Supremum modeling to extend model transferability in systems biology

A goal of physical modeling is to relate system-level phenomena to physical mechanisms. The complexity of biological systems makes it difficult to build models that balance parsimony and physical realism. The Manifold Boundary Approximation Method can derive simple models with limited scope from biological first-principles. However, these models may not reliably transfer since they abstract away the mechanisms irrelevant for their target context. I describe an approach to improve the transferablility of these reduced models. I consider the space of all possible reduced models. Given two minimal models, I construct the simplest model that can be reduced to them. This model is the least upper bound in complexity, and so we refer to it as the "supremum." By unifying the mechanistic explanations for different phenomena, the supremum model is predictive under diverse conditions. I illustrate for the Wnt signaling pathway. I build minimal models that describe Wnt signaling for two different developmental stages and construct their supremum. The supremum model predicts a new phenomenon: controlled pulsing, analogous to expression patterns of anterior-posterior axial development. The supremum principle is broadly applicable to create parsimonious, transferable models.