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

Abstract

The nearest-neighbor (micro = 1) variant of the Zimm and Bragg (ZB) model has been extensively used to describe the helix-coil transition in biopolymers. In this work, we investigate the helix-coil transition for a 21-residue alanine peptide (AP) with the ZB model up to fourth nearest neighbor (micro = 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 circular dichroism and Fourier transform infrared experimental spectra of the AP. All variants of the model fit the experimental data, thus giving similar results in terms of the macroscopic observables, such as temperature-dependent fractional helicity. However, the resulting microscopic parameters, such as distributions of the individual residue helical probabilities and free energy surfaces, vary significantly depending on the variant of the model. Overall, the mean residue enthalpy and entropy (in the absolute value) both increase with micro, but combined yield essentially the same "effective" value of the ZB propagation parameters for all micro. Greater helical probabilities for individual residues are predicted for larger micro, in particular, near the center of the sequence. The ZB nucleation parameters increase with increasing micro, which results in a lower free energy barrier to helix nucleation and lower apparent "cooperativity" of the transition. The significance of the long-range interactions for the predictions of ZB model for helix-coil transition, the calculated model parameters and the limitations of the model are discussed.