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Fukunishi Y, Mitomo D, Nakamura H. Protein−Ligand Binding Free Energy Calculation by the Smooth Reaction Path Generation (SRPG) Method. J Chem Inf Model 2009; 49:1944-51. [DOI: 10.1021/ci9002156] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yoshifumi Fukunishi
- Biomedicinal Information Research Center (BIRC), National Institute of Advanced Industrial Science and Technology (AIST), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, Pharmaceutical Innovation Value Chain, BioGrid Center Kansai, 1-4-2 Shinsenri-Higashimachi, Toyonaka, Osaka 560-0082, Japan, Japan Biological Informatics Consortium (JBIC), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, and Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Daisuke Mitomo
- Biomedicinal Information Research Center (BIRC), National Institute of Advanced Industrial Science and Technology (AIST), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, Pharmaceutical Innovation Value Chain, BioGrid Center Kansai, 1-4-2 Shinsenri-Higashimachi, Toyonaka, Osaka 560-0082, Japan, Japan Biological Informatics Consortium (JBIC), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, and Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Haruki Nakamura
- Biomedicinal Information Research Center (BIRC), National Institute of Advanced Industrial Science and Technology (AIST), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, Pharmaceutical Innovation Value Chain, BioGrid Center Kansai, 1-4-2 Shinsenri-Higashimachi, Toyonaka, Osaka 560-0082, Japan, Japan Biological Informatics Consortium (JBIC), 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan, and Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
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Asthagiri D, Neal BL, Lenhoff AM. Calculation of short-range interactions between proteins. Biophys Chem 2007; 78:219-31. [PMID: 17030310 DOI: 10.1016/s0301-4622(99)00028-9] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/1999] [Revised: 02/11/1999] [Accepted: 02/11/1999] [Indexed: 11/30/2022]
Abstract
Macromolecular association is an integral component of numerous cellular and technologically relevant processes. Most molecular theories of such association neglect the explicit solvent structure and rely on continuum concepts such as surface energies for calculating short-range interactions. We present a new such method for calculating the non-electrostatic component of the interaction-free energy, based on formalisms for calculating dispersion interactions between macromolecules. The interactions are separated into a short-ranged component that is treated atomistically, and a longer range component that is treated within the continuum Lifshitz-Hamaker approach. This description avoids the singularities inherent in the continuum dispersion formulation, and its effectiveness in characterizing the shape complementarity between interacting surfaces is shown to be comparable to that of surface area-based methods of similar parametric complexity. An advantage of the new method is that it allows facile calculation of the interaction free energy as a function of intermolecular separation, including steric effects; this makes it suitable for use in simulations of protein solutions.
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Affiliation(s)
- D Asthagiri
- Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA
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Makowski M, Liwo A, Scheraga HA. Simple Physics-Based Analytical Formulas for the Potentials of Mean Force for the Interaction of Amino Acid Side Chains in Water. 1. Approximate Expression for the Free Energy of Hydrophobic Association Based on a Gaussian-Overlap Model. J Phys Chem B 2007; 111:2910-6. [PMID: 17388416 DOI: 10.1021/jp065916s] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.
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Affiliation(s)
- Mariusz Makowski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA
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Geney R, Layten M, Gomperts R, Hornak V, Simmerling C. Investigation of Salt Bridge Stability in a Generalized Born Solvent Model. J Chem Theory Comput 2005; 2:115-27. [DOI: 10.1021/ct050183l] [Citation(s) in RCA: 99] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Raphaël Geney
- Department of Chemistry, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794-3400, and Silicon Graphics Inc., Applications Engineering Group, Hudson, Massachusetts 01749
| | - Melinda Layten
- Department of Chemistry, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794-3400, and Silicon Graphics Inc., Applications Engineering Group, Hudson, Massachusetts 01749
| | - Roberto Gomperts
- Department of Chemistry, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794-3400, and Silicon Graphics Inc., Applications Engineering Group, Hudson, Massachusetts 01749
| | - Viktor Hornak
- Department of Chemistry, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794-3400, and Silicon Graphics Inc., Applications Engineering Group, Hudson, Massachusetts 01749
| | - Carlos Simmerling
- Department of Chemistry, Graduate Program in Molecular and Cellular Biology, and Center for Structural Biology, Stony Brook University, Stony Brook, New York 11794-3400, and Silicon Graphics Inc., Applications Engineering Group, Hudson, Massachusetts 01749
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Masunov A, Lazaridis T. Potentials of mean force between ionizable amino acid side chains in water. J Am Chem Soc 2003; 125:1722-30. [PMID: 12580597 DOI: 10.1021/ja025521w] [Citation(s) in RCA: 181] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Potentials of mean force (PMF) between all possible ionizable amino acid side chain pairs in various protonation states were calculated using explicit solvent molecular dynamics simulations with umbrella sampling and the weighted histogram analysis method. The side chains were constrained in various orientations inside a spherical cluster of 200 water molecules. Beglov and Roux's Spherical Solvent Boundary Potential was used to account for the solvent outside this sphere. This approach was first validated by calculating PMFs between monatomic ions (K(+), Na(+), Cl(-)) and comparing them to results from the literature and results obtained using Ewald summation. The strongest interaction (-4.5 kcal/mol) was found for the coaxial Arg(+).Glu(-) pair. Many like-charged side chains display a remarkable lack of repulsion, and occasionally a weak attraction. The PMFs are compared to effective energy curves obtained with common implicit solvation models, namely Generalized Born (GB), EEF1, and uniform dielectric of 80. Overall, the EEF1 curves are too attractive, whereas the GB curves in most cases match the minima of the PMF curves quite well. The uniform dielectric model, despite some fortuitous successes, is grossly inadequate.
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Affiliation(s)
- Artëm Masunov
- City College of the City University of New York, Convent Ave. at 138 St., New York, New York 10031, USA
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Shimizu S, Chan HS. Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins. Proteins 2002; 48:15-30. [PMID: 12012334 DOI: 10.1002/prot.10108] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.
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Affiliation(s)
- Seishi Shimizu
- Department of Biochemistry and Department of Medical Genetics and Microbiology, Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada
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Cramer CJ, Truhlar DG. Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. Chem Rev 1999; 99:2161-2200. [PMID: 11849023 DOI: 10.1021/cr960149m] [Citation(s) in RCA: 1722] [Impact Index Per Article: 68.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christopher J. Cramer
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
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Abstract
We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type--hydrophobic. The other is a heterogeneous model consisting of two residue types--strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55-70 residues.
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Affiliation(s)
- Y Fukunishi
- Department of Chemistry, Rutgers, the State University of New Jersey, Piscataway, USA.
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