Bridging Mechanistic and Phenomenological Models of Complex Biological Systems

The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.Author Summary: Dynamic systems biology models typically involve many kinetic parameters that reflect the complexity of the constituent components. This mechanistic complexity is usually in contrast to relatively simple collective behavior exhibited by the system. We use a semi-global parameter reduction method known as the Manifold Boundary Approximation Method to construct simple phenomenological models of the behavior directly from complex models of the underlying mechanisms. We show that the well-known Michaelis-Menten approximation is a special case of this approach. We apply the method to several complex models exhibiting adaptation and show that they can all be characterized by a single parameter that we denote by τ. The scenario is similar to modeling complex systems in physics in which a large number of microscopically distinct systems are mapped onto relatively simple universality classes characterized by a small number of parameters. By generalizing this approach to dynamical systems biology models, we hope to identify the high-level governing principles that control system behavior and identify their mechanistic control knobs.