SCIENCE AT THE EDGE SEMINAR SERIES

Joint Seminar MATH/QB/GEDD

Monday, 21 November 2011 at 10:30am

Room 1400 Biomedical and Physical Sciences Bldg.

Refreshments at 10:15

Speaker:  Bob Eisenberg, Department of Molecular Biophysics & Physiology, Rush University

Title:  Ionic Interactions in Biological Systems: a Variational Treatment

Abstract:

Biology depends on interactions of ions. te the heart. Nucleic acids, enzymes, transporters, and channels are all charged macromolecules in a plasma of interacting Na+, K+, Ca2+ and Cl ions, along with hundreds of types of organic ions, acids and bases, most with specific functions. Bio-macromolecules concentrate small ions to number densities >10 M because their active sites have large densities of permanent charge. Solid Na+Cl is ~37 M.

Biomolecules are special structures. They are cathedrals of atoms made visible by the remarkable advances of structural biology. Biomolecules are controlled by ionic interactions and so it is natural that biologists should attribute those interactions to biology's special structures. But ions interact strongly wherever they are found, even without biology's special structures. An ion attracts opposite charges and creates an atmosphere of interaction in any solution. All molecules participate in an ionic atmosphere because (nearly) all molecules have charge. 'Everything' interacts with everything else.

Classical biochemical and biophysical theories rarely include ion-ion interactions. Enzymes and transporters are analyzed classically with the theory of ideal uncharged gases, without physical interactions between 'ions'. More modern electrostatic theories like Poisson Boltzmann and PNP deal with electrostatic interactions of point ions without steric repulsion. But ions are very crowded in and near nucleic acids  and proteins. Steric repulsion often controls natural function.

Ion-ion interactions of finite size ions have been ignored (in my view) because no one knew how to deal with them. Variational methods that allow interactions to be analyzed in conservative systems have not been available for dissipative systems. These mathematical problems are now resolved. A general Energetic Variational Approach to dissipative systems has been developed by Chun Liu, more than anyone else. Existence and uniqueness are proven and incompressible Navier Stokes equations have been derived. If a component is added to variational models, the resulting Euler Lagrange equations automatically describe new interactions with minimal new parameters. Thus, variational methods are quite specific when confronting new finite size ions in solution, or additional forms of transport, like convection, along with the usual diffusion and electrical migration.

A variational model of finite ions in solution is available. More atomic and chemical detail can be added as needed. The resulting Euler-Lagrange equations have been integrated in and near ion channels. The variational electrolyte model is a superset of models already used to analyze and predict selectivity of ryanodine receptors, and binding selectivity of Ca and Na+ channels in many conditions. Numerical inefficiencies are being removed but a great deal remains to be done and many new applications explored. We need all the help we can get!