Solvation energy contribution to protein-ligand binding conceptually consists of two different contributions. The first one is collective in nature, comes from the long range interaction of the molecules charges with polar water molecules. The other comes mostly from the short range interactions of the molecules in question with the adjacent layer of the water molecules.

The long range part can be, to a certain extent, be modeled within a continuous electrostatics framework. Recently we have posted a number of improvements to commonly used Generalized Born models. Let us show that GB models may naturally have a good built-in approximation for the surface accessible area for the non-polar contribution calculations.

To do that we take  FSBE model as the example and suggest the following equation for the surface area of a molecule:



where is a coefficient, are the surface tensions associated with the atom types, are the radii of the ions and are the Born radii defined according to the model settings, e.g.



The results of the model surface area differences for 230 protein ligand complexes (the model vs. exact surface data) are presented on the graph. The numbers show an impressive correlation with .

The surface area requires the same power of the Born radii for the evaluation and thus can be implemented both numerically accurate and computationally efficient.

Surface Charges Generalized Born (SCGB) family of the polar solvation energy caclulation methods is a recently developed approach aimed at getting fast numerical solutions of the Poisson Boltzmann equation in linear time (and memory). SCGB combines the bests of the two worlds: the simplicity of Generalized Born models with the sound physics behind exact continuous electrostatics. Does not only SCGB provide accurate solvation energies for realistic systems, the surface charges obtained in the course of the calculation can be compared directly to those found using a boundary-element version of Poisson equation.

Recently we reported calculation of the Born radii. Now we can use SCGB model expressions for the surface charges density to obtain the solvation energies in linear time as well. The results are represented on the Figure below:

SCGB energies of 233 proteins are calculated first directly (in steps, the horizontal horizontal axis) and then compared with the same energies calculated using FFTw (in steps, the data along the vertical axis). Both energies correlate pretty well aside of the extreme solvation energies region. While the nature of such deviation remains unknown and needs to be fully accounted for, the proof of concept calculation shows the method potential in practical calculations

P.O. Fedichev, E.G. Getmantsev, L.I. Men'shikov
(Submitted on 12 Aug 2009 (v1), last revised 9 Dec 2009 (this version, v2))
We report a development of a new fast surface-based method for numerical calculations of solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size both in time and memory requirements, is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point, provides both the solvation energy and its derivatives suitable for Molecular Dynamics simulations. The method works well both for large and small molecules and thus gives stable energy differences for quantities such as solvation energies of molecular complex formation.
Comments: 6 pages, 4 figures, more results, examples and references added
Subjects: Quantitative Methods (q-bio.QM); Chemical Physics (physics.chem-ph)
Cite as: arXiv:0908.1708v2 [q-bio.QM]

Not only our recently introduced surface charges generalized Born (SCGB) models prove to be reasonable in terms of providing solutions to Poisson Boltzmann equation in complicated geometries, such as biomolecules. By getting rid of the standard expression for the solvation energy we are able to formulate SCGB models in terms of a fast algorithm using FFT. The comparison between the Born radii calculated with the help of the fast method and the standard approach is presented below:

The calculation was performed for 2ht7 H1N1 neuromidase protein. The radii match over a broad range of the atoms locations within the protein. The fast method involves an (large) computational overhead due to FFT calculation and breaks even with the usual approach for any molecule exceeding about a thousand atoms.

Up to now, there have been at least two schools of thoughts among those trying to calculate electrostatics part of solvation energies. Half of the folks believe that only an exact solution of the Poisson equation can be better than the solution of the Poisson equation. The other half believes that though the exact solution of the Poisson equation can be obtained, it is too slow and numerically unstable. Here in Quantum we attempt to give Generalized Born models almost infinite credit of trust and push for a direct link between the Poisson equation solutions and Generalized Born models.

The missing link between the two worlds is established by the equation linking the Born radii with the water polarization charges on a molecular interface. If the surface charges are then interpreted on their own, we can calculate the solvation energy using its direct definition, rather than an approximate Born formula. The question is of course if it all works in real life.

To proof the concept we attempted the calculation of the solvation energies for about 580 proteins from our Quantum Pharmaceuticals target list of proteins with available 3D structure. The results obtained with 4 different types of Surface Charges Generalized Born (SCGB) models are compared with the Surface Electrostatics solutions of the Poisson eqaution and are summarized below:

Here the surface electrostatics solvation energies are measured along the horizontal axis, the vertical axis is used for the SCGB solvation energies values. The green dots represent SCGB model with FSBE radii, yellow and red dots are SCGB models with respectively. All the three models give exact solvation energies for an arbitrary system of charges within a shpere and cope fairly well with the realistic proteins. SCGB with standard CFA Born radii (the blue dots) are completely off. Given tremendous speed advantage of SCGB models over SE we end up with an approximation worth to be employed!