Coherent conformational degrees of freedom as a structural basis for allosteric communication

Abstract

Conformational changes in allosteric regulation can to a large extent be described as motion along one or a few coherent degrees of freedom. The states involved are inherent to the protein, in the sense that they are visited by the protein also in the absence of effector ligands. Previously, we developed the measure binding leverage to find sites where ligand binding can shift the conformational equilibrium of a protein. Binding leverage is calculated for a set of motion vectors representing independent conformational degrees of freedom. In this paper, to analyze allosteric communication between binding sites, we introduce the concept of leverage coupling, based on the assumption that only pairs of sites that couple to the same conformational degrees of freedom can be allosterically connected. We demonstrate how leverage coupling can be used to analyze allosteric communication in a range of enzymes (regulated by both ligand binding and post-translational modifications) and huge molecular machines such as chaperones. Leverage coupling can be calculated for any protein structure to analyze both biological and latent catalytic and regulatory sites.

Figure 1. Illustration of the concept of sites communicating through leverage coupling.

Figure 2. Leverage profile properties.

(A) The matrix measuring similarity between leverage profiles for different normal modes μ and ν, for 4 of the proteins studied. The magnitude of the leverage profiles are also plotted to indicate which are the most important modes. (B) The total leverage profile and the three most important individual leverage profiles for AdK (Λ ₁, Λ ₂, and Λ ₃). The average total binding leverage for the residues at the active site are indicated by black circles.

Figure 3. D_PQ and C_PQ matrices for PFK.

The single mode matrices for PFK were calculated like D_PQ but only using one normal mode. The color runs from 0 (cyan) to the maximal measured value (white) for D_PQ and from 0 to 1 for C_PQ.

Figure 4. Phosphofructokinase (PFK).

All 3D structures in this paper were drawn with PyMol. (A) Structure of PFK (PDB entry 3pfk). The effector ADP is drawn with orange spheres, and the substrate F6P with yellow spheres, ligand coordinates were taken from PBD entry 4pfk. (B) Leverage coupling D_Pi between ADP site of one chain (lower right ADP) and the rest of the protein. The surface is colored in a gradient from cyan to magenta where cyan represents the lowest measured value of D_Pi and magenta the highest value. (C) Same as (B) but for one of the F6P sites (lower right one).

Figure 5. GTP cyclohydrolase I (GTPCHI) with feedback regulatory protein (GFRP).

(A) Top: the matrix D_PQ for the whole protein. Bottom left: selected sections of the top matrix. Bottom right: same section as left panel, but calculated for structure without GFRP. (B) Structure (1wpl). The GTPCHI decamer is drawn in cyan, and the two GFRP pentamers in white. The inhibitor BH₂ is drawn with orange spheres and the Zn at the catalytic site in yellow. (C) Communication D_Pi between one BH₂-site and the rest of the protein. The color scheme is the same as in Figure 4. (D) Communication between one of the active sites and the rest of the protein. (E) Same as (D) but normal modes and docking calculations were done without GFRP.

Figure 6. Glycogen phosphorylase (GP).

(A) D_PQ matrix with AMP and PLP sites, plus the locations for the segment 1–20 in GPb (P1) and GPa (P2). (B) Structure of GPa (1gpa). The segment 1–20 that moves upon phosphorylation of Ser14 is green in the GPb form and red in the GPa form. The slightly hidden coenzyme PLP and the substrate GLS are drawn as yellow spheres. (C) and (D) Two views of the coupling D_Pi between active site and the rest of the protein. The color scheme for D_Pi is the same as in Figure 4.

Figure 7. Chaperones GroEL-GroES and CCT.

(A) Left: Structure of GroEL-GroES colored by the different domains (PDB entry 1sx4). Middle and right: surface and cross-section of GroEL-GroES displaying coupling between one ATP site and the rest of the protein D_Pi. ADP molecules are displayed as orange spheres throughout. The ATP site used for the calculation is the second one from the left in the present view of the cis ring (B) Left: Structure of CCT chaperone (PDB entry 3p9d) with subdomains and ligands colored analogously to GroEL-GroES. Middle and right: D_Pi for the second ATP site from the left in the upper ring. The color scheme for D_Pi is the same as in Figure 4.

Figure 8. Site-site communication in chaperons.

(A) Matrices D_PQ and C_PQ for GroEL-GroES complex. Equatorial, intermediate and apical domains are marked CE, CI, CA and TE, TI, TA for the cis and trans rings respectively. (B) Similar to (A) but for CCT. All 16 subunits have been divided into three subdomains, but there were only 13 ATP analogs bound to the crystal structure.