BioMathematics

Mary Lou Zeeman 

What’s it about?  It’s a modeling course, using mathematical insight and computational power to test hypotheses about biological/environmental mechanisms underlying observations, then answer questions and make predictions based on those hypotheses.  This is especially useful when there are too many variables to keep track of in your head, or when the variables interact in complex ways that lead to surprises in the data.  

What? A good part of the course is spent examining the process of translation from Biology to Mathematics to Computer and back again, as an iterative process.  We focus especially on getting clarity about the assumptions being made, and how those assumptions evolve, or are constrained, by the translation process. We get experience viewing biological systems through the computational lens, and identifying biological questions that may benefit from a modeling approach.  For the last quarter of the course the students conduct independent modeling projects of their own design. This involves choosing a biological topic, identifying a question of interest, developing a model, implementing the model computationally and translating the results back to the biological context.  The process is iterated a few times to refine the model and answer the original question.

How? The course focuses on processes that change in time. These processes are translated into difference or differential equations in mathematics, which in turn are translated into iterative computational algorithms using a variety of software packages.  The behavior of the system over time is analyzed computationally and mathematically, within the biological context.

Why? A mathematical or computational model of how things change, combined with data about how things are at a particular time can be used to “predict” how things will be at subsequent times, under different conditions or interventions. This can be extremely powerful for distinguishing between putative mechanisms, developing medical treatments, managing natural resources and scenario testing for informing policy decisions.  Given the importance of these models for policies and practices that directly impact people's lives, we also ask:  Which aspects of model predictions can we ‘trust’?  We discuss how models are validated using data, compatibility of the scenarios tested with the assumptions underlying the model, and sensitivity of the predictions to details of the assumptions, scenarios or measurements.  We also discuss how models may focus or broaden the medical/management/policy approach.