1. Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520, USA

Correspondence to: G. Marius Clore¹ Correspondence and requests for materials should be addressed to G.M.C. (Email: mariusc@intra.niddk.nih.gov).

The association of the N-terminal domain of enzyme I (EIN) and the phosphocarrier protein HPr (dissociation constant, K _d  10 M), the first binary complex in the bacterial phosphotransferase system¹¹, is in fast exchange on the chemical shift scale¹⁰. The structure of the stereospecific EIN–HPr complex has been solved by NMR on the basis of nuclear Overhauser enhancement (NOE) and residual dipolar coupling (RDC) data¹⁰. These data are fully consistent with a single, unique conformation that readily accounts for the phosphoryl transfer reaction between the two proteins¹⁰. However, neither the NOE nor the RDCs are sensitive to the presence of low-population (10%) intermediates. To detect such intermediates, we introduced a paramagnetic label at three sites on HPr, one at a time, and measured the transverse paramagnetic relaxation enhancement (PRE) rates, ₂, of the backbone amide protons (¹H_N) of EIN. In a fast exchanging system, the observed value of ₂ is the weighted average of the ₂ values for the various states present in solution^{12, 13}. Because ₂ is dependent on the sixth root of the distance (<r ^-6>) between the unpaired electron on the paramagnetic centre and the observed proton, and because the ₂ rates at short distances are very large owing to the large magnetic moment of the unpaired electrons, low-population intermediates can be detected. Glu 5, Glu 25 and Glu 32 of HPr, which are all located outside the specific interaction surface with EIN, were substituted individually by a cysteine residue, which was then conjugated to EDTA through a disulphide linkage to yield a (cysteaminyl-EDTA)-Cys adduct. The latter is chelated to either Mn²⁺ (paramagnetic state) or Ca²⁺ (diamagnetic state)¹⁴. These modifications do not change the net charge of HPr, nor do they perturb the binding equilibrium with EIN.

The intramolecular ¹H_N- ₂ rates for HPr in the EIN–HPR complex are fully consistent with the static structure of HPr, with an overall PRE Q-factor¹⁵ (for all three paramagnetic sites combined) of 0.18 and a correlation coefficient of 0.94 (Supplementary Fig. S1). (The Q-factor is a quantitative measure of agreement between observed and calculated ₂ rates and is given by equation (2) in the Methods section.) A comparison, however, of the observed intermolecular ¹H_N- ₂ rates measured on EIN with those back-calculated from the structure of the stereospecific complex as a function of residue number reveals regions with large discrepancies (Fig. 1). The correlation between observed and calculated intermolecular ¹H_N- ₂ rates is very poor, with an overall Q-factor of 0.61 (Fig. 2a). In the stereospecific complex, the intermolecular contacts predominantly involve helices 2 and 2', the carboxy-terminal end of helix 3 and the N-terminal end of helix 4 of the -domain of EIN, and helices 1 and 2 of HPr¹⁰. For each paramagnetic site, there are regions with large observed intermolecular ¹H_N- ₂ rates that are well predicted by the stereospecific complex (that is, they are in close proximity to the paramagnetic labels): namely, residues 110–137, 50–92 and 73–140 for Glu5Cys, Glu25Cys and Glu32Cys, respectively, within the -domain of EIN (Fig. 1). However, there are many other residues within the -domain of EIN that are far away (25 Å) from the paramagnetic labels but show large ¹H_N- ₂ rates that are inconsistent with the structure of the specific complex: namely, residues 59–97, 105–124 and 20–71 for Glu5Cys, Glu25Cys and Glu32Cys, respectively (Fig. 1). In addition, there are regions in the / domain, further away from the paramagnetic centres, where the agreement is poor to moderate: namely, residues 23–37, 183–189 and 241–249 for Glu25Cys, and residues 184–189 and 232–249 for Glu32Cys (Fig. 1). The discrepancies cannot be explained by a solvent PRE effect^{16, 17} involving diffusion and random collisions between EIN and the paramagnetically labelled HPr because, at the relatively low concentrations used (300 M), no significant PRE effects (>2 s^-1) were observed for a control protein (that does not interact with HPr) on addition of paramagnetically labelled HPr. Thus, the observed intermolecular PRE data provide unambiguous qualitative evidence for the existence of lowly populated (10%) minor species in rapid exchange with the final stereospecific complex (see Supplementary Information).

Figure 1: Observed and calculated intermolecular PREs for the EIN–HPr complex.

Shown is a comparison of observed intermolecular ¹H_N- ₂ rates (red diamonds) with those back-calculated (black lines) from the stereospecific complex; paramagnetic labels (EDTA-Mn²⁺) were introduced one at a time at three sites (E5C, E25C and E32C) on HPr. Red crosses indicate residues with ¹H_N/¹⁵N cross-peaks that are broadened beyond detection by PRE. Insets show the structure of the stereospecific EIN–HPr complex with EIN colour coded according to the difference, ₂, between the observed and calculated intermolecular ¹H_N- ₂ rates for each paramagnetic site. (HPr, green; three-member ensemble representation of EDTA-Mn²⁺ with EDTA and linkage, orange, and Mn²⁺, red spheres). Residues with large ₂ are labelled. Error bars indicate the s.d.

High resolution image and legend (156K)

Figure 2: Ensemble refinement and intermolecular PRE Q-factor.

a, b, Correlation between observed intermolecular ¹H_N- ₂ rates (501 data points) and those calculated from the structure of the stereospecific complex either alone (a) or with the addition of an ensemble of N = 20 to represent the non-specific encounter complex (b; p _minor = 10%; averaged over 100 independent calculations). c, Dependence of the working (Q _e, red; Q _ee, blue) and cross-validated (Q-free, green) Q-factors on ensemble size N (p _minor = 10%). d, Dependence of Q _e and Q _ee on p _minor (N = 20). The points in c and d at N = 0 and p _minor = 0, respectively, represent control calculations in which p _minor = 0 and the position of HPr for the single specific complex is optimized by rigid-body simulated annealing to satisfy the intermolecular PRE data. Error bars indicate the s.d.

High resolution image and legend (108K)

A semi-quantitative depiction of the minor species was obtained by using restrained rigid-body simulated annealing refinement¹⁸ to minimize the difference between observed and calculated ¹H_N- ₂ rates for all three paramagnetic sites simultaneously by representing the minor non-specific states by an ensemble of HPr molecules (with atomic overlap between HPr molecules allowed because the ensemble reflects a population distribution). We carried out 100 independent calculations with ensemble sizes N ranging from 1 to 20, varying the percentage of the minor species (p _minor) relative to the stereospecific complex. Complete cross-validation¹⁹, leaving out random portions of 10% of the complete PRE data set from all three sites, was done to assess how well the test PRE data sets (10% excluded from the refinement) are predicted by the working data sets (90% included in the refinement). Introduction of a single minor species results in only a modest decrease in the Q-factor, but, as the number of conformers is increased, a large decrease in the Q-factor is observed (Fig. 2c). Complete cross-validation indicates that the optimal number of conformers required to satisfy the data is 10–20 (Fig. 2c) and that the improvement in Q-factor is not a result of over-fitting the data. Thus, the minor species comprises many non-specific binding states that reflect an ensemble of transient encounter complexes.

The Q-factor decreases rapidly as p _minor is increased to 10% (Fig. 2d), a value that is still consistent with the NOE and RDC data, and thereafter slowly levels off. The Q-factor obtained by averaging the ¹H_N- ₂ rates over all ensembles (that is, the ensemble of ensembles average, Q _ee) is systematically smaller than the average Q-factor for the individual ensembles (Q _e). This is due to the stochastic rather than unique configuration of states within each ensemble, such that averaging over all ensembles affords a better representation of the data (Fig. 2c, d). For N = 20 and p _minor = 10%, Q _ee has a value of 0.21 and the correlation coefficient between observed and calculated ¹H_N- ₂ rates is 0.97 (Fig. 2b), which is comparable to the agreement observed for the intramolecular PRE data (Supplementary Fig. S1). The overall population of minor non-specific encounter complexes may seem to be relatively high but is perhaps not unexpected for a relatively weak protein–protein association. However, the occupancy of any individual conformer in the ensemble of non-specific encounter complexes is very small and has therefore eluded structural characterization by any other experimental method.

The minor species were visualized by using a reweighted atomic probability density map²⁰ derived from 100 independent calculations using an ensemble size of N = 20 (Fig. 3a–c, left). The distribution of non-specifically bound HPr molecules on the surface of EIN is essentially continuous but non-uniform. The probability density in the region of the specific complex is low, indicating that alternative modes of binding confined to the contact surfaces involved in the stereospecific complex do not significantly contribute to the discrepancy between the observed PREs and those calculated on the basis of the specific complex (Supplementary Figs S2 and S3).

Figure 3: Characterization of non-specific EIN–HPr encounter complexes.

a–c, Left, overall distribution of HPr molecules obtained from 100 calculations (N = 20) displayed as a reweighted atomic probability density map²⁰ (plotted at a threshold of 20% maximum, green) on the molecular surface of EIN (colour coded by electrostatic potential, 8 kT). Right, molecular surface of EIN in grey with the electrostatic potential isosurface of EIN, calculated at 5 kT, displayed as red (negative) and blue (positive) meshes. The disposition of HPr molecules (blue tubes) in a typical ensemble of N = 20 is shown in the right panel of a. The location of HPr in the stereospecific complex is shown as a blue ribbon in all panels. d, Histograms of interface-buried ASA and gap index for the non-specific encounter complexes. Red lines indicate values for the stereospecific complex.

High resolution image and legend (245K)

Outside the specific interaction surface, the distribution of HPr molecules (Fig. 3a–c, left) is qualitatively correlated with the negative electrostatic potential isosurface²¹ of EIN (Fig. 3a–c, right). EIN is an acidic protein and large areas of its surface are swathed by a negative electrostatic potential. About half the surface of HPr, including the interaction surface used in the specific complex, is positively charged, and the remaining surface (formed predominantly by the -sheet) is negatively charged. The HPr atomic probability density map heavily populates regions of EIN with highly negative electrostatic potentials, to a lesser extent around the C terminus of EIN, and minimally on the back of EIN (Supplementary Fig. S4a). Note that the HPr conformers located at the / domain are, on average, 50 Å from HPr in the stereospecific complex. In all cases, HPr preferentially uses its positively charged surface to interact with the negatively charged regions of EIN (Supplementary Fig. S5c). Thus, the modifications used to introduce paramagnetic groups on HPr do not affect the formation of non-specific encounter complexes. These findings suggest that the formation of non-specific EIN–HPr encounter complexes is predominantly driven by weak non-specific electrostatic attractions between the two molecules.

The total solvent accessible surface area (ASA) buried at the interfaces of the non-specific encounter complexes is, on average, an order of magnitude smaller than that of the stereospecific complex (1,945 Å²; Fig. 3d). The non-specific interfaces are also much less compact, with gap indices (defined as the ratio of gap volume to buried interface ASA²²) many times larger than that of the stereospecific complex (2.1 Å; Fig. 3d). In addition, the non-specific interfaces are more planar than the stereospecific one, indicative of the absence of lock-and-key binding (Supplementary Table S1). These observations are consistent with the correlation between the spatial distribution of non-specific encounter complexes and electrostatic potential isosurface, because electrostatic interactions are relatively long range (with a 1/r distance dependence) and do not necessarily require van der Waals contact. The role of electrostatic interactions is reinforced by the observation that the interfacial composition of charged residues is increased, whereas that of uncharged polar and non-polar residues is decreased in the non-specific encounter complexes relative to the stereospecific complex (Supplementary Fig. S4b).

Once a non-specific encounter complex is formed by weak non-specific electrostatic interactions, HPr can carry out a two-dimensional search on the surface of EIN, eventually falling into a narrow energy funnel that leads directly to the stereospecific complex characterized by an array of complementary van der Waals and electrostatic interactions. The observation that the region on EIN comprising the specific interaction surface for HPr is only minimally occupied by non-specific encounter complexes (Fig. 3a) indicates that once HPr reaches this region formation of the stereospecific complex occurs with high probability.

The direct detection of non-specific encounter complexes by PRE is not confined to the EIN–HPr complex. We observed similar effects for two other weak (K _d  30–50 M), fast-exchanging protein–protein complexes of the bacterial phosphotransferase system, IIA^Mannitol–HPr (Fig. 4) and IIA^Mannose–HPr (Supplementary Fig. S6), the stereospecific structures of which have been solved^{23, 24}. With the paramagnetic label on HPr located at Glu5Cys, on the opposite face to the stereospecific binding site, there are regions in both complexes where the observed intermolecular ¹H_N- ₂ rates are much larger than those back-calculated from the structures of the stereospecific complexes. The largest discrepancies involve acidic residues of IIA^Mannitol and IIA^Mannose, the distribution of which correlates qualitatively with the negative electrostatic potential on the surface of these proteins. Thus, in all likelihood the observations reported here reflect a general phenomenon of protein–protein association in which the initial formation of non-specific encounter complexes through long-range electrostatic interactions (possibly supplemented by short-range van der Waals interactions) facilitates the rapid formation of a stereospecific complex by reducing the dimensionality of the search process.

Figure 4: Observed and calculated PRE ¹H_N-₂ values for the IIA^Mannitol–HPr complex.

EDTA-Mn²⁺ paramagnetic labels were introduced onto HPr at E5C. a, Comparison of observed intermolecular ¹H_N- ₂ rates (red diamonds) with those back-calculated (black lines) from the stereospecific complex. Red crosses indicate residues with ¹H_N/¹⁵N cross-peaks that are broadened beyond detection by PRE; error bars indicate the s.d. b, Structure of the stereospecific complex with IIA^Mannitol colour coded according to the difference, ₂, between observed and calculated intermolecular ¹H_N- ₂ rates. Colouring for HPr and EDTA-Mn²⁺ as in Fig. 1 insets. c, Molecular surface representation of IIA^Mannitol in the stereospecific complex. Residues of IIA^Mannitol that show large ₂ are coloured cyan. d, Electrostatic potential isosurface of IIA^Mannitol (5 kT in blue and red, respectively). In c and d, HPr is shown as a green ribbon. The same view is shown in b–d.

High resolution image and legend (139K)

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Supplementary Information

Supplementary information accompanies this paper.

Acknowledgements

We thank C. Schwieters, A. Szabo and C. Bewley for discussions; and C. Byeon for assistance with initial sample preparation. This work was supported by funds from the Intramural Program of the NIH, NIDDK and the AIDS Targeted Antiviral program of the Office of the Director of the NIH (to G.M.C.).

Competing interests statement

The authors declare no competing financial interests.

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