Noise In Bistable Systems Research Articles

Visualized Stochastic Modeling of Galactose Regulatory Feedback Loops with Deep Learning Models

Feedback loops, which can produce significant phenotypic heterogeneity by links the output of a circuit back to its input. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, stochastic model is a much better way to studying the impact of both external or intrinsic noise in bistable systems, which is harder for deterministic modeling in the situation of lacking detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we build a stochastic system based on the yeast galactose regulatory network, and talk about the ways to determine the percentages of switching in the system with noise. The deep learning is integrated to reduce the complexity of the model.

Chaos and reverse transitions in stochastic resonance

Stochastic resonance is a phenomenon that a weak signal can be amplified and optimized by the assistance of noise in bistable system. There is still not enough research on the mutual interplay among system, noise and signal. In this paper, we study the role of every parameter in nonlinear transfer and discover chaos phenomenon in stochastic resonance. To measure the influence of chaos, a trajectory decision function was proposed. Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance.

Dynamics and reliability of bistable neurons driven with time-dependent stimuli.

The reliability of a spiking neuron depends on the frequency content of the driving input signal. Previous studies have shown that well above threshold, regularly firing neurons generate reliable responses when the input signal resonates with the firing frequency of the cell. Instead, well below threshold, reliable responses are obtained when the input frequency resonates with the subthreshold oscillations of the neuron. Previous theories, however, provide no clear prediction for the input frequency giving rise to maximally reliable spiking at threshold, which is probably the most relevant firing regime in mammalian cortex under physiological conditions. In particular, when the firing onset is governed by a subcritical Hopf bifurcation, the frequency of subthreshold oscillations often differs from the firing rate at threshold. The predictions of previous studies, hence, cannot be smoothly merged at threshold. Here we explore the behavior of reliability in bistable neurons near threshold using three types of driving stimuli: constant, periodic, and stochastic. We find that the two natural frequencies of the system, associated with the two coexisting attractors, provide a rich variety of possible locking modes with the external signal. Reliability is determined by the sensitivity to noise of each locking mode and by the transition probabilities between modes. Noise increases the amount of spike time jitter, and minimal jitter is obtained for input frequencies coinciding with the suprathreshold firing rate of the cell. In addition, noise may either enhance or inhibit transitions between the two attractors, depending on the input frequency. The dual role played by noise in bistable systems implies that reliability is determined by a delicate balance between spike time jitter and the rate of transitions between attractors.

Multiplicative Lévy noise in bistable systems

Stochastic motion in a bistable, periodically modulated potential is discussed. The system is stimulated by a white noise increments of which have a symmetric stable L\'evy distribution. The noise is multiplicative: its intensity depends on the process variable like |x|^{-\theta}. The Stratonovich and It\^o interpretations of the stochastic integral are taken into account. The mean first passage time is calculated as a function of \theta for different values of the stability index \alpha and size of the barrier. Dependence of the output amplitude on the noise intensity reveals a pattern typical for the stochastic resonance. Properties of the resonance as a function of \alpha, \theta\ and size of the barrier are discussed. Both height and position of the peak strongly depends on \theta\ and on a specific interpretation of the stochastic integral.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Quasi-monochromatic noise in bistable systems: The nature of large occasional fluctuations

The response of an overdamped system to quasi-monochromatic (high-frequency narrow band) noise (QMN) has been investigated by means of analogue electronic experiments. Measurements of the stationary and prehistory probability distributions demonstrate that large occasional, fluctuations are markedly different in character from those that occur when the system is driven by white or exponentially correlated noise. In particular, we report the first experimental observation of a switching point, a critical value of the coordinatex that separates regions which, with an overwhelming probability, are accessed by the fluctuating system along topologically different paths. The results are discussed in terms of, and shown to be consistent with, an existing theoretical description of the QMN-driven system.