Related papers: Gene expression dynamics with stochastic bursts: e…

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.…

We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…

This paper proposes a hierarchical generative model with a multi-grained latent variable to synthesize expressive speech. In recent years, fine-grained latent variables are introduced into the text-to-speech synthesis that enable the fine…

In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…

We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…

Gene expression consists in the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by taking…

Stochastic fluctuations in the copy number of gene products have perceivable effects on the functioning of gene regulatory networks (GRN). The Master equation (ME) provides a theoretical basis for studying such effects. However, solving the…

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve…

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node…

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…

Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…

Cell phenotype dynamic homeostasis contrasts with the inherent randomness of intracellular reactions. Although feedback control of master regulatory genes (MRG) is a key strategy for maintaining gene network expression ranges limited,…

Transcription of genes is the focus of most forms of regulation of gene expression. Even though careful biochemical experimentation has revealed the molecular mechanisms of transcription initiation for a number of different promoters in…

Gene expression (GE) is an inherently random or stochastic or noisy process. The randomness in different steps of GE, e.g., transcription, translation, degradation, etc., leading to cell-to-cell variations in mRNA and protein levels. This…

We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…

We have developed and implemented a numerical evolution scheme for a class of stochastic problems in which the temporal evolution occurs on widely-separated time scales, and for which the slow evolution can be described in terms of a small…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

We consider a model of mRNA production governed by the dynamics of a gene that exists in three possible states -- inactive, poised and active. The transitions between the adjacent states are controlled by stochastic processes characterized…