Discrete Nondeterministic Modeling of the Fas Pathway

Computer modeling of molecular signaling cascades can provide useful insight into the underlying complexities of biological systems. We present a refined approach for the discrete modeling of protein interactions within the environment of a single cell. The technique we offer utilizes the Membrane Systems paradigm which, due to its hierarchical structure, lends itself readily to mimic the behavior of cells. Since our approach is nondeterministic and discrete, it provides an interesting contrast to the standard deterministic ordinary differential equations techniques. We argue that our approach may outperform ordinary differential equations when modeling systems with relatively low numbers of molecules – a frequent occurrence in cellular signaling cascades. Refinements over our previous modeling efforts include the addition of nondeterminism for handling reaction competition over limited reactants, increased efficiency in the storing and sorting of reaction waiting times, and modifications of the model reactions. Results of our discrete simulation of the type I and type II Fas-mediated apoptotic signaling cascade are illustrated and compared with two approaches: one based on ordinary differential equations and another based on the well-known Gillespie algorithm.