Title: Membrane-associated intrinsically disordered signaling proteins can exhibit emergent cooperativity, even under symmetric reversible kinetics

Abstract: Recent evidence has demonstrated that the intrinsically disordered regions of signaling molecules can be more than just flexible linkers of functional domains, but rather confer non-linear functionality themselves. As a specific example, the T Cell Receptor zeta chain has been suggested to dynamically dissociate from the membrane upon receptor triggering, allowing it to become further phosphorylated. This implies a delicate balance: For membrane dissociation to have a substantial impact, the membrane must significantly occlude tyrosines from kinases, but not so much that initial triggering is inhibited. We present a general model of a multi-site disordered signaling molecule in simplified, theta-solvent, freely-jointed chain dynamics. We use this model to study the zeta chain association with the membrane. We find that for a wide range of molecular properties, the zeta-chain can be membrane-associated yet still accessible to kinases, and accessibility is dramatically increased upon phosphorylation. This leads to cooperativity of phosphorylation that allows membrane-association to serve as an effective binary switch in the signal transduction cascade. Surprisingly, we find that cooperativity persists even if phosphatases, and thus dephosphorylation, are assumed to operate with identical molecular features as the kinases. Our work adds to a growing body of research suggesting that disordered regions themselves may act as modules in signal transduction cascades.