| Correction Biophysical Journal, Volume 87, Issue 2, 1 August 2004, Pages 1398 Full Text | PDF (43 kb) |
| A Closed-Form Analytic Expression for FRAP Formula for the Binding Diffusion Model Biophysical Journal, Volume 95, Issue 2, 15 July 2008, Pages L13-L15 Minchul Kang and Anne K. Kenworthy Abstract One of the most dominant methods cells use for a large class of cellular processes is reaction (or binding) diffusion kinetics, which are controlled by kinetic constants such as diffusion coefficients and on/off binding rate constants. Fluorescence recovery after photobleaching (FRAP) can be used to determine these kinetic constants in living cells. While an analytic expression for FRAP formulae for pure diffusion has been available for some time, an analytic FRAP formula for the binding diffusion model has not been reported yet. Here, we present an analytic FRAP formula for the binding diffusion model in an explicit form allowing for diffusion of the bound complex for either a uniform circle laser profile or a Gaussian laser profile. Abstract | Full Text | PDF (235 kb) |
| Unbiased Rotational Moves for Rigid-Body Dynamics Biophysical Journal, Volume 85, Issue 5, 1 November 2003, Pages 2973-2976 Daniel A. Beard and Tamar Schlick Abstract We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach—based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity—removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying the noncommuting rotational matrices in an arbitrary order. Our algorithm should thus replace standard approaches to rotate local coordinate frames in Langevin and Brownian dynamics simulations. Abstract | Full Text | PDF (100 kb) |
Copyright © 2008 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 94, Issue 7, 2482-2491, 1 April 2008
doi:10.1529/biophysj.107.116046
Biophysical Theory and Modeling
Taner Z. Sen*, †,
,
, Margaret Kloster*, 1, Robert L. Jernigan*, †, Andrzej Kolinski‡, Janusz M. Bujnicki§, ¶ and Andrzej Kloczkowski*, †
* L. H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, Ames, Iowa
† Department of Biochemistry, Biophysics, and Molecular Biology, Iowa State University, Ames, Iowa
‡ Faculty of Chemistry, Warsaw University, Warsaw, Poland
§ Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology, Warsaw, Poland
¶ Institute of Molecular Biology and Biotechnology, Adam Mickiewicz University, Poznan, Poland
Address reprint requests to Taner Z. Sen, USDA-ARS Corn Insects and Crop Genetics Research Unit, Ames, IA 50011-3260; or Dept. of Genetics, Development and Cell Biology, Iowa State University, Ames, IA 50011-3260. Tel.: 515-294-4294.Cellular intake of iron is essential for the survival of Escherichia coli1,2. Iron is transported through the membrane in the form of ferric citrate by the FecA protein. FecA interacts with several intracellular membrane proteins to effect this intake. The ferric citrate is first transported to the periplasm by FecA, and then to the cytoplasm by the FecBCDE complex in the inner membrane. The TonB 3,4 protein provides energy required for the transportation of the ferric citrate into the cell 5.
Besides acting simply as a transporter, FecA also plays other roles. When ferric citrate binds to FecA, located in the outer membrane of E. coli, the protein initiates a signaling cascade from the surface through its plug and barrel domains leading to the N-terminal domain (NTD) located in the periplasm (Fig. 1) (Ala1–Glu79). The signal transduction events continue through conformational changes when the NTD interacts with the FecR regulator in the inner membrane. The regulatory protein FecR transmits the signal further into the cell 5 by activating the sigma factor FecI in the cytoplasm. This activation leads to transcription initiation of the FecABCDE genes by RNA polymerase 6.
The energy required for this active transport system is purported to be provided by the TonB-ExbB-ExbD complex in the inner membrane. The TonB box, formed by residues D80-A81-L82-T83-V84, interacts with TonB. Deletion experiments 7 show that excision of this region stops both transcription initiation and the whole transport process of FecA.
FecA consists of three domains: the plug, the barrel, and the NTD (see Fig. 1, adapted from Yue, Grizot, and Buchanan 5). The barrel domain forms an elliptical cylinder comprised primarily of β-sheets, typical for bacterial outer membrane proteins. The cross section of the barrel measures 35×47Å and the height of the barrel is 65 Å. FecA crosses the outer membrane and extends ∼30Å into the extracellular environment 8. The plug acts as a barrier between the environment outside the cell and the periplasm. It also serves as a binding site for ferric citrate. The NTD interacts with TonB and FecR proteins.
To elucidate the role of the interactions of FecA with TonB and with FecR for energy transduction and transcription signaling, the whole FecA structure is needed. However, x-ray crystallography has been able to determine only the plug and barrel domains of FecA, not its whole structure (the 80 N-terminal residues are missing in the pdb file 1kmo 5,8. The periplasmic domain structure has been determined separately by NMR 9,10. There has been one attempt to assemble FecA structure computationally. In their work, Garcia-Herrero and Vogel 10 proposed putative models of the entire FecA structure. These models are based on selected conformations of the linker from a large set of essentially randomly distributed conformations inferred from the NMR studies of the 96-residue construct containing the NTD. Thus, the proposed models 10 for the FecA complex are rather approximate. The models proposed in this work are results of extensive simulations that account for complex interactions between domains, and therefore are significantly more plausible. Based on our experience with hierarchical molecular docking using the CABS model (highly successful at CASP-6 11), the presented models and the mechanisms of assembly are likely to be correct (within the resolution of the modeled structure).
To analyze the domain motions and residue fluctuations of FecA, we use the Gaussian network model (GNM) 12 and the anisotropic network model (ANM) 13. Both of these elastic network models are based on the rubberlike elasticity theory of phantom polymer networks 14. The GNM considers a protein as a networked elastic body with residues as the nodes of the network. The coordinates of the nodes are usually given by the locations of the Cα atoms of amino acids. Additionally, it is assumed that all nodes interact with identical simple springlike harmonic potentials if the distance between two nodes falls within the cutoff distance, Rc; otherwise, the potential between nodes is zero. According to Tirion 15, all spring constants (and cutoffs, Rc) are assumed to have the same values, regardless of whether the pair is bonded or nonbonded. In addition to the residue-level coarse-grained models, atomic level 16, mixed coarse-grained models 17, and hierarchical coarse-graining methods 18 were developed by Bahar, Jernigan, and colleagues, and successfully applied to model proteins and other large biological structures, such as the ribosome 19,20. There are also elastic network models based on atomistic contacts with more detailed potentials 21,22. These approaches have now been widely applied by many groups to many problems 21,23,24,25,26,27,28,29,30.
The application of the GNM to biological structures is providing us with information and insights on global domain motions, which frequently relate to their biological function. For example, elastic network models are successful in capturing conformational changes upon binding 31. In our previous work, we used the GNM to explain the phenomenon of promiscuous protein binding, leading us to the general conclusion that both native and promiscuous functions can be comprehended as different combinations of the normal modes determined by protein shape and evolutionary constraints 32. The GNM is a simple model that captures the essential features of dense packing in proteins controlling their motions, and it is readily applicable to biological systems. The model allows us to calculate the mean-square fluctuations of residues, and therefore provides direct ways to compare its theoretical predictions with experimental data from x-ray crystallography 12, NMR 33,34, and hydrogen-exchange experiments 35. The GNM has also proved to be highly successful in prediction of the protein folding cores 36.
However, the GNM gives us only information for spherically symmetric fluctuations of residues about their equilibrium positions, with no directional information on domain motions. This limitation was overcome by the ANM, based on the second derivatives of the Hessian matrix. The ANM enables the calculation of the three-dimensional profile of residue fluctuations and yields direct information on the directions of global motions of biological structures.
In this article, we have applied these two elastic network models to the protein FecA to elucidate its domain dynamics and analyze how its NTD might interact with TonB and FecR. One advantage of using coarse-grained elastic network models for the analysis of NTD dynamics is their insensitivity to the protein resolution. As shown by Doruker and Jernigan 37, even highly coarse-grained protein models constructed on a lattice of varying resolution exhibit similar behavior of low-frequency normal modes that correspond to global motions 38,39.
A detailed description of the Gaussian network model can be found elsewhere 12,41. Readers can refer to the following reviews 23,27,42 for further discussion. The underlying concept of the original GNM treatment is to represent a protein as a collection of springs (with a uniform value of the spring constant) between all geometrically close pairs of residues. In this treatment, each residue is represented as a point (node) positioned at its Cα atom. There are two parameters in the model: the cutoff distance, Rc, and the spring constant, γ. The cutoff distance, Rc, determines whether two residues will be connected by a spring, i.e., if they are in contact, not differentiating between bonded and nonbonded interactions. These contacts are expressed in the contact (Kirchhoff) matrix Γ with its elements Γij defined as
![]() | (1) |
Here, Rij is the distance between nodes i and j, and Rc is the cutoff distance. The matrix Γ is singular, because some of its eigenvalues are zero, and hence it has no proper inverse. However, the pseudoinverse of Γ can be obtained with singular value decomposition (SVD) by elimination of the zero eigenvalues. It can be shown that correlations between the fluctuations in positions,
of nodes from their mean positions
are
![]() | (2) |
which in turn may be compared with the experimental crystallographic Debye-Waller temperature factors (B-factors), generally available in the PDB files. These are related to the mean-square atom fluctuations by![]() | (3) |
Although the GNM has been highly successful in predicting the normal modes of proteins, it does not provide the directionalities of these modes, since it is a spherically symmetric model. To overcome these difficulties, the ANM has been proposed. In the ANM, the contact matrix is replaced by the Hessian matrix of size 3N×3N, where N is the number of residues, formed by the second derivatives of the overall potential with respect to residue positions. The detailed theory of the ANM can be found in Atilgan et al. 13. Here, we used a cutoff value of 13Å.
We applied the ANM to predict the domain motions of FecA corresponding to the slowest normal modes (the lowest-frequency large-scale domain motions). These global motions enable large conformational changes in the protein that are vital for the fulfillment of its function. Although the global domain motions are the most crucial for protein function, it is extremely difficult to study them by computer simulation methods such as molecular dynamics, because the required simulation times are usually beyond present-day computer capabilities, especially for larger structures. In that respect, the ANM is an important, simple, and highly useful tool to predict and visualize these domain motions, providing immediate insights into the mechanisms of protein function.
Folding simulations of the entire Feca complex based on structural restraints for the N-terminal domain and the transmembrane domain are performed using the CABS method 44. The details and description of the force field can be found in Kolinski and Boniecki et al. 44,45. The docking of the N-terminal domain to the transmembrane fragment was done using the replica-exchange Monte Carlo sampling technique with unrestricted mutual orientation of the domains. The results of the CABS simulations were subjected to the average linkage hierarchical clustering 46, with the distance root mean-square separations being a measure of structural similarity. For each cluster, the centroid was calculated and a full atomic model rebuilt to provide the final model. The above-mentioned hybrid approach ranked among the best methods in the Sixth Critical Assessment of Techniques for Protein Structure Prediction (CASP-6) experiment 11 and has proven to predict appropriate protein models even in cases where no consensus fold was reported by the fold recognition servers 47,48. Several models of FecA were obtained, which differed in their relative orientation of the NTD with respect to the membrane.
We calculate the linear correlation coefficient C,
![]() | (4) |
are, respectively, the mean-square residue fluctuations from the GNM computations and the average fluctuation over all residues. Similarly, yi and
are the experimentally determined B-factors and their means. The linear correlation coefficient is a straightforward way to analyze the extent of linear dependence between two quantities. Its values range between 1 and −1, corresponding to perfect correlation and perfect anticorrelation, respectively. However, this coefficient has its limitations. The linear correlation coefficient shows only how two quantities deviate simultaneously from their means, without any reference to their relative amplitudes. Therefore, this parameter provides only information about the relative up-and-down patterns.Absolute overlap between two eigenvectors, each representing specific motions, is defined as
![]() | (5) |
In this equation, x and y are two eigenvectors, xi and yi denote their ith components, and θ is the angle between x and y. If two eigenvectors are exactly collinear, then their absolute overlap equals 1. If they are orthogonal to each other, then the absolute overlap is zero, and the angle between the two eigenvectors is 90°. This provides a measure of the extent of similarity in the directions of motions for different modes.
The FecA protein contains 741 residues and consists of three domains: the plug, the barrel, and the NTD. The crystallographic structure of the FecA plug and the barrel domains (residues 81–741) has been solved by x-ray crystallography (PDB code 1kmo 8). The N-terminal fragment of the plug domain, containing 17 residues, is variable and changes upon binding the substrate.
Recently, the 79-residue-long fragment, the NTD, was the subject of an NMR study 10. The authors found that the NTD has a well-structured, 74-residue N-terminal fragment that forms a closely packed α+β fold. The C-terminus of the NTD (residues 75–96) was found to be unstructured. The analysis of the NMR data for this fragment shows a large number of alternative conformers. The structure of the NTD domain has also been determined by NMR by another group 9 (PDB code 1zzv). That structure is similar to the one found by Garcia-Herrera and Vogel 10 (root mean-square deviation (RMSD)=2.3 Å 9), with only slight differences between the two. One important feature of the second NMR structure is that the hydrophobic core is well protected from the solvent 9.
The most interesting questions are: 1), What is the orientation (and resulting interactions) of the NTD with respect to the main portion of FecA? and 2), What is the structure of the linker and how does it influence the mobility of the NTD? Due to lack of sufficient experimental data we must resort to molecular modeling to solve these problems.
Unfortunately, the large size of the molecular system makes molecular dynamics impractical. Therefore, we have applied a hierarchical modeling protocol based on CABS, our reduced conformational space modeling tool. CABS employs a simplified representation of protein conformations: the modeled polypeptide is reduced to an α-carbon trace, up to two united atoms representing the side chain and a virtual atom located in the center of each connecting Cα-Cα vector. These virtual atoms define the positions of the main chain hydrogen bonds. The CABS force field consists of a balanced set of knowledge-based statistical potentials. The conformational space is sampled via an efficient Monte Carlo algorithm. As a result, the simulations performed with CABS can cover a time interval by orders of magnitude larger than would be possible using classical molecular dynamics. Details of the CABS model and its force field can be found elsewhere 44. CABS has been effectively used for a variety of molecular modeling tasks: comparative modeling, de novo folding 11, the study of macromolecular assemblies 49, and protein-protein docking 50, and also to study long-time protein dynamics 51.
The modeling process consists of several steps. First, we generate an initial structure of the entire molecule. The coordinates of residues 81–741 were taken for the 1kmo PDB file and projected onto the lattice representation of CABS. Then the N-terminal portion of the FecA chain was added as an unstructured random coil. During simulations, residues 97–741 were kept frozen. For the structured 1–74 fragment, a set of weak distance restraints (a few hundred Cα-Cα distances, uniformly distributed) was derived from the NMR structure (PDB code 1zzv 9). The strength of these restraints was set in such a way that the restrained residues were allowed to move 2–3Å with respect to each other in a single Monte Carlo cycle. The linker (residues 75–96), including the TonB box, was not restrained in any way, and was allowed to move freely and to interact with the entire molecule. Two types of simulations were performed. In the first simulation, we employed replica-exchange Monte Carlo (REMC) to minimize the entire structure. The initial replicas have different, randomly generated conformations of the 96-residue N-terminus. During the simulations, the NTD fold assembled very rapidly. Due to the way the restraints were imposed, the NTD remained mobile during the rest of the simulation. The NTD structure fluctuated around the equilibrium internal coordinates of the NMR structure, and the entire domain rotated and translated with respect to the two C-terminal domains, stretching and folding the portions of the linker and adjusting interactions with the transmembrane cap and the plug domain. The structure of the NTD never departed by >2–2.5Å from the NMR structure (cRMSD for the α-carbon traces).
After an initial equilibration (required for folding of the NTD), a large number of snapshots (a few thousand) were collected at equal intervals from a very long REMC simulation. These snapshots were subsequently subjected to hierarchical clustering 46. After this, atomic details for the cluster centroids were rebuilt 52 and the resulting all-atom structures were energy-minimized using an all-atom force field with an implicit solvent. In the all-atom minimization, the transmembrane barrel was frozen. Thus, no model of an implicit solvent was applied to this part of the assembly. The implicit solvent model was applied only to the NTD, and the membrane was treated as a nonpenetrable medium for the NTD. The changes of conformation for the NTD after the all-atom minimizations were small (essentially negligible), ranging from 0.2Å to 0.4Å (differing mainly in the orientations of the NTD with respect to the rest of the molecule). The all-atom energy was used to rank the models of the entire assembly. The minimization improved the packing of the side chains, allowing more exact analysis of the side-chain contacts. The use of all-atom energy has been shown to be highly effective in selecting the best models from the CABS simulations 53. Thus, we believe that the models presented are representative of the flexible orientations of the NTD with respect to the rest of the FecA structure.
To further verify the model, we additionally performed a long isothermal simulation (using a single replica) at a temperature at which the NTD structure is well defined yet allowed to move with respect to the rest of the assembly. During the single-replica simulations, the transmembrane barrel was again kept frozen. The results were consistent with the REMC simulations. The NTD rotated and translated with respect to the rest of the FecA structure. Periods of highly local fluctuations near the structures identified in the two leading clusters from the REMC simulations, and fast transitions between these structures, were observed many times. Thus, the simulations indicate the existence of two dominant conformations of the complex, which (under the studied conditions) exchange their structures frequently. The three remaining clusters from the REMC simulations seem to correspond to shallow free-energy minima marking transition states between the two major minima. Here, we will call the first model FecA complex A, and the second FecA complex B (Figure 2ab). The overall RMSD between the structures of these two leading clusters is 3.1Å. This value reflects different orientations of the NTD domains.
The behavior of the linker is interesting. During the stretching phases, it was essentially unstructured. During the compacting phases, the residues on its C-terminus (85–96) frequently formed a β-strand (expanding the β-sheet of the plug domain) and a short flexible helix next to the β-sheet. The 75–84 fragment of the linker always remained essentially unstructured and highly flexible.
The TonB box (D80–V84) is the interface where FecA interacts with the inner membrane protein TonB for energy transduction. The position of the TonB box differs in our two most reliable models of the FecA complex (Figure 2ab). In the first model, FecA complex A, the TonB box is partially exposed to the periplasm in a conformation that allows the docking of TonB to FecA. In contrast, for FecA complex B, the TonB box is in a more protected conformation, shielded on the sides by the plug and barrel domains and at the bottom by the N-terminal of the plug domain. Our simulations capture these two essential conformations, which may play a part in various stages of the FecA-TonB interaction. These two different states suggest that when the FecA complex-TonB docking is initiated, the FecA conformation should switch from FecA complex B to complex A, exposing and aligning the TonB box for proper docking to TonB.
We analyzed the functional motions of the structures obtained in the modeling procedures using the elastic network models 12,13. These models (see Methods) can reproduce experimental data such as temperature factors 12,13, and provide the cooperative, global protein motions at low frequencies. A comparison of calculated and experimental fluctuations (Fig. 3) shows that the GNM is successful in reproducing the experimental results: the qualitative agreement between the predicted mean-square fluctuations and the experimental B-factors is strong. For a quantitative comparison, we calculated the correlation between experimental fluctuations and theoretical predictions using both FecA complex models, A and B. For residues 81–741, for which experimental B-factors are available, the correlation is 0.57 for both models. This value is close to the average value of correlations, 0.59, obtained by GNM 54. In the fluctuation plots, maxima correlate with protein residues of high flexibility, whereas minima correspond to regions of restricted flexibility. In the case of the FecA complex, the high-mobility regions generally coincide with the extracellular and periplasmic loops of the barrel domain, whereas the low-mobility regions correspond to residues in the β-sheets interacting with the cell membrane.
To understand the functional motions of FecA embedded in the membrane, we applied the elastic network models to the plug and barrel domains to isolate the motions of these domains from the highly mobile NTD. Our elastic network analysis (see Methods) shows that in the slowest modes, FecA exhibits distinct motion patterns. The cross section of the plug and barrel domains noticeably opens and closes in a manner similar to a breathing motion. The most interesting observation is the high mobility of the periplasmic loops. The periplasmic loops swing as a result of the breathing motion of the plug and barrel domains. This high mobility suggests the functional importance of the periplasmic loops when FecA is interacting with the inner membrane proteins TonB and FecR. Both the extracellular and periplasmic loops are highly mobile in the slowest modes, but exhibit significantly correlated fluctuations (computed from Eq. (2)). This is an interesting observation, as it implicitly suggests the presence of a communication between the loops on both ends of the protein, a signaling mechanism by which a signal could be transmitted by conformational transitions in response to the binding of ferric citrate.
We analyzed the extent of similarity between the global motions of the two most probable computed conformations of the FecA complex (FecA complexes A and B.) Although FecA moves continuously during simulations and acquires various conformations, certain conformations are more preferred (Fig. 2). The main question, then, is, when FecA changes its conformation as a result of its dynamic nature, to what extent are the functional slow motions affected? A simple overlap between eigenvectors of the two preferred conformations can shed light on this issue. This overlap is shown in Fig. 4. Here, eigenvectors with smaller indexes refer to slower modes, and those with larger indexes to faster modes. In the 3D graph in Fig. 4, there are peaks and lighter colors when there is high overlap. The overlap is especially strong for the slowest modes along the diagonal.
We used FecA complexes A and B to investigate global motions of FecA. Fig. 5 shows the cross-correlation between the residue fluctuations of these two conformations calculated using the following formula:
![]() | (6) |
where C(k,l) is the cross-correlation between the fluctuations of residues k and l. For the plug and barrel domains, the correlations between two conformations are highly similar; the major difference occurs for the NTD domain. To gain a visual understanding of the motions, we have performed further analysis and computed the flexibility of various parts of the FecA structure (Fig. 6). The most mobile regions are shown in red and green; and rigid regions are shown in blue. A striking feature in Fig. 6 is the presence of the rigid regions: although the membrane structure has not been included in the model, the membrane-bound plug and barrel domains still display comparatively high rigidity. This rigidity emphasizes that β-barrel arrangements are structurally stable and suggests that the shape of the β-barrel fold may not require the bilipid membrane for its structural integrity. However, as has been observed in several studies 55,56,57,58, the nonpolar side chains are exposed on the outside of the barrel and thus require the hydrophobic environment of the outer membrane. Thus, in the case of the FecA complex, the shape-dependent stability is enhanced by chemical specificity of binding to ensure structural integrity.
The mobile regions are numbered in Fig. 5 for further analysis: Region 1, Asn477–Glu484; Region 2, Thr422–Arg438; Region 3, Ala1–Ile5; Region 4, Leu597–Asp602; Region 5, Ile397–Ala401; and Region 6, Asn38–Gly49. As Region 1 is the free chain end of the N-terminal, its mobility is not a consequence of cooperative motions, but originates as a result of the absence of structural constraints. Most of the other mobile regions are located on the loops connecting regular secondary structures. Because loops have a higher degree of freedom compared to the highly packed regions, their high mobility is usually expected. However, the slowest modes derived from elastic network models are highly specific: only certain loops—not all loops—show large correlated motions, which suggests that these mobile loops may have functional roles in the ferric citrate signaling and transfer. Directed single-site mutagenesis or deletion experiments may reveal details about which specific residue sites on the loops are essential.
Although the plug and barrel domains show less mobility, they do not stay entirely rigid, but rather show distinct motions: for example, the barrel cross section enlarges and contracts in a breathing motion, as discussed above. Through this mobility of the cross section, the plug and barrel domains serve as a connector between periplasmic and extracellular loops, transferring the mechanical energy in a collective manner.
Correlated motions between different parts of FecA have different characteristics at different slow modes. In some cases, they display “pinching motions,” such as between the periplasmic loops in Regions 5 and 6. In other cases, certain loops twist in coordination, such as the extracellular loops in Regions 1 and 2. However, the most striking feature in these correlations is not the type of motion they exhibit, but that in slow motions, at least one periplasmic and one extracellular loop move in coordination. This observation suggests the presence of allosteric communication between the extracellular and periplasmic sides of FecA. Such paths of communication are essential to relay the information of ferric citrate binding from the extracellular side to the periplasmic domain and, finally, to the cell interior.
One of the mobile regions that is particularly interesting is Region 6, as it has slightly different conformations in FecA complex models A and B. Region 6 (Fig. 6) is located at the periplasmic side of FecA and its mobility is not restricted to the loop, but extends to the helix structure. Although the helix orientation differs in both complex models, the helix-loop region moves in coordination with other mobile regions. This brings up the question of whether this region on the periplasmic side plays a critical role in docking to the inner membrane proteins.
Other slow modes show different combinations of coordinated movements of the periplasmic and extracellular loops, as well as other loops shown in Fig. 6. These examples support the point of view that, even for nonallosteric proteins 59, the protein shape is essential to allow for communication between distant sites executed through concerted motions.
The transmembrane protein FecA is located in the outer membrane of E. coli and is responsible for recognition and intake of ferric citrate, and transcription of the genes FecABCDE, which is required for ferric citrate transport to the cell cytoplasm. During this process, FecA interacts with inner membrane proteins and obtains its energy from the TonB-ExbB-ExbD complex. Although FecA plays a vital role in cellular fitness, its full structure is not completely known; the structures of the plug and barrel domains and the NTD are available separately. This structural information gap hinders our ability to fully elucidate the mechanism of ferric citrate transport in E. coli. To narrow this gap, we modeled the three-dimensional structure of the full FecA complex.
In our modeling, we carried out CABS folding simulations with a comprehensive force-field description, extracted several structures from multiple simulation samplings using hierarchical clustering, and validated plausible structures by checking interatomic distances to obtain the final model.
As the protein dynamics is inherently related to its function, we also applied elastic network models to probe FecA cooperative motions related to lowest normal modes. The NTD exhibits a range of motions, including swinging, twisting, and rotating, which harness the relative flexibility of the loop connecting the NTD to the plug domain. Such mobility is required for proper docking of the TonB protein to the TonB box, but the mechanistic details of this interaction are currently unknown. The two most striking features in the FecA global modes are 1), correlated motions of the NTD and the extracellular and periplasmic loops; and 2), the presence of two conformations that control the exposure of the TonB box to the periplasm, which may control TonB docking to FecA. These coupled motions may be useful in signal transduction associated with ferric citrate binding, as well as in ferric citrate transport. We expect that the structural models obtained in this study will stimulate more experiments and simulations for more detailed elucidation of these mechanisms in the future.
T.Z.S. thanks Ozge Kurkcuoglu for her assistance with graphics. The authors also thank two anonymous reviewers for helpful suggestions that improved this article.
M.K. received a fellowship from the National Institutes of Health (NIH) National Science Foundation BBSI Summer Institute in Bioinformatics and Computational Biology. T.Z.S., A.Klo., and R.L.J. acknowledge financial support provided by NIH grants 1R01GM072014-01 and 1R01GM073095-02. A.Klo., R.L.J., A.Kol., and J.M.B. acknowledge financial support provided by NIH grant 1R01GM081680-01.
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