  We study the role of active coupling on the transport properties of
homogeneously charged macromolecules in an infinitely dilute solution. An
enzyme becomes actively bound to a segment of the macromolecule, exerting an
electrostatic force on it. Eventually, thermal fluctuations cause it to become
unbound, introducing active coupling into the system. We study the mean-squared
displacement (MSD) and find a new scaling regime compared to the thermal
counterpart in the presence of hydrodynamic and segment-segment electrostatic
interactions. Furthermore, the study of segment-segment equal-time correlation
reveals the swelling of the macromolecule. Further, we derive the concentration
equation of the macromolecule with active binding and study how the cooperative
diffusivity of the macromolecules get modified by its environment, including
the macromolecules itself. It turns out that these active fluctuations enhance
the effective diffusivity of the macromolecules. The derived closed-form
expression for diffusion constant is pertinent to the accurate interpretation
of light scattering data in multi-component systems with binding-unbinding
equilibria.
