Progress in deep Markov state modeling: Coarse graining and experimental data restraints

Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems, such as proteins. In particular, the inclusion of physical constraints, e.g., time-reversibility, was a crucial step to make the methods applicable to biophysical systems. Furthermore, we advance the method by incorporating experimental observables into the model estimation showing that biases in simulation data can be compensated for. We further develop a new neural network layer in order to build a hierarchical model allowing for different levels of details to be studied. Finally, we propose an attention mechanism, which highlights important residues for the classification into different states. We demonstrate the new methodology on an ultralong molecular dynamics simulation of the Villin headpiece miniprotein.