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Kasahara K, Sato H. Dynamics theory for molecular liquids based on an interaction site model. Phys Chem Chem Phys 2017; 19:27917-27929. [DOI: 10.1039/c7cp05423h] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.
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Affiliation(s)
- Kento Kasahara
- Department of Molecular Engineering
- Kyoto University
- Japan
| | - Hirofumi Sato
- Department of Molecular Engineering and Elements Strategy for Catalysts and Batteries (ESICB)
- Kyoto University
- Japan
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2
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Lee JU, Lee WJ, Park HS, Lee SY. Calculation of the Absolute Rate of Human Cu/Zn Superoxide Dismutases from Atomic-Level Molecular Dynamics Simulations. B KOREAN CHEM SOC 2012. [DOI: 10.5012/bkcs.2012.33.3.862] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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3
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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: 555] [Impact Index Per Article: 39.6] [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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4
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Abstract
Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA.
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5
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Gabdoulline RR, Wade RC. On the contributions of diffusion and thermal activation to electron transfer between Phormidium laminosum plastocyanin and cytochrome f: Brownian dynamics simulations with explicit modeling of nonpolar desolvation interactions and electron transfer events. J Am Chem Soc 2009; 131:9230-8. [PMID: 19518050 DOI: 10.1021/ja809567k] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The factors that determine the extent to which diffusion and thermal activation processes govern electron transfer (ET) between proteins are debated. The process of ET between plastocyanin (PC) and cytochrome f (CytF) from the cyanobacterium Phormidium laminosum was initially thought to be diffusion-controlled but later was found to be under activation control (Schlarb-Ridley, B. G.; et al. Biochemistry 2005, 44, 6232). Here we describe Brownian dynamics simulations of the diffusional association of PC and CytF, from which ET rates were computed using a detailed model of ET events that was applied to all of the generated protein configurations. The proteins were modeled as rigid bodies represented in atomic detail. In addition to electrostatic forces, which were modeled as in our previous simulations of protein-protein association, the proteins interacted by a nonpolar desolvation (hydrophobic) force whose derivation is described here. The simulations yielded close to realistic residence times of transient protein-protein encounter complexes of up to tens of microseconds. The activation barrier for individual ET events derived from the simulations was positive. Whereas the electrostatic interactions between P. laminosum PC and CytF are weak, simulations for a second cyanobacterial PC-CytF pair, that from Nostoc sp. PCC 7119, revealed ET rates influenced by stronger electrostatic interactions. In both cases, the simulations imply significant contributions to ET from both diffusion and thermal activation processes.
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Affiliation(s)
- Razif R Gabdoulline
- Molecular and Cellular Modeling Group, EML Research gGmbH, Schloss-Wolfsbrunnenweg 33, D-69118 Heidelberg, Germany.
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Cheng Y, Holst MJ, McCammon JA. Finite element analysis of drug electrostatic diffusion: inhibition rate studies in N1 neuraminidase. PACIFIC SYMPOSIUM ON BIOCOMPUTING. PACIFIC SYMPOSIUM ON BIOCOMPUTING 2009:281-92. [PMID: 19209708 PMCID: PMC3107071 DOI: 10.1142/9789812836939_0027] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This article describes a numerical solution of the steady-state Poisson-Boltzmann-Smoluchowski (PBS) and Poisson-Nernst-Planck (PNP) equations to study diffusion in biomolecular systems. Specifically, finite element methods have been developed to calculate electrostatic interactions and ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to the wild-type and several mutated avian influenza neurominidase crystal structures. The calculated rates show very good agreement with recent experimental studies. Furthermore, these finite element methods require significantly fewer computational resources than existing particle-based Brownian dynamics methods and are robust for complicated geometries. The key finding of biological importance is that the electrostatic steering plays the important role in the drug binding process of the neurominidase.
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Affiliation(s)
- Yuhui Cheng
- University of California, San Diego, 9500 Gilman Dr., MC 0365, La Jolla, CA 92037, USA.
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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: 124] [Impact Index Per Article: 7.8] [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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Zhou HX, Qin S, Tjong H. Modeling Protein–Protein and Protein–Nucleic Acid Interactions: Structure, Thermodynamics, and Kinetics. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2008. [DOI: 10.1016/s1574-1400(08)00004-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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9
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Qin S, Zhou HX. Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II. J Phys Chem B 2007; 112:5955-60. [PMID: 18154282 DOI: 10.1021/jp075919k] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We have developed a computational approach for predicting protein-protein association rates (Alsallaq and Zhou, Structure 2007, 15, 215). Here we expand the range of applicability of this approach to protein-RNA binding and report the first results for protein-RNA binding rates predicted from atomistic modeling. The system studied is the U1A protein and stem/loop II of the U1 small nuclear RNA. Experimentally it was observed that the binding rate is significantly reduced by increasing salt concentration while the dissociation changes little with salt concentration, and charges distant from the binding site make marginal contribution to the binding rate. These observations are rationalized. Moreover, predicted effects of salt and charge mutations are found to be in quantitative agreement with experimental results.
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Affiliation(s)
- Sanbo Qin
- Department of Physics and Institute of Molecular Biophysics and School of Computational Science, Florida State University, Tallahassee, Florida 32306, USA
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Gabdoulline RR, Stein M, Wade RC. qPIPSA: relating enzymatic kinetic parameters and interaction fields. BMC Bioinformatics 2007; 8:373. [PMID: 17919319 PMCID: PMC2174957 DOI: 10.1186/1471-2105-8-373] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2007] [Accepted: 10/05/2007] [Indexed: 11/29/2022] Open
Abstract
Background The simulation of metabolic networks in quantitative systems biology requires the assignment of enzymatic kinetic parameters. Experimentally determined values are often not available and therefore computational methods to estimate these parameters are needed. It is possible to use the three-dimensional structure of an enzyme to perform simulations of a reaction and derive kinetic parameters. However, this is computationally demanding and requires detailed knowledge of the enzyme mechanism. We have therefore sought to develop a general, simple and computationally efficient procedure to relate protein structural information to enzymatic kinetic parameters that allows consistency between the kinetic and structural information to be checked and estimation of kinetic constants for structurally and mechanistically similar enzymes. Results We describe qPIPSA: quantitative Protein Interaction Property Similarity Analysis. In this analysis, molecular interaction fields, for example, electrostatic potentials, are computed from the enzyme structures. Differences in molecular interaction fields between enzymes are then related to the ratios of their kinetic parameters. This procedure can be used to estimate unknown kinetic parameters when enzyme structural information is available and kinetic parameters have been measured for related enzymes or were obtained under different conditions. The detailed interaction of the enzyme with substrate or cofactors is not modeled and is assumed to be similar for all the proteins compared. The protein structure modeling protocol employed ensures that differences between models reflect genuine differences between the protein sequences, rather than random fluctuations in protein structure. Conclusion Provided that the experimental conditions and the protein structural models refer to the same protein state or conformation, correlations between interaction fields and kinetic parameters can be established for sets of related enzymes. Outliers may arise due to variation in the importance of different contributions to the kinetic parameters, such as protein stability and conformational changes. The qPIPSA approach can assist in the validation as well as estimation of kinetic parameters, and provide insights into enzyme mechanism.
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Affiliation(s)
- Razif R Gabdoulline
- Molecular and Cellular Modeling Group, EML Research gGmbH, Schloss Wolfsbrunnenweg 33, Heidelberg, 69118, Germany.
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Cheng Y, Suen JK, Zhang D, Bond SD, Zhang Y, Song Y, Baker NA, Bajaj CL, Holst MJ, McCammon JA. Finite element analysis of the time-dependent Smoluchowski equation for acetylcholinesterase reaction rate calculations. Biophys J 2007; 92:3397-406. [PMID: 17307827 PMCID: PMC1853150 DOI: 10.1529/biophysj.106.102533] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
This article describes the numerical solution of the time-dependent Smoluchowski equation to study diffusion in biomolecular systems. Specifically, finite element methods have been developed to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to the mouse acetylcholinesterase (mAChE) monomer and several tetramers. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different time steps. Calculated rates show very good agreement with experimental and theoretical steady-state studies. Furthermore, these finite element methods require significantly fewer computational resources than existing particle-based Brownian dynamics methods and are robust for complicated geometries. The key finding of biological importance is that the rate accelerations of the monomeric and tetrameric mAChE that result from electrostatic steering are preserved under the non-steady-state conditions that are expected to occur in physiological circumstances.
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Affiliation(s)
- Yuhui Cheng
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, California, USA.
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Perret D, Rousseau F, Tran V, Gascan H. Reversal of some viral IL-6 electrostatic properties compared to IL-6 contributes to a loss of alpha receptor component recruitment. Proteins 2005; 60:14-26. [PMID: 15861391 DOI: 10.1002/prot.20445] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Human interleukin-6 (hIL-6) is a pleiotropic mediator of activation and proliferation across a large number of different cell types. Human herpesvirus-8 (HHV-8) has been associated with classical and AIDS-related Kaposi's sarcoma (KS). HHV-8 encodes viral IL-6 (vIL-6), a functional homolog of human interleukin-6, that promotes the growth of KS and of some lymphoma cells. Signaling induced by human IL-6 requires recruitment of the glycoprotein gp130, which acts as the signal transducing chain, and of IL-6Ralpha, which is necessary for cognate recognition and high affinity receptor complex formation. In contrast, the formation of a functional complex between vIL-6 and gp130 does not require the presence of IL-6Ralpha. The physico-chemical properties of vIL-6 have been analyzed and compared to those of hIL-6 and of the receptor chains, gp130 and IL-6Ralpha. Interaction sites on vIL-6 involve more hydrophobic residues than those of hIL-6. The electrostatic fields induced by vIL-6 and IL-6Ralpha are repulsive and prevent interaction between vIL-6 and IL-6Ralpha, whereas the electrostatic field induced by hIL-6 steers the complex formation with IL-6Ralpha. Subsequently, electrostatic binding free energy in the vIL-6/IL-6Ralpha complex is destabilizing, whereas it is stabilizing in the complex comprising hIL-6. These properties result from charge reversals between viral and human IL-6, an unusual phenomenon of amino acid substitutions within a homologous protein family. This suggests a selection pressure for vIL-6 to by-pass the IL-6Ralpha control of host defense against virus infection. This selection pressure has yielded the reversal of electrostatic properties of vIL-6 when compared to hIL-6.
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Zhang D, Suen J, Zhang Y, Song Y, Radic Z, Taylor P, Holst MJ, Bajaj C, Baker NA, McCammon JA. Tetrameric mouse acetylcholinesterase: continuum diffusion rate calculations by solving the steady-state Smoluchowski equation using finite element methods. Biophys J 2005; 88:1659-65. [PMID: 15626705 PMCID: PMC1305222 DOI: 10.1529/biophysj.104.053850] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2004] [Accepted: 12/15/2004] [Indexed: 11/18/2022] Open
Abstract
The tetramer is the most important form for acetylcholinesterase in physiological conditions, i.e., in the neuromuscular junction and the nervous system. It is important to study the diffusion of acetylcholine to the active sites of the tetrameric enzyme to understand the overall signal transduction process in these cellular components. Crystallographic studies revealed two different forms of tetramers, suggesting a flexible tetramer model for acetylcholinesterase. Using a recently developed finite element solver for the steady-state Smoluchowski equation, we have calculated the reaction rate for three mouse acetylcholinesterase tetramers using these two crystal structures and an intermediate structure as templates. Our results show that the reaction rates differ for different individual active sites in the compact tetramer crystal structure, and the rates are similar for different individual active sites in the other crystal structure and the intermediate structure. In the limit of zero salt, the reaction rates per active site for the tetramers are the same as that for the monomer, whereas at higher ionic strength, the rates per active site for the tetramers are approximately 67%-75% of the rate for the monomer. By analyzing the effect of electrostatic forces on ACh diffusion, we find that electrostatic forces play an even more important role for the tetramers than for the monomer. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.
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Affiliation(s)
- Deqiang Zhang
- Howard Hughes Medical Institute, University of California at San Diego, La Jolla, California 92093, USA.
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Song Y, Zhang Y, Shen T, Bajaj CL, McCammon JA, Baker NA. Finite element solution of the steady-state Smoluchowski equation for rate constant calculations. Biophys J 2004; 86:2017-29. [PMID: 15041644 PMCID: PMC1304055 DOI: 10.1016/s0006-3495(04)74263-0] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
Abstract
This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.
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Affiliation(s)
- Yuhua Song
- Department of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, St. Louis, Missouri 63110, USA
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De Rienzo F, Gabdoulline RR, Menziani MC, De Benedetti PG, Wade RC. Electrostatic analysis and Brownian dynamics simulation of the association of plastocyanin and cytochrome f. Biophys J 2001; 81:3090-104. [PMID: 11720977 PMCID: PMC1301771 DOI: 10.1016/s0006-3495(01)75947-4] [Citation(s) in RCA: 73] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
The oxidation of cytochrome f by the soluble cupredoxin plastocyanin is a central reaction in the photosynthetic electron transfer chain of all oxygenic organisms. Here, two different computational approaches are used to gain new insights into the role of molecular recognition and protein-protein association processes in this redox reaction. First, a comparative analysis of the computed molecular electrostatic potentials of seven single and multiple point mutants of spinach plastocyanin (D42N, E43K, E43N, E43Q/D44N, E59K/E60Q, E59K/E60Q/E43N, Q88E) and the wt protein was carried out. The experimentally determined relative rates (k(2)) for the set of plastocyanin mutants are found to correlate well (r(2) = 0.90 - 0.97) with the computed measure of the similarity of the plastocyanin electrostatic potentials. Second, the effects on the plastocyanin/cytochrome f association rate of these mutations in the plastocyanin "eastern site" were evaluated by simulating the association of the wild type and mutant plastocyanins with cytochrome f by Brownian dynamics. Good agreement between the computed and experimental relative rates (k(2)) (r(2) = 0.89 - 0.92) was achieved for the plastocyanin mutants. The results obtained by applying both computational techniques provide support for the fundamental role of the acidic residues at the plastocyanin eastern site in the association with cytochrome f and in the overall electron-transfer process.
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Affiliation(s)
- F De Rienzo
- Università di Modena e Reggio Emilia, Dipartimento di Chimica, Via Campi, 183-41100 Modena, Italy
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Gabdoulline RR, Wade RC. Protein-protein association: investigation of factors influencing association rates by brownian dynamics simulations. J Mol Biol 2001; 306:1139-55. [PMID: 11237623 DOI: 10.1006/jmbi.2000.4404] [Citation(s) in RCA: 185] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The rate of protein-protein association limits the response time due to protein-protein interactions. The bimolecular association rate may be diffusion-controlled or influenced, and in such cases, Brownian dynamics simulations of protein-protein diffusional association may be used to compute association rates. Here, we report Brownian dynamics simulations of the diffusional association of five different protein-protein pairs: barnase and barstar, acetylcholinesterase and fasciculin-2, cytochrome c peroxidase and cytochrome c, the HyHEL-5 antibody and hen egg lysozyme (HEL), and the HyHEL-10 antibody and HEL. The same protocol was used to compute the diffusional association rates for all the protein pairs in order to assess, by comparison to experimentally measured rates, whether the association of these proteins can be explained solely on the basis of diffusional encounter. The simulation protocol is similar to those previously derived for simulation of the association of barnase and barstar, and of acetylcholinesterase and fasciculin-2; these produced results in excellent agreement with experimental data for these protein pairs, with changes in association rate due to mutations reproduced within the limits of expected computational and modeling errors. Here, we find that for all protein pairs, the effects of mutations can be well reproduced by the simulations, even though the degree of the electrostatic translational and orientational steering varies widely between the cases. However, the absolute values of association rates for the acetylcholinesterase: fasciculin-2 and HyHEL-10 antibody: HEL pairs are overestimated. Comparison of bound and unbound protein structures shows that this may be due to gating resulting from protein flexibility in some of the proteins. This may lower the association rates compared to their bimolecular diffusional encounter rates.
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Abstract
Based on previous molecular dynamics simulation results for acetylcholinesterase dimer, we calculate and analyse the electrostatic field fluctuations around the enzyme. The results show that dynamic features of the electrostatic field favor attraction of the positively-charged substrate. An Internet link to an animation of the results is also provided.
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Affiliation(s)
- S T Wlodek
- National Center for Genome Resources, 1800-A Old Pecos Trail, Santa Fe, NM 87505, USA
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