Distance-dependent dielectric function

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). 

Finally, we note that this approach does not include screening of interaction between the excited electron and the remaining hole. To obtain this, one should apply perturbation theory (at least in first order) not only to the Hamiltonian, but also to the exciton wave function. Since this is not an easy task one can use alternatively a distance-dependent dielectric function e(r) (as Suhai did). The interpolation scheme proposed by Hermanson and Phillips enables this function to be expressed in the form... 

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. 

Primitive models consider the solvent as a continuum with a dielectric constant or sometimes a frequency- or distance-dependent dielectric function.The detailed structure ofthewater molecules and their possible geometrical rearrangement around ions are not or only very roughly taken into account. The ion specificity is considered through the charges and the radii of the ions. Since these two parameters define the charge density, they might be used to describe properly specific ion effects. However, since the ion-water interactions are modelled in a very crude way, the relative importance of ion-ion and ion-water interactions is difficult to estimate. 

You can use two types of dielectric functions a constant and a distance-dependent dielectric. Use constant dielectric for in vacuo systems and for molecular systems with explicit solvent molecules. 

The AMBER (271, 272) and CHARMM (179) nonbonded terms are used as scoring function in several docking programs. As mentioned above (Sections.1.1), protein terms are usually precalculated on a rectangular grid to speed up the energy calculation compared to traditional atom-by-atom evaluations (273). Distance-dependent dielectric constants are... 

The simple distance-dependent dielectric has no physical basis and so it is not generally recommended, except when no alternative is possible. More sophisticated distance-dependent functions can also be employed. Many of these have an approximately sigmoidal shape in which the relative permittivity is low at short distances and then rises towards the bulk value at long distances. One example of such a function is [Smith and Pettit 1994] ... 

Historically, MD simulations often relied on the so-called distance-dependent dielectric model [62] to account for solvation effects. In this approach, electrostatic effects are modeled by Coulomb s law with the dielectric being some fixed function of the charge-charge distance, e.g. e(r) = r in the most basic form of the model. Even though the model is generally expected to be less accurate than the GB [17], its utmost simplicity and computational efficiency keep it in active use today [63,64]. 

In Eqs. [15] and [16], D is the effective dielectric constant and is generally preset to a low value (1-1.5) to simulate the gas phase. However, most force fields optionally allow for a user-defined dielectric constant. In some force fields a distance-dependent dielectric constant (function) is used. In Eq. [16], and a describe the orientation of the bond dipoles, and x, and are the magnitudes of interacting dipoles i and /, respectively.22... 

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