On side-chain conformational entropy of proteins

Abstract

The role of side-chain entropy (SCE) in protein folding has long been speculated about but is still not fully understood. Utilizing a newly developed Monte Carlo method, we conducted a systematic investigation of how the SCE relates to the size of the protein and how it differs among a protein's X-ray, NMR, and decoy structures. We estimated the SCE for a set of 675 nonhomologous proteins, and observed that there is a significant SCE for both exposed and buried residues for all these proteins-the contribution of buried residues approaches approximately 40% of the overall SCE. Furthermore, the SCE can be quite different for structures with similar compactness or even similar conformations. As a striking example, we found that proteins' X-ray structures appear to pack more "cleverly" than their NMR or decoy counterparts in the sense of retaining higher SCE while achieving comparable compactness, which suggests that the SCE plays an important role in favouring native protein structures. By including a SCE term in a simple free energy function, we can significantly improve the discrimination of native protein structures from decoys.

Figure 1. Side-Chain Entropy (SCE), S_sc, of 675 Nonhomologous Proteins in the PDB

(A) Side-chain entropy versus chain length. Two results with α = 0.6 (red crosses) and 0.8 (green circles) are shown. (B) Percentage of SCE contributed by buried residues versus chain length.

Figure 2. SCE of Native and Decoy Structures

(A) SCE (S_sc) versus the radius of gyration (R_g). (B) SCE (S_sc) versus the number of residue contacts (N_c), for protein 1ctf and its decoys from the 4state_reduced decoy set. (C) SCE (S_sc) versus the number of interfacial contacts for protein–protein complex 1spb and its decoys. (D) SCE (S_sc) versus the number of interfacial contacts for protein–protein complex 1brc and its decoys. The black dot is the native structure, blue triangles (<2.0 Å RMSD to the native structure) and green circles (>2.0 Å) are decoy structures. The SCE of protein complexes are calculated using α = 0.7 (see Methods).

Figure 3. SCE of NMR and X-Ray Structures

(A) Box plot for distributions of the absolute pairwise SCE difference (|ΔS_N|) of NMR structures of 23 proteins. Different coloured boxes indicate different ranges of average RMSDs of the structure pairs. (B) Box plot for distributions of the SCE difference between X-ray and NMR structures (ΔS_XN) for 23 proteins. Different colours indicate different ranges of average RMSDs of the X-ray and NMR structure pairs. For proteins 1btv, 1vre, and 1ah2, α = 0.7 was used for both X-ray and NMR structures.

Figure 4. SCE of NMR and X-Ray Structures versus Rg

Average SCE difference between X-ray and NMR structures (ΔS_XN) versus the average difference of radius of gyration between X-ray and NMR backbones (ΔR_g) for the 23 proteins. ×, proteins whose X-ray structures have much higher SCE than but similar R_g to the corresponding NMR structures. Δ, proteins whose X-ray structures gain considerable SCE by packing a little looser. ○, proteins whose X-ray structures pack tighter than NMR structures but with comparable SCE. +, small proteins of which both ΔR_g and ΔS_XN are small.

Figure 5. Performance of the Sequential Monte Carlo Method

(A) Comparison of the SMC estimation with exhaustive enumeration for fragments of proteins 2ovo and 3ebx. (B) Standard deviation of the SMC estimation for four different sample sizes, 100, 500, 1,000, and 2,000, respectively, calculated from 20 independent SMC runs. The first number in each parentheses pair is the number of residues of the protein, and the second number the average SCE of 20 runs with 1,000 samples in each run.