Continuum electrostatics solvation

Huang, D., Caflisch, A. Efficient Evaluation of Binding Free Energy Using Continuum Electrostatics Solvation. J. Med. Chem. 2004, 47, 5791-5797. 

Huang, D. and Cafiisch, A. (2004) Efficient evaluation of binding free energy using continuum electrostatics solvation. Journal of Medicinal Chemistry, 47, 5791-5797. 

M. Nina, W. Im, and B. Roux. Optimized atomic radii for protein continuum electrostatics solvation forces. Biophys. Chem., 78(1-23 89-96,1999. 

Wood, R.H. Continuum electrostatics in a computational universe with finite cut-off radii and periodic boundary conditions Correction to computed free energies of ionic solvation. J. Chem. Phys. 103 (1995) 6177-6187. 

Hunenberger, P. H. McCammon, J. A., Ewald artifacts in computer simulations of ionic solvation and ion-ion interactions a continuum electrostatics study, J. Chem. Phys. 1999,110, 1856-1872... 

Given the somewhat ad hoc nature of most specific schemes for evaluating the non-electrostatic components of the solvation free energy, a reliance on a simpler, if somewhat more empirical, scheme has become widely accepted within available continuum models. In essence, the more empirical approach assumes that the free energy associated with the non-electrostatic solvation of any atom will be characteristic for that atom (or group) and proportional to its solvent-exposed surface area. Thus, the molecular Geos may be computed simply as... 

In the majority of continuum solvation models incorporating a surface-tension approach to estimating the non-electrostatic solvation components, the index k in Eq. (11.22) runs over a list of atom types, and die user assigns the appropriate type to each atom of the solute. This is particularly straightforward for MM models, like the Generalized Bom/Surface Area (GB/SA) model (Still el al. 1990 see also Best, Merz, and Reynolds 1997), since atom types are already intrinsic to the force field approach. This same formalism has been combined with the CHARMM and Cornell et al. force fields (see Table 2.1) to define GB models for proteins and nucleic acids (Dominy and Brooks 1999 Jayaram, Sprous, and Beveridge 1998). Considering this approach applied within the QM arena, the MST-ST models of Orozco and Luque have been the most extensively developed (see, for instance, Curutchet, Orozco, and Luque 2001). 

We remark that, in this formulation, we have collected into a single set of one-electron operators all the interaction operators we have defined in the preceding section, and, in parallel, we have put in the qk set both the apparent charges related to the electrons and nuclei of M. This is an apparent simplification as all the operators are indeed present. It is interesting here to note that this nesting of the electrostatic problem in the QM framework is performed in a similar way in all continuum QM solvation codes. 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

The electrostatic solvation energy is only a part of the total solvation energy. Cavitation, dispersion and repulsion terms must be added. We show below that the MPE method leads to similar electrostatic energies than the polarizable continuum model (PCM) of Tomasi and co-workers [10], provided the same cavities are used. Therefore, non-electrostatic terms in these methods may be computed using the same computational strategies [15]. We emphasize the fact that accurate non-electrostatic contributions are often difficult to compute since they are based on parameterized formulae that cannot be directly compared to experiment. The obtained data must therefore be used with prudence, especially if they are expected to play a major role in the process under study. Fortunately, in many circumstances, non-electrostatic terms are small and/or vary little, so that they can be neglected. Tunon et al. [80] developed a parameterized expression for the MPE method using an expression of the type... 

So, Born s equation remains a controversial part of the theory of solvation although there have been many recent attempts striving to justify it. The difficulty resides in the avoidance of molecular-level arguments and in applying continuum electrostatics, which clearly involves fundamental limitations when it comes to atomic... 

A theoretical study based on MP2/6-31+G(d,p) and HF/6-31G(d) ab initio quantum mechanical calculations coupled with Langevin dipoles (LD) and polarised continuum (PCM) solvation models have been carried out by Florian and Warshel [387] to achieve a first systematic study of the free energy surfaces for the hydrolysis of methylphosphate in aqueous solution. The important biological implication of this work is the fact that since the energetics of both the associative and the dissociative mechanics are not too different, the active sites of enzymes can select either mechanism depending on the particular electrostatic environment. This conclusion basically means that both mechanisms should be considered, and this fact seems to contradict some previous studies which have focused on phosphoryl transfer reactions. 

It should be emphasized that this description of solvation as a purely electrostatic process is greatly over-simplified. Short-range interactions exist as well, and the physical exclusion of the solvent from the space occupied by the solute must have its own dynamics. Still, for solvation of ions and dipolar molecules in polar solvents electrostatic solvent-solute and solvent-solvent interactions dominate, and disregarding short-range effects turns out to be a reasonable approximation. Of main concern should be the use of continuum electrostatics to describe a local molecular process and the fact that the tool chosen is a linear response theory. We will come to these points later. 

The second approach to the approximate description of the dynamic solvation effects is based on the semiempirical account for the time-dependent electrical polarization of the medium in the field of the solute molecule. In this case, the statistical averaging over the solute-solvent intennolecular distances and configurations is presumed before the solution of the SchrOdinger equation for the solute and correspondingly, the solvent is described as a polarizable dielectric continuum. The respective electrostatic solvation energy of a solute molecule is given by the following equation[13]... 

Continuum electrostatics A simplification of molecular electrostatics by using the same values throughout one or a range of molecules for computational efficiency. Continuum electrostatics is often used to mimic the properties of bulk water, not treating every single water molecule or atom as a separate entity, in order to compute molecular solvation implicitly rather than explicitly. 

Over the recent years implicit solvent models have undergone a transition to relatively mature methodology that is now widely employed in molecular dynamics simulations and related applications. Most popular are implicit solvent models based on a decomposition of the solvation free energy into electrostatic and nonpolar components. The electrostatic free energy is typically obtained according to a continuum electrostatics model that is described by Poisson theory or by the more approximate but much more efficient Generalized Born formalism. 

---