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

We test the efficiency of three minimization algorithms as applied to model s of peptides and proteins. These include: the limited memory quasi-Newton (L-BFGS) of Liu and Nocedal; the truncated Newton (TN) with automatic preco nditioner 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 a ccount the intramolecular interactions only; the second is defined by the e nergy E-tot = E-GRO + E-solv, where E-solv is an implicit solvation free ev ery term based on the solvent-accessible surface area of the atoms. The mol ecules studied are cyclo-(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) (31 atoms), axinastatin 2 [cyclo(Asn(1)-Pro(2)-Phe(3)-Val(4)-Leu(5)-Pro(6)-Val(7)), 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 similar to 1.2 to 2 times better than that of both L-BFGS an d 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 Noce dal. We find the distribution of the Hessian eigenvalues to be a reliable p redictor of efficiency. (C) 1999 John Wiley & Sons, Inc.