1
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Peters TJ, Jordan KE, Li J, Gardner K, Conchúir BÓ, Swope WC, Vassiliadis V, Johnston MA, Zaffetti P. Topological "Shape" in Micellar Dynamics. ACS Omega 2024; 9:16084-16088. [PMID: 38617615 PMCID: PMC11007857 DOI: 10.1021/acsomega.3c09754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Revised: 03/01/2024] [Accepted: 03/06/2024] [Indexed: 04/16/2024]
Abstract
For micelles, "shape" is prominent in rheological computations of fluid flow, but this "shape" is often expressed too informally to be useful for rigorous analyses. We formalize topological "shape equivalence" of micelles, both globally and locally, to enable visualization of computational fluid dynamics. Although topological methods in visualization provide significant insights into fluid flows, this opportunity has been limited by the known difficulties in creating representative geometry. We present an agile geometric algorithm to represent the micellar shape for input into fluid flow visualizations. We show that worm-like and cylindrical micelles have formally equivalent shapes, but that visualization accentuates unexplored differences. This global-local paradigm is extensible beyond micelles.
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Affiliation(s)
- Thomas J. Peters
- Department
of Computer Science and Engineering, 371 Fairfield Way, University of Connecticut, Storrs, Connecticut 06269, United States
| | - Kirk E. Jordan
- IBM
Research, 314 Main Street, Cambridge, Massachusetts 02141, United States
| | - Ji Li
- Department
of Computer Science and Engineering, 371 Fairfield Way, University of Connecticut, Storrs, Connecticut 06269, United States
| | - Kirk Gardner
- Department
of Computer Science and Engineering, 371 Fairfield Way, University of Connecticut, Storrs, Connecticut 06269, United States
| | | | - William C. Swope
- IBM
Research, 650 Harry Road, San Jose, California 95120, United States
| | | | | | - Peter Zaffetti
- Department
of Computer Science and Engineering, 371 Fairfield Way, University of Connecticut, Storrs, Connecticut 06269, United States
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2
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D’Amore L, Hahn DF, Dotson DL, Horton JT, Anwar J, Craig I, Fox T, Gobbi A, Lakkaraju SK, Lucas X, Meier K, Mobley DL, Narayanan A, Schindler CE, Swope WC, in ’t Veld PJ, Wagner J, Xue B, Tresadern G. Collaborative Assessment of Molecular Geometries and Energies from the Open Force Field. J Chem Inf Model 2022; 62:6094-6104. [PMID: 36433835 PMCID: PMC9873353 DOI: 10.1021/acs.jcim.2c01185] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
Force fields form the basis for classical molecular simulations, and their accuracy is crucial for the quality of, for instance, protein-ligand binding simulations in drug discovery. The huge diversity of small-molecule chemistry makes it a challenge to build and parameterize a suitable force field. The Open Force Field Initiative is a combined industry and academic consortium developing a state-of-the-art small-molecule force field. In this report, industry members of the consortium worked together to objectively evaluate the performance of the force fields (referred to here as OpenFF) produced by the initiative on a combined public and proprietary dataset of 19,653 relevant molecules selected from their internal research and compound collections. This evaluation was important because it was completely blind; at most partners, none of the molecules or data were used in force field development or testing prior to this work. We compare the Open Force Field "Sage" version 2.0.0 and "Parsley" version 1.3.0 with GAFF-2.11-AM1BCC, OPLS4, and SMIRNOFF99Frosst. We analyzed force-field-optimized geometries and conformer energies compared to reference quantum mechanical data. We show that OPLS4 performs best, and the latest Open Force Field release shows a clear improvement compared to its predecessors. The performance of established force fields such as GAFF-2.11 was generally worse. While OpenFF researchers were involved in building the benchmarking infrastructure used in this work, benchmarking was done entirely in-house within industrial organizations and the resulting assessment is reported here. This work assesses the force field performance using separate benchmarking steps, external datasets, and involving external research groups. This effort may also be unique in terms of the number of different industrial partners involved, with 10 different companies participating in the benchmark efforts.
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Affiliation(s)
- Lorenzo D’Amore
- Computational Chemistry, Janssen R&D, C/ Jarama 75A, 45007 Toledo, Spain
| | - David F. Hahn
- Computational Chemistry, Janssen R&D, Turnhoutseweg 30, Beerse B-2340, Belgium
| | - David L. Dotson
- The Open Force Field Initiative, Open Molecular Software Foundation, Davis, California 95616, USA
| | - Joshua T. Horton
- School of Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
| | - Jamshed Anwar
- Department of Chemistry, Lancaster University, Lancaster LA1 4YW, UK
| | - Ian Craig
- Molecular Modeling & Drug Discovery, BASF SE, 67056 Ludwigshafen, Germany
| | - Thomas Fox
- Medicinal Chemistry, Boehringer Ingelheim Pharma GmbH & Co KG, 88397 Biberach/Riss, Germany
| | - Alberto Gobbi
- Genentech, Inc., 1 DNA Way, South San Francisco, California, 94080, USA
| | | | - Xavier Lucas
- Roche Pharma Research and Early Development, Therapeutic Modalities, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd, Grenzacherstrasse 124, 4070 Basel, Switzerland
| | - Katharina Meier
- Computational Life Science Technology Functions, Crop Science, R&D, Bayer AG, 40789 Monheim, Germany
| | - David L. Mobley
- Departments of Pharmaceutical Sciences and Chemistry, University of California 92617, Irvine, USA
| | - Arjun Narayanan
- Data and Computational Sciences, Vertex Pharmaceuticals, 50 Northern Ave, Boston, MA 02210, USA
| | | | - William C. Swope
- Genentech, Inc., 1 DNA Way, South San Francisco, California, 94080, USA
| | | | - Jeffrey Wagner
- The Open Force Field Initiative, Open Molecular Software Foundation, Davis, California, 95616, USA,Chemistry Department, The University of California at Irvine, Irvine, California, 92617, USA
| | - Bai Xue
- XtalPi Inc. Floor 3, International Biomedical Innovation Park II, No. 2 Hongliu Road, Fubao Community, Fubao Street, Futian District, Shenzhen, Guangdong, 518040 China
| | - Gary Tresadern
- Computational Chemistry, Janssen R&D, Turnhoutseweg 30, Beerse B-2340, Belgium
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3
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Johnston MA, Duff AI, Anderson RL, Swope WC. Model for the Simulation of the C nE m Nonionic Surfactant Family Derived from Recent Experimental Results. J Phys Chem B 2020; 124:9701-9721. [PMID: 32986421 DOI: 10.1021/acs.jpcb.0c06132] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using a comprehensive set of recently published experimental results for training and validation, we have developed computational models appropriate for simulations of aqueous solutions of poly(ethylene oxide) alkyl ethers, an important class of micelle-forming nonionic surfactants, usually denoted CnEm. These models are suitable for use in simulations that employ a moderate amount of coarse graining and especially for dissipative particle dynamics (DPD), which we adopt in this work. The experimental data used for training and validation were reported earlier and produced in our laboratory using dynamic light scattering (DLS) measurements performed on 12 members of the CnEm compound family yielding micelle size distribution functions and mass-weighted mean aggregation numbers at each of several surfactant concentrations. The range of compounds and quality of the experimental results were designed to support the development of computational models. An essential feature of this work is that all simulation results were analyzed in a way that is consistent with the experimental data. Proper account is taken of the fact that a broad distribution of micelle sizes exists, so mass-weighted averages (rather than number-weighted averages) over this distribution are required for the proper comparison of simulation and experimental results. The resulting DPD force field reproduces several important trends seen in the experimental critical micelle concentrations and mass-averaged mean aggregation numbers with respect to surfactant characteristics and concentration. We feel it can be used to investigate a number of open questions regarding micelle sizes and shapes and their dependence on surfactant concentration for this important class of nonionic surfactants.
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Affiliation(s)
| | - Andrew Ian Duff
- STFC Hartree Centre, SciTech Daresbury, Warrington, Cheshire WA4 4AD, U.K
| | - Richard L Anderson
- STFC Hartree Centre, SciTech Daresbury, Warrington, Cheshire WA4 4AD, U.K
| | - William C Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
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4
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Klebes J, Finnigan S, Bray DJ, Anderson RL, Swope WC, Johnston MA, Conchuir BO. The Role of Chemical Heterogeneity in Surfactant Adsorption at Solid-Liquid Interfaces. J Chem Theory Comput 2020; 16:7135-7147. [PMID: 33081471 DOI: 10.1021/acs.jctc.0c00759] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Chemical heterogeneity of solid surfaces disrupts the adsorption of surfactants from the bulk liquid. While its presence can hinder the performance of some formulations, bespoke chemical patterning could potentially facilitate controlled adsorption for nanolithography applications. Although some computational studies have investigated the impact of regularly patterned surfaces on surfactant adsorption, in reality, many interesting surfaces are expected to be stochastically disordered and this is an area unexplored via simulations. In this paper, we describe a new algorithm for the generation of randomly disordered chemically heterogeneous surfaces and use it to explore the adsorption behavior of four model nonionic surfactants. Using novel analysis methods, we interrogate both the global surface coverage (adsorption isotherm) and behavior in localized regions. We observe that trends in adsorption characteristics as surfactant size, head/tail ratio, and surface topology are varied and connect these to underlying physical mechanisms. We believe that our methods and approach will prove useful to researchers seeking to tailor surface patterns to calibrate nonionic surfactant adsorption.
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Affiliation(s)
- Jason Klebes
- IBM Research Europe, The Hartree Centre, Daresbury, Warrington WA4 4AD, United Kingdom.,School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Sophie Finnigan
- IBM Research Europe, The Hartree Centre, Daresbury, Warrington WA4 4AD, United Kingdom.,Department of Chemistry, Molecular Sciences Research Hub, White City Campus, Imperial College London, Wood Lane, London W12 0BZ, United Kingdom
| | - David J Bray
- The Hartree Centre, STFC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom
| | - Richard L Anderson
- The Hartree Centre, STFC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom
| | - William C Swope
- IBM Almaden Research Center, San Jose, California 95120, United States
| | | | - Breanndan O Conchuir
- IBM Research Europe, The Hartree Centre, Daresbury, Warrington WA4 4AD, United Kingdom
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5
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Affiliation(s)
| | | | | | | | - David J Bray
- The Hartree Centre STFC Daresbury Laboratory Warrington WA4 4AD UK
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6
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Conchuir BO, Gardner K, Jordan KE, Bray DJ, Anderson RL, Johnston MA, Swope WC, Harrison A, Sheehy DR, Peters TJ. Efficient Algorithm for the Topological Characterization of Worm-like and Branched Micelle Structures from Simulations. J Chem Theory Comput 2020; 16:4588-4598. [DOI: 10.1021/acs.jctc.0c00311] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
| | - Kirk Gardner
- Department of Computer Science & Engineering, University of Connecticut, Storrs, Connecticut 06269, United States
| | - Kirk E. Jordan
- IBM T. J. Watson Research, Cambridge, Massachusetts 02142, United States
| | - David J. Bray
- The Hartree Centre, STFC Daresbury Laboratory, Warrington WA4 4AD, U.K
| | | | | | - William C. Swope
- IBM Almaden Research Center, San Jose, California 95120, United States
| | - Alex Harrison
- IBM Research Europe, The Hartree Centre, Daresbury WA4 4AD, U.K
| | - Donald R. Sheehy
- Department of Computer Science, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Thomas J. Peters
- Department of Computer Science & Engineering, University of Connecticut, Storrs, Connecticut 06269, United States
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7
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Swope WC, Johnston MA, Duff AI, McDonagh JL, Anderson RL, Alva G, Tek AT, Maschino AP. Challenge to Reconcile Experimental Micellar Properties of the CnEm Nonionic Surfactant Family. J Phys Chem B 2019; 123:1696-1707. [DOI: 10.1021/acs.jpcb.8b11568] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- William C. Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | | | | | | | | | - Gabriela Alva
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Andy T. Tek
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Alexander P. Maschino
- Dr. TJ Owens Gilroy Early College Academy, 5055 Santa Teresa Blvd, Gilroy, California 95020, United States
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8
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Abstract
In this work, we propose an improved QM/MM-based strategy to determine condensed-phase polarizabilities and we use this approach to optimize a new and simple polarizable four-site water model for classical molecular simulation. For the determination of the model value for the polarizability from QM/MM, we show that our proposed consensus-fitting strategy significantly reduces the uncertainty in calculated polarizabilities in cases where the size of the local external electric field is small. By fitting electrostatic, polarization and dispersion properties of our water model based on quantum and/or combined QM/MM calculations, only a single model parameter (describing exchange repulsion) is left for empirical calibration. The resulting model performs well in describing relevant pure-liquid thermodynamic and transport properties, which illustrates the merit of our approach to minimize the number of free variables in our model.
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Affiliation(s)
- Koen M Visscher
- AIMMS Division of Molecular Toxicology, Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, De Boelelaan 1108, 1081 HV Amsterdam, The Netherlands.
| | - William C Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA.
| | - Daan P Geerke
- AIMMS Division of Molecular Toxicology, Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, De Boelelaan 1108, 1081 HV Amsterdam, The Netherlands.
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9
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Carr AC, Piunova VA, Maarof H, Rice JE, Swope WC. Influence of Solvent on the Drug-Loading Process of Amphiphilic Nanogel Star Polymers. J Phys Chem B 2018; 122:5356-5367. [PMID: 29385796 DOI: 10.1021/acs.jpcb.7b10539] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present an all-atom molecular dynamics study of the effect of a range of organic solvents (dichloromethane, diethyl ether, toluene, methanol, dimethyl sulfoxide, and tetrahydrofuran) on the conformations of a nanogel star polymeric nanoparticle with solvophobic and solvophilic structural elements. These nanoparticles are of particular interest for drug delivery applications. As drug loading generally takes place in an organic solvent, this work serves to provide insight into the factors controlling the early steps of that process. Our work suggests that nanoparticle conformational structure is highly sensitive to the choice of solvent, providing avenues for further study as well as predictions for both computational and experimental explorations of the drug-loading process. Our findings suggest that when used in the drug-loading process, dichloromethane, tetrahydrofuran, and toluene allow for a more extensive and increased drug-loading into the interior of nanogel star polymers of the composition studied here. In contrast, methanol is more likely to support shallow or surface loading and, consequently, faster drug release rates. Finally, diethyl ether should not work in a formulation process since none of the regions of the nanogel star polymer appear to be sufficiently solvated by it.
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Affiliation(s)
- Amber C Carr
- IBM Almaden Research Center, IBM Research , 650 Harry Road , San Jose , California 95120 , United States
| | - Victoria A Piunova
- IBM Almaden Research Center, IBM Research , 650 Harry Road , San Jose , California 95120 , United States
| | - Hasmerya Maarof
- Department of Chemistry , Universiti Teknologi Malaysia , Johor Bahru , 81310 Johor , Malaysia
| | - Julia E Rice
- IBM Almaden Research Center, IBM Research , 650 Harry Road , San Jose , California 95120 , United States
| | - William C Swope
- IBM Almaden Research Center, IBM Research , 650 Harry Road , San Jose , California 95120 , United States
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10
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Wei G, Prabhu VM, Piunova VA, Carr AC, Swope WC, Miller RD. Spatial Distribution of Hydrophobic Drugs in Model Nanogel-Core Star Polymers. Macromolecules 2017; 50:9702-9712. [PMID: 32636533 DOI: 10.1021/acs.macromol.7b02061] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Star polymers with a cross-linked nanogel core are promising carriers of cargo for therapeutic applications due to the synthetic control of amphiphilicity of arms and stability at infinite dilution. Three nanogel-core star polymers were investigated to understand how the arm-block chemical structure controls loading efficiency of a model drug, ibuprofen, and its spatial distribution. The spatial distribution profiles of hydrophobic core, hydrophilic corona, and encapsulated drug were determined by small-angle neutron scattering (SANS). SANS provides the nanometer-scale sensitivity to determine how the arm-block chemistry enhances the sequestering of ibuprofen. Validated molecular dynamics simulations capture the trends in drug profile and polymer segment distribution with further details on drug orientation distribution. This work provides a basis to study structure-function relationships in macromolecular-based carriers of cargo and represents a path toward validated and predictive simulation.
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Affiliation(s)
- Guangmin Wei
- Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Vivek M Prabhu
- Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Victoria A Piunova
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Amber C Carr
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - William C Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Robert D Miller
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
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11
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Wang LP, McKiernan KA, Gomes J, Beauchamp KA, Head-Gordon T, Rice JE, Swope WC, Martínez TJ, Pande VS. Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15. J Phys Chem B 2017; 121:4023-4039. [PMID: 28306259 DOI: 10.1021/acs.jpcb.7b02320] [Citation(s) in RCA: 163] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.
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Affiliation(s)
- Lee-Ping Wang
- Department of Chemistry, University of California, Davis , Davis, California 95616, United States
| | - Keri A McKiernan
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Joseph Gomes
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Kyle A Beauchamp
- Counsyl, Inc. , South San Francisco, California 94080, United States
| | - Teresa Head-Gordon
- Departments of Chemistry, Bioengineering, Chemical and Biomolecular Engineering, and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley , Berkeley, California 94720, United States.,Chemical Sciences Division, Physical Biosciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Julia E Rice
- IBM Almaden Research Center, IBM Research , San Jose, California 95120, United States
| | - William C Swope
- IBM Almaden Research Center, IBM Research , San Jose, California 95120, United States
| | - Todd J Martínez
- Department of Chemistry, Stanford University , Stanford, California 94305, United States.,PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Vijay S Pande
- Department of Chemistry, Stanford University , Stanford, California 94305, United States.,Departments of Computer Science, Structural Biology, and Program in Biophysics, Stanford University , Stanford, California 94305, United States
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12
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Carr AC, Felberg LE, Piunova VA, Rice JE, Head-Gordon T, Swope WC. Effect of Hydrophobic Core Topology and Composition on the Structure and Kinetics of Star Polymers: A Molecular Dynamics Study. J Phys Chem B 2017; 121:2902-2918. [DOI: 10.1021/acs.jpcb.7b00865] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Amber C. Carr
- IBM
Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States
| | | | - Victoria A. Piunova
- IBM
Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States
| | - Julia E. Rice
- IBM
Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States
| | - Teresa Head-Gordon
- Chemical
Sciences Division, Lawrence Berkeley National Labs, Berkeley, California 94720, United States
| | - William C. Swope
- IBM
Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States
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13
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Felberg LE, Doshi A, Hura GL, Sly J, Piunova VA, Swope WC, Rice JE, Miller R, Head-Gordon T. Structural transition of nanogel star polymers with pH by controlling PEGMA interactions with acid or base copolymers. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1224942] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Lisa E. Felberg
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, USA
| | - Anjali Doshi
- Department of Bioengineering, University of California, Berkeley, CA, USA
| | - Greg L. Hura
- Physical Biosciences Division, Lawrence Berkeley National Labs, Berkeley, CA, USA
| | - Joseph Sly
- IBM Research, IBM Almaden Research Center, San Jose, CA, USA
| | | | | | - Julia E. Rice
- IBM Research, IBM Almaden Research Center, San Jose, CA, USA
| | - Robert Miller
- IBM Research, IBM Almaden Research Center, San Jose, CA, USA
| | - Teresa Head-Gordon
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, USA
- Department of Bioengineering, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Chemical Sciences Division, Lawrence Berkeley National Labs, Berkeley, CA, USA
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14
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Swope WC, Rice JE, Piunova VA, Carr AC, Miller RD, Sly J. Simulation and Experiments To Identify Factors Allowing Synthetic Control of Structural Features of Polymeric Nanoparticles. J Phys Chem B 2016; 120:7546-68. [DOI: 10.1021/acs.jpcb.6b03345] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- William C. Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Julia E. Rice
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Victoria A. Piunova
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Amber C. Carr
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Robert D. Miller
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
| | - Joseph Sly
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, United States
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15
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Affiliation(s)
| | - William C. Swope
- IBM Almaden Research Center, San Jose, California, United States
| | - Kirk E. Jordan
- IBM T.J. Watson Research, Cambridge, Massachusetts, United States
| | | | - Massimo G. Noro
- Unilever R&D Port Sunlight, Quarry Road East, Bebington, Wirral, CH63 3JW, U.K
| | - David J. Bray
- STFC
Hartree Centre, SciTech Daresbury, Warrington, Cheshire WA4
4AD, U.K
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16
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Chodera JD, Swope WC, Pitera JW, Seok C, Dill KA. Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations. J Chem Theory Comput 2015; 3:26-41. [PMID: 26627148 DOI: 10.1021/ct0502864] [Citation(s) in RCA: 362] [Impact Index Per Article: 40.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.
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Affiliation(s)
- John D Chodera
- Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea
| | - William C Swope
- Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea
| | - Jed W Pitera
- Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea
| | - Chaok Seok
- Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea
| | - Ken A Dill
- Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea
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Miller RD, Yusoff RM, Swope WC, Rice JE, Carr AC, Parker AJ, Sly J, Appel EA, Nguyen T, Piunova V. Water soluble, biodegradable amphiphilic polymeric nanoparticles and the molecular environment of hydrophobic encapsulates: Consistency between simulation and experiment. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.10.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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Felberg LE, Brookes DH, Head-Gordon T, Rice JE, Swope WC. Role of hydrophilicity and length of diblock arms for determining star polymer physical properties. J Phys Chem B 2014; 119:944-57. [PMID: 25254622 DOI: 10.1021/jp506203k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We present a molecular simulation study of star polymers consisting of 16 diblock copolymer arms bound to a small adamantane core by varying both arm length and the outer hydrophilic block when attached to the same hydrophobic block of poly-δ-valerolactone. Here we consider two biocompatible star polymers in which the hydrophilic block is composed of polyethylene glycol (PEG) or polymethyloxazoline (POXA) in addition to a polycarbonate-based polymer with a pendant hydrophilic group (PC1). We find that the different hydrophilic blocks of the star polymers show qualitatively different trends in their interactions with aqueous solvent, orientational time correlation functions, and orientational correlation between pairs of monomers of their polymeric arms in solution, in which we find that the PEG polymers are more thermosensitive compared with the POXA and PC1 star polymers over the physiological temperature range we have investigated.
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Affiliation(s)
- Lisa E Felberg
- Department of Chemical and Biomolecular Engineering, ‡Department of Chemistry, and §Department of Bioengineering, University of California Berkeley , Berkeley, California 94720, United States
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Cerutti DS, Swope WC, Rice JE, Case DA. ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins. J Chem Theory Comput 2014; 10:4515-4534. [PMID: 25328495 PMCID: PMC4196740 DOI: 10.1021/ct500643c] [Citation(s) in RCA: 76] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2014] [Indexed: 01/25/2023]
Abstract
![]()
We
present the ff14ipq force field, implementing the previously
published IPolQ charge set for simulations of complete proteins. Minor
modifications to the charge derivation scheme and van der Waals interactions
between polar atoms are introduced. Torsion parameters are developed
through a generational learning approach, based on gas-phase MP2/cc-pVTZ
single-point energies computed of structures optimized by the force
field itself rather than the quantum benchmark. In this manner, we
sacrifice information about the true quantum minima in order to ensure
that the force field maintains optimal agreement with the MP2/cc-pVTZ
benchmark for the ensembles it will actually produce in simulations.
A means of making the gas-phase torsion parameters compatible with
solution-phase IPolQ charges is presented. The ff14ipq model is an
alternative to ff99SB and other Amber force fields for protein simulations
in programs that accommodate pair-specific Lennard–Jones combining
rules. The force field gives strong performance on α-helical
and β-sheet oligopeptides as well as globular proteins over
microsecond time scale simulations, although it has not yet been tested
in conjunction with lipid and nucleic acid models. We show how our
choices in parameter development influence the resulting force field
and how other choices that may have appeared reasonable would actually
have led to poorer results. The tools we developed may also aid in
the development of future fixed-charge and even polarizable biomolecular
force fields.
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Affiliation(s)
- David S Cerutti
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University , 610 Taylor Road, Piscataway, New Jersey 08854-8066, United States
| | - William C Swope
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University , 610 Taylor Road, Piscataway, New Jersey 08854-8066, United States
| | - Julia E Rice
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University , 610 Taylor Road, Piscataway, New Jersey 08854-8066, United States
| | - David A Case
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University , 610 Taylor Road, Piscataway, New Jersey 08854-8066, United States
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20
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Swope WC. Personal observations: William C. Swope. J Phys Chem B 2014; 118:6360-3. [PMID: 24945855 DOI: 10.1021/jp502441b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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21
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Cerutti DS, Rice JE, Swope WC, Case DA. Derivation of fixed partial charges for amino acids accommodating a specific water model and implicit polarization. J Phys Chem B 2013; 117:2328-38. [PMID: 23379664 DOI: 10.1021/jp311851r] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
We have developed the IPolQ method for fitting nonpolarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest, followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side-chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general and applicable to arbitrary solutes.
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Affiliation(s)
- David S Cerutti
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers, the State University of New Jersey, 610 Taylor Road, Piscataway, New Jersey 08854-8066, United States.
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22
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Swope WC, Carr AC, Parker AJ, Sly J, Miller RD, Rice JE. Molecular Dynamics Simulations of Star Polymeric Molecules with Diblock Arms, a Comparative Study. J Chem Theory Comput 2012; 8:3733-49. [DOI: 10.1021/ct300188e] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- William C. Swope
- IBM Research, IBM Almaden Research
Center, San Jose, California 95120, United States
| | - Amber C. Carr
- Department of Chemistry and
Laufer Center for Physical and Quantitative Biology, Stony Brook University,
Stony Brook, New York, United States
| | - Amanda J. Parker
- MacDiarmid Institute for Advanced
Materials and Nanotechnology, School of Chemical and Physical Sciences,
Victoria University of Wellington, Wellington, New Zealand
| | - Joseph Sly
- IBM Research, IBM Almaden Research
Center, San Jose, California 95120, United States
| | - Robert D. Miller
- IBM Research, IBM Almaden Research
Center, San Jose, California 95120, United States
| | - Julia E. Rice
- IBM Research, IBM Almaden Research
Center, San Jose, California 95120, United States
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23
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Vosmeer CR, Rustenburg AS, Rice JE, Horn HW, Swope WC, Geerke DP. QM/MM-Based Fitting of Atomic Polarizabilities for Use in Condensed-Phase Biomolecular Simulation. J Chem Theory Comput 2012; 8:3839-53. [PMID: 26593025 DOI: 10.1021/ct300085z] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Accounting for electronic polarization effects in biomolecular simulation (by using a polarizable force field) can increase the accuracy of simulation results. However, the use of gas-phase estimates of atomic polarizabilities αi usually leads to overpolarization in condensed-phase systems. In the current work, a combined QM/MM approach has been employed to obtain condensed-phase estimates of atomic polarizabilities for water and methanol (QM) solutes in the presence of (MM) solvents of different polarity. In a next step, the validity of the linear response and isotropy assumptions were evaluated based on the observed condensed-phase distributions of αi values. The observed anisotropy and low average values for the polarizability of methanol's carbon atom in polar solvents was explained in terms of strong solute-solvent interactions involving its adjacent hydroxyl group. Our QM/MM estimates for atomic polarizabilities were found to be close to values used in previously reported polarizable water and methanol models. Using our estimate for αO of methanol, a single set of polarizable force field parameters was obtained that is directly transferable between environments of different polarity.
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Affiliation(s)
- C Ruben Vosmeer
- Leiden/Amsterdam Center for Drug Research, Division of Molecular and Computational Toxicology, Department of Chemistry and Pharmaceutical Sciences, Faculty of Sciences, VU University Amsterdam , De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Ariën S Rustenburg
- Leiden/Amsterdam Center for Drug Research, Division of Molecular and Computational Toxicology, Department of Chemistry and Pharmaceutical Sciences, Faculty of Sciences, VU University Amsterdam , De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Julia E Rice
- IBM Almaden Research Center , 650 Harry Road, San Jose, California 95120, United States
| | - Hans W Horn
- IBM Almaden Research Center , 650 Harry Road, San Jose, California 95120, United States
| | - William C Swope
- IBM Almaden Research Center , 650 Harry Road, San Jose, California 95120, United States
| | - Daan P Geerke
- Leiden/Amsterdam Center for Drug Research, Division of Molecular and Computational Toxicology, Department of Chemistry and Pharmaceutical Sciences, Faculty of Sciences, VU University Amsterdam , De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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Appel EA, Lee VY, Nguyen TT, McNeil M, Nederberg F, Hedrick JL, Swope WC, Rice JE, Miller RD, Sly J. Toward biodegradable nanogel star polymers via organocatalytic ROP. Chem Commun (Camb) 2012; 48:6163-5. [DOI: 10.1039/c2cc31406a] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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25
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Mobley DL, Liu S, Cerutti DS, Swope WC, Rice JE. Alchemical prediction of hydration free energies for SAMPL. J Comput Aided Mol Des 2011; 26:551-62. [PMID: 22198475 DOI: 10.1007/s10822-011-9528-8] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Accepted: 12/10/2011] [Indexed: 10/14/2022]
Abstract
Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.
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Affiliation(s)
- David L Mobley
- Department of Chemistry, University of New Orleans, 2000 Lakeshore Drive, New Orleans, LA 70148, USA.
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26
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Prinz JH, Chodera JD, Pande VS, Swope WC, Smith JC, Noé F. Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics. J Chem Phys 2011; 134:244108. [PMID: 21721613 DOI: 10.1063/1.3592153] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.
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Affiliation(s)
- Jan-Hendrik Prinz
- Institute for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany.
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27
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Chodera JD, Swope WC, Noé F, Prinz JH, Shirts MR, Pande VS. Dynamical reweighting: improved estimates of dynamical properties from simulations at multiple temperatures. J Chem Phys 2011; 134:244107. [PMID: 21721612 PMCID: PMC3143679 DOI: 10.1063/1.3592152] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2010] [Accepted: 01/19/2011] [Indexed: 11/14/2022] Open
Abstract
Dynamical averages based on functionals of dynamical trajectories, such as time-correlation functions, play an important role in determining kinetic or transport properties of matter. At temperatures of interest, the expectations of these quantities are often dominated by contributions from rare events, making the precise calculation of these quantities by molecular dynamics simulation difficult. Here, we present a reweighting method for combining simulations from multiple temperatures (or from simulated or parallel tempering simulations) to compute an optimal estimate of the dynamical properties at the temperature of interest without the need to invoke an approximate kinetic model (such as the Arrhenius law). Continuous and differentiable estimates of these expectations at any temperature in the sampled range can also be computed, along with an assessment of the associated statistical uncertainty. For rare events, aggregating data from multiple temperatures can produce an estimate with the desired precision at greatly reduced computational cost compared with simulations conducted at a single temperature. Here, we describe use of the method for the canonical (NVT) ensemble using four common models of dynamics (canonical distribution of Hamiltonian trajectories, Andersen thermostatting, Langevin, and overdamped Langevin or Brownian dynamics), but it can be applied to any thermodynamic ensemble provided the ratio of path probabilities at different temperatures can be computed. To illustrate the method, we compute a time-correlation function for solvated terminally-blocked alanine peptide across a range of temperatures using trajectories harvested using a modified parallel tempering protocol.
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Affiliation(s)
- John D Chodera
- California Institute of Quantitative Biosciences (QB3), University of California, Berkeley, California 94720, USA.
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28
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Abstract
Lambda repressor fragment λ(*)(6-85) is one of the fastest folding small protein fragments known to date. We hypothesized that removal of three out of five helices of λ(*)(6-85) would further reduce this protein to its smallest folding core. Molecular dynamics simulations singled out two energetically stable reduced structures consisting of only helices 1 and 4 connected by a short glycine/serine linker, as well as a less stable control. We investigated these three polypeptides and their fragments experimentally by using circular dichroism, fluorescence spectroscopy, and temperature jump relaxation spectroscopy to gain insight into their thermodynamic and kinetic properties. Based on the thermal melts, the order of peptide stability was in correspondence with theoretical predictions. The most stable two-helix bundle, λ(blue1), is a cooperatively folding miniprotein with the same melting temperature and folding rate as the full-length λ(*)(6-85) pseudo wild type and a well-defined computed structure.
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Affiliation(s)
- Maxim B Prigozhin
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
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29
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Swope WC, Horn HW, Rice JE. Accounting for polarization cost when using fixed charge force fields. I. Method for computing energy. J Phys Chem B 2010; 114:8621-30. [PMID: 20540503 DOI: 10.1021/jp911699p] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Although it is not currently standard practice, the cost to change the electronic polarization from one appropriate for the gas phase to that implied by the charge model should be considered when deriving force fields based on fits to certain types of experimental data and for using force fields to compute observables that involve changes in molecular polarization. We present mathematical expressions and a method to estimate this polarization cost implied by a fixed charge model force field, where the fixed charge model can be any combination of point charges, higher-order multipoles, or even distributed charge densities, as long as they do not change in response to environment. These expressions illuminate the relationship between polarization costs associated with fixed charge models, self-polarization energies of polarizable models, and quantum chemical based approaches that use continuum representations of the solvent, such as the self-consistent reaction field and polarizable continuum models. The technique takes account of the tensorial nature of the polarizabilities and includes quadrupole as well as dipole polarization. The consistency of this approach to one that estimates polarization cost using an implicit solvent quantum chemistry method (PCM) is demonstrated.
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Affiliation(s)
- William C Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA.
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30
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Swope WC, Horn HW, Rice JE. Accounting for polarization cost when using fixed charge force fields. II. Method and application for computing effect of polarization cost on free energy of hydration. J Phys Chem B 2010; 114:8631-45. [PMID: 20540502 DOI: 10.1021/jp911701h] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Polarization cost is the energy needed to distort the wave function of a molecule from one appropriate to the gas phase to one appropriate for some condensed phase. Although it is not currently standard practice, polarization cost should be considered when deriving improved fixed charge force fields based on fits to certain types of experimental data and when using such force fields to compute observables that involve changes in molecular polarization. Building on earlier work, we present mathematical expressions and a method to estimate the effect of polarization cost on free energy and enthalpy implied by a charge model meant to represent a solvated state. The charge model can be any combination of point charges, higher-order multipoles, or even distributed charge densities, as long as they do not change in response to environment. The method is illustrated by computing the effect of polarization cost on free energies of hydration for the neutral amino acid side chain analogues as predicted using two popular fixed charge force fields and one based on electron densities computed using quantum chemistry techniques that employ an implicit model to represent aqueous solvent. From comparison of the computed and experimental hydration free energies, we find that two commonly used force fields are too underpolarized in their description of the solute-water interaction. On the other hand, a charge model based on the charge density from a hybrid density functional calculation that used an implicit model for aqueous solvent performs well for hydration free energies of these molecules after the correction for dipole polarization is applied. As such, an improved description of the density (e.g., B3LYP, MP2) in conjunction with an implicit solvent (e.g., PCM) or explicit solvent (e.g., QM/MM) approach may offer promise as a starting point for the development of improved fixed charge models for force fields.
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Affiliation(s)
- William C Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA.
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31
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Chong LT, Pitera JW, Swope WC, Pande VS. Comparison of computational approaches for predicting the effects of missense mutations on p53 function. J Mol Graph Model 2008; 27:978-82. [PMID: 19168381 DOI: 10.1016/j.jmgm.2008.12.006] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2008] [Revised: 12/17/2008] [Accepted: 12/18/2008] [Indexed: 11/25/2022]
Abstract
We applied our recently developed kinetic computational mutagenesis (KCM) approach [L.T. Chong, W.C. Swope, J.W. Pitera, V.S. Pande, Kinetic computational alanine scanning: application to p53 oligomerization, J. Mol. Biol. 357 (3) (2006) 1039-1049] along with the MM-GBSA approach [J. Srinivasan, T.E. Cheatham 3rd, P. Cieplak, P.A. Kollman, D.A. Case, Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate-DNA helices, J. Am. Chem. Soc. 120 (37) (1998) 9401-9409; P.A. Kollman, I. Massova, C.M. Reyes, B. Kuhn, S. Huo, L.T. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D.A. Case, T.E. Cheatham 3rd., Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models, Acc. Chem. Res. 33 (12) (2000) 889-897] to evaluate the effects of all possible missense mutations on dimerization of the oligomerization domain (residues 326-355) of tumor suppressor p53. The true positive and true negative rates for KCM are comparable (within 5%) to those of MM-GBSA, although MM-GBSA is much less computationally intensive when it is applied to a single energy-minimized configuration per mutant dimer. The potential advantage of KCM is that it can be used to directly examine the kinetic effects of mutations.
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Affiliation(s)
- Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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32
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Chuma A, Horn HW, Swope WC, Pratt RC, Zhang L, Lohmeijer BGG, Wade CG, Waymouth RM, Hedrick JL, Rice JE. The Reaction Mechanism for the Organocatalytic Ring-Opening Polymerization of l-Lactide Using a Guanidine-Based Catalyst: Hydrogen-Bonded or Covalently Bound? J Am Chem Soc 2008; 130:6749-54. [DOI: 10.1021/ja0764411] [Citation(s) in RCA: 206] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Anthony Chuma
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Hans W. Horn
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - William C. Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Russell C. Pratt
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Lei Zhang
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Bas G. G. Lohmeijer
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Charles G. Wade
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Robert M. Waymouth
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - James L. Hedrick
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
| | - Julia E. Rice
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95032, Seeo, Inc., Berkeley, California 94710, Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, BASF SE, Global Polymer Research Division, 67056 Ludwigshafen, Germany, and Department of Chemistry, Stanford University, Stanford, California 94305
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33
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Srinivas G, Swope WC, Pitera JW. Interfacial Fluctuations of Block Copolymers: A Coarse-Grain Molecular Dynamics Simulation Study. J Phys Chem B 2007; 111:13734-42. [DOI: 10.1021/jp073347y] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Goundla Srinivas
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
| | - William C. Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
| | - Jed W. Pitera
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
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Horn HW, Swope WC, Pitera JW, Madura JD, Dick TJ, Hura GL, Head-Gordon T. Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. J Chem Phys 2007; 120:9665-78. [PMID: 15267980 DOI: 10.1063/1.1683075] [Citation(s) in RCA: 1371] [Impact Index Per Article: 80.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A re-parameterization of the standard TIP4P water model for use with Ewald techniques is introduced, providing an overall global improvement in water properties relative to several popular nonpolarizable and polarizable water potentials. Using high precision simulations, and careful application of standard analytical corrections, we show that the new TIP4P-Ew potential has a density maximum at approximately 1 degrees C, and reproduces experimental bulk-densities and the enthalpy of vaporization, DeltaH(vap), from -37.5 to 127 degrees C at 1 atm with an absolute average error of less than 1%. Structural properties are in very good agreement with x-ray scattering intensities at temperatures between 0 and 77 degrees C and dynamical properties such as self-diffusion coefficient are in excellent agreement with experiment. The parameterization approach used can be easily generalized to rehabilitate any water force field using available experimental data over a range of thermodynamic points.
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Affiliation(s)
- Hans W Horn
- IBM Almaden Research Center, San Jose, California 95120, USA.
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35
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Abstract
The liquid-vapor-phase equilibrium properties of the previously developed TIP4P-Ew water model have been studied using thermodynamic integration free-energy simulation techniques in the temperature range of 274-400 K. We stress that free-energy results from simulations need to be corrected in order to be compared to the experiment. This is due to the fact that the thermodynamic end states accessible through simulations correspond to fictitious substances (classical rigid liquids and classical rigid ideal gases) while experiments operate on real substances (liquids and real gases, with quantum effects). After applying analytical corrections the vapor pressure curve obtained from simulated free-energy changes is in excellent agreement with the experimental vapor pressure curve. The boiling point of TIP4P-Ew water under ambient pressure is found to be at 370.3+/-1.9 K, about 7 K higher than the boiling point of TIP4P water (363.7+/-5.1 K; from simulations that employ finite range treatment of electrostatic and Lennard-Jones interactions). This is in contrast to the approximately +15 K by which the temperature of the density maximum and the melting temperature of TIP4P-Ew are shifted relative to TIP4P, indicating that the temperature range over which the liquid phase of TIP4P-Ew is stable is narrower than that of TIP4P and resembles more that of real water. The quality of the vapor pressure results highlights the success of TIP4P-Ew in describing the energetic and entropic aspects of intermolecular interactions in liquid water.
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Affiliation(s)
- Hans W Horn
- International Business Machines Corporation (IBM) Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA.
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36
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Chodera JD, Singhal N, Pande VS, Dill KA, Swope WC. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J Chem Phys 2007; 126:155101. [PMID: 17461665 DOI: 10.1063/1.2714538] [Citation(s) in RCA: 463] [Impact Index Per Article: 27.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To meet the challenge of modeling the conformational dynamics of biological macromolecules over long time scales, much recent effort has been devoted to constructing stochastic kinetic models, often in the form of discrete-state Markov models, from short molecular dynamics simulations. To construct useful models that faithfully represent dynamics at the time scales of interest, it is necessary to decompose configuration space into a set of kinetically metastable states. Previous attempts to define these states have relied upon either prior knowledge of the slow degrees of freedom or on the application of conformational clustering techniques which assume that conformationally distinct clusters are also kinetically distinct. Here, we present a first version of an automatic algorithm for the discovery of kinetically metastable states that is generally applicable to solvated macromolecules. Given molecular dynamics trajectories initiated from a well-defined starting distribution, the algorithm discovers long lived, kinetically metastable states through successive iterations of partitioning and aggregating conformation space into kinetically related regions. The authors apply this method to three peptides in explicit solvent-terminally blocked alanine, the 21-residue helical F(s) peptide, and the engineered 12-residue beta-hairpin trpzip2-to assess its ability to generate physically meaningful states and faithful kinetic models.
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Affiliation(s)
- John D Chodera
- Graduate Group in Biophysics, University of California-San Francisco, San Francisco, CA 94143, USA
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Abstract
We have carried out extensive all atom explicit solvent simulations of the high-temperature folding and unfolding of the trpzip2 beta-hairpin peptide and examined the resulting trajectories for evidence of folding via a reptation mechanism. Over 300 microcanonical simulations of 10 ns each were initiated from a Boltzmann ensemble of conformations at 425 K. Though we observed numerous folding and unfolding events, no evidence of reptation was found. The diffusional dynamics of the peptide are orders of magnitude faster than any observed reptation-like motion. Our data suggest that the dominant mechanisms for beta-hairpin folding under these conditions are hydrophobic collapse and turn formation, and that rearrangements occur via significant expansion of the polypeptide chain.
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Affiliation(s)
- Jed W Pitera
- IBM Almaden Research Center, San Jose, California 95120, USA.
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38
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Affiliation(s)
- William C. Swope
- a Department of Chemistry and Materials and Molecular Research Division, Lawrence Berkeley Laboratory , University of California , Berkeley , California , 94720
| | - Henry F. Schaefer
- a Department of Chemistry and Materials and Molecular Research Division, Lawrence Berkeley Laboratory , University of California , Berkeley , California , 94720
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39
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Chong LT, Swope WC, Pitera JW, Pande VS. Kinetic Computational Alanine Scanning: Application to p53 Oligomerization. J Mol Biol 2006; 357:1039-49. [PMID: 16457841 DOI: 10.1016/j.jmb.2005.12.083] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2005] [Revised: 12/15/2005] [Accepted: 12/29/2005] [Indexed: 11/19/2022]
Abstract
We have developed a novel computational alanine scanning approach that involves analysis of ensemble unfolding kinetics at high temperature to identify residues that are critical for the stability of a given protein. This approach has been applied to dimerization of the oligomerization domain (residues 326-355) of tumor suppressor p53. As validated by experimental results, our approach has reasonable success in identifying deleterious mutations, including mutations that have been linked to cancer. We discuss a method for determining the effect of mutations on the location of the dimerization transition state.
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Affiliation(s)
- Lillian T Chong
- Department of Chemistry, Stanford University, Stanford, CA 94305-5447, USA
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Larios E, Pitera JW, Swope WC, Gruebele M. Correlation of early orientational ordering of engineered λ6–85 structure with kinetics and thermodynamics. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.08.048] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Affiliation(s)
- William C. Swope
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
| | - Jed W. Pitera
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120
| | - Frank Suits
- IBM Watson Research Center, Route 134, Yorktown Heights, New York 10598
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42
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Swope WC, Pitera JW, Suits F, Pitman M, Eleftheriou M, Fitch BG, Germain RS, Rayshubski A, Ward TJC, Zhestkov Y, Zhou R. Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 2. Example Applications to Alanine Dipeptide and a β-Hairpin Peptide. J Phys Chem B 2004. [DOI: 10.1021/jp037422q] [Citation(s) in RCA: 144] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Abstract
The beta-hairpin trpzip2 can be tuned continuously from a two-state folder to folding on a rough energy landscape without a dominant refolding barrier. At high denaturant concentration, this extremely stable peptide exhibits a single apparent "two-state" transition temperature when monitored by different spectroscopic techniques. However, under optimal folding conditions the hairpin undergoes an unusual folding process with three clusters of melting transitions ranging from 15 degrees C to 160 degrees C, as monitored by 12 different experimental and computational observables. We explain this behavior in terms of a rough free energy landscape of the unfolded peptide caused by multiple tryptophan interactions and alternative backbone conformations. The landscape is mapped out by potentials of mean force derived from replica-exchange molecular dynamics simulations. Implications for deducing cooperativity from denaturant titrations, for the origin of folding cooperativity, and for the folding of thermophilic proteins are pointed out. trpzip is an excellent small tunable model system for the glass-like folding transitions predicted by landscape theory.
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Affiliation(s)
- Wei Yuan Yang
- Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL 61801, USA
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44
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Shirts MR, Pitera JW, Swope WC, Pande VS. Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins. J Chem Phys 2003. [DOI: 10.1063/1.1587119] [Citation(s) in RCA: 543] [Impact Index Per Article: 25.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Swope WC, Andersen HC. A molecular dynamics method for calculating the solubility of gases in liquids and the hydrophobic hydration of inert-gas atoms in aqueous solution. ACTA ACUST UNITED AC 2002. [DOI: 10.1021/j150670a016] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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46
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Swope WC, Schaefer HF. Model organometallic systems. The interaction of 2S beryllium(1+) ion, 1S beryllium, and 3P beryllium atoms with acetylene and ethylene. J Am Chem Soc 2002. [DOI: 10.1021/ja00441a015] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Pitman MC, Huber WK, Horn H, Krämer A, Rice JE, Swope WC. FLASHFLOOD: a 3D field-based similarity search and alignment method for flexible molecules. J Comput Aided Mol Des 2001; 15:587-612. [PMID: 11688943 DOI: 10.1023/a:1011921423829] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
A three-dimensional field-based similarity search and alignment method for flexible molecules is introduced. The conformational space of a flexible molecule is represented in terms of fragments and torsional angles of allowed conformations. A user-definable property field is used to compute features of fragment pairs. Features are generalizations of CoMMA descriptors that characterize local regions of the property field by its local moments. The features are invariant under coordinate system transformations. Features taken from a query molecule are used to form alignments with fragment pairs in the database. An assembly algorithm is then used to merge the fragment pairs into full structures, aligned to the query. Key to the method is the use of a context adaptive descriptor scaling procedure as the basis for similarity. This allows the user to tune the weights of the various feature components based on examples relevant to the particular context under investigation. The property fields may range from simple, phenomenological fields, to fields derived from quantum mechanical calculations. We apply the method to the dihydrofolate/methotrexate benchmark system, and show that when one injects relevant contextual information into the descriptor scaling procedure, better results are obtained more efficiently. We also show how the method works and include computer times for a query from a database that represents approximately 23 million conformers of seventeen flexible molecules.
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Affiliation(s)
- M C Pitman
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.
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48
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Swope WC, Andersen HC. A computer simulation method for the calculation of chemical potentials of liquids and solids using the bicanonical ensemble. J Chem Phys 1995. [DOI: 10.1063/1.468663] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Swope WC, Andersen HC. Thermodynamics, statistical thermodynamics, and computer simulation of crystals with vacancies and interstitials. Phys Rev A 1992; 46:4539-4548. [PMID: 9908666 DOI: 10.1103/physreva.46.4539] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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