Born approximation is a weapon of choice for a (relatively) fast calculation of solvation energies in modeling. Although the approach is conceptually simple, it can not be correctly derived from first principles (i.e. does not correspond to a solution of electrostatic problem in a strict or even variational sense).In practice applications of Generalized Born models are further complicated by various approximations for calculating volume (or surface) integrals, removing atom overlaps etc. What remains left is some sort of approximation to molecular volume (surface) and the so called Born Radii for every atom.
Each of the Born radii quantitatively shows a degree to which an atom is "buried" within the protein. The presented graph gives a simple idea to a which extent GB can even be used for description of solvation energies of a simple, model spherical protein containing approx. 1000 atoms of carbon.
The red squares give the dependence of the Born Radii on the atom positions. The points are obtained using our own implementation of AGBNP, one of the best realizations of GB procedures available in the literature.
The yellow curve represents exact result for a spherical protein, where GB and exact analytical expressions coinside. As one can see, AGBNP result fails to grow inwards and saturates at a very small value at r=0.
The reason for this behaviour is two-fold: first AGBNP is based on the so-called Coulomb approximation and thus can not be exact. Indeed, Coulomb approximation fails at the protein boundary and gives d(Born Radius)/dr twice as large as the exact result. This is a true problem, but it can not explain fundamentally wrong results in the protein center!
The other problem of AGBNP (and in fact any GB model), is that the model implies a certain approximation for molecular surface and the surface may have water filled cavities inside the protein! The cavities represent (within the same model) a medium with high dielectric constant and decrease the value of the Born radii.
To check the last assumption we searched for the water filled cavities removed them (to a certain adjustable extent). The result is represented by the blue circles and shows a clear improvement towards reproducing the exact analytical result.
Conclusion? Dry your protein up before even attempting to use GB approximation to get a good solvation energy for a large molecule!
