Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Complex energy landscapes (addendum to SYEL)

DY 3.8: Vortrag

Montag, 22. März 2010, 15:45–16:00, H42

Efficient exploration of energy landscapes — •Martin Mann¹ and Konstantin Klemm² — ¹Bioinformatik, University of Freiburg, Germany — ²Bioinformatik, University of Leipzig, Germany

Many physical and chemical processes, such as folding of biopolymers, are best described as dynamics on large combinatorial energy landscapes. A concise approximate description of dynamics is obtained by partitioning the micro-states of the landscape into macro-states. Since most landscapes of interest are not tractable analytically, the probabilities of transitions between macro-states need to be extracted numerically from the microscopic ones, typically by full enumeration of the state space.

Here we suggest a Markov chain Monte-Carlo sampling method for transition matrix estimation [1]. The idea is to explicitly explore boundaries between macro-states. To this end, we confine the dynamics into a single macro-state b and find and count possible transitions from b to all adjacent macro-states. This strategy allows to select the regions of the landscape to be explored and to tune the desired accuracy of the estimated transition probabilites. At difference with earlier approaches, the memory requirement scales linearly with the number of non-zero transition probabilities to be determined.

For landscapes of the number partitioning problem and an RNA switch molecule we show that the method allows for accurate probability estimates with significantly reduced computational cost.

[1] M. Mann, K. Klemm, e-print arXiv:0910.2559