Related papers: Optimal Path to Epigenetic Switching
A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this…
The structure of a genetic network is uncovered by studying its response to external stimuli (input signals). We present a theory of propagation of an input signal through a linear stochastic genetic network. It is found that there are…
A control strategy is employed that modifies the stochastic escape times from one basin of attraction to another in a model of a double-gyre flow. The system studied captures the behavior of a large class of fluid flows that circulate and…
Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative…
Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a…
We consider the stochastic gene expression process with inter-state flip-flops. An exact steady-state solution to the master equation is calculated. One of the main goals in this paper is to investigate whether the probability distribution…
We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…
The phage $\lambda$ infection of an \textit{E. coli} cell has become a paradigm for understanding the molecular processes involved in gene expression and cell signaling. This system provides an example of a genetic switch, as cells with…
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition…
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of…
Multistable gene regulatory systems sustain different levels of gene expression under identical external conditions. Such multistability is used to encode phenotypic states in processes including nutrient uptake and persistence in bacteria,…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…
We consider the general problem of describing the dynamics of subnetworks of larger biochemical reaction networks, e.g. protein interaction networks involving complex formation and dissociation reactions. We propose the use of model…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of…
The digital nature of genes combined with the associated low copy numbers of proteins regulating them is a significant source of stochasticity, which affects the phase of biochemical oscillations. We provide a theoretical framework for…