Related papers: Bursting noise in gene expression dynamics: Linkin…

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…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

In this article we demonstrate that the so-called bursting production of molecular species during gene expression may be an artifact caused by low time resolution in experimental data collection and not an actual burst in production. We…

We study by simulation the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels in the case of a repressed gene. We find that spatial fluctuations due to diffusion can drastically enhance the noise…

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…

Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…

This paper considers adiabatic reduction in both discrete and continuous models of stochastic gene expression. In gene expression models, the concept of bursting is a production of several molecules simultaneously and is generally…

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow…

Single-cell data reveal the presence of biological stochasticity between cells of identical genome and environment, in particular highlighting the transcriptional bursting phenomenon. To account for this property, gene expression may be…

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…

Intrinsic transcriptional noise induced by operator fluctuations is investigated with a simple spin like stochastic model. The effects of transcriptional fluctuations in protein synthesis is probed by coupling transcription and translation…

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time…

We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…

At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…

Diffusion Probabilistic Models have demonstrated remarkable performance across a wide range of generative tasks. However, we have observed that these models often suffer from a Signal-to-Noise Ratio-timestep (SNR-t) bias. This bias refers…

Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…

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…

This paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional/translational bursting. We treat this problem in generality with respect to the distribution of the…

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA…

Several studies highlighted the relevance of extrinsic noise in shaping cell decision making and differentiation in molecular networks. Experimental evidences of phenotypic differentiation are given by the presence of bimodal distributions…