The Gearbox of the Bacterial Flagellar Motor Switch.

Switching of flagellar motor rotation sense dictates bacterial chemotaxis. Multi-subunit FliM-FliG rotor rings couple signal protein binding in FliM with reversal of a distant FliG C-terminal (FliGC) helix involved in stator contacts. Subunit dynamics were examined in conformer ensembles generated by molecular simulations from the X-ray structures. Principal component analysis extracted collective motions. Interfacial loop immobilization by complex formation coupled elastic fluctuations of the FliM middle (FliMM) and FliG middle (FliGM) domains. Coevolved mutations captured interfacial dynamics as well as contacts. FliGM rotation was amplified via two central hinges to the FliGC helix. Intrinsic flexibility, reported by the FliGMC ensembles, reconciled conformers with opposite FliGC helix orientations. FliG domain stacking deformed the inter-domain linker and reduced flexibility; but conformational changes were not triggered by engineered linker deletions that cause a rotation-locked phenotype. These facts suggest that binary rotation states arise from conformational selection by stacking interactions.

Introduction

The switching of bacterial flagellar rotation provides a remarkable example of a cooperative switch in a large, biomolecular assembly (Bray and Duke, 2004). The assembly, the rotor of the bacterial flagellar motor within the basal body, is composed of about 200 subunits of the component proteins (FliG, FliM, and FliN). These proteins attach to the membrane scaffold formed by FliF subunits forming the C and MS rings (Lux et al., 2000). The interaction of membrane-embedded Mot stator complexes with FliG subunits couples proton transfer to torque generation (Zhou et al., 1998). Chemotactic stimuli change the association of the CheY signal protein with the distal FliMNCFliN C ring (Dyer et al., 2009, Sarkar et al., 2010). Coupled conformational transitions in FliMM (Sircar et al., 2015) trigger large displacements of a distant α helix in FliG, involved in stator contacts (Lam et al., 2012, Paul et al., 2011), henceforth designated toque helix (TH). The chemotactic motor output is a changed clockwise (CW)/counter-clockwise (CCW) rotation bias. CW and CCW intervals have second lifetimes, but switch within milliseconds, mostly with no detectible change in rotation speed (Bai et al., 2013, Lele and Berg, 2015). Absence of intermediate states implies cooperative switching of the multiple subunits (Ma et al., 2012). Activated CheY elicits an “ultra-sensitive” (H = 21) change in CW/CCW bias (Yuan and Berg, 2013), but its binding to motors in situ or rotor assemblies in vitro is not cooperative (Sagi et al., 2003, Sourjik and Berg, 2002). Thus, cooperativity must arise from mechanical amplification within the rotor.

Genetic and biochemical studies on the enteric bacteria Escherichia coli and Salmonella enterica serovar (“Salmonella”) provide the paradigm for energization and switching of motor rotation. Non-motile, flagellate (mot) and non-chemotactic (che) mutations are found in all three proteins. The TH is targeted by mot mutations (Lloyd and Blair, 1997). The majority of che mutations are in FliM (Magariyama et al., 1990), FliG helixMC, and GG loop (Figure 2 of Brown et al., 2002). Other conserved loop motifs (GGXG in FliMM, EHPQ in FliGM, MFXF in FliGC (letter = conserved residue; X = variable residue), are also targeted by che mutations. Figure 1 shows the surmised location of one of ∼35 copies of the most complete X-ray structure (T. maritima FliMMFliGMC [Vartanian et al., 2012]) in the Salmonella basal body. FliMM, a dedicated switch module, is a pseudo-symmetric α/β/α sandwich with CW and CCW che mutations localized to distinct surface patches (Park et al., 2006). FliGMC has multiple armadillo (ARM) domains; an architectural design that characterizes the entire protein (Lee et al., 2010). The FliGC C-terminal six-helix bundle (C1-6) contains the TH, forming the motor module.

Figure 1

The Salmonella Basal Body MSC Ring and the T. maritima Proximal Switch Complex

(A) A cross-section through the Salmonella flagellar basal body electron microscopy reconstruction (Thomas et al., 2006) showing transmembrane MS ring and the cytoplasmic C ring. Blue line marks membrane cytoplasm boundary. Box marks the surmised location of FliG and associated FliMM. The FliG ring interacts with transmembrane Mot stator complexes. FliMM reports CheY binding to FliG and adjacent FliM subunits (gold arrows).

(B) The atomic structure (PDB: 4FHR) of the T. maritima complex: FliMM (gold), FliGM (green), FliGc ARM-C (olive), C1-6 (dark green), MFVF motif (orange), and TH (red side chains). Deletion of three Salmonella residues homologous to T. maritima PEV (magenta) produces a CW biased phenotype. See also Figure S1 for secondary structures and the contact interface.

Here we study the X-ray structures (noted by PDB IDs) to understand the conformational coupling between the switch and motor modules. The available FliG and FliM X-ray structure library is marked by conformational heterogeneity, exemplified by two FliGMC Helicobacter pylori structures with opposite (180°) FliGC C1-6 orientations relative to its N-terminal ARM-C (Lam et al., 2012), that has engendered a lively debate (Stock et al., 2012). The heterogeneity could arise because component subunits have discrete states trapped in different minima in the energy landscape; analogous to the open and closed states of sugar binding proteins (Morcos et al., 2013). Alternatively, it could be due to intrinsic flexibility, with the two rotation states generated by conformational selection as found for binding of ADP to the F0F1 ATP synthase (Czub and Grubmuller, 2014). We used tCONCOORD to discriminate between these alternatives. tCONCOORD generates atomic-detail conformational ensembles from a single structure based on distance constraints (de Groot et al., 1997). Detection of labile hydrogen bonds facilitates conformational transitions (Fernandez and Scheraga, 2003, Seeliger et al., 2007). Collective motions were extracted from principal component analysis (PCA) (Amadei et al., 1993) of the ensembles. The dynamics of successive four-residue fragments in conformers encoded as a set of strings with a structural alphabet (SA) (Pandini et al., 2010) unveiled the local motions generating collective modes. Network analysis related interfacial dynamics and coevolution; an important issue for protein machines being addressed by various groups (Morcos et al., 2013, Sfriso et al., 2016, Sutto et al., 2015). Finally, we engineered a three-residue FliG linker helixMC deletion in all structures to assess whether it triggers conversion to the stacked conformation observed for the deletion protein X-ray structure.

The FliMM structure ensembles reveal a stiff domain that fluctuates between two states. The FliGMC structure ensembles, irrespective of species, sample a broad conformer space that is constrained by FliG ARM domain stacking. Residue coevolution identifies both FliGMFliGMC interfacial contact and elastic couplings. Complex formation couples FliMM fluctuations to FlGM rotation, amplified via two central hinges to a large angular reorientation of FliGC C1-6. The design allows rapid reorientation of FliGC C1-6 upon altered tilt of the more rigid FliMM ring within the basal body. HelixMC architecture is too pliable for deletions within it to trigger ARM domain stacking. Instead, the stacking could select alternative rotation states from a broad conformational spectrum.

Results

Our analysis of the tCONCOORD conformational ensembles had two stages. First, we examined the ensemble from the FliMMFliGMC complex. Anharmonic collective motions were identified by PCA of residue Cα position fluctuations and the principal components (PCs) mapped onto the structure. Conformational dynamics of SA-encoded fragments were correlated with the PC motions and each other for characterization of the mechanical network, its relation to interface coevolution, and perturbation by engineered CW-locked deletion mimics. Second, we applied the methodology to the complete structure library of the component FliMM domains, FliGMC and FliMMFliGM complexes. The comparative analysis assessed the effects of complex formation on the individual components, determined a common mechanical design, and evaluated the species-dependent contribution to the variability.

The T. maritima FliMMFliGMC Conformer Ensemble Records Large FliGc Motor Domain Movements

Computed residue temperature factors (B factors) for the FliMMFliGMC ensemble were compared with experimental values (Figure 2A). The simulated FliMM B-factor profile was in reasonable agreement with the crystallographic factors. In contrast, the match was poor for FliGMC. The dominant peak in the simulated profile, at the TH, was damped in the experimental profile. The most prominent peak in the experimental profile bordered the missing seven-residue segment (V188SRTFSK194) adjacent to the G196G197, grafted in from another T. maritima structure (PDB: 1LKV). The second peak was centered at ARM-C E223. Downweighted, low-amplitude peaks were obtained at these positions in the simulated profile. Solvent-accessible surface area (SASA) variations within the ensemble (Figure 2B) identified the β1∗/H2∗ loop (E180-P184) as the most variable FliMM segment. In FliGMC, the high B-factor segments (H6/H7 GG, H8/H9 MXVF, and TH N-terminal loops) had the most variable SASA.

Figure 2

Residue Fluctuations in FliMMFliGMC

(A) Experimental B-factor values (solid line) compared with simulated values (dotted line). The B factors were normalized. B = ((Bres − Bmean)/σB), where Bmean and σB are mean and SD, respectively, of the simulated B-factor (Bres) distribution. Parameters in later figures are normalized similarly. Red bars denote residues in contact with neighboring complexes in the crystal. FliMM Pcorr = 0.63. FliGMC Pcorr = (−0.2 [overall]; 0 [non-contact N-terminal]). Inset: PDB: 4FHR unit cell (B factor high = orange; intermediate = green/cyan); low = blue) and neighboring complexes (white). H13 = TH.

(B) Residue SASA (mean [open circles] ± σ). Horizontal bar shows secondary structure elements: α helices (gray), β sheet (cyan), loops (white).

PCA Identifies TH Displacements as the Principal Collective Motion

The isotropic motions of an ideal molten globule have a flat PC spectrum with equal amplitude eigenvalues. Secondary structures create hinges and shear planes that coordinate collective, anisotropic movements to generate dominant PC modes. The complete PC spectrum measures overall flexibility. Domains were isolated from the complex in silico to assess the effects of complex formation. The relative PC amplitudes were normalized with respect to the summed amplitude of the FliMM eigenvalue spectrum (Figure 3A) to show that the intrinsic flexibility of FliGMC was substantially more than that of either the smaller FliMM or the larger FliMMFliGM complex. The variance of the ensemble was largely (∼90%) captured by the first three PCs. We plotted cumulative amplitudes to better determine differences in anisotropy (Figure 3B). The FliMM PC spectrum becomes more anisotropic upon complex formation with either FliMM or FliGMC. In contrast, FliGMC was not affected by complex formation.

Figure 3

PCA of the FliMMFliGMC Complex

(A) Eigenvalues for the first ten PCs of the ensembles normalized by the sum of the FliMM (gray) eigenvalues.

(B) Cumulative spectra (lines) show the anisotropy of FliMM motions is increased in complex with FliGM (dark gray line) or FliMMFliGMC (black line) than when alone (dashed gray line). The anisotropy of FliMMC (dashed black line) motions is not affected by complex formation.

(C) Schematic of the complex as a segmented rod with intervening hinges. FliMM (gold), FliGMC (green).

(D) Vectors (white lines) used for measurement of hinge and interfacial motions. White spheres mark Cα atoms of connected residues. White arrows show perpendiculars to the chosen planes (triangles). Orange vector (line) marks GGPG motif (spheres).

(E) First three PC amplitudes between vector pairs measured as the σ of the difference angle distributions. Bending = MP1.ML1, MP1.ML3, MP1.GP1, GP1.GL1, GP1.GL3. Rotation = ML2.MGG, ML0.GL0, GP2.GL2. Dashed line separates FliMM and FliGMC pairs. Vector labels are as in (D).

We constructed a mechanical analog to physically map the PC amplitudes onto the structure (Figure 3C). The FliMMFliGMC complex was represented as a segmented beam. The FliG GG and MXVF loops constituted flexible hinges consistent with the SASA profile, in addition to the subunit interface. Hinge motions were most simply deconvolved into bending and rotary components as measured for another segmented protein, the myosin rod (Highsmith et al., 1982). We marked line vectors within the structure (Figure 3D) and recorded ensemble distributions of angle fluctuations between vector pairs to refine the mechanical model. The SDs (σ) of the angle distributions (Figure 3E) showed that the subunit interface and inter-ARM loops were more flexible relative to other parts of the protein, consistent with the initial model. However, the GGPG loop rotary twist (ML2-MGG) was prominent in FliMM motions. FliGM, mechanically coupled to FliMM bends and rotates at the interface (ML0-GL0). C1-6 bending and rotary motions (GL2-GP2) relative to FliGM (GL1-GP2) are amplified from the interface motions. The overall amplification is 3.8-fold for PC2 and 4.2-fold for PC3. The PC contributions to the TH (GL2-GP2) σ were ±5.4° (PC1)/±9.6° (PC2)/±17.7° (PC3). PC1 (Movie S1) predominantly recorded bending motions at the interface and the MFVF motif, and PC3 (Movie S2) the rotation of FliG C1-6 relative to FliMM.

The Elastic Compliance in the Coupling between FliMM and FliG C1-6

Two angle distributions for the PC motions were examined in detail. The distribution for the TH PC3 rotation relative to the MFVF hinge is bimodal with the ends more populated than the center (Figure 4A). A two-Gaussian (R2 = 0.94) fit is also better than a single Gaussian (R2 = 0.78) for angular displacements measured across the subunit interface. The torsional stiffness estimated from the interface rotation is 740 pNnm (one state) to 1,500 pNnm (two states). C1-6 rotation determined the conformer spread as seen from projection of its angular distribution on the PC1PC3 plane. Similar results were obtained for projection onto the PC2PC3 plane.

Figure 4

Two-Stage Rotary Amplification

(A) (i) PC3 rotation angle distributions. Horizontal bars (red [<5°]/blue symbols [>5°]) denote subpopulations of the TH (GL2-GP2) distribution. Fits to the FliMFliG interface (ML0-GL0) distribution are single Gaussian (y = a∗exp(−0.5((x − x0)/b)2)), where a = 2,904, b = 5.48, x0 = 0.2 (dotted line) and double Gaussian (a∗exp(−0.5((x − x0)/b)2)) + (a∗exp(−0.5((x + x0)/b)2)), where a = 2,701, b = 2.72, x0 = 3.55 (dashed line). Combined PC1 + PC3 angle distribution (σ = ±13.0°) for both vector pairs (line). (ii) The subpopulations of the TH distribution partition to opposing ends of the PC1PC3 plot, showing that conformer spread (open symbols/gray edges) tracks TH motions.

(B) The coupling between interface and TH motions.

(C) Elastic coupling (PC3 rotation) between other elements in the complex. Vectors are as in Figure 3C. Mean orientations (0°) in (B) and (C) are for the ensemble-averaged structure.

The composite PC1 + PC3 rotation at the interface and MFVF hinge had a flat angular distribution with increased spread. The flat distribution resulted from summation of two PCs with different relations for the TH-interface motions (Figure 4B). For PC1, the relation between the interface and TH rotation amplitudes is monotonic. For PC3, there are end states where TH orientation is insensitive to interface motions, separated by a linear (8 ± 1) response. Both relations are distinct from relations between inter-domain bending motions that have a parabolic form consistent with motion in an elastic potential well (Figure 4C). Specifically, interface rotation of the GGPG loop relative to the FliMM H1/H2 long axis is constrained by H2 displacement from its favored orientation relative to β1-β3 sheets. Rotation of FliG C1-6c around the MFVF loop is constrained by its bending relative to FliGM. These elastic couplings preserve the protein fold. The C1-6 rotational flexibility at the MFVF hinge (GP2-GL2) from the complete PC has σ = ±28°.

Detailed Analysis of Hinge Elements

SA-encoded fragment motions (Figure S2) characterized local fluctuations (Figure 5A). Fragments from secondary structures in the crystal sampled conformations that preserved type throughout the ensemble. Short loops sampled loop-specific conformations; but long loops (e.g., GGPG loop), also sampled β-sheet conformations. The helixMC segment grafted from PDB: 1LKV sampled loop and β-sheet, rather than α-helix, conformations.

Figure 5

Hinge Elements for the PC Motions

(A) SA representation of ensemble fluctuations. SA letters readout of secondary structure (α helix [gray bar], β sheet [blue bar]) as detailed (Figure S2). Red bar denotes grafted PDB: 1LKV helixMC segment. Grayscale bar (black, high; white, low) denotes populated ensemble fraction.

(B) Superimposed nMIPC (black lines) and RMSF (dotted lines) profiles for PDB: 4FHR. Horizontal bar, colors as in (A), shows secondary structure profile. Peaks that represent hinges for the PC3 rotation in FliMM (yellow asterisks) and FliGMC (green asterisks) are marked. For FliMM RMSF-nMIPC1 Pcorr = −0.17, RMSF-nMIPC3 Pcorr = −0.2, nMIPC1-nMIPC3 Pcorr = 0.27. For FliGMC, RMSF-nMIPC1 Pcorr = −0.36, RMSF-nMIPC3 Pcorr = −0.21, nMIPC1-nMIPC3 Pcorr = 0.21.

See also Figure S2.

Local fragment fluctuations were correlated with trajectory displacements along the PCs (Figure 5B). Hinges, defined as segments with high nMIPC contribution, included both static (low root-mean-square fluctuation [RMSF]) and dynamic (high RMSF) elements. Within FliMM, the prominent static hinges were loops between H2/β2, H1∗/β1∗ (PC1), H1/β1, H2∗/β2∗ (PC2), and H2∗/β2∗, β2∗/β3∗ (PC3). For all three PCs, the long FliMM GGPG loop was a dynamic hinge. The FliMM HI long helix central segment, enriched in polar residues and thus susceptible to hydrolysis, was the second dynamic hinge (PC3). Within FliGMC, the N-terminal helixMC loop was a hinge for PC1 and PC3; while the EHPQ, GG, and MFVF motif loops formed additional PC3 hinges. For all three PCs, the RMSF profile peaked at or adjacent to the TH, accounting for the B-factor profile (Figure 2A).

In conclusion, the premise for the segmented beam model is validated, but supplemented with knowledge of the inherent elasticity of the FliMM and FliGM segments.

The Mechanical Network between FliM and FliG

We constructed FliMM and FliGMC centrality profiles from the covariance matrix of the encoded fragment correlations to measure the contribution of each fragment to the network of local motions (Figures 6A and 6B). The entropy profile identified flexible loops. The FliMM and FliGM loops form a distributed hinge system of network nodes in the composite profile. The remaining two nodes localized to the MFVF motif and the central C1-6 helix. The C1-6 loops inter-helix loops did not influence the network. The profile peaks represented the major nodes: nine for FliMM and ten for FliGMC. The profiles superimposed with the composite nMIPC profile for the PC1-PC3 motions (Pcorr > 0.9). Thus, the PC1-PC3 motions are the dominant output of the mechanical network.

Figure 6

Network Analysis of Local Correlations

(A) The eigenvector centrality tracks the averaged nMIPC profile for the PC1-PC3 motions (FliMM Pcorr = 0.96; FliGMC Pcorr = 0.90). Fragment centrality and entropy are correlated (FliMM Pcorr = 0.44; FliGMC Pcorr = 0.13). Horizontal bar shows secondary structure profile as in Figure 2B.

(B) The covariance matrix. Side bar shows nMIlocal color scale.

(C) The top (nMI > 0.15; red [high] − bluish brown [low]) (i) FliMM intra-domain, (ii) FliMMFliGM inter-subunit, and (iii) FliGMC intra-domain correlations; and (iv) top coevolved inter-subunit couplings mapped onto the PDB: 4FHR structure, color-coded as in Figure 1.

See also Figures S3 and S4.

Three helixMC residues (PEV) homologous to the CW-locked Salmonella deletion (PAA) form its N terminus close to the interface. Their deletion reduced FliGM intra-domain contacts as well as contacts with FliMM (Figure S4). However, long-range couplings between FliMM and loops adjacent to the FliG TH persisted and collective motions were largely unaltered (Movie S3), highlighting the robust nature of the distributed system.

Structural maps of the top nMIlocal correlations (Figure 6C) revealed the mechanical relay between FliMM and FliGC. FliMM, with its β-sheet center as pivot, connects to FliGM core helices H2 and H4. Comparison of the FliMFliG interface residue coevolution and dynamics (Figure S3) showed that, in addition to interface contacts, nodes of the coevolved network overlap/flank long-range dynamic network nodes. The overlap is evident in the structural maps of the communication pathways. However, coevolution only reports some β-sheet motions important for interface dynamics, for reasons not presently understood. FliGM also has a dense network built around its core helices with sparse connectivity to C1-6. The network centrality and spatial architecture are consistent with the idea that mechanical transmission may be conceptually divided into two stages: mechanical coupling at the interface that transmits fluctuations of the stiff FliMM domain to FliGM; with subsequent transmission via hinge motions to effect C1-6 rotation.

Comparative Analysis of Component Structures

X-Ray structures of component proteins and partial complexes were superimposed with the reference PDB: 4FHR structure on a domain-by-domain basis based on common residue positions. Superposition of these static structures did not reveal differences between the species (Figure S5). We proceeded with analysis of the conformer ensembles.

The FliMM GPGG Loop Is Immobilized by Complex Formation

The PC1PC2 plots for the FliMM monomers superimposed with the plot for PDB: 4FHR (Figure 7A). The FliMM plot of the H. pylori FliMMFliGM complex (PDB: 4FQ0) was displaced, albeit of similar form, from the other plots. The PC1-PC3 σ of the ensembles ranged from 0.628 ± 0.002 (PDB: 2HP7) to 0.448 ± 0.002 (PDB: 3SOH). The overlap showed that species differences and subsequent rearrangements of the stiff domain upon complex formation were small.

Figure 7

Comparative Dynamics of FliM Structures

(A) PC1PC2 plots of FliMM ensembles from the monomers (PDB: 2HP7, 4GC8) and complexes (PDB: 3SOH, 4FQ0, 4FHR). The PC1-PC3 conformer spread (σ) was 0.628 ± 0.002 (PDB: 2HP7) and 0.578 ± 0.002 (PDB: 4GC8); 0.448 ± 0.002 (PDB: 3SOH), 0.578 ± 0.002 (PDB: 4FQ0), and 0.582 ± 0.002 (PDB: 4FHR).

(B) Dynamic network nodes (white spheres) mapped onto the PDB: 4FHR FliMM backbone.

(C) Hinge detection from the fragment nMIPC, contribution. (i) Averaged nMIPC1 profile (±σ). (ii) Individual nMIPC1 profiles. Pcorr values (PDB: 4FHR reference) were 0.43 (PDB: 2HP7), 0.52 (PDB: 4GC8), 0.44 (PDB: 3SOH), and 0.57 (PDB: 4FQ0).

(D) First three PC distribution σ of the bending and rotary motions of PDB: 4FHR and FliMMFliGM complexes measured with vector pairs as defined in Figure 3D. Insets: snapshots from Movie S4 (PDB: 2HP7) and Movie S5 (PDB: 3SOH) documenting PC1 and complete PC motions.

See also Figure S5.

We correlated fragment dynamics with the global PC motions as for the PDB: 4FHR FliMM dynamic network (Figure 7B). The nMIPC1 profiles of the FliMM monomers and the FliMMFliGM complexes followed the PDB: 4FHR profile (Figure 5B) (average Pcorr = 0.49 ± 0.03) (Figure 7C), with some differences. The FliMM monomer profiles lacked the β2/β3 loop network node. In addition, the contribution of the central GGPG node was reduced in the T. maritima monomer (PDB: 2HP7). The dominant node for FliMMFliGM profiles, as in PDB: 4FHR, was N-terminal helixMC interfacial loop. In the H. pylori PDB: 4FQ0 profile the FliMM N-terminal H1 and the C-terminal β2∗/β3∗ loop were more prominent, the FliG H1/H2 EHPQ motif loop less so. The PDB: 4FHR profile agreed more with the profiles of the complexes rather than the monomers.

Rotary twist of the GGPG loop relative to the central long axis was the principal (PC1) motion in the FliMM monomers (T. maritima PDB: 2HP7 [σ = ±14°] [Movie S4], H. pylori PDB: 4GC8 [σ = ±11°]). These motions exceeded the combined PC1-PC3 PDB: 4FHR FliMM motion. The interfacial rotation of FliGM relative to FliMM was the principal PC1 motion in FliMMFliGM complexes (Movies S5 and S6); while bending dominated the PC2 and PC3 motions (Figure 7C). We conclude that species interface dynamics vary in degree, not strategy; with twist of the GGPG loop, the dominant intrinsic motion of FliMM, harnessed upon complex formation to drive FliGM rotation. Other features of the dynamic FliMM network are conserved across all ensembles.

Two Hinges Determine FliGMC Flexibility

The modulation of intrinsic FliGMC flexibility by complex formation was determined similarly. The first three PCs were projected onto 2D planes (Figures 8A and 8B). All FliGMC ensembles had greater spread (PC1-PC3 σ [nm]) than the FliMM ensembles. The ensembles were resolved into two sets based on overlap and spread (PC1-PC3 σ). The overlapping T. maritima PDB: 1LKV (2.04 ± 0.006), Aquifex aeolicus PDB: 3HJL (2.09 ± 0.006), and H. pylori PDB: 3USY (2.655 ± 0.006) and 3USW (3.86 ± 0.014) ensembles formed one set separate from the T. maritima PDB: 3AJC (1.36 ± 0.004) and 4FHR (2.42 ± 0.008) ensembles. The latter structures have FliGM/ARM-C stacking interactions.

Figure 8

Comparative Dynamics of FliGMC Structures

(A) PC1PC2 plots.

(B) PC1PC3 plots.

(C) Dynamic network nodes (white spheres) mapped onto the PDB: 4FHR FliGMc backbone. GG pair (asterisk), TH (red side chains).

(D) Averaged nMIPC1 profile (±σ) and the individual profiles.

See also Figure S5.

Correlations of the ensemble nMIPC1 profiles with PDB: 4FHR (Figure 8C) were worse (Pcorr = 0.16 ± 0.06) than for FliMM, consistent with greater conformational variability. The nMIPC1 profiles of all ensembles were merged to detect common nodes (Figure 8D). The interface (EHPQ and N-terminal helixMC) loops were not prominent in the FliGMC networks, showing that their PDB: 4FHR network centrality was due to complex formation. The GG and the MFVF loop formed the dominant nodes, with 3-fold greater amplitude than the next prominent node (TH C-terminal loop). This result extends the PDB: 4FHR segmented beam model to all FliGMC structures.

The Effects of Domain Stacking and FliMM Complex Formation on FliGMC Flexibility

We reasoned that FliGMC conformer ensembles are best compared by motions around the two central hinges. As for PDB: 4FHR, we generated ensembles from structures with engineered PEV or homologous deletions. Complete PC spectra recorded the bending (Figure 9A) and rotary (Figure 9B) flexibility of the two hinges. The hinge distributions formed two distinct relations. The T. maritima/A. aeolicus native and deletion FliGMC structure ensembles formed one relation (R2 = 0.99) that spanned a large GG hinge range due to the presence of both unstacked and stacked structures. The structures with the stacking interaction had markedly reduced GG hinge flexibility, partly compensated by increased flexibility at the MFVF hinge. The H. pylori relation (R2 = 0.97) had a similar range for MFVF hinge-bending flexibility, but its reduction was coupled to decrease, not increase, at the GG hinge. The deletions reduced GG hinge-bending flexibility, as expected from the reduced helixMC length, hence leverage.

Figure 9

Central Hinge Dynamics

(A) Complete PC hinge-bending amplitudes, recorded as difference angle distributions σ in FliGM and C1-6 helices relative to ARM-C (inset). Open symbols denote engineered deletion structures (edge color = native structure). Inset: example PDB: 3USY C1-6 terminal helix (1, pale brown), FliGM helixMC (2, yellow), and ARM-C plane (triangle) (GG pair [red], PQV [magenta], and TH [red side chains]).

(B) Complete PC hinge rotation amplitudes. GL1.GP2 (GG) and GP2.GL2 (MFXF) vector sets (defined in Figure 3C).

(C) PC1 (PDB: 3AJC, 3USY) and PC3 (PDB: 4FHR) MFXF hinge rotation. Colors denote structure ensembles as in Figure 8A.

See also Figures S6 and S7.

Comparison of the two most divergent T. maritima and H. pylori X-ray crystal structures reveals that in both cases, ARM-C moves between coaxial and orthogonal orientations with respect to FliGM (Figure S6). The coaxial ARM-C structures, H. pylori PDB: 3USW and T. maritima PDB: 3AJC, were most similar to PDB: 4FHR. TH displacements produced by rotational flexibility of the MFVF hinge were determined from the main PC modes. MFVF hinge rotation was the principal (PC1) motion for both structures (Movies S7 and S8). While the PDB: 3USW angle distribution has similar form to the PDB: 4FHR PC3 distribution, the PDB: 3AJC distribution is asymmetric. In both cases, the motions were restricted compared with the corresponding PDB: 4FHR rotation (Figure 9C). Therefore, the large PDB: 4FHR MFVF hinge rotation is not intrinsic to FliGMC, but a consequence of complex formation.

Local helixMC/GG hinge dynamics gave insight into the regulation of domain motions by this hinge and deletions within it (Figure S7). The dynamics are different for the unstacked versus stacked T. maritima conformations. The C-terminal half of this segmented hinge behaves as an unstructured loop element, rather than an α helix in the stacked (PDB: 3AJC, 4FHR) conformations, despite graft-in of seven missing residues from the unstacked (PDB: 1LKV) structure where these residues form an extended α helix. In contrast, helixMC is more flexible in both H. pylori conformations due to a long C-terminal loop segment. The long loop eliminates the compensatory coupling between the two hinges seen for T. maritima. In contrast to T. maritima, the homologous PQV deletion will more severely reduce the shorter helix in the H. pylori serial N-terminal helix/C-terminal loop relay and, hence, torque transfer to the MFVF hinge in the coaxial conformation. In the orthogonal conformation the long C-terminal loop will determine hinge flexibility.

Discussion

The analysis of the T. maritima FliGMFliMC complex revealed the following. (1) Large deviations in FliGc C1-6 residue positions were masked by inter-molecular crystal contacts. (2) Large C1-6 rotary and bending motions were the output of a two-stage amplification of FliMM rotary twist fluctuations mediated by the FliGMC GG and MFVF loops. (3) Interfacial loops coupled dynamics of the contacting domains while their internal loops preserved protein fold. (4) FliGM and ARM-C loops formed a sparsely distributed network. (5) A CW-locked Salmonella deletion mimic weakens adjacent FliGM couplings, but long-range couplings between FliMM and the TH persist.

The analysis of the FliM and FliG structure library established that: (1) immobilization of the FliMM GGPG loop upon complex formation generates coaxial rotation of FliGM relative to FliMM in H. pylori as well as T. maritima; (2) different FliGMC conformations from these species show distinct relations between central hinge motions; (3) FliGMC dynamic network architecture is minimally altered by CW-locked deletion mimics; and (4) the FliGMFliMC MFXF hinge C1-6 rotation is not matched in isolated FliGMC complexes, despite high intrinsic flexibility. These results integrated with previous knowledge lead to a model for flagellar switch mechanics.

A Mechanical Model for the Flagellar Motor Switch

The model (Figure 10) encapsulates the following mechanical properties.

Figure 10

Mechanical Model of the Flagellar Motor Switch

Rotary twist of the stiff FliMM domain is transmitted via a localized two-point contact to FliG ARM-M. Two central hinges (l1 = GG motif loop, l2 = MFXF motif loop) bounding ARM-C partition FliGMC into three segments, providing two-stage amplification for FliGC C1-6 reorientation. Long loop l1 flexibility depends on ARM-M/ARM-C stacking interactions. Arrowheads denote location of in situ FliG crosslinks (green) and conformational coupling between adjacent FliMM (yellow).

The FliMM Switch Module

FliMM is mechanically stiff, consistent with its role as a dedicated switch module able to propagate conformational transitions distally across FliG to reverse rotor-stator contacts. Complex formation effects a localized change, immobilization of a long loop tethered at both ends to α helices that pivot around the β-sheet center of the αβα sandwich to effect FliGM rotation. The mechanics support the role of FliMM inter-subunit contacts in transverse conformational spread, as localized by in situ crosslinks and indicated by CW mutations (Park et al., 2006), residue coevolution (Pandini et al., 2015a), and electron paramagnetic spectroscopy (Sircar et al., 2015). Atomic force microscopy data have documented the mechanical rigidity of folds with mixed αβ topology (Guzman et al., 2010), whereas unshielded β sheets alone deform readily to accommodate shear compared with more rigid, hydrogen-bonded α-helix backbones (Ackbarow et al., 2007). The FliMM mechanics are in accord with this knowledge.

The FliGM/ARM-C Mechanical Relay

The FliMMFliGM interface couples domain motions via a two-point contact between the FliMM GPGG long loop and FliGM EHPQ and N-terminal helixMC loops. These couplings link the three layers of the FliMM sandwich to ARM-M core helices. The ARM-M fold, composed of rigid α-helical levers linked by short loops, forms an elastic domain resilient to deformation during rotation. Its architecture is consistent with the mechanical properties of ARM proteins (Alfarano et al., 2012). HelixMC leverages ARM-M rotation to ARM-C. Engineered N-terminal PEV and homologous deletions in N-terminal helixMC have predictable effects consistent with a shortened lever arm. The MFVF motif, the second central hinge, amplifies ARM-C rotation to C1-6. Torque from FliMM twist fluctuations is distributed between the hinges, with constrained GG hinge motions compensated for by increased MFVF hinge motions. The flexibility of the composite helixMC/GG hinge may be a key source of species variation. Species differences in hinge length and sequence with consequent variations in ARM-C position and domain interactions offer a rationale for the weak ARM-C coevolution signal (Pandini et al., 2015a).

The C1-6 Motor Module

In contrast to FliGM the C1-6 module is largely devoid of hinge elements, as contacts with adjacent helices attach the TH onto the C3-6 fold, consistent with coevolution data (Pandini et al., 2015a). Short loops adjacent to the TH fine-tune its orientation relative to C1-6 collective motions. The in situ crosslinks target the loops adjacent to the TH as well as the FliGM interfacial loops (Figure 10). Steric constraints at these end locations would be maximally effective in blocking FliGMC bending motions.

Implications for Mechanism

Structural models of the flagellar motor switch, reviewed in Stock et al. (2012), seek to explain the large TH reorientation in terms of altered domain contacts. The models agree that FliMM contacts with FliGMC are critical, but differ on the nature of the contacts. One set of models, based on crystallographic data, takes alterations in the FliMM-FliGM contact as pivotal and sufficient to explain switching. Other models, based on biochemical evidence and presumed mismatch between FliM and FliG subunit stoichiometry in the C ring, posit the pivotal contact as being between FliMM and FliG ARM-C, although some FliMM units also contact FliGM. Our study strengthens the case for a pivotal FliMM-FliGM contact.

The PDB: 4FHR complex reveals that complex formation accentuates a large, angular TH reorientation. The reorientation is still 2-fold, or more, lower than is documented in situ. Additional factors will operate in the C ring. First, hinge-bending motions dominant in the isolated complexes are likely to be blocked by adjacent C-ring subunits and might be compensated for by increased rotation. Second, our study does not address whether intra- or inter-molecular FliGMC stacking interactions exist in the C ring. An extended helixMC in the alternative inter-molecular stacking interaction, as recently proposed (Baker et al., 2016, Sircar et al., 2015), would provide greater leverage for rotation of FliGC. Intra- and inter-molecular stacking contacts observed in the crystals are similar. A solution study of the salt dependence shows that the conformations are interchangeable (Baker et al., 2016).

The stacked T. martima conformation in the PEV deletion structure may represent a CW-locked state (Minamino et al., 2011). However, helixMC is soft due to an unstructured C-terminal segment and N-terminal PEV, and homologous deletions do not switch unstacked to stacked FliGMC configurations. Instead, the stacking interaction is strong enough to deform helixMC. The two H. pylori FliGMC conformations provide snapshots compatible with the in vivo data (Lam et al., 2012), yet their conformational ensembles overlap with themselves and with other unstacked FliGMC conformers (Figure 8). Therefore, we suggest that the stacking interaction provides a mechanism for conformational selection of an intrinsically flexible protein. Weak stacking interactions summed over the ring will provide the free energy difference to lock in the two rotation states. A functional design for the flagellar motor switch requires flexible downstream elements to rapidly switch conformation with minimal energy dissipation, once switching is initiated. Subunits chemically bonded in distinct conformations would dissipate energy and switch slowly. FliG assembles tightly onto FliF (Levenson et al., 2012) and templates the assembly of FliM(FliN)3 distal C-ring complexes (McDowell et al., 2015). Electron microscopy data indicate that the latter may stabilize the FliG ring since it is not clearly visualized in FliFFliG complexes due to presumed disorder (Suzuki et al., 2004), in contrast to the intact C ring (Thomas et al., 2006). Inter-molecular stacking provides a straightforward explanation for how FliG subunits carrying the PEV deletion would favor decreased circumference with a shortened helixMC, leading to smaller or more densely packed CW C rings consistent with adaptive remodeling (Lele and Berg, 2015).

The Broader Context: Relevance and Prospects

This study illustrates the importance of backbone flexibility analysis for interpretation of mutagenesis data. It extends earlier work on the F0 ATP synthase (Pandini et al., 2015b) to show that long-range elastic couplings across subunit interfaces contribute to the coevolution signal. Elastic backbone effects have also been noted in coevolution analysis of protein-folding landscapes (Morcos et al., 2014, Sutto et al., 2015). These studies add to the literature, cited in the Introduction, stating that coevolved mutations reflect protein conformational dynamics.

The challenge now is to understand the design principles for evolution of protein-protein interactions. Functional modes should provide a more fine-tuned analysis of the dynamics (Hub and de Groot, 2009). Comparative analysis between natural and designed sequences has shown that optimal backbone flexibility is needed for a strong coevolution signal (Ollikainen and Kortemme, 2013). Optimization constraints may explain why some dynamic couplings have coevolved in the FliMMFliGMC signal complex and others have not. X-Ray structure libraries of rotary motor assemblies, with mechanics that can be measured by single-molecule techniques, are an important stimulus for the development of such analytical tools to study the relation between protein evolution and dynamics.

Experimental Procedures

Generation of tCONCOORD Conformational Ensembles

The X-ray structure library used in this study was downloaded from the PDB. Secondary structure elements and the contact interface within the FliMMFliGMC complex (PDB: 4FHR) are mapped in Figure S1. Component structures (monomers and partial complexes) are described in Figure S2. tCONCOORD produced a conformational ensemble from each X-ray structure. First, atomic pair distances with upper and lower limits were generated from the structure based on tables of bonding interactions (covalent bonds, hydrogen bonds, salt bridges, etc.) constructed from statistical analysis of the PDB database (de Groot et al., 1997). Second, a new structure was built starting from atoms positioned randomly within a bounding volume around their X-ray coordinates. Successive iterations were performed until convergence was achieved upon satisfaction of the distance constraints or an iteration limit (500) was reached. The structure was rebuilt many times to generate (256)2 = 65,536 equilibrium conformations with full atom detail. tCONCOORD samples large conformational protein transitions by breakage of labile hydrogen bonds solvated by surrounding residues, as validated by test cases and MD simulations (Seeliger et al., 2007).

Principal Component Analysis

PCA, specifically of MD trajectories, was introduced when Amadei et al. (1993) showed that the configurational space can be partitioned into an “essential” subspace with few degrees of freedom describing large-scale slow anharmonic motions, with the remaining space describing local fluctuations. Functional motions of biologically relevant conformational transitions belong to the essential subspace defined by the first few PCs. These physically represent the largest-amplitude collective motions in the macromolecular assembly (de Groot et al., 1996). The variance (σ2) was taken as a measure of “motion” (Pandini et al., 2015b). The combined variance of the statistically independent, first three PCs (or subset) from the average structure was obtained by summation. Geometric angular distributions between selected vector pairs were used to compute the torsional stiffness and bending moments.

Network Analysis

The conformational dynamics of four-residue fragments were encoded with the SA (Figure S2) for elucidation of the mechanical relays underlying collective PC motions and comparison with the coevolution network. Frequently occurring conformations from 798 high-resolution X-ray structures were extracted as representative fragment states (letters) (Pandini et al., 2010). The SA provides an enriched string set of local conformational states for accurate reconstruction of protein fold. Statistically significant correlations were determined and analyzed with GSATools (Pandini et al., 2013).

Coevolution Analysis

Pfam protein sequence families FliMM (PF02154), FliGM (PF14821), and FliGC (PF01706) (Finn et al., 2010) were filtered at 80% redundancy level. PSICOV-based analysis of residue coevolution between FliM and FliG (Pandini et al., 2015a) was supplemented with direct coupling analysis (Morcos et al., 2011) to increase contact prediction accuracy (Jones et al., 2014). Sequences were matched based on organism membership and genomic locus proximity (<100 genes, fliG-fliM distance = 18 ± 24). The final dataset contained more than 1,400 non-redundant, concatenated sequences. The coevolution network was constructed from the top 1.5% correlations, a cut-off intermediate between 2σ (2.2%) and 3σ (0.3%). Randomized libraries generated by shuffling within MSA residue positions assessed significance (Pandini et al., 2015a).

See Supplemental Experimental Procedures for operational details and formalism.

Author Contributions

Conceptualization: A.P., F.M., and S.K.; Methodology: A.P., F.M., and S.K.; Software: A.P. and F.M.; Validation: S.K.; Writing – First Draft: A.P. and S.K.; Writing – Review & Editing: A.P., F.M., and S.K.; Visualization: F.M. and S.K.; Supervision/Project Administration: S.K.; Funding Acquisition: F.M. and S.K.