3,835 research outputs found
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 -unit
FitzHugh-Nagumo (FN) neurons with couplings whose average coordination number
may change from local () to global couplings () and/or
whose concentration of random couplings is allowed to vary from regular
() 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 -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 and . Our calculations have shown that with increasing
, 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 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. 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 -unit ensemble described by linear and nonlinear Langevin
equations with delays. In AMM, original -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 in the level- AMM (AMM), which
yields -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 hard-core interacting Brownian particles driven
by the space- and time-dependent external force. We give the exact solution of
the -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
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