Combining Agent-Based Models with Stochastic Differential Equations for Gene Regulatory Networks

Mathematical models in systems biology can use quantitative techniques to study the integrated behaviors of biological systems in macro level. Agent-based modeling provides a qualitative framework, focusing on how each individual molecule behaves in micro level. We are motivated to combine their features together to describe the gene regulatory networks, in particular the emergence of macro phenomena from micro interactions. An agent-based model will be well defined as general as possible, including of many agents of various molecular species interacting in it. The mathematical premises, which are grounded in the micro behaviors of agents, can derive the chemical master equations and the stochastic differential equations for modeling the integrated behaviors of systems in macro level. Combing agent-based models with stochastic differential equations affords a more complete perspective on gent regulatory networks. In addition, the sources and magnitudes of deterministic dynamics and random noises are explicitly characterized.