Coupled dynamics of charged macromolecules and counterions mediated actively by binding enzymes

We have studied the dynamics of a homogeneously charged flexible polymer in an environment where enzymes and counterions affect the dynamics of a polymer. An enzyme, in its bound state, exerts an electrostatic force on a monomer, and eventually, it gets unbound due to thermal fluctuations. This binding and unbinding process generates active fluctuations to the dynamics of the polymer. We have analytically investigated 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. The present charged macromolecular system defines a new class of active matter.