Langevine dipole method

Tiic Langevin dipole method of Warshel and Levitt [Warshel and Levitt 1976] i.itermediate between a continuum and an explicit solvation model. A three-dimension... 

E is the field due to the solute charges alone. The Langevin dipole method has been wide used by Warshel in his studies of enzyme reactions (see Section 11.13.3). 

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

The ASEP/MD method, acronym for Averaged Solvent Electrostatic Potential from Molecular Dynamics, is a theoretical method addressed at the study of solvent effects that is half-way between continuum and quantum mechanics/molecular mechanics (QM/MM) methods. As in continuum or Langevin dipole methods, the solvent perturbation is introduced into the molecular Hamiltonian through a continuous distribution function, i.e. the method uses the mean field approximation (MFA). However, this distribution function is obtained from simulations, i.e., as in QM/MM methods, ASEP/MD combines quantum mechanics (QM) in the description of the solute with molecular dynamics (MD) calculations in the description of the solvent. 

An appealing feature of the Protein Dipoles Langevin Dipoles method is that the water environment can be considered in a straightforward manner and that the dynamics of protein fluctuations can be simulated [219]. 

Although complete, fully polarizable QM/MM schemes are computationally demanding, a simplified version of this formalism was arguably the first QM/MM approach to be described (Warshel and Levitt 1976), and the method still sees some use today. The simplification involves replacing explicit, polarizable MM molecules with a three-dimensional grid of fixed, polarizable dipoles - each a so-called Langevin dipole (LD) as it is required to obey... 

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... 

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 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]. 

Bartkowiak, W., Strasburger, K., Leszczynski, J. Studie.s of molecular hyjierpolarizabilities (/3, y) for 4-nitroaniline (PNA). The application of quantum mechanical/Langevin dipoles/Monte Carlo (QM/LD/MC) and sum-over-orbitals (SOO) methods.. 1. Mol. Struct. (THELOCHEM) 549, 159-163 (2001)... 

Several different approaches have been developed for calculations of electrostatic energies in proteins. We have used the "Protein Dipoles, Langevin Dipoles" (PDLD) method (19,20), which has been applied to other related problems including electrostatic effects on redox potentials in cytochromes (21) and calculations of the energies of charge-transfer transitions in crystalline methylbacteriopheophorbide (22). The change in free energy associated with an electon-transfer reaction is writen as... 

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... 

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