## Professor Gerhard Stock

*Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, Freiburg, Germany*

The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables x_i = x that in some sense describe the essential dynamics of the system. Considering the distribution P(x) of the collective variables, the primal goal of a statistical analysis is to detect characteristic features of P(x), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape, and therefore amount to the metastable states and transition regions of the system. In this seminar, we outline a systematic strategy to identify collective variables and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally we discuss a machine learning approach to dimensionality reduction, that highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.

### References

[1] - F. Sittel and G. Stock, Perspective Article in J. Chem. Phys 149, 150901 (2018)

[2] - S.Brandt, F. Sittel, M. Ernst, and G. Stock, Machine Learning of Biomolecular Reaction Coordinates, J. Phys. Chem. Lett. 9, 2144 (2018)

## Recording:

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