Performance of efficient minimization algorithms as applied to models of peptides and proteins

We test the efficiency of three minimization algorithms as applied to models of peptides and proteins. These include: the limited memory quasi-Newton (L-BFGS) of Liu and Nocedal; the truncated Newton (TN) with automatic preconditioner of Nash; and the nonlinear conjugate gradients (CG) of Shanno and Phua. The molecules are modeled by two energy functions, one is the Gromos 87 united atoms force field (defining the energy E_GRO), which takes into account the intramolecular interactions only; the second is defined by the energy E_tot=E_GRO+E_solv, where E_solv is an implicit solvation free every term based on the solvent-accessible surface area of the atoms. The molecules studied are cyclo-(d -Pro¹–Ala²–Ala³–Ala⁴–Ala⁵) (31 atoms), axinastatin 2 cyclo-(Asn¹–Pro²–Phe³–Val⁴–Leu⁵–Pro⁶–Val⁷), 62 atoms], and the protein bovine pancreatic trypsin inhibitor (58 residues, 568 atoms). With E_GRO, the performance of TN with respect to the CPU time is found to be ∼1.2 to 2 times better than that of both L-BFGS and CG, whereas, with E_tot, L-BFGS outperforms TN by a factor of 1.5 to 2.5, and CG by a larger factor. Still, the quality of the solution in terms of the value of the minimized energy and the gradient norm, obtained with TN, is always equivalent to, or better than, those obtained with L-BFGS and CG. The performance is analyzed in terms of criteria outlined by Nash and Nocedal. We find the distribution of the Hessian eigenvalues to be a reliable predictor of efficiency. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 354–364, 1999