Modeling cellular signaling systems: An abstraction-refinement approach

The molecular mechanisms of cell communication with the environment involve many concurrent processes governing dynamically the cell function. This concurrent behavior makes traditional methods, such as differential equations, unsatisfactory as a modeling strategy since they do not scale well when a more detailed view of the system is required. Concurrent Constraint Programming (CCP) is a declarative model of concurrency closely related to logic for specifying reactive systems, i.e., systems that continuously react with the environment. Agents in CCP interact by telling and asking information represented as constraints (e.g., x > 42). In this paper we describe a modeling strategy for cellular signaling systems based on a temporal and probabilistic extension of CCP. Starting from an abstract model, we build refinements adding further details coming from experimentation or abstract assumptions. The advantages of our approach are: due to the notion of partial information as constraints in CCP, the model can be straightforwardly extended when more information is available; qualitative and quantitative information can be represented by means of probabilistic constructs of the language; finally, the model is a runnable specification and can be executed, thus allowing for the simulation of the system. We outline the use of this methodology to model the interaction of G-protein-coupled receptors with their respective G-proteins that activates signaling pathways inside the cell. We also present simulation results obtained from an implementation of the framework.