Working seminar — Stochastic techniques in microbiology

March 27, 2008, 2:00 pm, Lind Hall 409
Simple stochastic models for water dynamics near a solute

Abstract: I will present some work (which I originally intended to include in last Wednesday's seminar) which concerns the mathematical issues involved in constructing a simple stochastic model for water near a solute for the eventual goal of developing a means for accelerating molecular dynamics simulations through a simplified statistical description of the water molecules. So far only the most basic stochastic techniques have been used — the main issue has more been the distinction between mathematical and engineering-based views of the problem, a distinction upon which I will elaborate. In particular, the mathematics will be much less technical than for the stochastic immersed boundary method, and I will strive to explain the approach from an elementary standpoint. Indeed we use a very simple toy problem to help us figure out what's going on in molecular dynamics. As this general research program is at a rather early stage, I would be particularly interested in feedback from other mathematicians and scientists as we move forward.

April 3, 2008, 2:00 pm, Lind Hall 409
Informal working seminar on stochastic techniques in microbiology

Abstract: Based on the response I received, I propose to do the following:

I'll begin by briefly advertising the various projects in which I am actively interested since several new people have arrived since I did this before.

For most of the hour, I will again discuss the stochastic immersed boundary method for simulating microbiological systems, but the emphasis will not be so much on the method itself, but on more general issues raised in the design and analysis of the method. Possible topics for discussion include:

1) How do you add noise in a "correct" way to a physical system?

2) How can you check that a stochastic numerical method is simulating the correct statisical physics?

3) How can you use the method of stochastic mode reduction to analyze the effective coarse-grained behavior of a complex stochastic systems when a separation of time scales can be exploited. If desired, I can illustrate the stochastic mode reduction approach on the simple equation I described last week (showing that, on long-time scales, thermally driven Newton's law for particle motion (second order stochastic differential equation) can be approximated by a first order drift-diffusion model). I'll direct the discussion as best I can toward the interests of those who choose to attend, and pitch the technical level accordingly.

May 1, 2008, 2:00 pm, Lind Hall 409
Prescribing thermal forcing for physical systems

Abstract: I will describe the principles, particularly the fluctuation-dissipation theorem, involved in adding the appropriate stochastic driving terms to represent the effects of finite temperature on a given physical system. The concepts will be described both for an elementary example as well as for the more complicated immersed boundary method simulation scheme for flexible structures coupled to an ambient fluid.

May 15, 2008, 2:00 pm, Lind Hall 409
Theoretical framework for microscopic osmotic phenomena

Abstract: My main intention in this seminar is to think through, in simple physical terms, how osmotic pressure (for a semipermeable membrane confining a solute) manifests itself microscopically. That is, I will approach the question simply in terms of mechanical forces between the solute and membrane, and the pressure in the fluid. Somehow I am a little concerned that I may be naive about some aspects, and I would appreciate the current IMA visitors pointing out to me where my reasoning may be inadequate! The reason for this investigation was the recognition that the classical statistical mechanical formula for osmotic pressure (van't Hoff's law) requires corrections when some of the idealized assumptions (infinitesmal particles, hard-wall membrane) break down. In the physical modeling and numerical simulation of sub-micron scale systems, these deviations from the idealized limits appear to be relevant. I'll explain the change to the classical formulas in terms of simple examples; in particular the osmotic pressure registered in the fluid must be distinguished from that exerted on the membrane.

This discussion will primarily involve elementary statistical mechanics and fluid mechanics. Probability arises only in the prescription of the random configurations of the solute particles subject to the confining potential of the membrane.

June 5, 2008, 2:00 pm, Lind Hall 409
Stochastic mode reduction with metastability in biomolecular modeling

Abstract: One approach to accelerating biomolecular simulations is to simulate explicitly only certain slow degrees of freedom of interest, incorporating the effects of the remaining "fast" variables through effective stochastic models. We illustrate a systematic multi-scale stochastic mode reduction procedure on a simple model problem with metastability — a high potential energy barrier separating different conformational states. Metastability is a prevalent feature in biomolecular systems. We show in particular how the metastability can lead to various effective stochastic equations for the slow degrees of freedom depending on the relations between the physical parameters and properties of the potential energy landscape. This work is in collaboration with Jessika Walter at Ecole Polytechnique Federale de Lausanne and Christof Schuette at the Free University of Berlin. Time permitting, I will also discuss some general observations concerning the application of multiple scale asymptotics to problems with three (or more) active time scales (joint work with Adnan Khan (Lahore) and Robert E. Lee DeVille (University of Illinois)). ©2006 Regents of the University of Minnesota. All rights reserved. The University of Minnesota is an equal opportunity educator and employer.