Kinetic coherence underlies the dynamics of disordered proteins

The dynamics of two proteins of similar size, the globular lysozyme and the intrinsically disordered Huntingtin interacting protein, has been simulated in three states resembling a globule, a pre-molten globule, and a molten globule. A coherence time τ has been defined, measuring the delay in the display of a stochastic behaviour after a perturbation of the system. This time has been computed for two sets of collective variables: the projection of the phase point onto the positions and momenta subspaces (τ_r and τ_p), and the principal components (PCs) of positions q and momenta π produced by a covariance analysis in these subspaces (τ_q and τ_π). In all states τ_p ≈ 3.5τ_r, and τ_π ≈ 3.5τ_q. The coherence times of individual PCs, τ^(l)_q and τ^(l)_π, have also been computed, and τ^(l)_π > τ^(l)_q in all states. The prevalence of τ_p over τ_r, or of τ_π over τ_q, drives the dynamics of the protein over a time range of ≈1-2 ps; moreover, a hidden synchronism appears to raise the momenta subspace's coherence above that of its individual PCs. In the transition of lysozyme to the molten globule the τ^(l)_q decrease but, unexpectedly, the τ^(l)_π increase; after this transition τ_p ≈ 5τ_r and τ_π ≈ 5τ_q. A gain of kinetic coherence accompanies thus the loss of structural coherence caused by the denaturation of the protein in the transition from globule to molten globule. The increase of the τ^(l)_π does not take place in the analogous transition of the Huntingtin protein. These results are compared with those of a similar analysis performed on three pseudo-proteins designed by scrambling the primary sequence of the Huntingtin interacting protein, and on two oligopeptides. The hidden synchronism appears to be a generic property of these polypeptides. The τ^(l)_π spectrum is similar in denaturated and in intrinsically disordered biomolecules; but the gain of kinetic coherence as a result of denaturation seems to be a specific property of the biologically functional lysozyme.