TY - JOUR A1 - Koltai, Peter A1 - Wu, Hao A1 - Noé, Frank A1 - Schütte, Christof T1 - Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics JF - Computation Y1 - 2018 U6 - https://doi.org/10.3390/computation6010022 VL - 6 IS - 1 PB - MDPI CY - Basel, Switzerland ER - TY - JOUR A1 - Dibak, Manuel A1 - del Razo, Mauricio J. A1 - de Sancho, David A1 - Schütte, Christof A1 - Noé, Frank T1 - MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations JF - Journal of Chemical Physics N2 - Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported. Y1 - 2018 U6 - https://doi.org/10.1063/1.5020294 VL - 148 IS - 21 ER - TY - JOUR A1 - Klus, Stefan A1 - Nüske, Feliks A1 - Koltai, Peter A1 - Wu, Hao A1 - Kevrekidis, Ioannis A1 - Schütte, Christof A1 - Noé, Frank T1 - Data-driven model reduction and transfer operator approximation JF - Journal of Nonlinear Science Y1 - 2018 UR - https://link.springer.com/article/10.1007/s00332-017-9437-7 U6 - https://doi.org/10.1007/s00332-017-9437-7 VL - 28 IS - 3 SP - 985 EP - 1010 ER - TY - GEN A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Noé, Frank A1 - Weber, Marcus ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Design of functional molecules T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 49 EP - 65 PB - European Mathematical Society ER - TY - JOUR A1 - Charron, Nicholas A1 - Musil, Félix A1 - Guljas, Andrea A1 - Chen, Yaoyi A1 - Bonneau, Klara A1 - Pasos-Trejo, Aldo A1 - Jacopo, Venturin A1 - Daria, Gusew A1 - Zaporozhets, Iryna A1 - Krämer, Andreas A1 - Templeton, Clark A1 - Atharva, Kelkar A1 - Durumeric, Aleksander A1 - Olsson, Simon A1 - Pérez, Adrià A1 - Majewski, Maciej A1 - Husic, Brooke A1 - Patel, Ankit A1 - De Fabritiis, Gianni A1 - Noé, Frank A1 - Clementi, Cecilia T1 - Navigating protein landscapes with a machine-learned transferable coarse-grained model JF - Nature Chemistry N2 - The most popular and universally predictive protein simulation models employ all-atom molecular dynamics (MD), but they come at extreme computational cost. The development of a universal, computationally efficient coarse-grained (CG) model with similar prediction performance has been a long-standing challenge. By combining recent deep learning methods with a large and diverse training set of all-atom protein simulations, we here develop a bottom-up CG force field with chemical transferability, which can be used for extrapolative molecular dynamics on new sequences not used during model parametrization. We demonstrate that the model successfully predicts folded structures, intermediates, metastable folded and unfolded basins, and the fluctuations of intrinsically disordered proteins while it is several orders of magnitude faster than an all-atom model. This showcases the feasibility of a universal and computationally efficient machine-learned CG model for proteins. Y1 - 2025 U6 - https://doi.org/10.1038/s41557-025-01874-0 VL - 17 SP - 1284 EP - 1292 ER - TY - JOUR A1 - del Razo, Mauricio J. A1 - Dibak, Manuel A1 - Schütte, Christof A1 - Noé, Frank T1 - Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics JF - The Journal of Chemical Physics Y1 - 2021 U6 - https://doi.org/10.1063/5.0060314 VL - 155 IS - 12 ER - TY - JOUR A1 - Krämer, Andreas A1 - Durumeric, Aleksander A1 - Charron, Nicholas A1 - Chen, Yaoyi A1 - Clementi, Cecilia A1 - Noé, Frank T1 - Statistically optimal force aggregation for coarse-graining molecular dynamics JF - The Journal of Physical Chemistry Letters N2 - Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code. Y1 - 2023 U6 - https://doi.org/10.1021/acs.jpclett.3c00444 VL - 14 IS - 17 SP - 3970 EP - 3979 ER - TY - JOUR A1 - Durumeric, Aleksander A1 - Charron, Nicholas A1 - Templeton, Clark A1 - Musil, Félix A1 - Bonneau, Klara A1 - Pasos-Trejo, Aldo A1 - Chen, Yaoyi A1 - Kelkar, Atharva A1 - Noé, Frank A1 - Clementi, Cecilia T1 - Machine learned coarse-grained protein force-fields: Are we there yet? JF - Current Opinion in Structural Biology N2 - The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges. Y1 - 2023 U6 - https://doi.org/10.1016/j.sbi.2023.102533 VL - 79 ER - TY - JOUR A1 - Majewski, Maciej A1 - Pérez, Adrià A1 - Thölke, Philipp A1 - Doerr, Stefan A1 - Charron, Nicholas A1 - Giorgino, Toni A1 - Husic, Brooke A1 - Clementi, Cecilia A1 - Noé, Frank A1 - De Fabritiis, Gianni T1 - Machine learning coarse-grained potentials of protein thermodynamics JF - Nature Communications N2 - A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics. Y1 - 2023 U6 - https://doi.org/10.1038/s41467-023-41343-1 VL - 14 ER -