Langevin dipole model

FIGURE 2.4. A schematic description of the Langevin Dipole model. The figure illustrates the three steps involved in constructing the model. 

Langevin dipoles, 52, 53, 125 Langevin dipoles model, 49-53, 50. See also Protein dipoles-Langevin dipole model for catalytic effect of carbonic anhydrase, 199... 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

Page, M. I., and Jencks, W. P., entropic hypothesis of enzyme catalysis, 224-225 Papain, Cys-His proton transfer in, 140-143 Pauling, Linus, view of enzyme catalysis, 208 PDLD model, see Protein dipoles-Langevin dipoles model (PDLD)... 

Protein dipoles-Langevin dipoles model (PDLD), 123-125,124 Protein potential surfaces, see Enzyme potential surfaces... 

C-- This program uses THE LANGEVIN DIPOLE MODEL to evaluate ... 

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

Florian J, Warshel A (1997) Langevin dipoles model for Ab initio calculations of chemical processes in solution parametrization and application to hydration free energies of neutral and ionic solutes, and conformational analysis in aqueous solution, J Phys Chem B, 101 5583-5595... 

In addition, the pvalues of various residues within the surrounding protein environment were computed using the protein-dipoles Langevin-dipoles model, in a linear response approximation73 implementation (the PDLD/S-LRA method).84... 

The expressions of Vint which are now in use belong to two categories expressions based on a discrete distribution of the solvent, and expressions based on continuous distributions. The first approach leads to quite different methods. We quote here as examples the combined quantum me-chanics/molecular mechanics approach (QM/MM) which introduces in the quantum formulation computer simulation procedures for the solvent (see Gao, 1995, for a recent review), and the Langevin dipole model developed by Warshel (Warshel, 1991), which fits the gap between discrete and continuum approaches. We shall come back to the abundant literature on this subject later. 

The Langevin dipole model (LD) developed by Warshel (Warshel and Levitt, 1976) can be considered as an intermediate step between discrete and continuum models. Solvent (actually water) polarization is described by introducing a grid of polarizable point dipoles, responding to other electic fields according to Langevin s formula ... 

The most common boundary representation is periodic boundary conditions which assumes that the system consists of a periodic array (or a crystal ) of identical systems [1], Another common method, developed for the simulation of biomacromolecules, is the stochastic boundary approach, in which the influences of the atoms outside the boundary are replaced by a simple boundary force [78, 79, 80], Warshel uses a Langevin dipoles model in which the solvent is explicitly replaced by a grid of polarizable dipoles. The energy is calculated in a similar way to the polarization energy in a molecular mechanics force field (see above) [15]. 

An alternative approach to treating the dipole reorientation contribution that is particularly suited to the water surrounding the protein is the Langevin dipole model which describes the polarization due to a permanent solvent dipole of magnitude mLin terms of the applied field... 

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