Frequency-dependent fitness induces multistability in coevolutionary dynamics

Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a game-theoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyze the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.Comment: 12 pages, 6 figures; J. R. Soc. Interface (2012

Curvature Dependence of Hydrophobic Hydration Dynamics

We investigate the curvature-dependence of water dynamics in the vicinity of hydrophobic spherical solutes using molecular dynamics simulations. For both, the lateral and perpendicular diffusivity as well as for H-bond kinetics of water in the first hydration shell, we find a non-monotonic solute-size dependence, exhibiting extrema close to the well-known structural crossover length scale for hydrophobic hydration. Additionally, we find an apparently anomalous diffusion for water moving parallel to the surface of small solutes, which, however, can be explained by topology effects. The intimate connection between solute curvature, water structure and dynamics has implications for our understanding of hydration dynamics at heterogeneous biomolecular surfaces.Comment: 10 pages, 9 figure

Noise-induced Input Dependence in a Convective Unstable Dynamical System

Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow dynamics, shows both analogue and digital changes, where the former is represented by oscillation frequency and the latter by different type of dynamics. The underlying universal mechanism for these changes is clarified by the spatial change of the co-moving Lyapunov exponent, with which the condition for the input dependence is formulated. The mechanism has a remarkable dependence on the noise strength, and works only within its medium range. Relevance of our mechanism to intra-cellular signal dynamics is discussed, by making our dynamics correspond to the auto-catalytic biochemical reaction for the chemical concentration, and the input to the external signal, and the noise to the concentration fluctuation of chemicals.Comment: 31 pages (REVTeX) + 15 figure

Thermodynamic and structural aspects of the potential energy surface of simulated water

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition have been proposed over many years. The potential energy surface of model liquids has been increasingly studied since it provides a connection between the configurational component of the partition function on one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent inter-basin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model has been studied in great details in the last years. Specifically, we locate the minima sampled by the liquid by ``quenches'' from equilibrium configurations generated via molecular dynamics simulations. We calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling

Activity-dependence of synaptic vesicle dynamics

The proper function of synapses relies on efficient recycling of synaptic vesicles. The small size of synaptic boutons has hampered efforts to define the dynamical states of vesicles during recycling. Moreover, whether vesicle motion during recycling is regulated by neural activity remains largely unknown. We combined nanoscale-resolution tracking of individual synaptic vesicles in cultured hippocampal neurons from rats of both sexes with advanced motion analyses to demonstrate that the majority of recently endocytosed vesicles undergo sequences of transient dynamical states including epochs of directed, diffusional, and stalled motion. We observed that vesicle motion is modulated in an activity-dependent manner, with dynamical changes apparent in ∼20% of observed boutons. Within this subpopulation of boutons, 35% of observed vesicles exhibited acceleration and 65% exhibited deceleration, accompanied by corresponding changes in directed motion. Individual vesicles observed in the remaining ∼80% of boutons did not exhibit apparent dynamical changes in response to stimulation. More quantitative transient motion analyses revealed that the overall reduction of vesicle mobility, and specifically of the directed motion component, is the predominant activity-evoked change across the entire bouton population. Activity-dependent modulation of vesicle mobility may represent an important mechanism controlling vesicle availability and neurotransmitter release.SIGNIFICANCE STATEMENTMechanisms governing synaptic vesicle dynamics during recycling remain poorly understood. Using nanoscale resolution tracking of individual synaptic vesicles in hippocampal synapses and advanced motion analysis tools we demonstrate that synaptic vesicles undergo complex sets of dynamical states that include epochs of directed, diffusive, and stalled motion. Most importantly, our analyses revealed that vesicle motion is modulated in an activity-dependent manner apparent as the reduction in overall vesicle mobility in response to stimulation. These results define the vesicle dynamical states during recycling and reveal their activity-dependent modulation. Our study thus provides fundamental new insights into the principles governing synaptic function

Universality in edge-source diffusion dynamics

We show that in edge-source diffusion dynamics the integrated concentration N(t) has a universal dependence with a characteristic time-scale tau=(A/P)^2 pi/(4D), where D is the diffusion constant while A and P are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence N(t)=N0 sqrt(t/tau) while in the long-time dynamics N(t) saturates exponentially at N0. The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.Comment: 4 pages including 4 figures. Minor changes. Accepted for PR