Related papers: Stochastic mRNA production by a three-state gene

We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…

RNA forms elaborate secondary structures through intramolecular base pairing. These structures perform critical biological functions within each cell. Due to the availability of a polynomial algorithm to calculate the partition function…

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…

Stochastic simulation has been a powerful tool for studying the dynamics of gene regulatory networks, particularly in terms of understanding how cell-phenotype stability and fate-transitions are impacted by noisy gene expression. However,…

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and…

Molecular systems often remain trapped for long times around some local minimum of the potential energy function, before switching to another one -- a behavior known as metastability. Simulating transition paths linking one metastable state…

The methylation of DNA regulates gene expression. On cell division the methylation state of the DNA is typically inherited from parent to daughter cells. While the chemical bond between the methyl group and the DNA is very strong, changes…

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory…

In this work, we study a protein synthesis degradation process by defining a general mathematical model. Using generating function technique we present a method that allows exact calculation of joint probability distribution of protein…

We analyse transcriptional bursting within a stochastic non-equilibrium model which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a…

Gene Regulatory Networks are networks of interactions in biological organisms responsible for determining the production levels of proteins and peptides. Proteins are workers of a cell factory, and their production defines the goal of a…

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…

RNA structure and functional dynamics play fundamental roles in controlling biological systems. Molecular dynamics simulation, which can characterize interactions at an atomistic level, can advance the understanding on new drug discovery,…

DNA methylation is an important biological mechanism to regulate gene expression and control cell development. Mechanistic modeling has become a popular approach to enhance our understanding of the dynamics of methylation pattern formation…

Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually…

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…

We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…

This paper considers a stochastic production planning problem with regime switching. There are two regimes corresponding to different economic cycles. A factory is planning its production so as to minimize production costs. We analyze this…

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…

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,…