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* College of Life Science and Bioengineering, Beijing University of Technology, Beijing, China; and College of Science, Yanshan University, Qinhuangdao, China
Correspondence: Address reprint requests to Prof. Cun Xin Wang, College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100022, China. Tel.: 86-10-67392724; E-mail: cxwang{at}bjut.edu.cn.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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-helices and two ß-strands. The slowest mode of each three forms of GlnBP—ligand-free open, ligand-bound closed, and ligand-free closed GlnBP—shows that the open-closed motion of the two domains has a common hinge axis centered on Lys-87 and Gln-183. Accompanying the conformational transition, the residues within both large and small domains move in a highly coupled way. The peaks of the fast modes correspond to residues that were thought, in the GNM, to be important for the stability of the protein, and these residues may be involved in the interactions with the membrane-bound components. With the contacts between the large domain and the small domain increasing, the ability of the "open-closed" motion is decreased. All the results agree well with those of molecular dynamics simulations, and it is thought that the open-closed conformation transition is the nature of the topology structure of GlnBP. Also, the influence of the ligand on GlnBP is studied with a modified GNM method. The results obtained show that the ligand does not influence the closed-to-open transition tendency. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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,2). The outer membrane is semipermeable and acts as a coarse molecular sieve. The inner membrane contains numerous active transporters for some molecular compounds. Periplasmic binding proteins can carry small ligands from the periplasmic space into the cytoplasmic space via the inner membrane. When a ligand enters the periplasmic region, it will bind to the corresponding periplasmic binding protein with a high affinity. Upon ligand binding, the periplasmic binding protein adopts conformational changes so that the complex formed is recognized by the transporter, which is another component of the system embedded in the inner membrane. Then, the ligand is released from the binding protein and translocated across the cytoplasmic membrane by the transporter (3). The x-ray structures of more than 14 different periplasmic binding proteins share a similar fold topology containing two distinct domains linked by two or three short hinges (4).
GlnBP from Escherichia coli is one of the representative structures of the periplasmic binding proteins. Binding of glutamine at the cleft between two domains causes a conformational change corresponding to a closure of two domains around the ligand. Besides the ligand-free open (open-apo) and ligand-bound closed (closed-ligand) forms, there may also be a closed form of GlnBP in the absence of ligand (closed-apo) (5–7). It is suggested that both forms (open-apo and closed-apo) are present in equilibrium with a low activation energy barrier between them (6) and the equilibrium will be shifted toward the closed form upon ligand binding (8).
It seems to be clear that the open-closed transition of GlnBP is of utmost functional significance for ligand binding. Also, the significance of slow and fast modes of other proteins has been addressed in some recent work (9,10). But several questions still need to be answered. Is the transition encoded in the structure itself? Is it an intrinsic property of the system and can it be predicted from the structure alone? There is a tendency for a conformational change from the closed-apo form to the open-apo form (6,8). Then, for the case with the ligand bound to GlnBP, can the "closed-to-open" transition also occur? If so, how does the ligand affect the tendency of the closed-ligand structure to open?
To answer the above questions, we have used molecular dynamics (MD) simulations to study the sequence of events involved in the large-scale conformational change for the open-apo and closed-ligand forms (11). Pang et al. have explored the "open-closed" domain motion using MD simulations and essential dynamics analysis (12). Although the presence of the expected domain motion was indicated by extensive mobility in their direction, the short-timescale simulation could not detect the complete conformation transition, and the substantial energy barriers could impede simulations of the complete transition pathway.
In this work, these issues are investigated from a novel point of view through two simple coarse-grained schemes—a Gaussian network model (GNM) and an anisotropy elastic network model (ANM) (13–15). The GNM method allows direct estimation of the conformation transition from the crystal structures without the high computational cost of MD. Information about the directions of this transition can be obtained from analysis with the ANM. The mechanism of the open-closed transition and the influence of the ligand on the transition will be explored by analyzing the large-scale domain motions around a hinge with the GNM. The GNM method has been proved in numerous application studies to be a simple yet useful tool for investigating large-scale conformational motions, domain motions, and collective dynamics of the biomolecular systems (16–20). The GNM also has been used to find kinetically hot residues and folding cores of proteins (21,22). Several previous studies have proved that the results of the GNM are in agreement with those of MD simulation (23,24).
Because structure information is available both for the open and the closed forms, it is possible to compare the results obtained from the GNM and ANM with those from the crystal structures for the closed and open forms. In this work, the information about crystal structure will be used to compare and verify the conclusion reached using the GNM and ANM methods.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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) and the closed-ligand form (PDB code 1WDN) (8). The crystal structure of the open-apo form includes two monomers that have the same conformations. We chose only one monomer for our calculation in this work. The closed-apo structure was obtained by removing the bound glutamine from the closed-ligand structure. GlnBP contains a single polypeptide chain of 226 residues with a secondary structure of 
35% -helices and 37% ß-strands. The large domain, which contains both the N-terminal and C-terminal of the protein, is built from two separate peptide segments, residues 1–84 and 186–226. This domain includes five -helices and eight ß-strands. The small domain consists of residues 90–180, which form three -helices and four parallel and one antiparallel ß-strands connected by a large loop (residues 96–109). The two domains are connected by two ß-strands (residues 85–89 and 181–185). (see Fig. 1). The first four residues and the first three residues are missing in the crystal structures for the open-apo and closed-ligand structures, respectively. For our crystal structure comparison, all three coordinate sets were truncated to the shortest protein (1GGG) with residues from Leu5 to Glu224.
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atoms connected by harmonic springs within a certain cutoff distance (7.3 Å is adopted in this work). The force constant is identical for all springs. Considering all contacting residues, the internal Hamiltonian of the system can be written as (20)
 | (1) |
is the harmonic force constant; 
R represents the 3N-dimensional column vector of the X, Y, and Z components of the fluctuation vectors 
of the atoms, where N is the number of residues; the superscript T denotes the transposition; E is the third-order identity matrix; 
is the direct product; and 
is the 
symmetric Kirchhoff matrix in which the elements are written as (13,20)
 | (2) |
is the distance between the ith and jth atoms and 
is the cutoff distance.
The mean-square fluctuations of each atom and the cross-correlation fluctuations between different atoms are in proportion to the diagonal and off-diagonal elements of the pseudoinverse of the Kirchhoff matrix. The inverse of the Kirchhoff matrix can be decomposed as
 | (3) |
are the eigenvectors of , and 
is a diagonal matrix of eigenvalues 
of . The cross-correlation fluctuations between the ith and jth residues are given by
 | (4) |
is the Boltzmann constant, 
is the absolute temperature, and the meanings of and are the same as in Eq. 1. When 
, the mean-square fluctuations of the ith residue can be obtained. The Debye-Waller or B-factor, which is correlated to the mean-square fluctuation, can be calculated with the expression
 | (5) |
The mean-square fluctuation of the ith residue associating with the kth mode is given by
 | (6) |
In the GNM, the cross correlation is normalized as
 | (7) |
The GNM model can provide the amplitudes of residue fluctuations but no information about the directions of the fluctuations. Then an ANM model is introduced, by which information about the orientation of fluctuations is elicited. In ANM, the motion mode of a protein is determined by a Hessian matrix H.
 | (8) |
The elements of H are submatrix with size 3 x 3. The ijth submatrix hij is:
 | (9) |
, the analytic expression for the elements of 
is
 | (10) |
, the analytic expression for the elements of is
 | (11) |
The meanings of and 
are the same as in Eq. 1. 
represent the coordinates of atoms.
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CORRELATION COEFFICIENT AND OVERLAP |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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 | (12) |
and 
are the calculated and experimental B-factor values of the ith atom, 
and 
are the mean values of and , and N is the total number of atoms of the protein.
The overlap is used to measure the similarity between the direction given by motion mode j and the direction of the conformational change (26).
 | (13) |
In this expression, 
is the amount of the ith atomic coordinate's change between the open and closed structures. A higher value of the overlap means that the direction gotten from the motion mode is more similar to the one gotten from .
The correlation coefficient 
is used to measure the similarity of the patterns of atomic displacement in the conformational change and those in the jth motion mode:
 | (14) |
is the magnitude of the displacement of atom i involved in the mode j and 
is the amplitude of the displacement in the conformation change. The corresponding average displacements are marked as, respectively, 
and 
, and the corresponding root mean-square are 
and 
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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atoms (dotted line) and the experimental data from x-ray crystallography (solid line). It can be seen, from the theory described above, that the only adjustable parameter in this work is , which is determined by normalizing the theoretical distribution of the B-factors based on the experimental one. The resulting 
value used for the open-apo structure is 0.97 Å2, that for the closed-apo structure is 1.22 Å2, and that for the closed-ligand structure is 1.25 Å2.
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,27). Because the closed-apo structure is generated by removing the bound glutamine from the ligand-bound structure, the theoretical B-factor of the former is compared with the experimental B-factor of the latter. It is found that the closed-ligand structure gives a higher correlation coefficient than the closed-apo structure, which reflects the effect of the ligand glutamine on the residue fluctuations of the protein. In this regard, the difference between the B-factor values of the two structures was calculated to figure out which residues were affected by the ligand (see Fig. 3 A). The difference is obtained by subtracting the B-factor value of the closed-ligand structure from that of the closed-apo structure, and the result shows that the ligand reduces the fluctuations of the receptor's residues in contact with it, such as Gly68, Ile69, Thr70, Thr118, Gly119, Ser120, and Asp157, as well as the residues around them.
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). As shown in Fig. 3 B, the obvious difference between B-factor values is mainly located at the region of the contact interface between the two monomers, which suggests that the fluctuations of the residues in this region greatly decrease.
The slow modes of the motions
The slow and long-wavelength collective modes represent functionally relevant motions of protein (28). Fig. 4 displays the first mode of each three structures calculated by the GNM. The ordinates in Fig. 4 show the normalized distribution of squared fluctuations driven by the first slowest modes. From the figure, the two domains of the protein and the hinges between them are highly distinguished. All three structures have the common hinge axes located around Lys87 and Gln183, with the fluctuation values approximate to zero. Around the hinge axis, the major domain movements occur. It can also be seen that the -helix (residues Thr158–Thr167) near the hinges, which belongs to the small domain, has small fluctuation during the domain movements.
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-helices and two ß-strands (residues 110–150). This indicates that the open-closed conformational transition mainly exhibits as the large movement of the small domain, particularly part of the top region of it. This is consistent with the results of MD simulation, in which the corresponding residues have a large root mean-square fluctuation (RMSF) (13,14). As shown in Fig. 4, residues 212–225 in both ligand-free and ligand-bound closed structures also exhibit large fluctuation values corresponding to the flexibility of the C-terminal of the protein other than in the open-closed transition. Regarding the fluctuation of the closed-ligand structure, the value of ligand glutamine is very low, so there is a sharp decrease at the end of the curve.
From Fig. 4, comparing the slowest mode of the closed (closed-apo and closed-ligand) structures with that of the open-apo structure, it can be seen that the fluctuations of some residues in the closed structures are reduced remarkably. Those are the residues around Ala12, Asp49, Gly117, and Pro137. The inset in Fig. 4 shows the ribbon diagram of the closed-ligand structure, with those residues whose fluctuations decreased remarkably marked in black. Evidently, these residues are located in the jaws of the ligand docking pocket, among which Asp10 and Lys115 act as a doorkeeper that locks the glutamine ligand tightly inside the binding pocket (8). Thus, these residues play an important role in the open-closed transition of the pocket. The fluctuation decrease of these residues implies that the binding pocket became more stable in the closed structure than in the open-apo structure. It became difficult to open the binding pocket of the closed structure due to the tight binding of the ligand. Obviously, it should be noted that the first mode of the closed-apo in Fig. 4 is extremely similar to that of the closed-ligand structures. It suggests that the ligand of glutamine has little effect on the domain motion.
GNM can only provide the magnitude of displacement of atoms from their equilibrium positions for large-scale motions. To ascertain the direction of motion, ANM is applied to the three structures. For the open-apo structure, the ANM calculation shows a hinge-bending motion and a twisting motion, as seen in Fig. 5. The first slowest mode corresponds to the hinge-binding motion. This mode is explored in its two opposite directions, resulting in two structures. The magnitude of the amplification is adjusted so that the two structures have an RMSD of 2 Å, which makes the difference large enough and easily inspected visually. The two structures resulting from the first slowest mode are shown in Fig. 5 A. The hinge-bending motion can easily be identified and this motion results in the open-closed transition of the binding pocket. The second slowest mode can be described as a twisting motion involving the two lobes of the GlnBP, as shown in Fig. 5 B. Such a twisting motion of the periplasmic binding protein has been suggested previously (5).
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2Å, are shown in Fig. 5 C. From the figure, it is demonstrated that the binding pocket is stable in the closed-ligand structure. The hinge-bending motion can hardly result in the open-closed transition of the pocket. The most flexible regions for the hinge-bending motion are residues 18–26 of a ß-loop in the large domain and residues 96–109 of the large loop in the small domain. It was proposed that the ß-loop may be involved in interactions with the membrane-bound components of the glutamine transport system (8). Thus, the large fluctuation of this region may correlate to the binding of the closed-ligand complex with the membrane-bound components. The results of the closed-apo structure (data not shown) are the same as that of the closed-ligand structure. Fig. 6 shows the reciprocal of eigenvalues for all the modes, which represent the contribution of individual modes to the observed dynamics. To show the differences between the slow motion modes clearly, a local amplificatory graph for the first 16 slow motion modes is inserted in Fig. 6. The curve in Fig. 6 indicates that the first two slowest modes make a significant contribution to the motions of the open-apo structure. These modes make a fractional contribution of 0.2 to the observed dynamics. For the closed-ligand structure, this value is 0.06, which means that the twisting motion and the hinge-bending motion make a smaller contribution to the dynamics than the open-apo structure. The overlap and correlation coefficients of each mode for the two structures are calculated using Eqs. 13 and 14, respectively. The expression in Eq.13 describes the similarity between the mode calculated by ANM and the conformational change vector, and the expression in Eq. 14 describes the magnitude of the correlation between the two vectors. For the open-apo structure, the overlap and correlation values are 0.472 and 0.563, respectively, with respect to the first slowest mode, and 0.173 and 0.089 with respect to the second slowest mode. For the closed-ligand structure, these values are 0.194 and 0.00161 with respect to the first slowest mode, and 0.261 and 0.312 with respect to the second slowest mode, which indicates a remarkable decrease compared to the corresponding values in the open-apo structure.
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). Therefore, residues acting in the fast modes are thought to be kinetically hot residues and they are critically important for the stability of the tertiary fold (21,22,28). Fig. 7 shows the fastest six modes of the three structures. Surprisingly, the mode shapes of the three structures are found to be extremely similar, which implies that their local structures are substantially similar and the domains will keep their rigid structures during domain motions. That is to say, the residues within the two domains move in a highly coupled way, which will also be found from the cross-correlation maps discussed in the following section.
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-helix in the small domain and residues of a ß-strand in the large domain. It has been proposed that this "exposed region" may be involved in the interactions with the membrane-bound components (8). In Fig. 7, this exposed region corresponds to the region around Glu17 and the region around Leu146 and Val154.
Cross correlations between atomic fluctuations
The cross correlations between the fluctuations of atoms are calculated using Eq. 7. Since the modes with low frequency correspond to functional motions and those with high frequency correspond to localized motions, here only low-frequency modes are used to improve the signal/noise ratio. We used the first 40 modes in our calculation. The results are shown in Fig. 8. The cross-correlation value ranges from –1 to 1, in which range the values are positive when the residues move in the same direction and negative when they move in the opposite direction. The higher the absolute cross-correlation value, the better the two residues are correlated (or anticorrelated). Also, uncorrelated fluctuations yield 
. As shown in Fig. 8, there is negative correlation in the blue regions and positive correlation in the orange-red regions.
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Topology and interaction between domains determine domain motions
The directions of the displacements can be obtained from the ANM analysis. According to this information, three reconstructed models of the GlnBP were generated. The backbone of the protein is modified first, based on the information of direction at various coefficients, to make sure the RMSD between these three conformations and the open-apo structure is distinct. According to the open degree of the structure, the RMSD values are 2.9, 3.9, and 5.5 Å, respectively. The side chain is added. Then these resultant conformations are optimized by energy minimization followed by a 500-ps equilibrium dynamics with the GROMACS program. For each trajectory, an equilibrated conformation is picked out randomly to do the GNM analysis. These three structures are shown in Fig. 9 A. The slowest modes of motion of these structures are shown in Fig. 9 B and the reciprocals of their eigenvalues are shown in Fig. 9 C. Only for the first eigenvalue, corresponding to the slowest motion mode, is there a little difference between them. The other ranked eigenvalues of these three structures are very similar.
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In addition, the results of GNM analysis for several equilibrated structures selected randomly from a trajectory are very similar. It means that the partial change of the conformation does not affect the motion mode, which is considered from a holistic viewpoint.
From these analyses, it can be deduced that the open-closed transition is encoded in the structure, but the degree of this motion is related to the structure. When the GlnBP is free of the ligand, it has a remarkable open-closed motion and the extent of this motion is limited. Regarding the closed conformation of GlnBP with Gln bound, the trend of the open-closed transition is reduced.
Analysis of the influence of the ligand on the domain motions
The slowest mode shapes of the closed-apo and the closed-ligand structures are very similar as shown in Fig. 4. It means that the ligand has little influence on the tendency of the open-closed domain movement.
In the ligand-bound crystal structure, Gln is bound in a pocket formed between the two domains. The ligand is completely buried in the protein without any solvent accessibility. Gln is stabilized by hydrogen bonds and ionic interactions with Asp10, Gly68, Thr70, Ala67, Asp157, Arg75, Lys115, Gly119, and His156 (8). In the conventional GNM method, two residues will be connected by a harmonic spring when the distance between them is < (here 7.3 Å). With this method, Gln has harmonic force with Gly68, Ile69, Thr70, Thr118, Gly119, Ser120, and Asp157, but has no harmonic force with Asp10, Ala67, Arg75, Lys115, Gly119, and His156, which have hydrogen bonds or static-electric interactions with the ligand in the crystal structure. To emphasize the influence of Gln, in our work we add springs connecting them with Gln, and then we calculate the modes of the motions based on this new network. The slowest mode, which corresponds to the open-closed transition, is shown in Fig. 10 A.
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The slowest modes of the closed-ligand and the closed-apo structures obtained with the conventional GNM were also shown in Fig. 10 A. From the comparison between these results, it was shown that the shapes of these modes are extremely similar. The reciprocals of each eigenvalue corresponding to all motion modes for these structures are shown in Fig. 10 B. There is a small difference only between the first eigenvalues, which correspond to the slowest motion mode, and the maximal and minimal values are 7.44 and 6.09, respectively.
From the discussion above, a conclusion can be drawn that the ligand has little influence on the tendency of the domain transition. This result is consistent with the viewpoint of Lu and Ma (29), who found that the topology of a molecule plays a more dominant role in determining the low-frequency motions than the absolute values of strength and direction of local interactions. In our work, the ligand Gln only affects the local structure but does not change the motion nature of GlnBP. Therefore, the low-frequency motions of the closed-apo and the closed-ligand structures are fairly similar.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSCORRELATION COEFFICIENT AND...RESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Submitted on April 3, 2006; accepted for publication October 16, 2006.
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