B‐spline method for energy minimization in grid‐based molecular mechanics calculations

A method is described for molecular mechanics calculations based on a cubic B‐spline approximation of the potential energy. This method is useful when parts of the system are allowed to remain fixed in position so that a potential energy grid can be precalculated and used to approximate the interaction energy between parts of a molecule or between molecules. We adapted and modified the conventional B‐spline method to provide an approximation of the Empirical Conformational Energy Program for Peptides (ECEPP) potential energy function. The advantage of the B‐spline method over simpler approximations is that the resulting B‐spline function is C2 continuous, which allows minimization of the potential energy by any local minimization algorithm. The standard B‐spline method provides a good approximation of the electrostatic energy; but in order to reproduce the Lennard–Jones and hydrogen‐bonding functional forms accurately, it was necessary to modify the standard B‐spline method. This modification of the B‐spline method can also be used to improve the accuracy of trilinear interpolation for simulations that do not require continuous derivatives. As an example, we apply the B‐spline method to rigid‐body docking energy calculations using the ECEPP potential energy function. Energies are calculated for the complex of Phe‐Pro‐Arg with thrombin. For this system, we compare the performance of the B‐spline method to that of the standard pairwise summation in terms of speed, accuracy, and overhead costs for a variety of grid spacings. In our rigid‐body docking calculations, the B‐spline method provided an accurate approximation of the total energy of the system, and it resulted in an 180‐fold reduction in the time required for a single energy and gradient calculation for this system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 71–85, 1998