Allosteric communication occurs via networks of tertiary and quaternary motions in proteins

Abstract

Allosteric proteins bind an effector molecule at one site resulting in a functional change at a second site. We hypothesize that allosteric communication in proteins relies upon networks of quaternary (collective, rigid-body) and tertiary (residue-residue contact) motions. We argue that cyclic topology of these networks is necessary for allosteric communication. An automated algorithm identifies rigid bodies from the displacement between the inactive and the active structures and constructs "quaternary networks" from these rigid bodies and the substrate and effector ligands. We then integrate quaternary networks with a coarse-grained representation of contact rearrangements to form "global communication networks" (GCNs). The GCN reveals allosteric communication among all substrate and effector sites in 15 of 18 multidomain and multimeric proteins, while tertiary and quaternary networks exhibit such communication in only 4 and 3 of these proteins, respectively. Furthermore, in 7 of the 15 proteins connected by the GCN, 50% or more of the substrate-effector paths via the GCN are "interdependent" paths that do not exist via either the tertiary or the quaternary network. Substrate-effector "pathways" typically are not linear but rather consist of polycyclic networks of rigid bodies and clusters of rearranging residue contacts. These results argue for broad applicability of allosteric communication based on structural changes and demonstrate the utility of the GCN. Global communication networks may inform a variety of experiments on allosteric proteins as well as the design of allostery into non-allosteric proteins.

Figure 1. Allosteric coupling via quaternary motions.

In this sample graph, circular nodes represent “rigid body” groups of residues that move collectively, and rectangular nodes represent ligands. Circular node area is proportional to physical size in number of residues. Edges represent motions between physically contacting rigid bodies. A grey dashed line marks the boundary of the allosteric unit.

Figure 2. Rigid-body partitioning and quaternary network in phosphofructokinase (PFK).

(A) The active state structure (4PFK) colored by identified rigid bodies, except red, which marks flexible segments. (B) Quaternary network representation of the quaternary nodes (rigid bodies and flexible segments) shown in (A). Circular nodes represent rigid bodies and hexagonal nodes represent flexible segments. Areas of protein nodes correspond to their physical sizes in number of residues, and their colors correspond to the colors of the rigid bodies in (A). Each rigid body is labeled by the chains and domains it contains, e.g. the rigid body labeled “A1+B1” contains the largest portion of chain A and the largest portion of chain B, the rigid body labeled “D2” contains the second-largest portion of chain D, etc. Each flexible segment is labeled by its chain identifier followed by its range of residue numbers. Substrate and effector “sites” are shown as rectangles and diamonds, respectively. Each substrate (effector) site represents all the substrate (effector) molecules from a given chain in either the inactive or the active state. An edge indicates a quaternary interface, that is, two or more atomic (4.0 Å) contacts between a pair of quaternary nodes, or two or more atomic contacts between a quaternary node and a ligand. An edge between two rigid bodies is labeled by the rotation in degrees (see methods for rotation calculations), provided the smaller rigid body is ten residues or larger. A grey dashed line marks the boundary of the main allosteric unit of the graph. Graphs drawn by yEd graph editor (http://www.yworks.com).

Figure 3. Relationship of tertiary and quaternary communication in PFK.

(A) Contact rearrangement network (CRN) of phosphofructokinase. As described previously , nodes are protein residues (circles), effector sites (diamonds), and substrate sites (squares), and edges are contact rearrangements between protein residues and protein-ligand site contacts. Two of four symmetry-related contact rearrangement clusters are shown for clarity. Each protein residue is colored according to the color in Figure 2B of the quaternary node to which that residue belongs. (B) Quaternary network of Figure 2B, with each edge colored according to the CRN cluster (if any) to which the corresponding quaternary interface contributes. A red edge indicates that a quaternary interface contributes to more than one CRN cluster. A quaternary interface contributes to a CRN cluster if the CRN cluster contains two or more contact rearrangements that cross the quaternary interface.

Figure 4. Global communication networks in three proteins.

Global communication networks (GCNs) integrate tertiary (contact rearrangement) and quaternary networks. Quaternary nodes, substrate and effector sites, quaternary interfaces, and quaternary node – ligand site interactions are represented as in Figure 2 (for lac repressor (LacR), the DNA molecules are represented as substrates). Each quaternary node is mapped to its position in the three-dimensional structure of the active state (1EFA for LacR and 1PJ2 for malic enzyme) by the node's outline color (see Figure 2 for the mapping for PFK). Tertiary nodes comprising 10 or more residues or contacting a ligand site are represented as octagons with the area proportional to the number of residues; these nodes are numbered by size from largest to smallest. In addition, in lac repressor, square nodes represent segments present only in the active state structure. Modifications to both tertiary and quaternary node areas have been made to account for the participation of some residues in both tertiary and quaternary nodes. Quaternary node-tertiary node edges indicate intersections (shared residues) between these two types of nodes, and an edge between a tertiary node and a ligand site indicates that the ligand site participates in the CRN cluster corresponding to the tertiary node. Furthermore, for malic enzyme, grey dashed lines mark the allosteric unit boundaries (for both PFK and lac repressor, the entire protein is the allosteric unit). Finally, the density of dashing of a quaternary edge is proportional to the interfacial contact rearrangement f _CR. Solid: f _CR<10% (conserved interface); dashed: 10%≤f _CR≤50% (moderately rearranged); dotted: f _CR>50% (extensively rearranged). See the methods for the full details of the GCN representation and associated calculations. Graphs drawn by yEd graph editor. Specific residues comprised by each quaternary node are available in Dataset S1.

Figure 5. Proposed individual substrate-effector “pathways” in the PFK GCN.

The complete GCN of PFK is shown in Figure 4. We define a “pathway” between a substrate and an effector site in the GCN as the shortest loop containing them, plus any cross-interactions among members of that loop. If two or more loops are tied for the shortest, the union of all such loops constitutes the pathway. This pathway is the smallest (by number of nodes) subset of the GCN required to form an allosteric unit containing the two sites. Four symmetrically unique paths emanating from the effector site of chain A are shown.

Figure 6. Statistics of quaternary nodes and rigid-body motions in global communication networks.

(A) Rigid-body size versus protein size (number of residues) for all rigid bodies in the global communication networks (GCNs) of all proteins in the allosteric benchmark set . A point at (2800, 1200) is excluded for clarity. (B) histogram of rotation angle for all edges between all rigid bodies in these GCNs. (C) histogram of interfacial contact rearrangement f _CR for all edges between rigid bodies in these GCNs. For constructing the histograms in (B) and (C), each edge in each GCN is weighted by the inverse of the number of asymmetric units in the protein to normalize for multiple symmetry-related motions in some oligomers. Bin labels refer to the upper bound of the bin. Only edges between rigid bodies both of which comprise 30 or more residues are included in the histograms.

Figure 7. Elucidating quaternary motion network from two protein structures.