Fig 1.
The critical dynamics of proteins are robustly encoded in the native structure.
(A) An illustration of the elastic network model (rC = 9Å) of the protein CI2 (PDB code: 2CI2). The beads denote the residues, and the bonds denote the elastic springs in the model. (B) The correlation functions ϕ(r) for proteins at different sizes predicted by GNM with cutoff distance rC = 9Å. (C) Correlation functions scaled by the radius of gyration of the proteins Rg. (D) For proteins of similar sizes (19.5Å ≤ Rg < 20.5Å), with different cutoff distances rC, the correlation functions ϕ(r) predicted by GNM. (E) With different cutoff distances, for proteins of different sizes, the correlation length ξ is always proportional to the size of the protein Rg. (F) The susceptibility χ vs. chain length N shows the power-law relation: χ ∼ Nαγ/ν, and the scaling coefficient αγ/ν ≈ 1 can be kept with different rC (inset).
Fig 2.
The slow modes of proteins are robustly defined by native structure.
(A) The 1st, 2nd and the 3rd non-zero eigenvalues λ1, λ2, and λ3 vs. the chain length N of the proteins follows a power-law distribution. (Cutoff distance rC = 9Å, and the scaling coefficients of λ1(N), λ2(N), and λ3(N) are 1.074, 0.900, and 0.868, respectively). As comparison, similar scaling relations in lattices and ideal polymer chains are also illustrated, and the scaling coefficients are 0.728 (lattices) and 1.674 (polymer). (B) The eigenvalue of the slowest nonzero mode λ1 versus chain length N shows the scaling relation: λ1 ∼ N−ζ, and the inset shows scaling coefficient ζ vs. the cutoff distance rC. (C) For proteins at similar sizes (chain length 180 ≤ N < 220), the histogram for the eigenvalue distribution g(λ).
Fig 3.
The protein dynamics can be quantified by topological descriptors of the residue contact network.
(A) For the contact network of proteins (rC = 8Å), fcc lattices and ideal polymers, the average path length 〈l〉 vs. system size N. (B) Similarly for proteins, fcc lattice and ideal polymers, modulaity Q vs. system size N. The inset shows the log-log plot of 1 − Q vs. N. (C) For proteins at similar sizes (180 ≤ N < 220), the scattering plot (yellow dots, each dot represents a protein molecule), the binned average (red dots) and the basic trend (red curve) of the average path length 〈l〉 vs. Q, and (D) Smallest non-zero eigenvalue λ1 vs. Q.
Fig 4.
The shape factor correlates with the chain lengths of the proteins.
(A) Three proteins with similar chain lengths: (Left) The receptor-binding domain of T4 STF (PDB: 1OCY, s = 0.84, Q = 0.74); (Middle) Human Hsp90 protein (PDB: 3T0H, s = 1.77, Q = 0.65); and (Right) The DHR10 protein (PDB: 5CWG, s = 2.37, Q = 0.63). (B) For proteins at similar sizes (chain length 180 ≤ N < 220), the scattering plot (yellow dots), binned average (red dots) and the trend line (red line) of shape factor s vs. modularity Q are plotted. Besides, there are histograms of the shape factor s (right vertical) and modularity Q (top horizontal). (C) For all the proteins in our dataset, the 2D histogram (in the background) of s vs. N and the plot (in navy blue) of the most-probable shape factor s* vs. chain length N.