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Departments of Chemistry and Biochemistry, Duke University, Durham, North Carolina
Correspondence: Address reprint requests to Prof. David N. Beratan, Duke University, Dept. of Chemistry, 228C Gross Chem., Durham, NC 27708-0346. Tel.: 919-660-1526; E-mail: david.beratan{at}duke.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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; Cramer and Knaff, 1989). Our goal is to understand some of the minimal constraints on structure and dynamics for functioning ATP-driven protein machines. As prototypes, we examine two molecular machines, nitrogenase and the ATP binding-cassette vitamin B12 transporter, BtuCD.
Biological nitrogen fixation catalyzed by the enzyme nitrogenase produces more than 60% of the world's annual supply of new ammonia (Schlesinger, l991). Nitrogenase consists of two metalloproteins, a 64 kDa iron protein (Fe protein) and a 240 kDa molybdenum protein (MoFe protein) (Einsle et al., 2002; Howard and Rees, 1996; Eady, 1996). The Fe protein is a dimer with a single [4Fe4S] cluster linking the two subunits. The MoFe protein is an 
2ß2 tetramer that contains an iron-sulfur P-cluster, presumably the intermediate electron acceptor, and the catalytic nitrogen-reducing MoFe cofactor. The Fe protein delivers electrons to the MoFe protein in a transient complex triggered by ATP binding to the Fe protein.
The binding and hydrolysis of ATP, which is required for nitrogen fixation, changes the iron-protein conformation and is coupled to protein-protein binding. Binding ATP triggers substantial changes in the protein environment near the [4Fe4S] cluster (Schindelin et al., 1992), despite >15 Å distance between the edges of the ATP binding sites and the [4Fe4S] cluster. Experimental studies (Stephens et al., l996; Jang et al., 2000a) show ATP binding and protein-protein association leads to a lowering in the midpoint potential of the [4Fe4S] cluster, enhancing the driving force for electron transfer. Recent theoretical analysis (Kurnikov et al., 2002) suggests that the redox potential lowering in the [4Fe4S] cluster upon protein-protein binding results from cofactor desolvation.
The ATP binding-cassette (ABC) transporters are ubiquitous membrane proteins that couple ATP binding and hydrolysis to the translocation of substrates, including amino acids, peptides, ions, sugars, toxins, lipids, and drugs across membranes. Multidrug resistance is responsible for up to 60% of all hospital-acquired infections globally (WHO, 2000; Chang and Roth, 2001) and is associated with ABC transporters. Structural studies indicate that ABC transporters invariably contain two domains, a transmembrane (TM) binding domain, and a nucleotide-binding domain (i.e., ATP binding cassette). The transmembrane domain plays a primary role in recognizing and transporting substrates through the lipid bilayer. After the substrate is bound and transported across the membrane, the ABC transporter protein returns to its initial state. The ATP binding and hydrolysis drives the cycle. The ABC transporter proteins have a number of highly conserved ABC cassette motifs. The ATP binding and hydrolysis in ABC proteins couple to substantial conformational changes, such as the opening or closing of the chamber formed by the transmembrane domains. These openings are 
25 Å wide in the transmembrane direction in E. coli MsbA, for example (Chang and Roth, 2001). This large-scale conformational change is apparently related to unidirectional substrate translocation.
In recent years, considerable progress has been made in elucidating the structure of ABC transporters (Hung et al., 1998; Rosenberg et al., 2001; Yuan et al., 2001; Chang and Roth, 2001; Locher et al., 2002). Recently, a molecular dynamics (MD) simulation of the ABC nucleotide-binding domain was performed to identify hinges and switches of the nucleotide-binding domain conformational change and subunit-subunit interfaces (Jones and George, 2002). All of these studies suggest that the ABC transporters use a common mechanism to power the translocation of substrates across cell membranes (Locher et al., 2002; Chang and Roth, 2001). As an example, the BtuCD protein from Escherichia coli (Locher et al., 2002) is examined here. The ABC transporter BtuCD is a homodimer that mediates vitamin B12 uptake.
Despite the diversity in the function of these two proteins, the nitrogenase Fe protein and the E. coli BtuCD both have a dimeric structure. The dimeric structure suggests "lever arms" that could generate large-scale conformational changes involving the relative movement of these structural domains. This sort of domain motion likely arises in a variety of protein machines, from catalysts to regulatory proteins (Mogilner et al., 2002).
It is generally thought that nitrogenase and ABC transporter mechanisms are similar to those of the general class of nucleotide-utilizing proteins (Schindelin et al., 1992; Jang et al., 2000a; Strop et al., 2001; Chang and Roth, 2001; Locher et al., 2002). In nucleotide-binding proteins, MgATP acts at a distance to induce protein conformational changes that drive biological processes including signal transduction, membrane and organelle transport, DNA replication, and muscle contraction. Studies of these two specific proteins may, therefore, be of more general relevance.
Although considerable progress has been made in interpreting nitrogenase and ABC transporter mechanisms, two intriguing functional questions remain:
Protein motion, especially ATP-coupled motion, is highly anharmonic. Nevertheless, normal-mode analysis has been used successfully to provide qualitative and quantitative insights into protein structure and dynamics (Tama and Sanejouand, 2001). Normal-mode analysis (Li and Cui, 2002, 2004; Tama and Sanejouand, 2001) indicates that low-frequency modes are responsible for large-scale conformational changes. These modes are delocalized and can couple distant regions. In principle, the detailed dynamical behavior associated with large-scale conformational changes of proteins can be elucidated by combined molecular dynamics and normal-mode analysis (Tama and Sanejouand, 2001). However, all-atom MD approaches are not yet feasible for describing long timescale motion of these very large proteins (Karplus and McCammon, 2002). Coarse-grained models can be used to avoid some of the challenges associated with system size. Based on the finding that large-scale motion in proteins can be described approximately by using simple pairwise Hook's law potentials with a single spring-constant parameter (Tirion, 1996), the coarse-grained Gaussian network (GNM) (Bahar et al., 1997) and anisotropic network models (ANM) (Atilgan et al., 2002) were developed. In these models, the nodes of the network represent the amino acid residues, and the linkers are springs with a single spring constant connecting all nodes within a cutoff radius. As such, the fluctuations of the proteins around their equilibrium geometries are assumed to be Gaussian-distributed. Protein crystallographic B factors can be predicted well (Atilgan et al., 2002) with these harmonic methods. The GNM method assumes a one-dimensional chain and calculates the isotropic thermal-fluctuation amplitudes of amino acid residues (represented by their -carbons), whereas its extension, ANM, is three-dimensional. These elastic network models (ENMs) have been widely used to analyze protein dynamics (Tirion, 1996; Bahar et al., 1997, 1999; Keskin et al., 2000, 2002; Doruker et al., 2000). Detailed studies indicate that both of these models capture key autocorrelation fluctuations in agreement with x-ray crystallographic data. Cross-correlations are also calculated consistently between the GNM and ANM methods (Bahar et al., 1997; Atilgan et al., 2002; Isin et al., 2002; Xu et al., 2003).
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PROTEIN STRUCTURES |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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; Schlessman et al., 1998; Jang et al., 2001a,b; Strop et al., 2001).
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/ß-sheet polypeptide fold with an eight-strand ß-sheet flanked by nine -helices. A noncrystallographic twofold axis passes through the [4Fe4S] cluster and relates the two subunits in the Fe protein. The twisted ß-sheet core of each subunit contains seven parallel strands and one short antiparallel strand, ß3, which is located at one edge of the ß-sheet. The ß-strand order is 3-4-2-5-1-6-7-8. Crystal structures indicate topological switch points formed by the loops at the C-terminal ends of several ß-strands. The loops seem to create binding sites for ATP and cofactors, essential for Fe-protein function. For example, the loops following the ß1 and ß2 strands are associated with nucleotide binding (P-loop, see below), whereas the loops following ß5 and ß6 involve cysteine ligands to the [4Fe4S] cluster.
The crystal structures of the Av2 Fe protein indicate that there are three significant regions that may be related to the Av2 protein conformational changes: 1), a phosphate-binding loop (P-loop), or so-called Walker A motif (Schlessman et al., 1998) containing the G-X-X-X-X-G-K-S/T (X means "no consensus") motif corresponding to 9–16 residues in Av2; 2), a Switch I region located at the Fe-protein surface including residues 38–43, involved in interactions with the MoFe protein; and 3), a Switch II region consisting of residues from 125 to 135 (related to the conserved D-X-X-G sequence), in which Cys132 provides two of the four ligands to the [4Fe4S] cluster (Jang et al., 2000a). The crystal structures suggest that Switch I provides a mechanism for propagating the force generated from binding and hydrolysis of MgATP to the Fe-protein surface to control the protein-protein interaction (Jang et al., 2000b). The structure of Switch II suggests a mechanism for how nucleotide-binding couples to the [4Fe4S] cluster. The switch regions undergo conformational changes upon hydrolysis of nucleotide. The Fe protein displays structural similarity in these three regions to other nucleotide-binding proteins, including myosin and the G-protein ras. Therefore, investigations into the motion of these three regions in Av2 may provide clues to energy transduction in other nucleotide-dependent proteins. In nitrogenase, the protein environment surrounding the [4Fe4S] cluster is of particular interest. The crystal structures (Schlessman et al., 1998) indicate that the [4Fe4S] cluster is buttressed on three sides by the main-chain atoms of residues 96–100 and 132–134, as well as by hydrophobic side chains of residues 98, 130, and 135. These invariant residues are likely critical for maintaining the appropriate cluster environment (Schlessman et al., 1998). The thiol ligands of Cys97 and Cys132 from each of the two Av2 subunits coordinate the [4Fe4S] cluster (Schlessman et al., 1998).
BtuCD protein structure
The BtuCD structure from E coli, determined by x-ray crystallography (3.2 Å resolution) (Locher et al., 2002), is displayed in Fig. 2. The assembled complex of the BtuCD protein is 90 Å x 60 Å x 30 Å (Locher et al., 2002). Each subunit of the dimer contains a transmembrane domain and an ATP-binding domain (an ABC unit). The two transmembrane subunits and the two ABC units of the homodimer are designated BtuC and BtuD, respectively (Locher et al., 2002). A transmembrane domain contains 10 -helices, denoted TM1–TM10. Among these helices, TM4 (residues 114–138), TM5 (residues 142–166), and TM10 (and their counterparts in the other subunit) are related to the large conformational rearrangements in the protein. The interface between the two transmembrane domains is constructed by TM5 of one subunit and TM10 of the other (and vice versa). These four -helices define a cavity. This cavity is open to the periplasmic space and is closed to the cytoplasm by residues in TM4 and TM5, referred to as a gate at the transporter center. The transmembrane domains provide a pathway for substrate transport through the lipid bilayers.
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-helices and a peripheral three-strand ß-sheet. This domain contains a P-loop (Walker A), Walker B motif (including consensus sequence hhhhD; here h indicates a hydrophobic residue), ABC signature region, Q-loop, and switch region. The sequence comparison indicates that, like other ABC cassettes, residues critical to ATP binding are highly conserved. These residues involve those in the Walker-A/B motifs, a glutamine from the Q-loop, and a histidine from the switch region (Schneider and Hunke, 1998; Locher et al., 2002). The Walker A motif of BtuCD is believed to play a role in the binding of the ß- and 
-phosphates of the nucleotides (in analogy with the conserved aspartate in the Walker B motif of Av2). The ABC signature sequence preceding the Walker B region is highly conserved in all ABC transporter family members and is a hallmark of the family. The residues in the Q-loop located at the interface of BtuC with BtuD are believed to be responsible for the interaction between the two domains, i.e., through them the mechanical force generated by ATP binding is transmitted from the ABC cassettes to the transmembrane domain (Locher et al., 2002). |
ELASTIC NETWORK ANALYSIS |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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 | (1) |
R in Eq. 1 represents a 3N-dimensional vector in ANM and an N-dimensional vector in GNM. The superscript t denotes the matrix transpose. The Hessian matrix 
contains the second derivatives of the potential V. Elastic network analysis, which is the same as normal mode analysis, requires diagonalization of the Hessian matrix by solving the secular equation
 | (2) |
is the identity matrix and 
is the eigenvalue.
The Hessian matrix elements in Eq. 1 for GNM are 
and Hij(i 
j), which are given by
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is the spring constant. Typically, is 1.0 ± 0.5 kcal/(mol Å2) (Atilgan et al., 2002).
 | (4) |
 | (5) |
is the cutoff distance beyond which no interactions between residues occur. Earlier studies (Atilgan et al., 2002) show that a short cutoff value yields extremely large-amplitude unphysical fluctuations. Typical cutoff values that reproduce crystallographic B-factors are 12–15 Å in the ANM model (Atilgan et al., 2002). In our ANM calculations, is 15.0 Å for the nitrogenase Fe protein and 
for the BtuCD protein (a distance of 7 Å is used in our GNM computation for both proteins). Once the potential is defined, the Hessian matrix can be computed readily (Atilgan et al., 2002).
Correlation functions
Protein B-factors can be determined by x-ray crystallography. The mean-square (MS) fluctuation of the ith residue, 
(Ri)2
, defines the B-factor
 | (6) |
 | (7) |
, kB is Boltzmann's constant, T is the temperature, and R is a column vector consisting of R1,..., RN. The constant ZN is
 | (8) |
carbons) is
 | (9) |
 | (10) |
as
 | (11) |
k is the eigenvalue of the kth normal mode, and uik is the ith component of the kth eigenvector obtained by solving Eq. 2. The ANM cross-correlation function is the same as in Eq. 11, but Ri is replaced by its x, y, or z component and M = 3N–6. The analytical expression for the autocorrelation function in Eq. 7 is also obtained using Eq. 11 with i = j. Both GNM and ANM provide useful tools to describe the global fluctuation dynamics of proteins around the native state. The major advantage of GNM is that it provides an accurate evaluation of protein fluctuations (B-factors) with a minimal computational cost. Whereas GNM is limited to the description of protein MS displacements and correlations between fluctuations, ANM can predict the directionality of protein conformational fluctuations.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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) (PDB file 1Fe6P) was used. The B-factors (solid line) computed using GNM are compared with the experimental data (dashed line) in Fig. 3. The spring constant was 1.0 kcal/(mol Å2) (Atilgan et al., 2002). As displayed in Fig. 3, the calculated results capture the main features of the experimental B-factors. The ANM approach was also employed in the calculations. No qualitative difference was found between the ANM and GNM results for the B-factors and the cross-correlations.
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1–3, ß1–ß4, the P-loop, and the Switch I region. The region B contains residues 101–286, incorporating Switch II, the P-loop, and the secondary structures 4–9 and ß5–ß8. In this figure, the colors purple, blue, and yellow represent positive correlations (Cij > 0), denoted by the plus signs in the circles, whereas green indicates the negatively correlated regions (Cij < 0), labeled by the minus signs. The uncorrelated residue pairs (Cij = 0) are colored brown. Fig. 4 shows the nature of the concerted motion. In each subunit, the intraunit fluctuations are positively correlated and indicate that the monomer moves collectively. The negative correlation of the two subunits indicates that the dimeric Fe protein can act as a molecular machine with two "arms."
The residue fluctuation-correlation patterns in the dimeric Fe protein are reflected in the motion of the GNM slowest mode, shown in Fig. 5. Here, the amplitude of the eigenvector in the lowest-frequency mode is plotted on the ordinate whereas the abscissa shows the residue number. The motion of the subunits (AB and CD) reflects the noncrystallographic symmetry (Strop et al., 2001) of the protein. Consistent with the cross-correlations indicated in Fig. 4, this mode shows that the residues in each subunit move together. In contrast, the direction of the overall motions in different subunits is opposed. The residues involved in this lowest-frequency mode, seen from the figure, are associated with the nucleotide binding (P-loop), Switch I, Switch II, and the [4Fe4S] cluster.
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). Fig. 6 shows the residue MS fluctuations driven by the ANM slowest mode. The MS fluctuations of this mode display a symmetric pattern with respect to the twofold symmetry axis of the Fe protein. Here the data shown only for the first monomer (residues 1–287) are normalized by that of residue 28 for the convenience of plotting. The extrema displayed in this figure reflect the rigidity property of the protein. The maxima correspond to the flexible residues whereas the minima are associated with the stiff residues including the "hinge" sites. The significant peaks are labeled in the figure. As shown in Fig. 7 a, all these highly flexible residues are located on the surface of the protein. Among them, Glu59–Leu70 (labeled 3) at the interface that interacts with the MoFe protein are functionally associated with the protein-protein interaction.
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; Jang et al., 2000b). These interactions are important for communication between the nucleotide-binding domain and the [4Fe4S] cluster (Jang et al., 2000b). Switch I extends the interactions with the P-loop through Asp39 to the region of residues 59–69 (labeled 3 in Fig. 6) which interact with the MoFe protein in the nitrogenase complex. As such, Switch I is believed to propagate the force generated from binding and hydrolysis of MgATP to the interface between the Fe protein and the MoFe protein (Jang et al., 2000b). The residue MS fluctuations driven by the ANM slowest mode are also depicted in the ribbon diagram of Fig. 8. Flexibility increases in the color series red, green, and blue. The nucleotides and the [4Fe4S] cluster are shown with blue spheres. Asp125 and Asp39 are indicated with yellow lines.
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BtuCD
The x-ray structure of BtuCD in the PDB file 1L7V (Locher et al., 2002) was used in our analysis. The sequence in this PDB file was rearranged so that the transmembrane domain is followed by the ATP-binding domain of the same subunit for the convenience of analysis. The GNM-calculated B factors (solid line) compared with those from the experiments (dashed curve) are shown in Fig. 9. The calculations are in agreement with the experiments.
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). The concerted manner to open the transport pathway coupled to the lowest-frequency mode is shown in Fig. 13 b, evaluated with ANM. As with the nitrogenase Fe protein, the ANM-predicted directions of motion are consistent with the cross-correlated patterns computed with GNM.
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CONCLUDING REMARKS |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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Elastic network analysis provides insights into the mechanism of high-efficiency energy transduction over large distances. The ENM calculations indicate that these two proteins can act as semirigid lever arms to generate concerted large-scale conformational changes. Further evidence from the ENM investigation illustrates that this collective motion is dominated by the lowest-frequency normal mode. As such, we suggest that ATP binding and hydrolysis drives the motion of this mode, resulting in large-scale conformational changes to the proteins.
The elastic network analysis used above is closely related to the normal-mode analysis widely employed in the literature (e.g., Li and Cui, 2002, 2004), within a coarse-grained description. Our calculations indicate that elastic network analysis is a useful tool to analyze a large-scale conformational motion in large proteins. The nature of the biological processes driven by ATP binding and hydrolysis is, of course, highly anharmonic. These processes involve the transition between different chemical states. The crystal structures associated with these ATP- and ADP-bound states, for example, are available for the nitrogenase proteins (Jang et al., 2000a,b). The above elastic network model can be applied to these endpoint protein conformations and interpolated structures. Work along this line remains in the future.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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This work was supported by the National Institutes of Health (GM57876) and Duke University.
Submitted on December 17, 2003; accepted for publication April 2, 2004.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONPROTEIN STRUCTURESELASTIC NETWORK ANALYSISRESULTS AND DISCUSSIONCONCLUDING REMARKSACKNOWLEDGEMENTSREFERENCES |
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