1
|
Zia SR, Coricello A, Bottegoni G. Increased throughput in methods for simulating protein ligand binding and unbinding. Curr Opin Struct Biol 2024; 87:102871. [PMID: 38924980 DOI: 10.1016/j.sbi.2024.102871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2024] [Revised: 06/03/2024] [Accepted: 06/04/2024] [Indexed: 06/28/2024]
Abstract
By incorporating full flexibility and enabling the quantification of crucial parameters such as binding free energies and residence times, methods for investigating protein-ligand binding and unbinding via molecular dynamics provide details on the involved mechanisms at the molecular level. While these advancements hold promise for impacting drug discovery, a notable drawback persists: their relatively time-consuming nature limits throughput. Herein, we survey recent implementations which, employing a blend of enhanced sampling techniques, a clever choice of collective variables, and often machine learning, strive to enhance the efficiency of new and previously reported methods without compromising accuracy. Particularly noteworthy is the validation of these methods that was often performed on systems mirroring real-world drug discovery scenarios.
Collapse
Affiliation(s)
- Syeda Rehana Zia
- Department of Paediatrics and Child Health, Faculty of Health Sciences, Medical College, The Aga Khan University, Karachi, 74800, Pakistan
| | - Adriana Coricello
- Department of Biomolecular Sciences, University of Urbino Carlo Bo, Urbino, 61029, Italy.
| | - Giovanni Bottegoni
- Department of Biomolecular Sciences, University of Urbino Carlo Bo, Urbino, 61029, Italy; Institute of Clinical Sciences, College of Medical and Dental Sciences, University of Birmingham, B15 2TT, United Kingdom.
| |
Collapse
|
2
|
Spencer RKW, Smirnova YG, Soleimani A, Müller M. Transient pores in hemifusion diaphragms. Biophys J 2024:S0006-3495(24)00392-8. [PMID: 38867448 DOI: 10.1016/j.bpj.2024.06.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Revised: 05/07/2024] [Accepted: 06/07/2024] [Indexed: 06/14/2024] Open
Abstract
Exchange of material across two membranes, as in the case of synaptic neurotransmitter release from a vesicle, involves the formation and poration of a hemifusion diaphragm (HD). The nontrivial geometry of the HD leads to environment-dependent control, regarding the stability and dynamics of the pores required for this kind of exocytosis. This work combines particle simulations, field-based calculations, and phenomenological modeling to explore the factors influencing the stability, dynamics, and possible control mechanisms of pores in HDs. We find that pores preferentially form at the HD rim, and that their stability is sensitive to a number of factors, including the three line tensions, membrane tension, HD size, and the ability of lipids to "flip-flop" across leaflets. Along with a detailed analysis of these factors, we discuss ways that vesicles or cells may use them to open and close pores and thereby quickly and efficiently transport material.
Collapse
Affiliation(s)
- Russell K W Spencer
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| | - Yuliya G Smirnova
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany; Technische Universität Dortmund, Dortmund, Germany
| | - Alireza Soleimani
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| |
Collapse
|
3
|
Niu SJ, Ren FD. Finite Temperature String with Order Parameter as Collective Variables for Molecular Crystal: A Case of Polymorphic Transformation of TNT under External Electric Field. Molecules 2024; 29:2549. [PMID: 38893427 PMCID: PMC11173574 DOI: 10.3390/molecules29112549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2024] [Revised: 05/08/2024] [Accepted: 05/08/2024] [Indexed: 06/21/2024] Open
Abstract
An external electric field is an effective tool to induce the polymorphic transformation of molecular crystals, which is important practically in the chemical, material, and energy storage industries. However, the understanding of this mechanism is poor at the molecular level. In this work, two types of order parameters (OPs) were constructed for the molecular crystal based on the intermolecular distance, bond orientation, and molecular orientation. Using the K-means clustering algorithm for the sampling of OPs based on the Euclidean distance and density weight, the polymorphic transformation of TNT was investigated using a finite temperature string (FTS) under external electric fields. The potential of mean force (PMF) was obtained, and the essence of the polymorphic transformation between o-TNT and m-TNT was revealed, which verified the effectiveness of the FTS method based on K-means clustering to OPs. The differences in PMFs between the o-TNT and transition state were decreased under external electric fields in comparison with those in no field. The fields parallel to the c-axis obviously affected the difference in PMF, and the relationship between the changes in PMFs and field strengths was found. Although the external electric field did not promote the convergence, the time of the polymorphic transformation was reduced under the external electric field in comparison to its absence. Moreover, under the external electric field, the polymorphic transformation from o-TNT to m-TNT occurred while that from m-TNT to o-TNT was prevented, which was explained by the dipole moment of molecule, relative permittivity, chemical potential difference, nucleation work and nucleation rate. This confirmed that the polymorphic transformation orientation of the molecular crystal could be controlled by the external electric field. This work provides an effective way to explore the polymorphic transformation of the molecular crystals at a molecular level, and it is useful to control the production process and improve the performance of energetic materials by using the external electric fields.
Collapse
Affiliation(s)
- Shi-Jie Niu
- School of Chemistry and Chemical Engineering, North University of China, Taiyuan 030051, China;
- School of Management, Wuhan Polytechnic University, Wuhan 430040, China
| | - Fu-De Ren
- School of Chemistry and Chemical Engineering, North University of China, Taiyuan 030051, China;
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Barragan AM, Ghaby K, Pond MP, Roux B. Computational Investigation of the Covalent Inhibition Mechanism of Bruton's Tyrosine Kinase by Ibrutinib. J Chem Inf Model 2024; 64:3488-3502. [PMID: 38546820 DOI: 10.1021/acs.jcim.4c00023] [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: 04/23/2024]
Abstract
Covalent inhibitors represent a promising class of therapeutic compounds. Nonetheless, rationally designing covalent inhibitors to achieve a right balance between selectivity and reactivity remains extremely challenging. To better understand the covalent binding mechanism, a computational study is carried out using the irreversible covalent inhibitor of Bruton tyrosine kinase (BTK) ibrutinib as an example. A multi-μs classical molecular dynamics trajectory of the unlinked inhibitor is generated to explore the fluctuations of the compound associated with the kinase binding pocket. Then, the reaction pathway leading to the formation of the covalent bond with the cysteine residue at position 481 via a Michael addition is determined using the string method in collective variables on the basis of hybrid quantum mechanical-molecular mechanical (QM/MM) simulations. The reaction pathway shows a strong correlation between the covalent bond formation and the protonation/deprotonation events taking place sequentially in the covalent inhibition reaction, consistent with a 3-step reaction with transient thiolate and enolates intermediate states. Two possible atomistic mechanisms affecting deprotonation/protonation events from the thiolate to the enolate intermediate were observed: a highly correlated direct pathway involving proton transfer to the Cα of the acrylamide warhead from the cysteine involving one or a few water molecules and a more indirect pathway involving a long-lived enolate intermediate state following the escape of the proton to the bulk solution. The results are compared with experiments by simulating the long-time kinetics of the reaction using kinetic modeling.
Collapse
Affiliation(s)
- Angela M Barragan
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States
| | - Kyle Ghaby
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States
| | - Matthew P Pond
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois 60637, United States
| |
Collapse
|
6
|
Ding Y, Qiang B, Chen Q, Liu Y, Zhang L, Liu Z. Exploring Chemical Reaction Space with Machine Learning Models: Representation and Feature Perspective. J Chem Inf Model 2024; 64:2955-2970. [PMID: 38489239 DOI: 10.1021/acs.jcim.4c00004] [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: 03/17/2024]
Abstract
Chemical reactions serve as foundational building blocks for organic chemistry and drug design. In the era of large AI models, data-driven approaches have emerged to innovate the design of novel reactions, optimize existing ones for higher yields, and discover new pathways for synthesizing chemical structures comprehensively. To effectively address these challenges with machine learning models, it is imperative to derive robust and informative representations or engage in feature engineering using extensive data sets of reactions. This work aims to provide a comprehensive review of established reaction featurization approaches, offering insights into the selection of representations and the design of features for a wide array of tasks. The advantages and limitations of employing SMILES, molecular fingerprints, molecular graphs, and physics-based properties are meticulously elaborated. Solutions to bridge the gap between different representations will also be critically evaluated. Additionally, we introduce a new frontier in chemical reaction pretraining, holding promise as an innovative yet unexplored avenue.
Collapse
Affiliation(s)
- Yuheng Ding
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| | - Bo Qiang
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| | - Qixuan Chen
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| | - Yiqiao Liu
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| | - Liangren Zhang
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| | - Zhenming Liu
- Department of Pharmaceutical Science, Peking University, Beijing 100191, China
| |
Collapse
|
7
|
Spencer RKW, Santos-Pérez I, Rodríguez-Renovales I, Martinez Galvez JM, Shnyrova AV, Müller M. Membrane fission via transmembrane contact. Nat Commun 2024; 15:2793. [PMID: 38555357 PMCID: PMC10981662 DOI: 10.1038/s41467-024-47122-w] [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: 05/10/2023] [Accepted: 03/20/2024] [Indexed: 04/02/2024] Open
Abstract
Division of intracellular organelles often correlates with additional membrane wrapping, e.g., by the endoplasmic reticulum or the outer mitochondrial membrane. Such wrapping plays a vital role in proteome and lipidome organization. However, how an extra membrane impacts the mechanics of the division has not been investigated. Here we combine fluorescence and cryo-electron microscopy experiments with self-consistent field theory to explore the stress-induced instabilities imposed by membrane wrapping in a simple double-membrane tubular system. We find that, at physiologically relevant conditions, the outer membrane facilitates an alternative pathway for the inner-tube fission through the formation of a transient contact (hemi-fusion) between both membranes. A detailed molecular theory of the fission pathways in the double membrane system reveals the topological complexity of the process, resulting both in leaky and leakless intermediates, with energies and topologies predicting physiological events.
Collapse
Affiliation(s)
- Russell K W Spencer
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| | - Isaac Santos-Pérez
- Electron Microscopy and Crystallography Platform, Center for Cooperative Research in Biosciences (CIC bioGUNE), Derio, Spain
| | - Izaro Rodríguez-Renovales
- BREM Basque Resource for Electron Microscopy, Leioa, Spain
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain
| | - Juan Manuel Martinez Galvez
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain
- Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain
| | - Anna V Shnyrova
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain.
- Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain.
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| |
Collapse
|
8
|
McFarlane NR, Harvey JN. Exploration of biochemical reactivity with a QM/MM growing string method. Phys Chem Chem Phys 2024; 26:5999-6007. [PMID: 38293892 DOI: 10.1039/d3cp05772k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2024]
Abstract
In this work, we have implemented the single-ended growing string method using a hybrid internal/Cartesian coordinate scheme within our in-house QM/MM package, QoMMMa, representing the first implementation of the growing string method in the QM/MM framework. The goal of the implementation was to facilitate generation of QM/MM reaction pathways with minimal user input, and also to improve the quality of the pathways generated as compared to the widely used adiabatic mapping approach. We have validated the algorithm against a reaction which has been studied extensively in previous computational investigations - the Claisen rearrangement catalysed by chorismate mutase. The nature of the transition state and the height of the barrier was predicted well using our algorithm, where more than 88% of the pathways generated were deemed to be of production quality. Directly compared to using adiabatic mapping, we found that while our QM/MM single-ended growing string method is slightly less efficient, it readily produces reaction pathways with fewer discontinuites and thus minimises the need for involved remapping of unsatisfactory energy profiles.
Collapse
Affiliation(s)
- Neil R McFarlane
- Department of Chemistry, KU Leuven, B-3001 Leuven, Celestijnenlaan 200f, 2404, Belgium.
| | - Jeremy N Harvey
- Department of Chemistry, KU Leuven, B-3001 Leuven, Celestijnenlaan 200f, 2404, Belgium.
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Oh M, da Hora GCA, Swanson JMJ. tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation. J Chem Theory Comput 2023; 19:8886-8900. [PMID: 37943658 DOI: 10.1021/acs.jctc.3c00526] [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: 11/12/2023]
Abstract
Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artifacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings and that data reweighting is required to avoid deviations in the translational CV.
Collapse
Affiliation(s)
- Myongin Oh
- Department of Chemistry, University of Utah, 315 South 1400 East, Rm 2020, Salt Lake City, Utah 84112, United States
| | - Gabriel C A da Hora
- Department of Chemistry, University of Utah, 315 South 1400 East, Rm 2020, Salt Lake City, Utah 84112, United States
| | - Jessica M J Swanson
- Department of Chemistry, University of Utah, 315 South 1400 East, Rm 2020, Salt Lake City, Utah 84112, United States
| |
Collapse
|
11
|
Zhang Y, Xu C, Lan Z. Automated Exploration of Reaction Networks and Mechanisms Based on Metadynamics Nanoreactor Simulations. J Chem Theory Comput 2023. [PMID: 38031422 DOI: 10.1021/acs.jctc.3c00752] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
We developed an automated approach to construct a complex reaction network and explore the reaction mechanisms for numerous reactant molecules by integrating several theoretical approaches. Nanoreactor-type molecular dynamics was used to generate possible chemical reactions, in which the metadynamics was used to overcome the reaction barriers, and the semiempirical GFN2-xTB method was used to reduce the computational cost. Reaction events were identified from trajectories using the hidden Markov model based on the evolution of the molecular connectivity. This provided the starting points for further transition-state searches at the electronic structure levels of density functional theory to obtain the reaction mechanism. Finally, the entire reaction network containing multiple pathways was built. The feasibility and efficiency of the automated construction of the reaction network were investigated using the HCHO and NH3 biomolecular reaction and the reaction network for a multispecies system comprising dozens of HCN and H2O molecules. The results indicated that the proposed approach provides a valuable and effective tool for the automated exploration of the reaction networks.
Collapse
Affiliation(s)
- Yutai Zhang
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Chao Xu
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Zhenggang Lan
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| |
Collapse
|
12
|
Oh M, da Hora GCA, Swanson JMJ. tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.16.553477. [PMID: 37645884 PMCID: PMC10462029 DOI: 10.1101/2023.08.16.553477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artefacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings, and that data reweighting is required to avoid deviations in the translational CV.
Collapse
|
13
|
Buigues P, Gehrke S, Badaoui M, Dudas B, Mandana G, Qi T, Bottegoni G, Rosta E. Investigating the Unbinding of Muscarinic Antagonists from the Muscarinic 3 Receptor. J Chem Theory Comput 2023; 19:5260-5272. [PMID: 37458730 PMCID: PMC10413856 DOI: 10.1021/acs.jctc.3c00023] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Indexed: 08/09/2023]
Abstract
Patient symptom relief is often heavily influenced by the residence time of the inhibitor-target complex. For the human muscarinic receptor 3 (hMR3), tiotropium is a long-acting bronchodilator used in conditions such as asthma or chronic obstructive pulmonary disease (COPD). The mechanistic insights into this inhibitor remain unclear; specifically, the elucidation of the main factors determining the unbinding rates could help develop the next generation of antimuscarinic agents. Using our novel unbinding algorithm, we were able to investigate ligand dissociation from hMR3. The unbinding paths of tiotropium and two of its analogues, N-methylscopolamin and homatropine methylbromide, show a consistent qualitative mechanism and allow us to identify the structural bottleneck of the process. Furthermore, our machine learning-based analysis identified key roles of the ECL2/TM5 junction involved in the transition state. Additionally, our results point to relevant changes at the intracellular end of the TM6 helix leading to the ICL3 kinase domain, highlighting the closest residue L482. This residue is located right between two main protein binding sites involved in signal transduction for hMR3's activation and regulation. We also highlight key pharmacophores of tiotropium that play determining roles in the unbinding kinetics and could aid toward drug design and lead optimization.
Collapse
Affiliation(s)
- Pedro
J. Buigues
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Sascha Gehrke
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Magd Badaoui
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Balint Dudas
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Gaurav Mandana
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Tianyun Qi
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| | - Giovanni Bottegoni
- Dipartimento
di Scienze Biomolecolari (DISB), University
of Urbino, Urbino Piazza Rinascimento, 6, Urbino 61029, Italy
- Institute
of Clinical Sciences, University of Birmingham, Edgbaston, B15 2TT Birmingham, United Kingdom
| | - Edina Rosta
- Department
of Physics and Astronomy, University College
London, London WC1E 6BT, United
Kingdom
| |
Collapse
|
14
|
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.
Collapse
Affiliation(s)
- Chung F Wong
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, MO, USA
| |
Collapse
|
15
|
Buckner J, Liu X, Chakravorty A, Wu Y, Cervantes LF, Lai TT, Brooks CL. pyCHARMM: Embedding CHARMM Functionality in a Python Framework. J Chem Theory Comput 2023; 19:3752-3762. [PMID: 37267404 PMCID: PMC10504603 DOI: 10.1021/acs.jctc.3c00364] [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] [Indexed: 06/04/2023]
Abstract
CHARMM is rich in methodology and functionality as one of the first programs addressing problems of molecular dynamics and modeling of biological macromolecules and their partners, e.g., small molecule ligands. When combined with the highly developed CHARMM parameters for proteins, nucleic acids, small molecules, lipids, sugars, and other biologically relevant building blocks, and the versatile CHARMM scripting language, CHARMM has been a trendsetting platform for modeling studies of biological macromolecules. To further enhance the utility of accessing and using CHARMM functionality in increasingly complex workflows associated with modeling biological systems, we introduce pyCHARMM, Python bindings, functions, and modules to complement and extend the extensive set of modeling tools and methods already available in CHARMM. These include access to CHARMM function-generated variables associated with the system (psf), coordinates, velocities and forces, atom selection variables, and force field related parameters. The ability to augment CHARMM forces and energies with energy terms or methods derived from machine learning or other sources, written in Python, CUDA, or OpenCL and expressed as Python callable routines is introduced together with analogous functions callable during dynamics calculations. Integration of Python-based graphical engines for visualization of simulation models and results is also accessible. Loosely coupled parallelism is available for workflows such as free energy calculations, using MBAR/TI approaches or high-throughput multisite λ-dynamics (MSλD) free energy methods, string path optimization calculations, replica exchange, and molecular docking with a new Python-based CDOCKER module. CHARMM accelerated platform kernels through the CHARMM/OpenMM API, CHARMM/DOMDEC, and CHARMM/BLaDE API are also readily integrated into this Python framework. We anticipate that pyCHARMM will be a robust platform for the development of comprehensive and complex workflows utilizing Python and its extensive functionality as well as an optimal platform for users to learn molecular modeling methods and practices within a Python-friendly environment such as Jupyter Notebooks.
Collapse
Affiliation(s)
- Joshua Buckner
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | - Xiaorong Liu
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | | | - Yujin Wu
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | - Luis F. Cervantes
- Department of Medicinal Chemistry, University of Michigan, Ann Arbor, MI
| | - Thanh T. Lai
- Biophysics Program, University of Michigan, Ann Arbor, MI
| | - Charles L. Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, MI
- Biophysics Program, University of Michigan, Ann Arbor, MI
| |
Collapse
|
16
|
Chen H, Roux B, Chipot C. Discovering Reaction Pathways, Slow Variables, and Committor Probabilities with Machine Learning. J Chem Theory Comput 2023. [PMID: 37224455 DOI: 10.1021/acs.jctc.3c00028] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
A significant challenge faced by atomistic simulations is the difficulty, and often impossibility, to sample the transitions between metastable states of the free-energy landscape associated with slow molecular processes. Importance-sampling schemes represent an appealing option to accelerate the underlying dynamics by smoothing out the relevant free-energy barriers, but require the definition of suitable reaction-coordinate (RC) models expressed in terms of compact low-dimensional sets of collective variables (CVs). While most computational studies of slow molecular processes have traditionally relied on educated guesses based on human intuition to reduce the dimensionality of the problem at hand, a variety of machine-learning (ML) algorithms have recently emerged as powerful alternatives to discover meaningful CVs capable of capturing the dynamics of the slowest degrees of freedom. Considering a simple paradigmatic situation in which the long-time dynamics is dominated by the transition between two known metastable states, we compare two variational data-driven ML methods based on Siamese neural networks aimed at discovering a meaningful RC model─the slowest decorrelating CV of the molecular process, and the committor probability to first reach one of the two metastable states. One method is the state-free reversible variational approach for Markov processes networks (VAMPnets), or SRVs─the other, inspired by the transition path theory framework, is the variational committor-based neural networks, or VCNs. The relationship and the ability of these methodologies to discover the relevant descriptors of the slow molecular process of interest are illustrated with a series of simple model systems. We also show that both strategies are amenable to importance-sampling schemes through an appropriate reweighting algorithm that approximates the kinetic properties of the transition.
Collapse
Affiliation(s)
- Haochuan Chen
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, 60637, United States
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, 60637, United States
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| |
Collapse
|
17
|
Giese TJ, York DM. Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations. J Chem Phys 2023; 158:174105. [PMID: 37125722 PMCID: PMC10154067 DOI: 10.1063/5.0147218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 04/17/2023] [Indexed: 05/02/2023] Open
Abstract
We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.
Collapse
Affiliation(s)
- Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| |
Collapse
|
18
|
Dasgupta N, Ho TA, Rempe SB, Wang Y. Hydrophobic Nanoconfinement Enhances CO 2 Conversion to H 2CO 3. J Phys Chem Lett 2023; 14:1693-1701. [PMID: 36757174 DOI: 10.1021/acs.jpclett.3c00124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Understanding the formation of H2CO3 in water from CO2 is important in environmental and industrial processes. Although numerous investigations have studied this reaction, the conversion of CO2 to H2CO3 in nanopores, and how it differs from that in bulk water, has not been understood. We use ReaxFF metadynamics molecular simulations to demonstrate striking differences in the free energy of CO2 conversion to H2CO3 in bulk and nanoconfined aqueous environments. We find that nanoconfinement not only reduces the energy barrier but also reverses the reaction from endothermic in bulk water to exothermic in nanoconfined water. Also, charged intermediates are observed more often under nanoconfinement than in bulk water. Stronger solvation and more favorable proton transfer with increasing nanoconfinement enhance the thermodynamics and kinetics of the reaction. Our results provide a detailed mechanistic understanding of an important step in the carbonation process, which depends intricately on confinement, surface chemistry, and CO2 concentration.
Collapse
Affiliation(s)
- Nabankur Dasgupta
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Tuan A Ho
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Susan B Rempe
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Yifeng Wang
- Nuclear Waste Disposal Research and Analysis Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| |
Collapse
|
19
|
Kulshrestha A, Maurya S, Gupta T, Roy R, Punnathanam SN, Ayappa KG. Conformational Flexibility Is a Key Determinant for the Lytic Activity of the Pore-Forming Protein, Cytolysin A. J Phys Chem B 2023; 127:69-84. [PMID: 36542809 DOI: 10.1021/acs.jpcb.2c05785] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Several bacterial infections are mediated by pore-forming toxins (PFTs), a subclass of proteins that oligomerize on mammalian cell membranes forming lytic nanopores. Cytolysin A (ClyA), an α-PFT, undergoes a dramatic conformational change restructuring its two membrane-binding motifs (the β-tongue and the N-terminus helix), during pore formation. A complete molecular picture for this key transition and the driving force behind the secondary structure change upon membrane binding remain elusive. Using all-atom molecular dynamics (MD) simulations of the ClyA monomer and string method based free energy computations with path collective variables, we illustrate that an unfolded β-tongue motif is an on-pathway intermediate during the transition to the helix-turn-helix motif of the protomer. An aggregate of 28 μs of all-atom thermal unfolding MD simulations of wild-type ClyA and its single point mutants reveal that the membrane-binding motifs of the ClyA protein display high structural flexibility in water. However, point mutations in these motifs lead to a distinct reduction in the flexibility, especially in the β-tongue, thereby stabilizing the pretransition secondary structure. Resistance to unfolding was further corroborated by MD simulations of the β-tongue mutant motif in the membrane. Combined with the thermal unfolding simulations, we posit that the β-tongue as well as N-terminal mutants that lower the tendency to unfold and disorder the β-tongue are detrimental to pore formation by ClyA and its lytic activity. Erythrocyte turbidity and vesicle leakage assays indeed reveal a loss of activity for the β-tongue mutant, and delayed kinetics for the N-terminus mutants. On the other hand, a point mutation in the extracellular domain that did not abrogate lytic activity displayed similar unfolding characteristics as the wild type. Thus, attenuation of conformational flexibility in membrane-binding motifs correlates with reduced lytic and leakage activity. Combined with secondary structure changes observed in the membrane bound states, our study shows that the tendency to unfold in the β-tongue region is a critical step in the conformational transition and bistability of the ClyA protein and mutants that disrupt this tendency reduced pore formation. Overall, our finding suggests that inherent flexibility in the protein could play a wider and hitherto unrecognized role in membrane-mediated conformational transitions of PFTs and other membrane protein transformations.
Collapse
Affiliation(s)
- Avijeet Kulshrestha
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - Satyaghosh Maurya
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - Twinkle Gupta
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - Rahul Roy
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India.,Center for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - Sudeep N Punnathanam
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - K Ganapathy Ayappa
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
| |
Collapse
|
20
|
Persichetti JR, Jiang Y, Hudson PS, O'Brien EP. Modeling Ensembles of Enzyme Reaction Pathways with Hi-MSM Reveals the Importance of Accounting for Pathway Diversity. J Phys Chem B 2022; 126:9748-9758. [PMID: 36383711 DOI: 10.1021/acs.jpcb.2c04496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Conventional quantum mechanical-molecular mechanics (QM/MM) simulation approaches for modeling enzyme reactions often assume that there is one dominant reaction pathway and that this pathway can be sampled starting from an X-ray structure of the enzyme. These assumptions reduce computational cost; however, their validity has not been extensively tested. This is due in part to the lack of a rigorous formalism for integrating disparate pathway information from dynamical QM/MM calculations. Here, we present a way to model ensembles of reaction pathways efficiently using a divide-and-conquer strategy through Hierarchical Markov State Modeling (Hi-MSM). This approach allows information on multiple, distinct pathways to be incorporated into a chemical kinetic model, and it allows us to test these two assumptions. Applying Hi-MSM to the reaction carried out by dihydrofolate reductase (DHFR) we find (i) there are multiple, distinct pathways significantly contributing to the overall flux of the reaction that the conventional approach does not identify and (ii) that the conventional approach does not identify the dominant reaction pathway. Thus, both assumptions underpinning the conventional approach are violated. Since DHFR is a relatively small enzyme, and configuration space scales exponentially with protein size, accounting for multiple reaction pathways is likely to be necessary for most enzymes.
Collapse
|
21
|
Giese TJ, Zeng J, York DM. Multireference Generalization of the Weighted Thermodynamic Perturbation Method. J Phys Chem A 2022; 126:8519-8533. [PMID: 36301936 PMCID: PMC9771595 DOI: 10.1021/acs.jpca.2c06201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.
Collapse
Affiliation(s)
- Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Jinzhe Zeng
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| |
Collapse
|
22
|
Schmid F. Understanding and Modeling Polymers: The Challenge of Multiple Scales. ACS POLYMERS AU 2022. [DOI: 10.1021/acspolymersau.2c00049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128Mainz, Germany
| |
Collapse
|
23
|
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.
Collapse
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
| |
Collapse
|
24
|
Abstract
This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.
Collapse
Affiliation(s)
- Steven D Schwartz
- Department of Chemistry and Biochemistry University of Arizona Tucson, Arizona 85721, United States
| |
Collapse
|
25
|
Kulshrestha A, Punnathanam SN, Ayappa KG. Finite temperature string method with umbrella sampling using path collective variables: application to secondary structure change in a protein. SOFT MATTER 2022; 18:7593-7603. [PMID: 36165347 DOI: 10.1039/d2sm00888b] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The transition of an α-helix to a β-sheet in proteins is among the most complex conformational changes seen in biomolecular systems. Due to long time scales involved in the transition, it is challenging to study such protein conformational changes using direct molecular dynamics simulations. This limitation is typically overcome using an indirect approach wherein one computes the free energy landscape associated with the transition. Computation of free energy landscapes, however, requires a suitable set of collective variables that describe the transition. In this work, we demonstrate the use of path collective variables [D. Branduardi, F. L. Gervasio and M. Parrinello, J. Chem. Phys., 2007, 126, 054103] and combine it with the finite temperature string (FTS) method [E. Weinan, W. Ren and E. Vanden-Eijnden, J. Phys. Chem. B, 2005, 109, 6688-6693] to determine the molecular mechanisms involved during the structural transition of the mini G-protein from an α-helix to a β-hairpin. The transition from the α-helix proceeds via unfolding of the terminal residues, giving rise to a β-turn unfolded intermediate to eventually form the β-hairpin. Our proposed algorithm uses umbrella sampling simulations to simulate images along the string and the weighted histogram analysis to compute the free energy along the computed transition path. This work demonstrates that the string method in combination with path collective variables can be exploited to study complex protein conformational changes such as a complete change in the secondary structure.
Collapse
Affiliation(s)
- Avijeet Kulshrestha
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, 560012, India.
| | - Sudeep N Punnathanam
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, 560012, India.
| | - K Ganapathy Ayappa
- Department of Chemical Engineering, Indian Institute of Science, Bangalore, 560012, India.
| |
Collapse
|
26
|
Geiger J, Settels V, Deglmann P, Schäfer A, Bergeler M. Automated input structure generation for single-ended reaction path optimizations. J Comput Chem 2022; 43:1662-1674. [PMID: 35866245 DOI: 10.1002/jcc.26969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 06/21/2022] [Accepted: 06/22/2022] [Indexed: 11/05/2022]
Abstract
The exploration of a reaction network requires highly automated workflows to avoid error-prone and time-consuming manual steps. In this respect, a major bottleneck is the search for transition-state (TS) structures, which frequently fails and, therefore, makes (manual) revision necessary. In this work, we present a technique for obtaining suitable input structures for automated TS searches based on single-ended reaction path optimization algorithms, which makes subsequent TS searches via this method significantly more robust. First, possible input structures are generated based on the spatial alignment of the reactants. The appropriate orientation of reacting groups is achieved via stepwise rotations along selected torsional degrees of freedom. Second, a ranking of the obtained structures is performed according to selected geometric criteria. The main goals are to properly align the reactive atoms, to avoid hindrance within the reaction channel and to resolve steric clashes between the reactants. The developed procedure has been carefully tested on a variety of examples and provides suitable input structures for TS searches within seconds. The method is in daily use in an industrial setting.
Collapse
Affiliation(s)
- Julian Geiger
- Institute of Chemical Research of Catalonia (ICIQ), The Barcelona Institute of Science and Technology, Tarragona, Spain
| | | | | | | | - Maike Bergeler
- Institute of Chemical Research of Catalonia (ICIQ), The Barcelona Institute of Science and Technology, Tarragona, Spain
| |
Collapse
|
27
|
Lim CC, Lai SK. Metadynamics molecular dynamics and isothermal Brownian-type molecular dynamics simulations for the chiral cluster Au 18. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:325201. [PMID: 35580583 DOI: 10.1088/1361-648x/ac709f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
In an effort to gain insight into enantiomeric transitions, their transition mechanism, time span of transitions and distribution of time spans etc, we performed molecular dynamics (MD) simulations on chiral clusters Au10, Au15and Au18, and found that viable reaction coordinates can be deduced from simulation data for enlightening the enantiomeric dynamics for Au10and Au15, but not so for Au18. The failure in translating the Au18-L ⇌ Au18-R transitions by MD simulations has been chalked up to the thermal energykBTat 300 K being much lower than energy barriers separating the enantiomers of Au18. Two simulation strategies were taken to resolve this simulation impediment. The first one uses the well-tempered metadynamics MD (MMD) simulation, and the second one adeptly applies first a somewhat crude MMD simulation to locate a highly symmetrical isomer Au18Sand subsequently employed it as initial configuration in the MD simulation. In both strategies, we work in collective variable space of lower dimensionality. The well-tempered MMD simulation tactic was carried out aiming to offer a direct verification of Au18enantiomers, while the tactic to conduct MMD/MD simulations in two consecutive simulation steps was intended to provide an indirect evidence of the existence of enantiomers of Au18given that energy barriers separating them are much higher than ca.kBTat 300 K. This second tactic, in addition to confirming indirectly Au18-L and Au18-R starting from the symmetrical cluster Au18S, the simulation results shed light also on the mechanism akin to associative/nonassociative reaction transitions.
Collapse
Affiliation(s)
- C C Lim
- Complex Liquids Laboratory, Department of Physics, National Central University, Chungli 320, Taiwan
| | - S K Lai
- Complex Liquids Laboratory, Department of Physics, National Central University, Chungli 320, Taiwan
| |
Collapse
|
28
|
Li Y, Gong H. Identifying a Feasible Transition Pathway between Two Conformational States for a Protein. J Chem Theory Comput 2022; 18:4529-4543. [PMID: 35723447 DOI: 10.1021/acs.jctc.2c00390] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Proteins usually need to transit between different conformational states to fulfill their biological functions. In the mechanistic study of such transition processes by molecular dynamics simulations, identification of the minimum free energy path (MFEP) can substantially reduce the sampling space, thus enabling rigorous thermodynamic evaluation of the process. Conventionally, the MFEP is derived by iterative local optimization from an initial path, which is typically generated by simple brute force techniques like the targeted molecular dynamics (tMD). Therefore, the quality of the initial path determines the successfulness of MFEP estimation. In this work, we propose a method to improve derivation of the initial path. Through iterative relaxation-biasing simulations in a bidirectional manner, this method can construct a feasible transition pathway connecting two known states for a protein. Evaluation on small, fast-folding proteins against long equilibrium trajectories supports the good sampling efficiency of our method. When applied to larger proteins including the catalytic domain of human c-Src kinase as well as the converter domain of myosin VI, the paths generated by our method deviate significantly from those computed with the generic tMD approach. More importantly, free energy profiles and intermediate states obtained from our paths exhibit remarkable improvements over those from tMD paths with respect to both physical rationality and consistency with a priori knowledge.
Collapse
Affiliation(s)
- Yao Li
- MOE Key Laboratory of Bioinformatics, School of Life Sciences, Tsinghua University, Beijing 100084, China.,Beijing Advanced Innovation Center for Structural Biology, Tsinghua University, Beijing 100084, China
| | - Haipeng Gong
- MOE Key Laboratory of Bioinformatics, School of Life Sciences, Tsinghua University, Beijing 100084, China.,Beijing Advanced Innovation Center for Structural Biology, Tsinghua University, Beijing 100084, China
| |
Collapse
|
29
|
Li W. Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory. J Phys Chem A 2022; 126:3797-3810. [PMID: 35670470 DOI: 10.1021/acs.jpca.2c02221] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The transition path ensemble is of special interest in reaction coordinate identification as it consists of reactive trajectories that start from the reactant state and end in the product one. As a theoretical framework for describing the transition path ensemble, the transition path theory has been introduced more than 10 years ago, and so far, its applications have only been illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curves are derived here in the space of collective variables from the transition path theory, and they are applicable to time series obtained from molecular dynamics simulations of high-dimensional systems, i.e., the position coordinates as a function of time in the transition path ensemble. The connection of the transition path theory is made to a density-weighted average flux, a quantity proposed in a previous work to appraise the relevance of a coordinate to the reaction coordinate [Li, W. J. Chem. Phys. 2022, 156, 054117]. Most importantly, as an extension of the existing quantities, time-lagged quantities such as flux and current are also proposed. The main insights and objects provided by these time-lagged quantities are illustrated in the application to the alanine peptide in vacuum.
Collapse
Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
| |
Collapse
|
30
|
Ren Y, Li W. Droplet-like Defect Annihilation Mechanisms in Hexagonal Cylinder-Forming Block Copolymers. ACS Macro Lett 2022; 11:510-516. [PMID: 35575331 DOI: 10.1021/acsmacrolett.1c00670] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The annihilation of typical individual defects in hexagonal cylinder-forming block copolymers is investigated using the self-consistent field theory (SCFT) in conjunction with the string method. Usually, defect removal in two-dimensional hexagonal patterns involves reorganizing the cylindrical domains. Unlike atoms in solid crystals, the self-assembled cylindrical domains of block copolymers are "soft". Thus, the kinetic motions of the cylindrical domains resemble liquid droplets. Dislocations in hexagonal patterns are eliminated via creating and removing cylindrical domains. Our results show that new cylindrical domains are created via either a nucleation-like process or a fission-like process, whereas excessive domains are eliminated via a fusion-like or evaporation-like process. For weakly segregated block copolymers, the nucleation-like and evaporation-like processes are preferred.
Collapse
Affiliation(s)
- Yongzhi Ren
- Key Lab of In-fiber Integrated Optics, Ministry Education of China, Harbin 150001, China
- College of Physics and Optoelectronic Engineering, Harbin Engineering University, Harbin 150001, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| |
Collapse
|
31
|
Badaoui M, Buigues PJ, Berta D, Mandana GM, Gu H, Földes T, Dickson CJ, Hornak V, Kato M, Molteni C, Parsons S, Rosta E. Combined Free-Energy Calculation and Machine Learning Methods for Understanding Ligand Unbinding Kinetics. J Chem Theory Comput 2022; 18:2543-2555. [PMID: 35195418 PMCID: PMC9097281 DOI: 10.1021/acs.jctc.1c00924] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
![]()
The
determination of drug residence times, which define the time
an inhibitor is in complex with its target, is a fundamental part
of the drug discovery process. Synthesis and experimental measurements
of kinetic rate constants are, however, expensive and time consuming.
In this work, we aimed to obtain drug residence times computationally.
Furthermore, we propose a novel algorithm to identify molecular design
objectives based on ligand unbinding kinetics. We designed an enhanced
sampling technique to accurately predict the free-energy profiles
of the ligand unbinding process, focusing on the free-energy barrier
for unbinding. Our method first identifies unbinding paths determining
a corresponding set of internal coordinates (ICs) that form contacts
between the protein and the ligand; it then iteratively updates these
interactions during a series of biased molecular dynamics (MD) simulations
to reveal the ICs that are important for the whole of the unbinding
process. Subsequently, we performed finite-temperature string simulations
to obtain the free-energy barrier for unbinding using the set of ICs
as a complex reaction coordinate. Importantly, we also aimed to enable
the further design of drugs focusing on improved residence times.
To this end, we developed a supervised machine learning (ML) approach
with inputs from unbiased “downhill” trajectories initiated
near the transition state (TS) ensemble of the string unbinding path.
We demonstrate that our ML method can identify key ligand–protein
interactions driving the system through the TS. Some of the most important
drugs for cancer treatment are kinase inhibitors. One of these kinase
targets is cyclin-dependent kinase 2 (CDK2), an appealing target for
anticancer drug development. Here, we tested our method using two
different CDK2 inhibitors for the potential further development of
these compounds. We compared the free-energy barriers obtained from
our calculations with those observed in available experimental data.
We highlighted important interactions at the distal ends of the ligands
that can be targeted for improved residence times. Our method provides
a new tool to determine unbinding rates and to identify key structural
features of the inhibitors that can be used as starting points for
novel design strategies in drug discovery.
Collapse
Affiliation(s)
- Magd Badaoui
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom.,Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Pedro J Buigues
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Dénes Berta
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Gaurav M Mandana
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom
| | - Hankang Gu
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Tamás Földes
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Callum J Dickson
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Viktor Hornak
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Mitsunori Kato
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Carla Molteni
- Department of Physics, King's College London, London WC2R 2LS, United Kingdom
| | - Simon Parsons
- School of Computer Science, University of Lincoln, Lincoln LN6 7TS, United Kingdom
| | - Edina Rosta
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom.,Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| |
Collapse
|
32
|
Wang W, Poe D, Yang Y, Hyatt T, Xing J. Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor. eLife 2022; 11:74866. [PMID: 35188459 PMCID: PMC8920502 DOI: 10.7554/elife.74866] [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: 10/20/2021] [Accepted: 02/06/2022] [Indexed: 11/13/2022] Open
Abstract
How a cell changes from one stable phenotype to another one is a fundamental problem in developmental and cell biology. Mathematically, a stable phenotype corresponds to a stable attractor in a generally multi-dimensional state space, which needs to be destabilized so the cell relaxes to a new attractor. Two basic mechanisms for destabilizing a stable fixed point, pitchfork and saddle-node bifurcations, have been extensively studied theoretically; however, direct experimental investigation at the single-cell level remains scarce. Here, we performed live cell imaging studies and analyses in the framework of dynamical systems theories on epithelial-to-mesenchymal transition (EMT). While some mechanistic details remain controversial, EMT is a cell phenotypic transition (CPT) process central to development and pathology. Through time-lapse imaging we recorded single cell trajectories of human A549/Vim-RFP cells undergoing EMT induced by different concentrations of exogenous TGF-β in a multi-dimensional cell feature space. The trajectories clustered into two distinct groups, indicating that the transition dynamics proceeds through parallel paths. We then reconstructed the reaction coordinates and the corresponding quasi-potentials from the trajectories. The potentials revealed a plausible mechanism for the emergence of the two paths where the original stable epithelial attractor collides with two saddle points sequentially with increased TGF-β concentration, and relaxes to a new one. Functionally, the directional saddle-node bifurcation ensures a CPT proceeds towards a specific cell type, as a mechanistic realization of the canalization idea proposed by Waddington. Cells with the same genetic code can take on many different formss, or phenotypes, which have distinct roles and appearances. Sometimes cells switch from one phenotype to another as part of healthy growth or during disease. One such change is the epithelial-to-mesenchymal transition (EMT), which is involved in fetal development, wound healing and the spread of cancer cells. During EMT, closely connected epithelial cells detach from one another and change into mesenchymal cells that are able to migrate. Cells undergo a number of changes during this transition; however, the path they take to reach their new form is not entirely clear. For instance, do all cells follow the same route, or are there multiple ways that cells can shift from one state to the next? To address this question, Wang et al. studied individual lung cancer cells that had been treated with a protein that drives EMT. The cells were then imaged at regular intervals over the course of two to three days to see how they changed in response to different concentrations of protein. Using a mathematical analysis designed to study chemical reactions, Wang et al. showed that the cells transform into the mesenchymal phenotype through two main routes. This result suggests that attempts to prevent EMT, in cancer treatment for instance, would require blocking both paths taken by the cells. This information could be useful for biomedical researchers trying to regulate the EMT process. The quantitative approach of this study could also help physicists and mathematicians study other types of transition that occur in biology.
Collapse
Affiliation(s)
- Weikang Wang
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Dante Poe
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Yaxuan Yang
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Thomas Hyatt
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, United States
| | - Jianhua Xing
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| |
Collapse
|
33
|
Cui Q, Peng J, Xu C, Lan Z. Automatic Approach to Explore the Multireaction Mechanism for Medium-Sized Bimolecular Reactions via Collision Dynamics Simulations and Transition State Searches. J Chem Theory Comput 2022; 18:910-924. [DOI: 10.1021/acs.jctc.1c00795] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Qinghai Cui
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Jiawei Peng
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Chao Xu
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Zhenggang Lan
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| |
Collapse
|
34
|
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: 2] [Impact Index Per Article: 1.0] [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.
Collapse
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
| |
Collapse
|
35
|
Kaila VRI. Resolving Chemical Dynamics in Biological Energy Conversion: Long-Range Proton-Coupled Electron Transfer in Respiratory Complex I. Acc Chem Res 2021; 54:4462-4473. [PMID: 34894649 PMCID: PMC8697550 DOI: 10.1021/acs.accounts.1c00524] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
![]()
Biological energy conversion is catalyzed by membrane-bound proteins
that transduce chemical or light energy into energy forms that power
endergonic processes in the cell. At a molecular level, these catalytic
processes involve elementary electron-, proton-, charge-, and energy-transfer
reactions that take place in the intricate molecular machineries of
cell respiration and photosynthesis. Recent developments in structural
biology, particularly cryo-electron microscopy (cryoEM), have resolved
the molecular architecture of several energy transducing proteins,
but detailed mechanistic principles of their charge transfer reactions
still remain poorly understood and a major challenge for modern biochemical
research. To this end, multiscale molecular simulations provide a
powerful approach to probe mechanistic principles on a broad range
of time scales (femtoseconds to milliseconds) and spatial resolutions
(101–106 atoms), although technical challenges
also require balancing between the computational accuracy, cost, and
approximations introduced within the model. Here we discuss how the
combination of atomistic (aMD) and hybrid quantum/classical molecular
dynamics (QM/MM MD) simulations with free energy (FE) sampling methods
can be used to probe mechanistic principles of enzymes responsible
for biological energy conversion. We present mechanistic explorations
of long-range proton-coupled electron transfer (PCET) dynamics in
the highly intricate respiratory chain enzyme Complex I, which functions
as a redox-driven proton pump in bacterial and mitochondrial respiratory
chains by catalyzing a 300 Å fully reversible PCET process. This
process is initiated by a hydride (H–) transfer
between NADH and FMN, followed by long-range (>100 Å) electron
transfer along a wire of 8 FeS centers leading to a quinone biding
site. The reduction of the quinone to quinol initiates dissociation
of the latter to a second membrane-bound binding site, and triggers
proton pumping across the membrane domain of complex I, in subunits
up to 200 Å away from the active site. Our simulations across
different size and time scales suggest that transient charge transfer
reactions lead to changes in the internal hydration state of key regions,
local electric fields, and the conformation of conserved ion pairs,
which in turn modulate the dynamics of functional steps along the
reaction cycle. Similar functional principles, which operate on much
shorter length scales, are also found in some unrelated proteins,
suggesting that enzymes may employ conserved principles in the catalysis
of biological energy transduction processes.
Collapse
Affiliation(s)
- Ville R. I. Kaila
- Department of Biochemistry and Biophysics, Stockholm University, 10691 Stockholm, Sweden
| |
Collapse
|
36
|
Xu P, Mou X, Guo Q, Fu T, Ren H, Wang G, Li Y, Li G. Coarse-grained molecular dynamics study based on TorchMD. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2110218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Peijun Xu
- Liaoning Normal University, Dalian 116029, China
| | - Xiaohong Mou
- Liaoning Normal University, Dalian 116029, China
| | - Qiuhan Guo
- Liaoning Normal University, Dalian 116029, China
| | - Ting Fu
- Pharmacy Department of Affiliated Zhongshan Hospital of Dalian University, Dalian 116001, China
| | - Hong Ren
- Department of Ophthalmology Aerospace Center Hospital, Beijing 100049, China
| | - Guiyan Wang
- Dalian Ocean University, Dalian 116029, China
| | - Yan Li
- Dalian Institute of Chemical Physics, State Key Laboratory of Molecular Reaction Dynamics, Dalian 116023, China
| | - Guohui Li
- Dalian Institute of Chemical Physics, State Key Laboratory of Molecular Reaction Dynamics, Dalian 116023, China
| |
Collapse
|
37
|
Morita R, Shigeta Y, Harada R. A post-process to estimate an approximated minimal free energy path based on local centroids. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.139003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
38
|
Zhou S, Zhang Y, Cheng LT, Li B. Prediction of multiple dry-wet transition pathways with a mesoscale variational approach. J Chem Phys 2021; 155:124110. [PMID: 34598586 DOI: 10.1063/5.0061773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Water fluctuates in a hydrophobic confinement, forming multiple dry and wet hydration states through evaporation and condensation. Transitions between such states are critical to both thermodynamics and kinetics of solute molecular processes, such as protein folding and protein-ligand binding and unbinding. To efficiently predict such dry-wet transition paths, we develop a hybrid approach that combines a variational implicit solvation model, a generalized string method for minimum free-energy paths, and the level-set numerical implementation. This approach is applied to three molecular systems: two hydrophobic plates, a carbon nanotube, and a synthetic host molecule Cucurbit[7]uril. Without an explicit description of individual water molecules, our mesoscale approach effectively captures multiple dry and wet hydration states, multiple dry-wet transition paths, such as those geometrically symmetric and asymmetric paths, and transition states, providing activation energy barriers between different states. Further analysis shows that energy barriers depend on mesoscopic lengths, such as the separation distance between the two plates and the cross section diameter of the nanotube, and that the electrostatic interactions strongly influence the dry-wet transitions. With the inclusion of solute atomic motion, general collective variables as reaction coordinates, and the finite-temperature string method, together with an improved treatment of continuum electrostatics, our approach can be further developed to sample an ensemble of transition paths, providing more accurate predictions of the transition kinetics.
Collapse
Affiliation(s)
- Shenggao Zhou
- School of Mathematical Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yanan Zhang
- School of Mathematical Sciences, Soochow University, Suzhou 215006, China
| | - Li-Tien Cheng
- Department of Mathematics, University of California San Diego, La Jolla, California 92093-0112, USA
| | - Bo Li
- Department of Mathematics, University of California San Diego, La Jolla, California 92093-0112, USA
| |
Collapse
|
39
|
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.
Collapse
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
| |
Collapse
|
40
|
Kim B, Snyder R, Nagaraju M, Zhou Y, Ojeda-May P, Keeton S, Hege M, Shao Y, Pu J. Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force. J Chem Theory Comput 2021; 17:4961-4980. [PMID: 34283604 PMCID: PMC9064116 DOI: 10.1021/acs.jctc.1c00245] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.
Collapse
Affiliation(s)
- Bryant Kim
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Ryan Snyder
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Mulpuri Nagaraju
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Yan Zhou
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Pedro Ojeda-May
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Seth Keeton
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Mellisa Hege
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of
Oklahoma, 101 Stephenson Pkwy, Norman, OK 73019
| | - Jingzhi Pu
- Department of Chemistry and Chemical Biology, Indiana
University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN
46202
| |
Collapse
|
41
|
Aydin F, Durumeric AEP, da Hora GCA, Nguyen JDM, Oh MI, Swanson JMJ. Improving the accuracy and convergence of drug permeation simulations via machine-learned collective variables. J Chem Phys 2021; 155:045101. [PMID: 34340389 DOI: 10.1063/5.0055489] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Understanding the permeation of biomolecules through cellular membranes is critical for many biotechnological applications, including targeted drug delivery, pathogen detection, and the development of new antibiotics. To this end, computer simulations are routinely used to probe the underlying mechanisms of membrane permeation. Despite great progress and continued development, permeation simulations of realistic systems (e.g., more complex drug molecules or biologics through heterogeneous membranes) remain extremely challenging if not intractable. In this work, we combine molecular dynamics simulations with transition-tempered metadynamics and techniques from the variational approach to conformational dynamics to study the permeation mechanism of a drug molecule, trimethoprim, through a multicomponent membrane. We show that collective variables (CVs) obtained from an unsupervised machine learning algorithm called time-structure based Independent Component Analysis (tICA) improve performance and substantially accelerate convergence of permeation potential of mean force (PMF) calculations. The addition of cholesterol to the lipid bilayer is shown to increase both the width and height of the free energy barrier due to a condensing effect (lower area per lipid) and increase bilayer thickness. Additionally, the tICA CVs reveal a subtle effect of cholesterol increasing the resistance to permeation in the lipid head group region, which is not observed when canonical CVs are used. We conclude that the use of tICA CVs can enable more efficient PMF calculations with additional insight into the permeation mechanism.
Collapse
Affiliation(s)
- Fikret Aydin
- Quantum Simulation Group, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | | | - Gabriel C A da Hora
- Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| | - John D M Nguyen
- Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| | - Myong In Oh
- Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| | - Jessica M J Swanson
- Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| |
Collapse
|
42
|
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: 2] [Impact Index Per Article: 0.7] [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.
Collapse
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
| |
Collapse
|
43
|
Shrivastav G, Abrams CF. Optimizing String Method's Reproducibility Using Generalized Solute Tempering Replica Exchange. J Phys Chem B 2021; 125:6609-6616. [PMID: 34110824 DOI: 10.1021/acs.jpcb.1c02143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Obtaining accurate and reproducible free energies from molecular simulations is somewhat tricky due to incomplete knowledge of crucial slow degrees of freedom leading to hidden barriers that can stymie sampling. Employing a sufficiently large number of collective variables (CV) and ensuring ergodic sampling in orthogonal CV space, perhaps via tempering methods, can reduce these issues to some extent. For complex systems with high-dimensional free energy landscapes, both these approaches become computationally expensive. For high-dimensional landscapes, efficient exploration can be enabled by using temperature-accelerated MD (TAMD) and identification and characterization of minimum free energy pathways connecting minima can be found by using the string method (SM). Both TAMD and SM use mean-force estimates from finite MD simulations and are thus susceptible to sampling restrictions from hidden variables. A recent development in parallel tempering methods, "generalized replica exchange solute tempering" (gREST), can enhance sampling at a reasonable computational cost with its flexibility to target very specific "solutes" which can include arbitrary independent variables. Considering the advantages of both methods, we implement gREST-enabled TAMD and SM. By considering two different collective variable representations of the pentapeptide neurotransmitter met-enkephalin, we show that both gREST-enabled TAMD and SM yield more accurate and reproducible free energy predictions than TAMD and SM alone. Given the moderate computational cost of gREST compared with other replica-exchange methods, gREST-enabled SM represents a more attractive method for characterizing free energy minima and pathways among them for a large variety of systems.
Collapse
Affiliation(s)
- Gourav Shrivastav
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States
| | - Cameron F Abrams
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States
| |
Collapse
|
44
|
Dürr SL, Bohuszewicz O, Berta D, Suardiaz R, Jambrina PG, Peter C, Shao Y, Rosta E. The Role of Conserved Residues in the DEDDh Motif: the Proton-Transfer Mechanism of HIV-1 RNase H. ACS Catal 2021. [DOI: 10.1021/acscatal.1c01493] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Simon L. Dürr
- Department of Chemistry, King’s College London, London SE1 1DB, U.K
- Department of Chemistry, University of Konstanz, Konstanz 78457, Germany
| | - Olga Bohuszewicz
- Department of Chemistry, King’s College London, London SE1 1DB, U.K
| | - Dénes Berta
- Department of Physics and Astronomy, University College London; London WC1E 6BT, U.K
| | - Reynier Suardiaz
- Department of Chemistry, King’s College London, London SE1 1DB, U.K
| | | | - Christine Peter
- Department of Chemistry, University of Konstanz, Konstanz 78457, Germany
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, 101 Stephenson Parkway, Norman, Oklahoma 73019-5251, United States
| | - Edina Rosta
- Department of Chemistry, King’s College London, London SE1 1DB, U.K
- Department of Physics and Astronomy, University College London; London WC1E 6BT, U.K
| |
Collapse
|
45
|
Giese TJ, Ekesan Ş, York DM. Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis. J Phys Chem A 2021; 125:4216-4232. [PMID: 33784093 DOI: 10.1021/acs.jpca.1c00736] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
We redevelop the variational free energy profile (vFEP) method using a cardinal B-spline basis to extend the method for analyzing free energy surfaces (FESs) involving three or more reaction coordinates. We also implemented software for evaluating high-dimensional profiles based on the multistate Bennett acceptance ratio (MBAR) method which constructs an unbiased probability density from global reweighting of the observed samples. The MBAR method takes advantage of a fast algorithm for solving the unbinned weighted histogram (UWHAM)/MBAR equations which replaces the solution of simultaneous equations with a nonlinear optimization of a convex function. We make use of cardinal B-splines and multiquadric radial basis functions to obtain smooth, differentiable MBAR profiles in arbitrary high dimensions. The cardinal B-spline vFEP and MBAR methods are compared using three example systems that examine 1D, 2D, and 3D profiles. Both methods are found to be useful and produce nearly indistinguishable results. The vFEP method is found to be 150 times faster than MBAR when applied to periodic 2D profiles, but the MBAR method is 4.5 times faster than vFEP when evaluating unbounded 3D profiles. In agreement with previous comparisons, we find the vFEP method produces superior FESs when the overlap between umbrella window simulations decreases. Finally, the associative reaction mechanism of hammerhead ribozyme is characterized using 3D, 4D, and 6D profiles, and the higher-dimensional profiles are found to have smaller reaction barriers by as much as 1.5 kcal/mol. The methods presented here have been implemented into the FE-ToolKit software package along with new methods for network-wide free energy analysis in drug discovery.
Collapse
Affiliation(s)
- Timothy J Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854-8087, United States
| | - Şölen Ekesan
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854-8087, United States
| | - Darrin M York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854-8087, United States
| |
Collapse
|
46
|
Hooft F, Pérez de Alba Ortíz A, Ensing B. Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks. J Chem Theory Comput 2021; 17:2294-2306. [PMID: 33662202 PMCID: PMC8047796 DOI: 10.1021/acs.jctc.0c00981] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Indexed: 01/13/2023]
Abstract
With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson-Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.
Collapse
Affiliation(s)
- Ferry Hooft
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Alberto Pérez de Alba Ortíz
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Bernd Ensing
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| |
Collapse
|
47
|
Bolhuis PG, Swenson DWH. Transition Path Sampling as Markov Chain Monte Carlo of Trajectories: Recent Algorithms, Software, Applications, and Future Outlook. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000237] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Peter G. Bolhuis
- Amsterdam Center for Multiscale Modeling van 't Hoff Institute for Molecular Sciences University of Amsterdam PO Box 94157 1090 GD Amsterdam The Netherlands
| | - David W. H. Swenson
- Centre Blaise Pascal Ecole Normale Superieure 46, allée d'Italie 69364 Lyon Cedex 07 France
| |
Collapse
|
48
|
Radhakrishnan R. A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects. AIChE J 2021; 67:e17026. [PMID: 33790479 PMCID: PMC7988612 DOI: 10.1002/aic.17026] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 08/09/2020] [Accepted: 08/13/2020] [Indexed: 01/14/2023]
Abstract
Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.
Collapse
Affiliation(s)
- Ravi Radhakrishnan
- Department of Chemical and Biomolecular EngineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
- Department of BioengineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
| |
Collapse
|
49
|
Ding X, Lin X, Zhang B. Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface. Nat Commun 2021; 12:1091. [PMID: 33597548 PMCID: PMC7889939 DOI: 10.1038/s41467-021-21377-z] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2020] [Accepted: 01/22/2021] [Indexed: 01/01/2023] Open
Abstract
The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber. The three-dimensional organization of chromatin plays critical roles in regulating genome function. Here the authors apply a near atomistic model to study the structure and dynamics of the chromatin folding unit - the tetra-nucleosome - to provide insight into how chromatin folds.
Collapse
Affiliation(s)
- Xinqiang Ding
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Xingcheng Lin
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
| |
Collapse
|
50
|
Kang C, Sun R. Molecular Dynamics Study of the Interaction between the N-terminal of α-Synuclein and a Lipid Bilayer Mimicking Synaptic Vesicles. J Phys Chem B 2020; 125:1036-1048. [DOI: 10.1021/acs.jpcb.0c08620] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Christopher Kang
- Department of Chemistry, University of Hawai’i at Manoa, 2545 McCarthy
Mall, Honolulu 96822-2275, Hawaii, United States
| | - Rui Sun
- Department of Chemistry, University of Hawai’i at Manoa, 2545 McCarthy
Mall, Honolulu 96822-2275, Hawaii, United States
| |
Collapse
|