Energy landscape of domain motion in glutamate dehydrogenase deduced from cryo-electron microscopy

Abstract

Analysis of the conformational changes of protein is important to elucidate the mechanisms of protein motions correlating with their function. Here, we studied the spontaneous domain motion of unliganded glutamate dehydrogenase from Thermococcus profundus using cryo-electron microscopy and proposed a novel method to construct free-energy landscape of protein conformations. Each subunit of the homo-hexameric enzyme comprises nucleotide-binding domain (NAD domain) and hexamer-forming core domain. A large active-site cleft is situated between the two domains and varies from open to close according to the motion of a NAD domain. A three-dimensional map reconstructed from all cryo-electron microscopy images displayed disordered volumes of NAD domains, suggesting that NAD domains in the collected images adopted various conformations in domain motion. Focused classifications on NAD domain of subunits provided several maps of possible conformations in domain motion. To deduce what kinds of conformations appeared in EM images, we developed a novel analysis method that describe the EM maps as a linear combination of representative conformations appearing in a 200-ns molecular dynamics simulation as reference. The analysis enabled us to estimate the appearance frequencies of the representative conformations, which illustrated a free-energy landscape in domain motion. In the open/close domain motion, two free-energy basins hindered the direct transformation from open to closed state. Structure models constructed for representative EM maps in classifications demonstrated the correlation between the energy landscape and conformations in domain motion. Based on the results, the domain motion in glutamate dehydrogenase and the analysis method to visualize conformational changes and free-energy landscape were discussed.

Database

The EM maps of the four conformations were deposited to Electron Microscopy Data Bank (EMDB) as accession codes EMD-9845 (open), EMD-9846 (half-open1), EMD-9847 (half-open2), and EMD-9848 (closed), respectively. In addition, the structural models built for the four conformations were deposited to the Protein Data Bank (PDB) as accession codes 6JN9 (open), 6JNA (half-open1), 6JNC (half-open2), and 6JND (closed), respectively.

Abbreviations

AFM

atomic force microscopy

core domain

core domain engaging in hexamer formation

cryoEM

cryo-electron microscopy

FSC

Fourier shell correlation

GDH

glutamate dehydrogenase

GS-FSC

gold-standard Fourier shell correlation

MD

molecular dynamics

NAD domain

nucleotide-binding domain

PC

principal component

PCA

principal component analysis

R _g

radius of gyration

SAXS

small-angle X-ray scattering

T. profundus

Thermococcus profundus

tris

hydroxymethyl aminomethane

Introduction

Proteins display collective conformational motions in interactions with other biomolecules and ligands or in spontaneous fluctuation related to their biological functions [1, 2]. To understand the molecular mechanism of protein function, visualization of these conformational changes is essential. As specimens composed of a large number of molecules provide measurable but ensemble-averaged signals, it would be ideal to measure the motions occurring in a single protein molecule at a fine spatiotemporal resolution. Such efforts have been made using various techniques, including single-fluorophore imaging, and fluorescence resonance energy transfer between probes in a single protein molecule [3-5]. However, methods to visualize conformational changes in a single protein molecule are still under development. Molecular dynamics (MD) simulation provides trajectories at a high spatiotemporal resolution within a limited computational time [6], but has to be validated by comparisons with experimental data [7] because the results depend on force field parameters [8, 9].

In addition to these techniques, cryo-electron microscopy (cryoEM) with single particle analysis [10, 11] is a potential method to visualize conformational changes occurring in protein molecules. Since protein molecules are flash-cooled in cryoEM observations [12], they would be trapped in several conformations at ambient temperature. Image processing algorithms have been developed to analyze the structural heterogeneity in a large number of images of protein molecules without any prior information or assumptions on conformations, and have been successfully applied to reveal conformational changes of proteins and supramolecular complexes [13-17]. Therefore, cryoEM may potentially permit the study of the course of conformational changes and enable to deduce energy landscape during conformational changes [18].

Proteins composed of multiple functional domains are targets suitable to study conformational changes, because the functional domains are spatially separated and display changes in their relative positions and orientations. In this regard, we have been investigating the spontaneous domain motion of glutamate dehydrogenase (GDH) from Thermococcus profundus (T. profundus) in the unliganded state. GDH is composed of six identical subunits, each of which has a nucleotide-binding domain (NAD domain) and a core domain engaging in hexamer formation (core domain) [19] (Fig. 1). A large active-site cleft is situated between the two domains. A crystallographic study suggested a spontaneous motion of the NAD domain relative to the core domain to control the opening/closing of the active-site cleft [19] (Fig. 1B). However, crystal contacts would freeze the possible domain motions into a few. In fact, the scattering curve calculated from the crystal structure was inconsistent with that from a small-angle X-ray scattering (SAXS) measurement [19]. A 200-ns MD simulation of GDH immersed in explicit water confirmed spontaneous domain motions of subunits and suggested that the domain motion was partly controlled by hydration structure changes in the active-site cleft [20]. However, a single MD simulation of 200 ns may be insufficient to count the appearance frequencies of possible conformational states.

Figure 1

Crystal structure of GDH and its structural variety. (a) Hexameric crystal structure of GDH. The six subunits are differently colored. Regarding subunit A, the NAD- and core domains A are colored cyan and red, respectively, to clarify the domain organization. (b) Structural differences between subunit A in an open conformation and subunit E in a closed conformation after superimposing the core domains. The difference is explained as a rotation of the NAD domain around the hinge helix. Panels were prepared using pymol [52]

Here, we conducted a cryoEM study to reveal conformations in the domain motion of GDH occurring in solution. First, the overall structure of GDH was reconstructed at a resolution of 3.4 Å using all images. However, potential maps corresponding to NAD domains were poor probably due to the ensemble average of various conformations in the domain motion. A classification of EM images that focused on NAD domain revealed several conformations of domain motions at resolution of 3.7–3.9 Å. The novel analysis method based on representative conformations appearing in the previous MD simulation permitted the estimation of an energy landscape and a potential pathway of domain motion. Furthermore, some representative maps were refined at near-atomic resolution to discuss the correlation between conformations and energy landscape in spontaneous NAD domain motion.

Results

Overall structure of unliganded GDH

The three-dimensional (3D) map of unliganded GDH was reconstructed from 169 423 zero-loss-energy-filtered particle images under assuming D3 symmetry (Fig. 2). Approximately 30% of all subunits in the GDH images used in the reconstruction were disrupted probably because of adsorption at the air–water interface (Fig. 2D,E). The other 70% of the subunits allowed 3D reconstruction.

Figure 2

CryoEM observation and single particle analysis. (A) SDS/PAGE pattern of purified GDH (subunits; right lane) with molecular weight markers (left lane). (B) Electron micrograph of frozen-hydrated GDH molecules. (C) A set of averaged molecular images of GDH in eight classes after a 2D classification. (D) Eulerian plot displaying the frequencies with respect to the orientation of GDH molecule in EM images. There were three major preferred orientations (orientations 1, 2, and 3) with occupations of 2%, 38%, and 10%, respectively. Most of the GDH molecules in the preferred orientations were probably located at the air–water interface. (E) Illustration on six possible modes of adsorption of GDH hexamer at air–water interface. Parts of the subunits facing to the interface would be disrupted. The maximum number of subunits facing to the interface was four among six as in orientation 1. Taking the orientation estimated in the analysis into account, ~ 30% of all subunits in the observed images would be adsorbed and consequently disrupted. As the subunits in the other 70% faced to solvent, their structures were maintained as they were in solution. This figure was prepared using ucsf chimera [50, 51].

The resolution estimated by the gold-standard Fourier shell correlation (GS-FSC) [21] was 3.4 Å. The local resolution of the six core domains was 3.0–2.6 Å, while those of the six NAD domains were worse than 3.2 Å (Fig. 3A). For each core domain, secondary structures and side chains of amino acid residues were sufficiently visible (Fig. 3B) to compare with the crystal structure model of the core domains. An isolated density appeared near the glutamate binding site at the depth in the active-site cleft and could be interpreted as one hydroxymethyl aminomethane (tris) molecule (Fig. 3C).

Figure 3

CryoEM structure of GDH under assuming D3 symmetry. (A) Three-dimensional (3D) density map reconstructed from EM images under the assumption of D3 symmetry. The map is colored according to the local resolution. (B) Magnified views of maps of secondary structures in the core- and NAD domains of a subunit. The map is contoured at one standard deviation from the average. A structural model built in the map is also presented as stick models, and some of the amino acid residues are labeled. (C) An isolated map found in the depth of the active-site cleft and an atomic model of tris molecule as an interpretation. Possible hydrogen bonds are indicated by dashed lines. Among the molecules in the buffer composed of HCl, tris and water molecules, tris only has hydroxyl groups and an amino group as in substrate glutamate molecule. The spherical map was as large as the dimension of a tris molecule. Therefore, we assumed that the map was originated from a tris molecule bound to near a glutamate binding site. However, the map would be other unknown small molecules from E. coli. The map is contoured at one standard deviation level from the average. (D) Superimposition of subunit A in the crystal structure on the 3D map with a maximal overlap of the core domain. Panels (A) and (D) were prepared using ucsf chimera [50, 51], and (B) and (C) were prepared using pymol [52].

Around the boundary between the NAD- and core domains, the quality of maps was comparable with that of the core domain. In contrast, the map of the NAD domain appeared as an assembly of arc shapes along the direction of domain motion (Fig. 3D), and a crystal structure model of NAD domain was difficult to unambiguously superimpose onto the map. In contrast, the radius of gyration (R_g) value (42.6 Å) calculated from the map was consistent with that measured for GDH in solution by SAXS (43.9 Å) [19]. Since SAXS reflected GDH conformations possible in solution, the map reconstructed under D3 symmetry represented an ensemble average of different conformations occurring in NAD domain motion.

Conformations of NAD domain motion

Next, to analyze NAD domain motion, we applied classification focused on the NAD domain and an upper part of core domain for images including artificially replicated images from the originals according to the D3 symmetry (Fig. 4). Here, we assumed that the motion of a single NAD domain was independent from those of the other NAD domains based on the nonallosteric activity of T. profundus GDH [20]. To assess the incompleteness in the focused classification due to noisy and low-contrast images, we conducted 10 independent calculations (Fig. S1).

Figure 4

Schematic diagram showing focused classification. At the first step, a focused classification regarding the NAD domain and an upper part of core domain was carried out for symmetry-expanded images. Since the reconstructed maps lacked structural characteristics of NAD domain, probably because the subunits in the images (28% of all subunit images) were disrupted at the air-water interface, maps with volumes representing different states of NAD domain motion were reconstructed from the other 72% images of subunits in a classification (Fig. 2D). Maps in the other nine classification trials are shown in Fig. S1. Next, the second classification was applied to maps from the first classification to build structure models. Then, in three (open, half-open1, and half-open 2) of four maps in different conformations, 32–57% of images were discarded to improve apparent quality of maps. By using whole images and their orientation parameters determined from the two-step focused classifications, each 3D map of each subunit was refined. Maps are drawn by using ucsf chimera [50, 51].

In each focused classification, four or five 3D-reconstructed maps, each of which had volumes interpretable as NAD domain, were reconstructed from ~ 70% of the images (Fig. 5A and Fig. S1). On the other hand, maps reconstructed from the other 30% of images lacked structural features interpretable as NAD domain (Fig. 4). The number of images was comparable with that estimated as GDH subunits possibly disrupted at the air–water interface (Fig. 2D,E), and therefore, we did not use these possibly disrupted images in the subsequent analysis (Fig. 4).

Figure 5

Variety of maps after focused classification and the likelihood values of MD structures for cryoEM maps. (A) 3D density maps of four different conformations obtained by a classification focused on the NAD domain and an upper part of core domain. The maps are designated open, half-open1, half-open2, and closed with respect to the size of the active-site cleft. The dashed lines in each panel indicate the edges of the NAD domain. The edge of the open conformation is shown in every panel to demonstrate the conformational differences. This panel was prepared using ucsf chimera [50, 51]. (B) Illustration of two PC motions deduced from the 200-ns MD trajectory. The upper panel shows the magnitudes and directions (red lines) of NAD domain motion along the first PC representing a hinge-bending motion. The lower panel displays the magnitudes and directions (blue lines) of a shear motion along the second PC. (C) The frequency distribution of the conformations appeared in the 200-ns MD trajectory mapped on a plane spanned by eigenvectors of the first and second PCs. The triangle symbols indicate the positions of 28 representative MD conformations used in the analysis using Eqns (1-4). The position of each MD conformation was calculated by projecting the coordinates onto the eigenvectors. (D) Likelihood scores between MD conformations and each classified map in panel (A). The scores are illustrated as contour maps on the plane spanned by the two PCs.

In each classification, maps with different local resolution (3–4 Å) displayed variation regarding the width of the active-site cleft (Fig. 5A and Fig. S1). In addition, each classification gave maps that were different in the positions of NAD domains from those obtained by another classification. For instance, maps representing open, two types of half-open and closed conformations appeared in the first classification shown in Fig. 5a. On the other hand, another classification gave maps in several types of half-open conformations, including the intermediate conformations between open and half-open (designated open/half-open), and between half-open and closed (half-open/closed) as illustrated in Fig. S1. This inconsistency regarding the conformation and resolution among classifications could be attributed to the intrinsic conformational variety of NAD domain motion and to the incompleteness of the classification arising from the low-contrast and noisy images used. Therefore, we assumed that each map was reconstructed as an ensemble average of images in a variety of the conformation of NAD domain motion rather than a set of images of closely similar conformations.

To analyze what kind of conformations in NAD domain motion contributed to each reconstructed map, we used representative conformations observed in the previous MD simulation [20] as reference structures. The simulation was thought to sufficiently sample possible NAD domain motions in solution, because the displacement range of NAD domain in the simulation was qualitatively consistent with that measured by atomic force microscopy (AFM) for solvent-exposed NAD domain on a crystal surface [20]. The similarity between each map and MD conformations was evaluated by a likelihood score defined in reciprocal space [22] as

(1)

where and are structure factors of EM and n-th MD maps at l-th voxel in reciprocal space, respectively. is the uncertainty of evaluated from the images used in the 3D reconstruction. was calculated from atomic coordinates of a snapshot in the MD trajectory (see Materials and methods section). When an EM map is similar to a MD map, the score becomes large.

In a principal component analysis (PCA) of the simulation trajectory [23], eigenvectors of two principal components (PCs) were suitable to approximately describe the NAD domain motion [20]. The first PC represents a hinge-bending motion [24] of the NAD domain to open/close the active-site cleft, and the second does a shear motion [24] to slide the NAD domain in keeping the width of the cleft (Fig. 5B). We selected 28 structures representative MD conformations in the PC plane (Fig. 5C), and then evaluated their likelihood scores were mapped on a plane spanned by the two PCs (Fig. 5D and Fig. S1).

If each map is reconstructed from images in a single conformation, the scores on the PC plane would have a prominent single peak. However, the likelihood scores in each map gave one or two broad maxima (Fig. 5D and Fig. S1), indicating that each map was reconstructed from a set of subunit images with broadly similar conformations and those with less similar conformations. For instance, in the first classification, maps in open conformations were similar to MD conformations in the area of −5 < 1st PC < 5 and −10 < 2nd PC < 0 (Fig. 5D). For maps in half-open conformations, likelihood scores displayed two broad peaks, one in the area of −5 < 1st PC < +5 and −10 < 2nd PC < 0, and the other in −10 < 1st PC < 0 and +5 < 2nd PC < +10. MD conformations, which were located in an area of 1st PC > 0 and 2nd PC > −5, could contribute to maps of closed conformations. The wide variety in MD conformations contributing to the closed conformation resulted in the EM map lacking structural details in the NAD domain (Fig. 5A).

Energy landscape of NAD domain motion

When maps from different classifications were in a similar conformation, the distributions of likelihood scores were consistent with each other, as observed for half-open1 map of the first classification (Fig. 5A), #3 map (half-open) of the 7-th classification (Fig. S1), and so on. This result suggested that maps displaying similar conformations would be approximated as a unique mixture of specific MD conformations. Therefore, we assume that each EM map can be approximated as a weighted-sum of MD conformations. This assumption is expressed in reciprocal space as

(2)

where is a weight to determine the contribution of the i-th MD map to the m-th 3D EM map in a classification. A set of linear equations regarding could be derived from Eqns (1) and (2) (see Materials and methods), and then, we could determine by solving the linear equations.

The variation of weight values of MD conformations was mapped on the PC plane as well as the likelihood scores. In most cases, one or two broad maxima were dominant around those observed in the likelihood scores, although the relative heights of maxima were changed (Fig. 6A and Fig. S1). For open conformations, two sets of MD conformations were dominant. The first set was located at the broad peak position observed in the likelihood scores (Fig. 6A), and the other comprised conformations transformed from the first set by a shear motion. The maps of half-open conformations were predominantly described by the two MD conformational groups, one in the area of −10 < 1st PC < 0 and 0 < 2nd PC < 10, and the other in 0 < 1st PC < +10 and −10 < 2nd PC < 0. Maps of closed conformations were dominated by MD conformations with 1st PC of +30 and 2nd PC of +5, but MD maps of open conformations additionally contributed to the low-resolution map.

Figure 6

Free-energy landscape in the NAD domain motion. (A) Weight values of MD conformations to approximate each classified map in Fig. 5A. The values are illustrated as contour maps on the plane spanned by the two PCs. (B) Free-energy differences calculated from the weight values of MD conformations (upper panel) and from the appearance frequencies in a 200-ns MD simulation (lower panel) plotted on the plane spanned by the two PCs. In the upper panel, free-energy differences are illustrated as contour map estimated from the values for 28 representatives. Colored circles indicate the positions of open (magenta), half-open1 (green), half-open2 (orange), and closed (gray) models built from maps shown in Fig. 7A. The dashed lines in the upper panel indicate 1.0 k_BT level from the lowest difference free-energy values. The lines are also shown in the lower panel as dashed and gray lines.

When assuming that conformations in NAD domain motions at ambient temperature are trapped by flash-cooling, the appearance frequencies of cryoEM images are proportional to the population of the conformations in NAD domain motion. Then, the determined weight could be interpreted as appearance frequency of i-th MD structure in images comprising m-th reconstructed EM map. The appearance frequency of i-th MD structure in all EM images, , can be determined by averaging over m as

(3)

where is the number of images classified into the m-th EM map. The free-energy difference of the i-th MD conformation relative to the most populated conformation is evaluated as

(4)

where k_B and T are the Boltzmann's constant and absolute temperature, respectively. is the highest weight among . The derivation of this equation is shown in the Materials and methods section.

Ten classifications gave almost the same maps of free-energy differences (Fig. S2), despite different sets of reconstructed maps (Fig. 5A and Fig. S1). Although conformations suggested by reconstructed maps in a classification were different from those of other classification, the sum of appearance frequencies of MD conformations was ideally consistent among independent classifications against the same set of EM images. Therefore, the same results among the 10 classifications would validate the calculation using the proposed method.

Figure 6B shows a free-energy difference averaged over those from 10 classifications (Fig. S2). Along the 2nd PC of 0, a shallow and wide valley appeared with two basins. One of the basins was located around −5 < 1st PC < +10 and −10 < 2nd PC < 0, and the other around −10 < 1st PC < 0 and 0 < 2nd PC < +10. The free-energy difference between the bottoms of the two basins was 0.2 k_BT, and the height of the barrier lying between them was 1.0 k_BT. The variation of free-energy inside the valley was within 0.4 k_BT, which was comparable with thermal fluctuation at ambient temperature, and therefore ensured spontaneous NAD domain motion. As the two basins with free energies slightly lower than that of the valley, pathways of NAD domain motion became more complicated than that of a simple hinge-bending motion to open/close the active-site cleft. For instance, NAD domain motion from the open to closed conformations would be frequently trapped in the two basins. The NAD domain motion trapped in a basin would then escape to open, closed, or the other basins. Further details of the structural changes on the free-energy landscape were visualized by the refinement of representative set of reconstructed maps as described in the next section.

The free-energy difference from the EM analysis was substantially different from that calculated from the appearance frequency in the MD simulation (Fig. 6B). Half-open conformations were major in the 200-ns MD trajectory, but the appearance frequencies of open and closed conformation in solution would be larger than those expected in the MD simulation. The cause of this difference will be discussed later.

Structure models of representative conformations

To visualize conformational changes in the NAD domain motion at higher resolution, we further classified and refined the four maps in Fig. 5A using the protocol shown in Fig. 4. In the energy landscape (Fig. 6B), the maps of half-open conformations were representative of two shallow basins, and those of open and closed conformations were located at positions suitable to illustrate the hinge-bending motion.

In the refined maps (Fig. 7), both the secondary structures and the side chains of NAD domains appeared much more clearly than those in the reconstructed map under D3 symmetry (Fig. 3D). Each map at near-atomic resolution (Table 1) allowed us to fit crystal structure models of both the NAD- and core domains followed by a real-space refinement with respect to the fitness to the map and the stereochemistry.

Figure 7

Representative maps refined after focused classification and model building. (a) 3D density maps of whole subunit refined based on the orientation of subunits provided from a focused refinement in Fig. 5A. The maps are designated open, half-open1, half-open2, and closed conformations. Each map is colored according to the local resolution and viewed from two different directions. The dashed lines in each panel indicate the edges of the NAD domain in the open conformation to demonstrate the conformational differences. The maps are illustrated by using ucsf chimera [50, 51]. (B) Maps of NAD domains viewed from the top. A structural model superimposed on each map is shown with labels of some amino acid residues. Panels were prepared using pymol [52]. Maps in both panels (A) and (B) are contoured at one standard deviation from the average.

Table 1. Statistics of structural models of metastable conformations.

Conformation	Number of particle images used	Resolution estimated by GS-FSC	Averaged Resolution (Å) NAD Domain/Core Domain	RMSD of bond length (Å)/bond angle (degrees) from the ideal	Superimposable X-ray structure	Cα-RMSD from X-ray structure (Å)a
Open	118 299	3.8	3.6/3.2	0.006/0.914	Subunit A	1.32
Half-open1	109 568	3.8	3.6/3.3	0.007/0.867	—	1.16b
Half-open2	146 327	3.7	3.4/3.1	0.006/0.896	Subunits D (C)	0.90
Closed	97 002	4.9	4.0/3.3	0.006/0.905	Subunits E (B)	0.84
Others	545 322	—	—	—	—	—

• ^a The atomic structure model of each conformation was superimposed onto its superimposable X-ray structure with respect to their core domains.
• ^b Although the half-open1 conformation was exclusively found in this cryoEM analysis, the structures of the two domains are compared separately with those of subunit C in the crystal structure.

The refined structural models enabled us to visualize conformational differences (Fig. 8A) on the free-energy landscape in NAD domain motion (Fig. 6B). From open to half-open1 conformations with a free-energy difference of 0.2 k_BT a tip of the NAD domain moved by ~ 3 Å only by hinge-bending motion. The NAD domain could slide by 2.5 Å between the half-open1 and half-open2 conformations in different basins, while the width of the active-site cleft was maintained. A hinge-bending motion driving the tip of the NAD domain by 3.5 Å was observed between half-open2 and closed conformations with a free-energy difference of < 0.1 k_BT.

Figure 8

Four refined EM models with different states in the NAD domain motion. (A) Comparison of pairs of four structural models in Fig. 7 after superimposing their core domains. Open, half-open1, half-open2, and closed models are shown in magenta, green, yellow, and gray, respectively. (B) Comparison of the refined EM models with subunits in a crystal structure model of GDH hexamer (the accession code in the PDB: 1EUZ). Upper, middle, and lower panels compare open EM conformation (magenta) and subunit A of a crystal structure, half-open1 EM (yellow) and subunit C, and closed EM (gray) and subunit B, respectively. In both panels, the structural models are superimposed at the core domains, and are drawn by using pymol [52].

A comparison of the four refined EM structures revealed the locations of the crystal structures in the free-energy landscape. The three conformations found in the crystal structure were consistent with open, half-open2, and closed conformations as indicated by the RMSD values (Fig. 8B and Table 1). In contrast, half-open2 conformation was missed in the crystal structures. Crystal contacts inducing several hydrogen bonds probably forced to escape the NAD domain conformation from the basin of half-open2.

Structures in the active-site cleft

In the depth of the active-site clefts of the refined maps, we should note the variation in the maps of Trp89 of the core domain (Fig. 9 and Fig. S3). The previous crystal structure analysis and MD simulation revealed that the Trp89 side chain was one of the factors influencing the NAD domain motion, as some of its rotamers sterically hinder the closing motion of the NAD domain [19, 20]. While maps of Trp74 and Trp416 side chains in the core domain appeared as single conformations and were independent of classifications (Fig. 9A), maps of Trp89 varied among the 10 classifications and lacked a portion of the volume of the indole ring and/or were composed of a few bulges (Fig. 9B and Fig. S3). Although it was difficult to deduce the rotamers of Trp89 at a local resolution of ~ 3.5–4.0 Å, the side chains of Trp89 were a mixture of different rotamers in the four metastable conformations.

Figure 9

Variations in the conformation of Trp89 side chain in the cryoEM structure. Panels (A) and (B) show comparison of maps of three tryptophan residues in core domain. (A) Locations of Trp89 (red), Trp74 (blue), and Trp416 (blue) residues in a subunit. Left panel shows maps of Trp74 and Trp416, the side chains of which display single conformations. The local resolution values of Trp74 and Trp416 were 2.9 Å and 2.8 Å, respectively. (B) Magnified views of Trp89 residues in the four maps in Fig. 7A. The maps are colored according to the local resolution. The maps of Trp89 residues after the refinement of the other nine classifications are shown in Fig. S1. All maps are contoured at one standard deviation level from the average. Panels (A) and (b) were prepared using pymol [52] and ucsf chimera [50, 51], respectively.

In this regard, we determined a crystal structure of Trp89Phe-mutated GDH (Table S2). The mutant enzyme showed low ligand affinity but displayed a catalytic activity compared with the wild-type enzyme. The side chain of Phe89 was more disordered than Trp89 in most subunits (Fig. S4), suggesting that conformations of hydrophobic residues in the pocket would be unstable probably because of interactions with hydration water molecules as speculated from previous MD simulation [20].

Discussion

We studied the domain motion in unliganded GDH from T. profundus by cryoEM. A 3D reconstruction under D3 symmetry of the hexameric enzyme gave ensemble-averaged map, in which the position and the orientation of NAD domain were difficult to determine (Fig. 3). In contrast, classifications focusing on the NAD domain gave maps of several conformations (Figs 4 and 5, and Fig. S1). Furthermore, we estimated appearance frequencies of reference conformations from the previous MD simulations (Fig. 6A) and visualized the energy landscape in the NAD domain motion using the novel analysis method (Fig. 6B and Fig. S2). Structural models built in the refined maps enabled us to postulate the correlation between structures and energy landscape (Fig. 8A). Based on the results, we discuss the implication of the maps and structural models in the domain motion, and the advantage and weak points of the method to estimate the energy landscape.

Spontaneous NAD domain motion

On the NAD domain motion of GDH from T. profundus, a crystal structure analysis visualized three conformations stabilized by crystal contacts [19]. In a 200-ns MD simulation, possible conformations in domain motion were sparsely sampled, and the correlation with changes of hydration structure at the depth in the active-site cleft was discussed [20]. However, it was difficult to experimentally investigate the appearance frequency of possible conformations and energy landscapes.

CryoEM revealed the GDH structure without the influence of crystal contacts and could also sample a number of conformational states without bias (Figs 3 and 5). Moreover, the method proposed to analyze the reconstructed map provided appearance frequencies of MD-sampled conformations (Fig. 6A). Subsequently, the free-energy landscape of domain motion was visualized and was different from that estimated from the appearance frequencies of conformation in the 200-ns MD simulation (Fig. 6B). Therefore, a 200-ns MD simulation of GDH could effectively sample possible conformations but might be insufficient to quantitatively predict the appearance frequencies of possible conformations. The force field parameters may be still incomplete [9], and/or other simulation protocol may be necessary to reproduce the appearance frequencies of conformations within a limited computation time.

The free-energy landscape constructed by the cryoEM analysis comprises a large valley for a hinge-bending motion to open/close the active-site cleft, and two basins (Fig. 6B) preventing direct open/close motion and correlating to the shear motion of the NAD domain relative to the core domain. Therefore, NAD domain motion probably proceeds through a more complicated pathway than a simple open/close motion. As the half-open1 conformation representing one of two basins in the free-energy landscape was absent from the previous crystal structure [19], we misunderstood that NAD domain motion was driven by a simple hinge-bending. According to the 200-ns MD simulation [20], stochastic and cooperative dissociation of hydration water molecules at the depth of the cleft would be one of driving forces for random conformational transitions between adjacent basins and the valley.

To understand why two basins appeared in the NAD domain motion, it is necessary to obtain the information on hydration structures of different conformations and discuss the energy landscape of hydrated protein molecules. To experimentally observe hydration structure changes, the resolution in structural analysis must be much higher. However, even in a cryoEM structure of ferritin at 1.6Å resolution, the amount of hydration water molecules inside was much smaller than that found in the crystal structure analysis [25], probably because of the scattering cross-section of oxygen atom [26]. Therefore, the detection of hydration sites on molecular surfaces is hopeless in cryoEM. As an alternative, the prediction of hydration sites using an empirically obtained data base [27, 28] would compensate for the experimental difficulties and help to understand hydration structure changes.

In the next stage of cryoEM analyses on GDH including hydration and conformational fluctuation of Trp89, we would focus on the changes of the energy landscape induced by a point mutation (Table S2 and Fig. S4) and by the binding of co-enzyme and substrates in correlation with the measured association constants. Although a small molecule, tentatively assigned as tris (Fig. 3C), was bound to the substrate binding site, basins were absent around closed conformations in the energy landscape of an unliganded state. From the viewpoint of energy landscape, the closed conformations would be unstable in comparison with a closed conformation in a liganded state as expected from glutamate-liganded GDH from Clostridium symbiosum [29]. Therefore, it is interesting to investigate what interactions between NAD domain and glutamate molecule modify the energy landscape to stabilize the closed conformation.

Benefits and improvements of the proposed method to construct free-energy landscape

In this study, we proposed a method to construct the free-energy landscape of NAD domain motion (Materials and methods). For the application, disrupted particle images must be almost completely excluded. The present classification focusing on the NAD domain successfully identified those images with disrupted subunits (Fig. 4). A small number of disrupted images may be contained in the images used in the 3D classification. However, their influences would be negligible, as judged from the fact that 10 landscapes constructed from 10 independent classifications were closely similar to each other (Fig. S2). Therefore, the focused classification acted as a filter to discard the majority of disrupted particle images and to provide images used to estimate the energy landscape.

The most valuable feature of this method is its capability to analyze the motions of the NAD domain with a molecular weight of 23 kDa in the 280 kDa GDH hexamer. Various analysis methods to investigate conformational flexibilities in macromolecular complexes have been developed [30]. For instance, in multibody analysis [16, 17, 31], overall 3D map of a macromolecule is divided into some rigid bodies, and then, map of each body is independently refined. Another approach is manifold learning method to construct the distribution of the conformations from particle images in a multidimensional space [14, 32], and this method is advantageous to visualize free-energy landscape in structural changes of macromolecule (Fig. 6B). These approaches have been applied to large MDa-scale macromolecular complex, such as 4.5 MDa 80S ribosome [14] and 2.5 MDa spliceosome [17].

However, their application to protein molecules of several hundred kDa would be difficult, due to the low contrast and point spread arising from the defocus of electron microscope. In fact, although we applied the multibody refinement to the analysis of NAD domain motion, the calculation never converged, and the resolution worsened as the refinement progressed (data not shown). On the other hand, our method that utilized reference conformations successfully illustrated the free-energy landscape of the domain motion in GDH, which was much smaller than the MD complex.

The success in the application of the method to NAD domain motion suggested that the 200-ns MD simulation provided conformations necessary to approximate the EM images by using Eqn (2). Since MD simulation of molecules with several hundred kDa has become easy with the improvements in computational devices, our method would be advantageous in visualizing energy landscape of molecules like GDH. In addition, reference structures necessary in our method are not limited to MD conformations. Therefore, even when a target molecule is too large to survey conformational fluctuations by MD simulation, our method is applicable to such molecules with reference structures prepared by other methods, such as multibody refinement. In addition, when reconstructed maps are limited at low resolution, conformations sampled by coarse-grained MD simulation [33] may be sufficient to illustrate roughly energy landscape of macromolecular complex.

Improvements in the proposed method will involve the collection of possible conformations and description of the variety in the set of reference conformations. For efficient sampling of conformations using MD simulation, it is effective to generate a number of MD trajectories independently starting from different EM conformations obtained in a 3D classification. The efficiency can be increased using generalized-ensemble methods, such as replica exchange protocol [34] and parallel cascaded selection MD [35]. The former protocol can efficiently sample conformational space from a single simulation. The latter is suitable to search pathways of conformational changes between two different structures. In addition, experimental evidences are necessary to assess whether MD simulation sufficiently samples possible conformations. Global conformational fluctuations in proteins are reflected in SAXS profiles of proteins in solution at ambient temperature [7]. AFM is also one of the methods to detect global conformational fluctuation as demonstrated in our previous study on GDH [20].

An additional concern is the choice of coordinate systems that are suitable to describe the structural changes. In this study, we visualized the free-energy landscape on the plane spanned by eigenvectors of two PCs, which approximated the NAD domain motion in a linear regime. For more rigorous description, PCs would be insufficient particularly for large-scale motions in a nonlinear regime. Otherwise, deviation and distortion from a linear approximation of motions lead to inappropriate views on nonlinear motions. Therefore, more precise construction of the free-energy landscape will be necessary to reformulate our methods applicable to nonlinear conformational changes, for instance, by using manifold embedding [14, 36, 37].

Conformations of flash-cooled GDH

Flash-cooling of specimen solution to 90 K is supposed to trap conformations of proteins possible at ambient temperature. However, studies on conformations and dynamics of proteins at cryogenic temperature have suggested that proteins display nonlinear and global conformational fluctuations above their glassy transition temperatures at around 220 K [38-40]. In addition, the transition would be affected by the glass transition of water at around 150 K [40]. Therefore, we have an issue whether flash-cooled proteins are trapped into conformations possible only below the glassy transition temperature or those at ambient temperature.

As one of experimental evidences, SAXS of GDH at ambient temperature provides a clue to address the issue, since SAXS comes from an ensemble average of structure factors of possible protein conformations. Regarding GDH, the R_g value of the reconstructed map in Fig. 3A is consistent with that in solution, and the NAD domain motions possible at ambient temperature would be trapped by flash-cooling of thin films of GDH solution in holy carbons at a cooling-rate faster than 200 K/10 ms as we measured so far. Of course, further assessment on this issue would be necessary at higher resolution for many proteins displaying large-scale motions.

Materials and methods

Sample preparation

Glutamate dehydrogenase from T. profundus was purified as reported previously [19, 20]. In brief, GDH was expressed in Escherichia coli DB21 using the pET-26b expression vector, carrying the wild-type GDH gene. GDH was roughly purified from the lysate after freeze-and-thaw treatment of the culture solution by heating at 353 K for 10 min. Further purification was carried out using four chromatography columns: HiTrap Q HP anion-exchange, HiTrap Phenyl HP hydrophobic interaction, RESOURCE PHE hydrophobic interaction, and RESOURCE Q anion-exchange columns (GE Healthcare, Chicago, IL, USA). After demineralization by dialysis, GDH was further purified by affinity chromatography using a Reactive Red 120 gel (Sigma-Aldrich, St. Louis, MO, USA). Finally, the samples were concentrated using Centriprep YM50 (Merck Millipore, Burlington, MA, USA) to a final concentration of ~ 10 mg·mL⁻¹ in 5 mm Tris-HCl (pH 7.5). The final purity of GDH was examined by SDS/PAGE (Fig. 2A). The final yield from a 1-L culture was 10 mg of GDH.

CryoEM

Aliquots of 2 µL of purified GDH solution were placed on Mo R1.2/1.3, 200-mesh holey carbon grids (Quantifoil, Großlöbichau, Germany) treated by glow-discharge, and then flash-frozen in liquid ethane using a Vitrobot device (Thermo Fisher Scientific, Waltham, MA, USA). CryoEM imaging was automatically performed with a jadas data acquisition software on the CRYO ARM200 system (JEM-Z200FSC; JEOL, Tokyo, Japan), operating at an acceleration voltage of 200 kV and equipped with a Ω-type energy filter. Zero-energy-loss images (10 eV) were recorded with a Gatan K2-summit detector (Gatan, Pleasanton, CA, USA) in counting mode at a calibrated magnification of 56 179 (yielding a pixel size of 0.87 Å) at an exposure rate of 8.15 e⁻/Ų per second, which corresponds to approximately six electrons per pixel per second (Fig. 2B). Exposures of 10 s were dose-fractionated into 50 frames. The defocus values ranged from 0.5 to 2.3 μm.

Image processing

We used motioncor2 software for dose-fractionating motion correction [41], and the gctf program for estimating parameters of the contrast transfer function [42]. relion-2.1 was used for image processing steps except initial 3D model generation and local resolution estimation [22, 43, 44].

A reference-based particle-picking procedure was carried out using a set of template images obtained from 2D class-averaged images calculated from a manually picked subset of micrographs. Using templates that were low-pass-filtered to 20 Å, 339 009 particles were picked out automatically from a total of 1473 micrographs. The picked particle images included ones irrelevant to GDH, such as ice contamination and dusts on the detector. These images were discarded through reference-free 2D classification (Fig. 2C). Clustered GDH particles were also discarded. The number of isolated GDH images finally selected through 2D classification was 169 240.

We then applied an initial run of 3D classification (data not shown) to the selected particles for the first 3D refinement. An initial model for 3D classification was generated using the e2initialmodel.py program from eman2 [45]. After 3D classification, particle images were submitted to a 3D auto-refinement procedure imposing D3 symmetry. The orientation of particle images was sampled at 0.9 degrees. The resolution of the final map was estimated as 3.5 Å based on the GS-FSC criterion of 0.143. The FSC curve was corrected for the effects of a soft mask using high-resolution noise substitution (solvent-flattened FSC) [46]. In this paper, all the reported resolutions are based on gold-standard refinement procedures and the corresponding solvent-flattened FSC with a criterion of 0.143.

Before visualization, density maps were corrected for the modulation transfer function of the detector and then sharpened by applying a negative B-factor, which was estimated using an automated procedure [47]. Local resolution variations were estimated using the blocres program from bsoft [48, 49]. All of the EM maps in this paper were imaged by ucsf chimera [50, 51] and pymol [52].

Focused classification of the NAD domain

The model obtained under the assumption of D3 symmetry demonstrated the conformational variation of the NAD domain to open/close the active-site cleft (Fig. 3A,D) as expected from previous studies [19, 20]. Thus, in the next stage, we classified the EM images to characterize the conformational variation of NAD domain motion.

Classification focusing on one NAD domain of a GDH image was conducted using the symmetry expansion method. This method was first applied to each observed image to generate five replicated images, which are related by the D3 symmetry of GDH. To focus on the region of a single NAD domain with an upper part of core domain, we subtracted the other parts composed of five core domains and five NAD domains from the six symmetry-expanded particle images (Fig. 4). The mask for particle image subtraction was derived from the fitted crystal structure. The focused 3D classification for the subtracted images, each of which reflected signals of a single NAD domain, was then performed. The orientation of the NAD domains was fixed. The subtracted images were then classified into eight classes. According to this classification, the original particle images were also classified into those eight classes. For each class, 3D auto-refinement was applied to the original images to avoid artifacts originating from inaccurately prepared signal-subtracted images of the other NAD domains. The summary of this procedure is illustrated in Fig. 4.

MD simulation and analysis of trajectory

The MD simulation carried out previously [20] is summarized here. An atomic model of a GDH molecule composed of 39 136 protein atoms was made from a crystal structure [19] (accession code of the PDB: 1EUZ) and was immersed in a water box (144 × 144 × 160 Å³) including 94 799 TIP3P water molecules [53] and 12 Na⁺ ions to neutralize the system. The MD simulation was carried out using the marble program suite [54] and the CHARMM27 force field [55]. The particle-mesh Ewald method [56] was applied to treat electrostatic interactions. A symplectic integrator for rigid bodies [57] was used with a time step of 2 fs. The solvent region was equilibrated by a 1.2-ns NPT run at 293.15 K and 1.0 atm under a harmonic restraint for the GDH molecule in an energy-minimized system. MD coordinates were obtained every 1 ps through a production run of 200 ns under NPT condition without restraints.

Conformational fluctuations of each GDH subunit in the 200-ns MD trajectory were analyzed by a PCA (Fig. 5B). A set of Cα-atoms in rigid secondary structures of core domain was used as a reference to superimpose subunits, and then, the PCA regarding the NAD domain motion was carried out by focusing a Cα-atom set of the Rossmann fold in the NAD domain.

Calculation of map from MD conformation

A set of six core domains in the selected 28 MD conformations of GDH hexamer (Fig. 5C) were superimposed onto that of an atomic model built for EM map (Fig. 3D). The MD coordinates were converted to a 3D volume using molmap in ucsf chimera [50]. The structure factor of each map was calculated by using a custom-made program coded by one of the authors (MO).

Since EM maps lose contrast depending on spatial frequency, , due to factors such as partial coherence of the electron beam and modulation transfer function of a used detector [47], these influences were incorporated into MD maps in reciprocal space. Then, the structure factor of each MD map, , was multiplied by an appropriate damping factor so that the amplitude of became comparable to that of a EM map, , in the spatial frequency range of interest. Here, was determined as a ratio between spherically averaged amplitudes of and as

where the integration was taken over the solid angle in reciprocal space.

Each MD map after the correction by was processed by the mask used in focused classification (Fig. 4), and subsequently converted to reference structure factor used in the analysis using Eqns (1) and (2) (see below section).

Calculation of appearance frequencies of MD conformations in EM map

The similarity between an EM map and a MD structure is evaluated by a likelihood score defined as:

(5)

where and are structure factors of EM map and n-th structure of MD simulation at the l-th voxel in reciprocal space. is resolution-dependently scaled to . is the uncertainty of originated from the EM images used for the reconstruction of EM map.

Here, we assume that each EM map can be expressed as a weighted-sum of MD maps as expressed in reciprocal space:

(6)

where is a weight to determine the contribution of the i-th MD map to the EM map and satisfying the normalization condition. Then, Eqn (5) is rewritten as:

(7)

By using the normalization condition on , the numerator can be reduced as:

(8)

Then, the numerator is modified further by using the cosine formula as:

(9)

where is the phase of . By using Eqn (9), can be rewritten as:

(10)

As the sum in the second term is taken over structure factors of all MD structures, the term is constant and independent of n. Then, a set of linear equations regarding stands as

(11)

However, because the constant can be calculated only after the determination of , we here exclude the constant by introducing a new valuable as:

(12)

where M-th equation is selected for the exclusion. As this substitution makes all components in the M-th raw in Eqn (13) to be zero, the set of linear equation is impossible to be solved. To avoid this, we substitute the M-th raw by the normalization condition on as:

(13)

Then, a set of weight can be determined by numerical calculation.

Calculation of free energy

The appearance probability of the i-th state with a free-energy in an equilibrium system at an absolute temperature is given as

(14)

Then, the free-energy difference between the state and a reference state with a free-energy and an appearance probability is calculated as

(15)

This equation was used to investigate energy landscape of protein motions in cryoEM [14, 32] and MD simulation [35].

To visualize the free-energy landscape in the combined analysis of cryoEM and MD simulation by using Eqns (1) and (2), we numerically calculated a set of appearance probabilities (or weights) of selected MD conformations by using Eqn (13) in each classification as illustrated in Fig. 6A. After determining a set of weights in each 10 classifications (Fig. S1), we will find a MD conformation displaying the maximum weight value in the set. Then, according to the Eqn (4), which is a generalized version of Eqn (15) under the condition of Eqn (3), the free-energy differences were calculated for each MD conformations from that with the highest weight (most frequently appeared). The results from 10 classifications (Fig. S2) were merged to give an averaged energy landscape (Fig. 6B).

To visualize the variation of weight and free-energy difference values on two-dimensional plane as in Figs 5 and 6 and also in Figs S1 and S2, we used Igor Pro software (WaveMetrics, Portland, OR, USA).

Structure model for refined maps from a focused classification

In model building of the four states representative among the 10 focused classification (Figs 7 and 8A), a crystal structure model refined at a resolution of 1.8 Å [19] was used. Residues composing the core domain were fit into the four maps with positional adjustments of α-helices and β-strands using coot [58]. For each conformational state, NAD domain residues were fitted to the map by referring to the Rossmann fold predominantly composing the NAD domain. All models were refined in real space using phenix [59, 60].

Acknowledgements

The authors thank Professor Keiichi Namba of Osaka University for the use of the EM facility. Trp89Phe-mutated GDH was purified and crystallized by Ms. Yuka Matsui. This study was supported by grants from the Japan Society for the Promotion of Science (Nos. jp13480214, jp19204042, and jp22244054 to M.N.; Nos. jp26800227 and jp17H04854 to TO.; and No. 18J11653 to MO) and by grants from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. jp15076210, jp20050030, jp22018027, jp23120525, jp25120725, jp15H01647, and jp17H05891 to MN; and No. jp26104535 to TO). CryoEM observations were partially supported by the Platform Project for Supporting Drug Discovery and Life Science Research [Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS)] from the Japan Agency for Medical Research and Development (AMED) (project No. 0436). X-ray diffraction data collection of mutated GDH crystal was performed at BL26B2 with the approval of the RIKEN Harima Institute.

Conflicts of interest

The authors declare no conflict of interest.

Author contributions

MN and MO designed the study. MO purified the specimens. MO and TK performed the cryoEM observations. MO carried out image processing with advice from TK. MO and MN carried out the analysis, the derivation of equations in proposed analysis method, and built the structure models. TO provided structures appearing in the MD trajectory. MN and MO wrote the manuscript.