Dynamics of allosteric transitions in GroEL

Abstract

The chaperonin GroEL-GroES, a machine that helps proteins to fold, cycles through a number of allosteric states, the T state, with high affinity for substrate proteins, the ATP-bound R state, and the R" (GroEL-ADP-GroES) complex. Here, we use a self-organized polymer model for the GroEL allosteric states and a general structure-based technique to simulate the dynamics of allosteric transitions in two subunits of GroEL and the heptamer. The T --> R transition, in which the apical domains undergo counterclockwise motion, is mediated by a multiple salt-bridge switch mechanism, in which a series of salt-bridges break and form. The initial event in the R -->R" transition, during which GroEL rotates clockwise, involves a spectacular outside-in movement of helices K and L that results in K80-D359 salt-bridge formation. In both the transitions there is considerable heterogeneity in the transition pathways. The transition state ensembles (TSEs) connecting the T, R, and R" states are broad with the TSE for the T --> R transition being more plastic than the R --> R" TSE.

Fig. 1.

GroEL structure. From left to right, T, R, and R″ structures of GroEL structures are shown. The top view is given in Upper (for a side view, see Fig. 7, which is published as supporting information on the PNAS web site), and Lower displays the side view of a single subunit. The white ball represents D359. The helices that most directly influence the allosteric transitions are labeled.

Fig. 2.

GroEL dynamics monitored using various angles. (A) T → R transition dynamics for the heptamer monitored using angles α, β, and γ. An angle θ (= α, β) is defined by cosθ(t) = u⃗_θ(0)·u⃗_θ(t)/|u⃗_θ(0)||u⃗_θ(t)|. For α, we obtain u⃗_α(t) by projecting the vector (r⃗_236(i)(t) = R⃗_236(i)(t) − R⃗_CM) between the center of mass (R⃗_CM) and residue 236 on ith subunit [R⃗_236(i)(t)] onto the plane perpendicular to the principal axis (ê_P) of the heptamer, i.e., u⃗_α(t) = r⃗_236(i)(t) − (r⃗_236(i)(t)·e⃗_P)e⃗_P. The angle between H helices (residue 231–242) of ith subunit at times t = 0 and t using the vector, R⃗_231(i)(t) − R⃗_242(i)(t) is β. The sign of the angles (α and β) is determined using sgn[(u⃗(0) × u⃗(t))·ê_P], which is (+) for counterclockwise and (−) for clockwise rotation. γ measures the perpendicular motion of apical domain with respect to the hinge (residue 377). We defined u⃗_γ(t) = R⃗_236(i)(t) − R⃗_377(i)(t) at each subunit i, and γ(t) = 90° − cos⁻¹(u⃗_γ·ê_P). In A Right we plot the time dependence of α, β, and γ for each subunit in different color. The black line represents the average of 21 (= 3 × 7) values of each angle calculated from three trajectories of 7 subunits. (B) Same as in A except for the R → R″ transition.

Fig. 3.

RMSD as a function of time. (A) Time-dependence of RMSD of a few individual molecules are shown for T → R transition. Solid (dashed) lines are for RMSD/T (RMSD/R) [RMSD calculated with respect to the T (R) state]. The enlarged inset gives an example of a trajectory, in blue, that exhibits multiple passages across the transition region. (B) Ensemble averages of the RMSD for the T → R (Left) and R → R″ (Right) transitions are obtained over 50 trajectories. The solid lines are exponential fits to RMSD/R and RMSD/R″ relaxation kinetics. (C) Time-dependent changes in the angles (measured with respect to the T state) that F, M helices make during the T → R → R″ transitions. Inset shows the dispersion of individual trajectories for F-helix with the black line being the average. (D) Time-dependent changes in the angles (measured with respect to the T state) that K, L helices make during the T → R → R″ transitions. Upper Inset shows the structural changes in K, L helices during the T → R → R″ transitions. For clarity, residues 357–360 are displayed in space-filling representation in white. Lower Inset shows the dispersion of individual trajectories for the K-helix. The black line is the average. In C and D, θ = cos⁻¹(u⃗(0)·u⃗(t)).

Fig. 4.

T → R GroEL dynamics monitored using of two interacting subunits. Side views from outside to the center of the GroEL ring and top views are presented for the T (Left) and R (Right) states. Few residue pairs are annotated and connected with dotted lines. The ensemble average kinetics of a number of salt-bridges and contacts between few other residues are shown in Center. Distance changes for a single trajectory for few residues are given in Fig. 10, which is published as supporting information on the PNAS web site. Fits of the relaxation kinetics are: 〈d(t)〉_R58-E209/Å = 14.9 + 9.6(1 − 0.17e^−t/5.1μs − 0.83e^−t/825μs), 〈d(t)〉_D83-K327/Å = 8.5 + 4.9(1 − e^{−t/100.0μs}), 〈d(t)〉_P33-N153/Å = 7.3 + 4.2e^−t/6.3μs, 〈d(t)〉_R284-E386/Å = 13.2 + 16.5(1 − 0.49e^−t/20.8μs − 0.51e^−t/85.8μs), 〈d(t)〉_R285-E386/Å = 12.6 + 15.8(1 − 0.42e^−t/19.1μs − 0.51e^−t/88.8μs), 〈d(t)〉_R197-E386/Å = 11.9 + 9.0(1 − 0.29e^−t/0.67μs − 0.71e^−t/96.7μs), 〈d(t)〉_K80-E386/Å = 10.4 + 9.8(0.78e^−t/12.1μs + 0.22e^−t/61.8μs), 〈d(t)〉_E257-R268/Å = 9.7 + 12.1(1 − 0.35e^−t/26.2μs − 0.65e^−t/66.4μs). Initially, the dynamics of salt-bridge formation between E257 and K321, R322, K245 show nonmonotonic behavior. Thus, we did not perform a detailed kinetic analysis for these residues.

Fig. 5.

Dynamics of the R → R″ transition using two-subunit self-organized polymer model simulations. The dynamics along one trajectory are shown in Fig. 10. Intrasubunit salt-bridges (or residue pairs) of interest (D83-K327, E409-R501, and P33-N153) are plotted in Center Upper, and intersubunit salt-bridges (or residue pairs) of interest (E257-K246, E257-R268, E257-K321, E257-R322, and I305-A260) are plotted in Center Lower. For emphasis, K80-D359 salt-bridge dynamics, which provides a driving force to other residue dynamics, is specially plotted in Center Lower. The quantitative kinetic analysis performed for rupture of D83-K327 and formation of K80-E359 salt-bridges show 〈d(t)〉_D83-K327/Å = 10.4 + 26.9(1 − e^−t/77.9μs), 〈d(t)〉_K80-D359/Å = 14.1 + 26.4e^−t/28.0μs.

Fig. 6.

TSEs. (A) TSEs are represented in terms of distributions P(q^‡), where q^‡ ≡ Δ^‡ − min(RMSD/X)/max(RMSD/X) − min(RMSD/X). Histogram in red gives P(q^‡) for T → R (red) and the data in green are for the R → R″ transitions. For T → R, X = R, min(RMSD/X) = 1.5 Å, and max(RMSD/X) = 8.0 Å. For R → R″, X = R″, min(RMSD/X) = 1.5 Å, and max(RMSD/X) = 14.0 Å. To satisfy conservation of the number of molecules the distributions are normalized by using ∫dq^‡[P(q^‡|T → R) + P(q^‡|R → R″)] = 1. Twenty overlapped TSE structures for the two transitions are displayed. (Lower) Distributions of t_TS that satisfy δ^‡ < 0.2 Å plotted for the T [arrow] R and the R → R″ transitions. (B) For the T → R TSE we show the salt-bridge distances (d_TS^R197-E386, d_TS^K80-E386) with black dots. The red and the green dots are the equilibrium distances (〈d_TS^R197-E386〉, 〈d_TS^K80-E386〉) in the T and the R states, respectively. The distance distributions for the TSE are shown in blue.