The aim of this book is to give a short mathematical introduction to piecewise deterministic
Markov processes (PDMPs) and to present biological models where they appear. The book …

We present a theoretical framework to analyze the dynamics of gene expression with
stochastic bursts. Beginning with an individual-based model which fully accounts for the …

Transcription factors (TFs) interact with a multitude of binding sites on DNA and partner
proteins inside cells. We investigate how nonspecific binding/unbinding to such decoy …

Single-cell experiments show that gene expression is stochastic and bursty, a feature that
can emerge from slow switching between promoter states with different activities. In addition …

The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory
networks. We investigate the propagation of bursting noise between different levels of …

We consider a stochastic version of an excitable system based on the Morris-Lecar model of
a neuron, in which the noise originates from stochastic sodium and potassium ion channels …

We survey work that has been carried out in the attempts of biomathematicians to
understand the dynamic behavior of simple bacterial operons starting with the initial work of …

Noise induced excitability is studied in types I and II Morris--Lecar neurons subject to
constant subthreshold input, where fluctuations arise from sodium and potassium ion …

Inside individual cells, expression of genes is stochastic across organisms ranging from
bacterial to human cells. A ubiquitous feature of stochastic expression is burst-like synthesis …

Synthesis of gene products in bursts of multiple molecular copies is an important source of
gene expression variability. This paper studies large deviations in a Markovian drift-jump …