Simulating Apoptosis Using Discrete Methods: a Membrane System and a Stochastic Approach

Membrane Systems provide an intriguing method for modeling biological systems at a molecular level. The hierarchical structure of Membrane Systems lends itself readily to mimic the nature and behavior of cells. We have refined a technique for modeling the type I and type II FAS-induced apoptosis signalling cascade. Improvements over our previous modeling work on apoptosis include increased efficiency for storing and sorting waiting times of reactions, a nondeterministic approach for handling reactions competing over limited reactants and improvements, and refinements of the model reactions. The modular nature of our systems provides flexibility with respect to future discoveries on the signal cascade. We provide a breakdown of our algorithms and explanations on improvements we have implemented. We also give an exhaustive comparison to an established ordinary differential equations technique. Based on the results of our simulations, we conclude that Membrane Systems are a useful simulation tool in Systems Biology that could provide new insight into the subcellular processes, and provide also the argument that Membrane Systems may outperform ordinary differential equation simulations when simulating cascades of reactions (as they are observed in cells).