A Sequence-Specific Theory for Charge-Regulating IDPs

Intrinsically disordered proteins are a notable class of biological polymers whose physicochemical properties and biological functions are determined by an intricate interplay of chain connectivity, electrostatic interactions, the sequence of residues, and nonuniversal short-range interactions. An important phenomenon in these molecules is charge regulation, which arises from weakly acidic and basic residues, but is often neglected in theoretical descriptions. In this work, we use the Edwards-Singh variational method to derive an approximate theory that describes sequence effects in the charge regulation and chain conformation of intrinsically disordered proteins. The main result of our theory is a set of coupled algebraic equations yielding a renormalized Kuhn length and residue-specific mean-fields that determine the respective ionization states of the residues. We discuss limiting cases of these equations that underline the internal consistency of our theory and connect our results to earlier studies. To solve the full set of equations, we propose a simple numerical scheme. As test cases, we calculate the conformation and ionization state of a weak polyelectrolyte and of 30 sequence variants of the polypeptide (EK)25. For the weak polyelectrolyte, we show that the theory predicts phenomena such as the overall suppressed ionization due to electrostatic interactions and the enhanced ionization at the chain ends. In the case of the polypeptide (EK)25, we find strong effects of the sequence on ionization, with well-mixed sequences exhibiting a broad pH range where the polypeptide is net neutral, while blockier sequences exhibit a steeper ionization response. Moreover, we also observe pronounced sequence effects on the swelling behavior of the chains.