Discrete protein dynamics enable long-range communication

Allostery, in which perturbations at an input protein site tune the activity at a distant output site, allows proteins to serve as molecular logic gates. Often, information is transmitted without altering the structure outside of the input and output sites. This focalized allostery requires correlated motion between protein backbone dihedral angles that are separated by distances many times longer than the scale of electrostatic interactions. What physical properties of folded proteins enable such long-distance information sharing despite thermal noise is unclear. To address this question, we introduce a Variable-Well Dihedral (VWD) model Hamiltonian which removes dependence on chemical details and forces, instead only tuning the degree of nonlinearity of purely local interactions within a densely-packed polymer. We show that tuning the physical parameters of the model gives rise to focalized allostery in so far that doing so increases the discreteness of the internal degrees of freedom, with real proteins occupying the highly discrete regime. These results parallel, at the molecular scale, the superiority of digital compared to analog signal processing for telecommuncations under noisy conditions.