Related papers: Stochastic gene expression with delay
Gene expression is a random or noisy process. The process consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master…
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
Translation is the cellular process in which ribosomes make proteins from information encoded on messenger RNA (mRNA). We model translation with an exclusion process taking into account the experimentally determined, non-exponential,…
Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the…
In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on…
Gene regulation involves a hierarchy of events that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. The effects of DNA sequence on these processes have typically been studied based…
Translation is a central biological process by which proteins are synthesized from genetic information contained within mRNAs. Here we study the kinetics of translation at molecular level through a stochastic simulation model. The model…
For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate of transcription at steady state, and assess detailed balance breaking in transcription. Our analytics allow us to…
Recent work has shown that expression level is the main predictor of a gene’s evolutionary rate, and that more highly expressed genes evolve slower. A possible explanation for this observation is selection for proteins which fold…
In a general stochastic multistate promoter model of dynamic mRNA/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit `stick-breaking' construction of…
Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid…
The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling, and demonstrate that conventional…
Transcription factors (TFs) are key regulators of gene expression. Based on the classical scenario in which the TF search process switches between one-dimensional motion along the DNA molecule and free Brownian motion in the nucleus, we…
We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random…
Noise in gene expression, either due to inherent stochasticity or to varying inter- and intracellular environment, can generate significant cell-to-cell variability of protein levels in clonal populations. We present a theoretical…