Solvation energy of a large atom cluster: continuous solvation energy test - II

As it has been already stated here, binding energy calculation of a small molecule to a large protein poses a difficult problem: a method for molecular electrostatic energy calculation should work well both for the protein ligand complex, the protein and the ligand at infinite separation. The protein and the complex are large molecules, whereas the ligand is, by definition, small.

Not every computational approach for the solvation energy calculation is fit for the job though. To elucidate the nature of the problems at hand we performed the following model calculation:
- we prepared a spherical "protein" of a large (but realistic) radius
- we placed a single-atom ligand with a charge at a given distance from the "protein" center (see the Figure)
- we calculated the solvation energy of the system as a function of the ligand distance both when the protein is neutral and charged (in the latter case the protein charge is opposite to that of the "ligand")

We used four different methods for the electrostatic contribution to the solvation energy calculation: Poisson equation solver (in its surface electrostatic incarnation, blue) QUANTUM MGB (cyan) and the two "classic" GB methods, based on the Coulomb approximation: HCT (magenta) and AGBNP (yellow).

The first Figure, corresponding to an overall electrically neutral cluster, shows absolute deficiency of HCT approach deep enough inside the "protein". The problem is caused by unrealistic assumptions with regard to the overlap integrals calculations is occurs pretty frequently in realistic proteins. AGBNP method represents one of the latest GB approaches and is practically free of these difficulties. However, AGBNP is based on Coulomb approximation and thus fails to recover correct behavior of the solvation energy close to the "protein" boundary: AGBNP energy is off by a large number from both QMGB and the exact solution. QMGB and Poisson solutions agree very well everywhere!

The last Figure shows the same calculation for a charged model "protein-ligand" complex. Once again, HCT fails entirely, AGBNP does not work properly at the "protein" boundary and both Poisson solver and QMGB agree very well, though QMGB is about one order of magnitude faster than the Poisson solver!

Practically all this means that QMGB represents a fast and accurate approximation to the Poisson equation solution. QMGB approach does not rely on Coulomb approximation and is shown to work both for small molecules and large molecular clusters involving molecules of very different sizes. Therefore, with QMGB one can find a single transferable set of GB parameters capable of describing large and small molecules on the same footing.