Regularization of least squares problems in CHARMM parameter optimization by truncated singular value decompositions

We examine the use of truncated singular value decomposition and Tikhonov regularization in standard form to address ill-posed least squares problems Ax = b that frequently arise molecular mechanics force field parameter optimization. illustrate these approaches by applying them dihedral optimization genotoxic polycyclic aromatic hydrocarbon-DNA adducts are interest study chemical carcinogenesis. Utilizing discrete Picard condition and/or a well-defined gap spectrum when A has well-determined numerical rank, we able systematically determine truncation turn parameters correspondingly used produce regularized solutions problem at hand. These result optimized terms accurately parameterize torsional energy landscape. As produced this approach unique, it advantage avoiding multiple iterations guess check work often required optimize parameters.