To use all functions of this page, please activate cookies in your browser.

my.chemeurope.com

With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter.

- My watch list
- My saved searches
- My saved topics
- My newsletter

## Gillespie algorithmThe ## Additional recommended knowledge## Idea behind the algorithmTraditional continuous and deterministic biochemical rate equations do not accurately predict cellular reactions since they rely on bulk reactions that require the interactions of millions of molecules. They are typically modeled as a set of coupled ordinary differential equations. In contrast, the Gillespie algorithm allows a discrete and stochastic simulation of a system with few reactants because every reaction is explicitly simulated. When simulated, a Gillespie realization represents a random walk that exactly represents the distribution of the Master equation. The physical basis of the algorithm is the collision of molecules within a reaction vessel. It is assumed that collisions are frequent, but collisions with the proper orientation and energy are infrequent. Therefore, all reactions within the Gillespie framework must involve at most two molecules. Reactions involving three molecules are assumed to be extremely rare and are modeled as a sequence of binary reactions. It is also assumed that the reaction environment is well mixed. ## AlgorithmBelow is a summary of the steps to run the Gillespie algorithm (math omitted for now): - 0)
**Initialization**: Initialize the number of molecules in the system, reactions constants, and random number generators. - 1)
**Monte Carlo Step**: Generate random numbers to determine the next reaction to occur as well as the time interval. - 2)
**Update**: Increase the time step by the randomly generated time in Step 1. Update the molecule count based on the reaction that occurred. - 3)
**Iterate**: Go back to Step 1 unless the number of reactants is zero or the simulation time has been exceeded.
The algorithm is computationally expensive and thus many modifications and adaptations exist, including the Gibson & Bruck method, tau-leaping, as well as hybrid techniques where abundant reactants are modeled with deterministic behavior. Adapted techniques generally compromise the exactitude of the theory behind the algorithm as it connects to the Master equation, but offer reasonable realizations for greatly improved timescales. See the articles under further reading for details. ## Further reading- Summary of Gillespie Algorithm with Matlab examples
- Interactive Evaluation of the Gillespie Algorithm for Protein Synthesis
- Daniel T. Gillespie, "Exact Stochastic Simulation of Coupled Chemical Reactions". The Journal of Physical Chemistry, Vol. 81, No. 25, pp. 2340-2361 (1977).
- Daniel T. Gillespie, "A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions". Journal of Computational Physics 22(4), 403-434 (1976).
- M. Rathinam, L. R. Petzold, Y. Cao, and Daniel T. Gillespie, "Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method". Journal of Chemical Physics, Volume 119, Issue 24, pp. 12784-12794 (2003).
- M. A. Gibson and J. Bruck, "Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels". J. Phys. Chem. A 104: 1876-1889 (2000).
Categories: Chemical kinetics | Computational chemistry | Monte Carlo methods |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Gillespie_algorithm". A list of authors is available in Wikipedia. |