1
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Aristoff D, Johnson M, Simpson G, Webber RJ. The fast committor machine: Interpretable prediction with kernels. J Chem Phys 2024; 161:084113. [PMID: 39193940 DOI: 10.1063/5.0222798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Accepted: 08/07/2024] [Indexed: 08/29/2024] Open
Abstract
In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration x will reach a set B before a set A. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the A to B transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly with the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net.
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Affiliation(s)
- David Aristoff
- Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Mats Johnson
- Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Gideon Simpson
- Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Robert J Webber
- Mathematics, University of California San Diego, La Jolla, California 92093, USA
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2
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Spiriti J, Wong CF. Quantitative Prediction of Dissociation Rates of PYK2 Ligands Using Umbrella Sampling and Milestoning. J Chem Theory Comput 2024; 20:4029-4044. [PMID: 38640609 DOI: 10.1021/acs.jctc.4c00192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/21/2024]
Abstract
We used umbrella sampling and the milestoning simulation method to study the dissociation of multiple ligands from protein kinase PYK2. The activation barriers obtained from the potential of mean force of the umbrella sampling simulations correlated well with the experimental dissociation rates. Using the zero-temperature string method, we obtained optimized paths along the free-energy surfaces for milestoning simulations of three ligands with a similar structure. The milestoning simulations gave an absolute dissociation rate within 2 orders of magnitude of the experimental value for two ligands but at least 3 orders of magnitude too high for the third. Despite the similarity in their structures, the ligands took different pathways to exit from the binding site of PYK2, making contact with different sets of residues. In addition, the protein experienced different conformational changes for dissociation of the three ligands.
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Affiliation(s)
- Justin Spiriti
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121, United States
| | - Chung F Wong
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121, United States
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3
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Narayan B, Elber R. Comparison of Accuracy and Efficiency of Milestoning Variants: Introducing Buffer Milestoning. J Phys Chem B 2024; 128:1438-1447. [PMID: 38316620 DOI: 10.1021/acs.jpcb.3c07933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
The Milestoning algorithm is a method for long-time molecular dynamics simulations. It enables the sampling of rare events. The precise calculations of observables depend on accurately determining the first hitting point distribution (FHPD) for each milestone. There is no analytical expression for FHPD, which is estimated numerically. Several variants of Milestoning offer approximations to the FHPD. Here, we examine in detail the FHPD of an exact calculation and Milestoning variants. We also introduce a new version of the Milestoning algorithm, buffer Milestoning, with a comparable cost to conventional Milestoning but higher accuracy. We use the mean first passage time and the free energy to assess the simulation quality, and we compare the accuracy and efficiency of buffer Milestoning to exact calculations, conventional Milestoning, local-passage-time-weighted Milestoning, Markovian Milestoning with Voronoi tessellation, and exact Milestoning. Conventional Milestoning requires milestone decorrelation. If this condition is not satisfied, it is the least accurate approach of all the techniques we examined. We conclude that for a small increase in cost compared to conventional Milestoning, buffer Milestoning provides accurate results for a range of problems, including more correlated milestones and is, therefore, versatile compared to other variants. Local-passage-time-weighted Milestoning provides accuracy similar to that of buffer Milestoning but at an increased simulation cost. Markovian Milestoning with Voronoi tessellation is the most accurate compared with other approximations, but it is less stable for high barriers and more expensive.
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Affiliation(s)
- Brajesh Narayan
- Oden Institute for Computational Engineering and Science, University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Science, University of Texas at Austin, Austin, Texas 78712, United States
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4
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Ren FD, Liu YZ, Ding KW, Chang LL, Cao DL, Liu S. Finite temperature string by K-means clustering sampling with order parameters as collective variables for molecular crystals: application to polymorphic transformation between β-CL-20 and ε-CL-20. Phys Chem Chem Phys 2024; 26:3500-3515. [PMID: 38206084 DOI: 10.1039/d3cp05389j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Polymorphic transformation of molecular crystals is a fundamental phase transition process, and it is important practically in the chemical, material, biopharmaceutical, and energy storage industries. However, understanding of the transformation mechanism at the molecular level is poor due to the extreme simulating challenges in enhanced sampling and formulating order parameters (OPs) as the collective variables that can distinguish polymorphs with quite similar and complicated structures so as to describe the reaction coordinate. In this work, two kinds of OPs for CL-20 were constructed by the bond distances, bond orientations and relative orientations. A K-means clustering algorithm based on the Euclidean distance and sample weight was used to smooth the initial finite temperature string (FTS), and the minimum free energy path connecting β-CL-20 and ε-CL-20 was sketched by the string method in collective variables, and the free energy profile along the path and the nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations. In comparison with the average-based sampling, the K-means clustering algorithm provided an improved convergence rate of FTS. The simulation of transformation was independent of OP types but was affected greatly by finite-size effects. A surface-mediated local nucleation mechanism was confirmed and the configuration located at the shoulder of potential of mean force, rather than overall maximum, was confirmed to be the critical nucleus formed by the cooperative effect of the intermolecular interactions. This work provides an effective way to explore the polymorphic transformation of caged molecular crystals at the molecular level.
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Affiliation(s)
- Fu-de Ren
- School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China.
| | - Ying-Zhe Liu
- Xi'an Modern Chemistry Research Institute, Xi'an 710065, China
| | - Ke-Wei Ding
- Xi'an Modern Chemistry Research Institute, Xi'an 710065, China
| | - Ling-Ling Chang
- School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China.
| | - Duan-Lin Cao
- School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China.
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, USA.
- Depaertment of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
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5
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Ji X, Wang R, Wang H, Liu W. On committor functions in milestoning. J Chem Phys 2023; 159:244115. [PMID: 38153148 DOI: 10.1063/5.0180513] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 12/07/2023] [Indexed: 12/29/2023] Open
Abstract
As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.
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Affiliation(s)
- Xiaojun Ji
- Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong 266237, People's Republic of China
- Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao, Shandong 266237, People's Republic of China
| | - Ru Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
| | - Hao Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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6
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Ojha AA, Votapka LW, Amaro RE. QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations. Chem Sci 2023; 14:13159-13175. [PMID: 38023523 PMCID: PMC10664576 DOI: 10.1039/d3sc04195f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/22/2023] [Indexed: 12/01/2023] Open
Abstract
Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry and Biochemistry, University of California San Diego La Jolla California 92093 USA
| | - Lane William Votapka
- Department of Chemistry and Biochemistry, University of California San Diego La Jolla California 92093 USA
| | - Rommie Elizabeth Amaro
- Department of Molecular Biology, University of California San Diego La Jolla California 92093 USA
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7
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Wang R, Wang H, Liu W, Elber R. Approximating First Hitting Point Distribution in Milestoning for Rare Event Kinetics. J Chem Theory Comput 2023; 19:6816-6826. [PMID: 37695680 DOI: 10.1021/acs.jctc.3c00315] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/13/2023]
Abstract
Milestoning is an efficient method for rare event kinetics calculation using short trajectory parallelization. Mean first passage time (MFPT) is the key kinetic output of Milestoning, whose accuracy crucially depends on the initial distribution of the short trajectory ensemble. The true initial distribution, i.e., the first hitting point distribution (FHPD), has no analytic expression in the general case. Here, we introduce two algorithms, local passage time weighted Milestoning (LPT-M) and Bayesian inference Milestoning (BI-M), to accurately and efficiently approximate FHPD for systems at equilibrium condition. Starting from sampling the Boltzmann distribution on milestones, we calculate the proper weighting factor for the short trajectory ensemble. The methods are tested on two model examples for illustration purpose. Both methods improve significantly over the widely used classical Milestoning (CM) method in terms of the accuracy of MFPT. In particular, BI-M covers the directional Milestoning method as a special case in deterministic Hamiltonian dynamics. LPT-M is especially advantageous in terms of computational costs and robustness with respect to the increasing number of intermediate milestones. Furthermore, a locally iterative correction algorithm for nonequilibrium stationary FHPD is developed for exact MFPT calculation, which can be combined with LPT-M/BI-M and is much cheaper than the exact Milestoning (ExM) method.
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Affiliation(s)
- Ru Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Hao Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, United States
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
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8
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Kasahara K, Masayama R, Okita K, Matubayasi N. Elucidating protein-ligand binding kinetics based on returning probability theory. J Chem Phys 2023; 159:134103. [PMID: 37787130 DOI: 10.1063/5.0165692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 09/14/2023] [Indexed: 10/04/2023] Open
Abstract
The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.
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Affiliation(s)
- Kento Kasahara
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Ren Masayama
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kazuya Okita
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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9
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Wong CF. 15 Years of molecular simulation of drug-binding kinetics. Expert Opin Drug Discov 2023; 18:1333-1348. [PMID: 37789731 PMCID: PMC10926948 DOI: 10.1080/17460441.2023.2264770] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 09/26/2023] [Indexed: 10/05/2023]
Abstract
INTRODUCTION Drug-binding kinetics has been increasingly recognized as an important factor to be considered in drug discovery. Long residence time could prolong the action of some drugs while produce toxicity on others. Early evaluation of the binding kinetics of drug candidates could reduce attrition rate late in the drug discovery process. Computational prediction of drug-binding kinetics is useful as compounds can be evaluated even before they are made. However, simulation of drug-binding kinetics is a challenging problem because of the long-time scale involved. Nevertheless, significant progress has been made. AREAS COVERED This review illustrates the rapid evolution of qualitative to quantitative molecular dynamics-based methods that have been developed over the last 15 years. EXPERT OPINION The development of new methods based on molecular dynamics simulations now enables computation of absolute association/dissociation rate constants. Cheaper methods capable of identifying candidates with fast or slow binding kinetics, or rank-ordering rate constants are also available. Together, these methods have generated useful insights into the molecular mechanisms of drug-binding kinetics, and the design of drug candidates with therapeutically favorable kinetics. Although predicting absolute rate constants is still expensive and challenging, rapid improvement is expected in the coming years with the continuing refinement of current technologies, development of new methodologies, and the utilization of machine learning.
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Affiliation(s)
- Chung F Wong
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, MO, USA
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10
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Ojha AA, Srivastava A, Votapka LW, Amaro RE. Selectivity and Ranking of Tight-Binding JAK-STAT Inhibitors Using Markovian Milestoning with Voronoi Tessellations. J Chem Inf Model 2023; 63:2469-2482. [PMID: 37023323 PMCID: PMC10131228 DOI: 10.1021/acs.jcim.2c01589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
Abstract
Janus kinases (JAK), a group of proteins in the nonreceptor tyrosine kinase (NRTKs) family, play a crucial role in growth, survival, and angiogenesis. They are activated by cytokines through the Janus kinase-signal transducer and activator of a transcription (JAK-STAT) signaling pathway. JAK-STAT signaling pathways have significant roles in the regulation of cell division, apoptosis, and immunity. Identification of the V617F mutation in the Janus homology 2 (JH2) domain of JAK2 leading to myeloproliferative disorders has stimulated great interest in the drug discovery community to develop JAK2-specific inhibitors. However, such inhibitors should be selective toward JAK2 over other JAKs and display an extended residence time. Recently, novel JAK2/STAT5 axis inhibitors (N-(1H-pyrazol-3-yl)pyrimidin-2-amino derivatives) have displayed extended residence times (hours or longer) on target and adequate selectivity excluding JAK3. To facilitate a deeper understanding of the kinase-inhibitor interactions and advance the development of such inhibitors, we utilize a multiscale Markovian milestoning with Voronoi tessellations (MMVT) approach within the Simulation-Enabled Estimation of Kinetic Rates v.2 (SEEKR2) program to rank order these inhibitors based on their kinetic properties and further explain the selectivity of JAK2 inhibitors over JAK3. Our approach investigates the kinetic and thermodynamic properties of JAK-inhibitor complexes in a user-friendly, fast, efficient, and accurate manner compared to other brute force and hybrid-enhanced sampling approaches.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Ambuj Srivastava
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Lane William Votapka
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
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11
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Ojha AA, Thakur S, Ahn SH, Amaro RE. DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling. J Chem Theory Comput 2023; 19:1342-1359. [PMID: 36719802 DOI: 10.1021/acs.jctc.2c00282] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry, University of California San Diego, La Jolla, California92093, United States
| | - Saumya Thakur
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Maharashtra400076, India
| | - Surl-Hee Ahn
- Department of Chemical Engineering, University of California Davis, Davis, California95616, United States
| | - Rommie E Amaro
- Department of Chemistry, University of California San Diego, La Jolla, California92093, United States
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12
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Akalın AA, Dedekargınoğlu B, Choi SR, Han B, Ozcelikkale A. Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty. Pharm Res 2023; 40:501-523. [PMID: 35650448 PMCID: PMC9712595 DOI: 10.1007/s11095-022-03298-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 05/17/2022] [Indexed: 01/18/2023]
Abstract
Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.
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Affiliation(s)
- Ali Aykut Akalın
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey
| | - Barış Dedekargınoğlu
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey
| | - Sae Rome Choi
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA
| | - Bumsoo Han
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, USA.
- Center for Cancer Research, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA.
| | - Altug Ozcelikkale
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey.
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13
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Hasyim MR, Batton CH, Mandadapu KK. Supervised learning and the finite-temperature string method for computing committor functions and reaction rates. J Chem Phys 2022; 157:184111. [DOI: 10.1063/5.0102423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [ Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. In this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.
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Affiliation(s)
- Muhammad R. Hasyim
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, USA
| | - Clay H. Batton
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, USA
| | - Kranthi K. Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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14
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Cardenas AE, Hunter A, Wang H, Elber R. ScMiles2: A Script to Conduct and Analyze Milestoning Trajectories for Long Time Dynamics. J Chem Theory Comput 2022; 18:6952-6965. [PMID: 36191005 DOI: 10.1021/acs.jctc.2c00708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Milestoning is a theory and an algorithm that computes kinetics and thermodynamics at long time scales. It is based on partitioning the (phase) space into cells and running a large number of short trajectories between the boundaries of the cells. The termination points of the trajectories are analyzed with the Milestoning theory to obtain kinetic and thermodynamic information. Managing the tens to hundreds of thousands of Milestoning trajectories is a challenge, which we handle with a python script, ScMiles. Here, we introduce a new version of the python script ScMiles2 to conduct Milestoning simulations. Major enhancements are: (i) post analysis of Milestoning trajectories to obtain the free energy, mean first passage time, the committor function, and exit times; (ii) similar to (i) but the post analysis is for a single long trajectory; (iii) we support the use of the GROMACS software in addition to NAMD; (iv) a restart option; (v) the automated finding, sampling, and launching trajectories from new milestones that are found on the fly; and (vi) support Milestoning calculations with several coarse variables and for complex reaction coordinates. We also evaluate the simulation parameters and suggest new algorithmic features to enhance the rate of convergence of observables. We propose the use of an iteration-averaged kinetic matrix for a rapid approach to asymptotic values. Illustrations are provided for small systems and one large example.
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Affiliation(s)
- Alfredo E Cardenas
- The Oden Institute, University of Texas at Austin, Austin, Texas 78712, United States
| | - Allison Hunter
- The Oden Institute, University of Texas at Austin, Austin, Texas 78712, United States
| | - Hao Wang
- The Oden Institute, University of Texas at Austin, Austin, Texas 78712, United States.,Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Ron Elber
- The Oden Institute, University of Texas at Austin, Austin, Texas 78712, United States.,Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
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15
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Votapka LW, Stokely AM, Ojha AA, Amaro RE. SEEKR2: Versatile Multiscale Milestoning Utilizing the OpenMM Molecular Dynamics Engine. J Chem Inf Model 2022; 62:3253-3262. [PMID: 35759413 PMCID: PMC9277580 DOI: 10.1021/acs.jcim.2c00501] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
We present SEEKR2
(simulation-enabled estimation of kinetic rates
version 2)—the latest iteration in the family of SEEKR programs
for using multiscale simulation methods to computationally estimate
the kinetics and thermodynamics of molecular processes, in particular,
ligand-receptor binding. SEEKR2 generates equivalent, or improved,
results compared to the earlier versions of SEEKR but with significant
increases in speed and capabilities. SEEKR2 has also been built with
greater ease of usability and with extensible features to enable future
expansions of the method. Now, in addition to supporting simulations
using NAMD, calculations may be run with the fast and extensible OpenMM
simulation engine. The Brownian dynamics portion of the calculation
has also been upgraded to Browndye 2. Furthermore, this version of
SEEKR supports hydrogen mass repartitioning, which significantly reduces
computational cost, while showing little, if any, loss of accuracy
in the predicted kinetics.
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Affiliation(s)
- Lane W Votapka
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Andrew M Stokely
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Anupam A Ojha
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Rommie E Amaro
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
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16
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Cardenas AE, Drexler CI, Nechushtai R, Mittler R, Friedler A, Webb LJ, Elber R. Peptide Permeation across a Phosphocholine Membrane: An Atomically Detailed Mechanism Determined through Simulations and Supported by Experimentation. J Phys Chem B 2022; 126:2834-2849. [PMID: 35388695 PMCID: PMC9074375 DOI: 10.1021/acs.jpcb.1c10966] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Cell-penetrating peptides (CPPs) facilitate translocation across biological membranes and are of significant biological and medical interest. Several CPPs can permeate into specific cells and organelles. We examine the incorporation and translocation of a novel anticancer CPP in a dioleoylphosphatidylcholine (DOPC) lipid bilayer membrane. The peptide, NAF-144-67, is a short fragment of a transmembrane protein, consisting of hydrophobic N-terminal and charged C-terminal segments. Experiments using fluorescently labeled NAF-144-67 in ∼100 nm DOPC vesicles and atomically detailed simulations conducted with Milestoning support a model in which a significant barrier for peptide-membrane entry is found at the interface between the aqueous solution and membrane. The initial step is the insertion of the N-terminal segment and the hydrophobic helix into the membrane, passing the hydrophilic head groups. Both experiments and simulations suggest that the free energy difference in the first step of the permeation mechanism in which the hydrophobic helix crosses the phospholipid head groups is -0.4 kcal mol-1 slightly favoring motion into the membrane. Milestoning calculations of the mean first passage time and the committor function underscore the existence of an early polar barrier followed by a diffusive barrierless motion in the lipid tail region. Permeation events are coupled to membrane fluctuations that are examined in detail. Our study opens the way to investigate in atomistic resolution the molecular mechanism, kinetics, and thermodynamics of CPP permeation to diverse membranes.
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Affiliation(s)
- Alfredo E. Cardenas
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
| | - Chad I. Drexler
- Department of Chemistry, The University of Texas at Austin, Austin, TX 78712, USA
| | - Rachel Nechushtai
- The Alexander Silberman Institute of Life Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat-Ram, Jerusalem 91904, Israel
| | - Ron Mittler
- The Department of Surgery, University of Missouri School of Medicine. Christopher S. Bond Life Sciences Center, University of Missouri. 1201 Rollins St, Columbia, MO 65201, USA
| | - Assaf Friedler
- The Institute of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat-Ram, Jerusalem 91904, Israel
| | - Lauren J. Webb
- Department of Chemistry, The University of Texas at Austin, Austin, TX 78712, USA
| | - Ron Elber
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Chemistry, The University of Texas at Austin, Austin, TX 78712, USA
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17
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Lin YC, Luo YL. Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux. Front Mol Biosci 2022; 9:860933. [PMID: 35495625 PMCID: PMC9043130 DOI: 10.3389/fmolb.2022.860933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Accepted: 03/07/2022] [Indexed: 11/18/2022] Open
Abstract
Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.
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18
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Chen H, Ogden D, Pant S, Cai W, Tajkhorshid E, Moradi M, Roux B, Chipot C. A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls. J Chem Theory Comput 2022; 18:1406-1422. [PMID: 35138832 PMCID: PMC8904302 DOI: 10.1021/acs.jctc.1c01049] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.
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Affiliation(s)
- Haochuan Chen
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche no 7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
| | - Dylan Ogden
- Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701, United States
| | - Shashank Pant
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Wensheng Cai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
| | - Emad Tajkhorshid
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Biochemistry and Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Mahmoud Moradi
- Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701, United States
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637, United States
| | - Christophe Chipot
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche no 7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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19
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Sobeh MM, Kitao A. Dissociation Pathways of the p53 DNA Binding Domain from DNA and Critical Roles of Key Residues Elucidated by dPaCS-MD/MSM. J Chem Inf Model 2022; 62:1294-1307. [PMID: 35234033 DOI: 10.1021/acs.jcim.1c01508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
p53 is a transcriptional factor that regulates cell response to a variety of stresses. About a half of all human tumors contain p53 mutations, and the accumulation of mutations in the DNA binding domain of p53 (p53-DBD) can cause destabilization of p53 and its complex with DNA. To identify the key residues of the p53-DBD/DNA binding and to understand the dissociation mechanisms of the p53-DBD/DNA complex, the dissociation process of p53-DBD from a DNA duplex that contains the consensus sequence (the specific target of p53-DBD) was investigated by a combination of dissociation parallel cascade selection molecular dynamics (dPaCS-MD) and the Markov state model (MSM). This combination (dPaCS-MD/MSM) enabled us to simulate dissociation of the two large molecules based on an all-atom model with a short simulation time (11.2 ± 2.2 ns per trial) and to analyze dissociation pathways, free energy landscape (FEL), and binding free energy. Among 75 trials of dPaCS-MD, p53-DBD dissociated first from the major groove and then detached from the minor groove in 93% of the cases, while 7% of the cases unbinding from the minor groove occurred first. Minor groove binding is mainly stabilized by R248, identified as the most important residue that tightly binds deep inside the minor groove. The standard binding free energy calculated from the FEL was -10.9 ± 0.4 kcal/mol, which agrees with an experimental value of -11.1 kcal/mol. These results indicate that the dPaCS-MD/MSM combination can be a powerful tool to investigate dissociation mechanisms of two large molecules. Analysis of the p53 key residues for DNA binding indicates high correlations with cancer-related mutations, confirming that impairment of the interactions between p53-DBD and DNA can be frequently related to cancer.
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Affiliation(s)
- Mohamed Marzouk Sobeh
- School of Life Science and Technology, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan.,Physics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
| | - Akio Kitao
- School of Life Science and Technology, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
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20
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Hata H, Phuoc Tran D, Marzouk Sobeh M, Kitao A. Binding free energy of protein/ligand complexes calculated using dissociation Parallel Cascade Selection Molecular Dynamics and Markov state model. Biophys Physicobiol 2022; 18:305-316. [PMID: 35178333 PMCID: PMC8694779 DOI: 10.2142/biophysico.bppb-v18.037] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 12/02/2021] [Indexed: 01/01/2023] Open
Abstract
We recently proposed a computational procedure to simulate the dissociation of protein/ligand complexes using the dissociation Parallel Cascade Selection Molecular Dynamics simulation (dPaCS-MD) method and to analyze the generated trajectories using the Markov state model (MSM). This procedure, called dPaCS-MD/MSM, enables calculation of the dissociation free energy profile and the standard binding free energy. To examine whether this method can reproduce experimentally determined binding free energies for a variety of systems, we used it to investigate the dissociation of three protein/ligand complexes: trypsin/benzamine, FKBP/FK506, and adenosine A2A receptor/T4E. First, dPaCS-MD generated multiple dissociation pathways within a reasonable computational time for all the complexes, although the complexes differed significantly in the size of the molecules and in intermolecular interactions. Subsequent MSM analyses produced free energy profiles for the dissociations, which provided insights into how each ligand dissociates from the protein. The standard binding free energies obtained by dPaCS-MD/MSM are in good agreement with experimental values for all the complexes. We conclude that dPaCS-MD/MSM can accurately calculate the binding free energies of these complexes.
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Affiliation(s)
- Hiroaki Hata
- School of Life Science and Technology, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan
| | - Duy Phuoc Tran
- School of Life Science and Technology, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan
| | - Mohamed Marzouk Sobeh
- School of Life Science and Technology, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan.,Physics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
| | - Akio Kitao
- School of Life Science and Technology, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan
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21
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Guardiani C, Cecconi F, Chiodo L, Cottone G, Malgaretti P, Maragliano L, Barabash ML, Camisasca G, Ceccarelli M, Corry B, Roth R, Giacomello A, Roux B. Computational methods and theory for ion channel research. ADVANCES IN PHYSICS: X 2022; 7:2080587. [PMID: 35874965 PMCID: PMC9302924 DOI: 10.1080/23746149.2022.2080587] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023] Open
Abstract
Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.
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Affiliation(s)
- C. Guardiani
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - F. Cecconi
- CNR - Istituto dei Sistemi Complessi, Rome, Italy and Istituto Nazionale di Fisica Nucleare, INFN, Roma1 section. 00185, Roma, Italy
| | - L. Chiodo
- Department of Engineering, Campus Bio-Medico University, Rome, Italy
| | - G. Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Palermo, Italy
| | - P. Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Erlangen, Germany
| | - L. Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy, and Center for Synaptic Neuroscience and Technology, Istituto Italiano di Tecnologia, Genova, Italy
| | - M. L. Barabash
- Department of Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA
| | - G. Camisasca
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
- Dipartimento di Fisica, Università Roma Tre, Rome, Italy
| | - M. Ceccarelli
- Department of Physics and CNR-IOM, University of Cagliari, Monserrato 09042-IT, Italy
| | - B. Corry
- Research School of Biology, The Australian National University, Canberra, ACT 2600, Australia
| | - R. Roth
- Institut Für Theoretische Physik, Eberhard Karls Universität Tübingen, Tübingen, Germany
| | - A. Giacomello
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - B. Roux
- Department of Biochemistry & Molecular Biology, University of Chicago, Chicago IL, USA
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22
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Ray D, Stone SE, Andricioaei I. Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories. J Chem Theory Comput 2021; 18:79-95. [PMID: 34910499 DOI: 10.1021/acs.jctc.1c00803] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.
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Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Sharon Emily Stone
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States.,Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
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23
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Ahn SH, Ojha AA, Amaro RE, McCammon JA. Gaussian-Accelerated Molecular Dynamics with the Weighted Ensemble Method: A Hybrid Method Improves Thermodynamic and Kinetic Sampling. J Chem Theory Comput 2021; 17:7938-7951. [PMID: 34844409 DOI: 10.1021/acs.jctc.1c00770] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Gaussian-accelerated molecular dynamics (GaMD) is a well-established enhanced sampling method for molecular dynamics simulations that effectively samples the potential energy landscape of the system by adding a boost potential, which smoothens the surface and lowers the energy barriers between states. GaMD is unable to give time-dependent properties such as kinetics directly. On the other hand, the weighted ensemble (WE) method can efficiently sample transitions between states with its many weighted trajectories, which directly yield rates and pathways. However, convergence to equilibrium conditions remains a challenge for the WE method. Hence, we have developed a hybrid method that combines the two methods, wherein GaMD is first used to sample the potential energy landscape of the system and WE is subsequently used to further sample the potential energy landscape and kinetic properties of interest. We show that the hybrid method can sample both thermodynamic and kinetic properties more accurately and quickly compared to using either method alone.
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Affiliation(s)
- Surl-Hee Ahn
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - Anupam A Ojha
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - Rommie E Amaro
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - J Andrew McCammon
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States.,Department of Pharmacology, University of California San Diego, La Jolla 92093, California, United States
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24
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Vlachas PR, Zavadlav J, Praprotnik M, Koumoutsakos P. Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics. J Chem Theory Comput 2021; 18:538-549. [PMID: 34890204 DOI: 10.1021/acs.jctc.1c00809] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.
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Affiliation(s)
- Pantelis R Vlachas
- Computational Science and Engineering Laboratory, ETH Zurich, CH-8092, Switzerland
| | - Julija Zavadlav
- Professorship of Multiscale Modeling of Fluid Materials, TUM School of Engineering and Design, Technical University of Munich, 85748 Garching bei München, Germany.,Munich Data Science Institute, Technical University of Munich, 85748 Munich, Germany
| | - Matej Praprotnik
- Laboratory for Molecular Modeling, National Institute of Chemistry, SI-1001 Ljubljana, Slovenia.,Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Petros Koumoutsakos
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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25
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Roux B. String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor. J Phys Chem A 2021; 125:7558-7571. [PMID: 34406010 PMCID: PMC8419867 DOI: 10.1021/acs.jpca.1c04110] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Revised: 07/26/2021] [Indexed: 11/29/2022]
Abstract
The kinetics of a dynamical system comprising two metastable states is formulated in terms of a finite-time propagator in phase space (position and velocity) adapted to the underdamped Langevin equation. Dimensionality reduction to a subspace of collective variables yields familiar expressions for the propagator, committor, and steady-state flux. A quadratic expression for the steady-state flux between the two metastable states can serve as a robust variational principle to determine an optimal approximate committor expressed in terms of a set of collective variables. The theoretical formulation is exploited to clarify the foundation of the string method with swarms-of-trajectories, which relies on the mean drift of short trajectories to determine the optimal transition pathway. It is argued that the conditions for Markovity within a subspace of collective variables may not be satisfied with an arbitrary short time-step and that proper kinetic behaviors appear only when considering the effective propagator for longer lag times. The effective propagator with finite lag time is amenable to an eigenvalue-eigenvector spectral analysis, as elaborated previously in the context of position-based Markov models. The time-correlation functions calculated by swarms-of-trajectories along the string pathway constitutes a natural extension of these developments. The present formulation provides a powerful theoretical framework to characterize the optimal pathway between two metastable states of a system.
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Affiliation(s)
- Benoît Roux
- Department
of Biochemistry and Molecular Biology, The
University of Chicago, Chicago, Illinois 60637, United States
- Department
of Chemistry, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
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26
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Shannon RJ, Martínez-Núñez E, Shalashilin DV, Glowacki DR. ChemDyME: Kinetically Steered, Automated Mechanism Generation through Combined Molecular Dynamics and Master Equation Calculations. J Chem Theory Comput 2021; 17:4901-4912. [PMID: 34283599 DOI: 10.1021/acs.jctc.1c00335] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In many scientific fields, there is an interest in understanding the way in which chemical networks evolve. The chemical networks which researchers focus upon have become increasingly complex, and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a "black-box" manner, harnessing modern computing resources to automate mechanism discovery. In this work, we present a new approach to automated mechanism generation which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. The key to this chemical network mapping through combined dynamics and ME simulation approach is the concept of "kinetic convergence", whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system and a multiple oxygen addition system relevant to atmospheric aerosol formation.
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Affiliation(s)
- Robin J Shannon
- School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| | - Emilio Martínez-Núñez
- Department of Physical Chemistry, University of Santiago de Compostela, Santiago de Compostela 15705, Spain
| | | | - David R Glowacki
- ArtSci International Foundation, 5th floor Mariner House, Bristol BS1 4QD, U.K
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27
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Xi K, Hu Z, Wu Q, Wei M, Qian R, Zhu L. Assessing the Performance of Traveling-salesman based Automated Path Searching (TAPS) on Complex Biomolecular Systems. J Chem Theory Comput 2021; 17:5301-5311. [PMID: 34270241 DOI: 10.1021/acs.jctc.1c00182] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Though crucial for understanding the function of large biomolecular systems, locating the minimum free energy paths (MFEPs) between their key conformational states is far from trivial due to their high-dimensional nature. Most existing path-searching methods require a static collective variable space as input, encoding intuition or prior knowledge of the transition mechanism. Such information is, however, hardly available a priori and expensive to validate. To alleviate this issue, we have previously introduced a Traveling-salesman based Automated Path Searching method (TAPS) and demonstrated its efficiency on simple peptide systems. Having implemented a parallel version of this method, here we assess the performance of TAPS on three realistic systems (tens to hundreds of residues) in explicit solvents. We show that TAPS successfully located the MFEP for the ground/excited state transition of the T4 lysozyme L99A variant, consistent with previous findings. TAPS also helped identifying the important role of the two polar contacts in directing the loop-in/loop-out transition of the mitogen-activated protein kinase kinase (MEK1), which explained previous mutant experiments. Remarkably, at a minimal cost of 126 ns sampling, TAPS revealed that the Ltn40/Ltn10 transition of lymphotactin needs no complete unfolding/refolding of its β-sheets and that five polar contacts are sufficient to stabilize the various partially unfolded intermediates along the MFEP. These results present TAPS as a general and promising tool for studying the functional dynamics of complex biomolecular systems.
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Affiliation(s)
- Kun Xi
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Zhenquan Hu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Qiang Wu
- School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Meihan Wei
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Runtong Qian
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Lizhe Zhu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
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28
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Jiang W, Lin YC, Botello-Smith W, Contreras JE, Harris AL, Maragliano L, Luo YL. Free energy and kinetics of cAMP permeation through connexin26 via applied voltage and milestoning. Biophys J 2021; 120:2969-2983. [PMID: 34214529 DOI: 10.1016/j.bpj.2021.06.024] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 04/08/2021] [Accepted: 06/17/2021] [Indexed: 11/18/2022] Open
Abstract
The connexin family is a diverse group of highly regulated wide-pore channels permeable to biological signaling molecules. Despite the critical roles of connexins in mediating selective molecular signaling in health and disease, the basis of molecular permeation through these pores remains unclear. Here, we report the thermodynamics and kinetics of binding and transport of a second messenger, adenosine-3',5'-cyclophosphate (cAMP), through a connexin26 hemichannel (Cx26). First, inward and outward fluxes of cAMP molecules solvated in KCl solution were obtained from 4 μs of ± 200 mV simulations. These fluxes data yielded a single-channel permeability of cAMP and cAMP/K+ permeability ratio consistent with experimentally measured values. The results from voltage simulations were then compared with the potential of mean force (PMF) and the mean first passage times (MFPTs) of a single cAMP without voltage, obtained from a total of 16.5 μs of Voronoi-tessellated Markovian milestoning simulations. Both the voltage simulations and the milestoning simulations revealed two cAMP-binding sites, for which the binding constants KD and dissociation rates koff were computed from PMF and MFPTs. The protein dipole inside the pore produces an asymmetric PMF, reflected in unequal cAMP MFPTs in each direction once within the pore. The free energy profiles under opposite voltages were derived from the milestoning PMF and revealed the interplay between voltage and channel polarity on the total free energy. In addition, we show how these factors influence the cAMP dipole vector during permeation, and how cAMP affects the local and nonlocal pore diameter in a position-dependent manner.
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Affiliation(s)
- Wenjuan Jiang
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Yi-Chun Lin
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Wesley Botello-Smith
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Jorge E Contreras
- Department of Physiology and Membrane Biology, School of Medicine, University of California, Davis, California.
| | - Andrew L Harris
- Department of Pharmacology, Physiology, and Neuroscience, New Jersey Medical School, Rutgers, The State University of New Jersey, Newark, New Jersey.
| | - Luca Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy; Center for Synaptic Neuroscience and Technology, Italian Institute of Technology, Genoa, Italy.
| | - Yun Lyna Luo
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California.
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29
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Abstract
The protein HIV Reverse Transcriptase (HIV RT) synthesizes a DNA strand according to a template. During the synthesis, the polymerase slides on the double stranded DNA to allow the entry of a new nucleotide to the active site. We use Molecular Dynamics simulations to estimate the free energy profile and the time scale of the DNA-protein's relative displacement in the complex's closed state. We illustrate that the presence of the catalytic magnesium slows down the process. Upon removing the catalytic magnesium ion, the process is rapid and significantly faster than reopening the active site in preparation for the new substrate. We speculate that magnesium regulates DNA translocation. The magnesium locks the DNA into a specific orientation during the chemical addition of the nucleotide. The release of Mg2+ eases DNA sliding and the acceptance of a new substrate.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States.,Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
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30
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Alberini G, Benfenati F, Maragliano L. Structural Mechanism of ω-Currents in a Mutated Kv7.2 Voltage Sensor Domain from Molecular Dynamics Simulations. J Chem Inf Model 2021; 61:1354-1367. [PMID: 33570938 PMCID: PMC8023575 DOI: 10.1021/acs.jcim.0c01407] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
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Activation of voltage-gated
ion channels is regulated by conformational
changes of the voltage sensor domains (VSDs), four water- and ion-impermeable
modules peripheral to the central, permeable pore domain. Anomalous
currents, defined as ω-currents, have been recorded in response
to mutations of residues on the VSD S4 helix and associated with ion
fluxes through the VSDs. In humans, gene defects in the potassium
channel Kv7.2 result in a broad range of epileptic disorders, from
benign neonatal seizures to severe epileptic encephalopathies. Experimental
evidence suggests that the R207Q mutation in S4, associated with peripheral
nerve hyperexcitability, induces ω-currents at depolarized potentials,
but the fine structural details are still elusive. In this work, we
use atom-detailed molecular dynamics simulations and a refined model
structure of the Kv7.2 VSD in the active conformation in a membrane/water
environment to study the effect of R207Q and four additional mutations
of proven clinical importance. Our results demonstrate that the R207Q
mutant shows the most pronounced increase of hydration in the internal
VSD cavity, a feature favoring the occurrence of ω-currents.
Free energy and kinetics calculations of sodium permeation through
the native and mutated VSD indicate as more favorable the formation
of a cationic current in the latter. Overall, our simulations establish
a mechanistic linkage between genetic variations and their physiological
outcome, by providing a computational description that includes both
thermodynamic and kinetic features of ion permeation associated with
ω-currents.
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Affiliation(s)
- Giulio Alberini
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,Department of Experimental Medicine, Università degli Studi di Genova, Viale Benedetto XV, 3, 16132 Genova, Italy
| | - Fabio Benfenati
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,IRCCS Ospedale Policlinico San Martino, Largo Rosanna Benzi, 10, 16132 Genova, Italy
| | - Luca Maragliano
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,Department of Life and Environmental Sciences, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy
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31
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Elber R, Fathizadeh A, Ma P, Wang H. Modeling molecular kinetics with Milestoning. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1512] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Ron Elber
- Department of Chemistry, The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Arman Fathizadeh
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Piao Ma
- Department of Chemistry University of Texas at Austin Austin Texas USA
| | - Hao Wang
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
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32
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Elber R. Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics. Annu Rev Biophys 2020; 49:69-85. [PMID: 32375019 DOI: 10.1146/annurev-biophys-121219-081528] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.
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Affiliation(s)
- Ron Elber
- Oden Institute for Computational Engineering and Sciences, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA;
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33
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Ahn SH, Jagger BR, Amaro RE. Ranking of Ligand Binding Kinetics Using a Weighted Ensemble Approach and Comparison with a Multiscale Milestoning Approach. J Chem Inf Model 2020; 60:5340-5352. [PMID: 32315175 DOI: 10.1021/acs.jcim.9b00968] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
To improve lead optimization efforts in finding the right ligand, pharmaceutical industries need to know the ligand's binding kinetics, such as binding and unbinding rate constants, which often correlate with the ligand's efficacy in vivo. To predict binding kinetics efficiently, enhanced sampling methods, such as milestoning and the weighted ensemble (WE) method, have been used in molecular dynamics (MD) simulations of these systems. However, a comparison of these enhanced sampling methods in ranking ligands has not been done. Hence, a WE approach called the concurrent adaptive sampling (CAS) algorithm that uses MD simulations was used to rank seven ligands for β-cyclodextrin, a system in which a multiscale milestoning approach called simulation enabled estimation of kinetic rates (SEEKR) was also used, which uses both MD and Brownian dynamics simulations. Overall, the CAS algorithm can successfully rank ligands using the unbinding rate constant koff values and binding free energy ΔG values, as SEEKR did, with reduced computational cost that is about the same as SEEKR. We compare the CAS algorithm simulations with different parameters and discuss the impact of parameters in ranking ligands and obtaining rate constant and binding free energy estimates. We also discuss similarities and differences and advantages and disadvantages of SEEKR and the CAS algorithm for future use.
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Affiliation(s)
- Surl-Hee Ahn
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Benjamin R Jagger
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
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34
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Swinburne TD, Kannan D, Sharpe DJ, Wales DJ. Rare events and first passage time statistics from the energy landscape. J Chem Phys 2020; 153:134115. [PMID: 33032418 DOI: 10.1063/5.0016244] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.
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Affiliation(s)
- Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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35
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The trajectory of intrahelical lesion recognition and extrusion by the human 8-oxoguanine DNA glycosylase. Nat Commun 2020; 11:4437. [PMID: 32895378 PMCID: PMC7477556 DOI: 10.1038/s41467-020-18290-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 08/14/2020] [Indexed: 02/05/2023] Open
Abstract
Efficient search for DNA damage embedded in vast expanses of the DNA genome presents one of the greatest challenges to DNA repair enzymes. We report here crystal structures of human 8-oxoguanine (oxoG) DNA glycosylase, hOGG1, that interact with the DNA containing the damaged base oxoG and the normal base G while they are nested in the DNA helical stack. The structures reveal that hOGG1 engages the DNA using different protein-DNA contacts from those observed in the previously determined lesion recognition complex and other hOGG1-DNA complexes. By applying molecular dynamics simulations, we have determined the pathways taken by the lesion and normal bases when extruded from the DNA helix and their associated free energy profiles. These results reveal how the human oxoG DNA glycosylase hOGG1 locates the lesions inside the DNA helix and facilitates their extrusion for repair. DNA glycosylases are lesion-specific enzymes that recognize specific nucleobase damages and catalyze their excision through cleavage of the glycosidic bond. Here, the authors present the crystal structures of human 8-oxoguanine (oxoG) DNA glycosylase bound to undamaged DNA and to DNA containing an intrahelical oxoG lesion and further analyse these structures with molecular dynamics simulations, which allows them to characterise the base-extrusion pathways.
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36
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Cottone G, Chiodo L, Maragliano L. Thermodynamics and Kinetics of Ion Permeation in Wild-Type and Mutated Open Active Conformation of the Human α7 Nicotinic Receptor. J Chem Inf Model 2020; 60:5045-5056. [PMID: 32803965 PMCID: PMC8011927 DOI: 10.1021/acs.jcim.0c00549] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
![]()
Molecular
studies of human pentameric ligand-gated ion channels
(LGICs) expressed in neurons and at neuromuscular junctions are of
utmost importance in the development of therapeutic strategies for
neurological disorders. We focus here on the nicotinic acetylcholine
receptor nAChR-α7, a homopentameric channel widely expressed
in the human brain, with a proven role in a wide spectrum of disorders
including schizophrenia and Alzheimer’s disease. By exploiting
an all-atom structural model of the full (transmembrane and extracellular)
protein in the open, agonist-bound conformation we recently developed,
we evaluate the free energy and the mean first passage time of single-ion
permeation using molecular dynamics simulations and the milestoning
method with Voronoi tessellation. The results for the wild-type channel
provide the first available mapping of the potential of mean force
in the full-length α7 nAChR, reveal its expected cationic nature,
and are in good agreement with simulation data for other channels
of the LGIC family and with experimental data on nAChRs. We then investigate
the role of a specific mutation directly related to ion selectivity
in LGICs, the E-1′ → A-1′ substitution at the
cytoplasmatic selectivity filter. We find that the mutation strongly
affects sodium and chloride permeation in opposite directions, leading
to a complete inversion of selectivity, at variance with the limited
experimental results available that classify this mutant as cationic.
We thus provide structural determinants for the observed cationic-to-anionic
inversion, revealing a key role of the protonation state of residue
rings far from the mutation, in the proximity of the hydrophobic channel
gate.
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Affiliation(s)
- Grazia Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Viale delle Scienze Ed. 17, 90128 Palermo, Italy
| | - Letizia Chiodo
- Department of Engineering, Campus Bio-Medico University of Rome, Via Á. del Portillo 21, 00128 Rome, Italy
| | - Luca Maragliano
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,IRCCS Ospedale Policlinico San Martino, Largo Rosanna Benzi, 10, 16132 Genova, Italy
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37
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Jagger BR, Ojha AA, Amaro RE. Predicting Ligand Binding Kinetics Using a Markovian Milestoning with Voronoi Tessellations Multiscale Approach. J Chem Theory Comput 2020; 16:5348-5357. [DOI: 10.1021/acs.jctc.0c00495] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Benjamin R. Jagger
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
| | - Anupam A. Ojha
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
| | - Rommie E. Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
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38
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Ray D, Andricioaei I. Weighted ensemble milestoning (WEM): A combined approach for rare event simulations. J Chem Phys 2020; 152:234114. [DOI: 10.1063/5.0008028] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, California 92697, USA
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, California 92697, USA
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39
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Wang H, Elber R. Milestoning with wind: Exploring the impact of a biasing potential in exact calculation of kinetics. J Chem Phys 2020; 152:224105. [PMID: 32534551 DOI: 10.1063/5.0011050] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We consider the algorithm wind-assisted reweighted Milestoning of Grazioli and Andricioaei [J. Chem. Phys 149(8), 084103 (2018)], expand it, and assess its performance. We derive exact expressions for underdamped and overdamped Langevin dynamics and examine its efficiency for a simple model system (Mueller's potential) and for bond breaking in solution. The use of a biasing force (wind) significantly enhances the sampling of otherwise rare trajectories but also introduces an exponential weight to the trajectories that significantly impact the value of the statistics. In our examples, computing averages and standard deviations are not better using wind compared to straightforward Milestoning. However, the biasing force is useful for highly steep energy landscapes. On these landscapes, the probability of sampling straightforward Milestoning trajectories, which overcome the barrier, is low and the biasing force enables the observations of these rare events.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
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40
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Wang H, Huang N, Dangerfield T, Johnson KA, Gao J, Elber R. Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate. J Phys Chem B 2020; 124:4270-4283. [PMID: 32364738 PMCID: PMC7260111 DOI: 10.1021/acs.jpcb.0c02632] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin TX 78712
| | - Nathan Huang
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX 78712
| | - Tyler Dangerfield
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX 78712
| | - Kenneth A. Johnson
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX 78712
| | - Jiali Gao
- Department of Chemistry, University of Minnesota, Minneapolis, MN, 55455-0431
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin TX 78712
- Department of Chemistry, University of Texas at Austin, Austin, TX 78712
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41
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Narayan B, Fathizadeh A, Templeton C, He P, Arasteh S, Elber R, Buchete NV, Levy RM. The transition between active and inactive conformations of Abl kinase studied by rock climbing and Milestoning. Biochim Biophys Acta Gen Subj 2020; 1864:129508. [PMID: 31884066 PMCID: PMC7012767 DOI: 10.1016/j.bbagen.2019.129508] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2019] [Revised: 12/11/2019] [Accepted: 12/19/2019] [Indexed: 12/12/2022]
Abstract
BACKGROUND Kinases are a family of enzymes that catalyze the transfer of the ɤ-phosphate group from ATP to a protein's residue. Malfunctioning kinases are involved in many health problems such as cardiovascular diseases, diabetes, and cancer. Kinases transitions between multiple conformations of inactive to active forms attracted considerable interest. METHOD A reaction coordinate is computed for the transition between the active to inactive conformation in Abl kinase with a focus on the DFG-in to DFG-out flip. The method of Rock Climbing is used to construct a path locally, which is subsequently optimized using a functional of the entire path. The discrete coordinate sets along the reaction path are used in a Milestoning calculation of the free energy landscape and the rate of the transition. RESULTS The estimated transition times are between a few milliseconds and seconds, consistent with simulations of the kinetics and with indirect experimental data. The activation requires the transient dissociation of the salt bridge between Lys271 and Glu286. The salt bridge reforms once the DFG motif is stabilized by a locked conformation of Phe382. About ten residues are identified that contribute significantly to the process and are included as part of the reaction space. CONCLUSIONS The transition from DFG-in to DFG-out in Abl kinase was simulated using atomic resolution of a fully solvated protein yielding detailed description of the kinetics and the mechanism of the DFG flip. The results are consistent with other computational methods that simulate the kinetics and with some indirect experimental measurements. GENERAL SIGNIFICANCE The activation of kinases includes a conformational transition of the DFG motif that is important for enzyme activity but is not accessible to conventional Molecular Dynamics. We propose a detailed mechanism for the transition, at a timescale longer than conventional MD, using a combination of reaction path and Milestoning algorithms. The mechanism includes local structural adjustments near the binding site as well as collective interactions with more remote residues.
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Affiliation(s)
- Brajesh Narayan
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Arman Fathizadeh
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E. 24(th) Street, 1 University Station (C0200), Austin, TX 78712-1229, USA
| | - Clark Templeton
- McKetta Department of Chemical Engineering, University of Texas at Austin, 200 E. Dean Keaton St. Stop C0400, Austin, TX 78712-1589, USA
| | - Peng He
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
| | - Shima Arasteh
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E. 24(th) Street, 1 University Station (C0200), Austin, TX 78712-1229, USA; Department of Chemistry, University of Texas at Austin, 2506 Speedway STOP A5300, Austin, TX 78712-1224, USA.
| | | | - Ron M Levy
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
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Tang Z, Chen SH, Chang CEA. Transient States and Barriers from Molecular Simulations and the Milestoning Theory: Kinetics in Ligand-Protein Recognition and Compound Design. J Chem Theory Comput 2020; 16:1882-1895. [PMID: 32031801 DOI: 10.1021/acs.jctc.9b01153] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
This study presents a novel computational approach to study molecular recognition and binding kinetics for drug-like compounds dissociating from a flexible protein system. The intermediates and their free energy profile during ligand association and dissociation processes control ligand-protein binding kinetics and bring a more complete picture of ligand-protein binding. The method applied the milestoning theory to extract kinetics and thermodynamics information from running short classical molecular dynamics (MD) simulations for frames from a given dissociation path. High-dimensional ligand-protein motions (3N-6 degrees of freedom) during ligand dissociation were reduced by use of principal component modes for assigning more than 100 milestones, and classical MD runs were allowed to travel multiple milestones to efficiently obtain ensemble distribution of initial structures for MD simulations and estimate the transition time and rate during ligand traveling between milestones. We used five pyrazolourea ligands and cyclin-dependent kinase 8 with cyclin C (CDK8/CycC) as our model system as well as metadynamics and a pathway search method to sample dissociation pathways. With our strategy, we constructed the free energy profile for highly mobile biomolecular systems. The computed binding free energy and residence time correctly ranked the pyrazolourea ligand series, in agreement with experimental data. Guided by a barrier of a ligand passing an αC helix and activation loop, we introduced one hydroxyl group to parent compounds to design our ligands with increased residence time and validated our prediction by experiments. This work provides a novel and robust approach to investigate dissociation kinetics of large and flexible systems for understanding unbinding mechanisms and designing new small-molecule drugs with desired binding kinetics.
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Affiliation(s)
- Zhiye Tang
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
| | - Si-Han Chen
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
| | - Chia-En A Chang
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
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43
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Wolfe DK, Persichetti JR, Sharma AK, Hudson PS, Woodcock HL, O'Brien EP. Hierarchical Markov State Model Building to Describe Molecular Processes. J Chem Theory Comput 2020; 16:1816-1826. [PMID: 32011146 DOI: 10.1021/acs.jctc.9b00955] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.
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Affiliation(s)
| | | | - Ajeet K Sharma
- Department of Physics, Indian Institute of Technology, Jammu 181221, India
| | - Phillip S Hudson
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
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44
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Wei W, Elber R. ScMile: A Script to Investigate Kinetics with Short Time Molecular Dynamics Trajectories and the Milestoning Theory. J Chem Theory Comput 2020; 16:860-874. [PMID: 31922745 PMCID: PMC7031965 DOI: 10.1021/acs.jctc.9b01030] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Studies of complex and rare events in condensed phase systems continue to attract considerable attention. Milestoning is a useful theory and algorithm to investigate the long-time dynamics of activated molecular events. It is based on launching a large number of short trajectories and statistical analysis of the outcome. The implementation of the theory in a computer script is described that enables more efficient Milestoning calculation, reducing user time and errors, and automating a significant fraction of the algorithm. The script exploits a molecular dynamics engine, which at present is NAMD, to run the short trajectories. However, since the script is external to the engine, the script can be easily adapted to different molecular dynamics codes. The outcomes of the short trajectories are analyzed to obtain a kinetic and thermodynamic description of the entire process. While many examples of Milestoning were published in the past, we provide two simple examples (a conformational transition of alanine dipeptide in a vacuum and aqueous solution) to illustrate the use of the script.
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Affiliation(s)
- Wei Wei
- Oden Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
- Department of Chemistry , The University of Texas at Austin , Austin , Texas 78712 , United States
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45
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Lauricella M, Chiodo L, Ciccotti G, Albinati A. Ab initio accelerated molecular dynamics study of the hydride ligands in the ruthenium complex: Ru(H 2) 2H 2(P(C 5H 9) 3) 2. Phys Chem Chem Phys 2019; 21:25247-25257. [PMID: 31697300 DOI: 10.1039/c9cp03776d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dihydrogen complex Ru(H2)2H2(P(C5H9)3)2 has been investigated, via ab initio accelerated molecular dynamics, to elucidate the H ligands dynamics and possible reaction paths for H2/H exchange. We have characterized the free energy landscape associated with the H atoms positional exchange around the Ru centre. From the free energy landscape, we have been able to estimate a barrier of 6 kcal mol-1 for the H2/H exchange process. We have also observed a trihydrogen intermediate as a passing state along some of the possible reaction pathways.
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Affiliation(s)
- Marco Lauricella
- Istituto per le Applicazioni del Calcolo IAC-CNR, Via dei Taurini 19, 00185, Rome, Italy
| | - Letizia Chiodo
- Department of Engineering, Campus Bio-Medico University of Rome, Via Álvaro del Portillo 21, 00128, Rome, Italy.
| | - Giovanni Ciccotti
- Istituto per le Applicazioni del Calcolo IAC-CNR, Via dei Taurini 19, 00185, Rome, Italy and Physics Department, University of Rome La Sapienza, Ple. A. Moro 5, 00185 Roma, Italy and School of Physics, University College of Dublin, Belfield, Dublin 4, Ireland
| | - Alberto Albinati
- Chemistry Department, Milan University, Via C. Golgi 19, 20133, Milan, Italy
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Fathizadeh A, Kogan M, Anderson CM, Webb LJ, Elber R. Defect-Assisted Permeation Through a Phospholipid Membrane: Experimental and Computational Study of the Peptide WKW. J Phys Chem B 2019; 123:6792-6798. [PMID: 31304755 PMCID: PMC6687544 DOI: 10.1021/acs.jpcb.9b05414] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We investigate membrane permeation by the peptide WKW that is amidated at its C-terminus and therefore carries a positive charge of +2. To facilitate an efficient calculation, we introduce a novel set of simple coarse variables that measure permeation depth and membrane distortion. The phospholipid head groups shift toward the center of the membrane, following the permeating peptide, and create a defect that assists permeation. The Milestoning algorithm was used in the new coarse space to compute the free-energy profile and the mean first passage time. The barrier was lower than expected from a simple continuum estimate. This behavior is consistent with the known behavior of positively charged cell-penetrating peptides, and is explained by a detailed mechanism of defect formation and propagation revealed by the simulations.
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Affiliation(s)
- Arman Fathizadeh
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin. TX, 78712
| | - Molly Kogan
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Cari M. Anderson
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Lauren J. Webb
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin. TX, 78712
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
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47
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Lee CT, Moody JB, Amaro RE, McCammon JA, Holst MJ. The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. ASSOCIATION FOR COMPUTING MACHINERY 2019; 45:28. [PMID: 31474782 PMCID: PMC6716611 DOI: 10.1145/3321515] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2017] [Accepted: 03/01/2019] [Indexed: 06/10/2023]
Abstract
We introduce CASC: a new, modern, and header-only C++ library which provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata aware decimation algorithm which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.
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Affiliation(s)
- Christopher T Lee
- Department of Chemistry and Biochemistry, University of California San Diego
| | - John B Moody
- ViaSat, Inc. Carlsbad-Bldg 10-2063, 6155 El Camino Real, Carlsbad, CA 92009
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, University of California San Diego
| | - Michael J Holst
- Department of Mathematics, University of California San Diego
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Ernst N, Fackeldey K, Volkamer A, Opatz O, Weber M. Computation of temperature-dependent dissociation rates of metastable protein–ligand complexes. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1610949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Natalia Ernst
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
| | - Konstantin Fackeldey
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
- Institute for Mathematics, Technical University Berlin (TUB), Berlin, Germany
| | - Andrea Volkamer
- In silico Toxicology Group, Institute of Physiology, Charité Universittsmedizin Berlin, Berlin, Germany
| | - Oliver Opatz
- Center for Space Medicine Berlin, Institute of Physiology, Charité Universittsmedizin Berlin, Berlin, Germany
| | - Marcus Weber
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
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49
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Grazioli G, Roy S, Butts CT. Predicting Reaction Products and Automating Reactive Trajectory Characterization in Molecular Simulations with Support Vector Machines. J Chem Inf Model 2019; 59:2753-2764. [DOI: 10.1021/acs.jcim.9b00134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gianmarc Grazioli
- California Institute for Telecommunications and Information Technology, University of California, Irvine, California 92697, United States
- Department of Chemistry, University of California, Irvine, California 92697, United States
| | - Saswata Roy
- Department of Chemistry, University of California, Irvine, California 92697, United States
| | - Carter T. Butts
- California Institute for Telecommunications and Information Technology, University of California, Irvine, California 92697, United States
- Departments of Sociology, Statistics, and EECS, University of California, Irvine, California 92697, United States
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50
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Chakraborty D, Wales DJ. Dynamics of an adenine-adenine RNA conformational switch from discrete path sampling. J Chem Phys 2019; 150:125101. [DOI: 10.1063/1.5070152] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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