1
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Zhang Y, Zhu X, Zhang H, Yan J, Xu P, Wu P, Wu S, Bai C. Mechanism Study of Proteins under Membrane Environment. MEMBRANES 2022; 12:membranes12070694. [PMID: 35877897 PMCID: PMC9322369 DOI: 10.3390/membranes12070694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/12/2022] [Revised: 07/01/2022] [Accepted: 07/05/2022] [Indexed: 11/24/2022]
Abstract
Membrane proteins play crucial roles in various physiological processes, including molecule transport across membranes, cell communication, and signal transduction. Approximately 60% of known drug targets are membrane proteins. There is a significant need to deeply understand the working mechanism of membrane proteins in detail, which is a challenging work due to the lack of available membrane structures and their large spatial scale. Membrane proteins carry out vital physiological functions through conformational changes. In the current study, we utilized a coarse-grained (CG) model to investigate three representative membrane protein systems: the TMEM16A channel, the family C GPCRs mGlu2 receptor, and the P4-ATPase phospholipid transporter. We constructed the reaction pathway of conformational changes between the two-end structures. Energy profiles and energy barriers were calculated. These data could provide reasonable explanations for TMEM16A activation, the mGlu2 receptor activation process, and P4-ATPase phospholipid transport. Although they all belong to the members of membrane proteins, they behave differently in terms of energy. Our work investigated the working mechanism of membrane proteins and could give novel insights into other membrane protein systems of interest.
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Affiliation(s)
- Yue Zhang
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- School of Chemistry and Materials Science, University of Science and Technology of China, Hefei 230026, China
- Warshel Institute for Computational Biology, Shenzhen 518172, China
| | - Xiaohong Zhu
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- School of Chemistry and Materials Science, University of Science and Technology of China, Hefei 230026, China
- Warshel Institute for Computational Biology, Shenzhen 518172, China
| | - Honghui Zhang
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- Warshel Institute for Computational Biology, Shenzhen 518172, China
| | - Junfang Yan
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- Warshel Institute for Computational Biology, Shenzhen 518172, China
| | - Peiyi Xu
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- Warshel Institute for Computational Biology, Shenzhen 518172, China
| | - Peng Wu
- School of Biomedical Engineering, Health Science Center, Shenzhen University, Shenzhen 518055, China;
| | - Song Wu
- South China Hospital, Health Science Center, Shenzhen University, Shenzhen 518116, China
- Correspondence: (S.W.); (C.B.)
| | - Chen Bai
- School of Life and Health Sciences, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China; (Y.Z.); (X.Z.); (H.Z.); (J.Y.); (P.X.)
- Warshel Institute for Computational Biology, Shenzhen 518172, China
- Chenzhu Biotechnology Co., Ltd., Hangzhou 310005, China
- Correspondence: (S.W.); (C.B.)
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2
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Ryberg LA, Sønderby P, Bukrinski JT, Harris P, Peters GHJ. Investigations of Albumin–Insulin Detemir Complexes Using Molecular Dynamics Simulations and Free Energy Calculations. Mol Pharm 2019; 17:132-144. [DOI: 10.1021/acs.molpharmaceut.9b00839] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Line A. Ryberg
- Department of Chemistry, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Pernille Sønderby
- Department of Chemistry, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | | | - Pernille Harris
- Department of Chemistry, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Günther H. J. Peters
- Department of Chemistry, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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3
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Novichkova DA, Lushchekina SV, Dym O, Masson P, Silman I, Sussman JL. The four-helix bundle in cholinesterase dimers: Structural and energetic determinants of stability. Chem Biol Interact 2019; 309:108699. [PMID: 31202688 DOI: 10.1016/j.cbi.2019.06.012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 05/30/2019] [Accepted: 06/06/2019] [Indexed: 11/28/2022]
Abstract
The crystal structures of truncated forms of cholinesterases provide good models for assessing the role of non-covalent interactions in dimer assembly in the absence of cross-linking disulfide bonds. These structures identify the four-helix bundle that serves as the interface for formation of acetylcholinesterase and butyrylcholinesterase dimers. Here we performed a theoretical comparison of the structural and energetic factors governing dimerization. This included identification of inter-subunit and intra-subunit hydrogen bonds and hydrophobic interactions, evaluation of solvent-accessible surfaces, and estimation of electrostatic contributions to dimerization. To reveal the contribution to dimerization of individual amino acids within the contact area, free energy perturbation alanine screening was performed. Markov state modelling shows that the loop between the α13 and α14 helices in BChE is unstable, and occupies 4 macro-states. The order of magnitude of mean first passage times between these macrostates is ~10-8 s. Replica exchange molecular dynamics umbrella sampling calculations revealed that the free energy of human BChE dimerization is -15.5 kcal/mol, while that for human AChE is -26.4 kcal/mol. Thus, the C-terminally truncated human butyrylcholinesterase dimer is substantially less stable than that of human acetylcholinesterase. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:CHEMBIOINT:1.
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Affiliation(s)
- Dana A Novichkova
- N.M. Emanuel Institute of Biochemical Physics of Russian Academy of Sciences, 4 Kosygina St., Moscow, 119334, Russia
| | - Sofya V Lushchekina
- N.M. Emanuel Institute of Biochemical Physics of Russian Academy of Sciences, 4 Kosygina St., Moscow, 119334, Russia.
| | - Orly Dym
- Weizmann Institute of Science, 234 Herzl St., Rehovot, 7610001, Israel
| | - Patrick Masson
- Kazan Federal University, Neuropharmacology Laboratory, 18 Kremlevskaya St., Kazan, 420008, Russia
| | - Israel Silman
- Weizmann Institute of Science, 234 Herzl St., Rehovot, 7610001, Israel
| | - Joel L Sussman
- Weizmann Institute of Science, 234 Herzl St., Rehovot, 7610001, Israel
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4
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Liu X, Peng L, Zhang JZH. Accurate and Efficient Calculation of Protein–Protein Binding Free Energy-Interaction Entropy with Residue Type-Specific Dielectric Constants. J Chem Inf Model 2018; 59:272-281. [DOI: 10.1021/acs.jcim.8b00248] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Xiao Liu
- State Key Laboratory for Precision Spectroscopy, Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Long Peng
- State Key Laboratory for Precision Spectroscopy, Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - John Z. H. Zhang
- State Key Laboratory for Precision Spectroscopy, Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
- NYU−ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, United States
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5
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Izadi S, Harris RC, Fenley MO, Onufriev AV. Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies. J Chem Theory Comput 2018; 14:1656-1670. [PMID: 29378399 DOI: 10.1021/acs.jctc.7b00886] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ Gel) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ Gel estimates varies widely between different GB models and also across different types of biomolecular complexes, with R2 correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R2 = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ Gel. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.
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Affiliation(s)
- Saeed Izadi
- Early Stage Pharmaceutical Development , Genentech Inc. , 1 DNA Way , South San Francisco , California 94080 , United States
| | - Robert C Harris
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
| | - Marcia O Fenley
- Institute of Molecular Biophysics , Florida State University , Tallahassee , Florida 32306-3408 , United States
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Yang X, Lei H, Gao P, Thomas DG, Mobley DL, Baker NA. Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations. J Chem Theory Comput 2018; 14:759-767. [PMID: 29293342 DOI: 10.1021/acs.jctc.7b00905] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is underdetermined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parametrization problems, including those beyond continuum solvation calculations. The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters.
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Affiliation(s)
| | | | | | | | - David L Mobley
- Department of Pharmaceutical Sciences, University of California Irvine , Irvine, California 92697, United States
| | - Nathan A Baker
- Division of Applied Mathematics, Brown University , Providence, Rhode Island 02912, United States
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7
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Zhou HX, Pang X. Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation. Chem Rev 2018; 118:1691-1741. [PMID: 29319301 DOI: 10.1021/acs.chemrev.7b00305] [Citation(s) in RCA: 454] [Impact Index Per Article: 75.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Chemistry and Department of Physics, University of Illinois at Chicago , Chicago, Illinois 60607, United States.,Department of Physics and Institute of Molecular Biophysics, Florida State University , Tallahassee, Florida 32306, United States
| | - Xiaodong Pang
- Department of Physics and Institute of Molecular Biophysics, Florida State University , Tallahassee, Florida 32306, United States
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8
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Qiu L, Yan Y, Sun Z, Song J, Zhang JZ. Interaction entropy for computational alanine scanning in protein-protein binding. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1342] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Linqiong Qiu
- Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering; State Key Laboratory of Precision Spectroscopy, East China Normal University; Shanghai China
| | - Yuna Yan
- Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering; State Key Laboratory of Precision Spectroscopy, East China Normal University; Shanghai China
| | - Zhaoxi Sun
- Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering; State Key Laboratory of Precision Spectroscopy, East China Normal University; Shanghai China
| | - Jianing Song
- Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering; State Key Laboratory of Precision Spectroscopy, East China Normal University; Shanghai China
- NYU-ECNU Center for Computational Chemistry; NYU Shanghai; Shanghai China
| | - John Z.H. Zhang
- Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering; State Key Laboratory of Precision Spectroscopy, East China Normal University; Shanghai China
- NYU-ECNU Center for Computational Chemistry; NYU Shanghai; Shanghai China
- Department of Chemistry; New York University; New York NY USA
- Collaborative Innovation Center of Extreme Optics; Shanxi University; Taiyuan Shanxi China
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9
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Sun Z, Yan YN, Yang M, Zhang JZH. Interaction entropy for protein-protein binding. J Chem Phys 2017; 146:124124. [DOI: 10.1063/1.4978893] [Citation(s) in RCA: 76] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Zhaoxi Sun
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Yu N. Yan
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Maoyou Yang
- School of Science, Qilu University of Technology, Jinan, Shandong 250353, China
| | - John Z. H. Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
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10
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Batra J, Tjong H, Zhou HX. Electrostatic effects on the folding stability of FKBP12. Protein Eng Des Sel 2016; 29:301-308. [PMID: 27381026 PMCID: PMC4955870 DOI: 10.1093/protein/gzw014] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2016] [Revised: 03/28/2016] [Accepted: 04/15/2016] [Indexed: 01/17/2023] Open
Abstract
The roles of electrostatic interactions in protein folding stability have been a matter of debate, largely due to the complexity in the theoretical treatment of these interactions. We have developed computational methods for calculating electrostatic effects on protein folding stability. To rigorously test and further refine these methods, here we carried out experimental studies into electrostatic effects on the folding stability of the human 12-kD FK506 binding protein (FKBP12). This protein has a close homologue, FKBP12.6, with amino acid substitutions in only 18 of their 107 residues. Of the 18 substitutions, 8 involve charged residues. Upon mutating FKBP12 residues at these 8 positions individually into the counterparts in FKBP12.6, the unfolding free energy (ΔGu) of FKBP12 changed by -0.3 to 0.7 kcal/mol. Accumulating stabilizing substitutions resulted in a mutant with a 0.9 kcal/mol increase in stability. Additional charge mutations were grafted from a thermophilic homologue, MtFKBP17, which aligns to FKBP12 with 31% sequence identity over 89 positions. Eleven such charge mutations were studied, with ΔΔGu varying from -2.9 to 0.1 kcal/mol. The predicted electrostatic effects by our computational methods with refinements herein had a root-mean-square deviation of 0.9 kcal/mol from the experimental ΔΔGu values on 16 single mutations of FKBP12. The difference in ΔΔGu between mutations grafted from FKBP12.6 and those from MtFKBP17 suggests that more distant homologues are less able to provide guidance for enhancing folding stability.
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Affiliation(s)
- Jyotica Batra
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
- Present address: Department of Chemistry and Physics, Bellarmine University, 2001 Newburg Road, Louisville, KY40205, USA
| | - Harianto Tjong
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
- Present address: Molecular and Computational Biology Section, Department of Biological Sciences, University of Southern California, Los Angeles, CA 90089, USA
| | - Huan-Xiang Zhou
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
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11
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Harris RC, Mackoy T, Fenley MO. Problems of robustness in Poisson-Boltzmann binding free energies. J Chem Theory Comput 2016; 11:705-12. [PMID: 26528091 PMCID: PMC4610304 DOI: 10.1021/ct5005017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Indexed: 11/29/2022]
Abstract
Although models based on the Poisson–Boltzmann (PB) equation have been fairly successful at predicting some experimental quantities, such as solvation free energies (ΔG), these models have not been consistently successful at predicting binding free energies (ΔΔG). Here we found that ranking a set of protein–protein complexes by the electrostatic component (ΔΔGel) of ΔΔG was more difficult than ranking the same molecules by the electrostatic component (ΔGel) of ΔG. This finding was unexpected because ΔΔGel can be calculated by combining estimates of ΔGel for the complex and its components with estimates of the ΔΔGel in vacuum. One might therefore expect that if a theory gave reliable estimates of ΔGel, then its estimates of ΔΔGel would be reliable. However, ΔΔGel for these complexes were orders of magnitude smaller than ΔGel, so although estimates of ΔGel obtained with different force fields and surface definitions were highly correlated, similar estimates of ΔΔGel were often not correlated.
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Affiliation(s)
- Robert C Harris
- Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555-0304, United States
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12
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Sowmya G, Ranganathan S. Discrete structural features among interface residue-level classes. BMC Bioinformatics 2015; 16 Suppl 18:S8. [PMID: 26679043 PMCID: PMC4682381 DOI: 10.1186/1471-2105-16-s18-s8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Protein-protein interaction (PPI) is essential for molecular functions in biological cells. Investigation on protein interfaces of known complexes is an important step towards deciphering the driving forces of PPIs. Each PPI complex is specific, sensitive and selective to binding. Therefore, we have estimated the relative difference in percentage of polar residues between surface and the interface for each complex in a non-redundant heterodimer dataset of 278 complexes to understand the predominant forces driving binding. RESULTS Our analysis showed ~60% of protein complexes with surface polarity greater than interface polarity (designated as class A). However, a considerable number of complexes (~40%) have interface polarity greater than surface polarity, (designated as class B), with a significantly different p-value of 1.66E-45 from class A. Comprehensive analyses of protein complexes show that interface features such as interface area, interface polarity abundance, solvation free energy gain upon interface formation, binding energy and the percentage of interface charged residue abundance distinguish among class A and class B complexes, while electrostatic visualization maps also help differentiate interface classes among complexes. CONCLUSIONS Class A complexes are classical with abundant non-polar interactions at the interface; however class B complexes have abundant polar interactions at the interface, similar to protein surface characteristics. Five physicochemical interface features analyzed from the protein heterodimer dataset are discriminatory among the interface residue-level classes. These novel observations find application in developing residue-level models for protein-protein binding prediction, protein-protein docking studies and interface inhibitor design as drugs.
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13
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Wang B, Wei GW. Parameter optimization in differential geometry based solvation models. J Chem Phys 2015; 143:134119. [PMID: 26450304 PMCID: PMC4602332 DOI: 10.1063/1.4932342] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Accepted: 09/22/2015] [Indexed: 01/01/2023] Open
Abstract
Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and non-polar interactions in a self-consistent framework. Our earlier study indicates that DG based non-polar solvation model outperforms other methods in non-polar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and non-polar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.
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Affiliation(s)
- Bao Wang
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - G W Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
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14
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Izadi S, Aguilar B, Onufriev AV. Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation. J Chem Theory Comput 2015; 11:4450-9. [PMID: 26575935 PMCID: PMC5217485 DOI: 10.1021/acs.jctc.5b00483] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.
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Affiliation(s)
- Saeed Izadi
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24060, United States
| | - Boris Aguilar
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24060, United States
| | - Alexey V Onufriev
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer Science and Physics, Virginia Tech , Blacksburg, Virginia 24060, United States
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15
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Sowmya G, Breen EJ, Ranganathan S. Linking structural features of protein complexes and biological function. Protein Sci 2015; 24:1486-94. [PMID: 26131659 DOI: 10.1002/pro.2736] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Revised: 06/19/2015] [Accepted: 06/24/2015] [Indexed: 11/11/2022]
Abstract
Protein-protein interaction (PPI) establishes the central basis for complex cellular networks in a biological cell. Association of proteins with other proteins occurs at varying affinities, yet with a high degree of specificity. PPIs lead to diverse functionality such as catalysis, regulation, signaling, immunity, and inhibition, playing a crucial role in functional genomics. The molecular principle of such interactions is often elusive in nature. Therefore, a comprehensive analysis of known protein complexes from the Protein Data Bank (PDB) is essential for the characterization of structural interface features to determine structure-function relationship. Thus, we analyzed a nonredundant dataset of 278 heterodimer protein complexes, categorized into major functional classes, for distinguishing features. Interestingly, our analysis has identified five key features (interface area, interface polar residue abundance, hydrogen bonds, solvation free energy gain from interface formation, and binding energy) that are discriminatory among the functional classes using Kruskal-Wallis rank sum test. Significant correlations between these PPI interface features amongst functional categories are also documented. Salt bridges correlate with interface area in regulator-inhibitors (r = 0.75). These representative features have implications for the prediction of potential function of novel protein complexes. The results provide molecular insights for better understanding of PPIs and their relation to biological functions.
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Affiliation(s)
- Gopichandran Sowmya
- Department of Chemistry and Biomolecular Sciences, Macquarie University, Sydney, New South Wales 2109, Australia
| | - Edmond J Breen
- Australian Proteome Analysis Facility (APAF), Macquarie University, Sydney, New South Wales 2109, Australia
| | - Shoba Ranganathan
- Department of Chemistry and Biomolecular Sciences, Macquarie University, Sydney, New South Wales 2109, Australia
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16
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Harris RC, Boschitsch AH, Fenley MO. Sensitivities to parameterization in the size-modified Poisson-Boltzmann equation. J Chem Phys 2014; 140:075102. [PMID: 24559370 DOI: 10.1063/1.4864460] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimental results have demonstrated that the numbers of counterions surrounding nucleic acids differ from those predicted by the nonlinear Poisson-Boltzmann equation, NLPBE. Some studies have fit these data against the ion size in the size-modified Poisson-Boltzmann equation, SMPBE, but the present study demonstrates that other parameters, such as the Stern layer thickness and the molecular surface definition, can change the number of bound ions by amounts comparable to varying the ion size. These parameters will therefore have to be fit simultaneously against experimental data. In addition, the data presented here demonstrate that the derivative, SK, of the electrostatic binding free energy, ΔGel, with respect to the logarithm of the salt concentration is sensitive to these parameters, and experimental measurements of SK could be used to parameterize the model. However, although better values for the Stern layer thickness and ion size and better molecular surface definitions could improve the model's predictions of the numbers of ions around biomolecules and SK, ΔGel itself is more sensitive to parameters, such as the interior dielectric constant, which in turn do not significantly affect the distributions of ions around biomolecules. Therefore, improved estimates of the ion size and Stern layer thickness to use in the SMPBE will not necessarily improve the model's predictions of ΔGel.
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Affiliation(s)
- Robert C Harris
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306-3408, USA
| | | | - Marcia O Fenley
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306-3408, USA
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17
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Onufriev AV, Aguilar B. Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014; 13. [PMID: 26236064 DOI: 10.1142/s0219633614400069] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy ΔGel computed within the Poisson Boltzmann and the generalized Born models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent ΔGel are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in ΔGel than the molecular surface (MS) DB. The optimal probe radius ρw for which the MS DB yields the most accurate ΔGel varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at ρw ~ 0.2 Å (exact value is sensitive to the structure and atomic radii), at which point the average accuracy of ΔGel is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by ρw gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 Å radii can yield ΔGel estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by up to 5 kcal/mol for individual atomic pairs in small proteins, even when the total ΔGel are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS based definition of the dielectric boundary is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.
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Affiliation(s)
- Alexey V Onufriev
- Department of Computer Science and Department of Physics, Virginia Tech, Blacksburg, VA 24060, and Department of Computer Science, Virginia Tech, Blacksburg, VA 24060
| | - Boris Aguilar
- Department of Computer Science and Department of Physics, Virginia Tech, Blacksburg, VA 24060, and Department of Computer Science, Virginia Tech, Blacksburg, VA 24060
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18
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Qin S, Zhou HX. Using the concept of transient complex for affinity predictions in CAPRI rounds 20-27 and beyond. Proteins 2013; 81:2229-36. [PMID: 23873496 PMCID: PMC3842397 DOI: 10.1002/prot.24366] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Revised: 06/26/2013] [Accepted: 06/29/2013] [Indexed: 11/10/2022]
Abstract
Predictions of protein-protein binders and binding affinities have traditionally focused on features pertaining to the native complexes. In developing a computational method for predicting protein-protein association rate constants, we introduced the concept of transient complex after mapping the interaction energy surface. The transient complex is located at the outer boundary of the bound-state energy well, having near-native separation and relative orientation between the subunits but not yet formed most of the short-range native interactions. We found that the width of the binding funnel and the electrostatic interaction energy of the transient complex are among the features predictive of binders and binding affinities. These ideas were very promising for the five affinity-related targets (T43-45, 55, and 56) of CAPRI rounds 20-27. For T43, we ranked the single crystallographic complex as number 1 and were one of only two groups that clearly identified that complex as a true binder; for T44, we ranked the only design with measurable binding affinity as number 4. For the nine docking targets, continuing on our success in previous CAPRI rounds, we produced 10 medium-quality models for T47 and acceptable models for T48 and T49. We conclude that the interaction energy landscape and the transient complex in particular will complement existing features in leading to better prediction of binding affinities.
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Affiliation(s)
- Sanbo Qin
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
| | - Huan-Xiang Zhou
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
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19
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Rocklin GJ, Mobley DL, Dill KA, Hünenberger PH. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects. J Chem Phys 2013; 139:184103. [PMID: 24320250 PMCID: PMC3838431 DOI: 10.1063/1.4826261] [Citation(s) in RCA: 169] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Accepted: 09/30/2013] [Indexed: 01/12/2023] Open
Abstract
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.
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Affiliation(s)
- Gabriel J Rocklin
- Department of Pharmaceutical Chemistry, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA and Biophysics Graduate Program, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA
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20
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Andrews CT, Elcock AH. Molecular dynamics simulations of highly crowded amino acid solutions: comparisons of eight different force field combinations with experiment and with each other. J Chem Theory Comput 2013; 9. [PMID: 24409104 DOI: 10.1021/ct400371h] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Although it is now commonly accepted that the highly crowded conditions encountered inside biological cells have the potential to significantly alter the thermodynamic properties of biomolecules, it is not known to what extent the thermodynamics of fundamental types of interactions such as salt bridges and hydrophobic interactions are strengthened or weakened by high biomolecular concentrations. As one way of addressing this question we have performed a series of all-atom explicit solvent molecular dynamics (MD) simulations to investigate the effect of increasing solute concentration on the behavior of four types of zwitterionic amino acids in aqueous solution. We have simulated systems containing glycine, valine, phenylalanine or asparagine at concentrations of 50, 100, 200 and 300 mg/ml. Each molecular system has been simulated for 1 μs in order to obtain statistically converged estimates of thermodynamic parameters, and each has been conducted with 8 different force fields and water models; the combined simulation time is 128 μs. The density, viscosity, and dielectric increments of the four amino acids calculated from the simulations have been compared to corresponding experimental measurements. While all of the force fields perform well at reproducing the density increments, discrepancies for the viscosity and dielectric increments raise questions both about the accuracy of the simulation force fields and, in certain cases, the experimental data. We also observe large differences between the various force fields' descriptions of the interaction thermodynamics of salt bridges and, surprisingly, these differences also lead to qualitatively different predictions of their dependences on solute concentration. For the aliphatic interactions of valine sidechains, fewer differences are observed between the force fields, but significant differences are again observed for aromatic interactions of phenylalanine sidechains. Taken together, the results highlight the potential power of using explicit-solvent simulation methods to understand behavior in concentrated systems but also hint at potential difficulties in using these methods to obtain consistent views of behavior in intracellular environments.
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Affiliation(s)
- Casey T Andrews
- Department of Biochemistry, University of Iowa, Iowa City, IA 52242
| | - Adrian H Elcock
- Department of Biochemistry, University of Iowa, Iowa City, IA 52242
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21
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Harris RC, Boschitsch AH, Fenley MO. Influence of Grid Spacing in Poisson-Boltzmann Equation Binding Energy Estimation. J Chem Theory Comput 2013; 9:3677-3685. [PMID: 23997692 DOI: 10.1021/ct300765w] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Grid-based solvers of the Poisson-Boltzmann, PB, equation are routinely used to estimate electrostatic binding, ΔΔGel, and solvation, ΔGel, free energies. The accuracies of such estimates are subject to grid discretization errors from the finite difference approximation to the PB equation. Here, we show that the grid discretization errors in ΔΔGel are more significant than those in ΔGel, and can be divided into two parts: (i) errors associated with the relative positioning of the grid and (ii) systematic errors associated with grid spacing. The systematic error in particular is significant for methods, such as the molecular mechanics PB surface area, MM-PBSA, approach that predict electrostatic binding free energies by averaging over an ensemble of molecular conformations. Although averaging over multiple conformations can control for the error associated with grid placement, it will not eliminate the systematic error, which can only be controlled by reducing grid spacing. The present study indicates that the widely-used grid spacing of 0.5 Å produces unacceptable errors in ΔΔGel, even though its predictions of ΔGel are adequate for the cases considered here. Although both grid discretization errors generally increase with grid spacing, the relative sizes of these errors differ according to the solute-solvent dielectric boundary definition. The grid discretization errors are generally smaller on the Gaussian surface used in the present study than on either the solvent-excluded or van der Waals surfaces, which both contain more surface discontinuities (e.g., sharp edges and cusps). Additionally, all three molecular surfaces converge to very different estimates of ΔΔGel.
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Affiliation(s)
- Robert C Harris
- Department of Physics, Florida State University, Tallahasse, FL 32306
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22
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Yao X, Ji C, Xie D, Zhang JZH. Interaction specific binding hotspots in Endonuclease colicin-immunity protein complex from MD simulations. Sci China Chem 2013. [DOI: 10.1007/s11426-013-4877-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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23
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Pang X, Zhou HX. Poisson-Boltzmann Calculations: van der Waals or Molecular Surface? COMMUNICATIONS IN COMPUTATIONAL PHYSICS 2013; 13:1-12. [PMID: 23293674 PMCID: PMC3535440 DOI: 10.4208/cicp.270711.140911s] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The Poisson-Boltzmann equation is widely used for modeling the electrostatics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.
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Affiliation(s)
- Xiaodong Pang
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA
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24
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Kastritis PL, Bonvin AMJJ. On the binding affinity of macromolecular interactions: daring to ask why proteins interact. J R Soc Interface 2012; 10:20120835. [PMID: 23235262 PMCID: PMC3565702 DOI: 10.1098/rsif.2012.0835] [Citation(s) in RCA: 274] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
Interactions between proteins are orchestrated in a precise and time-dependent manner, underlying cellular function. The binding affinity, defined as the strength of these interactions, is translated into physico-chemical terms in the dissociation constant (Kd), the latter being an experimental measure that determines whether an interaction will be formed in solution or not. Predicting binding affinity from structural models has been a matter of active research for more than 40 years because of its fundamental role in drug development. However, all available approaches are incapable of predicting the binding affinity of protein–protein complexes from coordinates alone. Here, we examine both theoretical and experimental limitations that complicate the derivation of structure–affinity relationships. Most work so far has concentrated on binary interactions. Systems of increased complexity are far from being understood. The main physico-chemical measure that relates to binding affinity is the buried surface area, but it does not hold for flexible complexes. For the latter, there must be a significant entropic contribution that will have to be approximated in the future. We foresee that any theoretical modelling of these interactions will have to follow an integrative approach considering the biology, chemistry and physics that underlie protein–protein recognition.
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Affiliation(s)
- Panagiotis L Kastritis
- Bijvoet Center for Biomolecular Research, Faculty of Science, Chemistry, Utrecht University, , Padualaan 8, Utrecht, The Netherlands
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25
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Ji CG, Zhang JZH. Effect of interprotein polarization on protein-protein binding energy. J Comput Chem 2012; 33:1416-20. [PMID: 22495971 DOI: 10.1002/jcc.22969] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2012] [Accepted: 03/02/2012] [Indexed: 12/26/2022]
Abstract
Molecular dynamics simulation in explicit water for the binding of the benchmark barnase-barstar complex was carried out to investigate the effect polarization of interprotein hydrogen bonds on its binding free energy. Our study is based on the AMBER force field but with polarized atomic charges derived from fragment quantum mechanical calculation for the protein complex. The quantum-derived atomic charges include the effect of polarization of interprotein hydrogen bonds, which was absent in the standard force fields that were used in previous theoretical calculations of barnase-barstar binding energy. This study shows that this polarization effect impacts both the static (electronic) and dynamic interprotein electrostatic interactions and significantly lowers the free energy of the barnase-barstar complex.
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Affiliation(s)
- Chang G Ji
- State Key Laboratory of Precision Spectroscopy, Department of Physics, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
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26
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Salari R, Chong LT. Effects of High Temperature on Desolvation Costs of Salt Bridges Across Protein Binding Interfaces: Similarities and Differences between Implicit and Explicit Solvent Models. J Phys Chem B 2012; 116:2561-7. [DOI: 10.1021/jp210172b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Reza Salari
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Lillian T. Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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27
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Quantitative, directional measurement of electric field heterogeneity in the active site of ketosteroid isomerase. Proc Natl Acad Sci U S A 2012; 109:E299-308. [PMID: 22308339 DOI: 10.1073/pnas.1111566109] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Understanding the electrostatic forces and features within highly heterogeneous, anisotropic, and chemically complex enzyme active sites and their connection to biological catalysis remains a longstanding challenge, in part due to the paucity of incisive experimental probes of electrostatic properties within proteins. To quantitatively assess the landscape of electrostatic fields at discrete locations and orientations within an enzyme active site, we have incorporated site-specific thiocyanate vibrational probes into multiple positions within bacterial ketosteroid isomerase. A battery of X-ray crystallographic, vibrational Stark spectroscopy, and NMR studies revealed electrostatic field heterogeneity of 8 MV/cm between active site probe locations and widely differing sensitivities of discrete probes to common electrostatic perturbations from mutation, ligand binding, and pH changes. Electrostatic calculations based on active site ionization states assigned by literature precedent and computational pK(a) prediction were unable to quantitatively account for the observed vibrational band shifts. However, electrostatic models of the D40N mutant gave qualitative agreement with the observed vibrational effects when an unusual ionization of an active site tyrosine with a pK(a) near 7 was included. UV-absorbance and (13)C NMR experiments confirmed the presence of a tyrosinate in the active site, in agreement with electrostatic models. This work provides the most direct measure of the heterogeneous and anisotropic nature of the electrostatic environment within an enzyme active site, and these measurements provide incisive benchmarks for further developing accurate computational models and a foundation for future tests of electrostatics in enzymatic catalysis.
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28
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Alexov E, Mehler EL, Baker N, Baptista AM, Huang Y, Milletti F, Nielsen JE, Farrell D, Carstensen T, Olsson MHM, Shen JK, Warwicker J, Williams S, Word JM. Progress in the prediction of pKa values in proteins. Proteins 2011; 79:3260-75. [PMID: 22002859 PMCID: PMC3243943 DOI: 10.1002/prot.23189] [Citation(s) in RCA: 198] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2011] [Accepted: 09/12/2011] [Indexed: 01/18/2023]
Abstract
The pK(a) -cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pK(a) values and protein electrostatics in general. The first round of the pK(a) -cooperative, which challenged computational labs to carry out blind predictions against pK(a) s experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6-10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pK(a) calculations, emphasizing methods that were used by the participants in calculating the blind pK(a) values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pK(a) calculations.
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Affiliation(s)
- Emil Alexov
- Department of Physics, Clemson University, Clemson, SC, USA.
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29
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Chen Z, Baker NA, Wei GW. Differential geometry based solvation model II: Lagrangian formulation. J Math Biol 2011; 63:1139-200. [PMID: 21279359 PMCID: PMC3113640 DOI: 10.1007/s00285-011-0402-z] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2010] [Revised: 12/24/2010] [Indexed: 10/18/2022]
Abstract
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.
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Affiliation(s)
- Zhan Chen
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Nathan A. Baker
- Pacific Northwest National Laboratory,
902 Battelle Boulevard P.O. Box 999, MSIN K7-28, Richland, WA 99352 USA
| | - G. W. Wei
- Department of Mathematics, Michigan State University, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
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30
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Cai Q, Ye X, Wang J, Luo R. On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods. J Chem Theory Comput 2011; 7:3608-3619. [PMID: 24772042 PMCID: PMC3998210 DOI: 10.1021/ct200389p] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.
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Affiliation(s)
- Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, California
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
| | - Xiang Ye
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
- Department of Physics, Shanghai Normal University, Shanghai, China
| | - Jun Wang
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, California
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
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31
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Bhaskara RM, Srinivasan N. Stability of domain structures in multi-domain proteins. Sci Rep 2011; 1:40. [PMID: 22355559 PMCID: PMC3216527 DOI: 10.1038/srep00040] [Citation(s) in RCA: 78] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2011] [Accepted: 06/27/2011] [Indexed: 01/22/2023] Open
Abstract
Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.
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Patel CA, Wang J, Wang X, Dong F, Zhong P, Luo PP, Wang KC. Parallel selection of antibody libraries on phage and yeast surfaces via a cross-species display. Protein Eng Des Sel 2011; 24:711-9. [DOI: 10.1093/protein/gzr034] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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33
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Mendoza VL, Barón-Rodríguez MA, Blanco C, Vachet RW. Structural insights into the pre-amyloid tetramer of β-2-microglobulin from covalent labeling and mass spectrometry. Biochemistry 2011; 50:6711-22. [PMID: 21718071 DOI: 10.1021/bi2004894] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The main pathogenic process underlying dialysis-related amyloidosis is the accumulation of β-2-microglobulin (β2m) as amyloid fibrils in the musculoskeletal system, and some evidence suggests that Cu(II) may play a role in β2m amyloid formation. Cu(II)-induced β2m fibril formation is preceded by the formation of discrete, oligomeric intermediates, including dimers, tetramers, and hexamers. In this work, we use selective covalent labeling reactions combined with mass spectrometry to investigate the amino acids responsible for mediating tetramer formation in wild-type β2m. By comparing the labeling patterns of the monomer, dimer, and tetramer, we find evidence that the tetramer interface is formed by the interaction of D strands from one dimer unit and G strands from another dimer unit. These covalent labeling data along with molecular dynamics calculations allow the construction of a tetramer model that indicates how the protein might proceed to form even higher-order oligomers.
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Affiliation(s)
- Vanessa Leah Mendoza
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, USA
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34
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Abstract
Accurate computational methods for predicting electrostatic energies are of major importance for our understanding of protein energetics in general for computer-aided drug design as well as for the design of novel biocatalysts and protein therapeutics. Electrostatic energies are of particular importance in such applications as virtual screening, drug design and protein-protein docking due to the high charge density of protein ligands and small-molecule drugs, and the frequent protonation state changes observed when drugs bind to their protein targets. Therefore, the development of a reliable and fast algorithm for the evaluation of electrostatic free energies, as an important contributor to the overall protein energy function, has been the focus for many scientists over the past three decades. In this review we describe the current state-of-the-art in modeling electrostatic effects in proteins and protein-ligand complexes. We focus mainly on the merits and drawbacks of the continuum methodology, and speculate on future directions in refining algorithms for calculating electrostatic energies in proteins using experimental data.
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35
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Sabirianov RF, Rubinstein A, Namavar F. Enhanced initial protein adsorption on engineered nanostructured cubic zirconia. Phys Chem Chem Phys 2011; 13:6597-609. [DOI: 10.1039/c0cp02389b] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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36
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Kim B, Song X. Calculations of the second virial coefficients of protein solutions with an extended fast multipole method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011915. [PMID: 21405721 DOI: 10.1103/physreve.83.011915] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2010] [Indexed: 05/30/2023]
Abstract
The osmotic second virial coefficients B(2) are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B(2) of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B(2) are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions.
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Affiliation(s)
- Bongkeun Kim
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
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37
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Aguilar B, Shadrach R, Onufriev AV. Reducing the Secondary Structure Bias in the Generalized Born Model via R6 Effective Radii. J Chem Theory Comput 2010. [DOI: 10.1021/ct100392h] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Boris Aguilar
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24060, United States, Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States, and Departments of Computer Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Richard Shadrach
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24060, United States, Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States, and Departments of Computer Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Alexey V. Onufriev
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24060, United States, Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, United States, and Departments of Computer Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
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38
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Chen Z, Baker NA, Wei GW. Differential geometry based solvation model I: Eulerian formulation. JOURNAL OF COMPUTATIONAL PHYSICS 2010; 229:8231-8258. [PMID: 20938489 PMCID: PMC2951687 DOI: 10.1016/j.jcp.2010.06.036] [Citation(s) in RCA: 90] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.
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Affiliation(s)
- Zhan Chen
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Nathan A. Baker
- Pacific Northwest National Laboratory, PO Box 999, MS K7-28, Richland, WA 99352, USA
| | - G. W. Wei
- Department of Mathematics, Michigan State University, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
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39
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Salari R, Chong LT. Desolvation Costs of Salt Bridges across Protein Binding Interfaces: Similarities and Differences between Implicit and Explicit Solvent Models. J Phys Chem Lett 2010; 1:2844-2848. [PMID: 24920993 PMCID: PMC4047600 DOI: 10.1021/jz1010863] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2010] [Accepted: 09/05/2010] [Indexed: 06/01/2023]
Abstract
The prevalence of salt bridges across protein binding interfaces is surprising given the significant costs of desolvating the two charged groups upon binding. These desolvation costs, which are difficult to examine using laboratory experiments, have been computed in previous studies using the Poisson-Boltzmann (PB) implicit solvent model. Here, for the first time, we directly compare the PB implicit solvent model with several explicit water models in computing the desolvation penalties of salt bridges across protein-protein interfaces. We report both overall agreement as well as significant differences between the implicit and explicit solvent results. These differences highlight challenges to be faced in the application of implicit solvent methods.
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40
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Schreiber G, Haran G, Zhou HX. Fundamental aspects of protein-protein association kinetics. Chem Rev 2010; 109:839-60. [PMID: 19196002 DOI: 10.1021/cr800373w] [Citation(s) in RCA: 544] [Impact Index Per Article: 38.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- G Schreiber
- Department of Biological Chemistry, Weizmann Institute of Science, Rehovot, 76100, Israel.
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41
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Kim B, Song J, Song X. Calculations of the binding affinities of protein-protein complexes with the fast multipole method. J Chem Phys 2010; 133:095101. [DOI: 10.1063/1.3474624] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Rubinstein A, Sabirianov RF, Mei WN, Namavar F, Khoynezhad A. Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021915. [PMID: 20866845 DOI: 10.1103/physreve.82.021915] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2010] [Indexed: 05/29/2023]
Abstract
Using a nonlocal electrostatic approach that incorporates the short-range structure of the contacting media, we evaluated the electrostatic contribution to the energy of the complex formation of two model proteins. In this study, we have demonstrated that the existence of an ordered interfacial water layer at the protein-solvent interface reduces the charging energy of the proteins in the aqueous solvent, and consequently increases the electrostatic contribution to the protein binding (change in free energy upon the complex formation of two proteins). This is in contrast with the finding of the continuum electrostatic model, which suggests that electrostatic interactions are not strong enough to compensate for the unfavorable desolvation effects.
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Affiliation(s)
- A Rubinstein
- Department of Biomedical Sciences and Surgery, Creighton University Medical Center, Omaha, Nebraska 68131, USA.
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43
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Mendoza VL, Antwi K, Barón-Rodríguez MA, Blanco C, Vachet RW. Structure of the preamyloid dimer of beta-2-microglobulin from covalent labeling and mass spectrometry. Biochemistry 2010; 49:1522-32. [PMID: 20088607 PMCID: PMC2848472 DOI: 10.1021/bi901748h] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Beta-2-microglobulin (beta2m) self-associates into fibrillar amyloid deposits in the musculoskeletal system of patients undergoing hemodialysis treatment. Previous studies have shown that stoichiometric amounts of Cu(II) at near physiological conditions can cause beta2m to organize into native-like dimers prior to forming amyloid fibrils. Here, we report the results from selective covalent labeling reactions combined with mass spectrometry that provide insight into the amino acid residues that mediate dimer formation in the wild-type protein. Using three complementary covalent labeling reagents, we find that the dimer interface is formed by the antiparallel stacking of ABED beta-sheets from two beta2m monomers. In addition, our data clearly indicate that a dimer interface involving the interactions of D-D strands from separate protein units as seen in the recent crystal structures of two mutant beta2m oligomers is unlikely.
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Affiliation(s)
- Vanessa Leah Mendoza
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003
| | - Kwasi Antwi
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003
| | | | | | - Richard W. Vachet
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003
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44
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Długosz M, Antosiewicz JM, Trylska J. pH-dependent association of proteins. The test case of monoclonal antibody HyHEL-5 and its antigen hen egg white lysozyme. J Phys Chem B 2010; 113:15662-9. [PMID: 19883097 DOI: 10.1021/jp906829z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
We describe a method for determining diffusion-controlled rate constants for protein-protein association that explicitly includes the solution pH. The method combines the transient-complex theory for computing electrostatically enhanced association rates with an approach based on a rigorous thermodynamic cycle and partition functions for energy levels characterizing protonation states of associating proteins and their complexes. To test our method, we determine the pH-dependent kinetics of association of the HyHEL-5 antibody with its antigen hen egg white lysozyme. It was shown experimentally that their association rate constant depends on pH, increasing linearly in the pH range 6-8 and saturating or even exhibiting a flat maximum in the pH range 8-10. The presented methodology leads to a qualitative agreement with the experimental data. Our approach allows one to study diffusion-controlled protein-protein association under different pH conditions by taking into account the ensembles of protonation states rather than just the most probable protonation state of each protein.
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Affiliation(s)
- Maciej Długosz
- Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Zwirki i Wigury 93, Warsaw 02-089, Poland.
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45
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Das M, Basu G. Coulomb energies of protein-protein complexes with monopole-free charge distributions. J Mol Graph Model 2008; 27:846-51. [PMID: 19167253 DOI: 10.1016/j.jmgm.2008.12.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2008] [Revised: 12/11/2008] [Accepted: 12/12/2008] [Indexed: 01/06/2023]
Abstract
From an analysis of Coulomb energy distributions of a large set of protein-protein complexes we show that the positive tail in the energy distribution disappears when the monopole-monopole term, the only energy term independent of inter-subunit orientations, is removed. This indicates that unfavorable Coulomb energies associated with subunit orientations are excluded in protein-protein complexes. The overall result remained unchanged when solvent effects were included. Our results have important bearing on the restriction of subunit orientations in protein-protein complexes and complement a recent work [K. Brock, K. Talley, K. Coley, P. Kundrotas, E. Alexov, Optimization of electrostatic interactions in protein-protein complexes, Biophys. J. 93 (2007) 3340-3352.] which showed that Coulomb energy of interaction in protein-protein complexes is sequence-optimized.
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Affiliation(s)
- Madhurima Das
- Bioinformatics Centre, Bose Institute, P-1/12 CIT Scheme VIIM, Kolkata 700054, India
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46
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Talley K, Ng C, Shoppell M, Kundrotas P, Alexov E. On the electrostatic component of protein-protein binding free energy. PMC BIOPHYSICS 2008; 1:2. [PMID: 19351424 PMCID: PMC2666630 DOI: 10.1186/1757-5036-1-2] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2008] [Accepted: 11/05/2008] [Indexed: 01/02/2023]
Abstract
Calculations of electrostatic properties of protein-protein complexes are usually done within framework of a model with a certain set of parameters. In this paper we present a comprehensive statistical analysis of the sensitivity of the electrostatic component of binding free energy (DeltaDeltaGel) with respect with different force fields (Charmm, Amber, and OPLS), different values of the internal dielectric constant, and different presentations of molecular surface (different values of the probe radius). The study was done using the largest so far set of entries comprising 260 hetero and 2148 homo protein-protein complexes extracted from a previously developed database of protein complexes (ProtCom). To test the sensitivity of the energy calculations with respect to the structural details, all structures were energy minimized with corresponding force field, and the energies were recalculated. The results indicate that the absolute value of the electrostatic component of the binding free energy (DeltaDeltaGel) is very sensitive to the force field parameters, the minimization procedure, the values of the internal dielectric constant, and the probe radius. Nevertheless our results indicate that certain trends in DeltaDeltaGel behavior are much less sensitive to the calculation parameters. For instance, the fraction of the homo-complexes, for which the electrostatics was found to oppose binding, is 80% regardless of the force fields and parameters used. For the hetero-complexes, however, the percentage of the cases for which electrostatics opposed binding varied from 43% to 85%, depending on the protocol and parameters employed. A significant correlation was found between the effects caused by raising the internal dielectric constant and decreasing the probe radius. Correlations were also found among the results obtained with different force fields. However, despite of the correlations found, the absolute DeltaDeltaGel calculated with different force field parameters could differ more than tens of kcal/mol in some cases. Set of rules of obtaining confident predictions of absolute DeltaDeltaGel and DeltaDeltaGel sign are provided in the conclusion section.PACS codes: 87.15.A-, 87.15. km.
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Affiliation(s)
- Kemper Talley
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
| | - Carmen Ng
- James Byrnes High School, Duncan, SC 29334, USA
| | - Michael Shoppell
- South Carolina Governor School for Science and Mathematics, Hartsville, SC 29550, USA
| | - Petras Kundrotas
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
- Center for Bioinformatics, The University of Kansas, Lawrence, KS 66047, USA
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
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47
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Tjong H, Zhou HX. Accurate Calculations of Binding, Folding, and Transfer Free Energies by a Scaled Generalized Born Method. J Chem Theory Comput 2008; 4:1733-1744. [PMID: 23468599 DOI: 10.1021/ct8001656] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The Poisson-Boltzmann (PB) equation is widely used for modeling solvation effects. The computational cost of PB has restricted its applications largely to single-conformation calculations. The generalized Born (GB) model provides an approximation at substantially reduced cost. Currently the best GB methods reproduce PB results for electrostatic solvation energies with errors at ~5 kcal/mol. When two proteins form a complex, the net electrostatic contributions to the binding free energy are typically of the order of 5 to 10 kcal/mol. Similarly, the net contributions of individual residues to protein folding free energy are < 5 kcal/mol. Clearly in these applications the accuracy of current GB methods is insufficient. Here we present a simple scaling scheme that allows our GB method, GBr6, to reproduce PB results for binding, folding, and transfer free energies with high accuracy. From an ensemble of conformations sampled from molecular dynamics simulations, five were judiciously selected for PB calculations. These PB results were used for scaling GBr6. Tests on the binding free energies of the barnase-barstar, GTPase-WASp, and U1A-U1hpII complexes and on the folding free energy of FKBP show that the effects of point mutations calculated by scaled GBr6 are accurate to within 0.3 kcal/mol of PB results. Similar accuracy was also achieved for the free energies of transfer for ribonuclease Sa and insulin from the crystalline phase to the solution phase at various pH's. This method makes it possible to thoroughly sample the transient-complex ensemble in predicting protein binding rate constants and to incorporate conformational sampling in electrostatic modeling (such as done in the MM-GBSA approach) without loss of accuracy.
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Affiliation(s)
- Harianto Tjong
- Department of Physics and Institute of Molecular Biophysics and School of Computational Science, Florida State University, Tallahassee, FL 32306
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48
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Spontaneous conformational change and toxin binding in alpha7 acetylcholine receptor: insight into channel activation and inhibition. Proc Natl Acad Sci U S A 2008; 105:8280-5. [PMID: 18541920 DOI: 10.1073/pnas.0710530105] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Nicotinic AChRs (nAChRs) represent a paradigm for ligand-gated ion channels. Despite intensive studies over many years, our understanding of the mechanisms of activation and inhibition for nAChRs is still incomplete. Here, we present molecular dynamics (MD) simulations of the alpha7 nAChR ligand-binding domain, both in apo form and in alpha-Cobratoxin-bound form, starting from the respective homology models built on crystal structures of the acetylcholine-binding protein. The toxin-bound form was relatively stable, and its structure was validated by calculating mutational effects on the toxin-binding affinity. However, in the apo form, one subunit spontaneously moved away from the conformation of the other four subunits. This motion resembles what has been proposed for leading to channel opening. At the top, the C loop and the adjacent beta7-beta8 loop swing downward and inward, whereas at the bottom, the F loop and the C terminus of beta10 swing in the opposite direction. These swings appear to tilt the whole subunit clockwise. The resulting changes in solvent accessibility show strong correlation with experimental results by the substituted cysteine accessibility method upon addition of acetylcholine. Our MD simulation results suggest a mechanistic model in which the apo form, although predominantly sampling the "closed" state, can make excursions into the "open" state. The open state has high affinity for agonists, leading to channel activation, whereas the closed state upon distortion has high affinity for antagonists, leading to inhibition.
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49
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Coevolution at protein complex interfaces can be detected by the complementarity trace with important impact for predictive docking. Proc Natl Acad Sci U S A 2008; 105:7708-13. [PMID: 18511568 DOI: 10.1073/pnas.0707032105] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Protein surfaces are under significant selection pressure to maintain interactions with their partners throughout evolution. Capturing how selection pressure acts at the interfaces of protein-protein complexes is a fundamental issue with high interest for the structural prediction of macromolecular assemblies. We tackled this issue under the assumption that, throughout evolution, mutations should minimally disrupt the physicochemical compatibility between specific clusters of interacting residues. This constraint drove the development of the so-called Surface COmplementarity Trace in Complex History score (SCOTCH), which was found to discriminate with high efficiency the structure of biological complexes. SCOTCH performances were assessed not only with respect to other evolution-based approaches, such as conservation and coevolution analyses, but also with respect to statistically based scoring methods. Validated on a set of 129 complexes of known structure exhibiting both permanent and transient intermolecular interactions, SCOTCH appears as a robust strategy to guide the prediction of protein-protein complex structures. Of particular interest, it also provides a basic framework to efficiently track how protein surfaces could evolve while keeping their partners in contact.
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50
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Alsallaq R, Zhou HX. Electrostatic rate enhancement and transient complex of protein-protein association. Proteins 2008; 71:320-35. [PMID: 17932929 DOI: 10.1002/prot.21679] [Citation(s) in RCA: 132] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.
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Affiliation(s)
- Ramzi Alsallaq
- Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
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