Transfer Matrix Theory of Complex Coacervation for Patterned Polyelectrolytes

Polymeric complex coacervation is an associative phase separation process of oppositely charged polyelectrolytes. This is driven by electrostatic attraction between the polycation and polyanion species leading to polymer dense and polymer dilute phases. By understanding how charged monomer sequence plays a role in complex coacervation, we aim to gain a greater understanding of the physics involved with biological condensates. These intracellular compartments are formed from intrinsically disordered proteins and are sensitive to charged amino acid sequence. We have developed a theoretical approach to model polyelectrolytes that have different charged monomer sequences, as analogues to these biological macromolecules. We can predict how changes in the electrostatics of arbitrarily patterned polyelectrolytes affects the phase boundary and electrostatics of the system. Using a transfer matrix approach, we construct a statistical mechanical model that incorporates local correlations associated with nearest-neighbor monomer interactions. We show that predictions using this theoretical model are consistent with previous simulation-informed theory, both in terms of the phase behavior of sequence-defined polyelectrolytes as well as their sequence-dependent effective interaction energy.