English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The chemical master equation (CME) is frequently used in systems biology toquantify the effects of stochastic fluctuations that arise due to biomolecularspecies with low copy numbers. The CME is a system of ordinary differentialequations that describes the evolution of probability density for eachpopulation vector in the state-space of the stochastic reaction dynamics. Formany examples of interest, this state-space is infinite, making it difficult toobtain exact solutions of the CME. To deal with this problem, the Finite StateProjection (FSP) algorithm was developed by Munsky and Khammash (Jour. Chem.Phys. 2006), to provide approximate solutions to the CME by truncating thestate-space. The FSP works well for finite time-periods but it cannot be usedfor estimating the stationary solutions of CMEs, which are often of interest insystems biology. The aim of this paper is to develop a version of FSP which werefer to as the stationary FSP (sFSP) that allows one to obtain accurateapproximations of the stationary solutions of a CME by solving a finitelinear-algebraic system that yields the stationary distribution of acontinuous-time Markov chain over the truncated state-space. We derive boundsfor the approximation error incurred by sFSP and we establish that undercertain stability conditions, these errors can be made arbitrarily small byappropriately expanding the truncated state-space. We provide several examplesto illustrate our sFSP method and demonstrate its efficiency in estimating thestationary distributions. In particular, we show that using a quantised tensortrain (QTT) implementation of our sFSP method, problems admitting more than 100million states can be efficiently solved.

A finite state projection algorithm for the stationary solution of the chemical master equation