Yates, C. A. and Burrage, K. (2011) Look before you leap: a confidencebased method for selecting species criticality while avoiding negative populations in leaping. The Journal of Chemical Physics, 134 (8). 0841091.

PDF
1MB 
Abstract
The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, . This method is acceptable providing the leap condition, that no propensity function changes “significantly” during any timestep, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next timestep. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method
Item Type:  Article 

Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  1505 
Deposited By:  Sara Jolliffe 
Deposited On:  31 Mar 2012 08:23 
Last Modified:  29 May 2015 19:12 
Repository Staff Only: item control page