The Langevin Dipoles Model

CHEMICAL REACTIONS IN THE GAS PHASE AND IN SIMPLE SOLVENT MODELS 

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

Vo is given in A electron charge units, r is the closest distance (in A) between the grid points to the indicated solute atom. 

Exercise 2.2. Implement the Langevin Dipole method in a computer program. Use this model to evaluate the solvation energy of the CH30 ion. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

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

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 ... 

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... 

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. 

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... 

Treating the protein atoms as well as the surrounding solvent molecules explicitly constitutes the main alternative to continuum models. This obviously incurs a much heavier computational cost and simplified solvent models have been introduced to reduce it. The Langevin dipole (LD) model [299] is such an example here each molecule is represented by a polarisable point dipole, assumed to obey the Langevin polarisation law, located on a 3D grid with a cubic unit shell. This model has been progressively improved and recently used in free energy simulation calculations [370, 371]. 

Other recent microscopic approaches are based on the Langevin dipoles solvent model or on the all-atom solvent model, using a standard force field with van der Waals and electrostatic terms as well as intramolecular terms, and molecular dynamics simulations of the fluctuation of the solvent and the solute, incorporating the potential from the permanent and induced solvent dipoles in the solute Hamiltonian in a self-consistent way (Luzhkov and Warshel, 1991). 

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]. 

The Langevin dipole method of Warshel and Levitt [Warshel and Levitt 1976] is intermediate between a continuum and an explicit solvation model. A tluee-dimensional... 

Gibbs free energies of hydration, before and after ionization (AG y/l) and AGhyj(2)) were obtained by employing the Langevin dipole relaxation method (45-47) incorporated in the Polaris 3.2 program (46). Before and after ionization, solvent relaxation is modelled by evaluating the relaxation of discrete dipoles distributed on a lattice... 

Florihydration entropies of hydrophobic, polar, and ionic solutes in the framework of the langevin dipoles solvation model. Journal of Physical... 

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