Extended Data Fig. 10: Mean square displacement (MSD) curves from molecular dynamics simualtions simulations reveal subdiffusion.
a. Center-of-mass diffusion of ProTα in the dense phase (purple, average of 96 chains) compared to ProTα in the ProTα–H1 dimer (grey, average of 6 chains). In the dimer, at all timescales investigated, the diffusion of ProTα is Brownian, whereas in the dense phase, we observe subdiffusive behavior at timescales equal to or shorter than the chain reconfiguration time (shaded bands indicate full-length chain reconfiguration time ± uncertainty), as expected in the presence of cooperative dynamics of the network48 (MSDs are only shown for the time range where the standard deviation σMSD < 0.5·MSD). b,c. Comparison between the diffusion of residue 1 of ProTα, of the central residue 58, and of the ProTα center of mass in the dimer (b) and the dense phase (c). The residues of an ideal chain are expected to show subdiffusive behavior in a time window between tKuhn, the time a residue needs to diffuse over the Kuhn length of the chain, and the time the entire chain takes to diffuse a distance corresponding to its own size112, which, for a Rouse chain113, approximately corresponds to the chain reconfiguration time, τr. Below tKuhn, the individual residues are expected to diffuse independently of the chain. Building on the ideal chain model, in (f) we report the diffusion exponent for times below 2 ns (approximately tKuhn), where the single-residue behavior is largely unaffected by the slowdown due to chain reconfiguration. d,e. Same data as in (b,c), but in linear scale to highlight the transition at timescales >τr, where the diffusion of the entire chain dominates the diffusion of the individual residues. The yellow and orange vertical lines indicate the MSD travelled by the residue in excess of the MSD of the center of mass of the chain. Dashed lines indicate the slope expected for Brownian dynamics. f. Diffusion of individual ProTα residues (1–112) is examined in terms of their mean squared displacement, MSD(t) = 6Dtα, for timescales shorter than tKuhn (see b,c), where D is the diffusion coefficient, t is the lag time, and α = 1 for Brownian diffusion. Diffusion of the residues in the ProTα–H1 dimer is close to Brownian and does not correlate with the average contact lifetime of the corresponding residues, whereas in the dense phase, the diffusion of the residues is more subdiffusive (α < 1) and shows a negative correlation with their average contact lifetime. The residues in the dense phase with low average contact lifetime show less subdiffusive behavior but form a larger number of contacts per unit time (compare with Fig. 3g).
