Fig 1.
Radius of gyration, Rg, properties of two IDPs p53TAD and Pup from microsecond MD simulations.
Time-dependence of Rg(t) from representative 1-μs MD trajectories (cyan) of (A) p53TAD and (B) Pup where the horizontal blue lines correspond to the mean Rg values calculated from the trajectories and the black lines correspond to the experimentally determined Rg for p53TAD and the predicted Rg according to polymer theory (Eq 6) for Pup. Rg profiles for all 10 1-μs trajectories of each protein are shown in S1 Fig. Histograms of the Rg(t) distributions over all 10 MD simulations are shown in Panels C, D (blue and black lines have the same meaning as in Panels A, B). The standard deviation of Rg over all 10 MD trajectories is 5.4 Å for p53TAD and 5.0 Å for Pup. Offset-free time-correlation functions CRg(t) of Rg(t) averaged over all 10 1-μs MD trajectories are shown for (E) p53TAD and (F) Pup. The dashed lines belong to non-linear least squares fits of CRg(t) by biexponential functions whereby the best fits are obtained for p53TAD with τa = 12 ns (63% of total amplitude), τb = 62 ns (37%) and for Pup with τa = 8 ns (29%), τb = 48 ns (71%).
Fig 2.
Gyration tensor properties of IDP ensembles of p53TAD and Pup across 10 1-μs MD trajectories.
The distributions of gyration tensor asphericities A are shown for (A) p53TAD and (B) Pup in comparison with a (C) Gaussian chain. The distributions of gyration tensor prolateness P are shown for (D) p53TAD and (E) Pup in comparison with a (F) Gaussian chain.
Fig 3.
Back-calculated R1, R2 NMR 15N-spin relaxation rates in comparison with experiment along with underlying motional time-scale distributions.
R1, R2 rates calculated from average correlation functions are plotted in blue with error bars representing standard deviations across individual MD trajectories. Correlation time distribution of individual 15N-1H bonds of IDPs extracted from correlation functions for (E) p53TAD and (F) Pup where the sizes of the blue squares are proportional to the associated motional amplitudes Ai. The squares at the bottom indicate the aggregate of dynamics contributions with correlation times faster than 100 ps. Dominant dynamics time scales range from about 100 ps to about 10 ns depending on the residue, with the exception of Thr12 in Pup which exhibits dominant dynamics time scales faster than 100 ps.
Fig 4.
Average IDP contact maps and time-dependent secondary structure formation of each residue.
(A, B) Pairwise contact occupancies were determined from MD simulations (without outlier trajectories, S2 Fig, S4 and S5 Tables) for (A) p53TAD and (B) Pup. Darker/lighter shades of blue denote contacts that are more frequently/rarely formed according to legend (vertical bar). Self-contacts, first-neighbor contacts (between residues i,i+1), and second-neighbor contacts (between residues i,i+2) are not shown since they are present in most snapshots. (C, D) secondary structure of each residue in MD simulations are predicted using the DSSP algorithm with α-helices shown in red and β-strands in blue. (E, F) In the residue clusters at the bottom, pairwise contacts with occupancies > 0.2 are depicted as an edge connecting two nodes (residues) with edge widths proportional to the pairwise contact occupancies. Labels A1–A5 denote dominant clusters in p53TAD and B1–B8 in Pup. Examples of transiently formed subclusters are indicated by dashed lines (A1.1, A1.2, and A1.3 in p53TAD and B1.1 and B1.2 in Pup).
Fig 5.
Number of close contacts formed by each residue during MD simulations of p53TAD and Pup (without outliers) along with average residue-type specific contact propensities.
For each residue, the number of contacts was normalized by the number of snapshots for (A) p53TAD and (B) Pup. Residues with their number of contacts per snapshot below 0.5 are depicted in blue, 0.5–1.5 in black, 1.5–2 in yellow, and above 2 in red. Primary sequences of p53TAD and Pup are given at the bottom and colored as in Panels A, B. Average contact propensities according to amino-acid residue type, which is the number of contacts per snapshot averaged over all residues of the same type, are shown for (C) p53TAD and (D) Pup. Error bars correspond to the standard deviations among different residues of the same type.
Fig 6.
Graph theoretical analysis of inter-residual interactions and transient interaction networks of p53TAD and Pup.
(A) Clusters consisting of 2 nodes (residues) dominate in the MD structures of p53TAD and Pup (without outlier trajectories), followed by clusters of size 3, etc. (B) The majority of the unique clusters are sparse graphs, with their number of edges much smaller than the number of edges in complete graphs growing with N(N-1)/2 where N is the number of nodes. The average edge-to-node ratio is 1.54 (slope indicated by solid black line), indicating predominantly tree-like graphs that sometimes have a few additional edges (cross-linked branches).