Transfer Matrix Theory Model of Sequence-Dependent Polyampholyte Phase Separation

Intrinsically disordered proteins (IDPs) participate in many critical biological functions within the cell. These proteins lack a well-defined structure and can take on many conformations depending on its sequence and local environment. IDPs can be modeled as polyampholytes and can undergo a liquid-liquid phase separation that is primarily driven by electrostatic interactions. The charge sequence along the polymer is critical to the solution behavior. In this work, we present a Transfer Matrix (TM) model to describe this liquid-liquid phase separation as a function of charge sequence. We show how the TM theory is created for a polyampholyte, and how it can be used to determine the free energy of interaction between the polyampholyte and its local environment. In conjunction with the TM theory, we perform MD simulations of charge-patterned polyampholytes in solution to compare with the model. We find that increasing charge blockiness increases the tendency to undergo phase separation, limiting to the behavior typically seen in polymeric complex coacervates, while alternating positive and negative charges do not exhibit charge-induced phase separation.