Multiscale optimization of a truncated Newton minimization algorithm and application to proteins and protein-ligand complexes

We optimize a truncated Newton (TN) minimization algorithm and computer package, TNPACK, developed for macromolecular minimizations by applying multiscale methods, analogous to those used in molecular dynamics (e.g., r-RESPA). The molecular mechanics forces are divided into short- and long-range components, with the long-range forces updated only intermittently in the iterative evaluations. This algorithm, which we refer to as MSTN, is implemented as a modification to the TNPACK package and is tested on energy minimizations of protein loops, entire proteins, and protein-ligand complexes and compared with the unmodified truncated Newton algorithm, a quasi-Newton algorithm (LBFGS), and a conjugate gradient algorithm (CG+). In vacuum minimizations, the speedup of MSTN relative to the unmodified TN algorithm (TNPACK) depends on system size and the distance cutoffs used for defining the short- and long-range interactions and the long-range force updating frequency, but it is 4 to 5 times greater in the work reported here. This algorithm works best for the minimization of small portions of a protein and shows some degradation (speedup factor of 2-3) for the minimization of entire proteins. The MSTN algorithm is faster than the quasi-Newton and conjugate gradient algorithms by approximately 1 order of magnitude. We also present a modification of the algorithm which permits minimizations with a generalized Born implicit solvent model, using a self-consistent procedure that increases the computational expense, relative to a vacuum, by only a small factor (similar to 3-4).