A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications

We report the adaptation of the truncated Newton minimization package TNPACK for CHARMM and biomolecular energy minimization. TNPACK is based on the preconditioned linear conjugate-gradient technique for solving the Newton equations. The structure of the problem-sparsity of the Hessian-is exploited for preconditioning. Experience with the new version of TNPACK is presented on a series of molecular systems of biological and numerical interest: alanine dipeptide (N-methyl-alanyl-acetamide), a dimer of N-methyl-acetamide, deca-alanine, mellitin (26 residues), avian pancreatic polypeptide (36 residues), rubredoxin (52 residues), bovine pancreatic trypsin inhibitor (58 residues), a dimer of insulin (99 residues), and lysozyme (130 residues). Detailed comparisons among the minimization algorithms available in CHARMM, particularly those used for large-scale problems are presented along  with new mathematical developments in TNPACK. The new TNPACK version performs significantly better than ABNR, the most competitive minimizer in CHARMM, for all systems tested in terms of CPU time when curvature information (Hessian/vector product) is calculated by a finite-difference of gradients (the numeric option of TNPACK). The remaining derivative quantities are, however, evaluated analytically in TNPACK. The CPU gain is 50% or more (speedup factors of 1.5 to 2.5) for the largest molecular systems tested and even greater for smaller systems (CPU factors of 1 to 4 for small systems and 1 to 5 for medium systems). TNPACK uses curvature information to escape from undesired cofigurational regions and to ensure the identification of true local minima. It converges rapidly once a convex region is reached and achieves very low final gradient norms, such as of order 10-8, with little additional work. Even greater overall CPU gains are expected for large-scale minimization problems by making the architectures of CHARMM and TNPACK more compatible with respect to the second derivative calculations.

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