Voltage sensing in ion channels: Mesoscale simulations of biological devices

Electrical signaling via voltage-gated ion channels depends upon the function of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K+ channels. Here we investigate some energetic aspects of the sliding-helix model of the VS using simulations based on VS charges, linear dielectrics and whole-body motion. Model electrostatics in voltage-clamped boundary conditions are solved using a boundary element method. The statistical mechanical consequences of the electrostatic configurational energy are computed to gain insight into the sliding-helix mechanism and to predict experimentally measured ensemble properties such as gating charge displaced by an applied voltage. Those consequences and ensemble properties are investigated for two alternate S4 configurations, \alpha- and 3(10)-helical. Both forms of VS are found to have an inherent electrostatic stability. Maximal charge displacement is limited by geometry, specifically the range of movement where S4 charges and counter-charges overlap in the region of weak dielectric. Charge displacement responds more steeply to voltage in the \alpha-helical than the 3(10)-helical sensor. This difference is due to differences on the order of 0.1 eV in the landscapes of electrostatic energy. As a step toward integrating these VS models into a full-channel model, we include a hypothetical external load in the Hamiltonian of the system and analyze the energetic in/output relation of the VS.Comment: arXiv admin note: substantial text overlap with arXiv:1112.299

Optimization of the leak conductance in the squid giant axon

We report on a theoretical study showing that the leak conductance density, \GL, in the squid giant axon appears to be optimal for the action potential firing frequency. More precisely, the standard assumption that the leak current is composed of chloride ions leads to the result that the experimental value for \GL is very close to the optimal value in the Hodgkin-Huxley model which minimizes the absolute refractory period of the action potential, thereby maximizing the maximum firing frequency under stimulation by sharp, brief input current spikes to one end of the axon. The measured value of \GL also appears to be close to optimal for the frequency of repetitive firing caused by a constant current input to one end of the axon, especially when temperature variations are taken into account. If, by contrast, the leak current is assumed to be composed of separate voltage-independent sodium and potassium currents, then these optimizations are not observed.Comment: 9 pages; 9 figures; accepted for publication in Physical Review

Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings

By extending a dynamical mean-field approximation (DMA) previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 41903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a small-world network. Our network consists of noisy $N$-unit FitzHugh-Nagumo (FN) neurons with couplings whose average coordination number $Z$ may change from local ($Z \ll N$) to global couplings ($Z=N-1$) and/or whose concentration of random couplings $p$ is allowed to vary from regular ($p=0$) to completely random (p=1). We have taken into account three kinds of spatial correlations: the on-site correlation, the correlation for a coupled pair and that for a pair without direct couplings. The original $2 N$-dimensional {\it stochastic} differential equations are transformed to 13-dimensional {\it deterministic} differential equations expressed in terms of means, variances and covariances of state variables. The synchronization ratio and the firing-time precision for an applied single spike have been discussed as functions of $Z$ and $p$. Our calculations have shown that with increasing $p$, the synchronization is {\it worse} because of increased heterogeneous couplings, although the average network distance becomes shorter. Results calculated by out theory are in good agreement with those by direct simulations.Comment: 19 pages, 2 figures: accepted in Phys. Rev. E with minor change

Instability of synchronized motion in nonlocally coupled neural oscillators

We study nonlocally coupled Hodgkin-Huxley equations with excitatory and inhibitory synaptic coupling. We investigate the linear stability of the synchronized solution, and find numerically various nonuniform oscillatory states such as chimera states, wavy states, clustering states, and spatiotemporal chaos as a result of the instability.Comment: 8 pages, 9 figure

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

Single File Diffusion of particles with long ranged interactions: damping and finite size effects

We study the Single File Diffusion (SFD) of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We present simulations that exhibit new behaviors specifically associated to systems of small number of particles and to small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations, and provides convincing estimates of the crossover times between those regimes.Comment: 30 pages, 9 figure

An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model

By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {\it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {\it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures, accepted in Phys. Rev. E with some change

Single-File Diffusion of Externally Driven Particles

We study 1-D diffusion of $N$ hard-core interacting Brownian particles driven by the space- and time-dependent external force. We give the exact solution of the $N$-particle Smoluchowski diffusion equation. In particular, we investigate the nonequilibrium energetics of two interacting particles under the time-periodic driving. The hard-core interaction induces entropic repulsion which differentiates the energetics of the two particles. We present exact time-asymptotic results which describe the mean energy, the accepted work and heat, and the entropy production of interacting particles and we contrast these quantities against the corresponding ones for the non-interacting particles