Electrostatic interactions charge parameterization

Less is known about the interaction of the nucleosomes between themselves or with free DNA. The nucleosome-nucleosome interaction has recently been parameterized by using the surface charge density of the known crystal structure [39] in a point-charge model [51]. While in that work only electrostatic interactions were considered and the quantitative influence of the histone tails on the interaction potential still remains obscure, simulations based on this potential allowed to predict an ionic-strength dependent structural transition of a 50-nucleosome chromatin fragment that occurred at a salt concentration compatible with known experimental data (Ref. [65], see below). 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

In the case of ab initio methods the form of the electrostatic interaction integrals is fixed as the charges on the molecular mechanics atoms and the form of the basis functions are fully determined by the MM and QM models respectively. For semiempirical methods the interaction integrals between the QM and MM atoms must be parameterized to reproduce interactions obtained from quantum mechanical or experimental data (see reference [19] for details). 

Define the interaction Hamiltonian. For a Hamiltonian of the form of equation 24 and for ab initio QM methods the only parameters that need to be defined are the Lennard-Jones parameters for the QM atoms as the charges and Lennard-Jones parameters for the MM atoms are determined once the MM force field is specified. The QM atom parameters can be obtained from the MM force field or from a parameterization procedure. For semiempirical methods it is necessary to specify parameters for the evaluation of the one-electron electrostatic interaction integrals. 

G. E. W. Bauer and C. Huisr.oon, Mol. Phys., 47, 565 (1982). Parameterization of Site-Site Potentials. A Point Charge Model for the Electrostatic Interaction of the Aza-Benzene Molecules. 

Electrostatic interactions can be most simply modeled as the Coulomb interaction between partial atomic charges, while the repulsion-dispersion part is usually described by a Lennard-Jones or, more accurately, an exp-6 form, each of which contains parameters that must be fixed. High-quality empirically fitted parameter sets have been developed, where the atom-atom interactions are parameterized to reproduce the structures, sublimation enthalpies and, sometimes, further observable properties of organic molecular crystals [73,74]. Their use has been very effective in CSP. Nonempirical approaches to fitting intermolecular force fields, where the parameters are derived from quantum mechanical calculations, have occasionally been applied for CSP [75-78], but these are currently limited to small molecules, so currently lack relevance for typical pharmaceutical molecules. 

Parameterization and evaluation of the through-space nonbonded interactions in Eq. (1) presents the greatest difficulty in the development of empirical potentials for biological macromolecules. There are a number of reasons for this difficulty. First, the A and B parameters, which represent the repulsive van der Waals radius and attractive dispersion interactions, are not directly observable by experimental measurement. In fact, they represent a complicated and non-uniquely decomposable set of high level quantum chemical interactions (Pauli exclusion, nuclear repulsion, induced electronic effects, etc.) which are not readily amenable to theoretical analysis. A second problem arises in attempts to represent the electrostatic interactions due to a permanent charge distribution on particular atomic centers i.e. the q s in Eq. (1). 

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