Coulombic interactions distance-dependent dielectric

Macroscopic models have been developed that describe the protein and the water as macroscopic dielectric materials. In their simplest form these models use a distance-independent dielectric function, i.e. a simple Coulomb interaction. Others may apply a distance-dependent dielectric function. The more detailed implementatiorrs include a descriptions of the protein-solvent botmdary in terms of solvent accessibihty and ionic-strength effects (Gilson and Honig, 1988). 

Electrostatic interactions in the form of a Coulomb potential have been included in methods that rely on full molecular mechanics potentials, usually with a distance-dependent dielectric, e(r) = r ... 

Distance-dependent dielectric constant In computing the Coulomb interaction between two point charges, the dielectric constant is set to the value of the dielectric medium. In an attempt to implicitly simulate water, the dielectric constant should be 80 at long distances, but 1 at close range. Replacing the dielectric constant by r makes the dielectric effect distance-dependent at negligible computational cost. 

In force fields such as AMBERS or CHARMM designed for large biological molecules, the Coulombic interaction in Eq. [10] is sometimes modified by use of a distance-dependent dielectric constant. Another modification of Eqs. [10] and [11] is utilized in force fields designed for hydrocarbons and concerns the internuclear distance R, in the van der Waals interaction (the non-Coulom-bicpart of Eq. [10]) when one of the nonbonded atoms is a hydrogen. 

An alternative to the simple screened Coulomb interaction in protein modeling is the distance-dependent dielectric function [51]. In this approximation the effective electrostatic interaction between two partial charges q at distance r is written as... 

In the present implementation, the program uses a modified Coulombic potential to evaluate the electrostatic interactions between the two proteins, in each alternative association mode. The atomic point charges used are taken fi-om the molecular mechanics force field Amber 4.1 [25-27] and a distance-dependent dielectric function is used. 

Here the atoms in the system are numbered by i, j, k, l = 1,..., N. The distance between two atoms i, j is ry, q is the (partial) charge on an atom, 6 is the angle defined by the coordinates (i, j, k) of three consecutive atoms, and 4> is the dihedral angle defined by the positions of four consecutive atoms, e0 is the dielectric permittivity of vacuum, n is the dihedral multiplicity. The potential function, as given in equation (6), has many parameters that depend on the atoms involved. The first term accounts for Coulombic interactions. The second term is the Lennard-Jones interaction energy. It is composed of a strongly repulsive term and a van der Waals-like attractive term. The form of the repulsive term is chosen ad hoc and has the function of defining the size of the atom. The Ay coefficients are a function of the van der Waals radii of the... 

The course of the recombination processes in a particular system depends on several factors. One of the most important ones is the polarity of the system. Both geminate and bulk recombination processes are strongly influenced by the Coulomb attraction between electrons and cations, and the range of this interaction in condensed matter is determined by the dielectric constant e. The range of the Coulomb interaction in a particular system is usually represented by the Onsager radius, r, which is defined as the distance at which the electrostatic energy of a pair of elementary charges falls down to the thermal level kj,T. 

The solvent is often treated as a continuum with a particular dielectric constant. This continuum model is, however, not capable of describing the solvent effects. For example, acetonitril and methanol share about the same dielectric constant, but they exhibit fairly different solvation properties for many solutes. When the continuum model is adopted, the solvent has no effects except that the Coulombic interaction between atoms in a solute molecule is simply divided by the dielectric constant. Notice, however, that the division is valid only when the distance between the atoms is far larger than the atomic scale. The solvent effects are sensitively dependent on the conformation of the solvent molecule as well as that of the solute molecule and on the density and ori-... 

Figure 5.1 is a graph illustrating the relative importance of the flux correction term G with respect to the free-molecular flux term Gq. It is graphed for ej[ = 2 and = 1 which correspond to 13.9 nm particles with dielectric constants k = < and K = 1.67, respectively. The argument e e is simply a measure of the Coulomb interaction which is independent of k. For a constant Coulomb potential e e, an increase in k corresponds to an increase in the turnover distances. Since collisions with neutrals increase in importance as the capture distance increases, the flux correction G must increase. The fact that, e.g., ( i/%)e =i ( l o e =2 but both have the same functional dependence upon can be interpreted o mean... 

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