## A04 - Efficient calculation of slow and stationary scales in molecular dynamics

**Head(s):** Prof. Dr. Frank Noé (FU Berlin), Dr. Thomas Weikl

**Project member(s):** Moritz Hoffmann, Andreas Mardt, Katarzyna Ziolkowska

**Participating institution(s):** FU Berlin, MPIKG Potsdam

### Project Summary

Molecular dynamics (MD) simulation is a technique that may aid in the understanding of fundamental processes in biology and chemistry, and has important technological applications in pharmacy, biotechnology, and nanotechnology. Molecular processes are often highly multi-scale with timescales spanning 15 orders of magnitude beyond the integration time-step with no pronounced gap. The previous funding period has focused on the efficient calculation of slow and stationary scales in MD. Key developments in past few years, including our own, have transformed this area and solved some of the fundamental sampling and modeling problems.

As a result, we consider the original goal of calculating slow and stationary scales in MD largely solved for small to medium protein systems. In the next funding period we will focus on four aspects: (1) To develop multilayer (deep) learning models of molecular kinetics that are both highly accurate and can describe the emergence of kinetics from molecular structure by employing transferable modeling units, similar as in MD force fields. (2) To learn physically interpretable, simulatable models of the coarse-grained dynamics that can make predictions for perturbed molecules such as mutants. (3) To apply our methods on extensively simulating structures, dynamics and mechanisms of reversible protein-protein association. (4) To develop approximation methods that are applicable beyond equilibrium dynamics and employ them to study the long-timescale behaviour of weather, climate and geological systems.

### Project publications

Noé, F. and Wu, H.
(2018)
*Boltzmann Generators - Sampling Equilibrium States of Many-Body Systems with Deep Learning.*
SFB 1114 Preprint in arXiv:1812.01729
.
pp. 1-17.
(Unpublished)

Schulz, R. and von Hansen, Y. and Daldrop, J.O. and Kappler, J. and Noé, F. and Netz, R.R.
(2018)
*Collective hydrogen-bond rearrangement dynamics in liquid water.*
J. Chem. Phys., 149
(24).
-244504.
ISSN 0021-9606, ESSN: 1089-7690

Scherer, M. K. and Husic, B.E. and Hoffmann, M. and Paul, F. and Wu, H. and Noé, F.
(2018)
*Variational Selection of Features for Molecular Kinetics.*
SFB 1114 Preprint in arXiv:1811.11714
.
pp. 1-12.
(Unpublished)

Wehmeyer, C. and Scherer, M. K. and Hempel, T. and Husic, B.E. and Olsson, S. and Noé, F.
(2018)
*Introduction to Markov state modeling with the PyEMMA software — v1.0.*
LiveCoMS, 1
(1).
pp. 1-12.
ISSN E-ISSN: 2575-6524

Swenson, D.W.H. and Prinz, J.-H. and Noé, F. and Chodera, J. D. and Bolhuis, P.G.
(2018)
*OpenPathSampling: A Python Framework for Path Sampling Simulations. 1. Basics.*
Journal of Chemical Theory and Computation, Article ASAP
.
ISSN 1549-9618, ESSN: 15-49-9626

Swenson, D.W.H. and Prinz, J.-H. and Noé, F. and Chodera, J. D. and Bolhuis, P.G.
(2018)
*OpenPathSampling: A Python Framework for Path Sampling Simulations. 2. Building and Customizing Path Ensembles and Sample Schemes.*
Journal of Chemical Theory and Computation, Article ASAP
.
ISSN 1549-9618, ESSN: 15-49-9626

del Razo, M.J. and Qian, H. and Noé, F.
(2018)
*Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations.*
J. Chem. Phys., 149
(4).
044102.
ISSN 0021-9606, ESSN: 1089-7690

Dibak, M. and del Razo, M.J. and De Sancho, D. and Schütte, Ch. and Noé, F.
(2018)
*MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations.*
Journal of Chemical Physics, 148
(214107).
ISSN 0021-9606

Koltai, P. and Wu, H. and Noé, F. and Schütte, Ch.
(2018)
*Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics.*
Computation, 6(1)
(22).
ISSN 2079-3197 (online)

Klus, S. and Nüske, F. and Koltai, P. and Wu, H. and Kevrekidis, I. and Schütte, Ch. and Noé, F.
(2018)
*Data-driven model reduction and transfer operator approximation.*
Journal of Nonlinear Science, 28
(1).
pp. 1-26.

Paul, F. and Noé, F. and Weikl, T.
(2018)
*Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations.*
J. Phys. Chem. B
.

Paul, F. and Wehmeyer, C. and Abualrous, E. T. and Wu, H. and Crabtree, M. D. and Schöneberg, J. and Clarke, J. and Freund, C. and Weikl, T. and Noé, F.
(2017)
*Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations.*
Nat. Comm., 8
(1095).

Gerber, S. and Horenko, I.
(2017)
*Toward a direct and scalable identification of reduced models for categorical processes.*
Proceedings of the National Academy of Sciences, 114
(19).
pp. 4863-4868.

Nüske, F. and Wu, H. and Wehmeyer, C. and Clementi, C. and Noé, F.
(2017)
*Markov State Models from short non-Equilibrium Simulations - Analysis and Correction of Estimation Bias.*
J. Chem. Phys., 146
.
094104.

Olsson, Simon and Wu, H. and Paul, F. and Clementi, C. and Noé, F.
(2017)
*Combining experimental and simulation data of molecular processes via augmented Markov models.*
Proc. Natl. Acad. Sci. USA, 114
.
pp. 8265-8270.

Wu, H. and Noé, F.
(2017)
*Variational approach for learning Markov processes from time series data.*
https://arxiv.org/abs/1707.04659
.

Wu, H. and Paul, F. and Wehmeyer, C. and Noé, F.
(2016)
*Multiensemble Markov models of molecular thermodynamics and kinetics.*
Proceedings of the National Academy of Sciences, 113
(23).
E3221-E3230 .
ISSN 0027-8424

Nüske, F. and Schneider, R. and Vitalini, F. and Noé, F.
(2016)
*Variational Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems.*
J. Chem. Phys., 144
(5).
054105.

Paul, F. and Weikl, T.
(2016)
*How to Distinguish Conformational Selection and Induced Fit Based on Chemical Relaxation Rates.*
PLOS Computational Biology
.

Vitalini, F. and Noé, F. and Keller, B.
(2016)
*Molecular dynamics simulations data of the twenty encoded amino acids in different force fields.*
Data in Brief, 7
.
pp. 582-590.

Trendelkamp-Schroer, B. and Wu, H. and Paul, F. and Noé, F.
(2015)
*Estimation and uncertainty of reversible Markov models.*
J. Chem. Phys., 143
(17).
p. 174101.

Scherer, M. K. and Trendelkamp-Schroer, B. and Paul, F. and Pérez-Hernández, G. and Hoffmann, M. and Plattner, N. and Wehmeyer, C. and Prinz, J.-H. and Noé, F.
(2015)
*PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models.*
J. Chem. Theory Comput., 11
(11).
pp. 5525-5542.

Wu, H. and Prinz, J.-H. and Noé, F.
(2015)
*Projected Metastable Markov Processes and Their Estimation with Observable Operator Models.*
J. Chem. Phys., 143
(14).
p. 144101.

Wu, H. and Noé, F.
(2015)
*Gaussian Markov transition models of molecular kinetics.*
J. Chem. Phys., 142
(8).
084104.

Wu, H. and Mey, A.S.J.S. and Rosta, E. and Noé, F.
(2014)
*Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states.*
J. Chem. Phys., 141
(21).
p. 214106.

Mey, A.S.J.S. and Wu, H. and Noé, F.
(2014)
*xTRAM: Estimating equilibrium expectations from time-correlated simulation data at multiple thermodynamic states.*
Phys. Rev. X, 4
(4).
041018.