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Abstract: We study the oscillatory dynamics in the generic three-species rock–paper–scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude. [Copyright &y& Elsevier]

Highlights • We have corrected the paper in order to present more clearly the experimental results and also to comment more the simulations done for the present Boolean model. • As demanded by reviewers, we have added a short presentation of the R. Thomas' theory, and also a recall of the earlier Boolean model proposed with him for the experiments of stimulation of Bidens pilosus. • Eventually, we have tried to present the perspectives of a hybrid approach from the continuous model previously proposed for Bidens. Abstract This paper presents a new model of memory functions in plants, which improves the previous approaches done by René Thomas and colleagues. We have decomposed the plant memory processing into three main functions: learning, storing and recalling. We propose as main mechanism for these three functions the occurrence of a calcium wave consecutive to an environmental stimulus, followed by the activation of specific genes and proteins changing their phosphorylated state. Feedback is ensured by Calcium Dependent Protein Kinases and oxidative phosphorylation. [ABSTRACT FROM AUTHOR]

When biological cells divide, they divide on a given angle. It has been shown experimentally that the orientation of cell division angle for a single cell can be described by a probability density function. However, the way in which the probability density function underlying cell division orientation influences population or tissue scale morphogenesis is unknown. Here we show that a computational approach, with thousands of stochastic simulations modeling growth and division of a population of cells, can be used to investigate this unknown. In this paper we examine two potential forms of the probability density function: a wrapped normal distribution and a binomial distribution. Our results demonstrate that for the wrapped normal distribution the standard deviation of the division angle, potentially interpreted as biological noise, controls the degree of tissue scale anisotropy. For the binomial distribution, we demonstrate a mechanism by which direction and degree of tissue scale anisotropy can be tuned via the probability of each division angle. We anticipate that the method presented in this paper and the results of these simulations will be a starting point for further investigation of this topic. [ABSTRACT FROM AUTHOR]

• A new two-patch pollination-mutualisms system including interacting species is analyzed. • Rigorous analysis on the model exhibits existence of stable positive equilibria. • Dispersal can make the pollinator approach higher total population abundance than if non-diffusing. • The result is effective even though the mutualistic plant approaches a low density. • The result is effective even though the system is in source-sink populations. In this paper, we consider a two-patch pollination-mutualism model with dispersal, which is derived from resource-service exchange between the plant and pollinator. The pollinator is assumed to persist in one patch in the presence of pollination-mutualisms, while it can (or cannot) survive alone in the other. Rigorous study on the model exhibits that solutions of the equations are nonnegative and bounded, and there exist stable positive equilibria under conditions. Theoretical analysis on the equilibria demonstrates that if the pollinator can survive alone in the other patch, a small dispersal can make the pollinator approach higher total population abundance than if non-dispersing. If the pollinator cannot survive alone in the other patch, a small or large dispersal can make the pollinator approach higher size than if non-dispersing, which is not intuitive. A novel prediction of this work is that the pollinator with dispersal can reach high population abundance even though the mutualistic plant approaches a low density, while constructing a high-quality patch for pollinator can lead to extra individuals for both plant and pollinator via dispersal. Numerical simulations confirm and extend our results. [ABSTRACT FROM AUTHOR]

Abstract: Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a ‘push–pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker–Planck (drift–diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a ‘critical point’ for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm. [Copyright &y& Elsevier]

• Both essential and non-essential genes differ from random sequences the same in length. • The composition of nucleotides within sequences differs in these groups. • The distribution of nucleotides within sequences differs in these groups. • Essential genes constitute a representative group of genes for each bacterium. Proteins encoded by genes are engaged in most of the processes within a cell. Typing a minimal set of genes required for survival is still a challenging task. Essential genes seem to be more conservative and are usually responsible for basic functions, for instance, genetic information flow or energy production. Despite persistent advances in experimental methods, computer predictions may constitute an important part of this investigation. Firstly, they may embrace a huge amount of data and provide some characteristic patterns. Furthermore, they enable scientists to build models for predicting essential genes which are not yet verified experimentally. Some papers indicate interesting dependencies within essential genes sequences using different computer models. In this paper, an author took a three-step analysis for a deeper understanding of the fundamentals of essential and non-essential genes. Beginning from a simple nucleotide composition and finishing at long-range correlations, presents some characteristic patterns that are expected to be developed in future studies. [ABSTRACT FROM AUTHOR]

Abstract: Combining evolutionary models with behavioral experiments can generate powerful insights into the evolution of human behavior. The emergence of online labor markets such as Amazon Mechanical Turk (AMT) allows theorists to conduct behavioral experiments very quickly and cheaply. The process occurs entirely over the computer, and the experience is quite similar to performing a set of computer simulations. Thus AMT opens the world of experimentation to evolutionary theorists. In this paper, I review previous work combining theory and experiments, and I introduce online labor markets as a tool for behavioral experimentation. I review numerous replication studies indicating that AMT data is reliable. I also present two new experiments on the reliability of self-reported demographics. In the first, I use IP address logging to verify AMT subjects'' self-reported country of residence, and find that 97% of responses are accurate. In the second, I compare the consistency of a range of demographic variables reported by the same subjects across two different studies, and find between 81% and 98% agreement, depending on the variable. Finally, I discuss limitations of AMT and point out potential pitfalls. I hope this paper will encourage evolutionary modelers to enter the world of experimentation, and help to strengthen the bond between theoretical and empirical analyses of the evolution of human behavior. [Copyright &y& Elsevier]

Highlights • We propose a variable weight test for both rare and common variants association based on affected sib pairs. • The variable weight structure makes it possible to analyze rare and common variants simultaneously. • The new method can improve the power of simultaneously detecting rare and common variants. • The proposed method is more powerful than the existing and related methods for detecting effects of rare and common variants. Abstract Current genome-wide association analysis has identified a great number of rare and common variants associated with common complex traits, however, more effective approaches for detecting associations between rare and common variants with common diseases are still demanded. Approaches for detecting rare variant association analysis will compromise the power when detecting the effects of rare and common variants simultaneously. In this paper, we extend an existing method of testing for rare variant association based on affected sib pairs (TOW-sib) and propose a variable weight test for rare and common variants association based on affected sib pairs (abbreviated as VW-TOWsib). The VW-TOWsib can be used to achieve the purpose of detecting the association of rare and common variants with complex diseases. Simulation results in various scenarios show that our proposed method is more powerful than existing methods for detecting effects of rare and common variants. At the same time, the VW-TOWsib also performs well as a method for rare variant association analysis. [ABSTRACT FROM AUTHOR]

Highlights • We explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment, presenting sufficient conditions for coexistence or competitive exclusion. • If the only difference between the two competing populations is a diffusion strategy, we explore how harvesting can either promote coexistence or lead one of the species to extinction. • If, without harvesting, the two species coexist, we evaluate the relation of harvesting rates that keep the coexistence pattern, as well as give sufficient estimates when one of the competitors goes extinct. All the results are illustrated with numerical simulations, including sharpness of estimates. Abstract The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of "close enough" to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion. [ABSTRACT FROM AUTHOR]

Highlights • We study tumor microcalcification in complex, evolving geometries with deformable membranes. • Enhanced membrane deformability promotes tumor growth and tumor calcification. • Correlations between the extents of the mammographic and pathologic tumor change from linear to quadratic as the membrane deformability increases. Abstract In this paper, we apply the diffuse domain framework developed in Chen and Lowengrub (Tumor growth in complex, evolving microenvironmental geometries: A diffuse domain approach, J. Theor. Biol. 361 (2014) 14–30) to study the effects of a deformable basement membrane (BM) on the growth of a tumor in a confined, ductal geometry, such as ductal carcinoma in situ (DCIS). We use a continuum model of tumor microcalcification and investigate the tumor extent beyond the microcalcification. In order to solve the governing equations efficiently, we develop a stable nonlinear multigrid finite difference method. Two dimensional simulations are performed where the adhesion between tumor cells and the basement membrane is varied. Additional simulations considering the variation of duct radius and membrane stiffness are also conducted. The results demonstrate that enhanced membrane deformability promotes tumor growth and tumor calcification. When the duct radius is small, the cell-BM adhesion is weak or when the membrane is slightly deformed, the mammographic and pathologic tumor extents are linearly correlated, as predicted by Macklin et al. (J. Theor. Biol. 301 (2012) 122–140) using an agent-based model that does not account for the deformability of the basement membrane and the active forces that the membrane imparts on the tumor cells. Interestingly, we predict that when the duct radius is large, there is strong cell-BM adhesion or the membrane is highly deformed, the extents of the mammographic and pathologic tumors are instead quadratically correlated. The simulations can help surgeons to measure DCIS surgical margins while removing less non-cancerous tissue, and can improve targeting of intra- and post-operative radiotherapy. [ABSTRACT FROM AUTHOR]

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

Abstract: In a recent paper List, Elsholtz and Seeley () have devised an agent-based model of the nest-choice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. We here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on our analytical approaches it is possible to characterize the co-ordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agent-based level. In the second part of the paper we present a spatial extension, and show that transient non-trivial patterns emerge, before consensus is reached. Approaches in terms of Langevin equations for continuous field variables are discussed. [Copyright &y& Elsevier]

Abstract: This is the first paper in a two-part series in which we develop, analyze, and simulate a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions. Three-dimensional simulations of nonlinear tumor growth and neovascularization using this diffuse interface model were recently presented in Frieboes et al. [2007. Computer simulation of glioma growth and morphology. NeuroImage S59–S70], but that paper did not describe the details of the model or the numerical algorithm. This is done here. In this diffuse interface approach, sharp interfaces are replaced by narrow transition layers that arise due to differential adhesive forces among the cell species. Accordingly, a continuum model of adhesion is introduced. The model is thermodynamically consistent, is related to recently developed mixture models, and thus is capable of providing a detailed description of tumor progression. The model is well-posed and consists of fourth-order nonlinear advection–reaction–diffusion equations (of Cahn–Hilliard-type) for the cell species coupled with reaction–diffusion equations for the substrate components. We demonstrate analytically and numerically that when the diffuse interface thickness tends to zero, the system reduces to a classical sharp interface model. Using a new fully adaptive and nonlinear multigrid/finite difference method, the system is simulated efficiently. In this first paper, we present simulations of unstable avascular tumor growth in two and three dimensions and demonstrate that our techniques now make large-scale three-dimensional simulations of tumors with complex morphologies computationally feasible. In part II of this study, we will investigate multispecies tumor invasion, tumor-induced angiogenesis, and focus on the morphological instabilities that may underlie invasive phenotypes. [Copyright &y& Elsevier]

In this paper, a mathematical model describing the transmission of two-strain Dengue virus between mosquitoes and humans, incorporating vector control and awareness of susceptible humans, is proposed. By using the next generation matrix method, we obtain the threshold values to identify the existence and stability of three equilibria states, that is, a disease-free state, a state where only one serotype is present and another state where both serotypes coexist. Further, explicit conditions determining the persistence of this disease are also obtained. In addition, we investigate the sensitivity analysis of threshold conditions and the optimal control strategy for this disease. Theoretical results and numerical simulations suggest that the measures of enhancing awareness of the infected and susceptible human self-protection should be taken and the mosquito control measure is necessary in order to prevent the transmission of Dengue virus from mosquitoes to humans. [ABSTRACT FROM AUTHOR]

Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model considering the two key ingredients, in which the contacts are grouped into two classes: strong contacts and normal ones. Next, we present a unified edge-based compartmental approach to the spread dynamics on Erdös–Rényi (ER) networks and validate its results by extensive numerical simulations. In case that epidemic is totally drug-resistant, we both numerically and theoretically show a continuous growth of epidemics with infection probability when number of strong contacts is not enough for the emergence of null threshold. If the epidemic owns partial resistance, we would observe evident discontinuous growth with infection probability (discontinuous transitions) and larger final epidemic sizes for few strong contacts, instead of emergence of null threshold with increase of strong contacts. Inhibiting effect of infection threshold, positive roles of strong contacts and strength of strong contacts in promoting outbreaks are also approved. Throughout this paper, we could drive exact predictions through the analytical approach, showing good agreements with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a periodic SIS epidemic model with time delay and transport-related infection in a patchy environment. The basic reproduction number R 0 is derived which determines the global dynamics of the model system: if R 0  < 1, the disease-free periodic state is globally attractive while there exists at least one positive periodic state and the disease persists if R 0  > 1. Numerical simulations are performed to confirm the analytical results and to explore the dependence of R 0 on the transport-related infection parameters and the amplitude of fluctuations. [ABSTRACT FROM AUTHOR]

The theory of invasions and invasion speeds has traditionally been studied in macroscopic systems. Surprisingly, microbial invasions have received less attention. Although microbes share many of the features associated with competition between larger-bodied organisms, they also exhibit distinctive behaviors that require new mathematical treatments to fully understand invasions in microbial systems. Most notable is the possibility for long-distance interactions, including competition between populations mediated by diffusible toxins and cooperation among individuals of a single population using quorum sensing. In this paper, we model bacterial invasion using a system of coupled partial differential equations based on Fisher's equation. Our model considers a competitive system with diffusible toxins that, in some cases, are expressed in response to quorum sensing. First, we derive analytical approximations for invasion speeds in the limits of fast and slow toxin diffusion. We then test the validity of our analytical approximations and explore intermediate rates of toxin diffusion using numerical simulations. Interestingly, we find that toxins should diffuse quickly when used offensively, but that there are two optimal strategies when toxins are used as a defense mechanism. Specifically, toxins should diffuse quickly when their killing efficacy is high, but should diffuse slowly when their killing efficacy is low. Our approach permits an explicit investigation of the properties and characteristics of diffusible compounds used in non-local competition, and is relevant for microbial systems and select macroscopic taxa, such as plants and corals, that can interact through biochemicals. [ABSTRACT FROM AUTHOR]

Hormone suppression has been the primary modality of treatment for prostate cancer. However long-term androgen deprivation may induce androgen-independent (AI) recurrence. Intermittent androgen suppression (IAS) is a potential way to delay or avoid the AI relapse. Mathematical models of tumor growth and treatment are simple while they are capable of capturing the essence of complicated interactions. Game theory models have analyzed that tumor cells can enhance their fitness by adopting genetically determined survival strategies. In this paper, we consider the survival strategies as the competitive advantage of tumor cells and propose a new model to mimic the prostate tumor growth in IAS therapy. Then we investigate the competition effect in tumor development by numerical simulations. The results indicate that successfully IAS-controlled states can be achieved even though the net growth rate of AI cells is positive for any androgen level. There is crucial difference between the previous models and the new one in the phase diagram of successful and unsuccessful tumor control by IAS administration, which means that the suggestions from the models for medication can be different. Furthermore we introduce quadratic logistic terms to the competition model to simulate the tumor growth in the environment with a finite carrying capacity considering the nutrients or inhibitors. The simulations show that the tumor growth can reach an equilibrium state or an oscillatory state with the net growth rate of AI cells being androgen independent. Our results suggest that the competition and the restraint of a limited environment can enhance the possibility of relapse prevention. [ABSTRACT FROM AUTHOR]

• A PNP (or PDE) model is formulated for the mechanism of electrocyte. • The superposition of two membrane potentials is rigorously explained by PNP model. • Classical membrane (or ODE) model can not explain the above superposition principle. • PNP model reduces to the membrane model at leading order by asymptotic analysis. In this paper, we developed a one-dimensional model for electric potential generation of electrocytes in electric eels. The model is based on the Poisson–Nernst–Planck system for ion transport coupled with membrane fluxes including the Hodgkin–Huxley type. Using asymptotic analysis, we derived a simplified zero-dimensional model, which we denote as the membrane model in this paper, as a leading order approximation. Our analysis provides justification for the assumption in membrane models that electric potential is constant in the intracellular space. This is essential to explain the superposition of two membrane potentials that leads to a significant transcellular potential. Numerical simulations are also carried out to support our analytical findings. [ABSTRACT FROM AUTHOR]

In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and numerical analysis of stability of the steady states of the model we identify parameter regions associated with recovery and resistant phenotypes, as well as possible chronic infections. Dynamics of the system in these regimes is illustrated by numerical simulations of the model. [ABSTRACT FROM AUTHOR]

Individual migration plays a crucial role in evolutionary dynamics of population on networks. In this paper, we generalize the networked ultimatum game by diluting population structures as well as endowing individuals with migration ability, and investigate evolutionary dynamics of fairness on graphs with migration in the ultimatum game. We first revisit the impact of node degree on the evolution of fairness. Interestingly, numerical simulations reveal that there exists an optimal value of node degree resulting in the maximal offer level of populations. Then we explore the effects of dilution and migration on the evolution of fairness, and find that both the dilution of population structures and the endowment of migration ability to individuals would lead to the drop of offer level, while the rise of acceptance level of populations. Notably, natural selection even favors the evolution of self-incompatible strategies, when either vacancy rate or migration rate exceeds a critical threshold. To confirm our simulation results, we also propose an analytical method to study the evolutionary dynamics of fairness on graphs with migration. This method can be applied to explore any games governed by pairwise interactions in finite populations. [ABSTRACT FROM AUTHOR]

Abstract: Most neocortical neurons formed during embryonic brain development arise from radial glial cells which communicate, in part, via ATP mediated calcium signals. Although the intercellular signalling mechanisms that regulate radial glia proliferation are not well understood, it has recently been demonstrated that ATP dependent intracellular calcium release leads to an increase of nearly 100% in overall cellular proliferation. It has been hypothesised that cytoplasmic calcium accelerates entry into S phase of the cell cycle and/or acts to recruit otherwise quiescent cells onto the cell cycle. In this paper we study this cell cycle acceleration and recruitment by forming a differential equation model for ATP mediated calcium-cell cycle coupling via Cyclin D in a single radial glial cell. Bifurcation analysis and numerical simulations suggest that the cell cycle period depends only weakly on cytoplasmic calcium. Therefore, the accelerative impact of calcium on the cell cycle can only account for a small fraction of the large increase in proliferation observed experimentally. Crucially however, our bifurcation analysis reveals that stable fixed point and stable limit cycle solutions can coexist, and that calcium dependent Cyclin D dynamics extend the oscillatory region to lower Cyclin D synthesis rates, thus rendering cells more susceptible to cycling. This supports the hypothesis that cycling glial cells recruit quiescent cells (in G0 phase) onto the cell cycle, via a calcium signalling mechanism, and that this may be the primary means by which calcium augments proliferation rates at the population scale. Numerical simulations of two coupled cells demonstrate that such a scenario is indeed feasible. [Copyright &y& Elsevier]

Abstract: A medical experiment published in Nature has shown that humanized mice receiving the vectored immunoprophylaxis can be fully protected from HIV infection. In this paper, a mathematical model is proposed to investigate the viral dynamics under the effect of antibodies in the experiment. It is shown that the introduction of vectored immunoprophylaxis can induce the backward bifurcation and the ignorance of antibodies'' loss due to their involvement with virus may result in the loss of backward bifurcation. By numerical simulations, it is found that the model also exhibits some other complicated dynamical behaviors. A subcritical Hopf bifurcation, a fold bifurcation of equilibria and a limit point bifurcation of limit cycles are detected, which induce five typical patterns of dynamical behaviors including the bistable phenomenon. [Copyright &y& Elsevier]

Abstract: In this paper, we present a neural network system composed of two delay-coupled neural oscillators, where each of these can be regarded as the dynamical system describing the average activity of neural population. Analyzing the corresponding characteristic equation, the local stability of rest state is studied. The system exhibits the switch phenomenon between the rest state and periodic activity. Furthermore, the Hopf bifurcation is analyzed and the bifurcation curve is given in the parameters plane. The stability of the bifurcating periodic solutions and direction of the Hopf bifurcation are exhibited. Regarding time delay and coupled weight as the bifurcation parameters, the Fold–Hopf bifurcation is investigated in detail in terms of the central manifold reduction and normal form method. The neural system demonstrates the coexistence of the rest states and periodic activities in the different parameter regions. Employing the normal form of the original system, the coexistence regions are illustrated approximately near the Fold–Hopf singularity point. Finally, numerical simulations are performed to display more complex dynamics. The results illustrate that system may exhibit the rich coexistence of the different neuro-computational properties, such as the rest states, periodic activities, and quasi-periodic behavior. In particular, some periodic activities can evolve into the bursting-type behaviors with the varying time delay. It implies that the coexistence of the quasi-periodic activity and bursting-type behavior can be obtained if the suitable value of system parameter is chosen. [Copyright &y& Elsevier]

Abstract: We systematically investigate the stochastic dynamics of a single Hodgkin–Huxley neuron driven by stochastic excitatory and inhibitory input spikes via unreliable synapses in this paper. Based on the mean-filed theory, a novel intrinsic neuronal noise regulation mechanism stemming from unreliable synapses is presented. Our simulation results show that, under certain conditions, the stochastic resonance phenomenon is able to be induced by the unreliable synaptic transmission, which can be well explained by the theoretical prediction. To a certain degree, the results presented here provide insights into the functional roles of unreliable synapses in neural information processing. [Copyright &y& Elsevier]

Abstract: Direct Response Analysis is a general computational tool for quantifying direct functional interactions between components in cellular signalling systems from experimental perturbations and measurements alone. This paper aims to reveal the biological meaning of the direct response coefficients obtained upon applying DRA to simple Michaelis–Menten type proteomic and gene regulatory systems. These systems describe dimer formation and dissociation, protein preduction and decay, and transcription. We derive explicit formulae for the direct response coefficients in terms of biochemical reaction rates, and clarify the potential and limitations of the DRA method. We find that response coefficients are strongly asymmetric, and that they balance persistent characteristics of reactions (e.g. the ratios of on- and off rates) against the time-scales over which these reactions act; fast reactions give stronger response coefficients. The direct interactions between protein species, caused by dimer formation, are effectively negative. We illustrate our results with numerical simulations. [Copyright &y& Elsevier]

Abstract: Alzheimer Disease (AD) is the most prevalent form of dementia and the sixth leading cause of death in developed world. A substantial amount of data concerning the pathogenesis of this neurological disorder is available, but the complexity of the interactions they reveal makes it difficult to reason about them. This paper describes a computational model that represents known facts concerning AD pathophysiology and demonstrates the implications of those facts in the aggregate. The computational model is written in a mathematical language known as Maude. Because a Maude specification is an executable mathematical theory, it can be used not only to simulate but also to logically analyze the system it models. This model is based on the amyloid hypothesis, which posits that AD results from the build-up of the peptide beta-amyloid. The AD model represents beta-amyloid regulation, and shows through model analysis how that regulation can be disrupted through the interaction of pathological processes such as cerebrovascular insufficiency, inflammation, and oxidative stress. The model demonstrates many other effects that depend in complex ways on interactions between elements. It also shows how treatments directed at multiple targets could be more effective at reducing beta-amyloid than single-target therapies, and it makes several experimentally testable predictions. The work demonstrates that modeling AD as an executable mathematical theory using a specification language such as Maude is a viable adjunct to experiment, which allows insights and predictions to be derived that take more of the relevant biology into account than would be possible without the aid of the computational model. [Copyright &y& Elsevier]

Abstract: Fine/ultrafine particles can easily reach the pulmonary acinus, where gas is exchanged, but they need to mix with alveolar residual air to land on the septal surface. Classical fluid mechanics theory excludes flow-induced mixing mechanisms because of the low Reynolds number nature of the acinar flow. For more than a decade, we have been challenging this classical view, proposing the idea that chaotic mixing is a potent mechanism in determining the transport of inhaled particles in the pulmonary acinus. We have demonstrated this in numerical simulations, experimental studies in both physical models and in animals, and mathematical modeling. However, the mathematical theory that describes chaotic mixing in small airways and alveoli is highly complex; it not readily accessible by non-mathematicians. The purpose of this paper is to make the basic mechanisms that operate in acinar chaotic mixing more accessible, by translating the key mathematical ideas into physics-oriented language. The key to understanding chaotic mixing is to identify two types of frequency in the system, each of which is induced by a different mechanism. The way in which their interplay creates chaos is explained with instructive illustrations but without any equations. We also explain why self-similarity occurs in the alveolar system and was indeed observed as a fractal pattern deep in rat lungs (Proc. Natl. Acad. Sci. USA. 99:10173-10178, 2002). [Copyright &y& Elsevier]

Abstract: Mitochondria have long been known to sequester cytosolic Ca2+ and even to shape intracellular patterns of endoplasmic reticulum-based Ca2+ signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca2+ induced Ca2+ release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca2+ handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus–Keizer computational model for respiration-driven Ca2+ handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca2+ wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca2+ excitability seen in mitochondria. [Copyright &y& Elsevier]

Abstract: The correct localisation of transcription factors is vitally important for the proper functioning of many intracellular signalling pathways. Experimental data has shown that many pathways exhibit oscillations in concentrations of the substances involved, both temporally and spatially. Negative feedback loops are important components of these oscillations, providing fine regulation for the factors involved. In this paper we consider mathematical models of two such pathways—Hes1 and p53-Mdm2. Building on previous mathematical modelling approaches, we derive systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we show that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. The simulations of our models also allow us to calculate a diffusion coefficient range for the variables in each mRNA and protein system, as well as ranges for other key parameters of the models, where sustained oscillations are observed. Finally, by exploiting the explicitly spatial nature of the partial differential equations, we are also able to manipulate mathematically the spatial location of the ribosomes, thus controlling where the proteins are synthesized within the cytoplasm. The results of these simulations predict an optimal distance outside the nucleus where protein synthesis should take place in order to generate sustained oscillations. Using partial differential equation models, new information can be gained about the precise spatio-temporal dynamics of mRNA and proteins. The ability to determine spatial localisation of proteins within the cell is likely to yield fresh insight into a range of cellular diseases such as diabetes and cancer. [Copyright &y& Elsevier]

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

Abstract: In this paper, we proposed an efficient immunization—“high-risk immunization”. The standard SIRS model was modified, respectively, on WS small-world network and BA scale-free network. Based on our new SIRS model, the density of infected individuals was analyzed from a theoretical point of view, and computer simulation was implemented on different networks. The results indicate that the high-risk immunization is effective, and it is economic and feasible in practice. [Copyright &y& Elsevier]

Abstract: All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host–two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilising effect on the system whilst vertical transmission can destabilise it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever. [Copyright &y& Elsevier]

Abstract: Computer models of disease take a systems biology approach toward understanding host–pathogen interactions. In particular, data driven computer model calibration is the basis for inference of immunological and pathogen parameters, assessment of model validity, and comparison between alternative models of immune or pathogen behavior. In this paper we describe the calibration and analysis of an agent-based model of Leishmania major infection. A model of macrophage loss following uptake of necrotic tissue is proposed to explain macrophage depletion following peak infection. Using Gaussian processes to approximate the computer code, we perform a sensitivity analysis to identify important parameters and to characterize their influence on the simulated infection. The analysis indicates that increasing growth rate can favor or suppress pathogen loads, depending on the infection stage and the pathogen''s ability to avoid detection. Subsequent calibration of the model against previously published biological observations suggests that L. major has a relatively slow growth rate and can replicate for an extended period of time before damaging the host cell. [Copyright &y& Elsevier]

Abstract: This paper presents an extension of the Red Queen Hypothesis (hereafter, RQH) that we call the Red Tooth Hypothesis (RTH). This hypothesis suggests that predator–prey relations may play a role in the maintenance of sexual reproduction in many higher animals. RTH is based on an interaction between learning on the part of predators and evolution on the part of prey. We present a simple predator–prey computer simulation that illustrates the effects of this interaction. This simulation suggests that the optimal escape strategy from the prey''s standpoint would be to have a small number of highly reflexive, largely innate (and, therefore, very fast) escape patterns, but that would also be unlearnable by the predator. One way to achieve this would be for each individual in the prey population to have a small set of hard-wired escape patterns, but which were different for each individual. We argue that polymorphic escape patterns at the population level could be produced via sexual reproduction at little or no evolutionary cost and would be as, or potentially more, efficient than individual-level protean (i.e., random) escape behavior. We further argue that, especially under high predation pressure, sexual recombination would be a more rapid, and therefore more effective, means of producing highly variable escape behaviors at the population level than asexual reproduction. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a mathematical model concerning a chemostat with impulsive state feedback control to investigate the periodicity of bioprocess. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions under which the model has a periodic solution of order one are obtained. Furthermore, we estimate the position of the periodic solution of order one and discuss the existence of periodic solution of order two. The theoretical results and numerical simulations indicate that the chemostat system with impulsive state feedback control either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentrations of microorganisms and substrate. [Copyright &y& Elsevier]

Abstract: The recent Bayesian approaches to language evolution and change seem to suggest that genetic biases can impact on the characteristics of language, but, at the same time, that its cultural transmission can partially free it from these same genetic constraints. One of the current debates centres on the striking differences between sampling and a posteriori maximising Bayesian learners, with the first converging on the prior bias while the latter allows a certain freedom to language evolution. The present paper shows that this difference disappears if populations more complex than a single teacher and a single learner are considered, with the resulting behaviours more similar to the sampler. This suggests that generalisations based on the language produced by Bayesian agents in such homogeneous single agent chains are not warranted. It is not clear which of the assumptions in such models are responsible, but these findings seem to support the rising concerns on the validity of the “acquisitionist” assumption, whereby the locus of language change and evolution is taken to be the first language acquirers (children) as opposed to the competent language users (the adults). [Copyright &y& Elsevier]

Abstract: In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower–upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a mathematical expression of closure to efficient causation in terms of λ-calculus; we argue that this opens up the perspective of developing principled computer simulations of systems closed to efficient causation in an appropriate programming language. An important implication of our formulation is that, by exhibiting an expression in λ-calculus, which is a paradigmatic formalism for computability and programming, we show that there are no conceptual or principled problems in realizing a computer simulation or model of closure to efficient causation. We conclude with a brief discussion of the question whether closure to efficient causation captures all relevant properties of living systems. We suggest that it might not be the case, and that more complex definitions could indeed create crucial some obstacles to computability. [Copyright &y& Elsevier]

Abstract: Epstein–Barr virus (EBV) is an important human pathogen that establishes a life-long persistent infection and for which no precise animal model exists. In this paper, we describe in detail an agent-based model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer''s ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death. [Copyright &y& Elsevier]

The aim of this paper is to present the current state of a four-dimensional simulation model of solid tumour growth and response to radiotherapy developed by our group. The most prominent points of the algorithms describing the fundamental biological phenomena involved are outlined. A specific application of the model to a selected clinical case of glioblastoma multiforme is described and comparative studies are performed, using various exploratory values of the model parameters. Qualitative agreement with clinical observations has been achieved. Special emphasis is laid on the variability of radiosensitivity parameters throughout the cell cycle and on the influence of the genetic profile of the tumour on its radiosensitivity. The results of the simulation are three-dimensionally reconstructed. A valuable tool for getting insight into the biology of tumour growth and response to radiotherapy and at the same time an advanced patient specific decision support system is expected to emerge after the completion of the necessary extensive clinical evaluation. [Copyright &y& Elsevier]

• A PNP (or PDE) model is formulated for the mechanism of electrocyte discharge. • Time variation of the electric fields is essential for the conservation of total current. • PNP model reduces to an ordinary differential equations model at leading order by asymptotic analysis. • Delay in contact leads to interesting dynamics and new features, compared to the non-contact case investigated previously. In this paper, we investigate the electric discharge of electrocytes by extending our previous work on the generation of electric potential. We first give a complete formulation of a single cell unit consisting of an electrocyte and a resistor, based on a Poisson-Nernst-Planck (PNP) system with various membrane currents as interfacial conditions for the electrocyte and a Maxwell's model for the resistor. Our previous work can be treated as a special case with an infinite resistor (or open circuit). Using asymptotic analysis, we simplify our PNP system and reduce it to an ordinary differential equation (ODE) based model. Unlike the case of an infinite resistor, our numerical simulations of the new model reveal several distinct features. A finite current is generated, which leads to non-constant electric potentials in the bulk of intracellular and extracellular regions. Furthermore, the current induces an additional action potential (AP) at the non-innervated membrane, contrary to the case of an open circuit where an AP is generated only at the innervated membrane. The voltage drop inside the electrocyte is caused by an internal resistance due to mobile ions. We show that our single cell model can be used as the basis for a system with stacked electrocytes and the total current during the discharge of an electric eel can be estimated by using our model. [ABSTRACT FROM AUTHOR]