The Mathematics of Life: Decisions, Decisions

Start: 03/26/2014 - 4:15pm
End  : 03/26/2014 - 5:15pm


Jim Keener, University of Utah


As we learn more and more about biological processes, the need for mathematical methods to aid us in understanding these extremely complex processes becomes even greater.  The use of mathematics to describe biological processes has a long and impressive history with many famous names including Euler, Lotka, Volterra, Malthus, Fisher, Hodgkin, Huxley, and Turing.  The common feature of the   work of all of these scientists is that they used differential equations and the ideas of calculus to count things, and this way of counting has significant benefits.
 A fundamental problem that all living organisms must solve is how to take measurements and make decisions on the basis of those measurements.  The classic works of Hodgkin and Huxley and Turing showed us that   important biological processes such as signaling in nerves (HH) and morphogenetic pattern formation (Turing) can be understood via the mathematics of diffusion and reaction.   However, the mechanism by which measurements and decisions based on those measurements are made is still poorly understood, although there are some underlying principles that are coming to light.  What we are learning is that the rate of molecular diffusion contains quantifiable information that can be transduced through biochemical reactions to give control over physical measurements and decisions.  Equally important, however, is that these processes can be described and studied using differential equations.
In this talk, I will illustrate the use of mathematical models to examine two fascinating examples: quorum sensing (population measurement) by bacteria and length measurement of flagella by bacteria.  In this way, I hope to show how organisms can use the properties of molecular diffusion coupled with appropriate chemical reactions to make decisions that enable them to survive.

Shanahan Center for Teaching and Learning, Shanahan B460 (basement level), Harvey Mudd College, 320 E. Foothill Blvd.

Keener.pdf105.79 KB

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