104 research outputs found
Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
We consider a simple Markovian class of the stochastic Wilson-Cowan type
models of neuronal network dynamics, which incorporates stochastic delay caused
by the existence of a refractory period of neurons. From the point of view of
the dynamics of the individual elements, we are dealing with a network of
non-Markovian stochastic two-state oscillators with memory which are coupled
globally in a mean-field fashion. This interrelation of a higher-dimensional
Markovian and lower-dimensional non-Markovian dynamics is discussed in its
relevance to the general problem of the network dynamics of complex elements
possessing memory. The simplest model of this class is provided by a
three-state Markovian neuron with one refractory state, which causes firing
delay with an exponentially decaying memory within the two-state reduced model.
This basic model is used to study critical avalanche dynamics (the noise
sustained criticality) in a balanced feedforward network consisting of the
excitatory and inhibitory neurons. Such avalanches emerge due to the network
size dependent noise (mesoscopic noise). Numerical simulations reveal an
intermediate power law in the distribution of avalanche sizes with the critical
exponent around -1.16. We show that this power law is robust upon a variation
of the refractory time over several orders of magnitude. However, the avalanche
time distribution is biexponential. It does not reflect any genuine power law
dependence
Stochastic modeling of excitable dynamics: improved Langevin model for mesoscopic channel noise
Influence of mesoscopic channel noise on excitable dynamics of living cells
became a hot subject within the last decade, and the traditional biophysical
models of neuronal dynamics such as Hodgkin-Huxley model have been generalized
to incorporate such effects. There still exists but a controversy on how to do
it in a proper and computationally efficient way. Here we introduce an improved
Langevin description of stochastic Hodgkin-Huxley dynamics with natural
boundary conditions for gating variables. It consistently describes the channel
noise variance in a good agreement with discrete state model. Moreover, we show
by comparison with our improved Langevin model that two earlier Langevin models
by Fox and Lu also work excellently starting from several hundreds of ion
channels upon imposing numerically reflecting boundary conditions for gating
variables.Comment: V.M. Mladenov and P.C. Ivanov (Eds.): NDES 2014, Communications in
Computer and Information Science, vol. 438 (Springer, Switzerland, 2014), pp.
325-33
Molecular machines operating on nanoscale: from classical to quantum
The main physical features and operating principles of isothermal
nanomachines in microworld are reviewed, which are common for both classical
and quantum machines. Especial attention is paid to the dual and constructive
role of dissipation and thermal fluctuations, fluctuation-dissipation theorem,
heat losses and free energy transduction, thermodynamic efficiency, and
thermodynamic efficiency at maximum power. Several basic models are considered
and discussed to highlight generic physical features. Our exposition allows to
spot some common fallacies which continue to plague the literature, in
particular, erroneous beliefs that one should minimize friction and lower the
temperature to arrive at a high performance of Brownian machines, and that
thermodynamic efficiency at maximum power cannot exceed one-half. The emerging
topic of anomalous molecular motors operating sub-diffusively but highly
efficiently in viscoelastic environment of living cells is also discussed
Fractional Bhatnagar-Gross-Krook kinetic equation
The linear Boltzmann equation approach is generalized to describe fractional
superdiffusive transport of the Levy walk type in external force fields. The
time distribution between scattering events is assumed to have a finite mean
value and infinite variance. It is completely characterized by the two
scattering rates, one fractional and a normal one, which defines also the mean
scattering rate. We formulate a general fractional linear Boltzmann equation
approach and exemplify it with a particularly simple case of the Bohm and Gross
scattering integral leading to a fractional generalization of the Bhatnagar,
Gross and Krook kinetic equation. Here, at each scattering event the particle
velocity is completely randomized and takes a value from equilibrium Maxwell
distribution at a given fixed temperature. We show that the retardation effects
are indispensable even in the limit of infinite mean scattering rate and argue
that this novel fractional kinetic equation provides a viable alternative to
the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and
its generalization by Friedrich et al. based on the picture of divergent mean
time between scattering events. The case of divergent mean time is also
discussed at length and compared with the earlier results obtained within the
fractional KFP
Rate processes with non-Markovian dynamical disorder
Rate processes with dynamical disorder are investigated within a simple
framework provided by unidirectional electron transfer (ET) with fluctuating
transfer rate. The rate fluctuations are assumed to be described by a
non-Markovian stochastic jump process which reflects conformational dynamics of
an electron transferring donor-acceptor molecular complex. A tractable
analytical expression is obtained for the relaxation of the donor population
(in the Laplace-transformed time domain) averaged over the stationary
conformational fluctuations. The corresponding mean transfer time is also
obtained in an analytical form. The case of two-state fluctuations is studied
in detail for a model incorporating substate diffusion within one of the
conformations. It is shown that an increase of the conformational diffusion
time results in a gradual transition from the regime of fast modulation
characterized by the averaged ET rate to the regime of quasi-static disorder.
This transition occurs at the conformational mean residence time intervals
fixed much less than the inverse of the corresponding ET rates. An explanation
of this paradoxical effect is provided. Moreover, its presence is also
manifested for the simplest, exactly solvable non-Markovian model with a
biexponential distribution of the residence times in one of the conformations.
The nontrivial conditions for this phenomenon to occur are found
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