Dynamic Partitioning of Large Discrete Event Biological Systems for Hybrid Simulation and Analysis

Biological systems involving genetic reactions are large discrete event systems, and often contain certain species that occur in small quantities, and others that occur in large quantities, leading to a difficulty in modeling and simulation. Small populations inhibit the usefulness of utilizing differential equations to represent the system, while the large populations cause stochastic discrete event simulation to become computationally intensive. This paper presents an algorithmic approach for the dynamic partitioning and stochastic hybrid simulation of biological systems. The algorithm uses a Poisson approximation for discrete event generation and ordinary differential equations to model continuous behavior. The populations are dynamically partitioned so that some populations are simulated in a discrete stochastic fashion, while others are simulated by continuous differential equations, and this partition between discrete and continuous behavior is updated. A hybrid model of a biological toggle switch is used to illustrate our approach, and yields