Introduction
Area of application
The Tauleap method applies to chemically reacting systems.
The method applies to those categories of problems where the number of atoms/molecules involved in reactions is so small that solutions using deterministic reaction rate equations, such as Jarnac, do not give an adequate description. For these problems use could be made of stochastic simulators using rigorous Monte Carlo techniques, such as GillespieService. Although the latter gives exact results, the simulation times required can be prohibitive for larger number of molecules. Tauleap can be seen as a hybrid method which can be seen as a hybrid between a purely stochastic simulation and numerical solutions obtained from the rate equations.
How does it work?
In a rigorous Monte Carlo simulation, the time and reaction channel of every individual reaction is followed. In the Tauleap method on the other hand time leaps (increments) are chosen in such a way that the change in the system state within this leap is so small that no propensity function will change appreciably. At the same time the number of reactions occurring within the time leap can be considerable, leading to a large potential time saving. The number of reactions in each reaction channel is determined by sampling from appropriate Poisson distributions.
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What can be simulated?
The method is suitable for the simulation of chemically reacting systems where the number of molecules involved is roughly of the order of 1000 to 10,000,000 (although the actual implementation will accept numbers up to 2,000,000,000, this would be prohibitively slow). For larger molecule numbers it is more efficient to use a reaction rate method.
In the current version of Tauleap, the following types of chemical reactions can be modelled:
Boundary species can be defined. No global parameters are used. Simple rate laws with rate constants, based on the reactant stoichiometries, where the rate constant can be any order.
Future development
References
Gillespie D.T. The Chemical Langevin equation, Journal of Chemical Physics, 113 (1) 297-306 (2000)
last modified Monday, 16 December 2002