51
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Ojaghlou N, Airas J, McRae LM, Taylor CA, Miller BR, Parish CA. Understanding the Structure and Apo Dynamics of the Functionally Active JIP1 Fragment. J Chem Inf Model 2020; 61:324-334. [PMID: 33378183 DOI: 10.1021/acs.jcim.0c01008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Recent experiments indicate that the C-Jun amino-terminal kinase-interacting protein 1 (JIP1) binds to and activates the c-Jun N-terminal kinase (JNK) protein. JNK is an integral part of cell apoptosis, and misregulation of this process is a causative factor in diseases such as Alzheimer's disease (AD), obesity, and cancer. It has also been shown that JIP1 may increase the phosphorylation of tau by facilitating the interaction between the tau protein and JNK, which could also be a causative factor in AD. Very little is known about the structure and dynamics of JIP1; however, the amino acid composition of the first 350 residues suggests that it contains an intrinsically disordered region. Molecular dynamics (MD) simulations using AMBER 14 were used to study the structure and dynamics of a functionally active JIP1 10mer fragment to better understand the solution behavior of the fragment. Two microseconds of unbiased MD was performed on the JIP1 10mer fragment in 10 different seeds for a total of 20 μs of simulation time, and from this, seven structurally stable conformations of the 10mer fragment were identified via classical clustering. The 10mer ensemble was also used to build a Markov state model (MSM) that identified four metastable states that encompassed six of the seven conformational families identified by classical dimensional reduction. Based on this MSM, conformational interconversions between the four states occur via two dominant pathways with probability fluxes of 55 and 44% for each individual pathway. Transitions between the initial and final states occur with mean first passage times of 31 (forward) and 16 (reverse) μs.
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Affiliation(s)
- Neda Ojaghlou
- Department of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Justin Airas
- Department of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Lauren M McRae
- Department of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Cooper A Taylor
- Department of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Bill R Miller
- Department of Chemistry, Truman State University, Kirksville, Missouri 63501, United States
| | - Carol A Parish
- Department of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
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52
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Hruska E, Balasubramanian V, Lee H, Jha S, Clementi C. Extensible and Scalable Adaptive Sampling on Supercomputers. J Chem Theory Comput 2020; 16:7915-7925. [PMID: 33170696 DOI: 10.1021/acs.jctc.0c00991] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The accurate sampling of protein dynamics is an ongoing challenge despite the utilization of high-performance computer (HPC) systems. Utilizing only "brute force" molecular dynamics (MD) simulations requires an unacceptably long time to solution. Adaptive sampling methods allow a more effective sampling of protein dynamics than standard MD simulations. Depending on the restarting strategy, the speed up can be more than 1 order of magnitude. One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity of efficiently running adaptive sampling on HPC systems. We discuss how the ExTASY framework can set up new adaptive sampling strategies and reliably execute resulting workflows at scale on HPC platforms. Here, the folding dynamics of four proteins are predicted with no a priori information.
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Affiliation(s)
- Eugen Hruska
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Physics & Astronomy, Rice University, Houston, Texas 77005, United States
| | - Vivekanandan Balasubramanian
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Hyungro Lee
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Shantenu Jha
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Physics & Astronomy, Rice University, Houston, Texas 77005, United States.,Department of Physics, Freie Universität, 14195 Berlin, Germany.,Department of Chemistry, Rice University, Houston, Texas 77005, United States
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53
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Nagel D, Weber A, Stock G. MSMPathfinder: Identification of Pathways in Markov State Models. J Chem Theory Comput 2020; 16:7874-7882. [PMID: 33141565 DOI: 10.1021/acs.jctc.0c00774] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Markov state models represent a popular means to interpret biomolecular processes in terms of memoryless transitions between metastable conformational states. To gain insight into the underlying mechanism, it is instructive to determine all relevant pathways between initial and final states of the process. Currently available methods, such as Markov chain Monte Carlo and transition path theory, are convenient for identifying the most frequented pathways. They are less suited to account for the typically huge amount of pathways with low probability which, though, may dominate the cumulative flux of the reaction. On the basis of a systematic construction of all possible pathways, the here proposed method MSMPathfinder is able to characterize the multitude of unique pathways (say, up to 1010) in a complex system and to quantitatively calculate their correct weights and associated waiting times with predefined accuracy. Adopting the chiral transitions of a peptide helix and the folding of the villin headpiece as model problems, mechanisms and associated waiting times of these processes are discussed using a kinetic network representation. The analysis reveals that the waiting time distribution may yield only little insight into the diversity of pathways, because the measured folding times do typically not reflect the most probable path lengths but rather the cumulative effect of many different pathways.
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Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Anna Weber
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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54
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Tsai ST, Kuo EJ, Tiwary P. Learning molecular dynamics with simple language model built upon long short-term memory neural network. Nat Commun 2020; 11:5115. [PMID: 33037228 PMCID: PMC7547727 DOI: 10.1038/s41467-020-18959-8] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 09/23/2020] [Indexed: 12/04/2022] Open
Abstract
Recurrent neural networks have led to breakthroughs in natural language processing and speech recognition. Here we show that recurrent networks, specifically long short-term memory networks can also capture the temporal evolution of chemical/biophysical trajectories. Our character-level language model learns a probabilistic model of 1-dimensional stochastic trajectories generated from higher-dimensional dynamics. The model captures Boltzmann statistics and also reproduces kinetics across a spectrum of timescales. We demonstrate how training the long short-term memory network is equivalent to learning a path entropy, and that its embedding layer, instead of representing contextual meaning of characters, here exhibits a nontrivial connectivity between different metastable states in the underlying physical system. We demonstrate our model's reliability through different benchmark systems and a force spectroscopy trajectory for multi-state riboswitch. We anticipate that our work represents a stepping stone in the understanding and use of recurrent neural networks for understanding the dynamics of complex stochastic molecular systems.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA
| | - En-Jui Kuo
- Department of Physics and Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA.
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55
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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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56
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Sidky H, Chen W, Ferguson AL. Molecular latent space simulators. Chem Sci 2020; 11:9459-9467. [PMID: 34094212 PMCID: PMC8162036 DOI: 10.1039/d0sc03635h] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 08/20/2020] [Indexed: 12/30/2022] Open
Abstract
Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous atomistic molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous atomistic simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce atomistic molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates.
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Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago Chicago USA
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign Urbana USA
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago Chicago USA
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57
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Goossens K, Neves RP, Fernandes PA, De Winter H. A Computational and Modeling Study of the Reaction Mechanism of Staphylococcus aureus Monoglycosyltransferase Reveals New Insights on the GT51 Family of Enzymes. J Chem Inf Model 2020; 60:5513-5528. [PMID: 32786224 DOI: 10.1021/acs.jcim.0c00377] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Bacterial glycosyltransferases of the GT51 family are key enzymes in bacterial cell wall synthesis. Inhibiting cell wall synthesis is a very effective approach for development of antibiotics, as this can lead to either bacteriostatic or bactericidal effects. Even though the existence of this family has been known for over 50 years, only one potent inhibitor exists, which is an analog of the lipid IV product and derived from a natural product. Drug development focused on bacterial transglycosylase has been hampered due to little being know about its structure and reaction mechanism. In this study, Staphylococcus aureus monoglycosyltransferase was investigated at an atomistic level using computational methods. Classical molecular dynamics simulations were used to reveal information about the large-scale dynamics of the enzyme-substrate complex and the importance of magnesium in structure and function of the protein, while mixed mode quantum mechanics/molecular mechanics calculations unveiled a novel hypothesis for the reaction mechanism. From these results, we present a new model for the binding mode of lipid II and the reaction mechanism of the GT51 glycosyltransferases. A metal-bound hydroxide catalyzed reaction mechanism yields an estimated free energy barrier of 16.1 ± 1.0 kcal/mol, which is in line with experimental values. The importance of divalent cations is also further discussed. These findings could significantly aid targeted drug design, particularly the efficient development of transition state analogues as potential inhibitors for the GT51 glycosyltransferases.
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Affiliation(s)
- Kenneth Goossens
- Department of Pharmaceutical Sciences, Laboratory of Medicinal Chemistry, University of Antwerp, Universiteitsplein 1, 2610 Wilrijk, Belgium
| | - Rui Pp Neves
- LAQV@REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre s/n, 4169-007 Porto, Portugal
| | - Pedro A Fernandes
- LAQV@REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre s/n, 4169-007 Porto, Portugal
| | - Hans De Winter
- Department of Pharmaceutical Sciences, Laboratory of Medicinal Chemistry, University of Antwerp, Universiteitsplein 1, 2610 Wilrijk, Belgium
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58
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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59
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Spiwok V, Kříž P. Time-Lagged t-Distributed Stochastic Neighbor Embedding (t-SNE) of Molecular Simulation Trajectories. Front Mol Biosci 2020; 7:132. [PMID: 32714941 PMCID: PMC7344294 DOI: 10.3389/fmolb.2020.00132] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 06/03/2020] [Indexed: 11/30/2022] Open
Abstract
Molecular simulation trajectories represent high-dimensional data. Such data can be visualized by methods of dimensionality reduction. Non-linear dimensionality reduction methods are likely to be more efficient than linear ones due to the fact that motions of atoms are non-linear. Here we test a popular non-linear t-distributed Stochastic Neighbor Embedding (t-SNE) method on analysis of trajectories of 200 ns alanine dipeptide dynamics and 208 μs Trp-cage folding and unfolding. Furthermore, we introduce a time-lagged variant of t-SNE in order to focus on rarely occurring transitions in the molecular system. This time-lagged t-SNE efficiently separates states according to distance in time. Using this method it is possible to visualize key states of studied systems (e.g., unfolded and folded protein) as well as possible kinetic traps using a two-dimensional plot. Time-lagged t-SNE is a visualization method and other applications, such as clustering and free energy modeling, must be done with caution.
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Affiliation(s)
- Vojtěch Spiwok
- Department of Biochemistry and Microbiology, University of Chemistry and Technology, Prague, Czechia
| | - Pavel Kříž
- Department of Mathematics, University of Chemistry and Technology, Prague, Czechia
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60
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Pattis JG, May ER. Markov State Model of Lassa Virus Nucleoprotein Reveals Large Structural Changes during the Trimer to Monomer Transition. Structure 2020; 28:548-554.e3. [PMID: 32234493 DOI: 10.1016/j.str.2020.03.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 01/23/2020] [Accepted: 03/09/2020] [Indexed: 12/14/2022]
Abstract
Lassa virus contains a nucleoprotein (NP) that encapsulates the viral genomic RNA forming the ribonucleoprotein (RNP). The NP forms trimers that do not bind RNA, but a structure of only the NP N-terminal domain was co-crystallized with RNA bound. These structures suggested a model in which the NP forms a trimer to keep the RNA gate closed, but then is triggered to undergo a change to a form competent for RNA binding. Here, we investigate the scenario in which the trimer is disrupted to observe whether monomeric NP undergoes significant conformational changes. From multi-microsecond molecular dynamics simulations and an adaptive sampling scheme to sample the conformational space, a Markov state model (MSM) is constructed. The MSM reveals an energetically favorable conformational change, with the most significant changes occurring at the domain interface. These results support a model in which significant structural reorganization of the NP is required for RNP formation.
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Affiliation(s)
- Jason G Pattis
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, USA
| | - Eric R May
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, USA.
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61
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Sidky H, Chen W, Ferguson AL. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1737742] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
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62
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Orioli S, Larsen AH, Bottaro S, Lindorff-Larsen K. How to learn from inconsistencies: Integrating molecular simulations with experimental data. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:123-176. [PMID: 32145944 DOI: 10.1016/bs.pmbts.2019.12.006] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.
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Affiliation(s)
- Simone Orioli
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Andreas Haahr Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Sandro Bottaro
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Atomistic Simulations Laboratory, Istituto Italiano di Tecnologia, Genova, Italy
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark.
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63
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Dickson CJ, Velez-Vega C, Duca JS. Revealing Molecular Determinants of hERG Blocker and Activator Binding. J Chem Inf Model 2020; 60:192-203. [PMID: 31880933 DOI: 10.1021/acs.jcim.9b00773] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Kv11.1 potassium channel, encoded by the human ether-a-go-go-related gene (hERG), plays an essential role in the cardiac action potential. hERG blockade by small molecules can induce "torsade de pointes" arrhythmias and sudden death; as such, it is an important off-target to avoid during drug discovery. Recently, a cryo-EM structure of the open channel state of hERG was reported, opening the door to in silico docking analyses and interpretation of hERG structure-activity relationships, with a view to avoiding blocking activity. Despite this, docking directly to this cryo-EM structure has been reported to yield binding modes that are unable to explain known mutagenesis data. In this work, we use molecular dynamics simulations to sample a range of channel conformations and run ensemble docking campaigns at the known hERG binding site below the selectivity filter, composed of the central cavity and the four deep hydrophobic pockets. We identify a hERG conformational state allowing discrimination of blockers vs nonblockers from docking; furthermore, the binding pocket agrees with mutagenesis data, and blocker binding modes fit the hERG blocker pharmacophore. We then use the same protocol to identify a binding pocket in the hERG channel pore for hERG activators, again agreeing with the reported mutagenesis. Our approach may be useful in drug discovery campaigns to prioritize candidate compounds based on hERG liability via virtual docking screens.
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Affiliation(s)
- Callum J Dickson
- Computer-Aided Drug Discovery, Global Discovery Chemistry , Novartis Institutes for BioMedical Research , 181 Massachusetts Avenue , Cambridge , Massachusetts 02139 , United States
| | - Camilo Velez-Vega
- Computer-Aided Drug Discovery, Global Discovery Chemistry , Novartis Institutes for BioMedical Research , 181 Massachusetts Avenue , Cambridge , Massachusetts 02139 , United States
| | - Jose S Duca
- Computer-Aided Drug Discovery, Global Discovery Chemistry , Novartis Institutes for BioMedical Research , 181 Massachusetts Avenue , Cambridge , Massachusetts 02139 , United States
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64
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Noé F. Machine Learning for Molecular Dynamics on Long Timescales. MACHINE LEARNING MEETS QUANTUM PHYSICS 2020. [DOI: 10.1007/978-3-030-40245-7_16] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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65
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Klus S, Husic BE, Mollenhauer M, Noé F. Kernel methods for detecting coherent structures in dynamical data. CHAOS (WOODBURY, N.Y.) 2019; 29:123112. [PMID: 31893642 DOI: 10.1063/1.5100267] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Accepted: 11/08/2019] [Indexed: 06/10/2023]
Abstract
We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely, the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition called coherent mode decomposition. Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods.
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Affiliation(s)
- Stefan Klus
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Brooke E Husic
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Mattes Mollenhauer
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
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66
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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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67
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Durumeric AEP, Voth GA. Adversarial-residual-coarse-graining: Applying machine learning theory to systematic molecular coarse-graining. J Chem Phys 2019; 151:124110. [PMID: 31575201 DOI: 10.1063/1.5097559] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
We utilize connections between molecular coarse-graining (CG) approaches and implicit generative models in machine learning to describe a new framework for systematic molecular CG. Focus is placed on the formalism encompassing generative adversarial networks. The resulting method enables a variety of model parameterization strategies, some of which show similarity to previous CG methods. We demonstrate that the resulting framework can rigorously parameterize CG models containing CG sites with no prescribed connection to the reference atomistic system (termed virtual sites); however, this advantage is offset by the lack of a closed-form expression for the CG Hamiltonian at the resolution obtained after integration over the virtual CG sites. Computational examples are provided for cases in which these methods ideally return identical parameters as relative entropy minimization CG but where traditional relative entropy minimization CG optimization equations are not applicable.
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Affiliation(s)
- Aleksander E P Durumeric
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, Chicago, Illinois 60637, USA
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68
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Eberhardt J, Stote RH, Dejaegere A. Unrolr: Structural analysis of protein conformations using stochastic proximity embedding. J Comput Chem 2019; 39:2551-2557. [PMID: 30447084 DOI: 10.1002/jcc.25599] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 08/24/2018] [Accepted: 08/24/2018] [Indexed: 01/29/2023]
Abstract
Molecular dynamics (MD) simulations are widely used to explore the conformational space of biological macromolecules. Advances in hardware, as well as in methods, make the generation of large and complex MD datasets much more common. Although different clustering and dimensionality reduction methods have been applied to MD simulations, there remains a need for improved strategies that handle nonlinear data and/or can be applied to very large datasets. We present an original implementation of the pivot-based version of the stochastic proximity embedding method aimed at large MD datasets using the dihedral distance as a metric. The advantages of the algorithm in terms of data storage and computational efficiency are presented, as well as the implementation realized. Application and testing through the analysis of a 200 ns accelerated MD simulation of a 35-residue villin headpiece is discussed. Analysis of the simulation shows the promise of this method to organize large conformational ensembles. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Jérôme Eberhardt
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
| | - Roland H Stote
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
| | - Annick Dejaegere
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
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69
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Sidky H, Chen W, Ferguson AL. High-Resolution Markov State Models for the Dynamics of Trp-Cage Miniprotein Constructed Over Slow Folding Modes Identified by State-Free Reversible VAMPnets. J Phys Chem B 2019; 123:7999-8009. [DOI: 10.1021/acs.jpcb.9b05578] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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70
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Chen W, Sidky H, Ferguson AL. Capabilities and limitations of time-lagged autoencoders for slow mode discovery in dynamical systems. J Chem Phys 2019. [DOI: 10.1063/1.5112048] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
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71
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Husic BE, Noé F. Deflation reveals dynamical structure in nondominant reaction coordinates. J Chem Phys 2019. [DOI: 10.1063/1.5099194] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Brooke E. Husic
- Department of Mathematics and Computer Science, Freie Universität, 14195 Berlin, Germany
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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72
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Tribello GA, Gasparotto P. Using Dimensionality Reduction to Analyze Protein Trajectories. Front Mol Biosci 2019; 6:46. [PMID: 31275943 PMCID: PMC6593086 DOI: 10.3389/fmolb.2019.00046] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Accepted: 05/31/2019] [Indexed: 11/24/2022] Open
Abstract
In recent years the analysis of molecular dynamics trajectories using dimensionality reduction algorithms has become commonplace. These algorithms seek to find a low-dimensional representation of a trajectory that is, according to a well-defined criterion, optimal. A number of different strategies for generating projections of trajectories have been proposed but little has been done to systematically compare how these various approaches fare when it comes to analysing trajectories for biomolecules in explicit solvent. In the following paper, we have thus analyzed a molecular dynamics trajectory of the C-terminal fragment of the immunoglobulin binding domain B1 of protein G of Streptococcus modeled in explicit solvent using a range of different dimensionality reduction algorithms. We have then tried to systematically compare the projections generated using each of these algorithms by using a clustering algorithm to find the positions and extents of the basins in the high-dimensional energy landscape. We find that no algorithm outshines all the other in terms of the quality of the projection it generates. Instead, all the algorithms do a reasonable job when it comes to building a projection that separates some of the configurations that lie in different basins. Having said that, however, all the algorithms struggle to project the basins because they all have a large intrinsic dimensionality.
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Affiliation(s)
- Gareth A Tribello
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast, United Kingdom
| | - Piero Gasparotto
- Department of Physics and Astronomy, Thomas Young Centre, University College London, London, United Kingdom
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73
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Chen W, Sidky H, Ferguson AL. Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets. J Chem Phys 2019; 150:214114. [PMID: 31176319 DOI: 10.1063/1.5092521] [Citation(s) in RCA: 63] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest molecular systems, and their data-driven discovery directly from molecular simulation trajectories has been a central focus of the molecular simulation community to both unveil the important physical mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decomposition of the transfer operator that evolves equilibrium-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calculations. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to molecular dynamics simulations of alanine dipeptide and the WW domain protein.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Hythem Sidky
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - Andrew L Ferguson
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
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74
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Scherer MK, Husic BE, Hoffmann M, Paul F, Wu H, Noé F. Variational selection of features for molecular kinetics. J Chem Phys 2019; 150:194108. [PMID: 31117766 DOI: 10.1063/1.5083040] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.
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Affiliation(s)
- Martin K Scherer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Brooke E Husic
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Moritz Hoffmann
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Fabian Paul
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hao Wu
- School of Mathematical Sciences, Tongji University, Shanghai 200092, People's Republic of China
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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75
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Chen S, Wiewiora RP, Meng F, Babault N, Ma A, Yu W, Qian K, Hu H, Zou H, Wang J, Fan S, Blum G, Pittella-Silva F, Beauchamp KA, Tempel W, Jiang H, Chen K, Skene RJ, Zheng YG, Brown PJ, Jin J, Luo C, Chodera JD, Luo M. The dynamic conformational landscape of the protein methyltransferase SETD8. eLife 2019; 8:45403. [PMID: 31081496 PMCID: PMC6579520 DOI: 10.7554/elife.45403] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Accepted: 05/08/2019] [Indexed: 12/27/2022] Open
Abstract
Elucidating the conformational heterogeneity of proteins is essential for understanding protein function and developing exogenous ligands. With the rapid development of experimental and computational methods, it is of great interest to integrate these approaches to illuminate the conformational landscapes of target proteins. SETD8 is a protein lysine methyltransferase (PKMT), which functions in vivo via the methylation of histone and nonhistone targets. Utilizing covalent inhibitors and depleting native ligands to trap hidden conformational states, we obtained diverse X-ray structures of SETD8. These structures were used to seed distributed atomistic molecular dynamics simulations that generated a total of six milliseconds of trajectory data. Markov state models, built via an automated machine learning approach and corroborated experimentally, reveal how slow conformational motions and conformational states are relevant to catalysis. These findings provide molecular insight on enzymatic catalysis and allosteric mechanisms of a PKMT via its detailed conformational landscape. Our cells contain thousands of proteins that perform many different tasks. Such tasks often involve significant changes in the shape of a protein that allow it to interact with other proteins or ligands. Understanding these shape changes can be an essential step for predicting and manipulating how proteins work or designing new drugs. Some changes in protein shape happen quickly, whereas others take longer. Existing experimental approaches generally only capture some, but not all, of the different shapes an individual protein adopts. A family of proteins known as protein lysine methyltransferases (PKMTs) help to regulate the activities of other proteins by adding small tags called methyl groups to specific positions on their target proteins. PKMTs play important roles in many life processes including in activating genes, maintaining stem cells and controlling how organs develop. It is important for cells to properly control the activity of PKMTs because too much, or too little, activity can promote cancers and neurological diseases. For example, genetic mutations that increase the levels of a PKMT known as SETD8 appear to promote the progression of some breast cancers and childhood leukemia. There is a pressing need to develop new drugs that can inhibit SETD8 and other PKMTs in human patients. However, these efforts are hindered by the lack of understanding of exactly how the shape of PKMT proteins change as they operate in cells. Chen, Wiewiora et al. used a technique called X-ray crystallography to generate structural models of the human SETD8 protein in the presence or absence of native or foreign ligands. These models were used to develop computer simulations of how the shape of SETD8 changes as it operates. Further computational analysis and laboratory experiments revealed how slow changes in the shape of SETD8 contribute to the ability of the protein to attach methyl groups to other proteins. This work is a significant stepping-stone to developing a complete model of how the SETD8 protein works, as well as understanding how genetic mutations may affect the protein’s role in the body. The next step is to refine the model by integrating data from other approaches including biophysical models and mathematical calculations of the energy associated with the shape changes, with a long-term goal to better understand and then manipulate the function of SETD8.
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Affiliation(s)
- Shi Chen
- Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, United States.,Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Rafal P Wiewiora
- Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, United States.,Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Fanwang Meng
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China
| | - Nicolas Babault
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Anqi Ma
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Wenyu Yu
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Kun Qian
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Hao Hu
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Hua Zou
- Takeda California, Science Center Drive, San Diego, United States
| | - Junyi Wang
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Shijie Fan
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Gil Blum
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Fabio Pittella-Silva
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Kyle A Beauchamp
- Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Wolfram Tempel
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Hualiang Jiang
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Kaixian Chen
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Robert J Skene
- Takeda California, Science Center Drive, San Diego, United States
| | - Yujun George Zheng
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Peter J Brown
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Jian Jin
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Cheng Luo
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - John D Chodera
- Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Minkui Luo
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States.,Program of Pharmacology, Weill Cornell Medical College of Cornell University, New York, United States
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76
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Dämgen MA, Biggin PC. Computational methods to examine conformational changes and ligand-binding properties: Examples in neurobiology. Neurosci Lett 2019. [DOI: 10.1016/j.neulet.2018.03.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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77
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Paul F, Wu H, Vossel M, de Groot BL, Noé F. Identification of kinetic order parameters for non-equilibrium dynamics. J Chem Phys 2019; 150:164120. [PMID: 31042914 PMCID: PMC6486394 DOI: 10.1063/1.5083627] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Accepted: 04/04/2019] [Indexed: 12/17/2022] Open
Abstract
A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly varying collective variables, where subsequent analyses are made, such as clustering or estimation of free energy profiles or Markov state models. However, existing "dynamical" dimension reduction methods, such as the time-lagged independent component analysis (TICA), are only valid if the dynamics obeys detailed balance (microscopic reversibility) and typically require long, equilibrated simulation trajectories. Here, we develop a dimension reduction method for non-equilibrium dynamics based on the recently developed Variational Approach for Markov Processes (VAMP) by Wu and Noé. VAMP is illustrated by obtaining a low-dimensional description of a single file ion diffusion model and by identifying long-lived states from molecular dynamics simulations of the KcsA channel protein in an external electrochemical potential. This analysis provides detailed insights into the coupling of conformational dynamics, the configuration of the selectivity filter, and the conductance of the channel. We recommend VAMP as a replacement for the less general TICA method.
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Affiliation(s)
- Fabian Paul
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hao Wu
- Tongji University, School of Mathematical Sciences, Shanghai 200092, People's Republic of China
| | - Maximilian Vossel
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11 D-37077 Göttingen, Germany
| | - Bert L de Groot
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11 D-37077 Göttingen, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany
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78
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Pinamonti G, Paul F, Noé F, Rodriguez A, Bussi G. The mechanism of RNA base fraying: Molecular dynamics simulations analyzed with core-set Markov state models. J Chem Phys 2019; 150:154123. [DOI: 10.1063/1.5083227] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Giovanni Pinamonti
- Department for Mathematics and Computer Science, Freie Universität, Berlin, Germany
| | - Fabian Paul
- Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, The University of Chicago, Chicago, Illinois 60637, USA
| | - Frank Noé
- Department for Mathematics and Computer Science, Freie Universität, Berlin, Germany
| | - Alex Rodriguez
- ICTP, International Centre for Theoretical Physics, Trieste, Italy
| | - Giovanni Bussi
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, Trieste, Italy
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79
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Husic BE, Schlueter-Kuck KL, Dabiri JO. Simultaneous coherent structure coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity. PLoS One 2019; 14:e0212442. [PMID: 30865644 PMCID: PMC6415781 DOI: 10.1371/journal.pone.0212442] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Accepted: 02/01/2019] [Indexed: 11/24/2022] Open
Abstract
The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters. To achieve this, we obtain a set of orthogonal coordinates along which dissimilarity in the dataset is maximized from a generalized eigenvalue problem based on the pairwise dissimilarity between the data points to be clustered. This sequence of bifurcations produces a binary tree representation of the system, from which the number of clusters in the data and their interrelationships naturally emerge. To illustrate the effectiveness of the method in the absence of a priori assumptions, we apply it to three exemplary problems in fluid dynamics. Then, we illustrate its capacity for interpretability using a high-dimensional protein folding simulation dataset. While we restrict our examples to dynamical physical systems in this work, we anticipate straightforward translation to other fields where existing analysis tools require ad hoc assumptions on the data structure, lack the interpretability of the present method, or in which the underlying processes are less accessible, such as genomics and neuroscience.
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Affiliation(s)
- Brooke E. Husic
- Department of Chemistry, Stanford University, Stanford, California, United States of America
- * E-mail: (BEH); (JOD)
| | - Kristy L. Schlueter-Kuck
- Department of Mechanical Engineering, Stanford University, Stanford, California, United States of America
| | - John O. Dabiri
- Department of Mechanical Engineering, Stanford University, Stanford, California, United States of America
- Department of Civil and Environmental Engineering, Stanford University, Stanford, California, United States of America
- * E-mail: (BEH); (JOD)
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80
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Xiao J, Salsbury FR. Na +-binding modes involved in thrombin's allosteric response as revealed by molecular dynamics simulations, correlation networks and Markov modeling. Phys Chem Chem Phys 2019; 21:4320-4330. [PMID: 30724273 PMCID: PMC6993936 DOI: 10.1039/c8cp07293k] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The monovalent sodium ion (Na+) is a critical modulator of thrombin. However, the mechanism of thrombin's activation by Na+ has been widely debated for more than twenty years. Details of the linkage between thrombin and Na+ remain vague due to limited temporal and spatial resolution in experiments. In this work, we combine microsecond scale atomic-detailed molecular dynamics simulations with correlation network analyses and hidden Markov modeling to probe the detailed thermodynamic and kinetic picture of Na+-binding events and their resulting allosteric responses in thrombin. We reveal that ASP189 and ALA190 comprise a stable Na+-binding site (referred as "inner" Na+-binding site) along with the previously known one (referred as "outer" Na+-binding site). The corresponding newly identified Na+-binding mode introduces significant allosteric responses in thrombin's regulatory regions by stabilizing selected torsion angles of residues responsive to Na+-binding. Our Markov model indicates that the bound Na+ prefers to transfer between the two Na+-binding sites when an unbinding event takes place. These results suggest a testable hypothesis of a substrate-driven Na+ migration (ΔG ∼ 1.7 kcal mol-1) from the "inner" Na+-binding site to the "outer" one during thrombin's catalytic activities. The binding of a Na+ ion at the "inner" Na+-binding site should be inferred as a prerequisite for thrombin's efficient recognition to the substrate, which opens a new angle for our understanding of Na+-binding's allosteric activation on thrombin and sheds light on detailed processes in thrombin's activation.
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Affiliation(s)
- Jiajie Xiao
- Department of Physics, Wake Forest University, Winston Salem, NC, USA.
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81
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Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. J Chem Phys 2019; 149:244119. [PMID: 30599712 DOI: 10.1063/1.5053582] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Adaptive sampling methods, often used in combination with Markov state models, are becoming increasingly popular for speeding up rare events in simulation such as molecular dynamics (MD) without biasing the system dynamics. Several adaptive sampling strategies have been proposed, but it is not clear which methods perform better for different physical systems. In this work, we present a systematic evaluation of selected adaptive sampling strategies on a wide selection of fast folding proteins. The adaptive sampling strategies were emulated using models constructed on already existing MD trajectories. We provide theoretical limits for the sampling speed-up and compare the performance of different strategies with and without using some a priori knowledge of the system. The results show that for different goals, different adaptive sampling strategies are optimal. In order to sample slow dynamical processes such as protein folding without a priori knowledge of the system, a strategy based on the identification of a set of metastable regions is consistently the most efficient, while a strategy based on the identification of microstates performs better if the goal is to explore newer regions of the conformational space. Interestingly, the maximum speed-up achievable for the adaptive sampling of slow processes increases for proteins with longer folding times, encouraging the application of these methods for the characterization of slower processes, beyond the fast-folding proteins considered here.
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Affiliation(s)
- Eugen Hruska
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Jayvee R Abella
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
| | - Feliks Nüske
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Lydia E Kavraki
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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82
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Schöberl M, Zabaras N, Koutsourelakis PS. Predictive collective variable discovery with deep Bayesian models. J Chem Phys 2019; 150:024109. [DOI: 10.1063/1.5058063] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Markus Schöberl
- Center for Informatics and Computational Science, University of Notre Dame, 311 Cushing Hall, Notre Dame, Indiana 46556, USA
- Continuum Mechanics Group, Technical University of Munich, Boltzmannstraße 15, 85748 Garching, Germany
| | - Nicholas Zabaras
- Center for Informatics and Computational Science, University of Notre Dame, 311 Cushing Hall, Notre Dame, Indiana 46556, USA
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83
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Abstract
This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function as well as practical issues such as landmark selection and how these algorithms can be used when the data to be analyzed comes from enhanced sampling trajectories. In the later part a comparison between the results obtained by applying various algorithms to two sets of sample data is performed and discussed. This section is then followed by a summary of how one algorithm in particular, sketch-map, has been applied to a range of problems. The chapter concludes with a discussion on the directions that we believe this field is currently moving.
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84
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Yang W, Riley BT, Lei X, Porebski BT, Kass I, Buckle AM, McGowan S. Mapping the Pathway and Dynamics of Bestatin Inhibition of the
Plasmodium falciparum
M1 Aminopeptidase
Pf
A‐M1. ChemMedChem 2018; 13:2504-2513. [DOI: 10.1002/cmdc.201800563] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Revised: 10/04/2018] [Indexed: 12/26/2022]
Affiliation(s)
- Wei Yang
- Infection and Immunity Program, Department of Microbiology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
| | - Blake T. Riley
- Infection and Immunity Program, Department of Biochemistry and Molecular Biology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
| | - Xiangyun Lei
- School of Chemical and Biomolecular EngineeringGeorgia Institute of Technology Atlanta GA USA
| | - Benjamin T. Porebski
- Infection and Immunity Program, Department of Biochemistry and Molecular Biology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
- Current address: Medical Research Council Laboratory of Molecular Biology Francis Crick Avenue Cambridge CB2 0QH UK
| | - Itamar Kass
- Infection and Immunity Program, Department of Biochemistry and Molecular Biology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
- Victorian Life Sciences Computation CentreMonash University Clayton VIC 3800 Australia
| | - Ashley M. Buckle
- Infection and Immunity Program, Department of Biochemistry and Molecular Biology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
| | - Sheena McGowan
- Infection and Immunity Program, Department of Microbiology, Biomedicine Discovery InstituteMonash University Clayton VIC 3800 Australia
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85
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Bittracher A, Banisch R, Schütte C. Data-driven computation of molecular reaction coordinates. J Chem Phys 2018; 149:154103. [PMID: 30342463 DOI: 10.1063/1.5035183] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics are characterized by rare or slow transition events. In a recent publication, precise defining characteristics of such reaction coordinates were identified and linked to the existence of a so-called transition manifold. This theory gives rise to a novel numerical method for the pointwise computation of reaction coordinates that relies on short parallel MD simulations only, but yields accurate approximation of the long time behavior of the system under consideration. This article presents an extension of the method towards practical applicability in computational chemistry. It links the newly defined reaction coordinates to concepts from transition path theory and Markov state model building. The main result is an alternative computational scheme that allows for a global computation of reaction coordinates based on commonly available types of simulation data, such as single long molecular trajectories or the push-forward of arbitrary canonically distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, which computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a small protein system.
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Affiliation(s)
- Andreas Bittracher
- Department of Mathematics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Ralf Banisch
- Department of Mathematics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Christof Schütte
- Department of Mathematics, Freie Universität Berlin, 14195 Berlin, Germany
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86
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Chen W, Tan AR, Ferguson AL. Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design. J Chem Phys 2018; 149:072312. [PMID: 30134681 DOI: 10.1063/1.5023804] [Citation(s) in RCA: 80] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Auto-associative neural networks ("autoencoders") present a powerful nonlinear dimensionality reduction technique to mine data-driven collective variables from molecular simulation trajectories. This technique furnishes explicit and differentiable expressions for the nonlinear collective variables, making it ideally suited for integration with enhanced sampling techniques for accelerated exploration of configurational space. In this work, we describe a number of sophistications of the neural network architectures to improve and generalize the process of interleaved collective variable discovery and enhanced sampling. We employ circular network nodes to accommodate periodicities in the collective variables, hierarchical network architectures to rank-order the collective variables, and generalized encoder-decoder architectures to support bespoke error functions for network training to incorporate prior knowledge. We demonstrate our approach in blind collective variable discovery and enhanced sampling of the configurational free energy landscapes of alanine dipeptide and Trp-cage using an open-source plugin developed for the OpenMM molecular simulation package.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Aik Rui Tan
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Andrew L Ferguson
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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87
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Prakash A, Fu CD, Bonomi M, Pfaendtner J. Biasing Smarter, Not Harder, by Partitioning Collective Variables into Families in Parallel Bias Metadynamics. J Chem Theory Comput 2018; 14:4985-4990. [DOI: 10.1021/acs.jctc.8b00448] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Arushi Prakash
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Christopher D. Fu
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Massimiliano Bonomi
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jim Pfaendtner
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
- Senior Scientist, Pacific Northwest National Laboratory, Richland, Washington, United States
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88
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Peng JH, Wang W, Yu YQ, Gu HL, Huang X. Clustering algorithms to analyze molecular dynamics simulation trajectories for complex chemical and biological systems. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806147] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Jun-hui Peng
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Wei Wang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Ye-qing Yu
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Han-lin Gu
- Department of Mathematics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Center of Systems Biology and Human Health, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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89
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Hernández CX, Wayment-Steele HK, Sultan MM, Husic BE, Pande VS. Variational encoding of complex dynamics. Phys Rev E 2018; 97:062412. [PMID: 30011547 DOI: 10.1103/physreve.97.062412] [Citation(s) in RCA: 89] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Indexed: 11/07/2022]
Abstract
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.
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Affiliation(s)
| | | | - Mohammad M Sultan
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Brooke E Husic
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Vijay S Pande
- Biophysics Program, Stanford University, Stanford, California, USA.,Chemistry Department, Stanford University, Stanford, California, USA
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90
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Wehmeyer C, Noé F. Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics. J Chem Phys 2018; 148:241703. [PMID: 29960344 DOI: 10.1063/1.5011399] [Citation(s) in RCA: 170] [Impact Index Per Article: 28.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques.
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Affiliation(s)
- Christoph Wehmeyer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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91
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Orioli S, A Beccara S, Faccioli P. Self-consistent calculation of protein folding pathways. J Chem Phys 2018; 147:064108. [PMID: 28810783 DOI: 10.1063/1.4997197] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
We introduce an iterative algorithm to efficiently simulate protein folding and other conformational transitions, using state-of-the-art all-atom force fields. Starting from the Langevin equation, we obtain a self-consistent stochastic equation of motion, which directly yields the reaction pathways. From the solution of this set of equations we derive a stochastic estimate of the reaction coordinate. We validate this approach against the results of plain MD simulations of the folding of a small protein, which were performed on the Anton supercomputer. In order to explore the computational efficiency of this algorithm, we apply it to generate a folding pathway of a protein that consists of 130 amino acids and has a folding rate of the order of s-1.
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Affiliation(s)
- S Orioli
- Dipartimento di Fisica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento I-38123, Italy and INFN-TIFPA, Via Sommarive 14, Povo, Trento I-38123, Italy
| | - S A Beccara
- Dipartimento di Fisica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento I-38123, Italy and INFN-TIFPA, Via Sommarive 14, Povo, Trento I-38123, Italy
| | - P Faccioli
- Dipartimento di Fisica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento I-38123, Italy and INFN-TIFPA, Via Sommarive 14, Povo, Trento I-38123, Italy
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92
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Dibak M, Del Razo MJ, De Sancho D, Schütte C, Noé F. MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations. J Chem Phys 2018; 148:214107. [PMID: 29884049 DOI: 10.1063/1.5020294] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
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.
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Affiliation(s)
- Manuel Dibak
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Mauricio J Del Razo
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - David De Sancho
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Christof Schütte
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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93
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Abramyan AM, Quick M, Xue C, Javitch JA, Shi L. Exploring Substrate Binding in the Extracellular Vestibule of MhsT by Atomistic Simulations and Markov Models. J Chem Inf Model 2018; 58:1244-1252. [PMID: 29851339 DOI: 10.1021/acs.jcim.8b00175] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Neurotransmitter:sodium symporters (NSS) terminate neurotransmission through Na+-driven reuptake of cognate neurotransmitters. Crystallographically, whereas both substrates and inhibitors have been found to bind in the central binding (S1) site of NSS, inhibitors were found to bind to a second binding (S2) site in the extracellular vestibule (EV) of transporters for leucine (LeuT) and serotonin. On the basis of computational and experimental studies, we proposed that substrates bind to the S2 site of LeuT as well and that substrate binding to the S2 site is essential for Na+-coupled symport. Recent binding experiments show that substrate (l-Trp) binding in the S2 site of MhsT, another bacterial NSS, is also central to the allosteric transport mechanism. Here, we used extensive molecular dynamics simulations combined with Markov state model analysis to investigate the interaction of l-Trp with the EV of MhsT and identified potential binding poses of l-Trp as well as induced conformational changes in the EV. Our computational findings were validated by experimental mutagenesis studies and shed light on the ligand binding characteristics of the EV of NSS, which may facilitate development of allosteric ligands targeting NSS.
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Affiliation(s)
- Ara M Abramyan
- Computational Chemistry and Molecular Biophysics Unit, National Institute on Drug Abuse - Intramural Research Program , National Institutes of Health , Baltimore , Maryland 21224 , United States
| | - Matthias Quick
- Division of Molecular Therapeutics , New York State Psychiatric Institute , New York , New York 10032 , United States
| | - Catherine Xue
- Computational Chemistry and Molecular Biophysics Unit, National Institute on Drug Abuse - Intramural Research Program , National Institutes of Health , Baltimore , Maryland 21224 , United States
| | - Jonathan A Javitch
- Division of Molecular Therapeutics , New York State Psychiatric Institute , New York , New York 10032 , United States
| | - Lei Shi
- Computational Chemistry and Molecular Biophysics Unit, National Institute on Drug Abuse - Intramural Research Program , National Institutes of Health , Baltimore , Maryland 21224 , United States
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94
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Sbailò L, Noé F. An efficient multi-scale Green's function reaction dynamics scheme. J Chem Phys 2018; 147:184106. [PMID: 29141429 DOI: 10.1063/1.5010190] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Molecular Dynamics-Green's Function Reaction Dynamics (MD-GFRD) is a multiscale simulation method for particle dynamics or particle-based reaction-diffusion dynamics that is suited for systems involving low particle densities. Particles in a low-density region are just diffusing and not interacting. In this case, one can avoid the costly integration of microscopic equations of motion, such as molecular dynamics (MD), and instead turn to an event-based scheme in which the times to the next particle interaction and the new particle positions at that time can be sampled. At high (local) concentrations, however, e.g., when particles are interacting in a nontrivial way, particle positions must still be updated with small time steps of the microscopic dynamical equations. The efficiency of a multi-scale simulation that uses these two schemes largely depends on the coupling between them and the decisions when to switch between the two scales. Here we present an efficient scheme for multi-scale MD-GFRD simulations. It has been shown that MD-GFRD schemes are more efficient than brute-force molecular dynamics simulations up to a molar concentration of 102 μM. In this paper, we show that the choice of the propagation domains has a relevant impact on the computational performance. Domains are constructed using a local optimization of their sizes and a minimal domain size is proposed. The algorithm is shown to be more efficient than brute-force Brownian dynamics simulations up to a molar concentration of 103 μM and is up to an order of magnitude more efficient compared with previous MD-GFRD schemes.
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Affiliation(s)
- Luigi Sbailò
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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95
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Pronobis W, Tkatchenko A, Müller KR. Many-Body Descriptors for Predicting Molecular Properties with Machine Learning: Analysis of Pairwise and Three-Body Interactions in Molecules. J Chem Theory Comput 2018; 14:2991-3003. [DOI: 10.1021/acs.jctc.8b00110] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Wiktor Pronobis
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg L-1511, Luxembourg
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- Max Planck Institute for Informatics, 66123 Saarbrücken, Germany
- Department of Brain and Cognitive Engineering, Korea University, Seoul 136-713, South Korea
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96
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Examining a Thermodynamic Order Parameter of Protein Folding. Sci Rep 2018; 8:7148. [PMID: 29740018 PMCID: PMC5940758 DOI: 10.1038/s41598-018-25406-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 04/18/2018] [Indexed: 01/26/2023] Open
Abstract
Dimensionality reduction with a suitable choice of order parameters or reaction coordinates is commonly used for analyzing high-dimensional time-series data generated by atomistic biomolecular simulations. So far, geometric order parameters, such as the root mean square deviation, fraction of native amino acid contacts, and collective coordinates that best characterize rare or large conformational transitions, have been prevailing in protein folding studies. Here, we show that the solvent-averaged effective energy, which is a thermodynamic quantity but unambiguously defined for individual protein conformations, serves as a good order parameter of protein folding. This is illustrated through the application to the folding-unfolding simulation trajectory of villin headpiece subdomain. We rationalize the suitability of the effective energy as an order parameter by the funneledness of the underlying protein free energy landscape. We also demonstrate that an improved conformational space discretization is achieved by incorporating the effective energy. The most distinctive feature of this thermodynamic order parameter is that it works in pointing to near-native folded structures even when the knowledge of the native structure is lacking, and the use of the effective energy will also find applications in combination with methods of protein structure prediction.
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97
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Meng Y, Gao C, Clawson D, Atwell S, Russell M, Vieth M, Roux B. Predicting the Conformational Variability of Abl Tyrosine Kinase using Molecular Dynamics Simulations and Markov State Models. J Chem Theory Comput 2018; 14:2721-2732. [PMID: 29474075 PMCID: PMC6317529 DOI: 10.1021/acs.jctc.7b01170] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Understanding protein conformational variability remains a challenge in drug discovery. The issue arises in protein kinases, whose multiple conformational states can affect the binding of small-molecule inhibitors. To overcome this challenge, we propose a comprehensive computational framework based on Markov state models (MSMs). Our framework integrates the information from explicit-solvent molecular dynamics simulations to accurately rank-order the accessible conformational variants of a target protein. We tested the methodology using Abl kinase with a reference and blind-test set. Only half of the Abl conformational variants discovered by our approach are present in the disclosed X-ray structures. The approach successfully identified a protein conformational state not previously observed in public structures but evident in a retrospective analysis of Lilly in-house structures: the X-ray structure of Abl with WHI-P154. Using a MSM-derived model, the free energy landscape and kinetic profile of Abl was analyzed in detail highlighting opportunities for targeting the unique metastable states.
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Affiliation(s)
- Yilin Meng
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, 60637, USA
| | - Cen Gao
- Discovery Chemistry Research and Technologies, Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN, 46285, USA
| | - David Clawson
- Discovery Chemistry Research and Technologies, Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN, 46285, USA
| | - Shane Atwell
- Applied Molecular Evolution, Eli Lilly and Company, Lilly Biotechnology Center, 10290 Campus Point Drive, San Diego, CA, 92121, USA
| | - Marijane Russell
- Discovery Chemistry Research and Technologies, Eli Lilly and Company, Lilly Biotechnology Center, 10290 Campus Point Drive, San Diego, CA, 92121, USA
| | - Michal Vieth
- Discovery Chemistry Research and Technologies, Eli Lilly and Company, Lilly Biotechnology Center, 10290 Campus Point Drive, San Diego, CA, 92121, USA
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, 60637, USA
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98
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Litzinger F, Boninsegna L, Wu H, Nüske F, Patel R, Baraniuk R, Noé F, Clementi C. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. J Chem Theory Comput 2018; 14:2771-2783. [DOI: 10.1021/acs.jctc.8b00089] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Florian Litzinger
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - Lorenzo Boninsegna
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Hao Wu
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - Feliks Nüske
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Raajen Patel
- Rice University, Department of Electrical and Computer Engineering, Houston, Texas 77005, United States
| | - Richard Baraniuk
- Rice University, Department of Electrical and Computer Engineering, Houston, Texas 77005, United States
| | - Frank Noé
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Cecilia Clementi
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
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99
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Sultan MM, Wayment-Steele HK, Pande VS. Transferable Neural Networks for Enhanced Sampling of Protein Dynamics. J Chem Theory Comput 2018. [DOI: 10.1021/acs.jctc.8b00025] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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100
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Affiliation(s)
- Brooke E. Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
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