Stochastic modeling of gene expression: application of ensembles of trajectories

Abstract

It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with ensembles of trajectories for long but fixed times, instead of states or configurations, to study dynamics of these Markovian stochastic processes and glean more information. In this paper we aim to show that the concept of ensemble of trajectories can be applied to a variety of stochastic models of gene expression ranging from a simple birth-death process to a more sophisticate model containing burst and switch. By considering the protein numbers as a relevant dynamical observable, apart from asymptotic behavior of remote tails of probability distribution, generating function for the cumulants of this observable can also be obtained. We discuss the unconditional stochastic Markov processes which generate the statistics of rare events in these models.

arXiv comment23 pages, 5 figures, Accepted for publication in Physical Biology

References in corpus (22)

• The large deviation approach to statistical mechanics
• Fluctuation theorem for stochastic dynamics
• Analytical distributions for stochastic gene expression
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Thermodynamic formalism for systems with Markov dynamics
• Nonequilibrium Markov processes conditioned on large deviations
• Large deviations and ensembles of trajectories in stochastic models
• Effective interactions and large deviations in stochastic processes
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Connecting protein and mRNA burst distributions for stochastic models of gene expression
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Microscopic structure of shocks and antishocks in the ASEP conditioned on low current
• Analytic methods for modeling stochastic regulatory networks
• Rare-Event Sampling of Epigenetic Landscapes and Phenotype Transitions
• Stochastic gene expression conditioned on large deviations
• Thermodynamics of trajectories of the one-dimensional Ising model
• On Effective Stochastic Generators for Conditioned Dynamics at an Atypical Reaction-Diffusion Current