GB/SA model

The generalized Born/surface area (GB/SA) model is a combination of the Born and SASA models. This method has been effective in describing the solvation of biomolecular molecules. It is incorporated in the MacroModel software package. 

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). 

The choice of the partial charges requires some care when the GB/SA model is used. Still et al. note that the model is very sensitive to the charge set (e.g., OPTS) chosen. This issue is particularly important w hen comparing... 

The GB/SA model also correlates quite well with experiment for the neutral solutes. As expected, the regression slope and intercept are also nearly ideal. Conversely, based on the four ions for which results have been reported, there seems to be a tendency to overestimate ionic solvation free energies, but definite conclusions cannot be drawn from so small a sampling. Whereas the available data span a larger range of functionality than do those from the SASA model, there is still a paucity of results for complex and polyfunctional solutes. It would be very interesting to see how robust the model is in such instances. 

The effect of induced dipoles in the medium adds an extra term to the molecular Hamilton operator. = -r R (16.49) where r is the dipole moment operator (i.e. the position vector). R is proportional to the molecular dipole moment, with the proportional constant depending on the radius of the originally implemented for semi-empirical methods, but has recently also been used in connection with ab initio methods." Two other widely available method, the AMl-SMx and PM3-SMX models have atomic parameters for fitting the cavity/dispersion energy (eq. (16.43)), and are specifically parameterized in connection with AMI and PM3 (Section 3.10.2). The generalized Bom model has also been used in connection with force field methods in the Generalized Bom/Surface Area (GB/SA) model. In this case the Coulomb interactions between the partial charges (eq. (2.19)) are combined... 

The most rigorous dielectric continuum methods employ numerical solutions to the Poisson-Boltzmann equation [55]. As these methods are computationally quite expensive, in particular in connection with calculations of derivatives, much work has been concentrated on the development of computationally less expensive approximate continuum models of sufficient accuracy. One of the most widely used of these is the Generalized Born Solvent Accessible Surface Area (GB/SA) model developed by Still and coworkers [56,57]. The model is implemented in the MacroModel program [17,28] and parameterized for water and chloroform. It may be used in conjunction with the force fields available in MacroModel, e.g., AMBER, MM2, MM3, MMFF, OPTS. It should be noted that the original parameterization of the GB/SA model is based on the OPLS force field. 

As the present chapter is restricted to force-field calculations, only the GB/SA dielectric continuum model and similar models will be discussed. The aim is not to give an exhaustive review of the rapidly increasing literature in this area but to describe the basic properties of the GB/SA model and to discuss some aspects of the model and its use that are of particular interest in computational medicinal chemistry. 

In the GB/SA model, the solvation free energy (Gsoiv) is calculated as a sum of three terms... 

A computationally efficient analytical method has been developed for the crucial calculation of Born radii, which is required for each atom of the solute that carries a (partial) charge, and the Gpoi term has been parameterized to fit atomic polarization energies obtained by Poisson-Boltzmann equation [57]. The GB/SA model is thus fully analytical and affords first and second derivatives allowing for solvation effects to be included in energy minimizations, molecular dynamics, etc. The Gpoi term is most important for polar molecules and describes the polarization of the solvent by the solute. As force fields in general are not polarizable, it does not account for the polarization of the solute by the solvent. This is clearly an important limitation of this type of calculations. 

Qui et al. have compared experimental and calculated hydration free energies for a set of 35 small organic molecules with diverse functional groups by using the OPLS force field and the GB/SA hydration model [57], These calculations resulted in a mean absolute error of 0.9 kcal/mol. It is of interest to note that the results obtained with the GB/SA model were very similar to those obtained by the corresponding calculations using the full Poisson-Boltzmann equation. 

Dielectric continuum models such as the Generalized Born Solvent Accessible Surface Area (GB/SA) model are, in conjunction with force fields, excellent tools for fast and reliable calculations of hydration energies and solvent effects on, e.g., conformational equilibria and ligand-receptor interactions. The performance for neutral solutes is very good, whereas calculations on ionic compounds are currently more problematic. A solution to these problems most probably requires force fields that include polarization effects. For optimal accuracy of calculations using a dielectric continuum model, it is a clear advantage if the model is parameterized for the particular force field used. 

Reddy MR, Erion MD, Agarwal A, Viswabnadhan VN, McDonald DQ, Still WC. Solvation Free energies calculated using the GB/SA model sensitivity of results on charge sets, protocols and force fields. J Comput Chem 1998 19 769-780. 

A series of continuum solvation models (SMx, x = 1-5) has been developed by Truhlar and co-worker (Cramer and Truhlar [79]), based on the Generalized Born/Surface Area (GB/SA) model (Still et al. [86]). Recall that in the GB approach the molecular shape is taken into account as the solute charge is distributed over a set of atom-centered spheres. For this GB/SA model, the polarization free energy is given by... 

Using partial atomic charges in eq. (14.59) is often called the generalized Bom model, which has been used especially in connection with force field methods in the Generalized Born/Surface Area (GB/SA) model. In this case, the Coulomb interaction between the partial charges (eq. (2.20)) is combined with the Bom formula by means of a function fy depending on the intemuclear distance and Born radii for each of the two atoms,and aj. 

M. R, Reddy, M, D. Erion, A. Agarwal, V. N. Viswanadhan, D. Q. McDonald, and W. C. Still, /. Comput, Chem., 19, 769 (1998). Solvation Free Energies Calculated Usii the GB/SA Model Sensitivity of Results on Charge Sets, Protocols, and Force Fields. 

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