Figure 1.
GroEL consists of two rings, cis and trans, which assume the states: T: ATP-free; R: ATP-bound prior to substrate (peptide) and co-chaperonin (GroES) binding; R′: ATP-, substrate- and GroES-bound; R″: ADP-, substrate- and GroES-bound. Subunits in the T state are shown in red, R in cyan; R′ in green, R″ in blue, and the cap in purple. ATP and ADP are shown by blue and orange boxes. Successive events/reactions along the cycle are (A) binding of seven ATPs to induce the binding of the unfolded substrate (orange), (B) co-chaperonin binding, (C) ATP hydrolysis, (D) ATP binding to trans ring subunits, (E) release of ADPs, substrate (folded or partially folded) and GroES from the cis ring, (F) initiation of a new cycle where the roles of the cis and trans rings are inverted. Top-middle and bottom-left structures are related by rigid body rotation. Diagrams were generated using the data from the PDB in PyMOL (http://www.pymol.org), except for the schematic views of the substrate and ligands included to provide a clearer description. The PDB ids for the structures T/T, R/T, R″/R, R′/T and R″/T are 1GR5, 2C7E and 1GRU [68], 2C7C [15] and 1AON [20], respectively.
Figure 2.
Schematic description of aANM method.
Two sets of intermediate conformations are generated, and
(1≤k≤ktot), starting from the known substates
and
, illustrated here for k = 1 and 2. The distance vector between the instantaneous endpoints at the kth step is denoted as
, and the deformation at each step is
or
. Dashed ellipses indicate isoenergetic contours.
Figure 3.
Correlation cosine between instantaneous distance vector and eigenmodes.
Results are illustrated for aANM steps k = 1, 7 and 13 along the transition R″→T of a single subunit (subunit A in the respective PDB structures 1GRU and 1GR5). The left ordinate displays the correlation cosine between the distance vector d(k−1) and the eigenvectors for 1≤i≤30 (black bars), and the right ordinate shows the corresponding cumulative squared cosine (Eq. (5)) (blue curve). The threshold Fmin = 0.5 for the cumulative square cosine implies the selection of mA(1) = 1, mA(7) = 3, and mA(13) = 23 in evaluating v A (k) as indicated by the red lines and filled bars. See Table 1 for the complete list of
and
values and associated RMSDs between intermediate conformations.
Table 1.
aANM data for the transition of a GroEL subunit between R″ and T forms(*).
Table 2.
RMSD values (in Å) between (A) different forms of a subunit and (B) different states of the intact GroEL.
Table 3.
Contributions of the lowest frequency modes to the cycle T→R→R″→T (a).
Figure 4.
R″→T transition for a single subunit of GroEL.
(A) RMSD values, |d(k)| /N, between instantaneous endpoints plotted as a function of iteration number k. The end states refer to subunit A in the PDB structures 1GRU and 1GR5. Results are shown for Fmin = 0.4, 0.5, 0.6 and 0.7, corresponding to the allowable angular deviations of up to 50.8°, 45.0°, 39.2° and 33.2°, respectively, between and v A (k) (or v B (k)). (B) The energy profile for alternative pathways in arbitrary units. Note the significantly lower energy barrier compared to the interpolation (orange curve) between the endpoints. The black curve refers to the SDP trajectory. The reaction coordinate refers to the normalized projection of the instantaneous displacement on the original distance vector. (C) Series of conformations sampled along the reaction coordinate. The diagrams are colored by domains (equatorial, blue; intermediate, green; apical, red). (D) Movements of helices H, K and M sampled along the transition pathway. Three conformations are shown at decreasing transparency levels, starting from R″ (lightest color), to T (darkest).
Figure 5.
Comparison with the results from steepest descent pathway (SDP) based on action minimization.
(A) Fragmentation of the SDP pathway for the transition 1GRU←→1GR5 of a subunit into nine macrosteps, consisting each of five frames. Same color scheme is adopted in panels B and C. (B) Correlation between SDP macrosteps and ANM modes accessible to the original conformation . (C) Same as panel B, for the right portion of the trajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using the eigenvectors
generated for 1GRU_A. Note that the early macrosteps from both directions are accounted for by a few slowest ANM modes, while increasingly higher modes are being recruited as the molecule proceeds away from its original conformation, consistent with the results found by aANM (see Table 1). (D) RMSD values between the intermediate conformations sampled by the aANM and SDP methods. The aANM results refer to the trajectory Fmin = 0.5. The RMSDs between pairs of intermediates remain lower than 2.0 Å at all steps (see the color-coded scale on the right).
Table 4.
The contribution of lowest frequency modes to the three major steps of the chaperonin allosteric cycle(a).
Figure 6.
Transition among T/T→R/T→R″/R forms of the intact GroEL complex.
(A) Energy profiles of the intact GroEL complex (R/T→R″/R) along the reaction coordinate computed by aANM (blue) and Cartesian interpolation (orange) using the double-well potential given by Eq. (7). (B) Contribution of different modes at various steps (1, 6, 11 and 15) along the transition R/T→R″/R. Broader numbers of higher frequency modes are recruited as the structure approaches the energy barrier (see Table 5). (C) Top view of structures sampled along the transition. Snapshots corresponding to conformations ,
,
,
and
are shown. (D) Side view of the same structures. (E) Close-up views of pairs of adjacent subunits. The diagrams in panels C–E are color-coded according to the mobilities of residues (red: most mobile; blue: almost fixed). Note that the equatorial domains of cis ring subunits are almost fixed, while the largest motions occur at the apical domains of the same subunits.
Table 5.
aANM data for the transition of Intact GroEL complex(*).
Figure 7.
The cis ring inter-subunit interactions during the transition T→R″, based on the intact GroEL structure calculation.
(A) Intersubunit interface near the intermediate domains (green) of two adjacent subunits in the cis ring. The backbones are shown in cartoon view and colored by domains: A (orange), I (green), and E (blue). Backbone atoms of three charged residues are shown by spheres. Positively and negatively charged residues are colored blue and red, respectively. (B) The inter-subunit hydrogen bond, E386-R197, in the T state of the cis ring (1GR5). (C) During the transition to state R″/R, residue E386 in the I domain moves towards K80 (blue sphere) in the E domain of the adjacent subunit, while R197 on the A domain moves away from E386. (D) The final configuration in the R″ state of the cis ring, represented by 1GRU. Residue E386 now forms a new hydrogen bond with K80.
Figure 8.
Changes in the distances between salt-bridge forming pairs along the aANM reaction coordinate.
Results are shown for (A) T→R and (B) R→R″ transitions. See Figure S4 for the corresponding time dependences, and Table 6 for the kinetic expressions and the comparison with the results from BD simulations by Hyeon et al. [18].
Table 6.
Comparison of the kinetics of salt-bridge forming residues obtained by aANM and BD simulations(a).
Figure 9.
Evolution native contacts along the structural transition from R to R″ states.
The number of intra-subunit (panel A) and inter-subunit (panel B) native contacts that are disrupted (upper panel) and formed (lower panel) vs. the reaction coordinate. The results refer to Fmin = 0.5 for cis ring subunits along the transition from 2C7E (R/T) to 1GRU (R″/R). Each bar represents the number of native contacts formed/broken at a given aANM iteration. Note the sharp increase near the energy barrier. See Figure 10 for the corresponding critical contacts.
Figure 10.
Redistribution of inter-residue contacts at the transition from R to R″ state.
Panel (A) shows the inter-residue contacts between adjacent subunits of the cis ring, which break up during the transition. The two subunits are colored in light pink and blue. Contact pairs are represented by spheres at the Cα position, and by distinctive colors. Similarly, panel (B) shows the contacts newly formed during the transition. See Table 7 for the complete list of residue pairs shown here. The contacts involving a pair of conserved residues are labeled using the same colors as the corresponding residues.
Table 7.
Critical inter-subunit contacts broken/formed during R→R″.