Related papers: Modeling Stochasticity and Variability in Gene Reg…
Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in…
Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum…
Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative…
Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. What mechanisms might be responsible for these low in-degrees? Starting with an accepted framework of the…
Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations,…
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…
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…
Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness…
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,…
A wealth of new research has highlighted the critical roles of small RNAs (sRNAs) in diverse processes such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif comprising…
Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks…
We study a chemical kinetic system with uncertainty modeling a gene regulatory network in biology. Specifically, we consider a system of two equations for the messenger RNA and micro RNA content of a cell. Our target is to provide a simple…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a…
The inherent probabilistic nature of the biochemical reactions, and low copy number of species can lead to stochasticity in gene expression across identical cells. As a result, after induction of gene expression, the time at which a…
Stochastic Boolean networks, or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. Standard updating schedules…
Single-cell data provide high-dimensional measurements of the transcriptional states of cells, but extracting insights into the regulatory functions of genes, particularly identifying transcriptional mechanisms affected by biological…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…