Coupled dynamics of charged macromolecules and counterions mediated by binding enzymes

Abstract

We investigate the role of active coupling on the transport properties of the macromolecules. The active coupling comes due to bound enzymes with a segment of the macromolecule wherein the enzyme exerts an electrostatic force on the segment of the macromolecule, and eventually, it gets unbound due to the thermal fluctuations. This binding and unbinding process generates active fluctuations in the dynamics of the macromolecule. Starting with segment dynamics and correlations for three dynamical models with active coupling, we obtain the cooperative diffusivity for the realistic charged macromolecules with hydrodynamics. First, we construct the three models by incorporating the features of a real polymer systematically, starting from simple Rouse dynamics with active coupling. We further include segment-segment interactions and in addition, hydrodynamic interactions with active coupling. Our obtained scaling form for segment-segment correlations for the models in terms of the size exponent of the polymer indicating that hydrodynamic and segment-segment interactions along with the active coupling lead to new scaling regimes. We finally study the dynamics of a homogeneously charged flexible polymer in an infinitely dilute solution where enzymes and counterions affect the dynamics of the polymers. We analytically investigate how these active fluctuations affect the coupled dynamics of the polymer and counterions. It turns out that these active fluctuations enhance the effective diffusivity of the polymer. The derived closed-form expression for diffusivity is pertinent to accurate interpretation of light scattering data on multi-component systems with binding-unbinding equilibria.