  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 $\tau$ 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.
