Continuous solvation models in general and Generalized Born models alike in particular provide a simplified though fast assessment of the solvation energies of biomolecules. Continuous water models help effectively eliminate vast number of degrees of freedom associated with the dynamics of water molecules and thus empower molecular modelers with practical tools whenever solvation effects become very important.
One of the simplest possible continuous solvation models is continuous electrostatics. The molecules are normally treated as low-dielectric constant medium, whereas water is approximated as a medium of nearly infinite dielectric susceptibility. The mathematical model behind the picture is the Poisson-Boltzman equation (PBE).
Solving PBE normally implies iterative solution of PDEs or a surface integral equation. A faster, though even more approximate, alternative approach is provided by the family of surface-based Generalized Born models.
To control the level of approximation we attempted comparative study of various Generalized Born models. To compare various approximations we chose to plot the solvation energies vs. the polar solvation energies obtained by solving the Poisson-Boltzman equation directly with the help of COSMO approach.
The example above shows the relative performance of the two surface Generalized Born approaches, FSBE(6) and SCGB(3). The two demonstrate roughly the same level of errors (as compared to the PBE solution, the horizontal axis). To make things really interesting we plotted the solvation energies of formation calculated for roughly 500 protein ligand complexes. The difference between the solvation energy of a protein-ligand complex and the solvation energies of the protein and the ligand separately is a hard test for the model, since it implies substraction of large energies corresponding to molecules of sophisticated shapes and greatly different sizes. The graphs similar to that above let us compare surface Born models with each by calculating mean squared energy differences with respect to the “exact” COSMO energies (see below).
The results are interesting. The surface based post-Coulomb field approximations FSBE(*) perform clearly better than the classic Born model (GB). SCGB models are somewhat worse than FSBE, but still perform at competitive levels.
The best two models FSBE(6) and SCGB(3) emerge as clear winners.FSBE(6) appears to be a weapon of choice for protein-ligand complexes affinities calculations so far. SCGB(3) can be made O(N)- fast (with N being the size of the system), gives exact polarization charge of the liquid, and thus can be advised for large scale calculations.
Related posts:
- Protein solvation energies and GB surface charges: perfect match!
- O(N) Surface Charges Generalized Born calculation demonstration
- FFT acceleration demonstration for (surface)GB methods
- Effects of the surface density on the stability of surface electrostatics models
- Non-polar contribution to solvation energy from Born models:
