1
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Wu H, Huang H, Post CB. All-atom adaptively biased path optimization of Src kinase conformational inactivation: Switched electrostatic network in the concerted motion of αC helix and the activation loop. J Chem Phys 2020; 153:175101. [PMID: 33167630 DOI: 10.1063/5.0021603] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
A method to optimize a conformational pathway through a space of well-chosen reduced variables is employed to advance our understanding of protein conformational equilibrium. The adaptively biased path optimization strategy utilizes unrestricted, enhanced sampling in the region of a path in the reduced-variable space to identify a broad path between two stable end-states. Application to the inactivation transition of the Src tyrosine kinase catalytic domain reveals new insight into this well studied conformational equilibrium. The mechanistic description gained from identifying the motions and structural features along the path includes details of the switched electrostatic network found to underpin the transition. The free energy barrier along the path results from rotation of a helix, αC, that is tightly correlated with motions in the activation loop (A-loop) as well as distal regions in the C-lobe. Path profiles of the reduced variables clearly demonstrate the strongly correlated motions. The exchange of electrostatic interactions among residues in the network is key to these interdependent motions. In addition, the increased resolution from an all-atom model in defining the path shows multiple components for the A-loop motion and that different parts of the A-loop contribute throughout the length of the path.
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Affiliation(s)
- Heng Wu
- Department of Medicinal Chemistry and Molecular Pharmacology, Markey Center for Structural Biology, Purdue Center for Cancer Research, Purdue University, West Lafayette, Indiana 47907, USA
| | - He Huang
- Department of Medicinal Chemistry and Molecular Pharmacology, Markey Center for Structural Biology, Purdue Center for Cancer Research, Purdue University, West Lafayette, Indiana 47907, USA
| | - Carol Beth Post
- Department of Medicinal Chemistry and Molecular Pharmacology, Markey Center for Structural Biology, Purdue Center for Cancer Research, Purdue University, West Lafayette, Indiana 47907, USA
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2
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Cellular absorption of small molecules: free energy landscapes of melatonin binding at phospholipid membranes. Sci Rep 2020; 10:9235. [PMID: 32513935 PMCID: PMC7280225 DOI: 10.1038/s41598-020-65753-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2019] [Accepted: 05/05/2020] [Indexed: 12/28/2022] Open
Abstract
Free energy calculations are essential to unveil mechanisms at the atomic scale such as binding of small solutes and their translocation across cell membranes, eventually producing cellular absorption. Melatonin regulates biological rhythms and is directly related to carcinogenesis and neurodegenerative disorders. Free energy landscapes obtained from well-tempered metadynamics simulations precisely describe the characteristics of melatonin binding to specific sites in the membrane and reveal the role of cholesterol in free energy barrier crossing. A specific molecular torsional angle and the distance between melatonin and the center of the membrane along the normal to the membrane Z-axis have been considered as suitable reaction coordinates. Free energy barriers between two particular orientations of the molecular structure (folded and extended) have been found to be of about 18 kJ/mol for z-distances of about 1–2 nm. The ability of cholesterol to expel melatonin out of the internal regions of the membrane towards the interface and the external solvent is explained from a free energy perspective. The calculations reported here offer detailed free energy landscapes of melatonin embedded in model cell membranes and reveal microscopic information on its transition between free energy minima, including the location of relevant transition states, and provide clues on the role of cholesterol in the cellular absorption of small molecules.
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3
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Fu H, Chen H, Wang X, Chai H, Shao X, Cai W, Chipot C. Finding an Optimal Pathway on a Multidimensional Free-Energy Landscape. J Chem Inf Model 2020; 60:5366-5374. [DOI: 10.1021/acs.jcim.0c00279] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Haohao Fu
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Haochuan Chen
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Xin’ao Wang
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Hao Chai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Xueguang Shao
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Wensheng Cai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Christophe Chipot
- Laboratoire International Associé CNRS and University of Illinois at Urbana−Champaign, F-54506 Vandœuvre-lès-Nancy, France
- Department of Physics, University of Illinois at Urbana−Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
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4
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Zhou Y, Ojeda-May P, Nagaraju M, Kim B, Pu J. Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method. Molecules 2018; 23:molecules23102652. [PMID: 30332773 PMCID: PMC6222333 DOI: 10.3390/molecules23102652] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2018] [Revised: 10/09/2018] [Accepted: 10/10/2018] [Indexed: 11/16/2022] Open
Abstract
HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.
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Affiliation(s)
- Yan Zhou
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., LD326, Indianapolis, IN 46202, USA.
| | - Pedro Ojeda-May
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., LD326, Indianapolis, IN 46202, USA.
| | - Mulpuri Nagaraju
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., LD326, Indianapolis, IN 46202, USA.
| | - Bryant Kim
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., LD326, Indianapolis, IN 46202, USA.
| | - Jingzhi Pu
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., LD326, Indianapolis, IN 46202, USA.
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5
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Wu H, Post CB. Protein Conformational Transitions from All-Atom Adaptively Biased Path Optimization. J Chem Theory Comput 2018; 14:5372-5382. [PMID: 30222340 DOI: 10.1021/acs.jctc.8b00147] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Simulation methods are valuable for elucidating protein conformational transitions between functionally diverse states given that transition pathways are difficult to capture experimentally. Nonetheless, specific computational algorithms are required because of the high free energy barriers between these different protein conformational states. Adaptively biased path optimization (ABPO) is an unrestrained, transition-path optimization method that works in a reduced-variable space to construct an adaptive biasing potential to aid convergence. ABPO was previously applied using a coarse-grained Go̅-model to study conformational activation of Lyn, a Src family tyrosine kinase. How effectively ABPO can be applied at the higher resolution of an all-atom model to explore protein conformational transitions is not yet known. Here, we report the all-atom conformational transition paths of three protein systems constructed using the ABPO methodology. Two systems, triose phosphate isomerase and dihydrofolate reductase, undergo local flipping of a short loop that promotes ligand binding. The third system, estrogen receptor α ligand binding domain, has a helix that adopts different conformations when the protein is bound to an agonist or an antagonist. For each protein, distance-based or torsion-angle reduced variables were identified from unbiased trajectories. ABPO was computed in this reduced variable space to obtain the transition path between the two states. The all-atom ABPO is shown to successfully converge an optimal transition path for each of the three systems.
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Affiliation(s)
- Heng Wu
- Department of Medicinal Chemistry and Molecular Pharmacology, Markey Center for Structural Biology, Purdue Center for Cancer Research , Purdue University , West Lafayette , Indiana 47907 , United States
| | - Carol Beth Post
- Department of Medicinal Chemistry and Molecular Pharmacology, Markey Center for Structural Biology, Purdue Center for Cancer Research , Purdue University , West Lafayette , Indiana 47907 , United States
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6
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Zhao T, Fu H, Lelièvre T, Shao X, Chipot C, Cai W. The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations. J Chem Theory Comput 2017; 13:1566-1576. [PMID: 28253446 DOI: 10.1021/acs.jctc.7b00032] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Free-energy calculations in multiple dimensions constitute a challenging problem, owing to the significant computational cost incurred to achieve ergodic sampling. The generalized adaptive biasing force (gABF) algorithm calculates n one-dimensional lists of biasing forces to approximate the n-dimensional matrix by ignoring the coupling terms ordinarily taken into account in classical ABF simulations, thereby greatly accelerating sampling in the multidimensional space. This approximation may however occasionally lead to poor, incomplete exploration of the conformational space compared to classical ABF, especially when the selected coarse variables are strongly coupled. It has been found that introducing extended potentials coupled to the coarse variables of interest can virtually eliminate this shortcoming, and, thus, improve the efficiency of gABF simulations. In the present contribution, we propose a new free-energy method, coined extended generalized ABF (egABF), combining gABF with an extended Lagrangian strategy. The results for three illustrative examples indicate that (i) egABF can explore the transition coordinate much more efficiently compared with classical ABF, eABF, and gABF, in both simple and complex cases and (ii) egABF can achieve a higher accuracy than gABF, with a root mean-squared deviation between egABF and eABF free-energy profiles on the order of kBT. Furthermore, the new egABF algorithm outruns the previous ABF-based algorithms in high-dimensional free-energy calculations and, hence, represents a powerful importance-sampling alternative for the investigation of complex chemical and biological processes.
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Affiliation(s)
- Tanfeng Zhao
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China
| | - Haohao Fu
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China
| | - Tony Lelièvre
- Université Paris-Est , CERMICS (ENPC), INRIA, 77455 Marne-la-Vallée, France
| | - Xueguang Shao
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.,Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071, China.,State Key Laboratory of Medicinal Chemical Biology, Nankai University , Tianjin 300071, China
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign , Unité Mixte de Recherche No. 7565, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France.,Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.,Department of Physics, University of Illinois at Urbana-Champaign , 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Wensheng Cai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.,Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071, China
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7
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Fu H, Shao X, Chipot C, Cai W. Extended Adaptive Biasing Force Algorithm. An On-the-Fly Implementation for Accurate Free-Energy Calculations. J Chem Theory Comput 2016; 12:3506-13. [PMID: 27398726 DOI: 10.1021/acs.jctc.6b00447] [Citation(s) in RCA: 88] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Proper use of the adaptive biasing force (ABF) algorithm in free-energy calculations needs certain prerequisites to be met, namely, that the Jacobian for the metric transformation and its first derivative be available and the coarse variables be independent and fully decoupled from any holonomic constraint or geometric restraint, thereby limiting singularly the field of application of the approach. The extended ABF (eABF) algorithm circumvents these intrinsic limitations by applying the time-dependent bias onto a fictitious particle coupled to the coarse variable of interest by means of a stiff spring. However, with the current implementation of eABF in the popular molecular dynamics engine NAMD, a trajectory-based post-treatment is necessary to derive the underlying free-energy change. Usually, such a posthoc analysis leads to a decrease in the reliability of the free-energy estimates due to the inevitable loss of information, as well as to a drop in efficiency, which stems from substantial read-write accesses to file systems. We have developed a user-friendly, on-the-fly code for performing eABF simulations within NAMD. In the present contribution, this code is probed in eight illustrative examples. The performance of the algorithm is compared with traditional ABF, on the one hand, and the original eABF implementation combined with a posthoc analysis, on the other hand. Our results indicate that the on-the-fly eABF algorithm (i) supplies the correct free-energy landscape in those critical cases where the coarse variables at play are coupled to either each other or to geometric restraints or holonomic constraints, (ii) greatly improves the reliability of the free-energy change, compared to the outcome of a posthoc analysis, and (iii) represents a negligible additional computational effort compared to regular ABF. Moreover, in the proposed implementation, guidelines for choosing two parameters of the eABF algorithm, namely the stiffness of the spring and the mass of the fictitious particles, are proposed. The present on-the-fly eABF implementation can be viewed as the second generation of the ABF algorithm, expected to be widely utilized in the theoretical investigation of recognition and association phenomena relevant to physics, chemistry, and biology.
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Affiliation(s)
| | - Xueguang Shao
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche No. 7565, Université de Lorraine , B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France.,Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.,Department of Physics, University of Illinois at Urbana-Champaign , 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Wensheng Cai
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
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8
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Wu D, Fajer MI, Cao L, Cheng X, Yang W. Generalized Ensemble Sampling of Enzyme Reaction Free Energy Pathways. Methods Enzymol 2016; 577:57-74. [PMID: 27498634 PMCID: PMC4978182 DOI: 10.1016/bs.mie.2016.05.012] [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: 06/11/2024]
Abstract
Free energy path sampling plays an essential role in computational understanding of chemical reactions, particularly those occurring in enzymatic environments. Among a variety of molecular dynamics simulation approaches, the generalized ensemble sampling strategy is uniquely attractive for the fact that it not only can enhance the sampling of rare chemical events but also can naturally ensure consistent exploration of environmental degrees of freedom. In this review, we plan to provide a tutorial-like tour on an emerging topic: generalized ensemble sampling of enzyme reaction free energy path. The discussion is largely focused on our own studies, particularly ones based on the metadynamics free energy sampling method and the on-the-path random walk path sampling method. We hope that this minipresentation will provide interested practitioners some meaningful guidance for future algorithm formulation and application study.
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Affiliation(s)
- D Wu
- Institute of Molecular Biophysics, Florida State University, Tallahassee, FL, United States
| | - M I Fajer
- UT-ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, TN, United States; Florida State University, Tallahassee, FL, United States
| | - L Cao
- Florida State University, Tallahassee, FL, United States
| | - X Cheng
- UT-ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, TN, United States; The University of Tennessee, Knoxville, TN, United States.
| | - W Yang
- Institute of Molecular Biophysics, Florida State University, Tallahassee, FL, United States; Florida State University, Tallahassee, FL, United States.
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9
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Zinovjev K, Tuñón I. Transition state ensemble optimization for reactions of arbitrary complexity. J Chem Phys 2015; 143:134111. [DOI: 10.1063/1.4931596] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Kirill Zinovjev
- Departament de Química Física, Universitat de València, 46100 Burjassot, Spain
| | - Iñaki Tuñón
- Departament de Química Física, Universitat de València, 46100 Burjassot, Spain
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10
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Atomic-level characterization of transport cycle thermodynamics in the glycerol-3-phosphate:phosphate antiporter. Nat Commun 2015; 6:8393. [PMID: 26417850 PMCID: PMC4598623 DOI: 10.1038/ncomms9393] [Citation(s) in RCA: 68] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2015] [Accepted: 08/18/2015] [Indexed: 01/09/2023] Open
Abstract
Membrane transporters actively translocate their substrate by undergoing large-scale structural transitions between inward- (IF) and outward-facing (OF) states ('alternating-access' mechanism). Despite extensive structural studies, atomic-level mechanistic details of such structural transitions, and as importantly, their coupling to chemical events supplying the energy, remain amongst the most elusive aspects of the function of these proteins. Here we present a quantitative, atomic-level description of the functional thermodynamic cycle for the glycerol-3-phosphate:phosphate antiporter GlpT by using a novel approach in reconstructing the free energy landscape governing the IF↔OF transition along a cyclic transition pathway involving both apo and substrate-bound states. Our results provide a fully atomic description of the complete transport process, offering a structural model for the alternating-access mechanism and substantiating the close coupling between global structural transitions and local chemical events.
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11
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Branduardi D, Marinelli F, Faraldo-Gómez JD. Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method. J Comput Chem 2015; 37:575-86. [PMID: 26149527 DOI: 10.1002/jcc.23991] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2015] [Revised: 06/09/2015] [Accepted: 06/11/2015] [Indexed: 01/28/2023]
Abstract
The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.
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Affiliation(s)
- Davide Branduardi
- Theoretical Molecular Biophysics Group, Max Planck Institute of Biophysics, Max-von-Laue Strasse 3, Frankfurt-am-Main, DE 60438, Germany
| | - Fabrizio Marinelli
- Theoretical Molecular Biophysics Section, National Heart, Lung and Blood Institute, National Institutes of Health, Building 5635FL, Suite T-800, Bethesda, Maryland, 20892
| | - José D Faraldo-Gómez
- Theoretical Molecular Biophysics Group, Max Planck Institute of Biophysics, Max-von-Laue Strasse 3, Frankfurt-am-Main, DE 60438, Germany.,Theoretical Molecular Biophysics Section, National Heart, Lung and Blood Institute, National Institutes of Health, Building 5635FL, Suite T-800, Bethesda, Maryland, 20892
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12
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Hudson PS, White JK, Kearns FL, Hodoscek M, Boresch S, Lee Woodcock H. Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes. Biochim Biophys Acta Gen Subj 2014; 1850:944-953. [PMID: 25239198 DOI: 10.1016/j.bbagen.2014.09.016] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Revised: 09/09/2014] [Accepted: 09/10/2014] [Indexed: 11/25/2022]
Abstract
BACKGROUND Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting. METHODS Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes. RESULTS Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation. CONCLUSIONS The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures. GENERAL SIGNIFICANCE Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.
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Affiliation(s)
- Phillip S Hudson
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE205, Tampa, FL 33620-5250, USA
| | - Justin K White
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE205, Tampa, FL 33620-5250, USA
| | - Fiona L Kearns
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE205, Tampa, FL 33620-5250, USA
| | - Milan Hodoscek
- Center for Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, SI-1000 Ljubljana, Slovenia
| | - Stefan Boresch
- Department of Computational Biological Chemistry, Faculty of Chemistry, University of Vienna, Währingerstraße 17, A-1090 Vienna, Austria
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE205, Tampa, FL 33620-5250, USA.
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13
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Moradi M, Tajkhorshid E. Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems. J Chem Theory Comput 2014; 10:2866-2880. [PMID: 25018675 PMCID: PMC4089915 DOI: 10.1021/ct5002285] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Indexed: 11/30/2022]
Abstract
Characterizing large-scale structural transitions in biomolecular systems poses major technical challenges to both experimental and computational approaches. On the computational side, efficient sampling of the configuration space along the transition pathway remains the most daunting challenge. Recognizing this issue, we introduce a knowledge-based computational approach toward describing large-scale conformational transitions using (i) nonequilibrium, driven simulations combined with work measurements and (ii) free energy calculations using empirically optimized biasing protocols. The first part is based on designing mechanistically relevant, system-specific reaction coordinates whose usefulness and applicability in inducing the transition of interest are examined using knowledge-based, qualitative assessments along with nonequilirbrium work measurements which provide an empirical framework for optimizing the biasing protocol. The second part employs the optimized biasing protocol resulting from the first part to initiate free energy calculations and characterize the transition quantitatively. Using a biasing protocol fine-tuned to a particular transition not only improves the accuracy of the resulting free energies but also speeds up the convergence. The efficiency of the sampling will be assessed by employing dimensionality reduction techniques to help detect possible flaws and provide potential improvements in the design of the biasing protocol. Structural transition of a membrane transporter will be used as an example to illustrate the workings of the proposed approach.
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Affiliation(s)
- Mahmoud Moradi
- Department of Biochemistry,
Center for Biophysics and Computational Biology, and Beckman Institute
for Advanced Science and Technology, University
of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Emad Tajkhorshid
- Department of Biochemistry,
Center for Biophysics and Computational Biology, and Beckman Institute
for Advanced Science and Technology, University
of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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14
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Pathak AK, Bandyopadhyay T. Unbinding free energy of acetylcholinesterase bound oxime drugs along the gorge pathway from metadynamics-umbrella sampling investigation. Proteins 2014; 82:1799-818. [PMID: 24549829 DOI: 10.1002/prot.24533] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2013] [Revised: 01/17/2014] [Accepted: 01/28/2014] [Indexed: 12/20/2022]
Abstract
Because of the pivotal role that the nerve enzyme, acetylcholinesterase plays in terminating nerve impulses at cholinergic synapses. Its active site, located deep inside a 20 Å gorge, is a vulnerable target of the lethal organophosphorus compounds. Potent reactivators of the intoxicated enzyme are nucleophiles, such as bispyridinium oxime that binds to the peripheral anionic site and the active site of the enzyme through suitable cation-π interactions. Atomic scale molecular dynamics and free energy calculations in explicit water are used to study unbinding pathways of two oxime drugs (Ortho-7 and Obidoxime) from the gorge of the enzyme. The role of enzyme-drug cation-π interactions are explored with the metadynamics simulation. The metadynamics discovered potential of mean force (PMF) of the unbinding events is refined by the umbrella sampling (US) corrections. The bidimensional free energy landscape of the metadynamics runs are further subjected to finite temperature string analysis to obtain the transition tube connecting the minima and bottlenecks of the unbinding pathway. The PMF is also obtained from US simulations using the biasing potential constructed from the transition tube and are found to be consistent with the metadynamics-US corrected results. Although experimental structural data clearly shows analogous coordination of the two drugs inside the gorge in the bound state, the PMF of the drug trafficking along the gorge pathway point, within an equilibrium free energy context, to a multistep process that differs from one another. Routes, milestones and subtlety toward the unbinding pathway of the two oximes at finite temperature are identified.
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Affiliation(s)
- Arup K Pathak
- Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Trombay, Mumbai, India
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15
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Li W, Ma A. Recent developments in methods for identifying reaction coordinates. MOLECULAR SIMULATION 2014; 40:784-793. [PMID: 25197161 PMCID: PMC4152980 DOI: 10.1080/08927022.2014.907898] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.
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Affiliation(s)
- Wenjin Li
- Department of Bioengineering, The University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA
| | - Ao Ma
- Department of Bioengineering, The University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA
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16
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Branduardi D, Faraldo-Gómez JD. String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems. J Chem Theory Comput 2013; 9:4140-4154. [PMID: 24729762 PMCID: PMC3981481 DOI: 10.1021/ct400469w] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.
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Affiliation(s)
- Davide Branduardi
- Theoretical Molecular Biophysics Group, Max Planck Institute of Biophysics, Max-von-Laue Strasse 3, DE-60438, Frankfurt-am-Main, Germany
| | - José D. Faraldo-Gómez
- Theoretical Molecular Biophysics Group, Max Planck Institute of Biophysics, Max-von-Laue Strasse 3, DE-60438, Frankfurt-am-Main, Germany
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17
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Cao L, Lv C, Yang W. Hidden Conformation Events in DNA Base Extrusions: A Generalized Ensemble Path Optimization and Equilibrium Simulation Study. J Chem Theory Comput 2013; 9:10.1021/ct400198q. [PMID: 24250279 PMCID: PMC3829643 DOI: 10.1021/ct400198q] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
DNA base extrusion is a crucial component of many biomolecular processes. Elucidating how bases are selectively extruded from the interiors of double-strand DNAs is pivotal to accurately understanding and efficiently sampling this general type of conformational transitions. In this work, the on-the-path random walk (OTPRW) method, which is the first generalized ensemble sampling scheme designed for finite-temperature-string path optimizations, was improved and applied to obtain the minimum free energy path (MFEP) and the free energy profile of a classical B-DNA major-groove base extrusion pathway. Along the MFEP, an intermediate state and the corresponding transition state were located and characterized. The MFEP result suggests that a base-plane-elongation event rather than the commonly focused base-flipping event is dominant in the transition state formation portion of the pathway; and the energetic penalty at the transition state is mainly introduced by the stretching of the Watson-Crick base pair. Moreover to facilitate the essential base-plane-elongation dynamics, the surrounding environment of the flipped base needs to be intimately involved. Further taking the advantage of the extended-dynamics nature of the OTPRW Hamiltonian, an equilibrium generalized ensemble simulation was performed along the optimized path; and based on the collected samples, several base-flipping (opening) angle collective variables were evaluated. In consistence with the MFEP result, the collective variable analysis result reveals that none of these commonly employed flipping (opening) angles alone can adequately represent the base extrusion pathway, especially in the pre-transition-state portion. As further revealed by the collective variable analysis, the base-pairing partner of the extrusion target undergoes a series of in-plane rotations to facilitate the base-plane-elongation dynamics. A base-plane rotation angle is identified to be a possible reaction coordinate to represent these in-plane rotations. Notably, these in-plane rotation motions may play a pivotal role in determining the base extrusion selectivity.
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Affiliation(s)
- Liaoran Cao
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL, 32306
| | - Chao Lv
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL, 32306
| | - Wei Yang
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL, 32306
- Institute of Molecular Biophysics, Florida State University, Tallahassee, FL, 32306
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18
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Two typos need to be corrected in the article “On-the-path random walk sampling for efficient optimization of minimum free-energy path”. J Comput Chem 2013. [DOI: 10.1002/jcc.23411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Zinovjev K, Ruiz-Pernía JJ, Tuñón I. Toward an Automatic Determination of Enzymatic Reaction Mechanisms and Their Activation Free Energies. J Chem Theory Comput 2013; 9:3740-9. [PMID: 26584125 DOI: 10.1021/ct400153r] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
We present a combination of the string method and a path collective variable for the exploration of the free energy surface associated to a chemical reaction in condensed environments. The on-the-fly string method is employed to find the minimum free energy paths on a multidimensional free energy surface defined in terms of interatomic distances, which is a convenient selection to study bond forming/breaking processes. Once the paths have been determined, a reaction coordinate is defined as a measure of the advance of the system along these paths. This reaction coordinate can be then used to trace the reaction Potential of Mean Force from which the activation free energy can be obtained. This combination of methodologies has been here applied to the study, by means of Quantum Mechanics/Molecular Mechanics simulations, of the reaction catalyzed by guanidinoacetate methyltransferase. This enzyme catalyzes the methylation of guanidinoacetate by S-adenosyl-l-methionine, a reaction that involves a methyl transfer and a proton transfer and for which different reaction mechanisms have been proposed.
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Affiliation(s)
- Kirill Zinovjev
- Departament de Química Física, Universitat de València , 46100 Burjassot, Spain.,Departament de Química Física i Analítica, Universitat Jaume I , 12071 Castellón, Spain
| | - J Javier Ruiz-Pernía
- Departament de Química Física i Analítica, Universitat Jaume I , 12071 Castellón, Spain
| | - Iñaki Tuñón
- Departament de Química Física, Universitat de València , 46100 Burjassot, Spain
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20
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Tian C, Xiu P, Meng Y, Zhao W, Wang Z, Zhou R. Enantiomerization mechanism of thalidomide and the role of water and hydroxide ions. Chemistry 2012; 18:14305-13. [PMID: 23065668 DOI: 10.1002/chem.201202651] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2012] [Indexed: 11/07/2022]
Abstract
The significance of the molecular chirality of drugs has been widely recognized due to the thalidomide tragedy. Most of the new drugs reaching the market today are single enantiomers, rather than racemic mixtures. However, many optically pure drugs, including thalidomide, undergo enantiomerization in vivo, thus negating the single enantiomers' benefits or inducing unexpected effects. A detailed atomic level understanding of chiral conversion, which is still largely lacking, is thus critical for drug development. Herein, we use first-principle density function theory (DFT) to explore the mechanism of enantiomerization of thalidomide. We have identified the two most plausible interconversion pathways for isolated thalidomide: 1) proton transfer from the chiral carbon center to an adjacent carbonyl oxygen atom, followed by isomerization and rotation of the glutarimide ring (before the proton hops back to the chiral carbon atom); and 2) a pathway that is the same as "1", but with the isomerization of the glutarimide ring occurring ahead of the initial proton transfer reaction. There are two remarkable energy barriers, 73.29 and 23.59 kcal mol(-1), corresponding to the proton transfer and the rotation of the glutarimide ring, respectively. Furthermore, we found that water effectively catalyzes the interconversion by facilitating the proton transfer with the highest energy barrier falling to approximately 30 kcal mol(-1), which, to our knowledge, is the first time that this important role of water in chiral conversion has been demonstrated. Finally, we show that the hydroxide ion can further lower the enantiomerization energy barrier to approximately 24 kcal mol(-1) by facilitating proton abstraction, which agrees well with recent experimental data under basic conditions. Our current findings highlight the importance of water and hydroxide ions in the enantiomerization of thalidomide and also provide new insights into the mechanism of enantiomerization at an atomic level.
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Affiliation(s)
- Chuanjin Tian
- Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, PR China
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Abstract
We apply the adaptive biasing potential (ABP) method to optimize the principal curve defining a conformational transition between two known end states and to subsequently compute the one-dimensional potential of mean force as a function of arc length along the principal curve. This approach allows the use of the ABP method in a collective variable space of arbitrary dimension and offers several advantages over line-search methods. First, configurations are neither generated along an initial path for the transition nor equilibrated during evolution of the path. Second, and most importantly, the powerful sampling provided by the ABP serves to accelerate the dynamics during the optimization and computation of the free energy. Finally, the free energy is formulated as a potential of mean force that captures changes in the reaction channel along the principal curve, in contrast to the free energy profile evaluated from the local free-energy gradient in restrained path optimization methods. We first demonstrate the ABP formulation of path optimization using a two-dimensional potential surface and then with a more complex system of Src protein tyrosine kinase. The method is shown to be efficient and robust in the case of rugged, free-energy landscapes.
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Affiliation(s)
| | - He Huang
- Markey Center for Structural Biology, Department of Medicinal Chemistry, Purdue University, 240 S. Martin Jischke Drive, West Lafayette, Indiana 47907-1971, United States
| | - Carol Beth Post
- Markey Center for Structural Biology, Department of Medicinal Chemistry, Purdue University, 240 S. Martin Jischke Drive, West Lafayette, Indiana 47907-1971, United States
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22
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Witham S, Talley K, Wang L, Zhang Z, Sarkar S, Gao D, Yang W, Alexov E. Developing hybrid approaches to predict pKa values of ionizable groups. Proteins 2011; 79:3389-99. [PMID: 21744395 DOI: 10.1002/prot.23097] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2010] [Revised: 05/05/2011] [Accepted: 05/13/2011] [Indexed: 11/07/2022]
Abstract
Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.
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Affiliation(s)
- Shawn Witham
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, South Carolina 29634, USA
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23
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Haas K, Chu JW. Decomposition of energy and free energy changes by following the flow of work along reaction path. J Chem Phys 2009; 131:144105. [DOI: 10.1063/1.3243080] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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