Related papers: Optimal Path to Epigenetic Switching
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
We investigate the effect of noisy feed rates on the behavior of a cubic autocatalytic chemical reaction model. By combining the renormalization group and stoichiometric network analysis, we demonstrate how externally adjustable random…
We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this…
Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to…
Many processes in biology, from the regulation of gene expression in bacteria to memory in the brain, involve switches constructed from networks of biochemical reactions. Crucial molecules are present in small numbers, raising questions…
We show that noise-induced oscillations in a gene circuit model display stochastic coherence, that is, a maximum in the regularity of the oscillations as a function of noise amplitude. The effect is manifest as a system-size effect in a…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
We study the effect of external noise on resistive switching. Experimental results on a manganite sample are presented showing that there is an optimal noise amplitude that maximizes the contrast between high and low resistive states. By…
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer…
Electronic circuits are useful tools for studying potential dynamical behaviors of synthetic genetic networks. The circuit models are complementary to numerical simulations of the networks, especially providing a framework for verification…
Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible…
The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…
We propose and analyze a stochastic model to investigate epigenetic mutations, i.e., modifications of the genetic information that control gene expression patterns in a cell but do not alter the DNA sequence. Epigenetic mutations are…
We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system we distinguish four types of limits: continuous piecewise…