Abstract
ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models.
Highlights
Dynamic Monte Carlo methods are a common means of simulating the time-evolution of chemical systems
We develop a new algorithm, LOLCAT Method, that can speed up the exact stochastic simulation of a large class of well-mixed chemical systems by orders of magnitude
Because the probability of selecting any given reaction and the effect on propensities following its selection is identical for LOLCAT Method and the Gillespie Algorithm, we are guaranteed that LOLCAT Method is a correct implementation of the Gillespie Algorithm, assuming that a sufficient number of bits are used in the floating point representations of propensities
Summary
Dynamic Monte Carlo methods are a common means of simulating the time-evolution of chemical systems. Each iteration of the SSA may be viewed as two phases: a read phase, in which the algorithm chooses a random number and maps it to the reaction to execute (step 3), and a write phase, in which the reaction is executed, propensities are adjusted, and simulation time is advanced (steps 2, 4, and 5). We use this twophase view in describing LOLCAT Method, as focuses attention on the interaction of the algorithm with its supporting data structures. These methods sometimes perform better, the measured speedup is only a small constant, and we compare only against ODM and NRM
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