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Dong J, Wang S, Cui W, Sun X, Guo H, Yan H, Vogel H, Wang Z, Yuan S. Machine Learning Deciphered Molecular Mechanistics with Accurate Kinetic and Thermodynamic Prediction. J Chem Theory Comput 2024; 20:4499-4513. [PMID: 38394691 DOI: 10.1021/acs.jctc.3c01412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2024]
Abstract
Time-lagged independent component analysis (tICA) and the Markov state model (MSM) have been extensively employed for extracting conformational dynamics and kinetic community networks from unbiased trajectory ensembles. However, these techniques may not be the optimal choice for elucidating transition mechanisms within low-dimensional representations, especially for intricate biosystems. Unraveling the association mechanism in such complex systems always necessitates permutations of several essential independent components or collective variables, a process that is inherently obscure and may require empirical knowledge for selection. To address these challenges, we have implemented an integrated unsupervised dimension reduction model: uniform manifold approximation and projection (UMAP) with hierarchy density-based spatial clustering of applications with noise (HDBSCAN). This approach effectively generates low-dimensional configurational embeddings. The hierarchical application of this architecture, in conjunction with MSM, reveals global kinetic connectivity while identifying local conformational states. Consequently, our methodology establishes a multiscale mechanistic elucidation framework. Leveraging the benefits of the uniform sample distribution and a denoising approach, our model demonstrates robustness in preserving global and local data structures compared to traditional dimension reduction methods in the field of MD analysis area. The interpretability of hyperparameter selection and compatibility with downstream tasks are cross-validated across various simulation data sets, utilizing both computational evaluation metrics and experimental kinetic observables. Furthermore, the predicted Mcl1-BH3 association kinetics (0.76 s-1) is in close agreement with surface plasmon resonance experiments (0.12 s-1), affirming the plausibility of the identified pathway composed of representative conformations. We anticipate that the devised workflow will serve as a foundational framework for studying recognition patterns in complex biological systems. Its contributions extend to the exploration of protein functional dynamics and rational drug design, offering a potent avenue for advancing research in these domains.
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Affiliation(s)
- Junlin Dong
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shiyu Wang
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
- University of Chinese Academy of Sciences, Beijing 100049, China
- AlphaMol Science Ltd, Shenzhen 518055, China
| | - Wenqiang Cui
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiaolin Sun
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Haojie Guo
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Hailu Yan
- School of Biological Sciences, College of Science and Engineering, University of Edinburgh, Edinburgh EH8 9YL, U.K
| | - Horst Vogel
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Zhi Wang
- Artificial Intelligence Department, Zhejiang Financial College, Hangzhou 310018, China
| | - Shuguang Yuan
- Research Center for Computer-Aided Drug Discovery, Institute of Biomedicine and Biotechnology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
- AlphaMol Science Ltd, Shenzhen 518055, China
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Kozlowski N, Grubmüller H. Uncertainties in Markov State Models of Small Proteins. J Chem Theory Comput 2023; 19:5516-5524. [PMID: 37540193 PMCID: PMC10448719 DOI: 10.1021/acs.jctc.3c00372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Indexed: 08/05/2023]
Abstract
Markov state models are widely used to describe and analyze protein dynamics based on molecular dynamics simulations, specifically to extract functionally relevant characteristic time scales and motions. Particularly for larger biomolecules such as proteins, however, insufficient sampling is a notorious concern and often the source of large uncertainties that are difficult to quantify. Furthermore, there are several other sources of uncertainty, such as choice of the number of Markov states and lag time, choice and parameters of dimension reduction preprocessing step, and uncertainty due to the limited number of observed transitions; the latter is often estimated via a Bayesian approach. Here, we quantified and ranked all of these uncertainties for four small globular test proteins. We found that the largest uncertainty is due to insufficient sampling and initially increases with the total trajectory length T up to a critical tipping point, after which it decreases as 1 / T , thus providing guidelines for how much sampling is required for given accuracy. We also found that single long trajectories yielded better sampling accuracy than many shorter trajectories starting from the same structure. In comparison, the remaining sources of the above uncertainties are generally smaller by a factor of about 5, rendering them less of a concern but certainly not negligible. Importantly, the Bayes uncertainty, commonly used as the only uncertainty estimate, captures only a relatively small part of the true uncertainty, which is thus often drastically underestimated.
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Affiliation(s)
- Nicolai Kozlowski
- Department of Theoretical and Computational
Biophysics, Max-Planck-Institute for Multidisciplinary
Sciences, Göttingen 37077, Germany
| | - Helmut Grubmüller
- Department of Theoretical and Computational
Biophysics, Max-Planck-Institute for Multidisciplinary
Sciences, Göttingen 37077, Germany
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Bacci M, Sukys J, Reichert P, Ulzega S, Albert C. A comparison of numerical approaches for statistical inference with stochastic models. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT : RESEARCH JOURNAL 2023; 37:3041-3061. [PMID: 37502198 PMCID: PMC10368571 DOI: 10.1007/s00477-023-02434-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 03/23/2023] [Indexed: 07/29/2023]
Abstract
Due to our limited knowledge about complex environmental systems, our predictions of their behavior under different scenarios or decision alternatives are subject to considerable uncertainty. As this uncertainty can often be relevant for societal decisions, the consideration, quantification and communication of it is very important. Due to internal stochasticity, often poorly known influence factors, and only partly known mechanisms, in many cases, a stochastic model is needed to get an adequate description of uncertainty. As this implies the need to infer constant parameters, as well as the time-course of stochastic model states, a very high-dimensional inference problem for model calibration has to be solved. This is very challenging from a methodological and a numerical perspective. To illustrate aspects of this problem and show options to successfully tackle it, we compare three numerical approaches: Hamiltonian Monte Carlo, Particle Markov Chain Monte Carlo, and Conditional Ornstein-Uhlenbeck Sampling. As a case study, we select the analysis of hydrological data with a stochastic hydrological model. We conclude that the performance of the investigated techniques is comparable for the analyzed system, and that also generality and practical considerations may be taken into account to guide the choice of which technique is more appropriate for a particular application. Supplementary Information The online version contains supplementary material available at 10.1007/s00477-023-02434-z.
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Affiliation(s)
- Marco Bacci
- SIAM, Eawag: Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
| | - Jonas Sukys
- SIAM, Eawag: Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
| | - Peter Reichert
- SIAM, Eawag: Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
| | - Simone Ulzega
- Institute of Computational Life Sciences, ZHAW Zurich University of Applied Sciences, 8820 Wädenswil, Switzerland
| | - Carlo Albert
- SIAM, Eawag: Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
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Ojha AA, Thakur S, Ahn SH, Amaro RE. DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling. J Chem Theory Comput 2023; 19:1342-1359. [PMID: 36719802 DOI: 10.1021/acs.jctc.2c00282] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry, University of California San Diego, La Jolla, California92093, United States
| | - Saumya Thakur
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Maharashtra400076, India
| | - Surl-Hee Ahn
- Department of Chemical Engineering, University of California Davis, Davis, California95616, United States
| | - Rommie E Amaro
- Department of Chemistry, University of California San Diego, La Jolla, California92093, United States
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Kleiman DE, Shukla D. Multiagent Reinforcement Learning-Based Adaptive Sampling for Conformational Dynamics of Proteins. J Chem Theory Comput 2022; 18:5422-5434. [PMID: 36044642 DOI: 10.1021/acs.jctc.2c00683] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Machine learning is increasingly applied to improve the efficiency and accuracy of molecular dynamics (MD) simulations. Although the growth of distributed computer clusters has allowed researchers to obtain higher amounts of data, unbiased MD simulations have difficulty sampling rare states, even under massively parallel adaptive sampling schemes. To address this issue, several algorithms inspired by reinforcement learning (RL) have arisen to promote exploration of the slow collective variables (CVs) of complex systems. Nonetheless, most of these algorithms are not well-suited to leverage the information gained by simultaneously sampling a system from different initial states (e.g., a protein in different conformations associated with distinct functional states). To fill this gap, we propose two algorithms inspired by multiagent RL that extend the functionality of closely related techniques (REAP and TSLC) to situations where the sampling can be accelerated by learning from different regions of the energy landscape through coordinated agents. Essentially, the algorithms work by remembering which agent discovered each conformation and sharing this information with others at the action-space discretization step. A stakes function is introduced to modulate how different agents sense rewards from discovered states of the system. The consequences are three-fold: (i) agents learn to prioritize CVs using only relevant data, (ii) redundant exploration is reduced, and (iii) agents that obtain higher stakes are assigned more actions. We compare our algorithm with other adaptive sampling techniques (least counts, REAP, TSLC, and AdaptiveBandit) to show and rationalize the gain in performance.
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Affiliation(s)
- Diego E Kleiman
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Diwakar Shukla
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States.,Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States.,Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States.,Department of Plant Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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Ilie IM, Bacci M, Vitalis A, Caflisch A. Antibody binding modulates the dynamics of the membrane-bound prion protein. Biophys J 2022; 121:2813-2825. [PMID: 35672948 DOI: 10.1016/j.bpj.2022.06.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Revised: 04/20/2022] [Accepted: 06/01/2022] [Indexed: 11/18/2022] Open
Abstract
Misfolding of the cellular prion protein (PrPC) is associated with lethal neurodegeneration. PrPC consists of a flexible tail (residues 23-123) and a globular domain (residues 124-231) whose C-terminal end is anchored to the cell membrane. The neurotoxic antibody POM1 and the innocuous antibody POM6 recognize the globular domain. Experimental evidence indicates that POM1 binding to PrPC emulates the influence on PrPC of the misfolded prion protein (PrPSc) while the binding of POM6 has the opposite biological response. Little is known about the potential interactions between flexible tail, globular domain, and the membrane. Here, we used atomistic simulations to investigate how these interactions are modulated by the binding of the Fab fragments of POM1 and POM6 to PrPC and by interstitial sequence truncations to the flexible tail. The simulations show that the binding of the antibodies restricts the range of orientations of the globular domain with respect to the membrane and decreases the distance between tail and membrane. Five of the six sequence truncations influence only marginally this distance and the contact patterns between tail and globular domain. The only exception is a truncation coupled to a charge inversion mutation of four N-terminal residues, which increases the distance of the flexible tail from the membrane. The interactions of the flexible tail and globular domain are modulated differently by the two antibodies.
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Affiliation(s)
- Ioana M Ilie
- Department of Biochemistry, University of Zürich, Zürich, Switzerland
| | - Marco Bacci
- Department of Biochemistry, University of Zürich, Zürich, Switzerland
| | - Andreas Vitalis
- Department of Biochemistry, University of Zürich, Zürich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zürich, Zürich, Switzerland.
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Illig AM, Strodel B. Performance of Markov State Models and Transition Networks on Characterizing Amyloid Aggregation Pathways from MD Data. J Chem Theory Comput 2020; 16:7825-7839. [DOI: 10.1021/acs.jctc.0c00727] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Alexander-Maurice Illig
- Institute of Biological Information Processing: Structural Biochemistry (IBI-7), Forschungszentrum Jülich, 52428 Jülich, Germany
| | - Birgit Strodel
- Institute of Biological Information Processing: Structural Biochemistry (IBI-7), Forschungszentrum Jülich, 52428 Jülich, Germany
- Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
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8
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Affiliation(s)
- Francesco Cocina
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Andreas Vitalis
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Amedeo Caflisch
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
- Department of Physics, Freie Universität Berlin, Berlin, Germany
| | - Edina Rosta
- Department of Chemistry, Kings College London, London, England
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Ilie IM, Caflisch A. Simulation Studies of Amyloidogenic Polypeptides and Their Aggregates. Chem Rev 2019; 119:6956-6993. [DOI: 10.1021/acs.chemrev.8b00731] [Citation(s) in RCA: 93] [Impact Index Per Article: 18.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Ioana M. Ilie
- Department of Biochemistry, University of Zürich, Zürich CH-8057, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zürich, Zürich CH-8057, Switzerland
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