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Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

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The Journal of Physical Chemistry. B

American Chemical Society

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      Abstract

      Alkali (Li +, Na +, K +, Rb +, and Cs +) and halide (F , Cl , Br , and I ) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4P EW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.

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          Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory

          We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive-definite pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio L = 0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.
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            Author and article information

            Affiliations
            Department of Bioengineering, College of Engineering, and Departments of Medicinal Chemistry and of Pharmaceutics and Pharmaceutical Chemistry, College of Pharmacy, University of Utah, 2000 South 30 East, Skaggs Hall 201, Salt Lake City, UT 84112
            Author notes
            [* ] To whom correspondence should be addressed: Phone: (801) 587-9652. Fax: (801) 585-9119. E-mail: tec3@ 123456utah.edu .
            [†]

            Department of Bioengineering, College of Engineering.

            [‡]

            Department of Medicinal Chemistry, College of Pharmacy.

            [§]

            Department of Pharmaceutics and Pharmaceutical Chemistry, College of Pharmacy.

            Journal
            J Phys Chem B
            jp
            jpcbfk
            The Journal of Physical Chemistry. B
            American Chemical Society
            1520-6106
            1520-5207
            02 July 2008
            31 July 2008
            : 112
            : 30
            : 9020-9041
            18593145
            2652252
            10.1021/jp8001614
            Copyright © 2008 American Chemical Society

            This is an open-access article distributed under the ACS AuthorChoice Terms & Conditions. Any use of this article, must conform to the terms of that license which are available at http://pubs.acs.org.

            40.75

            Funding
            National Institutes of Health, United States
            Categories
            Article
            Custom metadata
            jp8001614
            jp-2008-001614

            Physical chemistry

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