Related papers: Optimal first-passage time in gene regulatory netw…
Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although…
This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past and closed-form expressions of the mean and variance have been obtained for a…
In a stochastic process, noise often modifies the picture offered by the mean field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary…
MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression. Recently, a mathematical model has been proposed to…
In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable…
Mathematical models of gene regulatory networks are widely used to study cell fate changes and transcriptional regulation. When designing such models, it is important to accurately account for sources of stochasticity. However, doing so can…
Interesting theoretical problems of target search or threshold crossing, formally known as {\it first passage}, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems…
When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here we explain the behavior of smooth FPT…
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…
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,…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
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…
Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical…
Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback…
Gene expression is a stochastic process in which cells produce biomolecules essential to the function of life. Modern experimental methods allow for the measurement of biomolecules at single-cell and single-molecule resolution over time.…
In this paper we develop a model of stochastic gene expression, which is an extension of the model investigated in the paper [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, Transcriptional stochasticity in gene…
Using an analytically solvable stochastic model, we study the properties of a simple genetic circuit consisting of multiple copies of an self-regulating gene. We analyse how the variation in gene copy number and the mutations changing the…
We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain,…
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…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…