Related papers: Analytical distributions for stochastic gene expre…
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…
Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal…
An important occurrence in many cellular contexts is the crossing of a prescribed threshold by a regulatory protein. The timing of such events is stochastic as a consequence of the innate randomness in gene expression. A question of…
The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
We study several Fokker-Planck equations arising from a stochastic chemical kinetic system modeling a gene regulatory network in biology. The densities solving the Fokker-Planck equations describe the joint distribution of the messenger RNA…
We derive exact solutions of simplified models for the temporal evolution of the protein concentration within a cell population arbitrarily far from the stationary state. We show that monitoring the dynamics can assist in modeling and…
We study a stochastic model of biosynthesis of proteins in generic bacterial operons. The stochasticity arises from two different processes, namely from `bursting' production of either mRNA and/or protein (in the transcription/translation…
We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
Gene expression is inherently noisy as many steps in the read-out of the genetic information are stochastic. To disentangle the effect of different sources of stochasticity in such systems, we consider various models that describe some…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…
The advent of new experimental genomic technologies and the massive increase of DNA sequence information is helping researchers better understand how our genes work. Recently, experiments on mRNA abundance (gene expression) have revealed…
A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…
Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and…
In genetic circuits, when the mRNA lifetime is short compared to the cell cycle, proteins are produced in geometrically-distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic…