Mechanical coupling analysis

Mechanical coupling analyses were conducted on the crystal structures of the ADP-bound nitrogenase complex (PDB ID: 2AFI[28], 3074 residues solved) and the AMPPCP-bound nitrogenase complex (PDB ID: 2AFK[28], 3064 residues solved). While the 2AFK structure is currently replaced by 4WZB, the major difference between the 4WZB and 2AFK structures is the nature of the FeMo-co central atom (C vs. N). The position of the Cα atoms, which are used in our normal mode analysis, is very similar in the two structures (RMSD = 0.18 Å). We adopted the 2AFK structure for modeling the ATP-bound complex for consistency with the structure adopted for the ADP-bound complex (2AFI structure). In the following, when discussing the computational results based on the above crystal structures, we refer to the nonhydrolyzable ATP-analog structure as the “ATP-bound” nitrogenase. In the present study, the explicit presence of the cofactors was neglected. Inclusion of the cofactors as done in earlier studies yields negligible differences in the covariance matrix, and the analysis based on it does not change.[5] The number of residues in 2AFK and 2AFI PDB structures is slightly different (3064 vs. 3074). Differences are limited to the (unstructured) termini regions and are not significant for the present analysis. In order to fully utilize the crystallographic information, we included all the residues contained in the crystallographic structures. However, analyses were performed only for the common residues. The general protocol adopted for the mechanical coupling analysis is described briefly here; further details can be found in our previous work.[38]

Our analysis is based on a coarse-grained ANM[39] as implemented in ProDy.[40] Coarse-grained ANM calculations are definitely more amenable for the type of analysis presented here than a principal component analysis based on molecular dynamics trajectory. Indeed, the size of the nitrogenase complex poses serious limitations on the convergence of long-time, large-amplitude motions, which are crucial for the long-range communication.

The normalized covariance matrix of interatomic motions C ≡ {C_ij} and the Euclidean distance matrix D ≡ {D_ij} are generated from the coordinates of the C_α atoms. The first 6 trivial modes (rotations and translations) are excluded. Using the covariance matrix, the adjacency matrix A ≡ {A_ij}, describing the network of the correlated motions in the protein is introduced as (2) In order to remove the trivial correlations, the matrix A is pruned according to the rule (3) where μ_|C| and σ_|C| are the mean and standard deviation of C, respectively, and D_cut is the contact distance cutoff set to 11 Å, which is the minimum distance to generate a direct path between any two given residues. The maximum coupling threshold C_thresh is set to 0.95, so any |C_ij| > C_thresh is set to C_thresh, and A_thresh = 1- C_thresh. Such a threshold is applied for numerical stability to avoid small elements in the A-matrix; the value is based on expected coupling within secondary structural elements.[38] The A matrix corresponds to a two-dimensional undirected graph, in which each node represents one residue, and the length of each edge connecting two nodes represents the strength of coupling between two residues. From the matrix A, the geodesic matrix G is generated as the sum of all edge lengths along the shortest path from node i to node j, using MATLAB.[41] We indicate the shortest path in the covariance space as the most efficient pathway between i and j. Because of the elongated shape of the nitrogenase complex, the shortest path in the covariance space is often similar (but not identical) to the shortest path in the cartesian space. Finally, the mechanical coupling matrix M is calculated from the correlation and geodesic matrices as (4) In the proposed mechanical coupling analysis, we filter out the purely coincidental correlated or anticorrelated motions inferred from the covariance analysis by weighting each element C_ij of the covariance matrix by the geodesic distance matrix in the covariance space between residue i and residue j. By doing so, we focus on how the motions of the nitrogenase complex about one equilibrium conformation allow for the communication between the distant sites. In this spirit, “mechanical coupling” here indicates that two residues or two regions not only have correlated dynamics, but, more importantly, there is an efficient allosteric communication pathway connecting them (i.e., short geodesic distance). However, it does not necessarily indicate any functional role, whose assessment is clearly beyond the coarse-grained description of the protein adopted here.

With the mechanical coupling graph of the protein at hand, the shortest path trees can be generated from a given site X to any other residue in the protein or between two given sites X and Y using MATLAB.[41] In the all-residue representation, the site of each [4Fe-4S] cluster includes four cysteines, the site of each P-cluster includes six cysteines, and the site of each FeMo-co includes one cysteine and one histidine.

Communication networks

The mechanical coupling matrix M highlights parts of the nitrogenase complex that have correlated motions and are coupled by efficient pathways between them. These pathways are dictated by the protein scaffold, which connect distant regions through delocalized vibrational modes. However, the matrix M does not directly provide any information on the identity of the residues that contribute to the mechanical coupling between two distant parts because this information is abstracted into the geodesic matrix G. Typically, there is a multitude of pathways connecting distant parts of a protein. We recently showed that these pathways may share a few common residues that are points of high traffic (many pathways passing through them) and represent effective “chokepoints” for the allosteric communication.[38] The contribution of each residue to the mechanical coupling can be obtained by calculating the shortest-path tree from a given region (e.g., the P-loop in the Fe protein) to another region (or all other residues) and merging the resulting trees to form a graph of strong coupling. The importance of a given residue can be then quantified by the number of pathways passing through it vs. the total number of possible pathways as measured by the cost-weighted betweenness centrality χ^X for each residue or χ^X-Y for any pair of residues. The cost-weighted betweenness centrality quantifies the influence of a residue on the mechanical coupling pathways originating from (or ending to) a given site X or between two sites, X and Y, of the protein. Therefore, perturbation of a residue with larger cost-weighted betweenness centrality is expected to have larger impact on the coupling, or more control over the allosteric network, because much of the allosteric signaling will pass through that residue.

Significance of individual normal modes for the strongest coupling pathways

The covariance matrix is given by the summation of all normal modes. In order to study the contribution of an individual normal mode to the strongest coupling pathways in the nitrogenase, a sub-covariance matrix C_−k can be obtained by subtracting the k-th mode from the full covariance matrix: (5) where λ_k and ν_k are the k-th eigenvalue and eigenvector of the covariance matrix obtained from the ANM. Then C_−k is normalized by the same mean-square fluctuations of the full covariance matrix, and the same procedures and cutoffs as above are applied to construct coupling pathways without the respective mode. Removing a significant mode will lead to a large change on the coupling pathways. The influence of an individual mode k can be quantified by the inner product of the betweenness of the nodes (i.e., residues) in the coupling pathways constructed from the sub-covariance matrix C_−k, i.e., the vector (χ_−k,1,χ_−k,2,⋯,χ_−k,N), and the betweenness of the nodes in the strongest coupling pathway constructed from the full covariance matrix, i.e., vector (χ_0,1,χ_0,2,⋯,χ_0,N). In order to take into account both the directionality and the magnitude of the two vectors, the overlap of the coupling pathways before and after removing mode k, O_k, is normalized as (6) where N is the total number of nodes. In fact, this overlap analysis can be used to identify the similarity of coupling pathways with respect to χ vectors between any two motions/displacements. The influence of the mode k is quantified as (7) The larger the impact of normal mode k, the higher the value of I_k is. The limiting value I_k = 1 implies that one single normal mode k gives rise to all necessary motions for the coupling. I_k can be smaller than 0 (i.e., O_k larger than 1), which indicates that removing the normal mode k may enhance the importance of specific residues.

ProDy is used to generate the normal modes and the Normal Mode Wizard (NMWiz) plugin to VMD is used to visualize the normal modes.[40]

Hydrogen/deuterium exchange experiments

Nitrogenase proteins were expressed and purified from Azotobacter vinelandii strains DJ995 (wild-type MoFe protein with His tag) and DJ884 (wild-type Fe protein) in anaerobic conditions as previously described.[42] Protein purity was assessed by SDS-PAGE analysis with Coomassie Blue stain used for protein detection. Protein concentration was determined by biuret assay against a bovine serum albumin standard.

The H/D exchange reaction was conducted in anaerobic conditions as described elsewhere.[43] Briefly, four solutions were prepared: deuterated buffer (50 mM Tris, 12 mM dithionite, pD 7.4), non-deuterated buffer (50 mM Tris, 12 mM dithionite, pH 7.4), quench solution (3% formic acid; FA, Sigma), and dilution buffer (15 mM ATP and 8 mM MgCl₂) MoFe protein in H₂O was diluted 10-fold during mixing with Fe protein in a D₂O dilution buffer. Samples were removed and quenched to stop exchange after 1 hour and 24 hours. Reactions were quenched by placing 10 μL of sample into a mixture of 3% formic acid and porcine pepsin (Sigma, 0.2 mg/mL final concentration) on ice. After a two-minute incubation with pepsin, the reaction sample was frozen in liquid nitrogen and stored at -80°C until liquid chromatography-mass spectrometry (LC-MS) analysis.

A 1290 UPLC series chromatography system (Agilent Technologies) coupled to a 6538 UHD Accurate-Mass Q-TOF LC-MS mass spectrometer (Agilent Technologies). MassHunter Qualitative Analysis version 6.0 (Agilent Technologies) was used to process raw data. Peptide identification used MS and MS/MS analysis which was augmented with Peptide Analysis Worksheet (PAWs, ProteoMetrics, LLC.). Peptide exchange values and deuterium uptake curves were generated using HDExaminer (Sierra Analytics, Inc.). Percent deuterium (%D) incorporation at each time point was calculated by dividing the number of deuterium atoms incorporated (#D) by total deuterium incorporated at 24 hours. Overlapping peptides were resolved as described by Pascal et al.[44] The investigation of the correlations between protein dynamics based on the difference in percent of deuterium exchange between each region of the MoFe protein was done in R 4.0 language and environment for statistical computing and graphics (R Development Core Team, 2020) using corrplot package.[45]

The analysis of the HDX data was a two-part process. First, compare deuterium incorporation in all conditions, the deuterium uptake was determined by monitoring shifts of the centroid peptide isotopic distribution in the mass spectra. The percent deuterium (%D) incorporated at a given condition was calculated by dividing the number of deuterium atoms incorporated by the number of deuterium atoms incorporated after 24 hours. Our investigation of the protein dynamics correlations and correlation patterns was based on the difference in %D between each region of the MoFe protein. The analysis was carried out using the symmetric matrix D_ij = |d_i−d_j|, which is defined in terms of the absolute values of the difference in the deuterium content %D of each peptide pairs (d_i and d_j). The correlation matrix was generated using Pearson correlation. To group patterns based on the correlation of difference in the matrix elements D_ij, hierarchical clustering was used (1-corr formula as distance and complete linkage as agglomeration method). The number of useful clusters (distinct patterns of protein dynamics correlations) was established based on k-means clustering.

Covariance and mechanical coupling analysis

Analysis of available crystal structures does not show conformational changes in the MoFe protein upon association with either the ATP- or ADP-bound Fe protein. Crystal structures provide us with a picture of the equilibrium structure and, clearly, do not inform us on potential transient changes. The root mean-square-deviation (RMSD) between the ATP- and ADP-bound complex is 6.6 Å. RMSD between the MoFe proteins complexed with the ADP- or ATP-bound Fe protein is ~0.3 Å, while the RMSD of the ADP- and ATP-bound Fe protein itself is ~2.5 Å (S1 Table). This shows that the two complexes at their corresponding equilibrium conformation captured by crystallography differ in the Fe proteins position through a rigid body reorientation of the Fe protein on the surface of the MoFe protein.[24,28]

The covariance matrix of the displacements of the residues C for both the ATP- and ADP-bound nitrogenase complex is reported in S2 Fig. The covariance matrix shows a large degree of correlation between the motions of various regions of the nitrogenase complex. The motion of the two αβ units of the MoFe protein is mostly positively correlated, whereas with the Fe proteins they are mostly negatively correlated. However, interesting exceptions were found. For instance, the residues near the cysteinate ligands of the P-cluster are positively correlated with the residues near the [4Fe-4S] cysteinate ligands (residue 97, 132) of the Fe proteins. The two Fe proteins are largely positively correlated, but they show negative correlation, e.g., near the [4Fe-4S] cysteinate ligands.

The mechanical coupling matrix M (Fig 2) is able to single out among the many regions with highly correlated or anti-correlated motions those that are also mechanically coupled through efficient paths. The magnitude of the mechanical coupling, as described by the matrix M, depends on the geodesic matrix. By construction, residues with a large covariance and geometrically close to each other have short geodesic distances, and thus, are strongly mechanically coupled. In addition, within each unit, the coupling is generally strong as a consequence of its compactness. Several correlated regions in the covariance matrix also appear in the mechanical coupling matrix (Fig 2), which indicates that the correlated motions between the two Fe proteins, between the two units of the MoFe protein, and between the Fe protein and the MoFe protein, have efficient mechanical routes connecting them. Overall, the ADP-bound complex has a slightly stronger mechanical coupling than the ATP-bound complex (S1 Fig, i.e., the difference between Fig 3A and 3B), with the largest differences within the Fe protein or at contact points between the Fe and MoFe proteins. Due to the general similarity between the ADP- and ATP-bound complex, in the following, the mechanical coupling between the various units of the ATP-bound nitrogenase complex is mainly discussed. The exceptions will be explicitly discussed as appropriate.

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Fig 2.

Mechanical coupling matrix M for (A) the ATP-bound nitrogenase complex and (B) the ADP-bound nitrogenase complex. The mechanical couplings between Fe₁ and α₁β₁, Fe₂ and α₂β₂, Fe₁ and Fe₂ are highlighted in dashed blocks.

https://doi.org/10.1371/journal.pcbi.1008719.g002

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Fig 3.

Maximum mechanical coupling M of (A) residues in α₁β₁ to any residue in Fe₁ and (B) residues in Fe₂ to any residue in Fe₁ in ATP-bound complex. The ATP analogues, [4Fe-4S] clusters, P-clusters, and FeMo-co are shown in mesh surface. Residue 186–190 in β₁ are highlighted in spheres in (A); one α-helix and three β-sheets in each monomer of Fe₂ appear red in (B) (following the numbering in the 2AFK PDB file).

https://doi.org/10.1371/journal.pcbi.1008719.g003

Within each Fe protein, the P-loops are coupled to the protein-protein interface and the [4Fe-4S] cluster through the switch region I and II, respectively. Liao and Beratan discussed this coupling in their computational analysis of the isolated Fe protein.[46] Using a coarse-grained model, they identified correlated regions in the Fe protein and reported that residues in the P-loops and switch regions are relatively rigid in the slowest normal mode, which can be important for function-relevant conformational change. As we will discuss below, we show that there is indeed an efficient communication pathway between these regions, which, in the nitrogenase complex, extends up to the interior of the MoFe protein. The mechanical coupling matrix M between Fe₁ and α₁β₁ for the ATP-bound complex is reported in Fig 3A. Three α-helices in the α (helices α₇, α₉ and α₁₀ following the numbering in the 2AFK PDB file) and the corresponding helices in the β component (helices α₃₃, α₃₅ and α₃₆) of the MoFe protein are strongly coupled to the Fe₁ protein. The α₁β₁ region involved in the coupling extends from these α-helices located at the docking interface near the P-cluster to the [4Fe-4S] cluster in the Fe protein. In particular, in the ATP-bound complex the loop containing β-188^Ser (residues 186–190) is highly coupled with the switch regions of the Fe protein (Fig 3A). This coupling is negligible in the ADP-bound nitrogenase (S3A Fig).

The mechanical coupling between the two Fe proteins is shown in Fig 3B. The coupling is relatively weak by construction, because of the long coupling pathway, i.e., a long geodesic distance in the covariance space. However, it highlights very specific coupling patterns. The residues in one Fe protein with the highest coupling to the residues of the other Fe protein are located in the P-loops, the α-helix (helix α₁₃₀ in Fe_2A and α₁₄₁ in Fe_2B) and the β-strand (strand Ο₅ in Fe_1A and strand P₅ in Fe_1B) that the P-loop is bridging, along with three other β-strands in the same β-sheet (strands Ο₆, Ο₇, Ο₈ in Fe_2A and strands P₆, P₇, P₈ in Fe_2B). All these structural elements envelope the nucleotide binding sites. This result suggests that a perturbation introduced in the nucleotide binding pockets (for instance, hydrolysis of the nucleotide or loss of the inorganic phosphate P_i) is propagated to the nucleotide binding sites in the opposite unit. The mechanical coupling in the ADP-bound complex (S3B Fig) is similar to the ATP-bound complex, but it appears to be smaller in the ATP-bound complex (26% smaller in average). These differences are consistent with the covariance matrix, which indicates that the ADP-bound complex has a more flexible structure.

Changes in protein flexibility and mechanical coupling upon ATP hydrolysis

As we highlighted above, the structure of the MoFe protein does not provide information for its change upon ATP hydrolysis. However, the rearrangement of the Fe protein on the MoFe protein upon hydrolysis influences the flexibility of various structural elements close to the Fe protein/MoFe protein interface. The influence of the Fe protein reorientation upon ATP hydrolysis was quantified in term of changes in the root mean-square fluctuation (RMSF) of the C_α atoms as obtained from the ATP- and ADP-bound structures. The RMSF analysis presented in Fig 4 shows that, apart from a trivial perturbation in the dynamics of the residues at the Fe protein/MoFe protein interface that are in close contact, longer range perturbations are also present. These perturbations extend up to the second coordination sphere of the P-cluster (Fig 4, inset). Interestingly, the largest of these perturbations involve the loop containing β-188^Ser, residues 186–190, which is located more than 10 Å from the closest residue of the Fe protein. Residues in this loop show an increase in the RMSF up to 16%. This increase should be compared to the maximum increase of about 24% for residues at the interface that lose contact with the Fe protein after the reorientation of the Fe protein on the MoFe protein upon ATP hydrolysis.

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Fig 4. Change in RMSF of the MoFe protein upon ATP hydrolysis.

The change is shown as deviation of the RMSF of the MoFe protein in the ADP-bound complex relative to the ATP-bound complex reported as a color scale and is projected on the ribbon representation of the protein. The positive changes, whereby the ADP-bound complex shows larger flexibility than the ATP-bound complex, are shown in red, and the negative values are shown in blue. For clarity of representation, the RMSF change for the Fe proteins is not color-coded. The ATP analogues, [4Fe-4S] clusters, P-clusters, and FeMo-co are shown in mesh surface. Residues 186–190 in β₁ are highlighted as space-filling structures (spheres). Residues at Fe protein/MoFe protein interface with large RMSF change upon ATP hydrolysis appear in orange or red.

https://doi.org/10.1371/journal.pcbi.1008719.g004

In addition to the differences in flexibility, the ATP- and ADP-bound complexes also present differences in the mechanical coupling. Some of these differences have already been highlighted above. Here, we further comment on additional differences at the Fe protein/MoFe protein interface. The change in the mechanical coupling between Fe₁ and α₁β₁ in the ADP- and ATP-bound complexes is illustrated in Fig 5. As can be seen, the mechanical coupling between the loop containing β-188^Ser and the Fe protein is smaller in the ADP-bound complex. The decreased mechanical coupling and the increased flexibility of this loop in the ADP-bound complex are a consequence of less efficient coupling pathways (larger geodesic distance elements, G_ij) between the loop and the Fe protein.

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Fig 5. Change in M between residues in α₁β₁ to any residue in Fe₁ upon ATP hydrolysis.

The change is shown as largest deviation of M in the ADP-bound complex relative to the ATP-bound complex, either positive (red) or negative (blue) following the same projection scheme discussed in Fig 4. The Fe₁, Fe₂, α₂β₂ proteins are shown in white. The ATP analogues, [4Fe-4S] clusters, P-clusters, and FeMo-co are shown in mesh surface. Residues 186–190 in β₁ are highlighted in spheres and residues 119–120 in α₁ are indicated by arrow. Residues at Fe protein/MoFe protein interface with large deviation upon ATP hydrolysis appear in dark red or dark blue. For clarity of representation only the change in one half of the MoFe protein is shown.

https://doi.org/10.1371/journal.pcbi.1008719.g005

In addition, the mechanical coupling between the Fe protein and the helices α₇, α₈ in the α component and the corresponding helices α₃₃, α₃₄ in the β component increase in the ADP-bound complex, except two residues at one end of the helix α₇, α-119^Gln and α-120^Glu, which are located near the β-188^Ser loop. The other two helices (α₃₅ and α₃₆) in the β component, which are also located near the protein-protein surface, have decreased mechanical coupling with the Fe₁ in the ADP-bound complex, while half of the corresponding helices α₉ and α₁₀ in the α component have increased. This asymmetric change of the mechanical coupling in the α and β component may be due to the rolling motion of the Fe protein over the surface of the MoFe protein, from β to α component (see below). This motion not only affects the protein-protein interaction at the interface but may also have influence on the mechanical coupling between the residues near the P-cluster and the Fe protein. The results between α₂β₂ and Fe₂ are shown in S4 Fig.

Communication network

The communication network between different regions of the nitrogenase complex was studied by analyzing the strongest mechanical coupling pathways between residues of one region and residues of another region as extracted from underlying mechanical coupling graph based on the most efficient paths described by the geodesic matrix. The residues with the largest influence on the mechanical coupling are identified by the cost-weighted betweenness centrality χ. As we discussed in the Methods, the higher the χ value of a given residue, the higher the number of pathways passing through it; residues with large χ value represent effective chokepoints for the communication between two regions. We analyzed the communication within each half of the nitrogenase complex, and between the two halves of the nitrogenase complex. Results for the most important residues in the communication within each half of the complex (Fe-αβ), between the two halves (from Fe₁ to Fe₂), and between a specific region, the P-loop in the two halves (from P-loop in Fe₁ to P-loop in Fe₂) are show in Fig 6. In this figure, dominant χ values are reported as iso-surface enclosing the corresponding residues whose size is proportional to the magnitude of χ.

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Fig 6.

Important residues for mechanical coupling between (A) Fe₁ and α₁β₁, (B) Fe₁ and Fe₂ and (C) P-loops in Fe₁ and P-loops in Fe₂ as identified by cost-weighted betweenness centrality, χ. For clarity, only residues with χ > 40% of maximum value are shown as hot pink space-filling structures, whose size is proportional to the magnitude of the corresponding χ value. The ribbon presentation of the ATP-bound nitrogenase complex is colored as follows: Fe₁, red; Fe₂, yellow; α₁β₁ unit of MoFe, blue; α₂β₂ unit of MoFe, green. ATP, [4Fe-4S] clusters, P-clusters and FeMo-co are shown in spheres. Residues among top 10% of χ or residues in/near the sites of interest are labeled.

https://doi.org/10.1371/journal.pcbi.1008719.g006

Mechanical coupling and conformational dynamics.

The mechanical coupling between distant parts of the nitrogenase complex is regulated by the underlying conformational dynamics. Allosteric signaling is instantaneously distributed through the scaffold of the complex via protein normal modes. Here, we analyze the protein vibrational modes that influence the communication network the most.

The influence of a given normal mode k on the mechanical coupling in the nitrogenase complex was quantified by the overlap between the χ values from the full covariance matrix, , and after removing normal mode k, (Eq 6). Results are better visualized through the complement to 1 of (Eq 7). It is expected that the large-amplitude, slow-frequency delocalized modes will be most important for the long-range coupling, i.e., they will have the highest . The I_k values for the coupling between Fe₁ and α₁β₁ and between Fe₁ and Fe₂ calculated for the top 50 normal modes are reported in S6 Fig. As can be seen, the first 9 modes (except mode 5 and/or 6) affect appreciably both the communication within each half of the nitrogenase complex or between the two halves. On the other hand, some individual modes, e.g., mode 1, 2, 3, or 4 have larger influence on the communication between the two halves (Fig 7B; I_k^Fe1-Fe2 > 0.40), while the influence is much smaller on the communication within each half of the complex (Fig 7A; I_k^Fe-αβ < 0.25). As expected, the communication between the two halves relies more on delocalized motions, while more localized motions between Fe and αβ can give rise to the coupling within each half of the complex.

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Fig 7. Normal mode decomposition.

Top 9 normal modes of the ATP-bound nitrogenase complex (top panels) and their influences on the mechanical coupling between (A) Fe₁ and α₁β₁, (B) Fe₁ and Fe₂, (C) P-loops in Fe₁ and P-loops in Fe₂; (D) overlap between the normal modes of the ATP-bound nitrogenase and the vector describing the displacement of the Fe protein that takes place upon ATP hydrolysis as inferred from the ATP- and ADP-bound crystal structures.

https://doi.org/10.1371/journal.pcbi.1008719.g007

The I_k values reported above refer to the global coupling between the Fe proteins and/or the MoFe protein, i.e., all residues-to-all residues. We have also explored how the conformational dynamics of the complex couple specific regions of the nitrogenase complex. Results are qualitatively similar to those obtained for the global coupling. As an example, the I_k^{Ploop1-Ploop2} for the coupling between the P-loops in the two Fe protein are given in Fig 7C.

The analysis discussed so far is based on harmonic vibrational modes, therefore on harmonic displacements about the equilibrium (crystallographic) configuration. Therefore, it cannot address the effect of transient structural changes, which can either enhance or weaken the relevance of the coupling pathways and, consequently, change the χ value associated with a given residue or region. More importantly, potential transient large-amplitude structural changes, postulated to be relevant for the electron transfer, are clearly not accessible through a Gaussian model. The only available information about the structural dynamics (change) during catalysis comes from the inspection of the crystal structure of the ATP- and ADP-bound nitrogenase complex, which reveals a structural, rigid body rearrangement of the Fe protein over the MoFe protein upon ATP hydrolysis. It is therefore of interest to see if this structural reorganization correlates with the mechanical coupling deduced from equilibrium structures. To this end, the overlap between the vibrational modes and the unit vector, ΔR, describing the conformational change from the ATP-bound to the ADP-bound Fe protein complex is calculated. As can be seen from Fig 7D, modes 1, 3 and 4 account for majority of the structural rearrangement occurring upon ATP hydrolysis, with mode 4 having the largest overlap with ΔR. Remarkably, these three modes are among the most important modes for the mechanical coupling, especially between the P-loops of two Fe proteins.

Taking a step further, we investigated what type of mechanical coupling the displacement described by only the vector ΔR would yield. In order to achieve this, the mechanical coupling analysis was repeated using a pseudo-“covariance matrix” constructed as (S7 Fig). Various mechanical coupling pathways are examined, including those between the sites of interest: P-loops, [4Fe-4S] cluster, P -cluster, FeMo-co, switch I and II regions, the loop containing residues 186–190 in the β component of the MoFe protein. Results are reported in S8 Fig. Small asymmetries in the crystallographic structures are amplified in this analysis and result in an asymmetric pseudo-“covariance matrix”, and consequently asymmetries in S8 Fig. It is clear that the motion described by the vector ΔR can introduce an efficient mechanical coupling between the switch region I and the [4Fe-4S] cluster, the β-Ser¹⁸⁸ loop and the P-cluster within either half of the ATP-bound complex. Asymmetry between the two halves is observed since the mechanical couplings between the P-loop and β-Ser¹⁸⁸ loop, the P-cluster and the FeMo-co within one half (i.e., Fe₁-α₁β₁) are similar to the ATP-bound complex itself, while the one between the [4Fe-4S] cluster and the P-cluster is similar within the other half (i.e., Fe₂-α₂β₂). Notably, the conformational motion taking place upon ATP hydrolysis can also introduce an efficient mechanical coupling between the loop containing β-Ser¹⁸⁸ of one half and the P-cluster of the other half of the ATP-bound complex.

Testing of the mechanical coupling model

The computational model for the mechanical coupling discussed in the previous sections was validated against an analysis of the solution phase dynamics of the protein complex. We conducted a set of hydrogen-deuterium exchange experiments on the MoFe protein under two conditions, alone in solution and in the presence of ATP-bound Fe protein. Specifically, we monitored deuterium exchange after 1 hour, at which point all relevant long-time scale motions in the nitrogenase complex would have been sampled. In general, greater exchange was observed for peptides from free MoFe protein, than in the presence of ATP-bound Fe protein (Fig 8). Decreased exchange proximal to the MoFe protein/Fe protein interface was expected due to the burial of surface area and the formation of protein-protein interaction. What was not immediately expected were changes in deuterium uptake distal from the Fe protein binding site as well as in the protein core. The region showing the greatest exchange was near the P-cluster, for peptides containing residues β-188^Ser and β-69^Ala. In the presence of the Fe protein, the peptide with β-188^Ser had a dramatic decrease in deuterium uptake, whereas the peptide with residue β-69^Ala showed only a slight change. The changes detected in regions distal from the Fe protein docking site are consistent with our model of mechanical coupling.

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Fig 8. HDX Mass Spectrometry measured deuterium exchange in the MoFe protein alone and in the presence of the ATP-bound Fe protein.

The percent deuterium uptake at 1 hour in selected regions of MoFe alone and in complex with Fe protein is shown as a histogram. Complete exchange was based on a 24-hour time point.

https://doi.org/10.1371/journal.pcbi.1008719.g008

To investigate the effects of the presence of Fe protein on long-distance communication of MoFe protein, we searched for regions with correlated patterns of H/D exchange. Based on the difference in percent deuterium exchange between regions, we built a correlation matrix for free MoFe protein and MoFe protein in the presence of ATP-bound Fe protein (S9 Fig). After one hour of exchange, seven well-defined correlation groups were identified for each condition. However, the exchange patterns and peptides in the correlation groups were not the same between conditions. In MoFe protein alone, about 62% of investigated peptides show strong positive correlation (blue), while 22% have a strong negative correlation (red). In the presence of ATP-bound Fe protein, MoFe protein exhibits much greater negative correlation (36%). In MoFe alone, only peptides in the fifth cluster (green bars) have significant negative correlation. These peptides are spread across structure including the MoFe protein dimer interface, near Fe protein binding site, P-cluster and FeMo-co. Enhanced negative correlation upon binding of Fe protein is consistent with a model of negative cooperativity between “halves” of MoFe protein.

To evaluate our mechanical coupling model, we investigated the correlation patterns of the “chokepoint" residues. On the experimental time scale, H/D exchange revealed four types of correlation patterns in free MoFe protein and in the presence of the ATP-bound Fe protein (Fig 9). The first group contains the following residues: α-50^Lys (peptide 39–54 near Switch I region of the Fe protein), α-63^Ala (peptide 63–85 near the P-cluster) and α-119^Gln (peptide 119–134 near Switch II region of the Fe protein). The second group contains the following residues: α-71^Val (peptide 67–85 near the FeMo-co), α-164^Glu (peptide 151–165 near the [4Fe-4S] cluster in the Fe protein), β-479^Leu and β-497^Leu (peptide 473–489 and 495–523 at the α₁β₁-α₂β₂ interface). Both groups show positive correlation with H/D exchange in the free MoFe protein. When the full nitrogenase complex is formed, trends in protein dynamics for group one and two become negatively correlated. The third and fourth groups contain residues in the β subunit that are near the P-cluster, β-69^Ala (peptide 58–77), β-90^His (peptide 78–98) and β188^Ser (peptide 183–192) and correlation patterns are dependent on complex stoichiometry. In the free MoFe protein, the residues β-69^Ala and β-188^Ser are strongly correlated with each other and negatively correlated with β-90^His as well as with the first and second group. In the ATP-bound Fe protein, these three residues are part of a more nuanced interaction network. For example, the region around residue β-90^His remains similarly correlated with all peptides except the one containing residue β-188^Ser (which changes from negative to positive). Whereas the peptide containing β-188^Ser has positive correlation with all residues from the second group and negative correlation with β-69^Ala. The peptide containing β-69^Ala changed from positive to negative correlation with β-188^Ser and from negative to positive correlation with group one upon Fe protein binding.

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Fig 9.

Correlation patterns of protein dynamics in (A) free MoFe protein and (B) MoFe protein in presence of ATP-bound Fe protein based on HDX measurements recorded after 1h of the deuterium exchange. Red and blue circles correspond to negative and positive correlations, respectively. An empty spot in the matrix (or white circle) signifies lack of any correlation. Size of the circle represents significance of the results: the larger the circle the more significant the correlation. Squares are drawn to highlight clusters with similar correlation patterns.

https://doi.org/10.1371/journal.pcbi.1008719.g009

Detailed analysis of the theoretical and experimental data made it immediately evident that regions identified as important for the Fe protein/MoFe protein coupling in the computational analysis correspond (or are adjacent) to regions with high H/D exchange correlation. In addition, the analysis revealed that the region surrounding the P-cluster is sensitive to the presence of ATP-bound Fe protein. This agrees with observed structural changes when nitrogenase is poised at different steps in the catalytic cycle.[28] Of particular interest is cross-talk between β-69^Ala and β-188^Ser, two resides proximal to the P-cluster ligation site. In free MoFe protein, these residues are positively correlated. Upon binding of ATP-bound Fe protein, β-69^Ala and β-188^Ser (along with the P-cluster environment in the β subunit) become negatively correlated. At the same time, H/D exchange of β-69^Ala is positively correlated with the P-cluster environment in the α subunit of the MoFe protein. Equally interesting is the relationship of β-188^Ser/β-69^Ala protein dynamics with α₁β₁-α₂β₂ interface (residues β-479^Leu/β-497^Leu). Despite spatial separation, the P-cluster ligation site and the α₁β₁/α₂β₂ interface show a strong correlation. However, only β-188^Ser is sensitive to the presence of ATP-bound Fe protein. In summary, our H/D exchange experiments reveal correlated patterns of dynamics precisely where computationally derived mechanical coupling networks predict.