Moment dynamics for gene regulation with rational rate laws.

This aim of this paper is mainly to investigate the performance of two typical moment closure schemes in gene regulatory master equations of rational rate laws. When the reaction rate is polynomial, the error bounds between the authentic and approximate moments obtained by schemes of Gaussian moment closure and log-normal moment closure are explicitly given. When the reaction rate is not polynomial, it is shown that the two schemes both behave well in the absence of active-inactive state switch, but in the presence of active-inactive state switch the log-normal closure scheme is far superior to the Gaussian closure scheme in capturing the asymptotic ensemble statistics.

Stochastic master equation for early protein aggregation in the transthyretin amyloid disease.

It is significant to understand the earliest molecular events occurring in the nucleation of the amyloid aggregation cascade for the prevention of amyloid related diseases such as transthyretin amyloid disease. We develop chemical master equation for the aggregation of monomers into oligomers using reaction rate law in chemical kinetics. For this stochastic model, lognormal moment closure method is applied to track the evolution of relevant statistical moments and its high accuracy is confirmed by the results obtained from Gillespie's stochastic simulation algorithm.

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input.

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H∈(1/2,1) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise.

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction.

The FitzHugh-Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon.

Switches in a genetic regulatory system under multiplicative non-Gaussian noise.

The non-Gaussian noise is multiplicatively introduced to model the universal fluctuation in the gene regulation of the bacteriophage λ. To investigate the key effect of non-Gaussian noise on the genetic on/off switch dynamics from the viewpoint of quantitative analysis, we employ the high-order perturbation expansion to deduce the stationary probability density of repressor concentration and the mean first passage time from low concentration to high concentration and vice versa. The occupation probability of different concentration states can be estimated from the height and shape of the peaks of the stationary probability density, which could be used to determine the overall expression level.

Classical swine fever virus suppresses maturation and modulates functions of monocyte-derived dendritic cells without activating nuclear factor kappa B.

Classical swine fever virus (CSFV) compromises the host immune system, causing the severe disease of pigs. Dendritic cells (DCs) are the most potent inducers of immune responses. In the present study, we investigated the functional properties of porcine monocyte-derived DCs (Mo-DCs) affected by CSFV.

Spectral density of fluctuations in fractional bistable Klein-Kramers systems.

We investigate the stationary spectral density of fractional bistable Klein-Kramers systems. First, we deduce a dissipation-fluctuation relation between the stationary spectral density at thermal equilibrium and the linear response of the system to an applied perturbation. Second, we describe how to obtain the linear dynamic susceptibility from the method of moments, and thus we derive the fluctuating spectral density from the dissipation-fluctuation relation.

Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model.

It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer's disease, and Parkinson's disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases.

Change in types of neuronal excitability via bifurcation control.

This paper proposes an approach to changing the types of neuronal excitability via bifurcation control. A washout filter-aided dynamic feedback controller is introduced to bifurcation dynamics of a two-dimensional Hindmarsh-Rose type model neuron, which shows a saddle-node on invariant circle (SNIC) bifurcation from quiescence to periodic spiking and then exhibits type-I excitability. At first, a Hopf bifurcation is created at a desired parameter value before the SNIC bifurcation occurs, and then the criticality of the created Hopf bifurcation is regulated by choosing appropriate values of the controller parameters.

Signal-to-noise ratio gain of a noisy neuron that transmits subthreshold periodic spike trains.

The transmission properties of an integrate-and-fire neuron model that transmits coherent subthreshold spike trains in a shot noise environment are investigated by numerical simulation. For very weak coherent couplings, it is shown that the input-output signal-to-noise ratio (SNR) gain is easier to exceed unity; while for stronger coherent couplings it is difficult to observe the SNR gain larger than unity at the optimal noise intensity. These observations are different from those acquired in the case of continuous noise.

Observing stochastic resonance in an underdamped bistable Duffing oscillator by the method of moments.

The method of moments is applied to an underdamped bistable oscillator driven by Gaussian white noise and a weak periodic force for the observations of stochastic resonance and the resulting resonant structures are compared with those from Langevin simulation. The physical mechanisms of the stochastic resonance are explained based on the evolution of the intrawell frequency peak and the above-barrier frequency peak via the noise intensity and the fluctuation-dissipation theorem, and the three possible sources of stochastic resonance in the system are confirmed. Additionally, with the noise intensity fixed, the stochastic resonant structures are also observed by adjusting the nonlinear parameter.

Parabolic bursting induced by veratridine in rat injured sciatic nerves.

A specific bursting, parabolic bursting induced by veratridine, has been observed in rat injured sciatic nerve. With the help of Plant model, the biophysical mechanism for such a phenomenon is revealed from the viewpoint of nonlinear dynamical theory. The slow sodium influx educed by veratridine and the calcium-dependent potassium outflux are regarded as the two slow variables, which are responsible for the parabolic bursting.