Conference Program

PLENARY AND SEMI-PLENARY TALKS

 (Add to Calendar)  Wednesday, August 22, 09:00 – 09:50 h, H0105:


Christof Schütte: Optimal control of molecular dynamics using Markov state models

Chair: Martin Skutella

 

Abstract:

Molecular systems exhibits complicated dynamical behavior that is responsible for its (biological or nanotechnological) functionality. The effective dynamics can be characterized by the switching behavior between several metastable states, the so-called conformations of the system. Therefore, steering a molecular system from one conformation into another one means controlling its functionality. This talk considers optimal control problems that appear relevant in molecular dynamics (MD) applications and belong to the class of ergodic stochastic control problems in high dimensions. It will be demonstrated how the associated Hamilton-Jacobi-Bellman (HJB) equation can be solved. The main idea is to first approximate the dominant modes of the MD transfer operator by a low-dimensional, so-called Markov state model (MSM), and then solve the HJB for the MSM rather than the full MD. The approach rests on the interpretation of the corresponding HJB equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem, for which the principal eigenvalue and the associated eigenfunction are sought. The resulting method will be illustrated in application to the maximization of the population of alpha-helices in an ensemble of small biomolecules (Alanine dipeptide).

 

Biographical sketch:

Christof Schütte is a professor in the Mathematics and Computer Science Department at Freie Universität Berlin (FU). He holds a diploma in physics from Paderborn University and a Ph.D in mathematics from FU. Since 2008, he is the co-chair of the DFG Research Center MATHEON in Berlin and the head of the Biocomputing Group at FU. Christof gave a plenary lecture at ICIAM 2007 in Zurich and was an invited speaker at the 2010 International Congress of Mathematicians in Hiderabad. His research is on modeling, simulation and optimization in the life sciences with a special focus on stochastic multiscale problems in molecular and systems biology and on information-based medicine. He is currently the head of the Innovation Laboratory "Math for Diagnostics" in Berlin.

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