ALGORITHMS FOR CALCULATING EXCLUDED VOLUME AND ITS DERIVATIVES AS A FUNCTION OF MOLECULAR-CONFORMATION AND THEIR USE IN ENERGY MINIMIZATION

A numerical method for calculating the volume of a macromolecule and its first and second derivatives as a function of atomic coordinates is presented. For N atoms, the method requires about 0.3 N ln(N) seconds of CPU time on a VAX-8800 to evaluate the volume and derivatives. As a test case, the method was used to evaluate a pressure-volume energy term in energy minimizations of the protein lysozyme at 1000 atm (1 atm = 1.013 x 10(5) Pa). R.m.s. gradients of 10(-4) kcal/mol/angstrom were obtained at convergence. The calculated structures exhibited pressure-induced changes which were qualitatively similar to the changes observed in the 1000 atm structure determined by X-ray crystallography.