No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

Steady-state simulation of metastable stochastic chemical systems

Rent:

Rent this article for

USD

10.1063/1.4804191

### Abstract

We address the problem of steady-state simulation for metastable continuous-time Markov chains with application to stochastic chemical kinetics. Such systems are characterized by the existence of two or more pseudo-equilibrium states and very slow convergence towards global equilibrium. Approximation of the stationary distribution of these systems by direct application of the Stochastic Simulation Algorithm (SSA) is known to be very inefficient. In this paper, we propose a new method for steady-state simulation of metastable Markov chains that is centered around the concept of stochastic complementation. The use of this mathematical device along with SSA results in an algorithm with much better convergence properties, that facilitates the analysis of rarely switching stochastic biochemical systems. The efficiency of our method is demonstrated by its application to two genetic toggle switch models.

© 2013 AIP Publishing LLC

Received 15 January 2013
Accepted 23 April 2013
Published online 13 May 2013

Acknowledgments: This work was supported by HYCON2 Network of Excellence, FP7-ICT- 257462, and the YeastX project of SystemsX.ch.

Article outline:

I. INTRODUCTION

II. INTRODUCTION TO STOCHASTIC COMPLEMENT THEORY

III. SIMULATION ALGORITHM

A. Setup

B. First step

C. Second step

D. Third step

IV. PRACTICAL IMPLEMENTATION

A. Definition of and

B. Matrix calculations and recursive calculations

C. Estimation of ν_{1} and ν_{2}

D. Dominant eigenvalue

V. EXAMPLES

A. 2D toggle switch

1. Steady-state simulation for set 1

2. Steady-state simulation for set 2

B. An exclusive genetic switch

VI. COMPARISON WITH NON-EQUILIBRIUM UMBRELLA SAMPLING

VII. CONCLUDING REMARKS

/content/aip/journal/jcp/138/18/10.1063/1.4804191

http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4804191

Article metrics loading...

/content/aip/journal/jcp/138/18/10.1063/1.4804191

2013-05-13

2014-04-19

Full text loading...

### Most read this month

Article

content/aip/journal/jcp

Journal

5

3

Commenting has been disabled for this content