Abstraction of Graph-Based Models of Bio-molecular Reaction Systems for Efficient Simulation

We propose a technique to simulate molecular reaction systems efficiently by abstracting graph models. Graphs (or networks) and their transitions give rise to simple but powerful models for molecules and their chemical reactions. Depending on the purpose of a graph-based model, nodes and edges of a graph may correspond to molecular units and chemical bonds, respectively. This kind of model provides naive simulations of molecular reaction systems by applying chemical kinetics to graph transition. Such naive models, however, can immediately cause a combinatorial explosion of the number of molecular species because combination of chemical bonds is usually unbounded, which makes simulation intractable. To overcome this problem, we introduce an abstraction technique to divide a graph into local structures. New abstracted models for simulating DNA hybridization systems and RNA interference are explained as case studies to show the effectiveness of our abstraction technique. We then discuss the trade-off between the efficiency and exactness of our abstracted models from the aspect of the number of structures and simulation error. We classify molecular reaction systems into three groups according to the assumptions on reactions. The first one allows efficient and exact abstraction, the second one allows efficient but approximate abstraction, and the third one does not reduce the number of structures by abstraction. We conclude that abstraction is a useful tool to analyze complex molecular reaction systems and measure their complexity.