Stochastic models of gene expression are typically formulated using the chemical master
equation, which can be solved exactly or approximately using a repertoire of analytical …

While the steady-state behavior of stochastic gene expression with auto-regulation has been
extensively studied, its time-dependent behavior has received much less attention. Here …

We approach the questions, what part of evolutionary change results from selection, and
what is the adaptive information flow into a population undergoing selection, as a problem of …

Stochastic reaction networks, which are usually modeled as continuous-time Markov chains
on Z≥ 0 d, and simulated via a version of the “Gillespie algorithm,” have proven to be a …

We show that discrete distributions on the d-dimensional non-negative integer lattice can be
approximated arbitrarily well via the marginals of stationary distributions for various classes …

In the study of reaction networks and the polynomial dynamical systems that they generate,
special classes of networks with important properties have been identified. These include …

We consider problems in the functional analysis and evolution of combinatorial chemical
reaction networks as rule-based, or three-level systems. The first level consists of rules …

Refractory period (RP), the waiting time between signals, can induce complex signaling
dynamics, such as acceleration, adaptation, and oscillation, within many cellular …

The first passage time (FPT) is a generic measure that quantifies when a random quantity
reaches a specific state. We consider the FTP distribution in nonlinear stochastic …

In many biological systems, chemical reactions or changes in a physical state are assumed
to occur instantaneously. For describing the dynamics of those systems, Markov models that …