Biological function arises from the fact that biomolecules and biomolecular aggregates can switch between functionally different conformations, such as folded/unfolded, bound/unbound, etc. These conformations are often dynamically metastable, and the essential molecular dynamics may be approximated by a Markov switching process between them [Noé & Fischer. Curr. Opin. Struct. Biol. 08]
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We are deriving Markov state models from complex time series that may have on the order of 10⁵ dimensions and on the order of 10⁸ timesteps. Usually, the data comes from computer simulations and the availability of massively parallel computing power is essential for this (collaboration with V. Pande, Stanford - folding@home project). The challenge is to identify the relevant conformations from the data and to find a quantitatively correct transition matrix, and we have done this for several molecular systems [Noé et al. JPCB in press, JCP 07]. Still a number of fundamental mathematical challenges remain for the generation of Markov models (Collaboration with C. Schütte) [Schütte et al. ICIAM 08]. People involved: Jan Wigger, Martin Fischbach, Martin Held, Frank Noé
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We are also pursuing to build such models directly from data of time-resolved single-molecule experiments (Collaboration with U. Nienhaus, Uni Ulm and U. Alexiev, FU Berlin). While this approach circumvents the sampling problem that exists in molecular simulation, the challenge here is that only a low-dimensional projection of the high-dimensional dynamics is observed, such that the switching process between conformations is hidden in the data. We develop methods based on Hidden Markov Models to deal with this. People involved: Hao Wu, Torsten Lüdge
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Recently, we have started to develop a theoretical framework to optimally combine both simulation and experimental data of the same biological system into a single, unified model. The key to this is a method which allows the complete probability distribution of Markov models corresponding to a set of simulation or experimental observations to be sampled [Noé, JCP 08]. The probability distributions from individual observations can then be joined into a unified distribution which provides the most likely model, along with its uncertainties, given all observations from simulation and experiment. People involved: Frank Noé
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Using Transition Path Theory, the protein folding pathways or the binding pathways can be computed from an existing discrete-state Markov model or an existing continuous Generator. This allows to understand the dominant mechanisms of the dynamical process. People involved: Martin Fischbach, Frank Noé
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