Deep learning to decompose macromolecules into independent Markovian domains.

The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data.

Effect of a U:G mispair on the water around DNA.

DNA repair proteins are able to discriminate DNA lesions among an abundance of intact DNA with high selectivity. To investigate detectable characteristics of one specific lesion, we compare statistical results from molecular dynamics simulations of two different DNA in water, one with an intact C:G pair and one that contains a U:G mispair, and perform a comparative analysis of the water dynamics around the two. Our data show that in addition to the local DNA conformation, also the surrounding water shell exhibits significant differences that may help mispair discrimination. The chemical groups which account for a U:G mispair to exhibit a wobble conformation instead of the 'proper' Watson-Crick pairing of a C:G pair, that is an oxygen atom (in uracil) instead of an amino group (in cytosine), also order the water molecules around the bases such that they act predominantly as hydrogen-bond donor or acceptor to the uracil or cytosine base, respectively. These changes in water conformation stretch into the second solvation shell, which may be exploited by repair enzymes to achieve lesion detection with high efficiency.

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.

Author Correction: VAMPnets for deep learning of molecular kinetics.

In the original version of this Article, financial support was not fully acknowledged. The PDF and HTML versions of the Article have now been corrected to include funding from the Deutsche Forschungsgemeinschaft Grant SFB958/A04.

VAMPnets for deep learning of molecular kinetics.

There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.