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Upcoming talks

Bob Eisenberg (U. Rush Chicago) WPI, OMP 1, Seminar Room 08.135 Fri, 11. Nov 16, 11:00
"Ions in Solutions and Channels: the plasma of life"
All of biology occurs in ionic solutions that are plasmas in both the physical and biological meanings of the word. The composition of these ionic mixtures has profound effects on almost all biological functions, whether on the length scale of organs like the heart or brain, of the length scale of proteins, like enzymes and ion channels. Ion channels are proteins with a hole down their middle that conduct ions (spherical charges like Na+ , K+ , Ca2+ , and Clƒ{ with diameter ~ 0.2 nm) through a narrow tunnel of fixed charge (”„doping”¦) with diameter ~ 0.6 nm. Ionic channels control the movement of electric charge and current across biological membranes and so play a role in biology as significant as the role of transistors in computers: almost every process in biology is controlled by channels, one way or the other. Ionic channels are manipulated with the powerful techniques of molecular biology in hundreds of laboratories. Atoms (and thus charges) can be substituted a few at a time and the location of every atom can be determined in favorable cases. Ionic channels are one of the few living systems of great importance whose natural biological function can be well described by a tractable set of equations. Ions can be studied as complex fluids in the tradition of physical science although classical treatments as simple fluids have proven inadequate and must be abandoned in my view. Ion channels can be studied by Poisson-Drift diffusion equations familiar in plasma and semiconductor physics ”X called Poisson Nernst Planck or PNP in biology. Ions have finite size and so the Fermi distribution must be introduced to describe their filling of volume. The PNP-Fermi equations form an adequate model of current voltage relations in many types of channels under many conditions if extended to include correlations, and can even describe ”„chemical”¦ phenomena like selectivity with some success. 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. An opportunity exists to apply the well established methods of computational physics to a central problem of computational biology. The plasmas of biology can be analyzed like the plasmas of physics.
  • Thematic program: Models in Biology and Medicine (MOBAM-16) (2016/2017)

Talks of the past month

Vuk Milisic WPI, OMP 1, Seminar Room 08.135 Fri, 21. Oct 16, 11:00
In this talk we present the starting mechanical model of the lamellipodial actin-cytoskeleton meshwork. The model is derived starting from the microscopic description of mechanical properties of filaments and cross-links and also of the life-cycle of cross-linker molecules. We introduce a simplified system of equations that accounts for adhesions created by a single point on which we apply a force. We present the non-dimensionalisation that led to a singular limit motivating our mathematical study. Then we explain the mathematical setting and results already published. In the last part we present the latest developments: we give results for the fully coupled system with unbounded non-linear off-rates. This leads to two possible regimes: under certain hypotheses on the data there is global existence, out of this range we are able to prove blow-up in finite time.
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