The canonical nuclear factor-κB (NF-κB) signaling pathway controls a gene network important in the cellular inflammatory response. Upon activation, NF-κB/RelA is released from cytoplasmic inhibitors, from where it translocates into the nucleus, …
Dynamical analysis tools are well established for deterministic models. However, for many biochemical phenomena in cells the molecule count is low, leading to stochastic behavior that causes deterministic macroscale reaction models to fail. The main …
Stochastic reaction networks modeled as jump Markov processes serve as the main mathematical representation of biochemical phenomena in cells, particularly when the relevant molecule count is low, causing deterministic macroscale chemical reaction …
We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining …
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which defines a threshold. Below the threshold, the population quickly becomes extinct; above, it persists for a long …
Diffusion processes intended to model the continuous state space limit of birth–death processes, chemical reactions, and other discrete particle systems often involve multiplicative noise where the diffusion vanishes near one (or more) of the state …