The role of memory-based movements in the formation of animal home ranges.

Most animals live in spatially-constrained home ranges. The prevalence of this space-use pattern in nature suggests that general biological mechanisms are likely to be responsible for their occurrence. Individual-based models of animal movement in both theoretical and empirical settings have demonstrated that the revisitation of familiar areas through memory can lead to the formation of stable home ranges. Here, we formulate a deterministic, mechanistic home range model that includes the interplay between a bi-component memory and resource preference, and evaluate resulting patterns of space-use. We show that a bi-component memory process can lead to the formation of stable home ranges and control its size, with greater spatial memory capabilities being associated with larger home range size. The interplay between memory and resource preferences gives rise to a continuum of space-use patterns-from spatially-restricted movements into a home range that is influenced by local resource heterogeneity, to diffusive-like movements dependent on larger-scale resource distributions, such as in nomadism. Future work could take advantage of this model formulation to evaluate the role of memory in shaping individual performance in response to varying spatio-temporal resource patterns.

Efficacy of Wolbachia-based mosquito control: Predictions of a spatially discrete mathematical model.

Wolbachia is an endosymbiont bacterium present in many insect species. When Wolbachia-carrying male Aedes aegypti mosquitoes mate with non-carrier females, their embryos are not viable due to cytoplasmic incompatibility. This phenomenon has been exploited successfully for the purpose of controlling mosquito populations and the spread of mosquito-borne illnesses: Wolbachia carriers are bred and released into the environment. Because Wolbachia is not harmful to humans, this method of mosquito control is regarded as a safer alternative to pesticide spraying. In this article, we introduce a mathematical framework for exploring (i) whether a one-time release of Wolbachia carriers can elicit a sustained presence of carriers near the release site, and (ii) the extent to which spatial propagation of carriers may allow them to establish fixation in other territories. While some prior studies have formulated mosquito dispersal models using advection-reaction-diffusion PDEs, the predictive power of such models requires careful ecological mapping: advection and diffusion coefficients exhibit significant spatial dependence due to heterogeneity of resources and topography. Here, we adopt a courser-grained view, regarding the environment as a network of discrete, diffusively-coupled "habitats"-distinct zones of high mosquito density such as stagnant ponds. We extend two previously published single-habitat mosquito models to multiple habitats, and calculate rates of migration between pairs of habitats using dispersal kernels. Our primary results are quantitative estimates regarding how the success of carrier fixation in one or more habitats is determined by: the number of carriers released, sizes of habitats, distances between habitats, and the rate of migration between habitats. Besides yielding sensible and potentially useful predictions regarding the success of Wolbachia-based control, our framework applies to other approaches (e.g., gene drives) and contexts beyond the realm of insect pest control.

Phylogenomic analyses of the genus Drosophila reveals genomic signals of climate adaptation.

Many Drosophila species differ widely in their distributions and climate niches, making them excellent subjects for evolutionary genomic studies. Here, we have developed a database of high-quality assemblies for 46 Drosophila species and one closely related Zaprionus. Fifteen of the genomes were newly sequenced, and 20 were improved with additional sequencing. New or improved annotations were generated for all 47 species, assisted by new transcriptomes for 19. Phylogenomic analyses of these data resolved several previously ambiguous relationships, especially in the melanogaster species group. However, it also revealed significant phylogenetic incongruence among genes, mainly in the form of incomplete lineage sorting in the subgenus Sophophora but also including asymmetric introgression in the subgenus Drosophila. Using the phylogeny as a framework and taking into account these incongruences, we then screened the data for genome-wide signals of adaptation to different climatic niches. First, phylostratigraphy revealed relatively high rates of recent novel gene gain in three temperate pseudoobscura and five desert-adapted cactophilic mulleri subgroup species. Second, we found differing ratios of nonsynonymous to synonymous substitutions in several hundred orthologues between climate generalists and specialists, with trends for significantly higher ratios for those in tropical and lower ratios for those in temperate-continental specialists respectively than those in the climate generalists. Finally, resequencing natural populations of 13 species revealed tropics-restricted species generally had smaller population sizes, lower genome diversity and more deleterious mutations than the more widespread species. We conclude that adaptation to different climates in the genus Drosophila has been associated with large-scale and multifaceted genomic changes.

The whale shark genome reveals how genomic and physiological properties scale with body size.

The endangered whale shark (Rhincodon typus) is the largest fish on Earth and a long-lived member of the ancient Elasmobranchii clade. To characterize the relationship between genome features and biological traits, we sequenced and assembled the genome of the whale shark and compared its genomic and physiological features to those of 83 animals and yeast. We examined the scaling relationships between body size, temperature, metabolic rates, and genomic features and found both general correlations across the animal kingdom and features specific to the whale shark genome. Among animals, increased lifespan is positively correlated to body size and metabolic rate. Several genomic traits also significantly correlated with body size, including intron and gene length. Our large-scale comparative genomic analysis uncovered general features of metazoan genome architecture: Guanine and cytosine (GC) content and codon adaptation index are negatively correlated, and neural connectivity genes are longer than average genes in most genomes. Focusing on the whale shark genome, we identified multiple features that significantly correlate with lifespan. Among these were very long gene length, due to introns being highly enriched in repetitive elements such as CR1-like long interspersed nuclear elements, and considerably longer neural genes of several types, including connectivity, activity, and neurodegeneration genes. The whale shark genome also has the second slowest evolutionary rate observed in vertebrates to date. Our comparative genomics approach uncovered multiple genetic features associated with body size, metabolic rate, and lifespan and showed that the whale shark is a promising model for studies of neural architecture and lifespan.

Apcdd1 is a dual BMP/Wnt inhibitor in the developing nervous system and skin.

Animal development and homeostasis depend on precise temporal and spatial intercellular signaling. Components shared between signaling pathways, generally thought to decrease specificity, paradoxically can also provide a solution to pathway coordination. Here we show that the Bone Morphogenetic Protein (BMP) and Wnt signaling pathways share Apcdd1 as a common inhibitor and that Apcdd1 is a taxon-restricted gene with novel domains and signaling functions. Previously, we showed that Apcdd1 inhibits Wnt signaling (Shimomura et al., 2010), here we find that Apcdd1 potently inhibits BMP signaling in body axis formation and neural differentiation in chicken, frog, zebrafish. Furthermore, we find that Apcdd1 has an evolutionarily novel protein domain. Our results from experiments and modeling suggest that Apcdd1 may coordinate the outputs of two signaling pathways that are central to animal development and human disease.

Modeling action potential reversals in tunicate hearts.

Tunicates are small invertebrates which possess a unique ability to reverse flow in their hearts. Scientists have debated various theories regarding how and why flow reversals occur. Here we explore the electrophysiological basis for reversals by simulating action potential propagation in an idealized model of the tubelike tunicate heart. Using asymptotic formulas for action potential duration and conduction velocity, we propose tunicate-specific parameters for a two-current ionic model of the action potential. Then, using a kinematic model, we derive analytical criteria for reversals to occur. These criteria inform subsequent numerical simulations of action potential propagation in a fiber paced at both ends. In particular, we explore the role that variability of pacemaker firing rates plays in generating reversals, and we identify various favorable conditions for triggering retrograde propagation. Our analytical framework extends to other species; for instance, it can be used to model competition between the sinoatrial node and abnormal ectopic foci in human heart tissue.

Restricted feedback control in discrete-time dynamical systems with memory.

When an equilibrium state of a physical or biological system suffers a loss of stability (e.g., via a bifurcation), it may be both possible and desirable to stabilize the equilibrium via closed-loop feedback control. Significant effort has been devoted towards using such control to prevent oscillatory or chaotic behavior in dynamical systems, both continuous-time and discrete-time. Regarding control in discrete-time systems, most prior attempts to stabilize unstable equilibria require that the system be perturbed once during each time step. However, there are examples of systems for which this is neither feasible nor possible. In this paper, we analyze a restricted feedback control method for discrete-time systems (restricted in the sense that the controller's perturbations may be applied only in every other time step). We apply our theoretical analysis to a specific example from cardiac electrophysiology in which this sort of restricted feedback control is especially relevant. The example is a useful test case for the theory, and one for which an experimental setup is rather straightforward.

Toward a classification of isodynamic feed-forward motifs.

A preceding study analysed how the topology of network motifs affects the overall rate of the underlying biochemical processes. Surprisingly, it was shown that topologically non-isomorphic motifs can still be isodynamic in the sense that they exhibit the exact same performance rate. Because of the high prevalence of feed-forward functional modules in biological networks, one may hypothesize that evolution tends to favour motifs with faster dynamics. As a step towards ranking the efficiency of feed-forward network motifs, we use a linear flow model to prove theorems establishing that certain classes of motifs are isodynamic. In partitioning the class of all motifs on n nodes into equivalence classes based upon their dynamics, we establish a basis for comparing the efficiency/performance rates of different motifs. The potential biological importance of the theorems is briefly discussed and is the subject of an ongoing large-scale project.

An in silico approach to the analysis of acute wound healing.

The complex interactions that characterize acute wound healing have stymied the development of effective therapeutic modalities. The use of computational models holds the promise to improve our basic approach to understanding the process. By modifying an existing ordinary differential equation model of systemic inflammation to simulate local wound healing, we expect to improve the understanding of the underlying complexities of wound healing and thus allow for the development of novel, targeted therapeutic strategies. The modifications in this local acute wound healing model include: evolution from a systemic model to a local model, the incorporation of fibroblast activity, and the effects of tissue oxygenation. Using these modifications we are able to simulate impaired wound healing in hypoxic wounds with varying levels of contamination. Possible therapeutic targets, such as fibroblast death rate and rate of fibroblast recruitment, have been identified by computational analysis. This model is a step toward constructing an integrative systems biology model of human wound healing.

Shortening of cardiac action potential duration near an insulating boundary.

It is known, from both experiments and simulations, that cardiac action potentials are shortened near a non-conducting boundary. In the present paper, this effect is studied in a simple, two-current ionic model, with propagation restricted to a 1D fibre. An asymptotic approximation for the dependence of action potential duration on distance to the boundary is derived. This estimate agrees well with simulations.

Cellular automata simulation of topological effects on the dynamics of feed-forward motifs.

BACKGROUND: Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. RESULTS: Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. CONCLUSION: It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization.

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as extended time-delay autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.

Criterion for stable reentry in a ring of cardiac tissue.

We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique equilibrium solution. Applying Jury's stability test, we prove a theorem concerning the local asymptotic stability of this equilibrium solution. Our results yield conditions for sustained reentrant tachycardia, a type of cardiac arrhythmia.

An ionically based mapping model with memory for cardiac restitution.

Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found that (i) the dynamic and S1-S2 restitution curves are different (rate dependence) and (ii) the approach to steady state, which requires many action potentials (accommodation), occurs along a curve distinct from either restitution curve. Neither behavior can be produced by a 1D mapping. To address these shortcomings, ad hoc 2D mappings, where the second variable is a "memory" variable, have been proposed; these models exhibit qualitative features of the relevant behavior, but a quantitative fit is not possible. In this paper we introduce a new 2D mapping and determine a set of parameters for it that gives a quantitatively accurate description of the full restitution portrait measured from a bullfrog ventricle. The mapping can be derived as an asymptotic limit of an idealized ionic model in which a generalized concentration acts as a memory variable. This ionic basis clarifies how the present model differs from previous models. The ionic basis also provides the foundation for more extensive cardiac modeling: e.g., constructing a PDE model that may be used to study the effect of memory on propagation. The fitting procedure for the mapping is straightforward and can easily be applied to obtain a mathematical model for data from other experiments, including experiments on different species.

DYNAMIC BEHAVIOR OF A PACED CARDIAC FIBER.

Consider a typical experimental protocol in which one end of a one-dimensional fiber of cardiac tissue is periodically stimulated, or paced, resulting in a train of propagating action potentials. There is evidence that a sudden change in the pacing period can initiate abnormal cardiac rhythms. In this paper, we analyze how the fiber responds to such a change in a regime without arrhythmias. In particular, given a fiber length L and a tolerance eta, we estimate the number of beats N = N(eta, L) required for the fiber to achieve approximate steady-state in the sense that spatial variation in the diastolic interval (DI) is bounded by eta. We track spatial DI variation using an infinite sequence of linear integral equations which we derive from a standard kinematic model of wave propagation. The integral equations can be solved in terms of generalized Laguerre polynomials. We then estimate N by applying an asymptotic estimate for generalized Laguerre polynomials. We find that, for fiber lengths characteristic of cardiac tissue, it is often the case that N effectively exhibits no dependence on L. More exactly, (i) there is a critical fiber length L* such that, if L < L*, the convergence to steady-state is slowest at the pacing site, and (ii) often, L* is substantially larger than the diameter of the whole heart.

Two-Term Asymptotic Approximation of a Cardiac Restitution Curve.

If spatial extent is neglected, ionic models of cardiac cells consist of systems of ordinary differential equations (ODEs) which have the property of excitability, i.e., a brief stimulus produces a prolonged evolution (called an action potential in the cardiac context) before the eventual return to equilibrium. Under repeated stimulation, or pacing, cardiac tissue exhibits electrical restitution: the steady-state action potential duration (APD) at a given pacing period B shortens as B is decreased. Independent of ionic models, restitution is often modeled phenomenologically by a one-dimensional mapping of the form APD(next) = f(B - APD(previous)). Under some circumstances, a restitution function f can be derived as an asymptotic approximation to the behavior of an ionic model.In this paper, extending previous work, we derive the next term in such an asymptotic approximation for a particular ionic model consisting of two ODEs. The two-term approximation exhibits excellent quantitative agreement with the actual restitution curve, whereas the leading-order approximation significantly underestimates actual APD values.

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber.

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, the wave-back velocity exhibits pronounced rate dependence and the wave-front velocity does not. Moreover, the discrepancy between wave-back velocity RCs is most significant for a small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wave-front and wave-back velocities. Our calculations show that rate-dependent wave-back velocity can be present even if neither APD nor wave-front velocity exhibits rate dependence.