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

**Head(s):** Prof. Dr, Cecilia Clementi (FU Berlin), Prof. Dr. Frank Noé (FU Berlin)**Project member(s):** Moritz Hoffmann, Sneha Dixit, Richard Kullmann**Participating institution(s):** FU Berlin

Project SummarMolecular dynamics (MD) simulations offer a unique way to probe structure, equilibrium and dynamical properties of molecular systems simultaneously which is not possible in most experimental techniques. However, one of the fundamental problems of MD is the rare event sampling problem which is caused by rare transitions between long-lived (metastable) states, corresponding to distinct probability modes in state space that are separated by low-probability transition states. The sampling problem is ubiquitous, and because of it, the reliable calculation of macroscopic thermodynamic or kinetic quantities in, e.g., protein folding or binding, is very difficult.

In the first two funding periods, this project has focused on the development of methods related to the conformation dynamics and Markov state modeling (MSM) frameworks which

describe MD as a propagation of probability densities by a transition operator that can be separated into dominant spectral components related to the rare events, and spectral components related to the fast events we are willing to discard. This framework has been extensively developed: we have proposed variational approaches to systematically approximate the dominant part of the transition operator spectrum, used that in order to implement deep learning frameworks that learn high-quality MSMs from data, and used Markov state modeling in conjunction with adaptive simulation techniques in order to simulate rare events such as protein-protein binding with orders of magnitude less computational effort than required by direct simulation.

While this methodological framework is now mature, we have always perceived it as a strong limitation that MSMs and related models only analyze a given simulated molecular

system but make no predictions about the effect of changes in the molecular system, such as changes in simulation temperature or the amino acid sequence of a protein. Ideally, we would like to have models that can efficiently predict thermodynamics and kinetics of molecules in a way that is transferable across thermodynamic or chemical space. In the second funding period we have begun to develop such transferable models. It has turned out that an essential model ingredient for implementing such transferability is a molecular energy function which generates the dynamics in conjunction with a dynamical model. This is because energy functions can be written as multi-body expansions whose terms can be reused for different molecules. For this reason, we will change gears in the last funding period and focus on the development of machine-learned molecular models at a coarser-than-atomistic resolution, which initially aim at reproducing the equilibrium (stationary) properties of a given atomistic model, and later also reproducing the dominant parts of the transition operator, i.e., the kinetics. We specifically focus on transferable machine-learned models, where the thermodynamic and kinetic behavior of peptides and small proteins shall be predicted by training the model on other protein sequences. Such a transferable coarse model for protein dynamics that faithfully reproduces properties of atomistic models is currently not available and would be an important contribution for the fields of Biophysics and computational Chemistry