1
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Huang YMM. Multiscale computational study of ligand binding pathways: Case of p38 MAP kinase and its inhibitors. Biophys J 2021; 120:3881-3892. [PMID: 34453922 PMCID: PMC8511166 DOI: 10.1016/j.bpj.2021.08.026] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Revised: 06/07/2021] [Accepted: 08/20/2021] [Indexed: 01/09/2023] Open
Abstract
Protein kinases are one of the most important drug targets in the past 10 years. Understanding the inhibitor association processes will profoundly impact new binder designs with preferred binding kinetics. However, after more than a decade of effort, a complete atomistic-level study of kinase inhibitor binding pathways is still lacking. As all kinases share a similar scaffold, we used p38 kinase as a model system to investigate the conformational dynamics and free energy transition of inhibitor binding toward kinases. Two major kinase conformations, Asp-Phe-Gly (DFG)-in and DFG-out, and three types of inhibitors, type I, II, and III, were thoroughly investigated in this work. We performed Brownian dynamics simulations and up to 340 μs Gaussian-accelerated molecular dynamics simulations to capture the inhibitor binding paths and a series of conformational transitions of the p38 kinase from its apo to inhibitor-bound form. Eighteen successful binding trajectories, including all types of inhibitors, are reported herein. Our simulations suggest a mechanism of inhibitor recruitment, a faster ligand association step to a pre-existing DFG-in/DFG-out p38 protein, followed by a slower molecular rearrangement step to adjust the protein-ligand conformation followed by a shift in the energy landscape to reach the final bound state. The ligand association processes also reflect the energetic favor of type I and type II/III inhibitor binding through ATP and allosteric channels, respectively. These different binding routes are directly responsible for the fast (type I binders) and slow (type II/III binders) kinetics of different types of p38 inhibitors. Our findings also echo the recent study of p38 inhibitor dissociation, implying that ligand unbinding could undergo a reverse path of binding, and both processes share similar metastates. This study deepens the understanding of molecular and energetic features of kinase inhibitor-binding processes and will inspire future drug development from a kinetic point of view.
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Affiliation(s)
- Yu-Ming M Huang
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan.
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2
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Wang J, Arantes PR, Bhattarai A, Hsu RV, Pawnikar S, Huang YMM, Palermo G, Miao Y. Gaussian accelerated molecular dynamics (GaMD): principles and applications. WILEY INTERDISCIPLINARY REVIEWS. COMPUTATIONAL MOLECULAR SCIENCE 2021; 11:e1521. [PMID: 34899998 PMCID: PMC8658739 DOI: 10.1002/wcms.1521] [Citation(s) in RCA: 95] [Impact Index Per Article: 31.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 01/28/2021] [Indexed: 12/20/2022]
Abstract
Gaussian accelerated molecular dynamics (GaMD) is a robust computational method for simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. It works by adding a harmonic boost potential to smooth biomolecular potential energy surface and reduce energy barriers. GaMD greatly accelerates biomolecular simulations by orders of magnitude. Without the need to set predefined reaction coordinates or collective variables, GaMD provides unconstrained enhanced sampling and is advantageous for simulating complex biological processes. The GaMD boost potential exhibits a Gaussian distribution, thereby allowing for energetic reweighting via cumulant expansion to the second order (i.e., "Gaussian approximation"). This leads to accurate reconstruction of free energy landscapes of biomolecules. Hybrid schemes with other enhanced sampling methods, such as the replica exchange GaMD (rex-GaMD) and replica exchange umbrella sampling GaMD (GaREUS), have also been introduced, further improving sampling and free energy calculations. Recently, new "selective GaMD" algorithms including the ligand GaMD (LiGaMD) and peptide GaMD (Pep-GaMD) enabled microsecond simulations to capture repetitive dissociation and binding of small-molecule ligands and highly flexible peptides. The simulations then allowed highly efficient quantitative characterization of the ligand/peptide binding thermodynamics and kinetics. Taken together, GaMD and its innovative variants are applicable to simulate a wide variety of biomolecular dynamics, including protein folding, conformational changes and allostery, ligand binding, peptide binding, protein-protein/nucleic acid/carbohydrate interactions, and carbohydrate/nucleic acid interactions. In this review, we present principles of the GaMD algorithms and recent applications in biomolecular simulations and drug design.
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Affiliation(s)
- Jinan Wang
- Center for Computational Biology and Department of Molecular Biosciences, University of Kansas, 2030 Becker Dr., Lawrence, KS, 66047, United States
| | - Pablo R Arantes
- Department of Bioengineering, University of California Riverside, 900 University Avenue, Riverside, CA 92512, United States
| | - Apurba Bhattarai
- Center for Computational Biology and Department of Molecular Biosciences, University of Kansas, 2030 Becker Dr, Lawrence, KS, 66047, United States
| | - Rohaine V Hsu
- Department of Bioengineering, University of California Riverside, 900 University Avenue, Riverside, CA 92512, United States
| | - Shristi Pawnikar
- Center for Computational Biology and Department of Molecular Biosciences, University of Kansas, 2030 Becker Dr., Lawrence, KS, 66047, United States
| | - Yu-Ming M Huang
- Department of Physics & Astronomy, Wayne State University, 666 W Hancock St, Detroit, MI 48207, USA
| | - Giulia Palermo
- Department of Bioengineering and Department of Chemistry, University of California Riverside, 900 University Avenue, Riverside, CA 92512, United States
| | - Yinglong Miao
- Center for Computational Biology and Department of Molecular Biosciences, University of Kansas, 2030 Becker Dr., Lawrence, Kansas 66047, United States
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3
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Chen H, Fu H, Chipot C, Shao X, Cai W. Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential. J Chem Theory Comput 2021; 17:3886-3894. [PMID: 34106706 DOI: 10.1021/acs.jctc.1c00103] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.
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Affiliation(s)
- 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
| | - 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
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n 7019, Université de Lorraine, BP 70239, 54506 Vandœuvre-lès-Nancy cedex, France.,Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - 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
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4
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Lin X, Qi Y, Latham AP, Zhang B. Multiscale modeling of genome organization with maximum entropy optimization. J Chem Phys 2021; 155:010901. [PMID: 34241389 PMCID: PMC8253599 DOI: 10.1063/5.0044150] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 04/28/2021] [Indexed: 12/15/2022] Open
Abstract
Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.
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Affiliation(s)
- Xingcheng Lin
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yifeng Qi
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Andrew P. Latham
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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5
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Latham AP, Zhang B. Consistent Force Field Captures Homologue-Resolved HP1 Phase Separation. J Chem Theory Comput 2021; 17:3134-3144. [PMID: 33826337 PMCID: PMC8119372 DOI: 10.1021/acs.jctc.0c01220] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Many proteins have been shown to function via liquid-liquid phase separation. Computational modeling could offer much needed structural details of protein condensates and reveal the set of molecular interactions that dictate their stability. However, the presence of both ordered and disordered domains in these proteins places a high demand on the model accuracy. Here, we present an algorithm to derive a coarse-grained force field, MOFF, which can model both ordered and disordered proteins with consistent accuracy. It combines maximum entropy biasing, least-squares fitting, and basic principles of energy landscape theory to ensure that MOFF recreates experimental radii of gyration while predicting the folded structures for globular proteins with lower energy. The theta temperature determined from MOFF separates ordered and disordered proteins at 300 K and exhibits a strikingly linear relationship with amino acid sequence composition. We further applied MOFF to study the phase behavior of HP1, an essential protein for post-translational modification and spatial organization of chromatin. The force field successfully resolved the structural difference of two HP1 homologues despite their high sequence similarity. We carried out large-scale simulations with hundreds of proteins to determine the critical temperature of phase separation and uncover multivalent interactions that stabilize higher-order assemblies. In all, our work makes significant methodological strides to connect theories of ordered and disordered proteins and provides a powerful tool for studying liquid-liquid phase separation with near-atomistic details.
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Affiliation(s)
- Andrew P Latham
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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6
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Huai Z, Yang H, Sun Z. Binding thermodynamics and interaction patterns of human purine nucleoside phosphorylase-inhibitor complexes from extensive free energy calculations. J Comput Aided Mol Des 2021; 35:643-656. [PMID: 33759016 DOI: 10.1007/s10822-021-00382-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 03/13/2021] [Indexed: 11/29/2022]
Abstract
Human purine nucleoside phosphorylase (hPNP) plays a significant role in the catabolism of deoxyguanosine. The trimeric protein is an important target in the treatment of T-cell cancers and autoimmune disorders. Experimental studies on the inhibition of the hPNP observe that the first ligand bound to one of three subunits effectively inhibits the protein, while the binding of more ligands to the subsequent sites shows negative cooperativities. In this work, we performed extensive end-point and alchemical free energy calculations to determine the binding thermodynamics of the trimeric protein-ligand system. 13 Immucillin inhibitors with experimental results are under calculation. Two widely accepted charge schemes for small molecules including AM1-BCC and RESP are adopted for ligands. The results of RESP are in better agreement with the experimental reference. Further investigations of the interaction networks in the protein-ligand complexes reveal that several residues play significant roles in stabilizing the complex structure. The most commonly observed ones include PHE200, GLU201, MET219, and ASN243. The conformations of the protein in different protein-ligand complexes are observed to be similar. We expect these insights to aid the development of potent drugs targeting hPNP.
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Affiliation(s)
- Zhe Huai
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai, 200062, China
| | - Huaiyu Yang
- College of Engineering, Hebei Normal University, Shijiazhuang, 050024, China
| | - Zhaoxi Sun
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai, 200062, China.
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7
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Huai Z, Shen Z, Sun Z. Binding Thermodynamics and Interaction Patterns of Inhibitor-Major Urinary Protein-I Binding from Extensive Free-Energy Calculations: Benchmarking AMBER Force Fields. J Chem Inf Model 2020; 61:284-297. [PMID: 33307679 DOI: 10.1021/acs.jcim.0c01217] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Mouse major urinary protein (MUP) plays a key role in the pheromone communication system. The one-end-closed β-barrel of MUP-I forms a small, deep, and hydrophobic central cavity, which could accommodate structurally diverse ligands. Previous computational studies employed old protein force fields and short simulation times to determine the binding thermodynamics or investigated only a small number of structurally similar ligands, which resulted in sampled regions far from the experimental structure, nonconverged sampling outcomes, and limited understanding of the possible interaction patterns that the cavity could produce. In this work, extensive end-point and alchemical free-energy calculations with advanced protein force fields were performed to determine the binding thermodynamics of a series of MUP-inhibitor systems and investigate the inter- and intramolecular interaction patterns. Three series of inhibitors with a total of 14 ligands were simulated. We independently simulated the MUP-inhibitor complexes under two advanced AMBER force fields. Our benchmark test showed that the advanced AMBER force fields including AMBER19SB and AMBER14SB provided better descriptions of the system, and the backbone root-mean-square deviation (RMSD) was significantly lowered compared with previous computational studies with old protein force fields. Surprisingly, although the latest AMBER force field AMBER19SB provided better descriptions of various observables, it neither improved the binding thermodynamics nor lowered the backbone RMSD compared with the previously proposed and widely used AMBER14SB. The older but widely used AMBER14SB actually achieved better performance in the prediction of binding affinities from the alchemical and end-point free-energy calculations. We further analyzed the protein-ligand interaction networks to identify important residues stabilizing the bound structure. Six residues including PHE38, LEU40, PHE90, ALA103, LEU105, and TYR120 were found to contribute the most significant part of protein-ligand interactions, and 10 residues were found to provide favorable interactions stabilizing the bound state. The two AMBER force fields gave extremely similar interaction networks, and the secondary structures also showed similar behavior. Thus, the intra- and intermolecular interaction networks described with the two AMBER force fields are similar. Therefore, AMBER14SB could still be the default option in free-energy calculations to achieve highly accurate binding thermodynamics and interaction patterns.
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Affiliation(s)
- Zhe Huai
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Zhaoxi Shen
- Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da Universidade, Taipa, Macau 999078, China
| | - Zhaoxi Sun
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
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8
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Chen M, Chen X, Schafer NP, Clementi C, Komives EA, Ferreiro DU, Wolynes PG. Surveying biomolecular frustration at atomic resolution. Nat Commun 2020; 11:5944. [PMID: 33230150 PMCID: PMC7683549 DOI: 10.1038/s41467-020-19560-9] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 10/13/2020] [Indexed: 01/12/2023] Open
Abstract
To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery. The analysis of biomolecular frustration yielded insights into several aspects of protein behavior. Here the authors describe a framework to efficiently quantify and localize biomolecular frustration within proteins at atomic resolution, and observe that drug specificity is correlated with a minimally frustrated binding pocket leading to a funneled binding landscape.
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Affiliation(s)
- Mingchen Chen
- Center for Theoretical Biological Physics, Rice University, Houston, TX, USA
| | - Xun Chen
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Nicholas P Schafer
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Elizabeth A Komives
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA, USA
| | - Diego U Ferreiro
- Protein Physiology Laboratory, University of Buenos Aires, Buenos Aires, Argentina
| | - Peter G Wolynes
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA. .,Department of Biosciences, Rice University, Houston, TX, USA.
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9
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SAMPL7 TrimerTrip host-guest binding affinities from extensive alchemical and end-point free energy calculations. J Comput Aided Mol Des 2020; 35:117-129. [PMID: 33037549 DOI: 10.1007/s10822-020-00351-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 09/30/2020] [Indexed: 12/12/2022]
Abstract
The prediction of host-guest binding affinities with computational modelling is still a challenging task. In the 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge, a new host named TrimerTrip was synthesized and the thermodynamic parameters of 16 structurally diverse guests binding to the host were characterized. In the TrimerTrip-guest challenge, only structures of the host and the guests are provided, which indicates that the predictions of both the binding poses and the binding affinities are under assessment. In this work, starting from the binding poses obtained from our previous enhanced sampling simulations in the configurational space, we perform extensive alchemical and end-point free energy calculations to calculate the host-guest binding affinities retrospectively. The alchemical predictions with two widely accepted charge schemes (i.e. AM1-BCC and RESP) are in good agreement with the experimental reference, while the end-point estimates perform poorly in reproducing the experimental binding affinities. Aside from the absolute value of the binding affinity, the rank of binding free energies is also crucial in drug design. Surprisingly, the end-point MM/PBSA method seems very powerful in reproducing the experimental rank of binding affinities. Although the length of our simulations is long and the intermediate spacing is dense, the convergence behavior is not very good, which may arise from the flexibility of the host molecule. Enhanced sampling techniques in the configurational space may be required to obtain fully converged sampling. Further, as the length of sampling in alchemical free energy calculations already achieves several hundred ns, performing direct simulations of the binding/unbinding event in the physical space could be more useful and insightful. More details about the binding pathway and mechanism could be obtained in this way. The nonequilibrium method could also be a nice choice if one insists to use the alchemical method, as the intermediate sampling is avoided to some extent.
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10
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Liwo A, Czaplewski C, Sieradzan AK, Lubecka EA, Lipska AG, Golon Ł, Karczyńska A, Krupa P, Mozolewska MA, Makowski M, Ganzynkowicz R, Giełdoń A, Maciejczyk M. Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:73-122. [PMID: 32145953 DOI: 10.1016/bs.pmbts.2019.12.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea.
| | | | - Adam K Sieradzan
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Emilia A Lubecka
- Institute of Informatics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, Gdańsk, Poland
| | | | - Łukasz Golon
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | | | - Paweł Krupa
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | | | | | | | - Artur Giełdoń
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | - Maciej Maciejczyk
- Department of Physics and Biophysics, Faculty of Food Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
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11
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Latham AP, Zhang B. Maximum Entropy Optimized Force Field for Intrinsically Disordered Proteins. J Chem Theory Comput 2019; 16:773-781. [PMID: 31756104 DOI: 10.1021/acs.jctc.9b00932] [Citation(s) in RCA: 57] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Intrinsically disordered proteins (IDPs) constitute a significant fraction of eukaryotic proteomes. High-resolution characterization of IDP conformational ensembles can help elucidate their roles in a wide range of biological processes but remains challenging both experimentally and computationally. Here, we present a generic algorithm to improve the accuracy of coarse-grained IDP models using a diverse set of experimental measurements. It combines maximum entropy optimization and least-squares regression to systematically adjust model parameters and improve the agreement between simulation and experiment. We successfully applied the algorithm to derive a transferable force field, which we term the maximum entropy optimized force field (MOFF), for de novo prediction of IDP structures. Statistical analysis of force field parameters reveals features of amino acid interactions not captured by potentials designed to work well for folded proteins. We anticipate its combination of efficiency and accuracy will make MOFF useful for studying the phase separation of IDPs, which drives the formation of various biological compartments.
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Affiliation(s)
- Andrew P Latham
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Bin Zhang
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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12
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Liwo A, Sieradzan AK, Lipska AG, Czaplewski C, Joung I, Żmudzińska W, Hałabis A, Ołdziej S. A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. III. Determination of scale-consistent backbone-local and correlation potentials in the UNRES force field and force-field calibration and validation. J Chem Phys 2019; 150:155104. [PMID: 31005069 DOI: 10.1063/1.5093015] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
| | - Adam K Sieradzan
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
| | - Agnieszka G Lipska
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
| | - Cezary Czaplewski
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
| | - InSuk Joung
- School of Computational Sciences, Korea Institute for Advanced Study, 87 Hoegiro, Dongdaemun-gu, 130-722 Seoul, South Korea
| | - Wioletta Żmudzińska
- Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, ul. Abrahama 58, 80-307 Gdańsk, Poland
| | - Anna Hałabis
- Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, ul. Abrahama 58, 80-307 Gdańsk, Poland
| | - Stanisław Ołdziej
- Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, ul. Abrahama 58, 80-307 Gdańsk, Poland
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13
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Miao Y, Huang YMM, Walker RC, McCammon JA, Chang CEA. Ligand Binding Pathways and Conformational Transitions of the HIV Protease. Biochemistry 2018; 57:1533-1541. [PMID: 29394043 PMCID: PMC5915299 DOI: 10.1021/acs.biochem.7b01248] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
It is important to determine the binding pathways and mechanisms of ligand molecules to target proteins to effectively design therapeutic drugs. Molecular dynamics (MD) is a promising computational tool that allows us to simulate protein-drug binding at an atomistic level. However, the gap between the time scales of current simulations and those of many drug binding processes has limited the usage of conventional MD, which has been reflected in studies of the HIV protease. Here, we have applied a robust enhanced simulation method, Gaussian accelerated molecular dynamics (GaMD), to sample binding pathways of the XK263 ligand and associated protein conformational changes in the HIV protease. During two of 10 independent GaMD simulations performed over 500-2500 ns, the ligand was observed to successfully bind to the protein active site. Although GaMD-derived free energy profiles were not fully converged because of insufficient sampling of the complex system, the simulations still allowed us to identify relatively low-energy intermediate conformational states during binding of the ligand to the HIV protease. Relative to the X-ray crystal structure, the XK263 ligand reached a minimum root-mean-square deviation (RMSD) of 2.26 Å during 2.5 μs of GaMD simulation. In comparison, the ligand RMSD reached a minimum of only ∼5.73 Å during an earlier 14 μs conventional MD simulation. This work highlights the enhanced sampling power of the GaMD approach and demonstrates its wide applicability to studies of drug-receptor interactions for the HIV protease and by extension many other target proteins.
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Affiliation(s)
- Yinglong Miao
- Center for Computational Biology and Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas 66047, United States
| | - Yu-ming M. Huang
- Department of Pharmacology, University of California at San Diego, La Jolla, California 92093, United States
| | - Ross C. Walker
- San Diego Supercomputer Center, University of California at San Diego, La Jolla, California 92093, United States
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, United States
| | - J. Andrew McCammon
- Department of Pharmacology, University of California at San Diego, La Jolla, California 92093, United States
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, United States
| | - Chia-en A. Chang
- Department of Chemistry, University of California, Riverside, Riverside, California 92521, United States
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14
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Krupa P, Hałabis A, Żmudzińska W, Ołdziej S, Scheraga HA, Liwo A. Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and Dynamics. J Chem Inf Model 2017; 57:2364-2377. [DOI: 10.1021/acs.jcim.7b00254] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Paweł Krupa
- Faculty of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | - Anna Hałabis
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Wioletta Żmudzińska
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Stanisław Ołdziej
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
- School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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15
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Miao Y, McCammon JA. Gaussian Accelerated Molecular Dynamics: Theory, Implementation, and Applications. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2017; 13:231-278. [PMID: 29720925 PMCID: PMC5927394 DOI: 10.1016/bs.arcc.2017.06.005] [Citation(s) in RCA: 78] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
A novel Gaussian Accelerated Molecular Dynamics (GaMD) method has been developed for simultaneous unconstrained enhanced sampling and free energy calculation of biomolecules. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of the biomolecules. Furthermore, by constructing a boost potential that follows a Gaussian distribution, accurate reweighting of GaMD simulations is achieved via cumulant expansion to the second order. The free energy profiles obtained from GaMD simulations allow us to identify distinct low energy states of the biomolecules and characterize biomolecular structural dynamics quantitatively. In this chapter, we present the theory of GaMD, its implementation in the widely used molecular dynamics software packages (AMBER and NAMD), and applications to the alanine dipeptide biomolecular model system, protein folding, biomolecular large-scale conformational transitions and biomolecular recognition.
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Affiliation(s)
- Yinglong Miao
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093
- Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093
| | - J Andrew McCammon
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093
- Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA 92093
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16
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Abstract
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Gaussian accelerated molecular dynamics
(GaMD) is a recently developed
enhanced sampling technique that provides efficient free energy calculations
of biomolecules. Like the previous accelerated molecular dynamics
(aMD), GaMD allows for “unconstrained” enhanced sampling
without the need to set predefined collective variables and so is
useful for studying complex biomolecular conformational changes such
as protein folding and ligand binding. Furthermore, because the boost
potential is constructed using a harmonic function that follows Gaussian
distribution in GaMD, cumulant expansion to the second order can be
applied to recover the original free energy profiles of proteins and
other large biomolecules, which solves a long-standing energetic reweighting
problem of the previous aMD method. Taken together, GaMD offers major
advantages for both unconstrained enhanced sampling and free energy
calculations of large biomolecules. Here, we have implemented GaMD
in the NAMD package on top of the existing aMD feature and validated
it on three model systems: alanine dipeptide, the chignolin fast-folding
protein, and the M3 muscarinic G protein-coupled receptor
(GPCR). For alanine dipeptide, while conventional molecular dynamics
(cMD) simulations performed for 30 ns are poorly converged, GaMD simulations
of the same length yield free energy profiles that agree quantitatively
with those of 1000 ns cMD simulation. Further GaMD simulations have
captured folding of the chignolin and binding of the acetylcholine
(ACh) endogenous agonist to the M3 muscarinic receptor.
The reweighted free energy profiles are used to characterize the protein
folding and ligand binding pathways quantitatively. GaMD implemented
in the scalable NAMD is widely applicable to enhanced sampling and
free energy calculations of large biomolecules.
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Affiliation(s)
- Yui Tik Pang
- Department of Physics, The Chinese University of Hong Kong , Shatin, New Territories, Hong Kong
| | | | - Yi Wang
- Department of Physics, The Chinese University of Hong Kong , Shatin, New Territories, Hong Kong
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17
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Zhang B, Zheng W, Papoian GA, Wolynes PG. Exploring the Free Energy Landscape of Nucleosomes. J Am Chem Soc 2016; 138:8126-33. [DOI: 10.1021/jacs.6b02893] [Citation(s) in RCA: 93] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
| | | | - Garegin A. Papoian
- Department
of Chemistry and Biochemistry and Institute for Physical Science and
Technology, University of Maryland, College Park, Maryland 20742, United States
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18
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Zhang B, Wolynes PG. Shape Transitions and Chiral Symmetry Breaking in the Energy Landscape of the Mitotic Chromosome. PHYSICAL REVIEW LETTERS 2016; 116:248101. [PMID: 27367409 DOI: 10.1103/physrevlett.116.248101] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Indexed: 05/18/2023]
Abstract
We derive an unbiased information theoretic energy landscape for chromosomes at metaphase using a maximum entropy approach that accurately reproduces the details of the experimentally measured pairwise contact probabilities between genomic loci. Dynamical simulations using this landscape lead to cylindrical, helically twisted structures reflecting liquid crystalline order. These structures are similar to those arising from a generic ideal homogenized chromosome energy landscape. The helical twist can be either right or left handed so chiral symmetry is broken spontaneously. The ideal chromosome landscape when augmented by interactions like those leading to topologically associating domain formation in the interphase chromosome reproduces these behaviors. The phase diagram of this landscape shows that the helical fiber order and the cylindrical shape persist at temperatures above the onset of chiral symmetry breaking, which is limited by the topologically associating domain interaction strength.
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Affiliation(s)
- Bin Zhang
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Peter G Wolynes
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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19
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Jia X, Wang M, Shao Y, König G, Brooks BR, Zhang JZH, Mei Y. Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics. J Chem Theory Comput 2016; 12:499-511. [DOI: 10.1021/acs.jctc.5b00920] [Citation(s) in RCA: 74] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Xiangyu Jia
- State
Key Laboratory of Precision Spectroscopy and Department of Physics
and Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
| | - Meiting Wang
- State
Key Laboratory of Precision Spectroscopy and Department of Physics
and Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
| | - Yihan Shao
- Q-Chem Inc., 6601 Owens Drive, Suite
105, Pleasanton, California 94588, United States
| | - Gerhard König
- Laboratory
of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute, 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - Bernard R. Brooks
- Laboratory
of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute, 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - John Z. H. Zhang
- State
Key Laboratory of Precision Spectroscopy and Department of Physics
and Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center
for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Ye Mei
- State
Key Laboratory of Precision Spectroscopy and Department of Physics
and Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center
for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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20
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Affiliation(s)
- Andre A. S. T. Ribeiro
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Vanessa Ortiz
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
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21
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Zaborowski B, Jagieła D, Czaplewski C, Hałabis A, Lewandowska A, Żmudzińska W, Ołdziej S, Karczyńska A, Omieczynski C, Wirecki T, Liwo A. A Maximum-Likelihood Approach to Force-Field Calibration. J Chem Inf Model 2015; 55:2050-70. [DOI: 10.1021/acs.jcim.5b00395] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Bartłomiej Zaborowski
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Dawid Jagieła
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Cezary Czaplewski
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Anna Hałabis
- Laboratory
of Biopolymer Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Kładki
24, 80-922 Gdańsk, Poland
| | - Agnieszka Lewandowska
- Laboratory
of Biopolymer Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Kładki
24, 80-922 Gdańsk, Poland
| | - Wioletta Żmudzińska
- Laboratory
of Biopolymer Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Kładki
24, 80-922 Gdańsk, Poland
| | - Stanisław Ołdziej
- Laboratory
of Biopolymer Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Kładki
24, 80-922 Gdańsk, Poland
| | - Agnieszka Karczyńska
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Christian Omieczynski
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Tomasz Wirecki
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Adam Liwo
- Faculty
of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
- Center
for In Silico Protein Structure and School of Computational Sciences, Korea Institute for Advanced Study, 87 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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22
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Miao Y, Feher VA, McCammon JA. Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation. J Chem Theory Comput 2015; 11:3584-3595. [PMID: 26300708 PMCID: PMC4535365 DOI: 10.1021/acs.jctc.5b00436] [Citation(s) in RCA: 494] [Impact Index Per Article: 54.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2015] [Indexed: 12/20/2022]
Abstract
A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively.
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Affiliation(s)
- Yinglong Miao
- Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California at San Diego , La Jolla, California 92093, United States
| | - Victoria A Feher
- Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California at San Diego , La Jolla, California 92093, United States
| | - J Andrew McCammon
- Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California at San Diego , La Jolla, California 92093, United States
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23
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Miao Y, Feixas F, Eun C, McCammon JA. Accelerated molecular dynamics simulations of protein folding. J Comput Chem 2015; 36:1536-49. [PMID: 26096263 DOI: 10.1002/jcc.23964] [Citation(s) in RCA: 110] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2015] [Revised: 05/11/2015] [Accepted: 05/19/2015] [Indexed: 02/02/2023]
Abstract
Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.
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Affiliation(s)
- Yinglong Miao
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, California
| | - Ferran Feixas
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California.,Department of Pharmacology, University of California at San Diego, La Jolla, California
| | - Changsun Eun
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, California
| | - J Andrew McCammon
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, California.,Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California.,Department of Pharmacology, University of California at San Diego, La Jolla, California
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24
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Schafer NP, Kim BL, Zheng W, Wolynes PG. Learning To Fold Proteins Using Energy Landscape Theory. Isr J Chem 2014; 54:1311-1337. [PMID: 25308991 PMCID: PMC4189132 DOI: 10.1002/ijch.201300145] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.
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Affiliation(s)
- N P Schafer
- Department of Physics, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - B L Kim
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - W Zheng
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - P G Wolynes
- Department of Physics, Rice University, Houston, TX 77005, USA ; Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
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25
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Miao Y, Sinko W, Pierce L, Bucher D, Walker RC, McCammon JA. Improved Reweighting of Accelerated Molecular Dynamics Simulations for Free Energy Calculation. J Chem Theory Comput 2014; 10:2677-2689. [PMID: 25061441 PMCID: PMC4095935 DOI: 10.1021/ct500090q] [Citation(s) in RCA: 311] [Impact Index Per Article: 31.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Indexed: 12/16/2022]
Abstract
![]()
Accelerated
molecular dynamics (aMD) simulations greatly improve
the efficiency of conventional molecular dynamics (cMD) for sampling
biomolecular conformations, but they require proper reweighting for
free energy calculation. In this work, we systematically compare the
accuracy of different reweighting algorithms including the exponential
average, Maclaurin series, and cumulant expansion on three model systems:
alanine dipeptide, chignolin, and Trp-cage. Exponential average reweighting
can recover the original free energy profiles easily only when the
distribution of the boost potential is narrow (e.g., the range ≤20kBT) as found in dihedral-boost aMD simulation
of alanine dipeptide. In dual-boost aMD simulations of the studied
systems, exponential average generally leads to high energetic fluctuations,
largely due to the fact that the Boltzmann reweighting factors are
dominated by a very few high boost potential frames. In comparison,
reweighting based on Maclaurin series expansion (equivalent to cumulant
expansion on the first order) greatly suppresses the energetic noise
but often gives incorrect energy minimum positions and significant
errors at the energy barriers (∼2–3kBT). Finally, reweighting using cumulant expansion to
the second order is able to recover the most accurate free energy
profiles within statistical errors of ∼kBT, particularly when the distribution of the boost potential
exhibits low anharmonicity (i.e., near-Gaussian distribution), and
should be of wide applicability. A toolkit of Python scripts for aMD
reweighting “PyReweighting” is distributed free of charge
at http://mccammon.ucsd.edu/computing/amdReweighting/.
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Affiliation(s)
- Yinglong Miao
- Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States
| | - William Sinko
- Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States
| | - Levi Pierce
- Schrodinger Inc., New York, New York 10036, United States
| | - Denis Bucher
- Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States
| | - Ross C Walker
- Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States ; Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States
| | - J Andrew McCammon
- Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States ; Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States ; Howard Hughes Medical Institute, Department of Pharmacology, Department of Chemistry and Biochemistry and San Diego Supercomputer Center, University of California at San Diego , La Jolla, California 92093, United States
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26
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Discrete kinetic models from funneled energy landscape simulations. PLoS One 2012; 7:e50635. [PMID: 23251375 PMCID: PMC3520928 DOI: 10.1371/journal.pone.0050635] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2012] [Accepted: 10/23/2012] [Indexed: 01/01/2023] Open
Abstract
A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.
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27
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Yin Y, Maisuradze GG, Liwo A, Scheraga HA. Hidden protein folding pathways in free-energy landscapes uncovered by network analysis. J Chem Theory Comput 2012; 8:1176-1189. [PMID: 22715321 DOI: 10.1021/ct200806n] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
A network analysis is used to uncover hidden folding pathways in free-energy landscapes usually defined in terms of such arbitrary order parameters as root-mean-square deviation from the native structure, radius of gyration, etc. The analysis has been applied to molecular dynamics (MD) trajectories of the B-domain of staphylococcal protein A, generated with the coarse-grained united-residue (UNRES) force field in a broad range of temperatures (270K ≤ T ≤ 325K). Thousands of folding pathways have been identified at each temperature. Out of these many folding pathways, several most probable ones were selected for investigation of the conformational transitions during protein folding. Unlike other conformational space network (CSN) methods, a node in the CSN variant implemented in this work is defined according to the nativelikeness class of the structure, which defines the similarity of segments of the compared structures in terms of secondary-structure, contact-pattern, and local geometry, as well as the overall geometric similarity of the conformation under consideration to that of the reference (experimental) structure. Our previous findings, regarding the folding model and conformations found at the folding-transition temperature for protein A (Maisuradze et al., J. Am. Chem. Soc. 132, 9444, 2010), were confirmed by the conformational space network analysis. In the methodology and in the analysis of the results, the shortest path identified by using the shortest-path algorithm corresponds to the most probable folding pathway in the conformational space network.
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Affiliation(s)
- Yanping Yin
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York, 14850-1301
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28
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Prentiss MC, Wales DJ, Wolynes PG. The energy landscape, folding pathways and the kinetics of a knotted protein. PLoS Comput Biol 2010; 6:e1000835. [PMID: 20617197 PMCID: PMC2895632 DOI: 10.1371/journal.pcbi.1000835] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2009] [Accepted: 05/25/2010] [Indexed: 11/18/2022] Open
Abstract
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N or C terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N terminus portion of the knot and a rate-determining step where the C terminus is incorporated. The low-lying minima with the N terminus knotted and the C terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N and C termini into the knot occurs late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.
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Affiliation(s)
- Michael C Prentiss
- Department of Chemistry, Center for Theoretical Biological Physics, University of California San Diego, La Jolla, California, United States of America.
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Oklejas V, Zong C, Papoian GA, Wolynes PG. Protein structure prediction: do hydrogen bonding and water-mediated interactions suffice? Methods 2010; 52:84-90. [PMID: 20561998 DOI: 10.1016/j.ymeth.2010.05.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2010] [Revised: 05/17/2010] [Accepted: 05/20/2010] [Indexed: 11/16/2022] Open
Abstract
The many-body physics of hydrogen bond formation in alpha-helices of globular proteins was investigated using a simple physics-based model. Specifically, a context-sensitive hydrogen bond potential, which depends on residue identity and degree of solvent exposure, was used in the framework of the Associated Memory Hamiltonian codes developed previously but without using local-sequence structure matches ("memories"). Molecular dynamics simulations employing the energy function using the context-sensitive hydrogen bond potential alone (the "amnesiac" model) were used to generate low energy structures for three alpha-helical test proteins. The resulting structures were compared to both the X-ray crystal structures of the test proteins and the results obtained using the full Associated Memory Hamiltonian previously used. Results show that the amnesiac Hamiltonian was able to generate structures with reasonably high structural similarity (Q approximately 0.4) to that of the native protein but only with the use of predicted secondary structure information encoding local steric signals. Low energy structures obtained using the amnesiac Hamiltonian without any a priori secondary structure information had considerably less similarity to the native protein structures (Q approximately 0.3). Both sets of results utilizing the amnesiac Hamiltonian are poorer than when local-sequence structure matches are used.
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Affiliation(s)
- Vanessa Oklejas
- Department of Chemistry and Biochemistry, University of California, La Jolla, CA 92093-0371, United States.
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30
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Prentiss MC, Wales DJ, Wolynes PG. Protein structure prediction using basin-hopping. J Chem Phys 2008; 128:225106. [PMID: 18554063 DOI: 10.1063/1.2929833] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower minima and conformations closer to the experimental structure than does molecular dynamics with simulated annealing. For large systems the efficiency of basin-hopping decreases for our initial implementation, where the steps consist of random perturbations to the Cartesian coordinates. We implemented umbrella sampling using basin-hopping to further confirm when the global minima are reached. We have also improved the energy surface by employing bioinformatic techniques for reducing the roughness or variance of the energy surface. Finally, the basin-hopping calculations have guided improvements in the excluded volume of the Hamiltonian, producing better structures. These results suggest a novel and transferable optimization scheme for future energy function development.
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Affiliation(s)
- Michael C Prentiss
- Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093, USA.
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31
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Shen T, Hamelberg D. A statistical analysis of the precision of reweighting-based simulations. J Chem Phys 2008; 129:034103. [PMID: 18647012 DOI: 10.1063/1.2944250] [Citation(s) in RCA: 98] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Various advanced simulation techniques, which are used to sample the statistical ensemble of systems with complex Hamiltonians, such as those displayed in condensed matters and biomolecular systems, rely heavily on successfully reweighting the sampled configurations. The sampled points of a system from an elevated thermal environment or on a modified Hamiltonian are reused with different statistical weights to evaluate its properties at the initial desired temperature or of the original Hamiltonian. Often, the decrease of accuracy induced by this procedure is ignored and the final results can be far from what is expected. We have addressed the reasons behind such a phenomenon and have provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these advanced simulation methods. We also provided examples from temperature histogram reweighting and accelerated molecular dynamics reweighting to illustrate this idea, which can be generalized to the dynamic reweighting as well. The study shows that this analysis may provide a priori guidance for the strategy of setting up the parameters of advanced simulations before a lengthy one is carried out. The method can therefore provide insights for optimizing the parameters for high accuracy simulations with finite amount of computational resources.
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Affiliation(s)
- Tongye Shen
- Theoretical Biology & Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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32
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Lätzer J, Shen T, Wolynes PG. Conformational switching upon phosphorylation: a predictive framework based on energy landscape principles. Biochemistry 2008; 47:2110-22. [PMID: 18198897 DOI: 10.1021/bi701350v] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We investigate how post-translational phosphorylation modifies the global conformation of a protein by changing its free energy landscape using two test proteins, cystatin and NtrC. We first examine the changes in a free energy landscape caused by phosphorylation using a model containing information about both structural forms. For cystatin the free energy cost is fairly large indicating a low probability of sampling the phosphorylated conformation in a perfectly funneled landscape. The predicted barrier for NtrC conformational transition is several times larger than the barrier for cystatin, indicating that the switch protein NtrC most probably follows a partial unfolding mechanism to move from one basin to the other. Principal component analysis and linear response theory show how the naturally occurring conformational changes in unmodified proteins are captured and stabilized by the change of interaction potential. We also develop a partially guided structure prediction Hamiltonian which is capable of predicting the global structure of a phosphorylated protein using only knowledge of the structure of the unphosphorylated protein or vice versa. This algorithm makes use of a generic transferable long-range residue contact potential along with details of structure short range in sequence. By comparing the results obtained with this guided transferable potential to those from the native-only, perfectly funneled Hamiltonians, we show that the transferable Hamiltonian correctly captures the nature of the global conformational changes induced by phosphorylation and can sample substantially correct structures for the modified protein with high probability.
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Affiliation(s)
- Joachim Lätzer
- Department of Chemistry & Biochemistry, University of California, San Diego, NSF Center for Theoretical Biological Physics, La Jolla, California 92093-0365, USA
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Biswas P, Zou J, Saven JG. Statistical theory for protein ensembles with designed energy landscapes. J Chem Phys 2007; 123:154908. [PMID: 16252973 DOI: 10.1063/1.2062047] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.
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Affiliation(s)
- Parbati Biswas
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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Liwo A, Khalili M, Czaplewski C, Kalinowski S, Ołdziej S, Wachucik K, Scheraga HA. Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins. J Phys Chem B 2007; 111:260-85. [PMID: 17201450 PMCID: PMC3236617 DOI: 10.1021/jp065380a] [Citation(s) in RCA: 157] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta
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Affiliation(s)
- Adam Liwo
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, N.Y., 14853-1301, U.S.A
| | - Mey Khalili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, N.Y., 14853-1301, U.S.A
| | - Cezary Czaplewski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, N.Y., 14853-1301, U.S.A
| | - Sebastian Kalinowski
- Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Stanisław Ołdziej
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, N.Y., 14853-1301, U.S.A
| | - Katarzyna Wachucik
- Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, N.Y., 14853-1301, U.S.A
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Jagielska A, Scheraga HA. Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: All-atom molecular dynamics in implicit solvent. J Comput Chem 2007; 28:1068-82. [PMID: 17279497 DOI: 10.1002/jcc.20631] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.
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Affiliation(s)
- Anna Jagielska
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA
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36
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Khalili M, Liwo A, Scheraga HA. Kinetic Studies of Folding of the B-domain of Staphylococcal Protein A with Molecular Dynamics and a United-residue (UNRES) Model of Polypeptide Chains. J Mol Biol 2006; 355:536-47. [PMID: 16324712 DOI: 10.1016/j.jmb.2005.10.056] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2005] [Revised: 10/10/2005] [Accepted: 10/21/2005] [Indexed: 11/23/2022]
Abstract
Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.
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Affiliation(s)
- Mey Khalili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301, USA
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37
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Papoian GA, Ulander J, Wolynes PG. Role of water mediated interactions in protein-protein recognition landscapes. J Am Chem Soc 2004; 125:9170-8. [PMID: 15369374 DOI: 10.1021/ja034729u] [Citation(s) in RCA: 143] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The energy landscape picture of protein folding and binding is employed to optimize a number of pair potentials for direct and water-mediated interactions in protein complex interfaces. We find that water-mediated interactions greatly complement direct interactions in discriminating against various types of trap interactions that model those present in the cell. We highlight the context dependent nature of knowledge-based binding potentials, as contrasted with the situation for autonomous folding. By performing a Principal Component Analysis (PCA) of the corresponding interaction matrixes, we rationalize the strength of the recognition signal for each combination of the contact type and reference trap states using the differential in the idealized "canonical" amino acid compositions of native and trap layers. The comparison of direct and water-mediated contact potential matrixes emphasizes the importance of partial solvation in stabilizing charged groups in the protein interfaces. Specific water-mediated interresidue interactions are expected to influence significantly the kinetics as well as thermodynamics of protein association.
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Affiliation(s)
- Garegin A Papoian
- Contribution from the Department of Chemistry & Biochemistry, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0371, USA
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38
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Matysiak S, Clementi C. Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go? J Mol Biol 2004; 343:235-48. [PMID: 15381433 DOI: 10.1016/j.jmb.2004.08.006] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2004] [Revised: 07/30/2004] [Accepted: 08/03/2004] [Indexed: 11/28/2022]
Abstract
The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.
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Affiliation(s)
- Silvina Matysiak
- Department of Chemistry, Rice University, 6100 Main Street, Houston, TX 77005, USA
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39
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Liwo A, Arłukowicz P, Ołdziej S, Czaplewski C, Makowski M, Scheraga HA. Optimization of the UNRES Force Field by Hierarchical Design of the Potential-Energy Landscape. 1. Tests of the Approach Using Simple Lattice Protein Models. J Phys Chem B 2004. [DOI: 10.1021/jp040327c] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Adam Liwo
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Piotr Arłukowicz
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Stanisław Ołdziej
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Cezary Czaplewski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Mariusz Makowski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
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Papoian GA, Ulander J, Eastwood MP, Luthey-Schulten Z, Wolynes PG. Water in protein structure prediction. Proc Natl Acad Sci U S A 2004; 101:3352-7. [PMID: 14988499 PMCID: PMC373465 DOI: 10.1073/pnas.0307851100] [Citation(s) in RCA: 233] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Proteins have evolved to use water to help guide folding. A physically motivated, nonpairwise-additive model of water-mediated interactions added to a protein structure prediction Hamiltonian yields marked improvement in the quality of structure prediction for larger proteins. Free energy profile analysis suggests that long-range water-mediated potentials guide folding and smooth the underlying folding funnel. Analyzing simulation trajectories gives direct evidence that water-mediated interactions facilitate native-like packing of supersecondary structural elements. Long-range pairing of hydrophilic groups is an integral part of protein architecture. Specific water-mediated interactions are a universal feature of biomolecular recognition landscapes in both folding and binding.
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Affiliation(s)
- Garegin A Papoian
- Department of Chemistry and Biochemistry and Center for Theoretical Biological Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0371, USA
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41
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Eastwood MP, Hardin C, Luthey-Schulten Z, Wolynes PG. Statistical mechanical refinement of protein structure prediction schemes. II. Mayer cluster expansion approach. J Chem Phys 2003. [DOI: 10.1063/1.1565106] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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42
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Saven JG. Connecting statistical and optimized potentials in protein folding via a generalized foldability criterion. J Chem Phys 2003. [DOI: 10.1063/1.1565995] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Hardin C, Eastwood MP, Prentiss MC, Luthey-Schulten Z, Wolynes PG. Associative memory Hamiltonians for structure prediction without homology: alpha/beta proteins. Proc Natl Acad Sci U S A 2003; 100:1679-84. [PMID: 12554830 PMCID: PMC149892 DOI: 10.1073/pnas.252753899] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/10/2002] [Indexed: 11/18/2022] Open
Abstract
We describe a method for predicting the structure of alpha beta class proteins in the absence of information from homologous structures. The method is based on an associative memory model for short to intermediate range in sequence contacts and a contact potential for long range in sequence contacts. The coefficients in the energy function are chosen to maximize the ratio of the folding temperature to the glass transition temperature. We use the resulting optimized model to predict the structure of three alpha beta protein domains ranging in length from 81 to 115 residues. The resulting predictions align with low rms deviations to large portions of the native state. We have also calculated the free energy as a function of similarity to the native state for one of these three domains, and we show that, as expected from the optimization criteria, the free energy surface resembles a rough funnel to the native state. Finally, we briefly demonstrate the effect of roughness in the energy landscape on the dynamics.
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Affiliation(s)
- Corey Hardin
- Center for Biophysics and Computational Biology and School of Chemical Sciences, University of Illinois, 600 South Mathews Avenue, Urbana, IL 61801, USA
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