Beyond the nearest neighbor Zimm - Bragg model for helix - coil transition in peptides

The nearest neighbor (μ =1) variant of the Zimm and Bragg (ZB) model has been extensively used to describe the helix-coil transition in biopolymers. In the present work we investigate the helix - coil transition for a 21 - residue alanine peptide (AP) with the ZB model up to fourth nearest neighbor (μ =1,2,3 and 4). We use a matrix approach that takes into account combinations of any number of helical stretches of any length and therefore gives the exact statistical weight of the chain within the assumptions of the ZB model. The parameters of the model are determined by fitting the temperature-dependent CD and FTIR experimental spectra of the AP peptide. All variants of the model fit the experimental data and, as a consequence, give similar results in terms of the overall macroscopic observables, such as temperature-dependent fractional helicity. However, the resulting microscopic parameters, distributions of the individual residue helical
probabilities and free energy surfaces differ depending on the variant of the model. Overall, with increasing μ the ZB nucleation parameters increase, which results in a lower free energy barrier to helix nucleation and lower apparent “cooperativity” of the transition, despite a greater inherent degree of cooperativity due to greater μ values. The mean residue enthalpy and entropy (in the absolute value) both increase with μ , but combined yield essentially the same value of the ZB propagation parameters for all μ. Finally, greater helical probabilities for individual residues are predicted for larger μ, in particular near the center of the sequence. The significance of the longer-range
interactions for the predictions of ZB model for helix-coil transition and the limitations of
the model are discussed.