IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Mathematics of Ions in Channels and Solutions: Stochastic Derivations, Direct, Variational and Inverse Solutions that fit Data

  • Feb. 16, 2015
  • 1 p.m.
  • LeConte 312

Abstract

Proteins called ionic channels are the ultimate multiscale device, the 'nanovalves of life' controlling most biological functions. A handful of atoms control biological function on the macroscale, so analysis must link atomic scales of distance 10-10 m and time 10-15 sec with biological scales >10-3 m and >10-4 sec. Ion channels have a role in biology like the channels of field effect transistors in computers: both are valves for electricity controlling nearly everything. Ion channels are proteins with a hole down their middle that catalyze the movement of sodium, potassium, calcium and chloride ions across the otherwise impermeable membranes that define cells. Once a channel opens, it has a single structure on the biological time scale slower than say 2 microseconds. The ions present around every cell and molecule in biology are hard spheres and so the calculation of how hard spheres go through a channel of one structure is a central problem in a wide range of biology. Literally thousands of biologists study the properties of channels in experiments every day. My collaborators and I have shown how the relevant equations can be derived (almost) from stochastic differential equations, and how they can be solved in inverse, variational, and direct problems using models that describe a wide range of biological situations with only a handful of parameters that do not change even when concentrations change by a factor of 107. Variational methods hold particular promise as a way to solve problems outstanding for more than a century because they describe interactions of 'everything with everything' else that characterize ions crowded into channels.

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