Coil-helix transition in macromolecules. II. Changes in chain size

Macromolecular coil-to-helix transitions simultaneously modify local geometry and persistence length, driving complex changes in overall chain size. Here, we apply the wormlike (persistent) chain model to both coil and helical fragments to examine how the degree of helicity, θ, and average helical fragment length, kh, dictate global chain dimensions. Using scaling arguments, we construct a conformational diagram comprising six distinct regimes for the end-to-end distance. We then employ a minimal coarse-grained molecular dynamics model to verify the theory. Mapping structural properties extracted from these simulations onto the proposed regime diagram enables direct quantitative comparison. This, alongside microscopic conformational analysis, corroborates our theoretical framework. We highlight that the competition between local chain compactization and increased stiffness upon helix formation produces a non-monotonic behavior of the end-to-end distance. Furthermore, to demonstrate the generality of our approach, we systematically vary the hydrogen-bonding monomer spacing m for pairs {i, i + m}. Spacings of m = 4, 5, and 6 are used as coarse-grained representations of α-, π-, and 1-7 helices, respectively. As m increases, the helix becomes locally more compact while its persistence length grows. The regime diagrams constructed for these distinct configurations, combined with robust quantitative agreement between theory and simulation, demonstrate that our framework effectively captures how variations in helix geometry and stiffness control macromolecular dimensions across the transition.