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Lagardère L, Maurin L, Adjoua O, El Hage K, Monmarché P, Piquemal JP, Hénin J. Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation. J Chem Theory Comput 2024; 20:4481-4498. [PMID: 38805379 DOI: 10.1021/acs.jctc.3c01249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.
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Affiliation(s)
- Louis Lagardère
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Institut Parisien de Chimie Physique et Théorique, FR2622 CNRS, 75005 Paris, France
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Lise Maurin
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Laboratoire Jacques-Louis Lions, UMR 7589 CNRS, 75005 Paris, France
| | - Olivier Adjoua
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
| | - Krystel El Hage
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Pierre Monmarché
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Laboratoire Jacques-Louis Lions, UMR 7589 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Jérôme Hénin
- Laboratoire de Biochimie Théorique, Université Paris Cité, CNRS, UPR 9080, 75005 Paris, France
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2
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Aina A, Hsueh SCC, Gibbs E, Peng X, Cashman NR, Plotkin SS. De Novo Design of a β-Helix Tau Protein Scaffold: An Oligomer-Selective Vaccine Immunogen Candidate for Alzheimer's Disease. ACS Chem Neurosci 2023; 14:2603-2617. [PMID: 37458595 DOI: 10.1021/acschemneuro.3c00007] [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] [Indexed: 08/03/2023] Open
Abstract
Tau pathology is associated with many neurodegenerative disorders, including Alzheimer's disease (AD), where the spatio-temporal pattern of tau neurofibrillary tangles strongly correlates with disease progression, which motivates therapeutics selective for misfolded tau. Here, we introduce a new avidity-enhanced, multi-epitope approach for protein-misfolding immunogen design, which is predicted to mimic the conformational state of an exposed epitope in toxic tau oligomers. A predicted oligomer-selective tau epitope 343KLDFK347 was scaffolded by designing a β-helix structure that incorporated multiple instances of the 16-residue tau fragment 339VKSEKLDFKDRVQSKI354. Large-scale conformational ensemble analyses involving Jensen-Shannon Divergence and the embedding depth D showed that the multi-epitope scaffolding approach, employed in designing the β-helix scaffold, was predicted to better discriminate toxic tau oligomers than other "monovalent" strategies utilizing a single instance of an epitope for vaccine immunogen design. Using Rosetta, 10,000 sequences were designed and screened for the linker portions of the β-helix scaffold, along with a C-terminal stabilizing α-helix that interacts with the linkers, to optimize the folded structure and stability of the scaffold. Structures were ranked by energy, and the lowest 1% (82 unique sequences) were verified using AlphaFold. Several selection criteria involving AlphaFold are implemented to obtain a lead-designed sequence. The structure was further predicted to have free energetic stability by using Hamiltonian replica exchange molecular dynamics (MD) simulations. The synthesized β-helix scaffold showed direct binding in surface plasmon resonance (SPR) experiments to several antibodies that were raised to the structured epitope using a designed cyclic peptide. Moreover, the strength of binding of these antibodies to in vitro tau oligomers correlated with the strength of binding to the β-helix construct, suggesting that the construct presents an oligomer-like conformation and may thus constitute an effective oligomer-selective immunogen.
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Affiliation(s)
- Adekunle Aina
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Shawn C C Hsueh
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Ebrima Gibbs
- Djavad Mowafaghian Centre for Brain Health, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Xubiao Peng
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Neil R Cashman
- Djavad Mowafaghian Centre for Brain Health, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Steven S Plotkin
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Genome Science and Technology Program, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
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3
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Inagaki T, Saito S. Hybrid Monte Carlo Method with Potential Scaling for Sampling from the Canonical Multimodal Distribution and Imitating the Relaxation Process. J Chem Phys 2022; 156:104111. [DOI: 10.1063/5.0082378] [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] Open
Affiliation(s)
| | - Shinji Saito
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Japan
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4
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Rick SW, Schwing GJ, Summa CM. An Implementation of Replica Exchange with Dynamical Scaling for Efficient Large-Scale Simulations. J Chem Inf Model 2021; 61:810-818. [PMID: 33496583 DOI: 10.1021/acs.jcim.0c01236] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An implementation of the replica exchange with dynamical scaling (REDS) method in the commonly used molecular dynamics program GROMACS is presented. REDS is a replica exchange method that requires fewer replicas than conventional replica exchange while still providing data over a range of temperatures and can be used in either constant volume or constant pressure ensembles. Details for running REDS simulations are given, and an application to the human islet amyloid polypeptide (hIAPP) 11-25 fragment shows that the model efficiently samples conformational space.
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Affiliation(s)
- Steven W Rick
- Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148, United States
| | - Gregory J Schwing
- Department of Computer Science, University of New Orleans, New Orleans, Louisiana 70148, United States
| | - Christopher M Summa
- Department of Computer Science, University of New Orleans, New Orleans, Louisiana 70148, United States
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5
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Faizi F, Buigues PJ, Deligiannidis G, Rosta E. Simulated tempering with irreversible Gibbs sampling techniques. J Chem Phys 2020; 153:214111. [PMID: 33291930 DOI: 10.1063/5.0025775] [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
We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.
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Affiliation(s)
- Fahim Faizi
- Department of Mathematics, King's College London, Strand, WC2R 2LS London, United Kingdom
| | - Pedro J Buigues
- Department of Chemistry, King's College London, 7 Trinity Street, SE1 1DB London, United Kingdom
| | - George Deligiannidis
- Department of Statistics, University of Oxford, 24-29 St Giles', OX1 3LB Oxford, United Kingdom
| | - Edina Rosta
- Department of Chemistry, King's College London, 7 Trinity Street, SE1 1DB London, United Kingdom
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6
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Hu W, Li P, Wang JN, Xue Y, Mo Y, Zheng J, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States. J Chem Theory Comput 2020; 16:6814-6822. [PMID: 32975951 PMCID: PMC7658029 DOI: 10.1021/acs.jctc.0c00794] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of the free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events, and some low-energy conformations may get oversampled in simulations of a finite length. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.
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Affiliation(s)
- Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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7
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Nishimura Y, Nakai H. Hierarchical parallelization of divide‐and‐conquer density functional tight‐binding molecular dynamics and metadynamics simulations. J Comput Chem 2020; 41:1759-1772. [DOI: 10.1002/jcc.26217] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 04/15/2020] [Accepted: 04/20/2020] [Indexed: 11/08/2022]
Affiliation(s)
- Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering Waseda University Tokyo Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering Waseda University Tokyo Japan
- Department of Chemistry and Biochemistry School of Advanced Science and Engineering, Waseda University Tokyo Japan
- Elements Strategy Initiative for Catalysts and Batteries Kyoto University Kyoto Japan
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8
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Cui D, Zhang BW, Tan Z, Levy RM. Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix. J Chem Theory Comput 2019; 16:67-79. [PMID: 31743019 DOI: 10.1021/acs.jctc.9b00740] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Free energy perturbation (FEP) simulations have been widely applied to obtain predictions of the relative binding free energy for a series of congeneric ligands binding to the same receptor, which is an essential component for the lead optimization process in computer-aided drug discovery. In the case of several congeneric ligands forming a perturbation map involving a closed thermodynamic cycle, the summation of the estimated free energy change along each edge in the cycle using Bennett acceptance ratio (BAR) usually will deviate from zero due to systematic and random errors, which is the hysteresis of cycle closure. In this work, the advanced reweighting techniques binless weighted histogram analysis method (UWHAM) and locally weighted histogram analysis method (LWHAM) are applied to provide statistical estimators of the free energy change along each edge in order to eliminate the hysteresis effect. As an example, we analyze a closed thermodynamic cycle involving four congeneric ligands which bind to HIV-1 integrase, a promising target which has emerged for antiviral therapy. We demonstrate that, compared with FEP and BAR, more accurate and hysteresis-free estimates of free energy differences can be achieved by using UWHAM to find a single estimate of the density of states based on all of the data in the cycle. Furthermore, by comparison of LWHAM results obtained from the inclusion of different numbers of neighboring states with UWHAM estimation involving all the states, we show how to determine the optimal neighborhood size in the LWHAM analysis to balance the trade-offs between computational cost and accuracy of the free energy prediction. Even with the smallest neighborhood, LWHAM can improve the BAR free energy estimates using the same input data as BAR. We introduce an overlapping states matrix that is constructed by using the global jump formula of LWHAM and plot its heat map. The heat map provides a quantitative measure of the overlap between pairs of alchemical/thermodynamic states. We explain how to identify and improve the FEP calculations along the edges that most likely cause large systematic errors by using the heat map of the overlapping states matrix and by comparing the BAR and UWHAM estimates of the free energy change.
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Affiliation(s)
- Di Cui
- Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Bin W Zhang
- Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Zhiqiang Tan
- Department of Statistics , Rutgers, The State University of New Jersey , Piscataway , New Jersey 08854 , United States
| | - Ronald M Levy
- Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science , Temple University , Philadelphia , Pennsylvania 19122 , United States
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9
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Ebrahimi P, Kaur S, Baronti L, Petzold K, Chen AA. A two-dimensional replica-exchange molecular dynamics method for simulating RNA folding using sparse experimental restraints. Methods 2019; 162-163:96-107. [PMID: 31059830 DOI: 10.1016/j.ymeth.2019.05.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Revised: 04/26/2019] [Accepted: 05/01/2019] [Indexed: 10/26/2022] Open
Abstract
We present a 2D replica exchange protocol incorporating secondary structure information to dramatically improve 3D RNA folding using molecular dynamics simulations. We show that incorporating base-pairing restraints into all-atom, explicit solvent simulations enables the accurate recapitulation of the global tertiary fold for 4 representative RNAs ranging in length from 24 to 68 nt. This method can potentially utilize base-pairing information from a wide variety of experimental inputs to predict complex RNA tertiary folds including pseudoknots, multi-loop junctions, and non-canonical interactions.
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Affiliation(s)
- Parisa Ebrahimi
- Department of Chemistry, University at Albany, State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA
| | - Simi Kaur
- Department of Chemistry, University at Albany, State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA
| | - Lorenzo Baronti
- Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden
| | - Katja Petzold
- Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden
| | - Alan A Chen
- Department of Chemistry, University at Albany, State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA; The RNA Institute, University at Albany, State University of New York, Albany, NY, USA.
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10
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Peter EK, Černý J. A Hybrid Hamiltonian for the Accelerated Sampling along Experimental Restraints. Int J Mol Sci 2019; 20:E370. [PMID: 30654563 PMCID: PMC6359555 DOI: 10.3390/ijms20020370] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 01/07/2019] [Accepted: 01/10/2019] [Indexed: 12/25/2022] Open
Abstract
In this article, we present an enhanced sampling method based on a hybrid Hamiltonian which combines experimental distance restraints with a bias dependent from multiple path-dependent variables. This simulation method determines the bias-coordinates on the fly and does not require a priori knowledge about reaction coordinates. The hybrid Hamiltonian accelerates the sampling of proteins, and, combined with experimental distance information, the technique considers the restraints adaptively and in dependency of the system's intrinsic dynamics. We validate the methodology on the dipole relaxation of two water models and the conformational landscape of dialanine. Using experimental NMR-restraint data, we explore the folding landscape of the TrpCage mini-protein and in a second example apply distance restraints from chemical crosslinking/mass spectrometry experiments for the sampling of the conformation space of the Killer Cell Lectin-like Receptor Subfamily B Member 1A (NKR-P1A). The new methodology has the potential to adaptively introduce experimental restraints without affecting the conformational space of the system along an ergodic trajectory. Since only a limited number of input- and no-order parameters are required for the setup of the simulation, the method is broadly applicable and has the potential to be combined with coarse-graining methods.
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Affiliation(s)
- Emanuel K Peter
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Prague West, Czech Republic.
| | - Jiří Černý
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Prague West, Czech Republic.
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11
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Bucci R, Contini A, Clerici F, Pellegrino S, Gelmi ML. From glucose to enantiopure morpholino β-amino acid: a new tool for stabilizing γ-turns in peptides. Org Chem Front 2019. [DOI: 10.1039/c8qo01116h] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
“Environmentally sustainable” synthesis of a new enantiopure morpholino β-amino acid from glucose: a new tool for exotic peptide architectures.
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Affiliation(s)
- Raffaella Bucci
- DISFARM-Sez
- Chimica Generale e Organica “A. Marchesini”
- Università degli Studi di Milano
- 20133 Milano
- Italy
| | - Alessandro Contini
- DISFARM-Sez
- Chimica Generale e Organica “A. Marchesini”
- Università degli Studi di Milano
- 20133 Milano
- Italy
| | - Francesca Clerici
- DISFARM-Sez
- Chimica Generale e Organica “A. Marchesini”
- Università degli Studi di Milano
- 20133 Milano
- Italy
| | - Sara Pellegrino
- DISFARM-Sez
- Chimica Generale e Organica “A. Marchesini”
- Università degli Studi di Milano
- 20133 Milano
- Italy
| | - Maria Luisa Gelmi
- DISFARM-Sez
- Chimica Generale e Organica “A. Marchesini”
- Università degli Studi di Milano
- 20133 Milano
- Italy
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12
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Peter EK, Cerny J. Enriched Conformational Sampling of DNA and Proteins with a Hybrid Hamiltonian Derived from the Protein Data Bank. Int J Mol Sci 2018; 19:E3405. [PMID: 30380800 PMCID: PMC6274895 DOI: 10.3390/ijms19113405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2018] [Revised: 10/22/2018] [Accepted: 10/27/2018] [Indexed: 12/26/2022] Open
Abstract
In this article, we present a method for the enhanced molecular dynamics simulation of protein and DNA systems called potential of mean force (PMF)-enriched sampling. The method uses partitions derived from the potentials of mean force, which we determined from DNA and protein structures in the Protein Data Bank (PDB). We define a partition function from a set of PDB-derived PMFs, which efficiently compensates for the error introduced by the assumption of a homogeneous partition function from the PDB datasets. The bias based on the PDB-derived partitions is added in the form of a hybrid Hamiltonian using a renormalization method, which adds the PMF-enriched gradient to the system depending on a linear weighting factor and the underlying force field. We validated the method using simulations of dialanine, the folding of TrpCage, and the conformational sampling of the Dickerson⁻Drew DNA dodecamer. Our results show the potential for the PMF-enriched simulation technique to enrich the conformational space of biomolecules along their order parameters, while we also observe a considerable speed increase in the sampling by factors ranging from 13.1 to 82. The novel method can effectively be combined with enhanced sampling or coarse-graining methods to enrich conformational sampling with a partition derived from the PDB.
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Affiliation(s)
- Emanuel K Peter
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Czech Republic.
| | - Jiri Cerny
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Czech Republic.
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13
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Lee M, Yoon J, Jang S, Shin S. Conformational sampling of metastable states: Tq-REM as a novel replica exchange method. Phys Chem Chem Phys 2017; 19:5454-5464. [PMID: 28165074 DOI: 10.1039/c6cp05322j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Although the replica exchange methods (REMs) were developed as efficient conformational sampling methods for bio-molecular simulations, their application to very large bio-systems is somewhat limited. We propose a new replica exchange scheme (Tq-REM) created by combining the conventional temperature-REM (T-REM) and one of the Hamiltonian-REMs, q-REM, using the effective potential with reduced barriers. In the proposed Tq-REM scheme, high temperature replicas in T-REM are substituted with q-replicas. This combined scheme is expected to exploit advantages of the T-REM and q-REM resulting in improved sampling efficiency while minimizing the drawbacks of both approaches. We investigated the performance of Tq-REM compared with T-REM by performing all-atom MD simulations on Met-enkephalin, (AAQAA)3, and Trpzip2. It was found that convergence of the free energy surfaces was improved by Tq-REM over the conventional T-REM. In particular, the trajectories of Tq-REM were able to sample the relevant conformations for all of the metastable folding intermediates, while some of the local minimum structures are poorly represented by T-REM. The results of the present study suggest that Tq-REM can provide useful tools to investigate systems where metastable states play important roles.
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Affiliation(s)
- MinJun Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, Korea.
| | - Jeseong Yoon
- Department of Chemistry, Seoul National University, Seoul 151-747, Korea.
| | - Soonmin Jang
- Department of Chemistry, Sejong University, Seoul 143-747, Korea
| | - Seokmin Shin
- Department of Chemistry, Seoul National University, Seoul 151-747, Korea.
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14
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Yu Y, Wang J, Chen Z, Wang G, Shao Q, Shi J, Zhu W. Structural insights into HIV-1 protease flap opening processes and key intermediates. RSC Adv 2017. [DOI: 10.1039/c7ra09691g] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The study provided an integrated view of the transition pathway of the flap opening of HIV-1 protease using MD simulation.
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Affiliation(s)
- Yuqi Yu
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
| | - Jinan Wang
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
| | - Zhaoqiang Chen
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
| | - Guimin Wang
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
| | - Qiang Shao
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
| | - Jiye Shi
- UCB Biopharma SPRL
- Chemin du Foriest
- Belgium
| | - Weiliang Zhu
- Drug Discovery and Design Center
- CAS Key Laboratory of Receptor Research
- Shanghai Institute of Materia Medica
- Chinese Academy of Sciences
- Shanghai
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15
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Weiergräber OH, Schwarten M, Strodel B, Willbold D. Investigating Structure and Dynamics of Atg8 Family Proteins. Methods Enzymol 2016; 587:115-142. [PMID: 28253952 DOI: 10.1016/bs.mie.2016.09.056] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Atg8 family members were the first autophagy-related proteins to be investigated in structural detail and continue to be among the best-understood molecules of the pathway. In this review, we will first provide a concise outline of the major methods that are being applied for structural characterization of these proteins and the complexes they are involved in. This includes a discussion of the strengths and limitations associated with each method, along with guidelines for successful adoption to a specific problem. Subsequently, we will present examples illustrating the application of these techniques, with a particular focus on the complementarity of information they provide.
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Affiliation(s)
- O H Weiergräber
- Institute of Complex Systems, ICS-6 (Structural Biochemistry), Forschungszentrum Jülich, Jülich, Germany
| | - M Schwarten
- Institute of Complex Systems, ICS-6 (Structural Biochemistry), Forschungszentrum Jülich, Jülich, Germany
| | - B Strodel
- Institute of Complex Systems, ICS-6 (Structural Biochemistry), Forschungszentrum Jülich, Jülich, Germany
| | - D Willbold
- Institute of Complex Systems, ICS-6 (Structural Biochemistry), Forschungszentrum Jülich, Jülich, Germany; Institut für Physikalische Biologie und BMFZ, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany.
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16
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Peter EK, Pivkin IV, Shea JE. A canonical replica exchange molecular dynamics implementation with normal pressure in each replica. J Chem Phys 2016; 145:044903. [DOI: 10.1063/1.4958325] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Emanuel K. Peter
- Institute of Computational Science, Faculty of Informatics, University of Lugano, Switzerland
| | - Igor V. Pivkin
- Institute of Computational Science, Faculty of Informatics, University of Lugano, Switzerland
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, Department of Physics, University of California, Santa Barbara, California 93106, USA
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17
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Carballo-Pacheco M, Strodel B. Advances in the Simulation of Protein Aggregation at the Atomistic Scale. J Phys Chem B 2016; 120:2991-9. [PMID: 26965454 DOI: 10.1021/acs.jpcb.6b00059] [Citation(s) in RCA: 91] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.
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Affiliation(s)
- Martín Carballo-Pacheco
- Institute of Complex Systems: Structural Biochemistry , Forschungszentrum Jülich, 52425 Jülich, Germany.,AICES Graduate School, RWTH Aachen University , Schinkelstraße 2, 52062 Aachen, Germany
| | - Birgit Strodel
- Institute of Complex Systems: Structural Biochemistry , Forschungszentrum Jülich, 52425 Jülich, Germany.,Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf , Universitätsstrasse 1, 40225 Düsseldorf, Germany
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18
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Peter EK, Shea JE, Pivkin IV. Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent. Phys Chem Chem Phys 2016; 18:13052-65. [DOI: 10.1039/c5cp06867c] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC).
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Affiliation(s)
- Emanuel K. Peter
- Institute of Computational Science
- Faculty of Informatics
- University of Lugano
- Switzerland
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry
- Department of Physics
- University of California
- Santa Barbara
- USA
| | - Igor V. Pivkin
- Institute of Computational Science
- Faculty of Informatics
- University of Lugano
- Switzerland
- Swiss Institute of Bioinformatics
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19
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Okur A, Roe DR, Cui G, Hornak V, Simmerling C. Improving Convergence of Replica-Exchange Simulations through Coupling to a High-Temperature Structure Reservoir. J Chem Theory Comput 2015; 3:557-68. [PMID: 26637035 DOI: 10.1021/ct600263e] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Parallel tempering or replica-exchange molecular dynamics (REMD) significantly increases the efficiency of conformational sampling for complex molecular systems. However, obtaining converged data with REMD remains challenging, especially for large systems with complex topologies. We propose a new variant to REMD where the replicas are also permitted to exchange with an ensemble of structures that have been generated in advance using high-temperature MD simulations, similar in spirit to J-walking methods. We tested this approach on two non-trivial model systems, a β-hairpin and a 3-stranded β-sheet and compared the results to those obtained from very long (>100 ns) standard REMD simulations. The resulting ensembles were indistinguishable, including relative populations of different conformations on the unfolded state. The use of the reservoir is shown to significantly reduce the time required for convergence.
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Affiliation(s)
- Asim Okur
- Department of Chemistry and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Daniel R Roe
- Department of Chemistry and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Guanglei Cui
- Department of Chemistry and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Viktor Hornak
- Department of Chemistry and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Carlos Simmerling
- Department of Chemistry and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
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20
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Okur A, Wickstrom L, Layten M, Geney R, Song K, Hornak V, Simmerling C. Improved Efficiency of Replica Exchange Simulations through Use of a Hybrid Explicit/Implicit Solvation Model. J Chem Theory Comput 2015; 2:420-33. [PMID: 26626529 DOI: 10.1021/ct050196z] [Citation(s) in RCA: 117] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The use of parallel tempering or replica exchange molecular dynamics (REMD) simulations has facilitated the exploration of free energy landscapes for complex molecular systems, but application to large systems is hampered by the scaling of the number of required replicas with increasing system size. Use of continuum solvent models reduces system size and replica requirements, but these have been shown to provide poor results in many cases, including overstabilization of ion pairs and secondary structure bias. Hybrid explicit/continuum solvent models can overcome some of these problems through an explicit representation of water molecules in the first solvation shells, but these methods typically require restraints on the solvent molecules and show artifacts in water properties due to the solvation interface. We propose an REMD variant in which the simulations are performed with a fully explicit solvent, but the calculation of exchange probability is carried out using a hybrid model, with the solvation shells calculated on the fly during the fully solvated simulation. The resulting reduction in the perceived system size in the REMD exchange calculation provides a dramatic decrease in the computational cost of REMD, while maintaining a very good agreement with results obtained from the standard explicit solvent REMD. We applied several standard and hybrid REMD methods with different solvent models to alanine polymers of 1, 3, and 10 residues, obtaining ensembles that were essentially independent of the initial conformation, even with explicit solvation. Use of only a continuum model without a shell of explicit water provided poor results for Ala3 and Ala10, with a significant bias in favor of the α-helix. Likewise, using only the solvation shells and no continuum model resulted in ensembles that differed significantly from the standard explicit solvent data. Ensembles obtained from hybrid REMD are in very close agreement with explicit solvent data, predominantly populating polyproline II conformations. Inclusion of a second shell of explicit solvent was found to be unnecessary for these peptides.
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Affiliation(s)
- Asim Okur
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Lauren Wickstrom
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Melinda Layten
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Raphäel Geney
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Kun Song
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Viktor Hornak
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
| | - Carlos Simmerling
- Department of Chemistry, Graduate Program in Biochemistry and Structural Biology, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794, and Computational Science Center, Brookhaven National Laboratory, Upton, New York 11973
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21
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Yu Y, Wang J, Shao Q, Shi J, Zhu W. Increasing the sampling efficiency of protein conformational transition using velocity-scaling optimized hybrid explicit/implicit solvent REMD simulation. J Chem Phys 2015; 142:125105. [PMID: 25833612 DOI: 10.1063/1.4916118] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The application of temperature replica exchange molecular dynamics (REMD) simulation on protein motion is limited by its huge requirement of computational resource, particularly when explicit solvent model is implemented. In the previous study, we developed a velocity-scaling optimized hybrid explicit/implicit solvent REMD method with the hope to reduce the temperature (replica) number on the premise of maintaining high sampling efficiency. In this study, we utilized this method to characterize and energetically identify the conformational transition pathway of a protein model, the N-terminal domain of calmodulin. In comparison to the standard explicit solvent REMD simulation, the hybrid REMD is much less computationally expensive but, meanwhile, gives accurate evaluation of the structural and thermodynamic properties of the conformational transition which are in well agreement with the standard REMD simulation. Therefore, the hybrid REMD could highly increase the computational efficiency and thus expand the application of REMD simulation to larger-size protein systems.
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Affiliation(s)
- Yuqi Yu
- ACS Key Laboratory of Receptor Research, Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
| | - Jinan Wang
- ACS Key Laboratory of Receptor Research, Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
| | - Qiang Shao
- ACS Key Laboratory of Receptor Research, Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
| | - Jiye Shi
- UCB Pharma, 216 Bath Road, Slough SL1 4EN, United Kingdom
| | - Weiliang Zhu
- ACS Key Laboratory of Receptor Research, Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
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22
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Roe D, Bergonzo C, Cheatham TE. Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods. J Phys Chem B 2014; 118:3543-52. [PMID: 24625009 PMCID: PMC3983400 DOI: 10.1021/jp4125099] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Revised: 03/10/2014] [Indexed: 11/28/2022]
Abstract
Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.
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Affiliation(s)
- Daniel
R. Roe
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
| | - Christina Bergonzo
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
| | - Thomas E. Cheatham
- Department of Medicinal Chemistry,
College of Pharmacy, University of Utah, 2000 South 30 East Room 105, Salt Lake City, Utah 84112, United States
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23
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A Hamiltonian replica exchange molecular dynamics (MD) method for the study of folding, based on the analysis of the stabilization determinants of proteins. Int J Mol Sci 2013; 14:12157-69. [PMID: 23743827 PMCID: PMC3709779 DOI: 10.3390/ijms140612157] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Revised: 04/29/2013] [Accepted: 05/14/2013] [Indexed: 11/16/2022] Open
Abstract
Herein, we present a novel Hamiltonian replica exchange protocol for classical molecular dynamics simulations of protein folding/unfolding. The scheme starts from the analysis of the energy-networks responsible for the stabilization of the folded conformation, by means of the energy-decomposition approach. In this framework, the compact energetic map of the native state is generated by a preliminary short molecular dynamics (MD) simulation of the protein in explicit solvent. This map is simplified by means of an eigenvalue decomposition. The highest components of the eigenvector associated with the lowest eigenvalue indicate which sites, named "hot spots", are likely to be responsible for the stability and correct folding of the protein. In the Hamiltonian replica exchange protocol, we use modified force-field parameters to treat the interparticle non-bonded potentials of the hot spots within the protein and between protein and solvent atoms, leaving unperturbed those relative to all other residues, as well as solvent-solvent interactions. We show that it is possible to reversibly simulate the folding/unfolding behavior of two test proteins, namely Villin HeadPiece HP35 (35 residues) and Protein A (62 residues), using a limited number of replicas. We next discuss possible implications for the study of folding mechanisms via all atom simulations.
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24
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Wu X, Hodoscek M, Brooks BR. Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling. J Chem Phys 2012; 137:044106. [PMID: 22852596 DOI: 10.1063/1.4737094] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.
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Affiliation(s)
- Xiongwu Wu
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland 20892, USA.
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25
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Kim J, Straub JE, Keyes T. Replica exchange statistical temperature molecular dynamics algorithm. J Phys Chem B 2012; 116:8646-53. [PMID: 22540354 PMCID: PMC11240102 DOI: 10.1021/jp300366j] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The replica exchange statistical temperature molecular dynamics (RESTMD) algorithm is presented, designed to alleviate an extensive increase of the number of replicas required as system size increases in the conventional temperature replica exchange method (tREM), and to obtain improved sampling in individual replicas. RESTMD optimally integrates multiple STMD (Phys. Rev. Lett. 2006, 97, 050601) runs with replica exchanges, giving rise to a flat energy sampling in each replica with a self-adjusting weight determination. The expanded flat energy dynamic sampling range allows the use of significantly fewer STMD replicas while maintaining the desired acceptance probability for replica exchanges. The computational advantages of RESTMD over conventional REM and single-replica STMD are explicitly demonstrated with an application to a coarse-grained protein model. The effect of two different kinetic temperature control schemes on the sampling efficiency is explored for diverse simulation conditions.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States.
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26
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Folding helical proteins in explicit solvent using dihedral-biased tempering. Proc Natl Acad Sci U S A 2012; 109:8139-44. [PMID: 22573819 DOI: 10.1073/pnas.1112143109] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Using a single-trajectory-based tempering method with a high-temperature dihedral bias, we repeatedly folded four helical proteins [α(3)D (PDB ID: 2A3D, 73 residues), α(3)W (1LQ7, 67 residues), Fap1-NR(α) (2KUB, 81 residues) and S-836 (2JUA, 102 residues)] and some of the mutants in explicit solvent within several microseconds. The lowest root-mean-square deviations of backbone atoms from the experimentally determined structures were 1.9, 1.4, 1.0, and 2.1 Å, respectively. Cluster analyses of folding trajectories showed the native conformation usually occupied the most populated cluster. The simulation protocol can be applied to large-scale simulations of other helical proteins on commonly accessible computing platforms.
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27
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Lu Q, Kim J, Straub JE. Exploring the Solid–Liquid Phase Change of an Adapted Dzugutov Model Using Generalized Replica Exchange Method. J Phys Chem B 2012; 116:8654-61. [DOI: 10.1021/jp300406c] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Qing Lu
- Division of Materials Science
and Engineering, Boston University, Brookline,
Massachusetts 02446, United States
| | - Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United
States
| | - John E. Straub
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United
States
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28
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Pham TT, Shirts MR. Optimal pairwise and non-pairwise alchemical pathways for free energy calculations of molecular transformation in solution phase. J Chem Phys 2012; 136:124120. [DOI: 10.1063/1.3697833] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Chodera JD, Shirts MR. Replica exchange and expanded ensemble simulations as Gibbs sampling: Simple improvements for enhanced mixing. J Chem Phys 2011; 135:194110. [DOI: 10.1063/1.3660669] [Citation(s) in RCA: 126] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Pham TT, Shirts MR. Identifying low variance pathways for free energy calculations of molecular transformations in solution phase. J Chem Phys 2011; 135:034114. [PMID: 21786994 DOI: 10.1063/1.3607597] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Improving the efficiency of free energy calculations is important for many biological and materials design applications, such as protein-ligand binding affinities in drug design, partitioning between immiscible liquids, and determining molecular association in soft materials. We show that for any pair potential, moderately accurate estimation of the radial distribution function for a solute molecule is sufficient to accurately estimate the statistical variance of a sampling along a free energy pathway. This allows inexpensive analytical identification of low statistical error free energy pathways. We employ a variety of methods to estimate the radial distribution function (RDF) and find that the computationally cheap two-body "dilute gas" limit performs as well or better than 3D-RISM theory and other approximations for identifying low variance free energy pathways. With a RDF estimate in hand, we can search for pairwise interaction potentials that produce low variance. We give an example of a search minimizing statistical variance of solvation free energy over the entire parameter space of a generalized "soft core" potential. The free energy pathway arising from this optimization procedure has lower curvature in the variance and reduces the total variance by at least 50% compared to the traditional soft core solvation pathway. We also demonstrate that this optimized pathway allows free energies to be estimated with fewer intermediate states due to its low curvature. This free energy variance optimization technique is generalizable to solvation in any homogeneous fluid and for any type of pairwise potential and can be performed in minutes to hours, depending on the method used to estimate g(r).
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Affiliation(s)
- Tri T Pham
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904-4741, USA
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31
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Mallajosyula SS, MacKerell AD. Influence of solvent and intramolecular hydrogen bonding on the conformational properties of o-linked glycopeptides. J Phys Chem B 2011; 115:11215-29. [PMID: 21823626 PMCID: PMC3179525 DOI: 10.1021/jp203695t] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
A detailed investigation of the conformational properties of all the biologically relevant O-glycosidic linkages using the Hamiltonian replica exchange (HREX) simulation methodology and the recently developed CHARMM carbohydrate force field parameters is presented. Fourteen biologically relevant O-linkages between the five sugars N-acetylgalactosamine (GalNAc), N-acetylglucosamine (GlcNAc), D-glucose (Glc), D-mannose (Man), and L-fucose (Fuc) and the amino acids serine and threonine were studied. The force field was tested by comparing the simulation results of the model glycopeptides to various NMR (3)J coupling constants, NOE distances, and data from molecular dynamics with time-averaged restraints (tar-MD). The results show the force field to be in overall agreement with experimental and previous tar-MD simulations, although some small limitations are identified. An in-depth hydrogen bond and bridging water analysis revealed an interplay of hydrogen bonding and bridge water interactions influencing the geometry of the underlying peptide backbone, with the O-linkages favoring extended β-sheet and polyproline type II (PPII) conformations over the compact α(R)-helical conformation. The newly developed parameters were also able to identify hydrogen bonding and water mediated interactions between O-linked sugars and proteins. These results indicate that the newly developed parameters in tandem with HREX conformational sampling provide the means to study glycoproteins in the absence of targeted NMR restraint data.
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Affiliation(s)
- Sairam S. Mallajosyula
- Department of Pharmaceutical Sciences, 20 Penn Street HSF II, University of Maryland, Baltimore, Maryland 21201
| | - Alexander D. MacKerell
- Department of Pharmaceutical Sciences, 20 Penn Street HSF II, University of Maryland, Baltimore, Maryland 21201
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32
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Simulated Q-annealing: conformational search with an effective potential. J Mol Model 2011; 18:213-20. [PMID: 21523533 DOI: 10.1007/s00894-011-1072-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2010] [Accepted: 03/24/2011] [Indexed: 10/18/2022]
Abstract
We have tested a version of the generalized simulated annealing algorithm based on molecular dynamics simulations with effective potential suggested by Tsallis statistics. The generalized annealing method, termed "simulated Q-annealing (SQ)," is applied to the simulations of a synthetic 11-residue peptide segment (1AQG). In SQ, the energy barriers between local minima change as the parameter q is varied and specific degrees of freedom can be selectively heated up and annealed. Conformational dynamics obtained by ordinary simulated annealing (SA) and SQ simulations are compared in order to illustrate the effectiveness of the SQ approach in conformational searching. We show that SQ can navigate the potential energy surface efficiently with a simple annealing protocol and demonstrate that conformations sampled by SQ can represent the funnel-like free energy surface.
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33
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Kim J, Straub JE. Generalized simulated tempering for exploring strong phase transitions. J Chem Phys 2011; 133:154101. [PMID: 20969364 DOI: 10.1063/1.3503503] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An extension of the simulation tempering algorithm is proposed. It is shown to be particularly suited to the exploration of first-order phase transition systems characterized by the backbending or S-loop in the statistical temperature or a microcanonical caloric curve. A guided Markov process in an auxiliary parameter space systematically combines a set of parametrized Tsallis-weight ensemble simulations, which are targeted to transform unstable or metastable energy states of canonical ensembles into stable ones and smoothly join ordered and disordered phases across phase transition regions via a succession of unimodal energy distributions. The inverse mapping between the sampling weight and the effective temperature enables an optimal selection of relevant Tsallis-weight parameters. A semianalytic expression for the biasing weight in parameter space is adaptively updated "on the fly" during the simulation to achieve rapid convergence. Accelerated tunneling transitions with a comprehensive sampling for phase-coexistent states are explicitly demonstrated in systems subject to strong hysteresis including Potts and Ising spin models and a 147 atom Lennard-Jones cluster.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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Abstract
Serial tempering is a computational method that turns the temperature T (or more generally any independent λ parameter) into a dynamical variable. It is shown that, under conditions for which this variable is fast, serial tempering is equivalent to the umbrella sampling method with a single effective potential. This equivalence is demonstrated using both a small one-dimensional system and a small solvated peptide. The suggestion is then made to replace the serial tempering protocol with the equivalent umbrella sampling calculation. This approach, serial tempering without exchange (STeWiE), has the same performance as serial tempering in the limit that exchanges are frequent, is simpler to implement, and has fewer adjustable parameters than conventional serial tempering. The equivalence of serial tempering and STeWiE also provides a convenient route for estimating and optimizing the performance of serial tempering simulations and other generalized-ensemble methods.
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Affiliation(s)
- Hugh Nymeyer
- The Center for Biological Physics, Arizona State University, Tempe, Arizona 85287, USA.
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35
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Kim J, Keyes T, Straub JE. Generalized replica exchange method. J Chem Phys 2010; 132:224107. [PMID: 20550390 PMCID: PMC2896417 DOI: 10.1063/1.3432176] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2010] [Accepted: 04/30/2010] [Indexed: 01/28/2023] Open
Abstract
We present a powerful replica exchange method, particularly suited to first-order phase transitions associated with the backbending in the statistical temperature, by merging an optimally designed generalized ensemble sampling with replica exchanges. The key ingredients of our method are parametrized effective sampling weights, smoothly joining ordered and disordered phases with a succession of unimodal energy distributions by transforming unstable or metastable energy states of canonical ensembles into stable ones. The inverse mapping between the sampling weight and the effective temperature provides a systematic way to design the effective sampling weights and determine a dynamic range of relevant parameters. Illustrative simulations on Potts spins with varying system size and simulation conditions demonstrate a comprehensive sampling for phase-coexistent states with a dramatic acceleration of tunneling transitions. A significant improvement over the power-law slowing down of mean tunneling times with increasing system size is obtained, and the underlying mechanism for accelerated tunneling is discussed.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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36
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Kim E, Jang S, Lim M, Pak Y. Free energy landscape of the FBP28 WW domain by all-atom direct folding simulation. J Phys Chem B 2010; 114:7686-91. [PMID: 20465282 DOI: 10.1021/jp102215j] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Using multiplexed Q-replica exchange molecular dynamics simulation (mQ-REMD) with a modified all-atom force field (param99MOD5/GBSA), direct folding simulation at the all-atom level was performed to investigate the folding free energy landscapes of the FBP28 WW domain: a 37-residue three-stranded beta-sheet. Starting from a fully extended conformation of the FBP28 WW domain, a total of 400 ns simulation was run for each replica with this simulation protocol. Free energy analysis showed that the folding of this protein substantially proceeded through the formation of folded turn 1, followed by the partial or misfolded formation of turn 2. More importantly, the folding process of turn 2 exhibited complicated folding behaviors in the presence of several intermediate states along multiple folding routes.
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Affiliation(s)
- Eunae Kim
- Department of Chemistry and Division of Functional Materials, Pusan National University, Busan 609-735, Korea
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37
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Nguyen PH. Replica exchange simulation method using temperature and solvent viscosity. J Chem Phys 2010; 132:144109. [DOI: 10.1063/1.3369626] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Kannan S, Zacharias M. Folding simulations of Trp-cage mini protein in explicit solvent using biasing potential replica-exchange molecular dynamics simulations. Proteins 2010; 76:448-60. [PMID: 19173315 DOI: 10.1002/prot.22359] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp-cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near-native conformations was observed after 30-40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of approximately 1.3 A from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp-cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein.
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39
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Kim E, Jang S, Pak Y. All-atom ab initio native structure prediction of a mixed fold (1FME): a comparison of structural and folding characteristics of various beta beta alpha miniproteins. J Chem Phys 2010; 131:195102. [PMID: 19929079 DOI: 10.1063/1.3266510] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We performed an all-atom ab initio native structure prediction of 1FME, which is one of the computationally challenging mixed fold beta beta alpha miniproteins, by combining a novel conformational search algorithm (multiplexed Q-replica exchange molecular dynamics scheme) with a well-balanced all-atom force field employing a generalized Born implicit solvation model (param99MOD5/GBSA). The nativelike structure of 1FME was identified from the lowest free energy minimum state and in excellent agreement with the NMR structure. Based on the interpretation of the free energy landscape, the structural properties as well as the folding behaviors of 1FME were compared with other beta beta alpha miniproteins (1FSD, 1PSV, and BBA5) that we have previously studied with the same force field. Our simulation showed that the 28-residue beta beta alpha miniproteins (1FME, 1FSD, and 1PSV) share a common feature of the free energy topography and exhibit the three local minimum states on each computed free energy map, but the 23-residue miniprotein (BBA5) follows a downhill folding with a single minimum state. Also, the structure and stability changes resulting from the two point mutation (Gln1-->Glu1 and Ile7-->Tyr7) of 1FSD were investigated in details for direct comparison with the experiment. The comparison shows that upon mutation, the experimentally observed turn type switch from an irregular turn (1FSD) to type I(') turn (1FME) was well reproduced with the present simulation.
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Affiliation(s)
- Eunae Kim
- Department of Chemistry, Pusan National University, Busan 609-735, Korea
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40
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Earl DJ, Deem MW. Parallel tempering: theory, applications, and new perspectives. Phys Chem Chem Phys 2009; 7:3910-6. [PMID: 19810318 DOI: 10.1039/b509983h] [Citation(s) in RCA: 592] [Impact Index Per Article: 39.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
We review the history of the parallel tempering simulation method. From its origins in data analysis, the parallel tempering method has become a standard workhorse of physicochemical simulations. We discuss the theory behind the method and its various generalizations. We mention a selected set of the many applications that have become possible with the introduction of parallel tempering, and we suggest several promising avenues for future research.
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Affiliation(s)
- David J Earl
- Department of Bioengineering, Rice University, 6100 Main Street MS142, Houston, Texas 77005, USA.
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42
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Zheng L, Chen M, Yang W. Simultaneous escaping of explicit and hidden free energy barriers: application of the orthogonal space random walk strategy in generalized ensemble based conformational sampling. J Chem Phys 2009; 130:234105. [PMID: 19548709 DOI: 10.1063/1.3153841] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To overcome the pseudoergodicity problem, conformational sampling can be accelerated via generalized ensemble methods, e.g., through the realization of random walks along prechosen collective variables, such as spatial order parameters, energy scaling parameters, or even system temperatures or pressures, etc. As usually observed, in generalized ensemble simulations, hidden barriers are likely to exist in the space perpendicular to the collective variable direction and these residual free energy barriers could greatly abolish the sampling efficiency. This sampling issue is particularly severe when the collective variable is defined in a low-dimension subset of the target system; then the "Hamiltonian lagging" problem, which reveals the fact that necessary structural relaxation falls behind the move of the collective variable, may be likely to occur. To overcome this problem in equilibrium conformational sampling, we adopted the orthogonal space random walk (OSRW) strategy, which was originally developed in the context of free energy simulation [L. Zheng, M. Chen, and W. Yang, Proc. Natl. Acad. Sci. U.S.A. 105, 20227 (2008)]. Thereby, generalized ensemble simulations can simultaneously escape both the explicit barriers along the collective variable direction and the hidden barriers that are strongly coupled with the collective variable move. As demonstrated in our model studies, the present OSRW based generalized ensemble treatments show improved sampling capability over the corresponding classical generalized ensemble treatments.
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Affiliation(s)
- Lianqing Zheng
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA
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43
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Roles of boundary conditions in DNA simulations: analysis of ion distributions with the finite-difference Poisson-Boltzmann method. Biophys J 2009; 97:554-62. [PMID: 19619470 DOI: 10.1016/j.bpj.2009.05.012] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2009] [Revised: 05/01/2009] [Accepted: 05/05/2009] [Indexed: 11/20/2022] Open
Abstract
The wide use of lattice-sum strategies in biomolecular simulations has raised many questions on potential artifacts in these strategies. One interesting question is the artifacts in the counterion distributions of highly charged systems. As one would anticipate, Coulombic interactions under the periodic boundary condition may deviate noticeably from those under the free boundary condition in the highly charged systems, significantly influencing their counterion distributions. On the other hand, the electrostatic screening due to water molecules and mobile ions may effectively damp the possible periodic distortions in Coulombic interactions. Therefore, the magnitude of periodicity-induced artifacts in counterion distributions is not straightforward to dissect without detailed analyses. In this study, we have developed a hybrid explicit counterion/implicit salt representation of mobile ions to address this question. We have chosen a well-studied DNA for easy validation of the minimal hybrid ion representation. Our detailed analysis of continuum ion distributions, explicit ion distributions, radial counterion distribution functions, and sequence-dependent counterion distributions, however, indicates that periodicity artifacts are not apparent at the surface of the tested DNA. Nevertheless, influence of boundary conditions does show up starting at the second solvation shell and becomes apparent at the cell boundary.
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44
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Kim J, Keyes T, Straub JE. Replica exchange statistical temperature Monte Carlo. J Chem Phys 2009; 130:124112. [PMID: 19334813 DOI: 10.1063/1.3095422] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The replica exchange statistical temperature Monte Carlo algorithm (RESTMC) is presented, extending the single-replica STMC algorithm [J. Kim, J. E. Straub, and T. Keyes, Phys. Rev. Lett. 97, 050601 (2006)] to alleviate the slow convergence of the conventional temperature replica exchange method (t-REM) with increasing system size. In contrast to the Gibbs-Boltzmann sampling at a specific temperature characteristic of the standard t-REM, RESTMC samples a range of temperatures in each replica and achieves a flat energy sampling employing the generalized sampling weight, which is automatically determined via the dynamic modification of the replica-dependent statistical temperature. Faster weight determination, through the dynamic update of the statistical temperature, and the flat energy sampling, maximizing energy overlaps between neighboring replicas, lead to a considerable acceleration in the convergence of simulations even while employing significantly fewer replicas. The performance of RESTMC is demonstrated and quantitatively compared with that of the conventional t-REM under varying simulation conditions for Lennard-Jones 19, 31, and 55 atomic clusters, exhibiting single- and double-funneled energy landscapes.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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45
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Abstract
We introduce a replica exchange (parallel tempering) method in which attempted configuration swaps are generated using nonequilibrium work simulations. By effectively increasing phase space overlap, this approach mitigates the need for many replicas. We illustrate our method by using a model system and show that it is able to achieve the computational efficiency of ordinary replica exchange, using fewer replicas.
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46
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Mitsutake A, Okamoto Y. Multidimensional generalized-ensemble algorithms for complex systems. J Chem Phys 2009; 130:214105. [DOI: 10.1063/1.3127783] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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47
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Kim J, Straub JE. Optimal replica exchange method combined with Tsallis weight sampling. J Chem Phys 2009; 130:144114. [PMID: 19368436 PMCID: PMC2736612 DOI: 10.1063/1.3108523] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2009] [Accepted: 03/08/2009] [Indexed: 02/03/2023] Open
Abstract
A unified framework integrating the generalized ensemble sampling associated with the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] and the replica exchange method (REM) has been proposed to accelerate the convergence of the conventional temperature REM (t-REM). Using the effective temperature formulation of the Tsallis weight sampling, it is shown that the average acceptance probability for configurational swaps between neighboring replicas in the combination of Tsallis weight sampling and REM (Tsallis-REM) is directly proportional to an overlap integral of the energy distributions of neighboring replicas as in the t-REM. Based on this observation, we suggest a robust method to select optimal Tsallis parameters in the conventional parametrization scheme and present new parametrization schemes for the Tsallis-REM, which significantly improves the acceptance of configurational swaps by systematically modulating energy overlaps between neighboring replicas. The distinguished feature of our method is that all relevant parameters in the Tsallis-REM are automatically determined from the equilibrium phase simulation using the t-REM. The overall performance of our method is explicitly demonstrated for various simulation conditions for the Lennard-Jones 31 atom clusters, exhibiting a double-funneled energy landscape.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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48
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Kannan S, Zacharias M. Folding of Trp-cage mini protein using temperature and biasing potential replica-exchange molecular dynamics simulations. Int J Mol Sci 2009; 10:1121-37. [PMID: 19399241 PMCID: PMC2672022 DOI: 10.3390/ijms10031121] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2009] [Revised: 03/05/2009] [Accepted: 03/09/2009] [Indexed: 11/16/2022] Open
Abstract
The folding process of the 20 residue Trp-cage mini-protein was investigated using standard temperature replica exchange molecular dynamics (T-RexMD) simulation and a biasing potential RexMD (BP-RexMD) method. In contrast to several conventional molecular dynamics simulations, both RexMD methods sampled conformations close to the native structure after 10-20 ns simulation time as the dominant conformational states. In contrast, to T-RexMD involving 16 replicas the BP-RexMD method achieved very similar sampling results with only five replicas. The result indicates that the BP-RexMD method is well suited to study folding processes of proteins at a significantly smaller computational cost, compared to T-RexMD. Both RexMD methods sampled not only similar final states but also agreed on the sampling of intermediate conformations during Trp-cage folding. The analysis of the sampled potential energy contributions indicated that Trp-cage folding is favored by both van der Waals and to a lesser degree electrostatic contributions. Folding does not introduce any significant sterical strain as reflected by similar energy distributions of bonded energy terms (bond length, bond angle and dihedral angle) of folded and unfolded Trp-cage structures.
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Affiliation(s)
- Srinivasaraghavan Kannan
- School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, D-28759 Bremen, Germany
| | - Martin Zacharias
- School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, D-28759 Bremen, Germany
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49
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Mitsutake A. Simulated-tempering replica-exchange method for the multidimensional version. J Chem Phys 2009; 131:094105. [DOI: 10.1063/1.3204443] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Xu C, Wang J, Liu H. A Hamiltonian Replica Exchange Approach and Its Application to the Study of Side-Chain Type and Neighbor Effects on Peptide Backbone Conformations. J Chem Theory Comput 2008; 4:1348-59. [DOI: 10.1021/ct7003534] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Chao Xu
- School of Life Sciences, and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China (USTC), Hefei, Anhui 230027, China
| | - Jun Wang
- School of Life Sciences, and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China (USTC), Hefei, Anhui 230027, China
| | - Haiyan Liu
- School of Life Sciences, and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China (USTC), Hefei, Anhui 230027, China
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