From heteropolymer stiffness distributions to effective homopolymers. I. Theoretical modeling and computational verification

Synthetic copolymers and biopolymers, such as polypeptides and double-stranded DNA, often exhibit strong variations in bending stiffness along their contours, which can significantly impact conformational behavior at larger scales. To investigate these effects, we employ a discretized heterogeneous worm-like chain model, where the local persistence lengths are drawn from a Gaussian distribution. We develop a theoretical model that maps such heterogeneous chains to homogeneous chains with a single effective persistence length. For uncorrelated disorder, our model predicts that this effective stiffness is systematically smaller than the arithmetic mean of the local persistence lengths, indicating that flexible segments have a bigger influence on the overall chain stiffness than rigid segments. We validate our model predictions using off-lattice Monte Carlo simulations, considering both ideal and self-avoiding chains in a good solvent, and find excellent agreement in the regime where the persistence lengths are on the order of a few bond lengths, consistent with typical values observed in polypeptides.