventions to restore or restructure natural ecosystems require the exclusion of a population from the ecosystem or the inclusion of a population if robust biodiversity is the objective. The problem of how best to bring this about is not easy to solve in highly nonlinear systems, especially if the system is exposed to significant time varying external forces. We wish here to build on the understanding gained from previous work by developing an algebraic methodology that yields explicit formulae to analyse the effect of moderate multi-component forcing on the invasion/exclusion process. This can be of assistance to management in designing suitable intervention strategies if one or more of the forcing components is under management control. We apply this methodology to look at three important issues, involving the relationships between resonance and control, between vaccination policy and the stage structure of a disease and between apparent competition and coexistence.

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Predicting template-based catalysis rates in a simple catalytic reaction model.

Publication Date: 2012 Feb 21 PMID: 22142623
Authors: Hordijk, W. - Steel, M.
Journal: J Theor Biol

We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical concordance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular, we derive an analytical calculation that allows us to accurately predict the (observed) required level of catalysis in one version of the model from that in the other version, for a given probability of having self-sustaining autocatalytic sets exist in instances of both model versions. This provides a tractable connection between two models that have been investigated in theoretical origin-of-life studies.

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A computational model of auxin and pH dynamics in a single plant cell.

Publication Date: 2012 Mar 7 PMID: 22142622
Authors: Steinacher, A. - Leyser, O. - H Clayton, R.
Journal: J Theor Biol

Directed cell-to-cell movement of the plant growth hormone auxin is often referred to as polar auxin transport, and has gained much interest since its discovery at the beginning of the 20th century, both by biologists and theoreticians. Computational modelling of auxin transport at tissue and whole plant scales has given valuable insights into the feedback dynamics between auxin and its transport, which often leads to cell polarisation. However, one cellular feedback mechanism that has been overlooked so far in previous models is the interplay between auxin and pH during auxin transport, even though this is well known from biology. We propose a kinetic model of such a feedback mechanism, linking knowledge about auxin-induced acidification of cell wall compartments to the chemiosmotic hypothesis of auxin transport. Our results suggest that proton fluxes may play a significant role in auxin transport. Since active auxin transport relies on the proton motive force over the cellular membrane, allocation of auxin is linked to its effects on compartmental pH. Our auxin/pH feedback model predicts enhanced accumulation of auxin in cells and increases in both auxin influx and efflux when this feedback is in effect. These results were robust in all simulations and consistent with biological evidence, thus providing a framework for generating and testing hypotheses of auxin-related polarisation events at a cellular level.

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Importance of metabolic coupling for the dynamics of gene expression following a diauxic shift in Escherichia coli.

Publication Date: 2012 Feb 21 PMID: 22138386
Authors: Baldazzi, V. - Ropers, D. - Geiselmann, J. - Kahn, D. - de Jong, H.
Journal: J Theor Biol

Gene regulatory networks consist of direct interactions, but also include indirect interactions mediated by metabolism. We investigate to which extent these indirect interactions arising from metabolic coupling influence the dynamics of the system. To this end, we build a qualitative model of the gene regulatory network controlling carbon assimilation in Escherichia coli, and use this model to study the changes in gene expression following a diauxic shift from glucose to acetate. In particular, we compare the relative variation in the steady-state concentrations of enzymes and transcription regulators during growth on glucose and acetate, as well as the dynamic response of gene expression to the exhaustion of glucose and the subsequent assimilation of acetate. We find significant differences between the dynamics of the system in the absence and presence of metabolic coupling. This shows that interactions arising from metabolic coupling cannot be ignored when studying the dynamics of gene regulatory networks.

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Alignment free comparison: Similarity distribution between the DNA primary sequences based on the shortest absent word.

Publication Date: 2012 Feb 21 PMID: 22138094
Authors: Yang, L. - Zhang, X. - Zhu, H.
Journal: J Theor Biol

This work proposes an alignment free comparison model for the DNA primary sequences. In this paper, we treat the double strands of the DNA rather than single strand. We define the shortest absent word of the double strands between the DNA sequences and some properties are studied to speed up the algorithm for searching the shortest absent word. We present a novel model for comparison, in which the similarity distribution is introduced to describe the similarity between the sequences. A distance measure is deduced based on the Shannon entropy meanwhile is used in phylogenetic analysis. Some experiments show that our model performs well in the field of sequence analysis.

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Relating ranging ecology, limb length, and locomotor economy in terrestrial animals.

Publication Date: 2012 Mar 7 PMID: 22138093
Authors: Pontzer, H.
Journal: J Theor Biol

Ecomorphological analyses have identified a number of important evolutionary trends in vertebrate limb design, but the relationships between daily travel distance, locomotor ecology, and limb length in terrestrial animals remain poorly understood. In this paper I model the net rate of energy intake as a function of foraging efficiency, and thus of locomotor economy; improved economy leads to greater net energy intake. However, the relationship between locomotor economy and net intake is highly dependent on foraging efficiency; only species with low foraging efficiencies experience strong selection pressure for improved locomotor economy and increased limb length. Examining 237 terrestrial species, I find that nearly all taxa obtain sufficiently high foraging efficiencies that selection for further increases in economy is weak. Thus selection pressures for increased economy and limb length among living terrestrial animals may be relatively weak and similar in magnitude across ecologically diverse species. The Economy Selection Pressure model for locomotor economy may be useful in investigating the evolution of limb design in early terrestrial taxa and the coevolution of foraging ecology and locomotor anatomy in lineages with low foraging efficiencies.

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Multistability and oscillations in genetic control of metabolism.

Publication Date: 2012 Feb 21 PMID: 22137968
Authors: Oyarzun, D. A. - Chaves, M. - Hoff-Hoffmeyer-Zlotnik, M.
Journal: J Theor Biol

Genetic control of enzyme activity drives metabolic adaptations to environmental changes, and therefore the feedback interaction between gene expression and metabolism is essential to cell fitness. In this paper we develop a new formalism to detect the equilibrium regimes of an unbranched metabolic network under transcriptional feedback from one metabolite. Our results indicate that one-to-all transcriptional feedback can induce a wide range of metabolic phenotypes, including mono-, multistability and oscillatory behavior. The analysis is based on the use of switch-like models for transcriptional control and the exploitation of the time scale separation between metabolic and genetic dynamics. For any combination of activation and repression feedback loops, we derive conditions for the emergence of a specific phenotype in terms of genetic parameters such as enzyme expression rates and regulatory thresholds. We find that metabolic oscillations can emerge under uniform thresholds and, in the case of operon-controlled networks, the analysis reveals how nutrient-induced bistability and oscillations can emerge as a consequence of the transcriptional feedback.

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Within-host demographic fluctuations and correlations in early retroviral infection.

Publication Date: 2012 Feb 21 PMID: 22133472
Authors: Vaughan, T. G. - Drummond, P. D. - Drummond, A. J.
Journal: J Theor Biol

In this paper we analyze the demographic fluctuations and correlations present in within-host populations of viruses and their target cells during the early stages of infection. In particular, we present an exact treatment of a discrete-population, stochastic, continuous-time master equation description of HIV or similar retroviral infection dynamics, employing Monte Carlo simulations. The results of calculations employing Gillespie's direct method clearly demonstrate the importance of considering the microscopic details of the interactions which constitute the macroscopic dynamics. We then employ the tau-leaping approach to study the statistical characteristics of infections involving realistic absolute numbers of within-host viral and cellular populations, before going on to investigate the effect that initial viral population size plays on these characteristics. Our main conclusion is that cross-correlations between infected cell and virion populations alter dramatically over the course of the infection. We suggest that these statistical correlations offer a novel and robust signature for the acute phase of retroviral infection.

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Flow currents and ventilation in Langstroth beehives due to brood thermoregulation efforts of honeybees.

Publication Date: 2012 Feb 21 PMID: 22126904
Authors: Sudarsan, R. - Thompson, C. - Kevan, P. G. - Eberl, H. J.
Journal: J Theor Biol

Beekeepers universally agree that ensuring sufficient ventilation is vital for sustaining a thriving, healthy honeybee colony. Despite this fact, surprisingly little is known about the ventilation and flow patterns in bee hives. We take a first step towards developing a model-based approach that uses computational fluid dynamics to simulate natural ventilation flow inside a standard Langstroth beehive. A 3-D model of a Langstroth beehive with one brood chamber and one honey super was constructed and inside it the honeybee colony was distributed among different clusters each occupying the different bee-spaces between frames in the brood chamber. For the purpose of modeling, each honeybee cluster was treated as an air-saturated porous medium with constant porosity. Heat and mass transfer interactions of the honeybees with the air, the outcome of metabolism, were captured in the porous medium model as source and sink terms appearing in the governing equations of fluid dynamics. The temperature of the brood that results from the thermoregulation efforts of the colony is applied as a boundary condition for the governing equations. The governing equations for heat, mass transport and fluid flow were solved using Fluent((c)), a commercially available CFD program. The results from the simulations indicate that (a) both heat and mass transfer resulting from honeybee metabolism play a vital role in determining the structure of the flow inside the beehive and mass transfer cannot be neglected, (b) at low ambient temperatures, the nonuniform temperature profile on comb surfaces that results from brood incubation enhances flow through the honeybee cluster which removes much of the carbon-dioxide produced by the cluster resulting in lower carbon-dioxide concentration next to the brood, (c) increasing ambient (outside) air temperature causes ventilation flow rate to drop resulting in weaker flow inside the beehive. Flow visualization indicates that at low ambient air temperatures the flow inside the beehive has an interesting 3-D structure with the presence of large recirculating vortices occupying the space between honey super frames above the honeybee clusters in the brood chamber and the structure and strength of the flow inside and around the honeybee clusters changes as we increase the ambient air temperature outside the beehive.

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The relationship between syllable repertoire similarity and pairing success in a passerine bird species with complex song.

Publication Date: 2012 Feb 21 PMID: 22123372
Authors: Garamszegi, L. Z. - Zsebok, S. - Torok, J.
Journal: J Theor Biol

Repertoire size, i.e. the number of unique song elements that an individual possesses, is thought to be an important target of female preference. However, the use of repertoire size reflects how researchers work with complex songs; while it does not necessary describe biological functions, as listeners of song may also rely on song composition. Specific syllables may have coherent consequences for mate attraction because they are costly to produce, mediate syllable sharing or indicate the dialect of origin. We tested for the relationship between song composition and pairing success in the collared flycatcher (Ficedula albicollis). We applied a tree-clustering method to hierarchically classify males based on the degree of repertoire overlap, and then used a phylogenetic approach to assess the degree by which pairing speed matches the hierarchically structured song data. We found that males using similar syllables also find a breeding partner at a similar speed. Partitioning the variance components of pairing speed, we detected that the consequences of particular syllables for mating are repeatable across males. When assessing the role of repertoire similarity in mediating direct syllable sharing, we derived a positive relationship between the physical distance between pairs of males and their repertoire overlap implying that neighboring males avoid copying each other's song. Finally, we were unable to demonstrate that syllables related to higher mating success are more common in the population, which would support mechanisms based on female preference for local songs. Our results imply that individual-specific song organization may be relevant for sexual selection.

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The interplay of double phosphorylation and scaffolding in MAPK pathways.

Publication Date: 2012 Feb 21 PMID: 22123371
Authors: Kocieniewski, P. - Faeder, J. R. - Lipniacki, T.
Journal: J Theor Biol

The MAPK cascades are principal kinase transduction pathways in eukaryotic cells. This family includes RAF/ERK, JNK, and p38 pathways. In the MAPK cascade, the signal is transmitted through three layers of sequentially activated kinases, MAP3K, MAP2K, and MAPK. The latter two kinases require dual phosphorylation for activation. The dual phosphorylation requirement has been implicated in bringing about bistability and switch-like responses in the cascade. MAPK signaling has been known to involve scaffolds-multidomain proteins that can assemble protein complexes; in this case the three MAPK components. Scaffolds are thought to increase the specificity of signaling by pairing enzymes and substrates. Scaffolds have been shown to biphasically control the response (the level of activated MAPK) and amplify it at a certain scaffold concentration range. In order to understand the interplay of scaffolding and multisite phosphorylation, in this study we analyze simplified MAPK signaling models in which we assume that either mono- or double phosphorylation of MAP2K and MAPK is required for activation. We demonstrate that the requirement for double phosphorylation directs signaling through scaffolds. In the hypothetical scenario in which mono-phosphorylation suffices for kinase activity, the presence of scaffolds has little effect on the response. This suggests that double phosphorylation in MAPK pathways, although not as efficient as mono-phosphorylation, evolved together with scaffolds to assure the tighter control and higher specificity in signaling, by enabling scaffolds to function as response amplifiers.

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Spatiotemporal effects of a possible chemorepulsion of tumor cells by immune system effectors.

Publication Date: 2012 Mar 7 PMID: 22119911
Authors: d'Onofrio, A.
Journal: J Theor Biol

Tumor-immune system interplay is a landmark of tumor development, and chemotactic attraction of immune system cells towards a tumor is a landmark of immune control. Since tumor cells are capable of chemotactic and chemorepulsive motion, based on a number of analogies between the behavior of tumor cells and that of bacteria, and on the production of potentially chemorepulsive semaphorins by immune systems effectors, we propose here the possibility of chemorepulsion of tumor cells, elicited by chemicals produced by immune system effectors such as macrophages and cytotoxic T lymphocytes. To study the effects of this hypothesized phenomenon within the framework of the interplay of neoplasias with the innate and adaptive immune system, we appropriately extend two well-known models: the tumor-macrophage models by Owen and Sherratt [Owen and Sherratt, J. Theor. Biol., 1998] and the Matzavinos-Chaplain model of tumor-CTL interaction [Matzavinos, Chaplain and Kuznetsov, Math. Med. Biol., 2004]. Our simulations suggest that this mechanism might allow a faster expansion of tumors, and in the concluding remarks we envisage a new possible route of immunoevasion.

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The effects of a telomere destabilizing agent on cancer cell-cycle dynamics-Integrated modelling and experiments.

Publication Date: 2012 Feb 21 PMID: 22108242
Authors: Hirt, B. V. - Wattis, J. A. - Preston, S. P. - Laughton, C. A.
Journal: J Theor Biol

The pentacyclic acridinium salt RHPS4 displays anti-tumour properties in vitro as well as in vivo and is potentially cell-cycle specific. We have collected experimental data and formulated a compartmental model using ordinary differential equations to investigate how the compound affects cells in each stage of the cell cycle. In addition to a control case in which no drug was used, we treated colorectal cancer cells with three different concentrations of the drug and fitted simulations from our models to experimental observations. We found that RHPS4 caused a concentration-dependent, marked cell death in treated cells, which is best modelled by allowing the rate parameters corresponding to cell death to be sigmoidal functions of time. We have shown that the model is "identifiable", meaning that, at least in principle, the parameter values can be determined from observable quantities. We find that at low concentrations RHPS4 primarily affects the cells in the G(2)/M phase, and that the drug has a delayed effect with the delay decreasing at larger doses. Since the drug diffuses into the nucleus, the observed delayed effect of the compound is unexpected and is a novel finding of our research into this compound.

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Energetics of the yo-yo dives of predatory sharks.

Publication Date: 2012 Feb 7 PMID: 22108240
Authors: Iosilevskii, G. - Papastamatiou, Y. P. - Meyer, C. G. - Holland, K. N.
Journal: J Theor Biol

Sharks zigzag vertically through the water in a series of alternating ascending and descending segments, changing depth by a few tens of meters over a period of a few hundred seconds. This 'yo-yo' like behavior has several characteristic patterns, identifiable by the way the swimming and vertical velocities vary along the dive. We suggest that these patterns represent different optimal strategies minimizing the cost of locomotion under different constraints; moreover, these constraints can be inferred by matching the pattern of a dive with a (standard) optimal swimming strategy for which the constraints are known. We used three sets of constraints and two definitions of the 'cost of locomotion' to analytically generate four standard optimal strategies; we have used high resolution tracking data from four tiger sharks to identify two different yo-yo diving patterns. These patterns seem to match two of the standard strategies: one that maximizes range, given an alternating power supply (e.g., swimming actively on ascents and lazily on descents); and the other that maximizes range, given an alternating vertical velocity (implying an 'intentional' up-and-down motion).

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A game dynamic model for vaccine skeptics and vaccine believers: Measles as an example.

Publication Date: 2012 Feb 21 PMID: 22108239
Authors: Shim, E. - Grefenstette, J. J. - Albert, S. M. - Cakouros, B. E. - Burke, D. S.
Journal: J Theor Biol

Widespread avoidance of Measles-Mumps-Rubella vaccination (MMR), with a consequent increase in the incidence of major measles outbreaks, demonstrates that the effectiveness of vaccination programs can be thwarted by the public misperceptions of vaccine risk. By coupling game theory and epidemic models, we examine vaccination choice among populations stratified into two behavioral groups: vaccine skeptics and vaccine believers. The two behavioral groups are assumed to be heterogeneous with respect to their perceptions of vaccine and infection risks. We demonstrate that the pursuit of self-interest among vaccine skeptics often leads to vaccination levels that are suboptimal for a population, even if complete coverage is achieved among vaccine believers. The demand for measles vaccine across populations driven by individual self-interest was found to be more sensitive to the proportion of vaccine skeptics than to the extent to which vaccine skeptics misperceive the risk of vaccine. Furthermore, as the number of vaccine skeptics increases, the probability of infection among vaccine skeptics increases initially, but it decreases once the vaccine skeptics begin receiving the vaccination, if both behavioral groups are vaccinated according to individual self-interest. Our results show that the discrepancy between the coverages of measles vaccine that are driven by self-interest and those driven by population interest becomes larger when the cost of vaccination increases. This research illustrates the importance of public education on vaccine safety and infection risk in order to maintain vaccination levels that are sufficient to maintain herd immunity.

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Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding.

Publication Date: 2012 Mar 7 PMID: 22100501
Authors: Jia, C. - Liu, X. F. - Qian, M. P. - Jiang, D. Q. - Zhang, Y. P.
Journal: J Theor Biol

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of the rate of product formation in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.

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The relative contributions of propulsive forces and receptor-ligand binding forces during early contact between spermatozoa and zona pellucida of oocytes.

Publication Date: 2012 Feb 7 PMID: 22100500
Authors: Kozlovsky, P. - Gefen, A.
Journal: J Theor Biol

When reaching the zona pellucida (ZP) of the oocyte, spermatozoa apply propulsive forces produced by the motion of their flagella, which push against the ZP and theoretically should contribute to their penetration into the ZP. Additionally, specific receptors on the spermatozoon head bind to ZP3 ligands located on the surface of the ZP, which locks the sperm's head onto the oocyte. Both mechanisms are important cofactors in the initial sperm penetration into the ZP, which is required for successful fertilization of the oocyte, but it is unclear which forces-mechanical thrust or biochemical binding-are more influential at this stage. To address this question, we developed a biomechanical sperm-oocyte contact model, which is based on the Johnson-Kendall-Roberts model adopted from the contact mechanics theory. The modeling predicted that during the early stage of penetration into the ZP, biochemical binding forces acting on spermatozoa, which are swimming at a (normal) velocity of 100mum/s are approximately 4.2-times to approximately 16.7-times less than the mechanically-generated propulsive forces. In a simulated pathology of a low number of properly functioning receptors (50 out of 300receptors/mum(2)), the biochemical binding forces are approximately 63-times less than the propulsive forces for the normally swimming sperm. It is suggested that such dominance of the propulsive forces over the biochemical binding forces can prevent efficient binding of spermatozoa to the ZP of the oocyte due to continuous movement of the sperm (which is not necessarily perpendicular to the ZP surface, and can cause sliding of sperm over the ZP). Thus, our theoretical analysis indicates that a sufficiently large density of receptors to ZP3 ligands on the sperm head is critical at the stage of early sperm-oocyte contact, in order to allow an efficient acrosome reaction to follow, so that the spermatozoon can start penetrating into the ZP.

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Dynamic modelling of cell death during biofilm development.

Publication Date: 2012 Feb 21 PMID: 22100489
Authors: Fagerlind, M. G. - Webb, J. S. - Barraud, N. - McDougald, D. - Jansson, A. - Nilsson, P. - Harlen, M. - Kjelleberg, S. - Rice, S. A.
Journal: J Theor Biol

Biofilms are currently recognised as the predominant bacterial life-style and it has been suggested that biofilm development is influenced by a number of different processes such as adhesion, detachment, mass transport, quorum sensing, cell death and active dispersal. One of the least understood processes and its effects on biofilm development is cell death. However, experimental studies suggest that bacterial death is an important process during biofilm development and many studies show a relationship between cell death and dispersal in microbial biofilms. We present a model of the process of cell death during biofilm development, with a particular focus on the spatial localisation of cell death or cell damage. Three rules governing cell death or cell damage were evaluated which compared the effects of starvation, damage accumulation, and viability during biofilm development and were also used to design laboratory based experiments to test the model. Results from model simulations show that actively growing biofilms develop steep nutrient gradients within the interior of the biofilm that affect neighbouring microcolonies resulting in cell death and detachment. Two of the rules indicated that high substrate concentrations lead to accelerated cell death, in contrast to the third rule, based on the accumulation of damage, which predicted earlier cell death for biofilms grown with low substrate concentrations. Comparison of the modelling results with experimental results suggests that cell death is favoured under low nutrient conditions and that the accumulation of damage may be the main cause of cell death during biofilm development.

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T-cell movement on the reticular network.

Publication Date: 2012 Feb 21 PMID: 22100488
Authors: Donovan, G. M. - Lythe, G.
Journal: J Theor Biol

The idea that the apparently random motion of T cells in lymph nodes is a result of movement on a reticular network (RN) has received support from dynamic imaging experiments and theoretical studies. We present a mathematical representation of the RN consisting of edges connecting vertices that are randomly distributed in three-dimensional space, and models of lymphocyte movement on such networks including constant speed motion along edges and Brownian motion, not in three-dimensions, but only along edges. The simplest model, in which a cell moves with a constant speed along edges, is consistent with mean-squared displacement proportional to time over intervals long enough to include several changes of direction. A non-random distribution of turning angles is one consequence of motion on a preformed network. Confining cell movement to a network does not, in itself, increase the frequency of cell-cell encounters.

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Stochastic approximation to the T cell mediated specific response of the immune system.

Publication Date: 2012 Feb 21 PMID: 22100422
Authors: Figueroa-Morales, N. - Leon, K. - Mulet, R.
Journal: J Theor Biol

We develop a stochastic model to study the specific response of the immune system. The model is based on the dynamical interaction between Regulatory and Effector CD4+ T cells in the presence of Antigen Presenting Cells inside a lymphatic node. At a mean field level the model predicts the existence of different regimes where active, tolerant, or cyclic immune responses are possible. To study the model beyond mean field and to understand the specific responses of the immune system we use the Linear Noise Approximation and show that fluctuations due to finite size effects may strongly alter the mean field scenario. Moreover, it was found that the existence of a certain characteristic frequency for the fluctuations. All the analytical predictions were compared with simulations using Gillespie's algorithm.

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Model-independent plot of dynamic PET data facilitates data interpretation and model selection.

Publication Date: 2012 Feb 21 PMID: 22094364
Authors: Munk, O. L.
Journal: J Theor Biol

When testing new PET radiotracers or new applications of existing tracers, the blood-tissue exchange and the metabolism need to be examined. However, conventional plots of measured time-activity curves from dynamic PET do not reveal the inherent kinetic information. A novel model-independent volume-influx plot (vi-plot) was developed and validated. The new vi-plot shows the time course of the instantaneous distribution volume and the instantaneous influx rate. The vi-plot visualises physiological information that facilitates model selection and it reveals when a quasi-steady state is reached, which is a prerequisite for the use of the graphical analyses by Logan and Gjedde-Patlak. Both axes of the vi-plot have direct physiological interpretation, and the plot shows kinetic parameter in close agreement with estimates obtained by non-linear kinetic modelling. The vi-plot is equally useful for analyses of PET data based on a plasma input function or a reference region input function. The vi-plot is a model-independent and informative plot for data exploration that facilitates the selection of an appropriate method for data analysis.

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Confinement of gene drive systems to local populations: A comparative analysis.

Publication Date: 2012 Feb 7 PMID: 22094363
Authors: Marshall, J. M. - Hay, B. A.
Journal: J Theor Biol

Mosquito-borne diseases such as malaria and dengue fever pose a major health problem through much of the world. One approach to disease prevention involves the use of selfish genetic elements to drive disease-refractory genes into wild mosquito populations. Recently engineered synthetic drive systems have provided encouragement for this strategy; but at the same time have been greeted with caution over the concern that transgenes may spread into countries and communities without their consent. Consequently, there is also interest in gene drive systems that, while strong enough to bring about local population replacement, are unable to establish themselves beyond a partially isolated release site, at least during the testing phase. Here, we develop simple deterministic and stochastic models to compare the confinement properties of a variety of gene drive systems. Our results highlight several systems with desirable features for confinement-a high migration rate required to become established in neighboring populations, and low-frequency persistence in neighboring populations for moderate migration rates. Single-allele underdominance and single-locus engineered underdominance have the strongest confinement properties, but are difficult to engineer and require a high introduction frequency, respectively. Toxin-antidote systems such as Semele, Merea and two-locus engineered underdominance show promising confinement properties and require lower introduction frequencies. Killer-rescue is self-limiting in time, but is able to disperse to significant levels in neighboring populations. We discuss the significance of these results in the context of a phased release of transgenic mosquitoes, and the need for characterization of local ecology prior to a release.

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A letter to the editor about the article "A model for environmental sex reversal in fish".

Publication Date: 2012 Feb 7 PMID: 22094362
Authors: Shen, Z. G. - Fan, Q. X. - Hurley, M. A. - Xie, C. X. - Yang, W. - Zhang, Y. L.
Journal: J Theor Biol

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Modeling morphogen gradient formation from arbitrary realistically shaped sources.

Publication Date: 2012 Feb 7 PMID: 22094361
Authors: Dalessi, S. - Neves, A. - Bergmann, S.
Journal: J Theor Biol

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

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Mathematical modeling of transport and degradation of feedstuffs in the small intestine.

Publication Date: 2012 Feb 7 PMID: 22085739
Authors: Taghipoor, M. - Lescoat, P. - Licois, J. R. - Georgelin, C. - Barles, G.
Journal: J Theor Biol

We describe a mathematical model of digestion in the small intestine. The main interest of our work is to consider simultaneously the different aspects of digestion i.e. transport of the bolus all along the intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. A system of coupled ordinary differential equations is used to model these phenomena. The major unknowns of this system are the position of the bolus and its composition. This system of equations is solved numerically. We present several numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy regarding the overall behavior of the model and also when challenged versus experimental data. The main feature and interest of this model are its genericity. Even if we are at an early stage of development, our approach can be adapted to deal with contrasted feedstuffs in non-ruminant animal to predict the composition and velocity of bolus in the small intestine.

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On the meaning and estimation of plasmid transfer rates for surface-associated and well-mixed bacterial populations.

Publication Date: 2012 Feb 7 PMID: 22085738
Authors: Zhong, X. - Droesch, J. - Fox, R. - Top, E. M. - Krone, S. M.
Journal: J Theor Biol

Conjugative plasmid transfer is key to the ability of bacteria to rapidly adapt to new environments, but there is no agreement on a single quantitative measure of the rate of plasmid transfer. Some studies derive estimates of transfer rates from mass-action differential equation models of plasmid population biology. The often-used 'endpoint method' is such an example. Others report measures of plasmid transfer efficiency that simply represent ratios of plasmid-bearing and plasmid-free cell densities and do not correspond to parameters in any mathematical model. Unfortunately, these quantities do not measure the same thing - sometimes differing by orders of magnitude - and their use is often clouded by a lack of specificity. Moreover, they do not distinguish between bulk transfer rates that are only relevant in well-mixed populations and the 'intrinsic' rates between individual cells. This leads to problems for surface-associated populations, which are not well-mixed but spatially structured. We used simulations of a spatially explicit mathematical model to evaluate the effectiveness of these various plasmid transfer efficiency measures when they are applied to surface-associated populations. The simulation results, supported by some experimental findings, showed that these measures can be affected by initial cell densities, donor-to-recipient ratios and initial cell cluster size, and are therefore flawed as universal measures of plasmid transfer efficiency. The simulations also allowed us to formulate some guiding principles on when these estimates are appropriate for spatially structured populations and how to interpret the results. While we focus on plasmid transfer, the general lessons of this study should apply to any measures of horizontal spread (e.g., infection rates in epidemiology) that are based on simple mass-action models (e.g., SIR models in epidemiology) but applied to spatial settings.

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Environ centrality reveals the tendency of indirect effects to homogenize the functional importance of species in ecosystems.

Publication Date: 2012 Feb 7 PMID: 22085737
Authors: Fann, S. L. - Borrett, S. R.
Journal: J Theor Biol

Ecologists and conservation biologists need to identify the relative importance of species to make sound management decisions and effectively allocate scarce resources. We introduce a new method, termed environ centrality, to determine the relative importance of a species in an ecosystem network with respect to ecosystem energy-matter exchange. We demonstrate the uniqueness of environ centrality by comparing it to other common centrality metrics and then show its ecological significance. Specifically, we tested two hypotheses on a set of 50 empirically based ecosystem network models. The first concerned the distribution of centrality in the community. We hypothesized that the functional importance of species would tend to be concentrated into a few dominant species followed by a group of species with lower, more even importance as is often seen in dominance-diversity curves. Second, we tested the systems ecology hypothesis that indirect relationships homogenize the functional importance of species in ecosystems. Our results support both hypotheses and highlight the importance of detritus and nutrient recyclers such as fungi and bacteria in generating the energy-matter flow in ecosystems. Our homogenization results suggest that indirect effects are important in part because they tend to even the importance of species in ecosystems. A core contribution of this work is that it creates a formal, mathematical method to quantify the importance species play in generating ecosystem activity by integrating direct, indirect, and boundary effects in ecological systems.

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Biophysical connection between evolutionary dynamics and thermodynamics in in vitro evolution.

Publication Date: 2012 Feb 7 PMID: 22085736
Authors: Aita, T. - Husimi, Y.
Journal: J Theor Biol

We analyzed a mathematical model of in vitro evolution conducted by repetition of mutagenesis and selection processes. The selection process consists of the selective enrichment and subsequent sampling as follows: each mutant with fitness W is amplified by the Boltzmann factor exp(rW/k(B)T(the)), where the fitness W is defined as the negative Gibbs free energy (-DeltaG) in a reaction of the phenotypic molecules and r is the round number of the selective enrichment; then, an arbitrary mutant is randomly chosen from the resulting mutant population and it becomes a new parent in the next generation. As a result, we found that the evolutionary dynamics is described in a mathematical framework similar to thermodynamics: the "evolution constant" k(E) and "evolutionary temperature" T(evo) play key roles similar to the Boltzmann constant k(B) and thermodynamic temperature T(the), respectively. In the stationary state of the evolutionary dynamics, the attractor of the fitness is in inverse proportion to k(E)T(evo). Furthermore, beyond the mathematical analogy, we obtained a biophysical connection between evolutionary dynamics and thermodynamics. Particularly, we found that T(evo) and T(the) are connected by k(E)T(evo) approximately k(B)T(the)/2r. These results suggest that we can predict the fitness value in the stationary state by the thermodynamic temperature T(the) in the experimental setup.

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Campus quarantine (Fengxiao) for curbing emergent infectious diseases: Lessons from mitigating A/H1N1 in Xi'an, China.

Publication Date: 2012 Feb 21 PMID: 22079943
Authors: Tang, S. - Xiao, Y. - Yuan, L. - Cheke, R. A. - Wu, J.
Journal: J Theor Biol

During the 2009 A/H1N1 influenza pandemic, very strict interventions including campus quarantine (Fengxiao) (restrictions on the movements of university personnel) were taken in mainland China to slow down the initial spread of the disease from the university network to a wider community. The decision for implementation and/or relaxation of Fengxiao depends on the assessment of the level of infection within the university network compared with that in the wider community and on the degree of interruption of normal academic activities and the associated social/economic costs. However, the most important consideration influencing the decision is whether the initiation and termination of Fengxiao can alter the pattern of disease spread in the entire community for effective prevention and control of the emerging disease. Here we formulate and analyze a dynamic model to evaluate the effectiveness of Fengxiao as a social distance measure for curbing the outbreak in major cities of China. Using data from the initial laboratory-confirmed cases admitted to the 8th Hospital of Xi'an (the capital city of the Shaanxi Province), we estimated the reproduction number for the period under consideration in the range 1.273-1.784 and concluded that the population's mobility, combined with the suspension of the Fengxiao strategy, was a key factor contributing to a subsequent epidemic wave. Fengxiao in China is a reversal of the usual strategy of school closures adopted in many other countries, but the lessons learnt from it may be useful for disease management in other countries where restrictions on the movements across a facility boundary and close monitoring of the infection within the facility are feasible in the long term.

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Regulation of task differentiation in wasp societies: A bottom-up model of the "common stomach".

Publication Date: 2012 Feb 7 PMID: 22079942
Authors: Karsai, I. - Phillips, M. D.
Journal: J Theor Biol

Metapolybia wasps live in small societies (around one hundred adults) and rear their young in nests they construct on flat surfaces from plant materials. For processing nest paper, they must gather plant materials and process it into pulp with water. The water is collected by water foragers and is transferred to pulp foragers indirectly via a "common stomach." The common stomach, or social crop, is formed by generalist wasps called laborers. These wasps can engage in water exchange, store water in their crops, and may become specialist foragers or builders. We provide an alternative model for regulating task partitioning in construction behavior by using an agent based modeling framework parameterized by our field observations. Our model predicts that assessing colony needs via individual interactions with the common stomach leads to a robust regulation of task partitioning in construction behavior. By using perturbation experiments in our simulations, we show that this emergent task allocation is able to dynamically adapt to perturbations of the environment and to changes in colony-level demands or population structure. The robustness of our model stems from the fact that the common stomach is both a strong buffer and a source of several feedback mechanisms that affect the individual wasps. We show that both the efficiency and the task fidelity of these colonies are dependent upon colony size. We also demonstrate that the emergence of specialist wasps (individuals with high task fidelity) does not require any special initial conditions or reinforcement at the individual level, but it is rather a consequence of colony-level workflow stability. Our model closely mimics the behavior of Metapolybia wasps, demonstrating that a regulation mechanism based on simple pair-wise interactions through a common stomach is a plausible hypothesis for the organization of collective behavior.

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Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks.

Publication Date: 2012 Feb 7 PMID: 22079419
Authors: Nishiura, H. - Yan, P. - Sleeman, C. K. - Mode, C. J.
Journal: J Theor Biol

Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k=1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97-1.38). When less dispersed with k=2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.

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Deconvolution of the vestibular evoked myogenic potential.

Publication Date: 2012 Feb 7 PMID: 22079097
Authors: Lutkenhoner, B. - Basel, T.
Journal: J Theor Biol

The vestibular evoked myogenic potential (VEMP) and the associated variance modulation can be understood by a convolution model. Two functions of time are incorporated into the model: the motor unit action potential (MUAP) of an average motor unit, and the temporal modulation of the MUAP rate of all contributing motor units, briefly called rate modulation. The latter is the function of interest, whereas the MUAP acts as a filter that distorts the information contained in the measured data. Here, it is shown how to recover the rate modulation by undoing the filtering using a deconvolution approach. The key aspects of our deconvolution algorithm are as follows: (1) the rate modulation is described in terms of just a few parameters; (2) the MUAP is calculated by Wiener deconvolution of the VEMP with the rate modulation; (3) the model parameters are optimized using a figure-of-merit function where the most important term quantifies the difference between measured and model-predicted variance modulation. The effectiveness of the algorithm is demonstrated with simulated data. An analysis of real data confirms the view that there are basically two components, which roughly correspond to the waves p13-n23 and n34-p44 of the VEMP. The rate modulation corresponding to the first, inhibitory component is much stronger than that corresponding to the second, excitatory component. But the latter is more extended so that the two modulations have almost the same equivalent rectangular duration.

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A potential in silico antibody-antigen based diagnostic test for precise identification of Acinetobacter baumannii.

Publication Date: 2012 Feb 7 PMID: 22079096
Authors: Rahbar, M. R. - Rasooli, I. - Gargari, S. L. - Sandstrom, G. - Amani, J. - Fattahian, Y. - Jahangiri, A. - Jalali, M.
Journal: J Theor Biol

Acinetobacter baumannii is a problematic nosocomial pathogen. The resistance to a wide range of antimicrobial agents, attributable to its biofilm phenotype, makes the treatment very difficult. Biofilm is a common feature of most pathogens. Biofilm associated proteins (Bap) are cellular surface components directly involved in biofilm formation process. The dearth of a fast precise diagnostic test and versatility of Bap sequences in A. baumannii were intuitions to design this study. In silico analysis is a reliable alternative to laborious experimental work in this connection. Databases were searched for an antigenic conserved region of Bap specific to A. baumannii. The region was selected based on alignments and propensity scales. Tertiary structure for this region was built and predicted B-cell epitopes were mapped on the surface of the built model. Our protein subunit was found to be a potential antigen, possessing several antigenic determinants, eliciting antibody. Hence this subunit could be used as a suitable agent for antibody-antigen based diagnostic test. This specific antigen can minimize laboratory errors in identification of A. baumannii and thus help clinicians to quick and precise diagnosis of the bacteria and initiatives to the treatment of the infection. Antigenicity of the region could also be explored for elicitation of antibody to protect the individuals exposed to A. baumannii.

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Incentives in the family II: Behavioral dynamics and the evolution of non-costly signaling.

Publication Date: 2012 Feb 7 PMID: 22067366
Authors: Akcay, E.
Journal: J Theor Biol

In many biological and social interactions, individuals with private information have incentives to misrepresent their information. A prominent example is when offspring know their need or condition but the parents do not. Theory showed that signal costs can ensure truthful communication in such situations, but further studies have cast in doubt whether empirically measured costs are high enough to sustain honesty, and whether the costly signaling equilibrium represents a fitness advantage over non-signaling. Here, I tackle these issues with a model of signaling that takes place at the behavioral time-scale through dynamic responses of individuals to each other. I then embed this behavioral model in an evolutionary one that asks how the decision rules of the parent and offspring evolve in response to the trade-off between signal costs and the costs of provisioning. I find that a non-costly honest signaling equilibrium can evolve when relatedness between siblings is above a certain threshold. This threshold is lower when (i) offspring get satiated more quickly, (ii) the cost of provisioning to the parent escalates less rapidly, or (iii) the variation in offspring need is higher. These results provide a potential resolution to the apparent paradox of costly begging. I also discuss the relation between costly signaling and mechanism design theories.

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A mathematical model of tumor-immune interactions.

Publication Date: 2012 Feb 7 PMID: 22051568
Authors: Robertson-Tessi, M. - El-Kareh, A. - Goriely, A.
Journal: J Theor Biol

A mathematical model of the interactions between a growing tumor and the immune system is presented. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector T-cell mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for. The model is applied to tumors with different growth rates and antigenicities to gauge the relative importance of various immunosuppressive mechanisms. The most important factors leading to tumor escape are TGF-beta-induced immunosuppression, conversion of helper T cells into regulatory T cells, and the limitation of immune cell access to the full tumor at large tumor sizes. The results suggest that for a given tumor growth rate, there is an optimal antigenicity maximizing the response of the immune system. Further increases in antigenicity result in increased immunosuppression, and therefore a decrease in tumor killing rate. This result may have implications for immunotherapies which modulate the effective antigenicity. Simulation of dendritic cell therapy with the model suggests that for some tumors, there is an optimal dose of transfused dendritic cells.

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Animal social networks as substrate for cultural behavioural diversity.

Publication Date: 2012 Feb 7 PMID: 22051567
Authors: Whitehead, H. - Lusseau, D.
Journal: J Theor Biol

We used individual-based stochastic models to examine how social structure influences the diversity of socially learned behaviour within a non-human population. For continuous behavioural variables we modelled three forms of dyadic social learning, averaging the behavioural value of the two individuals, random transfer of information from one individual to the other, and directional transfer from the individual with highest behavioural value to the other. Learning had potential error. We also examined the transfer of categorical behaviour between individuals with random directionality and two forms of error, the adoption of a randomly chosen existing behavioural category or the innovation of a new type of behaviour. In populations without social structuring the diversity of culturally transmitted behaviour increased with learning error and population size. When the populations were structured socially either by making individuals members of permanent social units or by giving them overlapping ranges, behavioural diversity increased with network modularity under all scenarios, although the proportional increase varied considerably between continuous and categorical behaviour, with transmission mechanism, and population size. Although functions of the form [Formula: see text] predicted the mean increase in diversity with modularity (m) and population size (N), behavioural diversity could be highly unpredictable both between simulations with the same set of parameters, and within runs. Errors in social learning and social structuring generally promote behavioural diversity. Consequently, social learning may be considered to produce culture in populations whose social structure is sufficiently modular.

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Constructing ecologies.

Publication Date: 2012 Feb 7 PMID: 22051566
Authors: Cropp, R. - Norbury, J.
Journal: J Theor Biol

We synthesize the generic properties of ecologically realistic multi-trophic level models and define criteria for ecological realism. We define an "ecospace" in which all ecologically realistic dynamics are confined, and construct "resource rays" that define the resources available to each species at every point in the ecospace. Resource rays for a species are lines from a vertex of maximum resource to the opposite boundary where no resources are available. The growth functions of all biota normally decrease along their resource rays, and change sign from positive to negative. This property prescribes that each species must have a zero isosurface within the ecospace. We illustrate our conditions on a highly cited three trophic level model from population dynamics, showing how to extend this system biologically consistently to a closed ecological system. Our synthesis extends the concept of carrying capacity of population models to explicitly include exhaustion of limiting resources, and so allows for population biology models to be considered as ecologically closed systems with respect to a key limiting nutrient. This approach unifies many theoretical and applied models in a common biogeochemical framework, facilitates better understanding of the key structures of complex ecologies, and suggests strategies for efficient design of experiments.

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Mirror images: Fish versus terrestrial animals.

Publication Date: 2012 Feb 7 PMID: 22044608
Authors: Lev-Yadun, S. - Katzir, G.
Journal: J Theor Biol

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Metabolic network analysis of perfused livers under fed and fasted states: incorporating thermodynamic and futile-cycle-associated regulatory constraints.

Publication Date: 2012 Jan 21 PMID: 22037644
Authors: Orman, M. A. - Androulakis, I. P. - Berthiaume, F. - Ierapetritou, M. G.
Journal: J Theor Biol

Isolated liver perfusion systems have been extensively used to characterize intrinsic metabolic changes in liver under various conditions, including systemic injury, hepatotoxin exposure, and warm ischemia. Most of these studies were performed utilizing fasted animals prior to perfusion so that a simplified metabolic network could be used in order to determine intracellular fluxes. However, fasting induced metabolic alterations might interfere with disease related changes. Therefore, there is a need to develop a "unified" metabolic flux analysis approach that could be similarly applied to both fed and fasted states. In this study we explored a methodology based on elementary mode analysis in order to determine intracellular fluxes and active pathways simultaneously. In order to decrease the solution space, thermodynamic constraints, and enzymatic regulatory properties for the formation of futile cycles were further considered in the model, resulting in a mixed integer quadratic programming problem. Given the published experimental observations describing the perfused livers under fed and fasted states, the proposed approach successfully determined that gluconeogenesis, glycogenolysis and fatty acid oxidation were active in both states. However, fasting increased the fluxes in gluconeogenic reactions whereas it decreased fluxes associated with glycogenolysis, TCA cycle, fatty acid oxidation and electron transport reactions. This analysis further identified that more pathways were found to be active in fed state while their weight values were relatively lower compared to fasted state. Glucose, lactate, glutamine, glutamate and ketone bodies were also found to be important external metabolites whose extracellular fluxes should be used in the hepatic metabolic network analysis. In conclusion, the mathematical formulation explored in this study is an attractive tool to analyze the metabolic network of perfused livers under various disease conditions. This approach could be simultaneously applied to both fasted and fed data sets.

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Evolution of cooperation facilitated by reinforcement learning with adaptive aspiration levels.

Publication Date: 2012 Jan 21 PMID: 22037063
Authors: Tanabe, S. - Masuda, N.
Journal: J Theor Biol

Repeated interaction between individuals is the main mechanism for maintaining cooperation in social dilemma situations. Variants of tit-for-tat (repeating the previous action of the opponent) and the win-stay lose-shift strategy are known as strong competitors in iterated social dilemma games. On the other hand, real repeated interaction generally allows plasticity (i.e., learning) of individuals based on the experience of the past. Although plasticity is relevant to various biological phenomena, its role in repeated social dilemma games is relatively unexplored. In particular, if experience-based learning plays a key role in promotion and maintenance of cooperation, learners should evolve in the contest with nonlearners under selection pressure. By modeling players using a simple reinforcement learning model, we numerically show that learning enables the evolution of cooperation. We also show that numerically estimated adaptive dynamics appositely predict the outcome of evolutionary simulations. The analysis of the adaptive dynamics enables us to capture the obtained results as an affirmative example of the Baldwin effect, where learning accelerates the evolution to optimality.

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Prediction of protein-protein interaction sites using patch-based residue characterization.

Publication Date: 2012 Jan 21 PMID: 22037062
Authors: Qiu, Z. - Wang, X.
Journal: J Theor Biol

Identifying protein-protein interaction sites provides important clues to the function of a protein and is becoming increasingly relevant in topics such as systems biology and drug discovery. Using a patch-based model for residue characterization, we trained random forest classifiers for residue-based interface prediction, which was followed by a clustering procedure to produce patches for patch-based interface prediction. For residue-based interface prediction, our method achieves a specificity rate of 0.7 and a sensitivity rate of 0.78. For patch-based interface prediction, a success rate of 0.80 is achieved. Based on same datasets, we also compare it with several published methods. The results show that our method is a successful predictor for residue-based and patch-based interface prediction.

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Elastic and viscoelastic properties of a type I collagen fiber.

Publication Date: 2012 Jan 21 PMID: 22037061
Authors: Sopakayang, R. - De Vita, R. - Kwansa, A. - Freeman, J. W.
Journal: J Theor Biol

A new mathematical model is presented to describe the elastic and viscoelastic properties of a single collagen fiber. The model is formulated by accounting for the mechanical contribution of the collagen fiber's main constituents: the microfibrils, the interfibrillar matrix and crosslinks. The collagen fiber is modeled as a linear elastic spring, which represents the mechanical contribution of the microfibrils, and an arrangement in parallel of elastic springs and viscous dashpots, which represent the mechanical contributions of the crosslinks and interfibrillar matrix, respectively. The linear elastic spring and the arrangement in parallel of elastic springs and viscous dashpots are then connected in series. The crosslinks are assumed to gradually break under strain and, consequently, the interfibrillar is assumed to change its viscous properties. Incremental stress relaxation tests are conducted on dry collagen fibers reconstituted from rat tail tendons to determine their elastic and viscoelastic properties. The elastic and total stress-strain curves and the stress relaxation at different levels of strain collected by performing these tests are then used to estimate the parameters of the model and evaluate its predictive capabilities.

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Neutrophil dynamics in response to chemotherapy and G-CSF.

Publication Date: 2012 Jan 21 PMID: 22037060
Authors: Zhuge, C. - Lei, J. - Mackey, M. C.
Journal: J Theor Biol

We have used a mathematical model of the combined dynamics of the hematopoietic stem cells and the differentiated neutrophil progeny to examine the effects of periodic chemotherapy in generating neutropenia, and the corresponding response of this system to granulocyte colony stimulating factor given to counteract the neutropenia. We find that there is a significant period of chemotherapy delivery that induces resonance in the system (at a period twice the average neutrophil lifespan from commitment to death) and a corresponding neutropenia suggesting that myelosuppressive protocols should avoid this period to minimize hematopoietic damage. The response to G-CSF is highly variable.

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Multi-kernel transfer learning based on Chou's PseAAC formulation for protein submitochondria localization.

Publication Date: 2012 Jan 21 PMID: 22037046
Authors: Mei, S.
Journal: J Theor Biol

Protein sub-organelle localization, e.g. submitochondria, seems more challenging than general protein subcellular localization, because the determination of protein's micro-level localization within organelle by fluorescent imaging technique would face up with more difficulties. Up to present, there are far few computational methods for protein submitochondria localization, and the existing sequence-based predictive models demonstrate moderate or unsatisfactory performance. Recent researches have demonstrated that gene ontology (GO) is a convincingly effective protein feature for protein subcellular localization. However, the GO information may not be available for novel proteins or sparsely annotated protein subfamilies. In allusion to the problem, we transfer the homology's GO information to the target protein and propose a multi-kernel transfer learning model for protein submitochondria localization (MK-TLM), which substantially extends our previously published work (gene ontology based transfer learning model for protein subcellular localization, GO-TLM). To reduce the risk of performance overestimation, we conduct a more comprehensive survey of the model performance in optimistic case, moderate case and pessimistic case according to the abundance of target protein's GO information. The experiments on submitochondria benchmark datasets show that MK-TLM significantly outperforms the baseline models, and demonstrates excellent performance for novel mitochondria proteins and those mitochondria proteins that belong to the subfamily we know little about.

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Stable trimorphic coexistence in a lattice model of spatial competition with two site types.

Publication Date: 2012 Feb 21 PMID: 22037045
Authors: Karonen, I.
Journal: J Theor Biol

I examine the effect of exogenous spatial heterogeneity on the coexistence of competing species using a simple model of non-hierarchical competition for site occupancy on a lattice. The sites on the lattice are divided into two types representing two different habitats or spatial resources. The model features no temporal variability, hierarchical competition, type-dependent interactions or other features traditionally known to support more competing species than there are resources. Nonetheless, stable coexistence of two habitat specialists and a generalist is observed in this model for a range of parameter values. In the spatially implicit mean field approximation of the model, such coexistence is shown to be impossible, demonstrating that it indeed arises from the explicit spatial structure.

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New Markov-Shannon Entropy models to assess connectivity quality in complex networks: from molecular to cellular pathway, Parasite-Host, Neural, Industry, and Legal-Social networks.

Publication Date: 2012 Jan 21 PMID: 22037044
Authors: Riera-Fernandez, P. - Munteanu, C. R. - Escobar, M. - Prado-Prado, F. - Martin-Romalde, R. - Pereira, D. - Villalba, K. - Duardo-Sanchez, A. - Gonzalez-Diaz, H.
Journal: J Theor Biol

Graph and Complex Network theory is expanding its application to different levels of matter organization such as molecular, biological, technological, and social networks. A network is a set of items, usually called nodes, with connections between them, which are called links or edges. There are many different experimental and/or theoretical methods to assign node-node links depending on the type of network we want to construct. Unfortunately, the use of a method for experimental reevaluation of the entire network is very expensive in terms of time and resources; thus the development of cheaper theoretical methods is of major importance. In addition, different methods to link nodes in the same type of network are not totally accurate in such a way that they do not always coincide. In this sense, the development of computational methods useful to evaluate connectivity quality in complex networks (a posteriori of network assemble) is a goal of major interest. In this work, we report for the first time a new method to calculate numerical quality scores S(L(ij)) for network links L(ij) (connectivity) based on the Markov-Shannon Entropy indices of order k-th (theta(k)) for network nodes. The algorithm may be summarized as follows: (i) first, the theta(k)(j) values are calculated for all j-th nodes in a complex network already constructed; (ii) A Linear Discriminant Analysis (LDA) is used to seek a linear equation that discriminates connected or linked (L(ij)=1) pairs of nodes experimentally confirmed from non-linked ones (L(ij)=0); (iii) the new model is validated with external series of pairs of nodes; (iv) the equation obtained is used to re-evaluate the connectivity quality of the network, connecting/disconnecting nodes based on the quality scores calculated with the new connectivity function. This method was used to study different types of large networks. The linear models obtained produced the following results in terms of overall accuracy for network reconstruction: Metabolic networks (72.3%), Parasite-Host networks (93.3%), CoCoMac brain cortex co-activation network (89.6%), NW Spain fasciolosis spreading network (97.2%), Spanish financial law network (89.9%) and World trade network for Intelligent & Active Food Packaging (92.8%). In order to seek these models, we studied an average of 55,388 pairs of nodes in each model and a total of 332,326 pairs of nodes in all models. Finally, this method was used to solve a more complicated problem. A model was developed to score the connectivity quality in the Drug-Target network of US FDA approved drugs. In this last model the theta(k) values were calculated for three types of molecular networks representing different levels of organization: drug molecular graphs (atom-atom bonds), protein residue networks (amino acid interactions), and drug-target network (compound-protein binding). The overall accuracy of this model was 76.3%. This work opens a new door to the computational reevaluation of network connectivity quality (collation) for complex systems in molecular, biomedical, technological, and legal-social sciences as well as in world trade and industry.

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The effect of public health interventions on the spread of influenza among cities.

Publication Date: 2012 Jan 21 PMID: 22033506
Authors: Lee, J. M. - Choi, D. - Cho, G. - Kim, Y.
Journal: J Theor Biol

Infectious disease is no longer a local problem. Modern populations are more mobile than ever before, and with this mobility comes active global mixing of infectious disease. To understand the spread of diseases such as influenza, we use a multi-city epidemic model. We extend the SEIR (susceptible-exposed-infectious-recovered) model to incorporate population migration between cities, and use this model to analyze the geographic spread of influenza. We investigate the effectiveness of travel restrictions as a control against the spread of influenza. First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing the number of clinically ill individuals that are treated, and reducing the interval between infection and treatment of such individuals. We evaluate the effectiveness of the three control strategies with numerical simulations. It is shown that travel restrictions are less effective than the other two strategies. In general, travel restriction tends to delay the spread of the disease into new cities. However, it can increase the peak height of infected populations in all cities. An understanding of the epidemiological structures of related cities is strongly recommended in order to effectively apply the travel restriction strategy.

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A mathematical model of effects of environmental contamination and presence of volunteers on hospital infections in China.

Publication Date: 2012 Jan 21 PMID: 22024632
Authors: Wang, X. - Xiao, Y. - Wang, J. - Lu, X.
Journal: J Theor Biol

Deterministic and stochastic mathematical models were formulated to investigate the roles that environmental contamination and the presence of volunteers played in the dynamics of hospital infections in China. Semi-stochastic simulation was used to estimate some of the parameters by fitting the observed data and investigating the impacts of interventions such as cleaning, hand hygiene and isolation of admitted MRSA (Methicillin-resistant Staphylococcus aureus) patients on mean prevalence of infection. The basic reproduction number was estimated to be 0.9753. Numerical simulations show that environmental contamination is a threat to hospital infection and free-living bacteria in the environment can promote transmission and initiate infection even if an infection has died out among HCWs (health-care workers) and patients. Sensitivity analysis indicates that a contaminated environment and volunteers contribute substantially to MRSA transmission in hospital infections, and hence effective control measures should be targeted. Hand hygiene of volunteers and cleaning are more effective in reducing the mean prevalence of colonized patients than isolation of newly admitted MRSA-positive patients and hand hygiene of HCWs. Hence volunteers, a cadre of semi-professional nurses, are beneficial to both disease control and supplementary treatment of HCWs if they are well trained. However, isolation of newly admitted MRSA-positive patients could be influential and dominant in reducing the prevalence of infection when the environment within a ward is sufficiently clean.

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Mathematical model of GAL regulon dynamics in Saccharomyces cerevisiae.

Publication Date: 2012 Jan 21 PMID: 22024631
Authors: Apostu, R. - Mackey, M. C.
Journal: J Theor Biol

Genetic switches are prevalent in nature and provide cells with a strategy to adapt to changing environments. The GAL switch is an intriguing example which is not understood in all detail. The GAL switch allows organisms to metabolize galactose, and controls whether the machinery responsible for the galactose metabolism is turned on or off. Currently, it is not known exactly how the galactose signal is sensed by the transcriptional machinery. Here we utilize quantitative tools to understand the S. cerevisiae cell response to galactose challenge, and to analyze the plausible molecular mechanisms underlying its operation. We work at a population level to develop a dynamic model based on the interplay of the key regulatory proteins Gal4p, Gal80p, and Gal3p. To our knowledge, the model presented here is the first to reproduce qualitatively the bistable network behavior found experimentally. Given the current understanding of the GAL circuit induction (Wightman et al., 2008; Jiang et al., 2009), we propose that the most likely in vivo mechanism leading to the transcriptional activation of the GAL genes is the physical interaction between galactose-activated Gal3p and Gal80p, with the complex Gal3p-Gal80p remaining bound at the GAL promoters. Our mathematical model is in agreement with the flow cytometry profiles of wild type, gal3Delta and gal80Delta mutant strains from Acar et al. (2005), and involves a fraction of actively transcribing cells with the same qualitative features as in the data set collected by Acar et al. (2010). Furthermore, the computational modeling provides an explanation for the contradictory results obtained by independent laboratories when tackling experimentally the issue of binary versus graded response to galactose induction.

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Climbing in hexapods: a plain model for heavy slopes.

Publication Date: 2012 Jan 21 PMID: 22019507
Authors: Gunther, M. - Weihmann, T.
Journal: J Theor Biol

Usually, a climbing cockroach attaches with three legs to a substrate. According to a recent model study, pulling forces underneath the front leg are required at some critical slope angle in upward locomotion. This critical angle depends on the animal's anatomy and leg positioning. In this study, we asked especially how this critical angle can be biased by one parameter that may be controlled during climbing: the body height above the substrate. We found that the typical ratio between body height and length (0.2) adopted by cockroaches is slightly higher than the very ratio (0.15) at which the critical slope angle can be increased most strongly for a given decrease in body height. In other words, it is likely that a geometrical body design of cockroaches evolved, which enables a delicate reduction in body height perfectly suitable for preventing the danger of slipping or even falling over rearwards at steepening slopes (approaching the vertical). In that sense, our model predicts, not just for hexapods but rather for any three-point climber, that taking up a low ratio of body height to the distance between the foremost and the hindmost attachment point (very crouched posture) makes body height a good parameter for climbing control.

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The fine art of surfacing: Its efficacy in broadcast spawning.

Publication Date: 2012 Feb 7 PMID: 22019506
Authors: Molacek, J. - Denny, M. - Bush, J. W.
Journal: J Theor Biol

Many organisms reproduce by releasing gametes into the surrounding fluid. For some such broadcast spawners, gametes are positively or negatively buoyant, and, as a result, fertilization occurs on a two-dimensional surface rather than in the bulk of the air or water. We here rationalize this behaviour by considering the encounter rates of gametes on the surface and in the fluid bulk. The advantage of surfacing is quantified by considering an infinitely wide body of water of constant depth. Differential loss rates at the surface and in the bulk are considered and their influence on the robustness of surface search assessed. For small and moderate differential loss rates, the advantage of surfacing is very robust and significant; only for large loss rate differences can the advantage of surfacing be nullified.

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Invasion threshold in structured populations with recurrent mobility patterns.

Publication Date: 2012 Jan 21 PMID: 22019505
Authors: Balcan, D. - Vespignani, A.
Journal: J Theor Biol

In this paper we develop a framework to analyze the behavior of contagion and spreading processes in complex subpopulation networks where individuals have memory of their subpopulation of origin. We introduce a metapopulation model in which subpopulations are connected through heterogeneous fluxes of individuals. The mobility process among communities takes into account the memory of residence of individuals and is incorporated with the classical susceptible-infectious-recovered epidemic model within each subpopulation. In order to gain analytical insight into the behavior of the system we use degree-block variables describing the heterogeneity of the subpopulation network and a time-scale separation technique for the dynamics of individuals. By considering the stochastic nature of the epidemic process we obtain the explicit expression of the global epidemic invasion threshold, below which the disease dies out before reaching a macroscopic fraction of the subpopulations. This threshold is not present in continuous deterministic diffusion models and explicitly depends on the disease parameters, the mobility rates, and the properties of the coupling matrices describing the mobility across subpopulations. The results presented here take a step further in offering insight into the fundamental mechanisms controlling the spreading of infectious diseases and other contagion processes across spatially structured communities.

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Sequence-dependent prediction of recombination hotspots in Saccharomyces cerevisiae.

Publication Date: 2012 Jan 21 PMID: 22016025
Authors: Liu, G. - Liu, J. - Cui, X. - Cai, L.
Journal: J Theor Biol

Meiotic recombination does not occur randomly across the genome, but instead occurs at relatively high frequencies in some genomic regions (hotspots) and relatively low frequencies in others (coldspots). Hotspots and coldspots would shed light on the mechanism of recombination, but the accurate prediction of hot/cold spots is still an open question. In this study, we presented a model to predict hot/cold spots in yeast using increment of diversity combined with quadratic discriminant analysis (IDQD) based on sequence k-mer frequencies. 5-fold cross validation showed a total prediction accuracy of 80.3%. Compared with other machine-learning algorithms, IDQD approach is as powerful as random forest (RF) and outperforms support vector machine (SVM) in identifying hotspots and coldspots. We also predicted increased recombination rates in the upstream regions of transcription start sites and in the downstream regions of transcription termination sites. Additionally, genome-wide recombination map in yeast obtained by IDQD model is in close agreement with the experimentally generated map, especially for the Peak locations, although some fine-scale differences exist. Our results highlight the sequence dependency of recombination.

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The cumulative effect of genetic markers on classification performance: Insights from simple models.

Publication Date: 2012 Jan 21 PMID: 22004997
Authors: Tal, O.
Journal: J Theor Biol

The cumulative effect of markers on classification accuracy, with even slight between-population allele frequency differences, has been a mainstay of empirical genetic research. The simple theoretical model of Edwards (2003) has enabled a clear elucidation of the effect of additional markers on average classification error. The present paper describes a mathematical generalization necessary to alleviate an oversimplification, but at the same time revealing an inherent drawback of the simple model. An alternative model for explaining the effect of additional loci on classification is proposed based on an optimal classifier. In particular, cases in which the expected performance does not profit from information at additional loci are characterized in simple terms. Further insight into the capacity of classifiers to exploit the potential afforded by each additional locus comes from an information-theoretic perspective. Multilocus correlation and multivariate mutual information measures are shown to tightly correspond with the dynamics of misclassification rates, under the cumulative effect of loci.

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Microbial dormancy in batch cultures as a function of substrate-dependent mortality.

Publication Date: 2012 Jan 21 PMID: 22004996
Authors: Ayati, B. P.
Journal: J Theor Biol

We present models and computational studies of dormancy in batch cultures to try to understand the relationship between reculturing time and death penalty for low substrate and the relative advantage of fast versus slow reawakening on the part of the bacteria. We find that the advantage goes to the faster waker for shorter reculturing times and lower mortality under low substrate, and moves to the slower waker as reculturing times and death penalty increase. The advantage returns again to the fast waker for very high death penalties. We use an explicit, continuous structure variable to represent dormancy so as to allow for flexibility in substrate usage on the part of dormant cells, and for a more mechanistic representation of the reawakening process.

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Computational analysis of RNA-protein interaction interfaces via the Voronoi diagram.

Publication Date: 2012 Jan 21 PMID: 22004995
Authors: Mahdavi, S. - Mohades, A. - Salehzadeh Yazdi, A. - Jahandideh, S. - Masoudi-Nejad, A.
Journal: J Theor Biol

Cellular functions are mediated by various biological processes including biomolecular interactions, such as protein-protein, DNA-protein and RNA-protein interactions in which RNA-Protein interactions are indispensable for many biological processes like cell development and viral replication. Unlike the protein-protein and protein-DNA interactions, accurate mechanisms and structures of the RNA-Protein complexes are not fully understood. A large amount of theoretical evidence have shown during the past several years that computational geometry is the first pace in understanding the binding profiles and plays a key role in the study of intricate biological structures, interactions and complexes. In this paper, RNA-Protein interaction interface surface is computed via the weighted Voronoi diagram of atoms. Using two filter operations provides a natural definition for interface atoms as classic methods. Unbounded parts of Voronoi facets that are far from the complex are trimmed using modified convex hull of atom centers. This algorithm is implemented to a database with different RNA-Protein complexes extracted from Protein Data Bank (PDB). Afterward, the features of interfaces have been computed and compared with classic method. The results show high correlation coefficients between interface size in the Voronoi model and the classical model based on solvent accessibility, as well as high accuracy and precision in comparison to classical model.

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Effects of causal networks on the structure and stability of resource allocation trait correlations.

Publication Date: 2012 Jan 21 PMID: 22004994
Authors: Gove, R. P. - Chen, W. - Zweber, N. B. - Erwin, R. - Rychtar, J. - Remington, D. L.
Journal: J Theor Biol

Discovering the mechanisms by which genetic variation influences phenotypes is integral to understanding life-history evolution. Models describing causal relationships among traits in a developmental hierarchy provide a functional basis for understanding the correlations often observed among life-history traits. In this paper, we evaluate a developmental network model of life-history traits based on the perennial herb Arabidopsis lyrata, evaluate phenotypic, genetic, and environmental covariance matrices obtained under different scenarios of quantitative trait locus (QTL) effects in simulated crosses, test the efficacy of structural equation modeling to identify the correct basis for multiple-trait QTL effects, and compare model predictions with field data. We found that the trait network constrained the phenotypic covariance patterns to varying degrees, depending on which traits were directly affected by QTLs. Genetic and environmental covariance matrices were strongly correlated only when direct QTL effects were spread over many traits. Structural equation models that included all simulated traits correctly identified traits directly affected by QTLs, but heuristic search algorithms found several network structures other than the correct one that also fit the data closely. Estimated correlations among a subset of traits in F(2) data from field studies corresponded closely to model predictions when simulated QTLs affected traits known to differ between the parental populations. Our results show that causal trait network models can unify several aspects of quantitative genetic theory with empirical observations on genetic and phenotypic covariance patterns, and that incorporating trait networks into genetic analysis offers promise for elucidating mechanisms of life history evolution.

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An agent-based model for the transmission dynamics of Toxoplasma gondii.

Publication Date: 2012 Jan 21 PMID: 22004993
Authors: Jiang, W. - Sullivan, A. M. - Su, C. - Zhao, X.
Journal: J Theor Biol

Toxoplasma gondii (T. gondii) is a unicellular protozoan that infects up to one-third of the world's human population. Numerous studies revealed that a latent infection of T. gondii can cause life-threatening encephalitis in immunocompromised people and also has significant effects on the behavior of healthy people and animals. However, the overall transmission of T. gondii has not been well understood although many factors affecting this process have been found out by different biologists separately. Here we synthesize what is currently known about the natural history of T. gondii by developing a prototype agent-based model to mimic the transmission process of T. gondii in a farm system. The present model takes into account the complete life cycle of T. gondii, which includes the transitions of the parasite from cats to environment through feces, from contaminated environment to mice through oocysts, from mice to cats through tissue cysts, from environment to cats through oocysts as well as the vertical transmission among mice. Although the current model does not explicitly include humans and other end-receivers, the effect of the transition to end-receivers is estimated by a developed infection risk index. The current model can also be extended to include human activities and thus be used to investigate the influences of human management on disease control. Simulation results reveal that most cats are infected through preying on infected mice while mice are infected through vertical transmission more often than through infection with oocysts, which clearly suggests the important role of mice during the transmission of T. gondii. Furthermore, our simulation results show that decreasing the number of mice on a farm can lead to the eradication of the disease and thus can lower the infection risk of other intermediate hosts on the farm. In addition, with the assumption that the relation between virulence and transmission satisfies a normal function, we show that intermediate virulent lineages (type II) can sustain the disease most efficiently, which can qualitatively agree with the fact that the evolution of the parasite favors intermediate virulence. The effects of other related factors on transmission, including the latent period and imprudent behavior of mice, and prevention strategies are also studied based on the present model.

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Clustering in cell cycle dynamics with general response/signaling feedback.

Publication Date: 2012 Jan 7 PMID: 22001733
Authors: Young, T. R. - Fernandez, B. - Buckalew, R. - Moses, G. - Boczko, E. M.
Journal: J Theor Biol

Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behavior of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as "uniform" solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments.

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Multiallelic polymorphism maintained under unpredictable migration and selection.

Publication Date: 2012 Jan 21 PMID: 22001732
Authors: Bonneuil, N.
Journal: J Theor Biol

The question of protected polymorphism is addressed in terms of dynamic maintenance within a set of constraints defining polymorphism. Stricto sensu, the maintenance of polymorphism is identified with the set of states, called the C-viability kernel, from which there exists at least one trajectory remaining in the set of constraints. Protected polymorphism under time-dependent selection and migration is re-formulated as a C-viability problem. The C-viability kernel is computed under conditions of time-dependent unpredictable migration and selection, from the case of two demes and two alleles up to that of three demes and three alleles. It delineates the trade-off between isolation and openness to migration combined with relative fitness values. The problem of protected polymorphism in time-varying conditions is then answered in its full dimensionality.

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A new hybrid fractal algorithm for predicting thermophilic nucleotide sequences.

Publication Date: 2012 Jan 21 PMID: 22001320
Authors: Lu, J. L. - Hu, X. H. - Hu, D. G.
Journal: J Theor Biol

Knowledge of thermophilic mechanisms about some organisms whose optimum growth temperature (OGT) ranges from 50 to 80 degree plays a major role in helping design stable proteins. How to predict a DNA sequence to be thermophilic is a long but not fairly resolved problem. Chaos game representation (CGR) can investigate the patterns hiding in DNA sequences, and can visually reveal previously unknown structure. Fractal dimensions are good tools to measure sizes of complex, highly irregular geometric objects. In this paper, we convert every DNA sequence into a high dimensional vector by CGR algorithm and fractal dimension, and then predict the DNA sequence thermostability by these fractal features and support vector machine (SVM). We have conducted experiments on three groups: 17-dimensional vector, 65-dimensional vector, and 257-dimensional vector. Each group is evaluated by the 10-fold cross-validation test. For the results, the group of 257-dimensional vector gets the best results: the average accuracy is 0.9456 and average MCC is 0.8878. The results are also compared with the previous work with single CGR features. The comparison shows the high effectiveness of the new hybrid fractal algorithm.

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Transcriptional noise as a driver of gene evolution.

Publication Date: 2012 Jan 21 PMID: 22001319
Authors: Polev, D.
Journal: J Theor Biol

As novel genes emerge in the evolution of species, pre-existing genes expand their expression patterns to diversify their functions and the expression patterns of gene duplicates diverge to pursue functional specialization. All these processes require genes to be expressed, however, the level and specificity of gene expression at the early stages of these processes are unclear. In this study, I propose that transcriptional noise is a mechanism to test genes for new functions, and I hypothesize the 'in-service' mechanism of gene evolution. In contrast to other hypotheses that suggest that there are specialized sites for gene evolution, such as tumors (Kozlov, 2010) or the testis (Kaessmann, 2010) this hypothesis proposes that emerging genes are expressed nonspecifically in many normal tissues, due to transcriptional noise. New genes are continuously 'tested' in various cells and under various conditions, thereby allowing the genes to evolve functions at the sites of their future work. The hypothesis of 'in-service' gene evolution also proposes that pre-existing genes are continuously tested under extrinsic conditions, due to transcriptional noise; this testing facilitates the emergence of alternative promoters and the diversification of the genes' expression patterns and functions.

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Sequence comparison via polar coordinates representation and curve tree.

Publication Date: 2012 Jan 7 PMID: 22001081
Authors: Dai, Q. - Guo, X. - Li, L.
Journal: J Theor Biol

Sequence comparison has become one of the essential bioinformatics tools in bioinformatics research, which could serve as evidence of structural and functional conservation, as well as of evolutionary relations among the sequences. Existing graphical representation methods have achieved promising results in sequence comparison, but there are some design challenges with the graphical representations and feature-based measures. We reported here a new method for sequence comparison. It considers whole distribution of dual bases and employs polar coordinates method to map a biological sequence into a closed curve. The curve tree was then constructed to numerically characterize the closed curve of biological sequences, and further compared biological sequences by evaluating the distance of the curve tree of the query sequence matching against a corresponding curve tree of the template sequence. The proposed method was tested by phylogenetic analysis, and its performance was further compared with alignment-based methods. The results demonstrate that using polar coordinates representation and curve tree to compare sequences is more efficient.

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Piezoelectricity could predict sites of formation/resorption in bone remodelling and modelling.

Publication Date: 2012 Jan 7 PMID: 22001080
Authors: Fernandez, J. R. - Garcia-Aznar, J. M. - Martinez, R.
Journal: J Theor Biol

We have developed a mathematical approach for modelling the piezoelectric behaviour of bone tissue in order to evaluate the electrical surface charges in bone under different mechanical conditions. This model is able to explain how bones change their curvature, where osteoblasts or osteoclasts could detect in the periosteal/endosteal surfaces the different electrical charges promoting bone formation or resorption. This mechanism also allows to understand the BMU progression in function of the electro-mechanical bone behaviour.

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MemHyb: predicting membrane protein types by hybridizing SAAC and PSSM.

Publication Date: 2012 Jan 7 PMID: 22001079
Authors: Hayat, M. - Khan, A.
Journal: J Theor Biol

About 50% of available drugs are targeted against membrane proteins. Knowledge of membrane protein's structure and function has great importance in biological and pharmacological research. Therefore, an automated method is exceedingly advantageous, which can help in identifying the new membrane protein types based on their primary sequence. In this paper, we tackle the interesting problem of classifying membrane protein types using their sequence information. We consider both evolutionary and physicochemical features and provide them to our classification system based on support vector machine (SVM) with error correction code. We employ a powerful sequence encoding scheme by fusing position specific scoring matrix and split amino acid composition to effectively discriminate membrane protein types. Linear, polynomial, and RBF based-SVM with Bose, Chaudhuri, Hocquenghem coding are trained and tested. The highest success rate of 91.1% and 93.4% on two datasets is obtained by RBF-SVM using leave-one-out cross-validation. Thus, our proposed approach is an effective tool for the discrimination of membrane protein types and might be helpful to researchers/academicians working in the field of Drug Discovery, Cell Biology, and Bioinformatics. The web server for the proposed MemHyb-SVM is accessible at http://111.68.99.218/MemHyb-SVM.

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A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks.

Publication Date: 2012 Jan 7 PMID: 21983269
Authors: Fleming, R. M. - Maes, C. M. - Saunders, M. A. - Ye, Y. - Palsson, B. O.
Journal: J Theor Biol

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen's theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed.

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Functional contributions of astrocytes in synchronization of a neuronal network model.

Publication Date: 2012 Jan 7 PMID: 21978738
Authors: Amiri, M. - Bahrami, F. - Janahmadi, M.
Journal: J Theor Biol

In the present study, a biologically plausible neuronal population model is developed, which considers functional outcome of neuron-astrocyte interactions. Based on established neurophysiologic findings, astrocytes dynamically regulate the synaptic transmission of neuronal networks. The employed structure is based on the main physiological and anatomical features of the CA1 subfield of the hippocampus. Utilizing our model, we demonstrate that healthy astrocytes provide appropriate feedback control in regulating neural activity. In this way, the astrocytes compensate the increase of excitation coupling strength among neurons and stabilize the normal level of synchronized behavior. Next, malfunction of astrocytes in the regulatory feedback loop is investigated. In this way, pathologic astrocytes are no longer able to regulate and/or compensate the excessive increase of the excitation level. Consequently, disruption of astrocyte signaling initiates hypersynchronous firing of neurons. Our results suggest that diminishing of neuron-astrocyte cross-talk leads to an abnormal synchronized neuronal firing, which suggests that astrocytes could be a proximal target for the treatment of related disorders including epilepsy.

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The impact of sexually abstaining groups on persistence of sexually transmitted infections in populations with ephemeral pair bonds.

Publication Date: 2012 Jan 7 PMID: 21978737
Authors: Maxin, D. - Berec, L. - Covello, M. - Jessee, J. - Zimmer, M.
Journal: J Theor Biol

Individuals often stop reproducing some time before they die. In this paper we compose and analyze a logistic two-sex population model in which individuals form pairs just to mate (i.e. pair bonds are ephemeral) and later move on to sexually abstaining groups. Using this model, we study the impact of sexually abstaining groups on persistence of a benign sexually transmitted infection (STI) in populations with such ephemeral pair bonds. We observe that the presence of sexually abstaining groups cannot prevent an STI from invasion or eliminate it when already present if the transition rates to the sexually abstaining groups are independent of the infection status of individuals (susceptible or infected). On the other hand, if they depend on that status, the presence of sexually abstaining groups can prevent an STI from invasion or eliminate it when present. Specifically, in the simple case of sex-independent vital parameters, this happens if the transition rate of the infected individuals to the sexually abstaining group is higher than the transition rate of the susceptible ones. These results contrast the earlier results based on assuming long-term, stable pair bonds, in which case one is capable of preventing or eliminating the disease with the same isolation rate for the susceptible and infected individuals.

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A mathematical representation of the development of Mycobacterium tuberculosis active, latent and dormant stages.

Publication Date: 2012 Jan 7 PMID: 21968442
Authors: Magombedze, G. - Mulder, N.
Journal: J Theor Biol

The majority of individuals infected with Mycobacterium tuberculosis (Mtb) bacilli develop latent infection. Mtb becomes dormant and phenotypically drug resistant when it encounters multiple stresses within the host, and expresses a set of genes, known as the dormancy regulon, in vivo. These genes are expressed in vitro in response to nitric oxide (NO), hypoxia (oxygen deprivation), and nutrient starvation. The occurrence and reactivation of latent tuberculosis (TB) is not clearly understood. The ability of the pathogen to enter and exit from different states is associated with its ability to cause persistent infection. During infection it is not known whether the organism is in a persistent slow replicating state or a dormant non-replicating state, with the latter ultimately causing a latent infection with the potential to reactivate to active disease. We collected gene expression data for Mtb bacilli under different stress conditions that simulate latency or dormancy. Time course experiments were selected and differentially expressed gene profiles were determined at each time point. A mathematical model was then developed to show the dynamics of Mtb latency based on the profile of differentially expressed genes. Analysis of the time course data show the dynamics of latency occurrence in vitro and the mathematical model reveals all possible scenarios of Mtb latency development with respect to the different conditions that may be produced by the immune response in vivo. The mathematical model provides a biological explanation of how Mtb latency occurs based on observed gene expression changes in in vitro latency models.

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Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.

Publication Date: 2012 Jan 21 PMID: 21968441
Authors: Borgogno, F. - D'Odorico, P. - Laio, F. - Ridolfi, L.
Journal: J Theor Biol

Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers.

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Multiple feedback loops achieve robust localization of wingless expression in Drosophila notum development.

Publication Date: 2012 Jan 7 PMID: 21964462
Authors: Hironaka, K. - Iwasa, Y. - Morishita, Y.
Journal: J Theor Biol

Organ morphogenesis starts with the spatial patterning of different gene expressions in organ primordia, which is based on positional information provided by morphogens. To generate precise positional information, the robust localization of morphogen sources is needed. This can be realized by several different mechanisms, such as (i) by reducing the variations in spatial arrangement of morphogen sources, (ii) by reducing the variations in their source levels, and (iii) by increasing the degree of source localization with the sharp boundary that makes morphogen gradients steeper. Here we focus on the mechanism of localization of wingless expression, one of the important morphogens in Drosophila notum development. The mechanism of wingless-localization can be explained by a simple feed-forward loop network motif, but the real molecular network adopted by the organism is much more complex; it includes multiple feedback loops that function with the feed-forward loop in a coordinated manner. To clarify the functions of the molecular network, we decompose it into three sub-modules, each of which includes a single feedback loop, and examine their possible roles using a mathematical model. We demonstrate how the regulatory network for wingless expression realizes the conditions (i)-(iii) for its robust localization.

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An evolutionary advantage for extravagant honesty.

Publication Date: 2012 Jan 7 PMID: 21964260
Authors: Bullock, S.
Journal: J Theor Biol

A game-theoretic model of handicap signalling over a pair of signalling channels is introduced in order to determine when one channel has an evolutionary advantage over the other. The stability conditions for honest handicap signalling are presented for a single channel and are shown to conform with the results of prior handicap signalling models. Evolutionary simulations are then used to show that, for a two-channel system in which honest signalling is possible on both channels, the channel featuring larger advertisements at equilibrium is favoured by evolution. This result helps to address a significant tension in the handicap principle literature. While the original theory was motivated by the prevalence of extravagant natural signalling, contemporary models have demonstrated that it is the cost associated with deception that stabilises honesty, and that the honest signals exhibited at equilibrium need not be extravagant at all. The current model suggests that while extravagant and wasteful signals are not required to ensure a signalling system's evolutionary stability, extravagant signalling systems may enjoy an advantage in terms of evolutionary attainability.

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A model-experiment comparison of system dynamics for human walking and running.

Publication Date: 2012 Jan 7 PMID: 21959315
Authors: Lipfert, S. W. - Gunther, M. - Renjewski, D. - Grimmer, S. - Seyfarth, A.
Journal: J Theor Biol

The human musculo-skeletal system comprises high complexity which makes it difficult to identify underlying basic principles of bipedal locomotion. To tackle this challenge, a common approach is to strip away complexity and formulate a reductive model. With utter simplicity a bipedal spring-mass model gives good predictions of the human gait dynamics, however, it has not been fully investigated whether center of mass motion over time of walking and running is comparable between the model and the human body over a wide range of speed. To test the model's ability in this respect, we compare sagittal center of mass trajectories of model and human data for speeds ranging from 0.5 m/s to 4 m/s. For simulations, system parameters and initial conditions are extracted from experimental observations of 28 subjects. The leg parameters stiffness and length are extracted from functional fitting to the subjects' leg force-length curves. With small variations of the touch-down angle of the leg and the vertical position of the center of mass at apex, we find successful spring-mass simulations for moderate walking and medium running speeds. Predictions of the sagittal center of mass trajectories and ground reaction forces are good, but their amplitudes are overestimated, while contact time is underestimated. At faster walking speeds and slower running speeds we do not find successful model locomotion with the extent of allowed parameter variation. We conclude that the existing limitations may be improved by adding complexity to the model.

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Quantification of gastrointestinal sodium channelopathy.

Publication Date: 2012 Jan 21 PMID: 21959314
Authors: Poh, Y. C. - Beyder, A. - Strege, P. R. - Farrugia, G. - Buist, M. L.
Journal: J Theor Biol

Na(v)1.5 sodium channels, encoded by SCN5A, have been identified in human gastrointestinal interstitial cells of Cajal (ICC) and smooth muscle cells (SMC). A recent study found a novel, rare missense R76C mutation of the sodium channel interacting protein telethonin in a patient with primary intestinal pseudo-obstruction. The presence of a mutation in a patient with a motility disorder, however, does not automatically imply a cause-effect relationship between the two. Patch clamp experiments on HEK-293 cells previously established that the R76C mutation altered Na(v)1.5 channel function. Here the process through which these data were quantified to create stationary Markov state models of wild-type and R76C channel function is described. The resulting channel descriptions were included in whole cell ICC and SMC computational models and simulations were performed to assess the cellular effects of the R76C mutation. The simulated ICC slow wave was decreased in duration and the resting membrane potential in the SMC was depolarized. Thus, the R76C mutation was sufficient to alter ICC and SMC cell electrophysiology. However, the cause-effect relationship between R76C and intestinal pseudo-obstruction remains an open question.

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Optimality in DNA repair.

Publication Date: 2012 Jan 7 PMID: 21945337
Authors: Richard, M. - Fryett, M. - Miller, S. - Booth, I. - Grebogi, C. - Moura, A.
Journal: J Theor Biol

DNA within cells is subject to damage from various sources. Organisms have evolved a number of mechanisms to repair DNA damage. The activity of repair enzymes carries its own risk, however, because the repair of two nearby lesions may lead to the breakup of DNA and result in cell death. We propose a mathematical theory of the damage and repair process in the important scenario where lesions are caused in bursts. We use this model to show that there is an optimum level of repair enzymes within cells which optimises the cell's response to damage. This optimal level is explained as the best trade-off between fast repair and a low probability of causing double-stranded breaks. We derive our results analytically and test them using stochastic simulations, and compare our predictions with current biological knowledge.

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Multi-player games on the cycle.

Publication Date: 2012 Jan 7 PMID: 21907215
Authors: van Veelen, M. - Nowak, M. A.
Journal: J Theor Biol

In multi-player games n individuals interact in any one encounter and derive a payoff from that interaction. We assume that individuals adopt one of two strategies, and we consider symmetric games, which means the payoff depends only on the number of players using either strategy, but not on any particular configuration of the encounter. On the cycle we assume that any string of n neighbouring players interacts. We study fixation probabilities of stochastic evolutionary dynamics. We derive analytical results on the cycle both for linear and exponential fitness for any intensity of selection, and compare those to results for the well-mixed population. As particular examples we study multi-player public goods games, stag hunt games and snowdrift games.

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