Asymmetry in charge density and size in polymer complexation: partially ionizable polyelectrolytes and intrinsically disordered proteins

The thermodynamics of a charged polymer system is characterized by the interaction potentials, conformational entropy of the polymer chains and entropy of free counterions and salt ions. We present a theory which investigates the role of enthaply and entropy, and calculates the driving force, of complexation between oppositely charged polyelectrolytes which are partially ionizable and, in general, asymmetric in charge density and size. The analysis delineates the enthalpy- and entropy-driven regimes in electrostatic strength, and also calculates the potential of mean force, as functions of charge density. The general concepts such as of counterion release entropy and its effect on complexation drive apply equally well to symmetric, fully ionizable, or asymmetric and partially ionizable polyelectrolytes, and also to intrinsically disordered proteins (IDP).