Empirical parameterization of a model for predicting peptide helix/coil equilibrium populations

A modification of the Lifson-Roig formulation of helix/coil transitions is presented; it (1) incorporates end-capping and coulombic (salt bridges, hydrogen bonding, and side-chain interactions with charged termini and the helix dipole) effects, (2) helix-stabilizing hydrophobic clustering, (3) allows for different inherent termination probabilities of individual residues, and (4) differentiates helix elongation in the first versus subsequent turns of a helix. Each residue is characterized by six parameters governing helix formation. The formulation of the conditional probability of helix initiation and termination that we developed is essentially the same as one presented previously (Shalongo W, Stellwagen, E. 1995. Protein Sci 4:1161-1166) and nearly the mathematical equivalent of the new capping formulation incorporated in the model presented by Rohl et al. (1996. Protein Sci 5:2623-2637). Side-chain/side-chain interactions are, in most cases, incorporated as context dependent modifications of propagation rather than nucleation parameters. An alternative procedure for converting [theta](221) values to experimental fractional helicities ([f(H)]) is presented. Tests of the program predictions suggest this method may have some advantages both for designed peptides and for the analysis of secondary structure preferences that could drive the formation of molten-globule intermediates on protein folding pathways. The model predicts the fractional helicity of 385 peptides with a root-mean-square deviation (RMSD) of 0.050 and locates (with precise definition of the termini in many cases) helices in proteins as well as competing methods. The propagation and nucleation parameters were derived from NMR data and from the CD data for a 79 peptide ''learning set'' for which an excellent fit resulted (RMSD = 0.0295). The current set of parameter corrections for capping boxes, helix dipole interactions, and side-chain/side-chain interactions (coulombic, hydrogen bonding, and hydrophobic clustering), although still under development, provide a significant improvement in both helix/coil equilibrium prediction for peptides and helix location in protein sequences. This is clearly evident in the rms deviations between CD measures and calculated values of fractional helicity for different classes of peptides before and after applying the corrections: for peptides lacking capping boxes and i/i + 3 and i/i + 4 side-chain/side-chain interactions RMSD = 0.044 (n = 164) versus RMSD = 0.054 (0.172 without the corrections, n = 221) for peptides that required context-dependent corrections of the parameters. If we restrict the analysis to N-acylated peptides with helix stabilizing side-chain/side-chain interactions (including N-capping boxes), the degree to which our corrections account for the stabilizing interaction can be judged from the change in helicity underestimation, ([f(H)](calc) - [f(H)](CD)): -0.15 +/- 0.10, which is reduced to -0.018 +/- 0.048 (n = 191) upon applying the corrections.