Spatial coherence resonance in excitable biochemical media induced by internal noise

Fast regular firings induced by intra- and inter-time delays in two clustered neuronal networks

In this paper, we consider two clustered neuronal networks with dense intra-synaptic links within each cluster and sparse inter-synaptic links between them. We focus on the effects of intra- and inter-time delays on the spiking regularity and timing in both clusters. With the aid of simulation results, we show that intermediate intra- and inter-time delays are able to separately induce fast regular firing - spiking activity with a high firing rate as well as a high spiking regularity. Moreover, when both intra- and inter-time delays are present, we find that fast regular firings are induced much more frequently than if only a single type of delay is present in the system. Our results indicate that appropriately adjusted intra- and inter-time delays can significantly facilitate fast regular firing in neuronal networks. Based on a detailed analysis, we conjecture that this is most likely when the largest value of common divisors of the intra- and inter-time delays falls into a range where fast regular firings are induced by suitable intra- or inter-time delays alone.

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. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

Role of time delay on intracellular calcium dynamics driven by non-Gaussian noises

Effect of time delay (τ) on intracellular calcium dynamics with non-Gaussian noises in transmission processes of intracellular Ca²⁺ is studied by means of second-order stochastic Runge-Kutta type algorithm. By simulating and analyzing time series, normalized autocorrelation function, and characteristic correlation time of cytosolic and calcium store’s Ca²⁺ concentration, the results exhibit: (i) intracellular calcium dynamics’s time coherence disappears and stability strengthens as τ → 0.1s; (ii) for the case of τ < 0.1s, the normalized autocorrelation functions of cytosolic and calcium store’s Ca²⁺ concentration show damped motion when τ is very short, but they trend to a level line as τ → 0.1s, and for the case of τ > 0.1s, they show different variation as τ increases, the former changes from underdamped motion to a level line, but the latter changes from damped motion to underdamped motion; and (iii) at the moderate value of time delay, reverse resonance occurs both in cytosol and calcium store.

Neurodynamics of up and down transitions in a single neuron

Recent experimental studies have revealed that up and down transitions exist in membrane potential of neurons. This paper focuses on the neurodynamical research of these transitions in a single neuron since it is the basic to study the transitions in the neural network for further work. The results show there exists two stable levels in the neuron called up and down states. And transitions between these two states are bidirectional or unidirectional with the values of parameters changing. We also study the periodic spontaneous activity of the transitions between up and down states without any inputting stimulus which coheres with the experimental results.

Stochastic simulations of pattern formation in excitable media

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction-diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca2+ oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to 10(10) particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration.

Spatial pattern formation in external noise: theory and simulation

Spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept. A reaction-diffusion system with external noise is considered as a model of such media. Stochastic equations for unstable mode amplitudes (order parameters), the dispersion equation for averaged amplitudes of unstable modes, and the Fokker-Planck equation for the order parameters are obtained. The theory developed makes it possible to analyze different noise-induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise.

Noise amplification in human tumor suppression following gamma irradiation

The influence of noise on oscillatory motion is a subject of permanent interest, both for fundamental and practical reasons. Cells respond properly to external stimuli by using noisy systems. We have clarified the effect of intrinsic noise on the dynamics in the human cancer cells following gamma irradiation. It is shown that the large amplification and increasing mutual information with delay are due to coherence resonance. Furthermore, frequency domain analysis is used to study the mechanisms.

Internal noise enhanced oscillation in a delayed circadian pacemaker

The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ(h). We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ(EO), shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ(EO). The decay rate K(d) could significantly affect Δτ(EO), while varying the gene expression rate K(e) has no obvious effect if K(e) is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.

Analytical and simulation results for the stochastic spatial Fitzhugh-Nagumo model neuron

For the Fitzhugh-Nagumo system with space-time white noise, we use numerical methods to consider the generation of action potentials and the reliability of transmission in the presence of noise. The accuracy of simulated solutions is verified by comparison with known exact analytical results. Noise of small amplitude may prevent transmission directly, whereas larger-amplitude noise may also interfere by producing secondary nonlocal responses. The probability of transmission as a function of noise amplitude is found for both uniform noise and noise restricted to a patch. For certain parameter ranges, the recovery variable may be neglected to give a single-component nonlinear diffusion with space-time white noise. In this case, analytical results are obtained for small perturbations and noise, which agree well with simulation results. For the voltage variable, expressions are given for the mean, covariance, and variance and their steady-state forms. The spectral density of the voltage is also obtained. Numerical examples are given of the difference between the properties of nonlinear and linear cables, and the validity of the expressions obtained for the statistical properties is investigated as a function of noise amplitude. For given parameters, analytical results are in good agreement with simulation until a certain critical noise amplitude is reached, which can be estimated. The role of trigger zones in increasing the reliability of transmission is discussed.

Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.