Conceived and designed the experiments: CA ARA. Performed the experiments: CA ARA. Analyzed the data: CA ARA. Contributed reagents/materials/analysis tools: CA ARA. Wrote the paper: CA ARA.
The authors have declared that no competing interests exist.
We study apo and holo forms of the bacterial ferric binding protein (FBP) which exhibits the so-called ferric transport dilemma: it uptakes iron from the host with remarkable affinity, yet releases it with ease in the cytoplasm for subsequent use. The observations fit the “conformational selection” model whereby the existence of a weakly populated, higher energy conformation that is stabilized in the presence of the ligand is proposed. We introduce a new tool that we term perturbation-response scanning (PRS) for the analysis of remote control strategies utilized. The approach relies on the systematic use of computational perturbation/response techniques based on linear response theory, by sequentially applying directed forces on single-residues along the chain and recording the resulting relative changes in the residue coordinates. We further obtain closed-form expressions for the magnitude and the directionality of the response. Using PRS, we study the ligand release mechanisms of FBP and support the findings by molecular dynamics simulations. We find that the residue-by-residue displacements between the apo and the holo forms, as determined from the X-ray structures, are faithfully reproduced by perturbations applied on the majority of the residues of the apo form. However, once the stabilizing ligand (Fe) is integrated to the system in holo FBP, perturbing only a few select residues successfully reproduces the experimental displacements. Thus, iron uptake by FBP is a favored process in the fluctuating environment of the protein, whereas iron release is controlled by mechanisms including chelation and allostery. The directional analysis that we implement in the PRS methodology implicates the latter mechanism by leading to a few distant, charged, and exposed loop residues. Upon perturbing these, irrespective of the direction of the operating forces, we find that the cap residues involved in iron release are made to operate coherently, facilitating release of the ion.
Upon binding ligands, many proteins undergo structural changes compared to the unbound form. We introduce a methodology to monitor these changes and to study which mechanisms arrange conformational shifts between the liganded and free forms. Our method is simple, yet it efficiently characterizes the response of proteins to a given perturbation on systematically selected residues. The coherent responses predicted are validated by molecular dynamics simulations. The results indicate that the iron uptake by the ferric binding protein is favorable in a thermally fluctuating environment, while release of iron is allosterically moderated. Since ferric binding protein exhibits a high sequence identity with human transferrin whose allosteric anion binding sites generate large conformational changes around the binding region, we suggest mutational studies on remotely controlling sites identified in this work.
Functional proteins are complex structures, which may remain mainly unmodified as a result of a multitude of mutations
Linear response theory (LRT) has been recently used to study conformational changes undergone by proteins under selected external perturbations
PRS relies on systematically applying forces at singly selected residues and recording the linear response of the whole protein. The response is quantified as both the magnitude of the displacements undergone by the residues, and their directionality. Closed form expressions that summarize the theoretical implications of the PRS technique in the limit of a large number of perturbations introduced at a given residue are provided. We note that we have previously studied the stability of proteins using a similar sequential perturbation-response approach, based on inserted displacements followed by energy minimization of the system
Using PRS, we analyze the ferric binding protein A (FBP) as an example system, and describe alternative approaches that may have evolved in the structure to control function. The validity of the methodology is supported by molecular dynamics (MD) simulations. FBP is involved in the shuttling of Fe+3 from the mammalian host to the cytoplasm of pathogenic bacteria. To make iron unavailable to such pathogens, host organisms have iron transport systems such as the protein transferrin that tightly sequester the ion. Pathogens have developed strategies to circumvent this approach, one of them being the development of receptors for the iron transport proteins of the host. FBP resides in the periplasm, and receives iron from these receptors to eventually deliver it to the cytosol
Fe+3 is bound to FBP with remarkable affinity, with association constants on the order of 1017–1022 M−1 depending on the measurement conditions
FBP is referred to as bacterial transferrin due to the similarities with transferrin in the structural folds, the highly conserved set of iron-coordinating residues, and their usage of a synergistic anion
In the current work, we study FBP in detail due to an extensive literature on the iron uptake mechanisms of this and evolutionarily related proteins; moreover, the molecular dynamics (MD) results of the apo structure have previously been analyzed by perturbing a singly selected residue with linear response theory
The new tool introduced in this work for the analysis of remote control strategies utilized by proteins is based on applying forces at a given residue as a perturbation, and recording the displacements of all the residues as the response. Since the procedure is repeated sequentially for all the residues in the protein, we term the technique, perturbation-response scanning (PRS). Below, we first review the theory and then outline the details of the PRS technique. Finally, we describe the MD simulations.
Here we present a derivation of how a structure may be manipulated by external forces
Excerpted from the protein chain (upper panel), scheme depicting the free body diagram of a Cα
In the notation used,
In the presence of an external force, Δ
Thus, rearranging equations 3–5, one gets the forces necessary to induce a given point-by-point displacement of residues:
Our detailed PRS analysis is based on a systematic application of equation 7. We apply a force on the Cα atom of each residue by forming the Δ
We then compute the resulting (Δ
One may further obtain a theoretical limit on the displacements, as we shall show below. The elements and properties of
The average displacement on residue
Using PRS, we scan the protein by consecutively perturbing each residue, and record the associated displacements as a result of the linear response of the protein. We define
If the collection of forces applied on a specific residue is independent and large in number, they will appear in a spherically symmetric set of directions. The responses, however, may be distributed along a line or in a plane so that the net response is still zero. Thus, although the perturbations are isotropic, the response may well be anisotropic. Deviations from such a spherically symmetric distribution of responses hint at the roles of certain residues in the remote control of the ligand, as will be shown in the
For an analysis that probes the directionality of the recorded responses, we proceed as follows: We first concentrate on those residues for which the Pearson correlation between experimental and theoretical displacements is large. Amongst them, we further locate those residues,
One may further analyze the eigenvalue structure of the
The degree of collectivity of the response of a group of neighboring residues to a perturbation on
We analyze FBP in detail, using both PRS and MD. In addition, the PRS methodology is applied to several other cases to demonstrate how the approach may be used. These are included in
The apo and holo forms of FBP have PDB codes 1D9V and 1MRP, respectively; in the latter case the Fe ion is treated as an additional node of the network. The protein has two domains, and upon binding one moves relative to the other as shown in
As a cut-off distance, we seek the smallest value for which the experimental B-factors are well-reproduced (equation 9 with
To provide a basis for comparison with results from an all-atom approach, we have performed MD simulations on both the apo and the holo forms of FBP in water. The systems are prepared using the VMD 1.8.6 program with solvate plug-in version 1.2.
The binding site parameters are as follows: The exogenous phosphate is modeled in the H2PO4− state using the parameters reported in detail in the literature
Long range electrostatic interactions were calculated using particle mesh Ewald (PME) method
Both systems were first subjected to energy minimization with the conjugate gradients algorithm until the gradient tolerance was less than 10−2 kcal/mol/Å. 500 ps MD runs in the NVT ensemble at 310 K were carried out on the resulting systems. The final structures were then run in the NPT ensemble at 1 atm and 310 K until volumetric fluctuations were stable to maintain the desired average pressure. This process required 500 ps long MD runs at the end of which the average volume is maintained at 196900±700 and 203300±600 Å3 in the apo and holo structure runs, respectively. Finally, the runs in the NPT ensemble were extended to a total of 10 ns. The coordinate sets were saved at 2 ps intervals for subsequent analysis.
The RMSD of the trajectories were calculated (
The correlations between residue pairs derived from the MD trajectories are of particular interest. The snapshots recorded during the MD simulations are organized in the fluctuation trajectory matrix of order 3N×T,
Note that a each nanosecond of an MD simulation takes ca. 9.8 hours on a server with 2 GB memory and eight CPUs each with 2.4 GHz quadcore architecture. Five complete scans of the protein with the PRS method uses three minutes on a single CPU of the same server.
Based on linear response theory, we apply perturbations at selected points along the chain to diagnose the response of FBP. The protein is known to have a Fe3+ binding location, and the structure of the holo form is also known. The overall RMSD between the two forms is 2.48 Å. FBP has two domains, termed as the fixed and moving domains, respectively (in
Since the methodology employs the Hessian obtained from a coarse-grained potential in equation 7, we first determine the extent to which this potential represents the actual interactions between residue pairs. We compare the correlations obtained from the network model with those from the MD simulations for both the apo and the holo forms (by applying equations 8 and 9 for the former, and equations 22, 8, and 9 for the latter). We find that the coarsened protein model reproduces the residue-wise MD correlations; the Pearson correlations between the data are 0.76 and 0.74, respectively for the apo and holo forms. In
The relative magnitudes of the residue-by-residue displacement vectors between the experimental apo – holo structures after superimposing their fixed domains is shown in the bottom curve of
The latter two curves are nudged for ease of comparison; their baselines are shown by dashed lines. Since the calculated displacement is proportional to the imposed force in LRT and therefore may be rescaled by a proportionality constant, the magnitude of the force is adjusted so as to make the average displacement the same as that of the x-ray experiment.
We now perform the residue-by-residue scan on the protein. Starting from each of the initial conformations, (i) apo form and (ii) holo form with the Fe ion as an additional node in the network, we compute Δ
The displacements are compared with those of the crystal structures, for
In perturbing the residues of the apo FBP, the residues that give the worst correlations are 105 and 205–207, all in the fixed domain of the protein. Residue 105 is in the core of the β sheet structure located in this domain and 205–207 are at the turn adjoining a helix to a β strand. Additional residues with the largest deviations between the experiments and predicted values of the structural differences are due to perturbations in the fixed domain. Finally, residues 23 and 249, located in the core of the moving domain also lead to poorer predictions. These relatively low-correlation responses (
In perturbing the residues of the holo FBP, the number of residues that leads to a highly correlated Δ
The high
To provide further understanding of how the protein operates structurally, we turn to the few residues that give high correlations in the presence of the ligand. These include residues that are either in the fixed domain that support the ferric binding region or those that are located in the moving domain loops. Thus, it is possible to manipulate the bound form of the protein towards the unbound form by either directly perturbing the Fe-binding residues, or by controlling the distant flexible loops. If there is a directionality preference in the response of residues, they should additionally be revealed by the current analysis. Such a preference may be imposed by the excluded volume, or may be the result of coupling between the motions of subsets of nodes.
In the previous subsection we have shown that in holo FBP, singly placed forces on the residues listed under the caption to
The residues for which
fractional contribution of the highest eigenvalue |
angle |
|||
perturbed residue, |
PRS | MD | PRS | MD |
D47 | 0.95/0.92/0.81 | 0.78/0.83/0.60 | 9/16 | 5/28 |
D52 | 0.88/0.90/0.81 | 0.91/0.95/0.79 | 9/14 | 4/18 |
E57 | 0.54/0.56/0.50 | 0.77/0.86/0.57 | 36/38 | 4/16 |
Fe ion | 0.56/0.67/0.54 | 0.74/0.81/0.59 | 25/36 | 5/28 |
V105 | 0.73/0.77/0.62 | 0.89/0.88/0.92 | 7/11 | 6/19 |
As computed from equation 20.
Computed through equation 21; relative response of cap residues in the moving domain,
On the other hand, directly perturbing the Fe ion, as well as other local residues for which
In the lower left panel of
Thus, by jointly focusing on the specific distantly located residues which (i) invoke a large amount of correlations in the whole protein, and (ii) induce local cooperativity in the binding domain, one may be able to uncover sites that remotely control function in the protein. Interestingly, the same analysis carried out on the N-lobe of human transferrin implies K278 in that protein as an allosteric controller (see
In this study we introduce the PRS methodology based on systematically perturbing all residues of a protein, and classifying both the magnitude and the directionality of the recorded linear response. The approach is unique in that the cross-correlations between residues are processed as input for further predictions on the system behavior, unlike other methods where they are the final results. Closed-form expressions for the magnitude and the directionality of the response are also provided. The protein FBP is studied in detail, and results using PRS for additional cases are presented in
For the particular case of FBP, our analysis suggest the existence of two alternative mechanism of Fe ion release in FBP: (i) Local control of the ion by synergistic anions and chelators acting in the binding groove, and (ii) remote control by ions acting on distant charged residues located in solvent exposed loops (
The results resolve the so-called Fe+3 transport dilemma: The protein is ready to uptake the ion in the apo structure (
In summary, the PRS methodology introduces an efficient approach to determine regions in the protein that mechanically moderate binding region motions. It may therefore be used to determine candidate sites for mutational studies. In a forthcoming study, the biological implications from the results of PRS will be presented on set of twenty proteins that display various types of motions such as shear, hinge, allosteric, partial refolding as well as more complex protein motions, as classified in the Database of Macromolecular Motions
Although studies such as the current one help estimate allosteric sites, they do not provide information on pathways along which the remote communication takes place. As future work, it is of interest to locate these paths. Robust techniques to predict them using evolutionary information
The RMSD values of the 10 ns long MD trajectories. The holo form is stabilized by the ligand, while the apo form displays larger fluctuations.
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Sample applications of the PRS method.
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