Coil-helix transition in macromolecules. I. Minimal model

This work presents a minimal coarse-grained molecular dynamics model for the coil-helix transition in polymers. We demonstrate that the addition of a Morse potential to a freely jointed chain with volume and bond potentials is sufficient to reproduce the essential thermodynamic features of the transition. From the simulations performed, the Zimm-Bragg propagation parameter s and nucleation parameter σ are extracted, providing quantitative measures of helical propensity and cooperativity, respectively. To illustrate the versatility of the model, this study systematically varies the spacing between hydrogen-bonding monomers using an i → i + m motif, with m = 4, 5, and 6 corresponding to coarse-grained representations of α-, π-, and 1-7 helices. This approach is used to evaluate how hydrogen-bond spacing influences the transition behavior and the resulting cooperativity. As the monomer spacing m between hydrogen-bonding pairs increases, the number of monomers that must be confined for the first hydrogen bond to form also increases, leading to increased cooperativity (lower nucleation parameter σ) and a sharper transition, as reflected in the simulation results. This behavior is consistent with that observed in natural helices of different types, underscoring the model's ability to capture how molecular architecture governs helix formation.