Weak Intra-Ring Allosteric Communications of the Archaeal Chaperonin Thermosome Revealed by Normal Mode Analysis

Abstract

Chaperonins are molecular machines that use ATP-driven cycles to assist misfolded substrate proteins to reach the native state. During the functional cycle, these machines adopt distinct nucleotide-dependent conformational states, which reflect large-scale allosteric changes in individual subunits. Distinct allosteric kinetics has been described for the two chaperonin classes. Bacterial (group I) chaperonins, such as GroEL, undergo concerted subunit motions within each ring, whereas archaeal and eukaryotic chaperonins (group II) undergo sequential subunit motions. We study these distinct mechanisms through a comparative normal mode analysis of monomer and double-ring structures of the archaeal chaperonin thermosome and GroEL. We find that thermosome monomers of each type exhibit common low-frequency behavior of normal modes. The observed distinct higher-frequency modes are attributed to functional specialization of these subunit types. The thermosome double-ring structure has larger contribution from higher-frequency modes, as it is found in the GroEL case. We find that long-range intersubunit correlation of amino-acid pairs is weaker in the thermosome ring than in GroEL. Overall, our results indicate that distinct allosteric behavior of the two chaperonin classes originates from different wiring of individual subunits as well as of the intersubunit communications.

Introduction

Chaperonins are a family of ubiquitous double-ring shaped biological nanomachines whose function is to assist protein folding within the crowded cellular environment (1,2). To achieve this function, chaperonins undergo ATP-driven cycles in which their two rings operate out-of-phase to repetitively encapsulate misfolded substrate proteins (SPs) within the central cavity and release them into the cellular environment. According to structural and mechanistic features, chaperonins are differentiated into two classes. Group I (bacterial) chaperonins, whose most studied representative is GroEL of Escherichia coli, have seven identical subunits within each ring and, during each hemicycle, they undergo cooperative ATP-driven conformational transitions to nearly double the size of the central cavity of one ring (3–9). This spectacular conformational change is complemented by binding the co-chaperonin GroES, a single homoheptameric ring, to seal the cavity and transiently seclude the SP. Group II chaperonins, which are found in archaeal (thermosome of Thermoplasma acidophilum) and in eukaryotic (chaperonin-containing TCP-1 or CCT) species, have eight or nine subunits per ring made of two (thermosome) or eight (CCT) types of subunits (10–12). Conformational transitions in group II chaperonins are sequential and take place without assistance from a cofactor. Instead, during the encapsulation stage, access to the chaperonin cavity is blocked by a diaphragm formed by helical-protrusion structural elements of each subunit (10,13,14). Helical protrusions consist of the long extension of an apical domain helix and a flexible loop that are loosely connected within their subunit and therefore available for extensive intersubunit contacts.

Although the thermosome and GroEL have similar domain folds and both employ large-scale conformational changes of subunits to assist protein folding, kinetic studies of ATP binding indicate distinct allosteric properties of the two chaperonin classes. In GroEL, there is positive cooperativity with respect to ATP binding and hydrolysis within a ring (15,16), whereas in the thermosome and CCT such cooperativity is absent or weak (17,18). Allosteric transitions in chaperonins have been characterized by using classical models of enzyme activity. In particular, intra-ring conformational transitions induced by ATP-hydrolysis have been described by the Monod-Wyman-Changeux model (19) in the case of concerted subunit motions of group I chaperonins (20,21) and the Koshland-Némethy-Filmer model (22) in the case of sequential subunit motions of group II chaperonins (20,23). Despite advances in characterizing diverse kinetics of chaperonin allostery, it is still unclear what structural aspects of chaperonins underlie this divergent behavior.

Our aim is to understand, by using normal mode analysis (NMA), how different dynamic properties of the two chaperonin groups arise from intrinsic structural characteristics. Generally, normal mode studies identify natural vibrations of molecules in configurations that correspond to local free energy minima. A simplified description of the protein, such as one or two virtual particles per amino acid, is sufficient to obtain a detailed vibrational behavior of the system and to identify the small subset of normal modes compatible with large-scale conformational changes. Multiple studies of GroEL normal modes (24–29) have effectively probed the dynamics of allosteric transitions between different functional states. In accord with experimental observations, these normal mode approaches highlight strong intra-ring cooperativity of GroEL (24–28) and the dominant contribution of one or two normal modes for chaperonin conformational transitions (27–29).

In this study, we examine normal modes of basic units (monomers) and of the double-ring structure of thermosome. The study of the monomeric structures allows us to discern subunit-specific signatures on allosteric mechanisms of the chaperonin ring. The role of heterogeneity in the dynamics of group II chaperonins is of particular interest due to subunit specialization in recruiting SPs. Interestingly, we identify both universal (independent of subunit type) and specific features of normal modes of subunits, namely common behavior at low frequency (here, the modes with the five smallest eigenvalues) and distinct behavior at higher frequency. Comparative analysis of pairwise correlation of amino-acid motions of thermosome and GroEL constructs reveals, in accord with kinetics experiments, weaker coupling of group II chaperonin subunits.

Importantly, we find that large flexibility, particularly within the helical protrusion region, and weak long-range coordination of subunits within the thermosome ring, gives rise to multiple high-frequency modes that contribute substantially to these transitions. Modes can be described as swinglike motions, which contribute to ring-opening and closing, and torsional motions, which enable the reorientation of apical domains for substrate recognition. Allosteric signals of specific structural elements that differentiate motions of the two subunit types, such as the stem loop region (residues 45–63), provide information about intrasubunit mechanisms within the thermosome ring structure. Overall, our results indicate significant variance of the allosteric networks of the two chaperonin classes.

Materials and Methods

Three-dimensional structures of nucleotide states of thermosome

We used the x-ray structure of the closed state (ADP-bound) conformation (Protein Data Bank (PDB) 1A6D) (10) of thermosome to determine normal modes in the R^″ state. Atomic coordinates for the open state were obtained from the cryo-EM density map (EMDB:EM-1397 (30)) by using a three-dimensional reconstruction method that combines rigid body fitting with map-constrained dynamics.

Rigid-body fitting

We used the EMAP module (31) of the CHARMM package (32) to fit the electronic densities corresponding to the x-ray structure of the closed state of thermosome within the cryo-EM density map. This rigid-body fitting was optimized based on a core-weighted correlation function combined with grid-threading Monte Carlo (31). The best fit was obtained by performing three Monte Carlo cycles of 200 steps, with translation steps of 1 Å and rotation steps of 1°, and the fitting criterion LOOP=10 in the EMAP module.

Map-constrained self-guided Langevin dynamics simulation

This refinement method involves relaxing atomic coordinates, by removing rigid-body constraints, to optimally fit the open-state density map. To achieve the local relaxation, map-constrained molecular-dynamics simulations are performed. In these simulations, the map-constraint energy of the following form is applied,

$$E_{map}=\frac{c\sum _i^{N_c}{m}_i\rho \left(r_i\right)}{\delta \rho \sum _i^{N_c}{m}_i},$$ (1)

where ρ(r_i) is the image density at position r_i of atom i, which is interpolated through the b-spline of the fourth order from neighboring image grid points. Here, δρ is the standard deviation of densities, m_i is atomic mass of atom i, N_c is the number of constrained atoms, and c = 1000 kcal/mol is a constant that defines the strength of the map constraint. A self-guided Langevin dynamics (33) simulation of 1 ns is performed to adequately sample the conformational space for conformations that satisfy the map constraints. In the self-guided Langevin dynamics simulations, the friction constant was set to 1 ps⁻¹, the local averaging time t_L to 0.5 ps, and the guiding factor to 0.5. To account for solvent effects, we used the SCPISM implicit solvation model (34). The final conformation is minimized using the adapted basis Newton-Raphson method for 1000 steps.

Normal mode computation and analysis

We used an elastic network model (35) that represents each amino acid by a virtual particle located at the C_α position. The potential energy of the protein is given by

$$E=\frac{1}{2}\sum _{d_{ij}^0<R_c}K{\left(d_{ij}-d_{ij}^0\right)}^2,$$ (2)

where d_ij is the distance between interaction sites i and j, d_ij⁰ is the corresponding distance in the native structure, and K is the spring constant. The value of R_c, 8 Å for thermosome monomers and 10 Å for the GroEL monomer and chaperonin rings, is chosen such that the correlation between the experimental and computed B-factors is maximized (28). Normal modes of the monomers were computed using the AD-ENM web server at the National Heart, Lung, and Blood Institute (http://enm.lobos.nih.gov) (28,36).

Overlap function

The overlap function quantifies how a given normal mode compares with the conformational change along a transition pathway. This function is computed by projecting the normalized eigenvector ${\overrightarrow{a}}_M$ of mode M onto the displacement vector between two functional states, α and β, as

$$I_M^{\alpha \to \beta }=\frac{\left|\sum _{i=1}^N{\overrightarrow{a}}_{iM}\Delta {\overrightarrow{r}}_i\right|}{{\left[{\sum }_{i=1}^N{\overrightarrow{a}}_{iM}^2{\sum }_{i=1}^N\Delta {\overrightarrow{r}}_i^2\right]}^{1/2}}$$

(37), where the sum is over the N nodes, $\Delta {\overrightarrow{r}}_i={\overrightarrow{r}}_i^{\alpha }-{\overrightarrow{r}}_i^{\beta }$, and ${\overrightarrow{r}}_i^{\alpha \left(\beta \right)}$ are position vectors of the i^th node in the α (β) structures. A value of one for the overlap corresponds to the direction given by ${\overrightarrow{a}}_M$ being identical with that of $\Delta \overrightarrow{r}$. The relative amplitude of node i in mode M is obtained using

$$\delta q_{iM}=\sqrt{a_{i_{x}M}^2+a_{i_{y}M}^2+a_{i_{z}M}^2},$$

where $a_{i_{\alpha }M}$, $\alpha =x,y,z$, are the ${\overrightarrow{a}}_M$ components.

Mode collectivity

This quantity reflects the number of C_α nodes, which move significantly during the structural motion described by a given normal mode (38). The collectivity κ_M of mode M is defined as the exponential of the information entropy of eigenvector ${\overrightarrow{a}}_M$,

$${\kappa }_M=\frac{1}{N}exp\left(-\sum _{i=1}^N{\left(\delta q_{iM}\right)}^{2}log{\left(\delta q_{iM}\right)}^2\right).$$ (3)

Here, the square relative displacements,

$${\left(\delta q_{iM}\right)}^2,i=\overline{1,N},$$

are interpreted as probabilities of N outcomes, with uncertainties –log(δq_iM)², of a random variable (note that ${\sum }_i{\left(\delta q_{iM}\right)}^2=1$). The collectivity measures the number of nodes that are active in mode M, reflecting the contribution of this mode to the entropy. κ_M takes values between 1/N and 1. In the limit of maximally collective structural motion, κ = 1 and δq_iM is independent of i in mode M. In the limit of minimally collective motion, κ = 1/N, a single atom moves.

Directional correlation coefficient

This quantity measures the pairwise correlation of amino acids in structural motions and we compute it using the covariance matrix of principal modes of thermosome (GroEL) (27),

$$C_{ij}=\frac{\sum _M\left({\overrightarrow{a}}_{iM}·{\overrightarrow{a}}_{jM}\right)/{\lambda }_M}{{\left[\sum _M\left({\overrightarrow{a}}_{iM}·{\overrightarrow{a}}_{iM}\right)/{\lambda }_M\right]}^{1/2}{\left[\sum _M\left({\overrightarrow{a}}_{jM}·{\overrightarrow{a}}_{jM}\right)/{\lambda }_M\right]}^{1/2}},$$ (4)

where λ_M is the mode M eigenvalue. To quantify correlations between like domains, we define the average pairwise correlation

$$\langle C_{A,A+\Delta }\rangle =\frac{1}{N_{A,\gamma }{N}_{A+\Delta ,\gamma }}\sum _{i=1}^{N_{A,\gamma }}\sum _{j=1}^{N_{A+\Delta ,\gamma }}{C}_{ij},$$ (5)

where A = even(odd) represents an α-(β-) subunit, Δ is the subunit separation, and N_A,γ is the number of nodes in domain γ of subunit A.

Structural perturbation method

To probe the effect of a point mutation (local perturbation) at node i on normal mode M, we calculated the global first-order response,

$$\delta {\omega }_{iM}=\frac{1}{2}\sum _{j,d_{ij}^0<R_c}\delta K{\left(d_{ij,M}-d_{ij}^0\right)}^2$$

(29,39), where δK is the perturbation to the spring constant and d_ij,M is the change in the distance between residues i and j in mode M. The response, δω_iM, is directly proportional to the contribution of a residue i to the total network energy. The higher the value of δω_iM, the more sensitive a functional mode M is to the contribution, and the larger the energetic penalty is to create a mutation at a site i. In practice, we use the criterion δω_iM > 2〈δω_M〉 to identify hot-spot residues that are critical for mode M, where 〈δω_M〉 is given by

$$\langle \delta {\omega }_M\rangle =\sum _{i=1}^N\left(\frac{\delta {\omega }_{iM}}{N}\right).$$

Results and Discussion

Dramatic ATP-dependent conformational changes indicate a highly dynamic nature of group II chaperonins

Functional motions of chaperonins, which involve strong subunit plasticity, enable dramatic changes in volume and chemical character of the folding chamber. The detailed characterization of nucleotide-bound states of GroEL (3–5) revealed concerted rotations of apical domains within one ring (cis) upon ATP binding (T → R transition) and large conformational changes upon GroES binding (R → R^′) and ATP hydrolysis (R^′ → R^″) that increase the cavity volume by a factor of two. ATP binding to the distal ring prompts the release of GroES and nucleotide in the cis ring to complete the chaperonin hemicycle (R^″ → T).

Recent imaging studies of archaeal (10,30) and eukaryotic (12) chaperonins indicate that weak coordination of subunits and the lack of a co-chaperonin in group II chaperonins yield distinct character of conformational transitions. These aspects are illustrated by cryo-EM images of three distinct nucleotide states—apo (open conformation), ATP-bound (partially closed), and ADP-bound (closed)—of an archaeal chaperonin cpn60 from Methanococcus maripaludis (30). In the open (T) state, extensive contacts between subunits within one ring are largely concentrated in the equatorial region, endowing the chaperonin structure with high flexibility. Binding of ATP (R state) to that ring induces ordering of subunits and results in a partially closed conformation. After ATP hydrolysis, the chaperonin ring adopts a closed conformation (denoted R^″ to use the same nomenclature as for GroEL) in which subunits establish contacts between apical domains and the cavity volume is reduced by a factor of approximately two.

To probe the allosteric communications within the archaeal chaperonin thermosome, we compute its normal modes in the R^″ state (PDB:1A6D) (10), which involves extensive intersubunit contacts (Fig. 1 a). Information about the functional role of the normal modes can be gleaned by determining the overlap (see Materials and Methods) with the R^″ → T transition. To this end, we obtained atomic coordinates for the T state (Fig. 1 b) by using a rigid fitting approach combined with map-constrained molecular dynamics (see Materials and Methods). As shown in Fig. 1, c and d, the largest atomic displacements in the R^″ → T transition are found in the apical domain, which includes the highly flexible helical protrusion region (245–274), and in the intermediate domain. In the equatorial domain, relatively small displacements are found for all amino acids except those located on the stem loop region 45–63 (Fig. 1 d). This suggests that conformational transitions of archaeal chaperonin subunits are well described by domain motions around interdomain hinge regions, as it is the case for GroEL transitions.

Figure 1.

Conformational changes of the thermosome during the R^″ → T transition. (a) Crystal structure of the closed (R^″) state (10). (b) Open (T) state structure, obtained by fitting the closed-state thermosome in the cryo-EM map of cpn60 (30) and refinement using map-constrained dynamics (see Materials and Methods). The heterooligomeric structure of the thermosome is indicated (α-subunit, red; β, blue). (c) Conformational changes within the α-subunit during the transition, illustrated by a best fit of the R^″ (opaque) and T (transparent) state structures. The apical (red), intermediate (blue), and equatorial (green) domains and important structural elements (yellow), helical protrusion, ββ-turn, and stem loop, are shown. To permit visualization of structural elements, the viewpoint of the monomer structure is different from those in panels a and b. (d) Displacements of C_α atoms between closed and open states. (Color bars indicate domain regions; domain colors as in panel c.) Molecular images in this article are rendered using VMD (54) and POV-Ray (55).

Multiple normal modes contribute to the thermosome R^″ → T conformational transition

The effect of sequence and structural variability within the two chaperonin classes on conformational dynamics can be gleaned from the normal modes of vibration of the monomeric building blocks. Consistent with previous studies (27–29), our results show that the lowest-frequency normal mode dominates the conformational transition of a single GroEL subunit (PDB:1AON for the R^″ state and 1OEL for the T state), with an overlap contribution of 0.83 (Fig. 2 a). A single additional mode, 6, is found to have an overlap contribution >0.2.

Figure 2.

Overlap of normal modes of GroEL and the thermosome with amino-acid displacements in the R^″ → T transition. (a) Overlap values (see Materials and Methods) of modes of GroEL (black dots) and thermosome monomers, α (red) and β (blue). (Solid lines are drawn as a guide to the eye.) The lowest-frequency mode provides the dominant overlap contribution for the GroEL monomer. Thermosome monomers have common patterns of overlap contributions of low-frequency modes (1 and 3 provide significant overlap contributions) and distinct higher-frequency behavior. (b) Overlap of double-ring modes of GroEL (black) and thermosome (red). A single high-frequency mode dominates the GroEL transition, whereas multiple high-frequency modes contribute to the thermosome transitions.

In contrast to GroEL, the R^″ → T transition of thermosome subunits is described by multiple modes (Fig. 2 a). For the α-monomer, the modes with the largest contribution are 1 (overlap 0.29), 3 (0.30), and 9 (0.36) and for the β-monomer modes 1 (0.34) and 3 (0.37). In addition, three modes (5,13,16) of the α-monomer and six modes (2,6,7,10,11,15) of the β-monomer have overlap between 0.14 and 0.21. Our results indicate that the two types of thermosome subunits share a common pattern of normal mode behavior at low-frequency (modes 1–4 shown in Fig. 2 a), which reflects their high structural homology (59% sequence identity and root mean-square deviation of 1.2 Å). Nevertheless, at higher frequency, overlap contributions of normal modes of the two subunit types are distinct. Mode 9 of the α-monomer provides the largest overlap contribution for this subunit type, whereas modes 6–8, 10, 11, and 15 of the β-monomer provide smaller contributions than lower-frequency modes 1 and 3, revealing the heterogeneity of the allosteric network of the two subunit types.

To understand the origin of the differences in mode contribution to conformational transitions of chaperonins, we compute the normal mode collectivity (see Materials and Methods and see Fig. S1 in the Supporting Material). This parameter (38) provides a measure of the number of network nodes with significant displacement within a normal mode. The remarkable difference between the behaviors of the two chaperonin classes is that the collectivity of low-frequency modes of GroEL is significantly larger than in thermosome modes. High collectivity of the lowest-frequency GroEL mode ensures that this dominant mode satisfies the requirement of large rigid body rearrangements of monomer subdomains in the course of the R^″ → T transition. By contrast, multiple modes of thermosome monomers have moderate values of collectivity κ ≃ 0.4, in accord with the absence of a single dominant mode.

The underlying structural origin of these collectivity values in thermosome monomers is the high flexibility of the helical protrusion region. Weak intrasubunit constraints exerted onto the helical protrusion allow it to execute large excursions even as the rest of the apical domain undergoes small amplitude motions. This effective decoupling of the helical protrusion from monomer motions dampens the overall collectivity value and renders the corresponding modes unproductive toward the R^″ → T transition pathway. The near coincidence of κ-values for low-frequency modes of the two thermosome subunit types supports the strong similarity of these modes. At higher frequency, these values are subunit-specific, in agreement with the overlap contributions noted above.

Universal and specific behavior of normal modes of thermosome subunits

Subunit heterogeneity in Group II chaperonins, found primarily within the apical domains, has important consequences for the functional specialization of ring components. To understand the role of heterogeneity in subunit dynamics, we analyze conformational changes and amino-acid pair correlations associated with normal modes of monomers that contribute significantly to the R^″ → T transition. Low-frequency modes 1 and 3 of both monomers consist of swing motions (Fig. 3 and see Movie S1 in the Supporting Material) that assist the opening of the thermosome ring and therefore they are naturally independent of the subunit type.

Figure 3.

Motions associated with significant normal modes of the α-monomer the thermosome. (a) Mode 1 consists of swing motions of the apical and equatorial domains that contribute to the expansion of the thermosome cavity. (b) Mode 9 consists of torsional motions that orient the apical domains for substrate recognition. Spheres indicate the amplitude and direction of motions of amino acids in each mode. Oversize displacements in the helical protrusion and the stem loop are omitted for clarity.

Pairwise correlations (Fig. 4, a and b, and see Fig. S2) indicate strong coupling of amino acids within the same domain, which is consistent with the rigid-body domain motions noted above. Interdomain couplings are limited and the most extensive regions that are correlated include, on the one hand, region 40–75 in the equatorial domain and the intermediate domain, and, on the other hand, region 440–500 in the equatorial domain and the apical domain. As shown in Fig. 5 a, the dominant amplitude contribution to these swing motions corresponds to the helical protrusion region, within the apical domain. The large displacement associated with the helical protrusion is consistent with its role as a built-in lid for the thermosome cavity. Smaller amplitude motions are found in equatorial and intermediate domains, because large motions of these two domains are not required to expand the chaperonin cavity.

Figure 4.

Pairwise correlations of amino-acid motions in significant normal modes of monomers. (a–c) Modes 1, 3, and 9 of the thermosome α-monomer. A sequence offset of −16 is used. (d) Mode 1 of the GroEL monomer. Strong intradomain correlations and limited interdomain correlation are found in modes 1 and 3 of thermosome and mode 1 of GroEL. Higher-frequency mode, 9, of thermosome is characterized by weak correlations within the apical domain. (Dashed lines) Boundaries between domains.

Figure 5.

Amplitudes of amino-acid motions associated with important modes of the thermosome (a) α-monomer and (b) double-ring. (a) Large-amplitude displacements of the helical protrusion region in modes 1 (black) and 3 (red) are consistent with the role of this element as a built-in lid for the thermosome cavity. Mode 9 (blue) involves significant displacements of regions in equatorial and intermediate domains that assist in torsional motions of the monomer. (b) Amplitudes of ring-based amino-acid motions in the two types of thermosome subunits associated with modes 7 (black), 12 (red), 33 (blue), and 83 (green).

The distinct higher-frequency behavior of the two subunit types is best illustrated by the important contribution of mode 9 to the conformational transition of the α, but not the β, subunit. This mode represents a torsional motion of the α-subunit comprising rotations of the apical and intermediate domains in opposite directions (Fig. 3 b and see Movie S2). Although this motion does not significantly affect the size of the chaperonin cavity, its likely functional role is to position the apical domain binding site for recognition of substrate proteins. In this mode of the α-subunit, large-amplitude motions take place in the stem loop region 45–63 and the ββ-turn region (186–190) of the intermediate domain. These are precisely the regions that are wired differently in the two subunit types. In the α-subunit, these regions are weakly coordinated with other domains, allowing large flexibility, whereas in the β-subunit they are implicated in interdomain contacts. In addition, pairwise correlations corresponding to mode 9 of the α-monomer (Fig. 4 c) indicate strong collaboration between the intermediate and the equatorial domains, whereas intradomain correlations, particularly in the apical domain, are relatively weak. The specialization of α- and β-subunits for substrate protein recognition is thus reflected in their normal mode behavior at higher frequency.

Normal modes of the thermosome share aspects of the lowest-frequency, dominant, mode of a GroEL monomer (29), which contributes to both a dramatic reduction in the size of the chaperonin cavity through large amplitude motions in the apical domain, and to the repositioning of apical domain binding site through its rotation with respect to the equatorial domain. In this mode, pairwise correlations (Fig. 4 d) are mostly confined to intradomain interactions, consistent with predominant rigid-body motions. An important difference between the two chaperonin classes is the dominant contribution of the helical protrusion region to the thermosome motion compared with the relatively uniform contribution of apical domain amino acids in GroEL. This prominence of the helical protrusion region is due to its role as a built-in lid in the absence of a co-chaperonin for the thermosome. These findings suggest that torsional, swing motions of subunits are conserved features of normal modes of the two chaperonin classes, and that these are likely to play a significant role for the protein folding reaction cycle.

Higher-frequency normal modes contribute significantly to the motion of the chaperonin ring

Normal mode analysis of double-ring structures (Fig. 2 b) reveals, in accord with observations of monomer behavior, that multiple modes are required to describe the R^″ → T transition of the thermosome, whereas a single mode was shown (28) to provide the dominant contribution for GroEL. Nevertheless, the behavior of chaperonin rings is distinguished from that of monomers by the small relative contribution of low-frequency modes (28). To account for this difference, we examine 94 nonzero normal modes of the double-ring chaperonin (Fig. 2 b). For GroEL, our calculations, using a nonsymmetrized structure, indicate a behavior consistent with that of the symmetrized GroEL double barrel (28), which has a dominant high-frequency normal mode and several subdominant modes.

In the thermosome case, four normal modes, 7 (overlap 0.4), 12 (0.28), 33 (0.28), and 83 (0.42), provide the largest contributions to the overlap (Fig. 2 b). These modes involve both swing-type and torsional motions of thermosome subunits. In particular, modes 7 and 33 involve swinglike motions with distinct relative displacements of structural elements of α- and β-subunits. Mode 7, in both subunits, involves large-amplitude motions of the helical protrusion and the stem loop, and, in the α-subunit, the ββ turn (Fig. 5 b and Movie S3). In mode 33, large-amplitude motions occur in the helical protrusion region of both subunit types, but the displacement of the stem loop and the ββ turn is more prominent in the α-subunit (Fig. 5 b and see Movie S4). Mode 12 involves torsional subunit motion characterized by hinge-based rotations of the apical and equatorial domains (Fig. 5 b and see Movie S5) and mode 83 comprises large displacement of apical domains, except for the helical protrusion, combined with torsional motions of the subunits (Fig. 5 b and Movie S6).

Thus, our analysis reveals that the principal modes of the thermosome ring involve complex dynamics that comprise swinglike and torsional motions. Although motions of these type were described for monomers, ring dynamics deviates from pure subunit-specific modes. Instead, in several of the ring modes, subunit specificity is delineated by dynamics of particular structural elements, which indicates the loose character of ring constraints within this chaperonin class. The requirement that multiple modes be considered in describing the thermosome transition is therefore a natural consequence of the significant flexibility retained by individual subunits within the ring structure. Because the relative contribution of low-frequency modes is small, we surmise that universal low-frequency modes of α- and β-monomers play a small functional role for the double-ring thermosome structures.

Weak coupling of subunits within the thermosome ring

Nonconservation of intra-ring cooperativity among chaperonin classes prompts the question of which structural features underlie this distinct behavior. To address this question, we compute the covariance matrix of the four principal modes of thermosome, which provides a measure of directional correlation of amino-acid pairs weighted by the inverse eigenvalue and we compare these results to the correlations present in the dominant mode of GroEL (see Materials and Methods). We find that the principal modes of the thermosome ring are characterized by weaker long-range intersubunit correlations than those found in the dominant mode of the GroEL ring (Fig. 6 and see Fig. S3, a–d). Within thermosome subunits, stronger coupling is largely confined to intradomain amino-acid pairs. Intersubunit interactions couple primarily homologous domains of neighboring subunits and decay rapidly around the ring.

Figure 6.

Pairwise correlations of amino-acid motions in normal modes of chaperonin rings. (a) Covariance matrix of the four principal modes of thermosome and (b) mode 18 of GroEL. (In the second and third quadrants, the antidiagonal corresponds to subunits in contact.) Long-range intersubunit correlations are weaker within the thermosome ring than in GroEL. (c) Average pairwise correlations (see Materials and Methods) of amino acids in apical (top panel), intermediate (middle), and equatorial (bottom) domains of subunits with separation Δ in the GroEL ring (black) and thermosome (α-subunit, red; β, blue). (Standard deviations are commensurate with dimensions of circles representing data points.) Apical-apical and equatorial-equatorial interactions in GroEL are more strongly anticorrelated at long-range (Δ = ±3).

To assess the strength and range of these interactions relative to those of the cis ring of GroEL, we compute the average pairwise correlations (see Materials and Methods) between homologous domains of ring subunits (Fig. 6 c). At short range (subunit separation Δ = ±1), coupling between GroEL apical (equatorial) domains is approximately equal to values found for the thermosome, except for the stronger βα apical interface (Fig. 6 c). At long range, motions of maximally separated (Δ = ±3) apical (equatorial) domains of GroEL indicate stronger anticorrelation than distant (Δ = ±3, ±4) interapical (equatorial) interactions involving α (β) subunits of the thermosome. Nevertheless, allosteric signals between thermosome subunits are strongly propagated through the helical protrusion network (see Fig. S3 e), which involves particularly long-range communications in the swinglike mode 33. We also note the asymmetric correlation of thermosome subunit types, indicating the role of interface heterogeneity in intra-ring communications. Tighter coupling at the βα interface (Fig. 6 c) indicates a biasing factor in sequential allosteric motions within one ring.

The set of hot-spot residues that are critical for allosteric communications within the thermosome structure can be gleaned by using the Structural Perturbation Method (see Materials and Methods). This approach, which describes mutations as local perturbations of the elastic network (29,39), maps the propagation of the allosteric signal by identifying the set of amino acids with large response, δω_iM > 2〈δω_M〉, in each normal mode. As shown in Fig. 7 and Fig. S4 and Table S1 in the Supporting Material, we find that, within the four principal modes, hot-spot positions are clustered primarily in the apical and equatorial domains. The key role in these modes is assumed by the helical protrusion region, which is strongly represented in modes of both subunit types. Another structural element identified in our NMA, the stem loop of the equatorial domain, also includes several hot-spots (see Table S1 ). These results support our conclusion that the helical protrusion is a universal conduit of allosteric communications in the two types of thermosome subunits and underscore the importance of the equatorial interface for interring communications.

Figure 7.

Structural perturbation results of the thermosome ring. The structural location of hot-spot residues (see Materials and Methods) is highlighted (green, apical domain; purple, intermediate domain; and black, equatorial domain) within each subunit type. The list of hot-spot residues in each mode is shown in Table S1.

Conclusions

In this study, we examined normal modes of the group II chaperonin thermosome. We find that normal modes of thermosome subunits comprise universal behavior of low-frequency motions and specific characteristics at higher frequency. The low-frequency modes support conformational transitions of subunits that underlie large volume changes of the chaperonin cavity, therefore these modes do not require subunit-specific allostery. By contrast, sequence heterogeneity of thermosome subunits plays an important role in normal modes with higher frequency, with α- and β-monomers displaying distinct behavior. The likely functional significance of these subunit-specific modes in the R^″ → T transition is to reposition each subunit type into its binding-active state. Consistent with this hypothesis, the high-frequency motions described here involve all of the CCT regions that have been implicated in substrate recognition by experimental (12,14,40–43) and computational (44) studies.

Distinct normal mode behavior of thermosome subunits is in accord with subunit specialization for SP recognition in group II chaperonins, as observed for actin and tubulin (45,46). Based on these results, we propose that normal modes of the monomers of the eukaryotic chaperonin CCT, which has eight nonidentical subunits, comprise divergent higher-frequency motions to enable access to SP binding sites. Indeed, the recently resolved crystal structure of CCT in complex with actin (12) emphasizes the highly asymmetric structure of the eukaryotic subunits and distinct subunit-subunit interactions.

Our results are also consistent with distinct SP release mechanisms in the two types of allosteric transitions. Sequential intra-ring transitions of a GroEL mutant have been shown to effect domain-by-domain SP release, whereas concerted transitions of wild-type GroEL result in an all-or-none mechanism (47–49). We propose that weak intra-ring coupling, which gives rise to sequential allostery in group II chaperonins, provides high conformational flexibility of individual subunits that allows them to assist the stepwise SP release. Mutational experiments (50) and bioinformatic studies (44) should provide guidelines concerning subunit specificity for substrate binding and release. We expect that future NMA studies of CCT will reveal a richer behavior than in the case of thermosome and will delineate generic mechanisms of group II chaperonin motions.

We contrast normal modes of the two chaperonin classes by comparing the behavior of monomer and double-ring assemblies of thermosome and GroEL. The R^″ → T transition of the GroEL monomer is well characterized by the lowest-frequency mode, whereas thermosome monomers require multiple modes. These distinct aspects reflect the separate functional requirements of the two chaperonin classes. GroEL monomers have evolved to execute a limited set of motions compatible with highly cooperative transitions of each ring. By contrast, weak coupling of thermosome subunits allows significant specialization of subunit-level normal modes and ensures their compatibility with ring-based conformational transitions.

Our results also highlight the importance of high-frequency normal modes for conformational transitions of thermosome. This conclusion is underscored by findings of NMA studies of large protein assemblies, such as myosin II (51), which support the hypothesis that coupling of multiple high-frequency modes is required for conformational changes of large complexes. In addition, for toroidal structures (52), high-frequency modes are associated with nondegenerate, rotationally invariant, motions that mediate cooperative transitions, whereas low-frequency modes tend to be doubly degenerate motions that break the cylindrical symmetry.

Thus, large contribution of nondegenerate high-frequency modes to allosteric transitions has greater significance for highly symmetric structures, such as the fourfold symmetric thermosome and the eight-spoke nuclear pore complex (52). Toroidal structures with lower symmetry, such as the sevenfold symmetric GroEL and the seven- and nine-spoke nuclear pore complex, have smaller numbers of degenerate modes. From this perspective, the dominant contribution of a single high-frequency mode for GroEL transitions (28) is consistent with the concerted cooperativity mechanism, whereas the combination of multiple high-frequency modes of thermosome enables sequential cooperativity.

Sequential conformational transitions are also present in homooligomeric, ring-shaped, biological nanomachines. For example, Clp ATPase components of homohexameric bacterial proteases undergo asymmetric nucleotide-dependent transitions to unfold and translocate SPs through a narrow central channel (53). This indicates that networking of protein sites is as important as sequence variability in determining the types of conformational transitions accessible to subunits of the ring-shaped molecule.

Future NMA studies of homooligomeric rings of group II chaperonins and Clp ATPases will elucidate the detailed tertiary and quaternary structure requirements of each type of cooperativity. In summary, our NMA of thermosome motions reveals mechanisms of sequential transitions within group II chaperonins and functionally relevant subunit-specific behavior. Comparison with normal modes of GroEL allows us to discriminate sequence and structural factors that differentiate intra-ring cooperativity of the two chaperonin classes.