Change in Chain Dimensions upon Coil-Helix Transition

When a macromolecule transitions from a coil state to a the helix state, both local geometry and stiffness are simultaneously affected, leading to non-trivial behavior of the chain dimensions. We combine theory of persistent chains with a two-state (coil/helix) description to predict how the degree of helicity θ and the average helical fragment length〈k_h〉 govern the overall chain size. This yields a scaling diagram with six distinct regimes for chain end-to-end distance, which differ in the fraction of helical monomers and conformational statistics of helical fragments (coil-like vs rod-like). We also report how different helices with different local geometrical features and persistence lengths affect the scaling diagram, eliminating certain regimes in some cases. Using a minimal coarse-grained simulation model for the coil-helix transition, we extract θ and 〈k_h〉across different strengths of hydrogen bonding interactions; simulation trajectories are traced on the theoretical scaling diagram. Our results demonstrate that coil-helix transition can be accompanied by monotonic or non-monotonic change in the chain dimensions, depending on the compactness of the helical structure and its bending stiffness.