Related papers: Stochastic single-gene auto-regulation
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…
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…
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…
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
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…
Many cellular responses to surrounding cues require temporally concerted transcriptional regulation of multiple genes. In prokaryotic cells, a single-input-module motif with one transcription factor regulating multiple target genes can…
The production processes of proteins in prokaryotic cells are investigated. Most of the mathematical models in the literature study the production of {\em one} fixed type of proteins. When several classes of proteins are considered, an…
This paper analyzes the stationary distributions of populations governed by the discrete stochastic logistic and Ricker difference equations at equilibrium examines with the gamma distribution. We identify mathematical relationships between…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
We develop an general formalism of single enzyme kinetics in two dimension where substrates diffuse stochastically on a square lattice in presence of disorder. The dynamics of the model could be decoupled effectively to two stochastic…
Stochastic reaction networks is a powerful class of models for the representation a wide variety of population models including biochemistry. The control of such networks has been recently considered due to their important implications for…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that…
Gene expression in response to stimuli is regulated by transcription factors (TFs) through feedback loop motifs, aimed at maintaining the desired TF concentration despite uncertainties and perturbations. In this work, we consider a…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
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…
Imperfect molecular detection in single-cell experiments introduces technical noise that obscures the true stochastic dynamics of gene regulatory networks. While binomial models of molecular capture provide a principled description of…