Born radii

A. rather complex procedure is used to determine the Born radii a values of which. calculated for each atom in the molecule that carries a charge or a partial charge. T Born radius of an afom (more correctly considered to be an effective Born radii corresponds to the radius that would return the electrostatic energy of the system accordi to the Bom equation if all other atoms in the molecule were uncharged (i.e. if the other ato only acted to define the dielectric boundary between the solute and the solvent). In Sti force field implementation, atomic radii from the OPLS force field are assigned to ec... 

The author assumed that the Born radii of atoms can be estimated from the solvent exposure factors for sampling spheres around the atoms. Two spheres were used in a five-parameter equahon to calculate the Born radii. The parameters of the equahon were eshmated using numerical calculahons from X-ray protein structures for dihydrofolate reductase. In addition to AGol the author also considered the AGJ term accounting for cavity formahon and dispersion of the solute-solvent interactions as ... 

The bottleneck of GB calculations is the determination of the effective Born radii (a), since their magnitude depends not only on the intrinsic atomic (Bondi, or atomic) radii of the atom (p), but also on the geometry of the rest of the molecule, which modulates the average distance of the atom to the solvent. Original formulations of the method used Equation (4.19) for the computation of Born s radii, but all current version rely on an approximate formalism, such as that developed by Hawkins et al. [34], where a pairwise approximation to atomic overlap is used to simplify Equation (4.19) see Equations (4.20)-(4.22). Using this approach Born s radii can be computed very fast, which makes the method suitable for MD calculations ... 

The GB model is a modification of the Coulomb equation to include the Born radius of the particle or atom which estimates the degree of the particle s burial within the molecule. Equation 5 relates AGdec to the solvent/solute dielectric (e), the separation between the partial atomic charges r, the effective Born radii R(i and /), and the smoothing function fGR. A Debye-Hiickel screening parameter (k) similar to that used in the PB equation is used to account for the monovalent ions. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii. 

A number of popular methods for computing the GB radii were proposed. The most popular one is based on the Coulomb field approximation, in which the generalized Born radii are defined by the equation ... 

Nina M, Beglov D, Roux B (1997) Atomic Born radii for continuum electrostatic calculations based on molecular dynamics free energy simulations, J Phys Chem B, 101 5239-5248... 

Qiu D, Shenkin PS, Hollinger FP, Still WC (1997) The GB/SA continuum model for solvation a fast analytical method for the calculation of approximate born radii, J Phys Chem A, 101 3005-3014... 

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. 

The first term in the series expansion in Eq. (3) corresponds to the Coulomb field approximation that is used in GB formalisms to calculate GB radii [37]. Born radii calculated solely based on the Coulomb field approximation are therefore not sensitive to the dielectric environment (as they should be). However, recent GB implementations that include an additional higher-order correction term [13,38] allow the e-dependent calculation of GB radii and consequently an accurate reproduction of solvation energies over the entire range of dielectric constants [35]. 

Onufriev, A., Case, D., Bashford, D. Effective Born radii in fhe Generalized Bom approximation The imporfance of being perfecf. J. Compuf. Chem. 2002, 23,1297-304. 

Grycuk,T. [2003]. Deficiency ofthe Coulomb-field approximation in the generalized Born model An improved formula for Born radii evaluation, /. Chem. Phys 119, pp. 4817-4826. 

Mongan, J., Svrcek-Seiler, W. A., and Onufriev, A. [2007]. Analysis of integrai expressions for effective Born radii, / Chem. Phys. 127, pp. 185101 1-10. 

Onufriev, A, Case, D. A, and Bashford, D. (2002). Effective Born radii in the generalized Born model approximation The importance of being perfect,/. Comput. Chem. 23,14, pp. 1297-1304. 

J, Zhu, E. Alexov, and B. Honig. Comparative study of generalized Born models Born radii and peptide folding./ Phys. Chem. B, 109(7) 3008-3022,2005. 

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. 

Gp is taken as equal to the Still expression (17.94), except that the 4 in the exponential is replaced by 4.2 when the two atoms i and j are C and H. The Born radii are calculated using Still s procedure or a faster procedure called pairwise descreening (PD) that is an approximation to Still s procedure [Hawkins et al., J. Phys. Chem., 100, 19824 (1996)]. 

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