### General introduction

Many biological processes can be studied using the tool of molecular dynamics simulations. As of today, scientist are able to simulate important biological systems as proteins or DNA to study their behavior.

The size and length scales of simulations are only restricted by the current computational power, which also becomes the bottleneck of going to larger systems. For that reason, many research groups are placing their focus on the development of *coarse-graining methods* that try to reduce the overall degrees of freedom by, for instance, grouping many atoms into one "bead".

A different route is pursued by the methodology of Markov state modeling (MSM). Instead of reducing the degrees of freedom, MSM approximates the complete system of interest by discretizing its configuration space and time evolution. The latter is then modeled by a discrete Markov jump process. The benefit of this approach is that only short (but multiple) trajectories are necessary to obtain statistical information about conformational transitions (dynamics) on long time scales that are far beyond what can be simulated by continuous trajectories.

Our research focuses on two areas: systems driven into a non-equilibrium steady state and the systematic derivation of coarse-grained models that preserve certain dynamic properties such as mean first-passage times.

**Figure:** The left panel shows a sketch of the configuration space partitioned into discrete states and an example trajectory. Right: Example trajectory as time trace.

### Non-equilibrium Markov state modeling

Markov State Modeling has been developed over the past 10 years and successfully applied to different molecular systems ranging from peptides to polymers and RNA to DNA under equilibrium conditions. However, most of the interesting phenomena in biology are inherently in non-equilibrium, for instance all biochemical reactions and systems exposed to oscillating electro-magnetic fields or hydrodynamic flows.

Unfortunately, the hallmark of equilibrium, detailed-balance, which is also one of the key ingredients for Markov State Modeling, is broken in non-equilibrium. The research interest of our group is to extend the current Markov State Modeling approach to non-equilibrium situations, where we focus on systems driven into a non-equilibrium steady state. The key concept of our approach are cycles (closed loops in configuration space) that have preferred directions along which the system evolves in phase space.

**References**