Date: January 11, 2021 @ 4:00PM
Speaker: Dr. Mark Transtrum
Bio: Dr. Mark Transtrum is a professor of Physics and Astronomy at Brigham Young University where he has been since 2013. Before joining the BYU faculty, he received a PhD in Physics from Cornell in 2011 and then worked as a post-doc in computational biology at MD Anderson Cancer Center in Houston Texas. His research interests center on methods in mathematical modeling in a variety of inter-disciplinary topics. In addition to his work in biology, he actively collaborates on modeling projects in material science, power systems, machine learning, and neuroscience.
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.