Derivation of Process Algebraic Models of Biochemical Systems

Biochemical pathways have traditionally been modeled using ordinary di erential equations (ODEs), and this approach has resulted in a huge knowledge-base of inter-species interaction mechanisms found in biological systems. However, di erential equation based modeling has a few disadvantages and it has been argued that a new perspective of a system can be derived by looking at its stochastic variant. On the other hand, collaboration between computer scientists and biologists has resulted in the application of process-algebras for modeling of biological systems, which allows these systems to be seen as concurrent and communicating sets of independent agents trying to achieve a common goal. Process-algebra based modeling has several advantages of its own and is gaining popularity among researchers. A problem that is apparent is that many of the biological models that exist currently are in the form of ODEs, and there isn't an easy way to reuse this information in creating new process-algebraic, stochastic models. In the present work, we developed a methodology to translate simple ODE models into stochastic π-calculus models. We used BioSPI as a platform for representation and stochastic simulation of the process-algebraic model to study its time-dependent behavior. We demonstrated our approach with two case studies dealing with the in uence of Raf Kinase Inhibitor Protein (RKIP) on the Extra cellular signal Regulated Kinase (ERK) pathway, and a molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium. We used existing mathematical models for these systems represented with a set of di erential equations. We applied our algorithm to extract a set of chemical reactions from the mathematical equations and modeled the new systems using stochastic π-calculus. To verify the accuracy of the models, we simulated it and compared the results with the results obtained by the deterministic models. We found the behaviour of both deterministic and stochastic models to be similar, thus proving the stochastic π-calculus representation to be acceptable for abstraction of biological systems described by the set of ODEs.