Spiking behavior in a noise-driven system combining oscillatory and excitatory properties

We show that firing activity (spiking) can be regularized by noise in a FitzHugh-Nagumo (FHN) neuron model when operating slightly beyond the supercritical Hopf bifurcation (in the "canard" region). We also provide the conditions for imperfect phase locking between interspike intervals and low amplitude quasiharmonic oscillations. For the imperfect phase locking no need exists of an external signal as it follows from the FHN intrinsic dynamics.     

Renormalized phase dynamics in oscillatory media

Based on the complex Ginzburg-Landau equation (CGLE), a new mapping model of oscillatory media is proposed. The present dynamics is fully determined by an effective phase field renormalized by amplitude. The model exhibits phase turbulence, amplitude turbulence, and a frozen state reported in the CGLE. In addition, we find a state in which the phase and amplitude have spiral structures with opposite rotational directions. This state is found to be observed also in the CGLE. Thus, one concludes that the behaviors observed in the CGLE can be described by only the phase dynamics appropriately constructed.     

Vortex dynamics in oscillatory chemical systems

Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter-rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave-front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg-Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.     

Collective dynamics of interacting molecular motors

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N> or approximately 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.     

Entanglement dynamics for two interacting spins

We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s₁ and s₂, in a constant magnetic field. Two different situations are considered: (a) s₁ → ∞, s₂ = 1/2 and (b) s₁ = s₂ → ∞, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.     

Molecular dynamics of interacting kinks. I

A system consisting of a large number (up to 40 000) of kinks and antikinks moving under attractive interactions, which are annihilated on contacting each other, is studied using the method of molecular dynamics computer simulation. The average distance between neighboring kinks increases logarithmically in time after a short initial transient period. The size distribution function of domains between neighboring kinks is also computed and found to develop a characteristic cut-off structure. Interpretation of the results in terms of simple kinetic models is given. The results are compared with the recent neutron scattering experiments on layered antiferromagnets by Ikeda.     

Ordering of interacting subsystems. Molecular dynamics

The molecular dynamics method is used to examine the ordering of interacting subsystems in a two-component, two-dimensional Coulomb gas, consisting of equal amounts of positively and negatively charged particles, which simulates the behavior of a system of interacting vortices. In particular, it is found that when the system temperature is lowered from the Kosterlitz-Thouless transition point, additional ordering of the vortex chains may take place. It is noted that this process may stimulate the development of vortex chains observed in real superfluid, magnetic, and superconducting systems. Possible applications of the molecular dynamics method to phase separation and the ordering of adiabatically slowly moving subsystems in the collective field of a fast subsystem are considered. Fiz. Tverd. Tela (St. Petersburg) 40, 1701–1704 (September 1998)     

Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.     

Global organization of dynamics in oscillatory heterogeneous excitable media

An oscillatory heterogeneous excitable medium undergoes a transition from periodic target patterns to a bursting rhythm driven by the spontaneous initiation and termination of spiral waves as coupling or density is reduced. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium-sensitive fluorescent dyes. These results are modeled in a heterogeneous cellular automaton in which the neighborhood of interaction and cell density is modified. Parameters that give rise to bursting rhythms are organized in distinct zones in parameter space, leading to a global organization that should be applicable to the dynamics in a large class of excitable media.     

Spiking neurons learning phase delays: how mammals may develop auditory time-difference sensitivity

Time differences between the two ears are an important cue for animals to azimuthally locate a sound source. The first binaural brainstem nucleus, in mammals the medial superior olive, is generally believed to perform the necessary computations. Its cells are sensitive to variations of interaural time differences of about 10 micros. The classical explanation of such a neuronal time-difference tuning is based on the physical concept of delay lines. Recent data, however, are inconsistent with a temporal delay and rather favor a phase delay. By means of a biophysical model we show how spike-timing-dependent synaptic learning explains precise interplay of excitation and inhibition and, hence, accounts for a physical realization of a phase delay.     

Models for the dynamics of interacting magnetic nanoparticles

A critical review of models for the dynamics of interacting magnetic nanoparticles is given. It is shown that the basic assumptions in the Dormann–Bessais–Fiorani model are unrealistic. The experimental observations on systems of interacting magnetic nanoparticles can, at least qualitatively, be explained by the model derived by Mørup and Tronc for weakly interacting particles, in combination with a transition to an ordered state in the case of strong interactions.     

How effective delays shape oscillatory dynamics in neuronal networks

Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit, fixed delay (Roxin et al. (2005,2006) [29] and [30]). Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. We arrive at two general observations of physiological relevance that could not be explained in previous work. These are: 1 — fast oscillations are always supercritical for realistic transfer functions and 2 — traveling waves are preferred over standing waves given plausible patterns of local connectivity. We finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of Hodgkin-Huxley neurons.     

Disturbed oscillatory brain dynamics in subcortical ischemic vascular dementia

Background

This study examined the effects of dietary polyunsaturated fatty acids (PUFA) as different n-6: n-3 ratios on spatial learning and gene expression of peroxisome- proliferator-activated receptors (PPARs) in the hippocampus of rats. Thirty male Sprague?CDawley rats were randomly allotted into 3 groups of ten animals each and received experimental diets with different n-6: n-3 PUFA ratios of either 65:1, 22:1 or 4.5:1. After 10?weeks, the spatial memory of the animals was assessed using the Morris Water Maze test. The expression of PPAR?? and PPAR?? genes were determined using real-time PCR.

Results

Decreasing dietary n-6: n-3 PUFA ratios improved the cognitive performance of animals in the Morris water maze test along with the upregulation of PPAR?? and PPAR?? gene expression. The animals with the lowest dietary n-6: n-3 PUFA ratio presented the highest spatial learning improvement and PPAR gene expression.

Conclusion

It can be concluded that modulation of n-6: n-3 PUFA ratios in the diet may lead to increased hippocampal PPAR gene expression and consequently improved spatial learning and memory in rats.     

Anti-phase wave patterns in a ring of electrically coupled oscillatory neurons

Space-time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the dimensionless Morris–Lecar system. It is shown that such a system yields a special class of traveling localized collective activity so called “anti-phase wave patterns”. The mechanisms of formation of the patterns are discussed and the region of their existence is obtained by using the weakly coupled oscillators theory.     

Microscopic dynamics in a strongly interacting Bose-Einstein condensate

An initially stable 85Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse near a Feshbach resonance. This pulse probed the strongly interacting regime for the BEC, with the diluteness parameter (na(3)) ranging from 0.01 to 0.5. Condensate number loss resulted from the pulse, and for triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until very short time scales (approximately 10 micros) were reached. The observed time dependence is very different from that expected in traditional inelastic loss processes, suggesting the presence of new microscopic BEC physics.     

Nonequilibrium parton dynamics in the strongly interacting QGP

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results—including the partonic equation of state—in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energymomentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant ‘pre-hadronic’ color-dipole states (q [`(q)]bar q or qqq) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. When applying the PHSD approach to Pb + Pb colllisions at 158 A GeV we find a significant effect of the partonic phase on the production of multi-strange antibaryons due to a slightly enhanced s [`(q)]bar q pair production from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.     

Tracer dynamics in Dyson's model of interacting Brownian particles

We prove that the mean square displacement of a tracer particle grows as logt for larget. We point out a connection to the low-temperature floating phase of the ANNNI model.