Folding Transition of Single Semiflexible Polymers Controlled by the Range of Intermonomer Attractions

Semiflexible polymer folding has been employed by nature for protein folding and by researchers for designing smart materials and nanomachines. Hence, it is of great importance to understand and control semiflexible polymer folding. Here, we find that the range of intermonomer attraction, or the width of attraction (w), can significantly control the structural phase diagram of a semiflexible polymer through entropic effects. As w decreases, the extent of entropy loss depends on the specific folded structures, reshaping the energy landscape and resulting in a change in the folding mechanism. Furthermore, a reduced width of attraction can facilitate specific interactions and the formation of particular structures, which may further enhance folding and binding capabilities of some biomacromolecules. For the coil-globule transition of stiff chains, the critical temperature approximately follows k_BT*/ε ∼ w^1/3, and the entropic loss is approximately described by ΔS/k_B ∼ w^-1/3. Notably, this effective exponent of 1/3 differs from the scaling exponent of 2/3 derived from Odijk's theory. To better understand the underlying mechanisms contributing to this discrepancy, we mapped the polymer folding problem to an adsorption problem. Our findings suggest that the deviation from Odijk scaling is likely due to differences in the shapes of the attractive potentials.