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.

Rapid Assessment of T-Cell Receptor Specificity of the Immune Repertoire.

Accurate assessment of TCR-antigen specificity at the whole immune repertoire level lies at the heart of improved cancer immunotherapy, but predictive models capable of high-throughput assessment of TCR-peptide pairs are lacking. Recent advances in deep sequencing and crystallography have enriched the data available for studying TCR-p-MHC systems. Here, we introduce a pairwise energy model, RACER, for rapid assessment of TCR-peptide affinity at the immune repertoire level. RACER applies supervised machine learning to efficiently and accurately resolve strong TCR-peptide binding pairs from weak ones. The trained parameters further enable a physical interpretation of interacting patterns encoded in each specific TCR-p-MHC system. When applied to simulate thymic selection of an MHC-restricted T-cell repertoire, RACER accurately estimates recognition rates for tumor-associated neoantigens and foreign peptides, thus demonstrating its utility in helping address the large computational challenge of reliably identifying the properties of tumor antigen-specific T-cells at the level of an individual patient's immune repertoire.

Markov state modeling reveals alternative unbinding pathways for peptide-MHC complexes.

Peptide binding to major histocompatibility complexes (MHCs) is a central component of the immune system, and understanding the mechanism behind stable peptide-MHC binding will aid the development of immunotherapies. While MHC binding is mostly influenced by the identity of the so-called anchor positions of the peptide, secondary interactions from nonanchor positions are known to play a role in complex stability. However, current MHC-binding prediction methods lack an analysis of the major conformational states and might underestimate the impact of secondary interactions. In this work, we present an atomically detailed analysis of peptide-MHC binding that can reveal the contributions of any interaction toward stability. We propose a simulation framework that uses both umbrella sampling and adaptive sampling to generate a Markov state model (MSM) for a coronavirus-derived peptide (QFKDNVILL), bound to one of the most prevalent MHC receptors in humans (HLA-A24:02). While our model reaffirms the importance of the anchor positions of the peptide in establishing stable interactions, our model also reveals the underestimated importance of position 4 (p4), a nonanchor position. We confirmed our results by simulating the impact of specific peptide mutations and validated these predictions through competitive binding assays. By comparing the MSM of the wild-type system with those of the D4A and D4P mutations, our modeling reveals stark differences in unbinding pathways. The analysis presented here can be applied to any peptide-MHC complex of interest with a structural model as input, representing an important step toward comprehensive modeling of the MHC class I pathway.

Combining experimental and simulation data of molecular processes via augmented Markov models.

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few [Formula: see text], which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps.

Identification of the collective coordinates that describe rare events in complex molecular transitions such as protein folding has been a key challenge in the theoretical molecular sciences. In the Diffusion Map approach, one assumes that the molecular configurations sampled have been generated by a diffusion process, and one uses the eigenfunctions of the corresponding diffusion operator as reaction coordinates. While diffusion coordinates (DCs) appear to provide a good approximation to the true dynamical reaction coordinates, they are not parametrized using dynamical information. Thus, their approximation quality could not, as yet, be validated, nor could the diffusion map eigenvalues be used to compute relaxation rate constants of the system. Here we combine the Diffusion Map approach with the recently proposed Variational Approach for Conformation Dynamics (VAC). Diffusion Map coordinates are used as a basis set, and their optimal linear combination is sought using the VAC, which employs time-correlation information on the molecular dynamics (MD) trajectories. We have applied this approach to ultra-long MD simulations of the Fip35 WW domain and found that the first DCs are indeed a good approximation to the true reaction coordinates of the system, but they could be further improved using the VAC. Using the Diffusion Map basis, excellent approximations to the relaxation rates of the system are obtained. Finally, we evaluate the quality of different metric spaces and find that pairwise minimal root-mean-square deviation performs poorly, while operating in the recently introduced kinetic maps based on the time-lagged independent component analysis gives the best performance.

From coarse-grain to all-atom: toward multiscale analysis of protein landscapes.

Multiscale methods are becoming increasingly promising as a way to characterize the dynamics of large protein systems on biologically relevant time-scales. The underlying assumption in multiscale simulations is that it is possible to move reliably between different resolutions. We present a method that efficiently generates realistic all-atom protein structures starting from the C(alpha) atom positions, as obtained for instance from extensive coarse-grain simulations. The method, a reconstruction algorithm for coarse-grain structures (RACOGS), is validated by reconstructing ensembles of coarse-grain structures obtained during folding simulations of the proteins src-SH3 and S6. The results show that RACOGS consistently produces low energy, all-atom structures. A comparison of the free energy landscapes calculated using the coarse-grain structures versus the all-atom structures shows good correspondence and little distortion in the protein folding landscape.

Minimalist protein model as a diagnostic tool for misfolding and aggregation.

We propose a realistic coarse-grained protein model and a technique to "anchor" the model to available experimental data. We apply this procedure to characterize the effect of multiple mutations on the folding mechanism of protein S6. We show that the mutation of a few "gatekeeper" residues triggers significant changes on the folding landscape of S6. These results suggest that gatekeeper residues control the flexibility of critical regions of S6, that in turn regulates the delicate balance between folding and aggregation. Although obtained with a minimalist protein model, these results are fully consistent with experimental evidence and offer a clue to understand the interplay between folding and aggregation in protein S6.