Table of Contents Author Guidelines Submit a Manuscript
Journal of Biomedicine and Biotechnology
Volume 2011 (2011), Article ID 572492, 5 pages
Review Article

Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics

Medical Biophysics Group, Institute of Physiology and Pathophysiology, University of Heidelberg, 69120 Heidelberg, Germany

Received 1 July 2011; Accepted 25 August 2011

Academic Editor: Aikaterini Kontrogianni-Konstantopoulos

Copyright © 2011 Nicolas Wieder et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.