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, the 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 for describing biopolymer dynamics, 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 for interpreting heterogeneous extensibility from experimental data, especially for biopolymers, as well as for designing heteropolymers with tailored structural and dynamic properties.