A theoretical framework for investigating the role of heterogeneity of extensibility in structure and dynamics of flexible polymer.

Heteropolymers are ubiquitous in both synthetic systems, such as block copolymers, and biological macromolecules, including proteins and nucleic acids. Beyond their chemical composition, these polymers often exhibit spatial variations in physical properties. For instance, in biopolymers such as chromatin, heterogeneity of extensibility arises from inherent molecular features as well as extensile or contractile active forces. In this article, we develop a theoretical framework that extends the physics of flexible polymers, a widely used tool to describe biopolymer dynamic, to incorporate spatially varying extensibility. Using this approach, we specifically analyze the structure and dynamics of flexible heteropolymers with periodic stepwise extensibility profiles. We find that this heterogeneity leads to qualitative deviations in dynamical observables such as mean squared displacement while also increasing structural anisotropy. Altogether, this framework provides a platform to interpret heterogeneous extensibility from experimental data especially for biopolymers as well as to design heteropolymers with tailored structural and dynamic properties.