Empirical Parameterization of a Model for Predicting
Peptide Helix/Coil Equilibrium Populations

Niels Andersen and Hui Tong
Department of Chemistry, University of Washington

Abstract

A modification of the Lifson-Roig formulation of helix/coil transitions is presented; it i) incorporates end-capping and coulombic (salt bridges, hydrogen bonding and sidechain interactions with charged termini and the helix dipole) effects, ii) helix-stabilizing hydrophobic clustering, iii) allows for different inherent termination probabilities of individual residues, and iv) 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 which 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, accompanying article). Sidechain/sidechain interactions appear largely as context dependent modifications of propagation rather than nucleation parameters. An alternative procedure for converting [theta]221 values to experimental fractional helicities (<fH>) is presented. Tests of the program predictions suggest this method may have some advantages both for designed peptides and for the an analysis of secondary structure preferences that could drive the formation of molten-globule intermediates on the protein folding pathways. The model predicts the fractional helicity of 385 peptides with a root-mean-square deviation 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 which were derived from NMR data and 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 sidechain/sidechain 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 can be seen in the rms deviations between CD measures and calculated values of fractional helicity for different classes of peptides: peptides lacking capping boxes, i/i+3 and i/i+4 sidechain/sidechain interactions (n=164 - rmsd = 0.044), peptides which have capping box and/or helix-stabilizing coulombic interactions but lack hydrophobic cluster interactions [n=84 - without corrections, (<f_H>_calc - <f_H>_CD) = -0.20 and rmsd = 0.24; after applying the corrections, (<f_H>_calc - <f_H>_CD) = -0.013 and rmsd = 0.047], and peptides with only stabilizing hydrophobic cluster interactions [n=49 - without corrections, (<f_H>_calc - <f_H>_CD) = -0.08, rmsd = 0.101; with corrections, (<f_H>_calc - <f_H>_CD) = -0.015, rmsd = 0.047].

Keywords

helix propensity parameters, N-capping boxes, sidechain/sidechain interactions, hydrophobic and coulombic adjustments for propagation parameters

Abbreviations

CD, circular dichroism; DR, Doig-Rohl; IL, interleukin; LR, Lifson-Roig; NMR, Nuclear Magnetic Resonance; ZB, Zimm-Bragg; the accepted one and three-letter codes are employed for amino acids; Aib, -aminoisobutyric acid.