Date: January 11, 2022
Speaker: Dr. Mark Transtrum
Affiliation: Brigham Young University
Title: Using Simple Models to Understand Complex Biological Processes
Abstract: Simple mathematical models play an important role in how we reason about the world. Although real physical processes are very complicated, useful models abstract away irrelevant details to reveal the key features driving the phenomenon of interest. In contrast, overly complex models can be difficult to evaluate, suffer from numerical instabilities, and may over-fit data. They also obscure useful insights that could guide new experiments or intervention strategies. I use information geometry to explore the role simple models play in understanding complex biological processes. I interpret a multi-parameter model as a high-dimensional “surface” (i.e., manifold) embedded in the space of all possible data. These surfaces are often bounded and very thin, so they can be approximated by low-dimensional, simple models, much like how a ribbon can be approximated by a surface although it is three dimensional. For biological models, there is a hierarchy of natural approximations that reside on the manifold’s boundary. These approximations are not black-boxes. They remain expressed in terms of the relevant combinations of mechanistic parameters and reflect the biological principles on which the complicated model was built. They can also be constructed in a systematic way using computational differential geometry. I illustrate with models of EGFR signaling and blood coagulation and discuss broader implications for biological modeling.