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Gao A, Remsing RC, Weeks JD. Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions. J Phys Chem B 2023; 127:809-821. [PMID: 36669139 DOI: 10.1021/acs.jpcb.2c06988] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.
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Affiliation(s)
- Ang Gao
- Department of Physics, Beijing University of Posts and Telecommunications, Beijing, China 100876
| | - Richard C Remsing
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - John D Weeks
- Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
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Zhang Z, Ricci CG, Fan C, Cheng LT, Li B, McCammon JA. Coupling Monte Carlo, Variational Implicit Solvation, and Binary Level-Set for Simulations of Biomolecular Binding. J Chem Theory Comput 2021; 17:2465-2478. [PMID: 33650860 DOI: 10.1021/acs.jctc.0c01109] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
We develop a hybrid approach that combines the Monte Carlo (MC) method, a variational implicit-solvent model (VISM), and a binary level-set method for the simulation of biomolecular binding in an aqueous solvent. The solvation free energy for the biomolecular complex is estimated by minimizing the VISM free-energy functional of all possible solute-solvent interfaces that are used as dielectric boundaries. This functional consists of the solute volumetric, solute-solvent interfacial, solute-solvent van der Waals interaction, and electrostatic free energy. A technique of shifting the dielectric boundary is used to accurately predict the electrostatic part of the solvation free energy. Minimizing such a functional in each MC move is made possible by our new and fast binary level-set method. This method is based on the approximation of surface area by the convolution of an indicator function with a compactly supported kernel and is implemented by simple flips of numerical grid cells locally around the solute-solvent interface. We apply our approach to the p53-MDM2 system for which the two molecules are approximated by rigid bodies. Our efficient approach captures some of the poses before the final bound state. All-atom molecular dynamics simulations with most of such poses quickly reach the final bound state. Our work is a new step toward realistic simulations of biomolecular interactions. With further improvement of coarse graining and MC sampling, and combined with other models, our hybrid approach can be used to study the free-energy landscape and kinetic pathways of ligand binding to proteins.
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Affiliation(s)
- Zirui Zhang
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Clarisse G Ricci
- Department of Chemistry and Biochemistry and Department of Pharmacology, University of California, San Diego, La Jolla, California 92093-0365, United States
| | - Chao Fan
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Bo Li
- Department of Mathematics and Quantitative Biology Ph.D. Program, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry and Department of Pharmacology, University of California, San Diego, La Jolla, California 92093-0365, United States
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Abstract
Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent-solvent and solute-solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.
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Abstract
Brownian dynamics (BD) is a technique for carrying out computer simulations of physical systems that are driven by thermal fluctuations. Biological systems at the macromolecular and cellular level, while falling in the gap between well-established atomic-level models and continuum models, are especially suitable for such simulations. We present a brief history, examples of important biological processes that are driven by thermal motion, and those that have been profitably studied by BD. We also present some of the challenges facing developers of algorithms and software, especially in the attempt to simulate larger systems more accurately and for longer times.
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Affiliation(s)
- Gary A Huber
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, CA 92093-0340, USA.,Department of Pharmocology, University of California San Diego, La Jolla, CA 92093-0636, USA
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, CA 92093-0340, USA.,Department of Pharmocology, University of California San Diego, La Jolla, CA 92093-0636, USA
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Gadzała M, Dułak D, Kalinowska B, Baster Z, Bryliński M, Konieczny L, Banach M, Roterman I. The aqueous environment as an active participant in the protein folding process. J Mol Graph Model 2018; 87:227-239. [PMID: 30580160 DOI: 10.1016/j.jmgm.2018.12.008] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2018] [Revised: 12/05/2018] [Accepted: 12/12/2018] [Indexed: 01/27/2023]
Abstract
Existing computational models applied in the protein structure prediction process do not sufficiently account for the presence of the aqueous solvent. The solvent is usually represented by a predetermined number of H2O molecules in the bounding box which contains the target chain. The fuzzy oil drop (FOD) model, presented in this paper, follows an alternative approach, with the solvent assuming the form of a continuous external hydrophobic force field, with a Gaussian distribution. The effect of this force field is to guide hydrophobic residues towards the center of the protein body, while promoting exposure of hydrophilic residues on its surface. This work focuses on the following sample proteins: Engrailed homeodomain (RCSB: 1enh), Chicken villin subdomain hp-35, n68h (RCSB: 1yrf), Chicken villin subdomain hp-35, k65(nle), n68h, k70(nle) (RCSB: 2f4k), Thermostable subdomain from chicken villin headpiece (RCSB: 1vii), de novo designed single chain three-helix bundle (a3d) (RCSB: 2a3d), albumin-binding domain (RCSB: 1prb) and lambda repressor-operator complex (RCSB: 1lmb).
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Affiliation(s)
| | - Dawid Dułak
- ABB Business Services Sp. z o.o. ul. Żegańska 1, 04-713, Warszawa, Poland.
| | - Barbara Kalinowska
- Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 11 Łojasiewicza Street, Kraków, Poland; Department of Bioinformatics and Telemedicine, Jagiellonian University - Medical College, Łazarza 16, 31-530, Kraków, Poland
| | - Zbigniew Baster
- Department of Molecular and Interfacial Biophysics, Faculty of Physics, Astronomy, Applied Computer Science Jagiellonian University, 11 Łojasiewicza Street, Kraków, Poland; Markey Cancer Center, University of Kentucky, 789 South Limestone Street, Lexington, KY, USA
| | - Michał Bryliński
- Department of Biological Sciences, Louisiana State University, Baton Rouge, LA, 70803, USA; Center for Computation & Technology, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Leszek Konieczny
- Chair of Medical Biochemistry, Jagiellonian University - Medical College, Kopernika 7E, 31-034, Kraków, Poland
| | - Mateusz Banach
- Department of Bioinformatics and Telemedicine, Jagiellonian University - Medical College, Łazarza 16, 31-530, Kraków, Poland
| | - Irena Roterman
- Department of Bioinformatics and Telemedicine, Jagiellonian University - Medical College, Łazarza 16, 31-530, Kraków, Poland.
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