Section 22.1.2.2.7. Approximations to the surface

The methods discussed above are computationally quite cumbersome, especially if they need to be repeated many times. Thus, they are not well suited to comparisons of many structures. They are also not well suited to the calculation of surface-area-dependent energy terms during dynamics simulation or energy minimization, which require the calculation of the derivatives of the surface area with respect to atomic position. It has been argued by several (including A. Nicholls and K. Sharp, personal communications) that simplifying approximations to the surface-area calculations are in order, because the common uses of surface area already embody crude ad hoc approximations, such as non-integer numbers of spherical solvent molecules.

In the treatments discussed earlier, the volume of the protein is (implicitly) described by a set of overlapping step functions that have a constant value if close enough to an atom, or zero if not. Several authors have replaced these step functions with continuous spherical Gaussian functions centred on each atom (Gerstein, 1992; Grant & Pickup, 1995) in treatments reminiscent of Ten Eyck's electron-density calculations (Ten Eyck, 1977). This speeds up the calculation and also facilitates the calculation of analytical derivatives of the surface area. A surface can be calculated for graphical display by contouring the continuous function at an appropriate threshold. The final envelope can be modified by using iterative procedures that fill cavities and crevices that are (nearly) surrounded by protein atoms (Gerstein, 1992).