Universal Scaling Law for Polypeptide Backbone Dynamics on the Pico- to Millisecond Time Scale

UV-photolysis of an aromatic disulfide bond which holds a protein or peptide in a non-native conformation has been used to trigger polypeptide backbone relaxation. Geminate recombination of the disulfide bond was used as probe for non-equilibrium backbone dynamics; as the thiyl radicals separate under the influence of backbone motion, their recombination rate decreases, so that observation of the transient thiyl absorbance provides access to backbone dynamics. Unlike fluorescence or triplet quenching experiments, which often are used for the study of polypeptide dynamics, this method observes processes far from equilibrium, and has no intrinsic limitation of the accessible time scale.The encounter probability of the thiyl radicals was found to decay with time following a power law t-0.94 which is incompatible with simple diffusion. Thus, the relative motion of the radicals is affected by the dynamics of the connecting backbone, resulting in an unusual power law for the re-encounter probability which could be described as (fractal) diffusion in a reduced non-integer dimensional space. The scaling law was found to extend over the full experimental time window, covering nine orders of magnitude in time (1 ps to 1 ms), although very different processes govern backbone motion on these different time scales. Furthermore, the same scaling law was observed in a folding protein having secondary and tertiary structure, in simple model peptides forming only secondary structure, and in a protein under unfolding conditions, indicating an intrinsic behaviour of the polypeptide backbone itself.