Elucidating transient macromolecular interactions using paramagnetic relaxation enhancement

Abstract

Recent advances in the use of paramagnetic relaxation enhancement (PRE) in structure refinement and in the analysis of transient dynamic processes involved in macromolecular complex formation are presented. In the slow exchange regime, we show, using the SRY/DNA complex as an example, that the PRE provides a powerful tool that can lead to significant increases in the reliability and accuracy of NMR structure determinations. Refinement necessitates the use of an ensemble representation of the paramagnetic center and a model free extension of the Solomon-Bloembergen equations. In the fast exchange regime, the PRE provides insight into dynamic processes and the existence of transient, low population intermediate species. The PRE allows one to characterize dynamic non-specific binding of a protein to DNA; to directly demonstrate that the search process whereby a transcription factor locates its specific DNA target site involves both intramolecular (sliding) and intermolecular (hopping and intersegment transfer) translocation; and to detect and visualize the distribution of an ensemble of transient encounter complexes in protein-protein association.

Introduction

The history of paramagnetic relaxation enhancement (PRE) and the nuclear Overhauser effect (NOE) dates back to the 1950's (1). The NOE delineates short interproton distance contacts (≤ 6 Å) and provides the main source of geometric information currently used in macromolecular NMR structure determination (2,3). The PRE arises from magnetic dipolar interactions between a nucleus (e.g. ¹H) and the unpaired electrons of a paramagnetic center, and results in an increase in the relaxation rate of the nuclear magnetization (4). For an electron-nucleus distance r, the magnitude of the PRE is proportional to r⁻⁶, a relationship analogous to that between the magnitude of the NOE and interproton distance. However, because the magnetic moment of the unpaired electron is large, the PRE effects are large and can provide long-range distance information, extending in the case of Mn²⁺, for example, up to ~35 Å.

Not surprisingly, the PRE has seen extensive use in metalloproteins that possess a rigid intrinsic paramagnetic center (5–7). Other systems necessitate the attachment of an extrinsic paramagnetic group to the macromolecule of interest through appropriate chemical modification. As a result, it is only relatively recently, with advances in biochemical methodology that permit the reliable conjugation of a paramagnetic group to a specific site, that the use of the PRE has seen a resurgence. The potential of the PRE for protein structure determination, however, was first demonstrated about 20 years ago on spin-labeled lysozyme and bovine pancreatic trypsin inhibitor (8,9).

Nitroxide spin labels or EDTA-Mn²⁺ which have an unpaired electron with an isotropic g-tensor, are particularly suited for PRE measurements since they do not give rise to pseudo-contact shifts and Curie-spin relaxation is negligible. Recent applications include rapid determination of protein folds (10–15), analysis of unfolded and partially unfolded states (16–20), elucidation of protein-protein (21–24), protein-oligosaccharide (25–27) and protein-nucleic acid (28–32) complexes, and studies of membrane protein structure (33,34). Perhaps the most intriguing new application of the PRE relates to the study of low population encounter complexes involved in protein-nucleic acid (35) and protein-protein (36–38) recognition, as well as the study of large scale dynamics that entail significant changes in paramagnetic center-¹H distances, including for example, non-specific protein-DNA interactions (39,40) and large scale domain motions (41).

Measurement of the PRE

The PRE rate, Γ, is simply given by the difference in relaxation rates measured in the paramagnetic and control diamagnetic states. In general, we feel that the transverse PRE (Γ₂) is the most reliable way to make use of the PRE for two reasons (42). First, the large magnitude of the ¹H-Γ₂ PRE makes it a highly sensitive probe. This is due to the large nuclear gyromagnetic ratio of the proton and the primary dependence of ¹H-Γ₂ on the spectral density function at zero-frequency. Second, the transverse ¹H-Γ₂ rate is much less susceptible to internal motions and cross-relaxation than the longitudinal PRE rate, ¹H-Γ₁.

Quantitative application of the PRE requires that ¹H-Γ₂ rates be measured precisely and accurately. The majority of examples in the literature make use of a single time-point measurement in which two regular HSQC correlation spectra, one of the paramagnetic state, the other of the diamagnetic state at the same concentration, are used to determine ¹H-Γ₂ rates from the equation I_para(0)/I_dia(0)=R_2,diae^−Γ2τ/(R_2,dia + Γ₂), where I_para(0) and I_dia(0) are the peak intensities in the paramagnetic and diamagnetic states, respectively, R_2,dia is the transverse relaxation rate in the diamagnetic state, and τ is the overall ¹H transverse period for coherence transfers (42). Unfortunately, this simplistic approach severely underestimates the true value of ¹H-Γ₂ unless a very long repetition delay is employed (>20 s for a ²H-labeled protein). This is because at short repetition delays, the recovery levels for the paramagnetic sample are always higher than those of the corresponding diamagnetic sample owing to the PRE on longitudinal relaxation rates (Γ₁). Accurate 1H-Γ₂ rates, however, can be obtained in the same measurement time from a two time-point measurement without requiring any fitting procedures or complicated error estimations. ¹H-Γ₂ for the two time-point measurement is given by (31,42):

$${\mathrm{\Gamma }}_2=R_{2,\mathit{para}}-R_{2,\mathit{dia}}=\frac{1}{T_b-T_a}ln\frac{I_{\mathit{dia}}(T_b)I_{\mathit{para}}(T_a)}{I_{\mathit{dia}}(T_a)I_{\mathit{para}}(T_b)}$$ (1)

with errors in Γ₂ given by:

$$\sigma ({\mathrm{\Gamma }}_2)=\frac{1}{T_b-T_a}\sqrt{{\left\{\frac{{\sigma }_{\mathit{dia}}}{I_{\mathit{dia}}(T_a)}\right\}}^2+{\left\{\frac{{\sigma }_{\mathit{dia}}}{I_{\mathit{dia}}(T_b)}\right\}}^2+{\left\{\frac{{\sigma }_{\mathit{para}}}{I_{\mathit{para}}(T_a)}\right\}}^2+{\left\{\frac{{\sigma }_{\mathit{para}}}{I_{\mathit{para}}(T_b)}\right\}}^2}$$ (2)

where T_a and T_b are the two time points, σ_para and σ_dia are the standard deviations of the noise in the spectra recorded for the paramagnetic and diamagnetic states, respectively. By using a relatively short time interval for the two time-point measurement, errors in Γ₂ introduced by any potential diamagnetic contamination can also be significantly reduced (42).

Using the PRE for structure determination

One of the most difficult aspects of using NOEs for protein structure determination relates to unambiguous cross-peak assignment (2,3). Owing to extensive spectral overlap, it is often difficult to unambiguously assign a NOE cross-peak to a single interaction, even in four-dimensional spectra. Consequently, the strategy for structure determination generally relies on an iterative strategy in which a low resolution fold is calculated on the basis of relatively few unambiguous NOE cross-peaks, followed by iterative refinement to assign all the remaining cross-peaks in the NOE spectra (3). Not surprisingly, it is quite easy to make mistakes (i.e. proceed down an incorrect path), whether this process is carried out manually or automatically by computer algorithms (43). The identification of a PRE effect, just like a residual dipolar coupling, on the other hand, is entirely straightforward, since the assignment of cross-peaks in the correlation spectra are already known from through-bond scalar triple resonance experiments.

One of the intrinsic problems in making use of the PRE for structure determination is the fact that extrinsic paramagnetic probes are invariably conjugated to the macromolecule of interest via a flexible linker with several rotatable bonds. Thus, it is absolutely essential to treat the paramagnetic center by a multiple conformer representation (31). If only a single conformer representation is employed, it may still be possible to fit the PRE data but at the expense of coordinate accuracy; that it to say inappropriate treatment of the PRE data will actually result in structural distortion and reduced coordinate accuracy (31). Generally, a three-member ensemble for the paramagnetic center is sufficient, but in some cases a larger ensemble may be required. For a N-site jump model with appropriate ensemble averaging for the PRE, Γ₂, using a model-free extension of the Solomon-Bloembergen equations, is given by (31):

$${\mathrm{\Gamma }}_2=S_{\mathit{PRE}}^2<r^{-6}>f_{SB,2}({\tau }_c)+(1-S_{\mathit{PRE}}^2)<r^{-6}>f_{SB,2}({\tau }_t)$$ (3)

where τ_c is the correlation time defined as (τ_r⁻¹ + τ_s⁻¹)⁻¹, and τ_t the total correlation time defined as (τ_r⁻¹ + τ_s⁻¹ + τ_i⁻¹)⁻¹. τ_r, τ_s and τ_i are the rotational correlation time, the effective electron relaxation time and the internal correlation time, respectively. r⁻⁶f_SB,2(τ_c) corresponds to the classical Solomon-Bloembergen equation for Γ₂ (31). <r⁻⁶> is calculated as:

$$<r^{-6}>=\frac{1}{N{n}_p}\sum _h^N\sum _s^{n_p}{r_{hs}}^{-6}$$ (4)

where N is the ensemble size and n_p the number of equivalent protons. The PRE order parameter $S_{\mathit{PRE}}^2$ is given by the product of angular and radial components:

$$S_{\mathit{PRE}}^2\approx S_{\mathit{PRE},\mathit{angular}}^2{S}_{\mathit{PRE},\mathit{radial}}^2$$ (5)

where the angular and radial components are given by:

$$S_{\mathit{PRE},\mathit{angular}}^2=\frac{1}{N^2{n}_p^2}\sum _{h,k}^N\sum _{s,t}^{n_p}\left\{\frac{3}{2}{\left(\frac{{\overrightarrow{r}}_{hs}·{\overrightarrow{r}}_{kt}}{r_{hs}{r}_{kt}}\right)}^2-\frac{1}{2}\right\}$$ (6)

$$S_{\mathit{PRE},\mathit{radial}}^2=\frac{{\left(\sum _h^N\sum _s^{n_p}{r_{hs}}^{-3}\right)}^2}{N{n}_p\sum _h^N\sum _s^{n_p}{r}_{hs}^{-6}}$$ (7)

Optimization of the conformer representation for the paramagnetic center is readily achieved using simulated annealing in torsion angle space (31). A quantitative measure of agreement between observed and calculated Γ₂ rates can be obtained by calculating a Q-factor given by (31):

$$Q=\sqrt{\frac{\sum _i{\left\{{\mathrm{\Gamma }}_2^{\mathit{obs}}(i)-{\mathrm{\Gamma }}_2^{\mathit{cal}}(i)\right\}}^2}{\sum _i{\mathrm{\Gamma }}_2^{\mathit{obs}}{(i)}^2}}$$ (8)

In the context of tight macromolecular complexes, the PRE provides a very powerful additional source of intermolecular distance restraints containing both translational and orientational information. Fig. 1 shows an example of the results of structure refinement incorporating intermolecular PRE data for the SRY/DNA complex (31). Using an ensemble size of N = 3 for each paramagnetic center, 438 intermolecular ¹H-Γ₂ restraints, derived from three complexes with dT-EDTA-Mn²⁺ incorporated at three different sites, are readily satisfied without impacting the agreement with other experimental restraints, including residual dipolar couplings. In addition, complete cross-validation was able to demonstrate that the incorporation of PRE restraints results in significant gains in coordinate accuracy. The power of the PRE for studying intermolecular complexes is illustrated in Fig. 2, which compares an ensemble of structures for the SRY/DNA complex calculated on the basis of only a single intermolecular NOE restraint: with no PRE data the orientation of SRY relative to the DNA cannot be determined; addition of the intermolecular PRE data allows the structure to be resolved unambiguously (31).

Fig. 1.

The intermolecular PRE in structure refinement of the SRY/DNA complex. (a) Oligonucleotides with location of the paramagnetic center (dT-EDTA-Mn²⁺) indicated by an asterisk and color-coded. The location of the specific SRY binding site is indicated by the solid bars and the site of intercalation of Ile13 is shown by an arrow. (b) Best-fit superposition of 40 simulated annealing structures (red) refined against 438 intermolecular ¹H-PRE restraints (31) on the restrained regularized mean coordinates (cyan) generated from structures based on NOE, dipolar coupling, J coupling and torsion angle restraints calculated without ¹H-PRE restraints (58). (c) Agreement between observed and calculated values of ¹H-Γ₂ rates for backbone and side-chain ¹H-PREs after refinement using a three-conformer ensemble representation for each paramagnetic center. Adapted from ref. 31.

Fig. 2.

Impact of intermolecular PRE on coordinate accuracy of the SRY/DNA complex when only a single intermolecular NOE restraint located at the center of the protein-DNA interface is employed. Best-fit superposition of 30 simulated annealing structures (SRY, red, DNA, blue) calculated (a) without and (b) with 438 intermolecular ¹H-PRE restraints. The original restrained regularized mean structure of the SRY/DNA complex (58) determined using 168 intermolecular NOE restraints and 375 residual dipolar couplings is shown in cyan (SRY) and yellow (DNA). Adapted from ref. 31.

Intermolecular PRE and non-specific protein-DNA interactions

Structural characterization of non-specific protein-DNA interactions in a system where the protein is not constrained to a single location but can dynamically sample all possible binding sites on the DNA during the course of the measurement represents a challenging problem since the experimental observables represent ensemble averages of all the states present in solution (39,40). Fig. 3a compares the PRE profiles observed for the specific SRY/DNA complex versus that for the non-specific HMG-1A/DNA complex (39). The two proteins are members of the HMG-box family, bind in the minor groove and bend the DNA. The PRE profile for the SRY/DNA complex is fully consistent with a single specific complex (cf. Fig. 1). For the HMG-1A/DNA complex, however, the PRE profiles observed with the dT-EDTA-Mn²⁺ paramagnetic center placed at either end of the DNA duplex are not only significantly larger than those observed for the specific SRY/DNA complex, but even more importantly are very similar to one another. The latter is diagnostic of multiple binding sites in multiple orientations. The former indicates the presence of binding sites close to the paramagnetic center, since Γ₂ is proportional to <r_Mn-H>⁻⁶ and hence strongly influenced by the minimum value of r_Mn-H. Similar results have been observed for non-specific HoxD9 homeodomain/DNA complexes (40).

Fig. 3.

Characterization of non-specific DNA binding of HMGB-1A by PRE. (a) Comparison of PRE profiles observed for the non-specific HMGB-1A/DNA complex and the specific SRY/DNA complex with two DNA duplexes bearing dT-EDTA-Mn²⁺ at opposite ends of the DNA. A diagrammatic depiction of the states giving rise to the observed PREs is shown on the right hand-side of the figure. (b) Semi-quantitative estimation of the distribution and occupancy of HMGB-1A binding sites along a 14-bp duplex DNA. There are 13 potential intercalation sites and HMGB-1A can bind in two orientations related by a 180° rotation (top left panel). The optimized distribution for the two orientations (bottom two panels) yields a PRE Q-factor of 0.36 (top right panel). Adapted from ref. 39.

It is possible to go one step further by carrying out a semi-quantitative analysis to ascertain the populations of individual binding states (39). If we assume an N discrete binding state model where the transitions between the states are slower than the rotational correlation time but fast on the chemical shift time scale, the spectral density for a dipole-dipole interaction vector is independent of the transition rates rates and angles between the vectors of the individual states. The ensemble average <Γ₂> rate is therefore given by the weighted average of the Γ₂ rates for the individual states (39):

$$\langle {\mathrm{\Gamma }}_2\rangle =\sum _{k=1}^N{\rho }_k{\mathrm{\Gamma }}_{2,k}$$ (9)

where ρ_k and Γ_2,k are the population and ¹H_N-Γ₂ PRE rate, respectively, for state k. The populations ρ_k can be obtained by back-calculating the Γ₂ rates from structural models of the individual states and minimizing the χ² function (39):

$${\chi }^2=\sum _i\frac{{\left\{{\mathrm{\Gamma }}_{2,\mathit{obs}}(i)-\sum _{k=1}^N{\rho }_k{\mathrm{\Gamma }}_{2,\mathit{cal}c,k}(i)\right\}}^2}{\sigma {(i)}^2}$$ (10)

where i is the index for each data point; Γ_2,obs(i), the observed value of ¹H-Γ₂; Γ_2,calc,k(i), the calculated value of ¹H-Γ₂ for binding state k; and σ(i), the experimental error for Γ_2,obs(i). The highest populations of binding are located around the central region of the DNA duplex, and the population in the two possible orientations is approximately equal (Fig. 3b).

Using the PRE to study transient low-population intermediates in macromolecular interactions

In an exchanging system comprising two or more species in equilibrium, the observed PRE measured on the resonance of the major species will be modulated by the minor species, the extent of which depends upon the rate of exchange (k_ex) between the species (35). This phenomenon is most easily appreciated by considering a simple two-site exchange system in which the major species (A) has an occupancy of 99% with a paramagnetic center-proton distance of 30 Å, while the minor species (B, only 1%) has a paramagnetic center-proton distance of 8 Å (Fig. 4). For a 30 kDa system, the ¹H-Γ₂ rate arising from Mn²⁺ will be ~2 s⁻¹ for the major species and ~5600 s⁻¹ for the minor one. When k_ex is slow (<50 s⁻¹), the presence of the minor species has no impact on the apparent Γ₂ rate ( ${\mathrm{\Gamma }}_2^{\mathit{app}}$) observed on the resonance of the major species. As k_ex increases, so the apparent Γ₂ rate increases, When $k_{ex}\gg ({\mathrm{\Gamma }}_2^B-{\mathrm{\Gamma }}_2^A),\hspace{0.17em}{\mathrm{\Gamma }}_2^{\mathit{app}}$ is given by the population weighted average of the Γ₂ rates of the two species. In this particular example, ${\mathrm{\Gamma }}_2^{\mathit{app}}$ will be ~30 times larger than ${\mathrm{\Gamma }}_2^A$, allowing one to both infer the presence of the minor species and derive structural information on it.

Fig. 4.

Intermolecular PRE in an exchanging system. (a) Diagrammatic depiction of a two site-exchange process involving major (99%) and minor (1%) species with paramagnetic-¹H distances of 30 and 8 Å, respectively. (b) Effect of increasing exchange rate on NMR line-shape with (red) and without (black) PRE. In the slow exchange regime the PRE is insensitive to presence of minor state; in the fast exchange regime, however, the PRE sensitive to the presence of minor species and can be used to reveal footprint of minor species. Adapted from ref. 35.

Intra- and intermolecular translocation in specific protein-DNA recognition

A long-standing question in protein-DNA recognition pertains to the search process whereby a transcription factor locates its specific cognate site among a sea of non-specific sites. Both kinetic and theoretical considerations have suggested that non-specific binding can significantly enhance the rate of specific recognition via two complementary mechanisms (44–47): (a) intramolecular translocation or sliding that results in a reduction in the dimensionality of the search process from three-dimensions to one; and (b) intermolecular translocation or hopping from one DNA molecule to another or from one DNA segment to another via looping.

¹⁵N z-exchange spectroscopy in which the HoxD9 homeodomain was mixed with an equimolar concentration of two DNA duplexes differing in only a single base pair mutation at the edge of the specific binding site demonstrated that intermolecular translocation occurs very efficiently at relatively high (submillimolar) DNA concentrations even at low salt (20 mM NaCl) (48). The apparent rate of this process is proportional to the concentration of free DNA, is highly dependent on salt concentration, and occurs via direct transfer without ever involving the intermediary of free protein (48). Given the extremely high concentration of DNA in the nucleus, intermolecular translocation represents an important pathway for the transfer of a transcription factor from one DNA site to another.

PRE measurements at low salt (20 mM NaCl) on the specific HoxD9/DNA complex are fully consistent with the crystal structure of the highly homologous antennapedia homeodomain/DNA complex (35). The overall PRE Q-factor (Q_PRE) for the data collected from four different locations of the paramagnetic center along the DNA was 0.26 (Fig. 5). As the salt concentration is raised to 100 and 160 mM NaCl, however, the PRE data are completely inconsistent with the structure of the specific complex (Q_PRE = 0.66), and the profiles reflect the footprint of binding intermediates involved in the target search process (Fig. 5), even though the value of K_diss is 1.5 nM at 100 mM NaCl. The observed PREs at high salt cannot be attributed to structural changes since the observed spectrum remains unaltered and the dipolar coupling data are fully consistent with the crystal structure (35).

Fig. 5.

Intermolecular PREs observed for the HoxD9/DNA complex in the slow (20 mM NaCl) and fast (160 mM NaCl) exchange regimes. (a) DNA duplex containing the HoxD9 specific binding site (boxed) and showing the location of the 4 sites used to introduce dT-EDTA-Mn²⁺ (one at a time). (b) Schematic illustration of the ground state specific complex and the target search process. (c) and (d) PRE profiles observed for site 1 at low (20 mM NaCl) and high (100 and 160 mM NaCl) salt, respectively. (e) and (f) Correlation between observed and calculated PREs for all 4 sites at low (20 mM NaCl) and high (160 mM NaCl) salt, respectively. Below the correlation diagrams, the PRE data are mapped on the structural model of the HoxD9/DNA complex, with the color scale depicting Γ₂ rates. Adapted from ref. 35.

The observed PRE profiles on the specific HoxD9/DNA complex can be attributed to intra- and/or inter-molecular translocation. To assess the relative contributions of these two processes, two experiments were carried out involving HoxD9 in the presence of equal mixtures of two DNA duplexes (Fig. 6): sample 1 comprised the specific duplex without a paramagnetic center and a non-specific duplex bearing the dT-EDTA-Mn²⁺ paramagnetic center; sample 2 comprised the specific duplex with dT-EDTA-Mn²⁺ and a non-specific duplex without a paramagnetic center (35). In sample 1, intermolecular PREs can only occur via a mechanism involving intermolecular translocation, while for sample 2 both intra- and intermolecular translocation can contribute to the observed PREs. The PRE profiles for the two samples are very similar, indicating that intermolecular translocation is a major contributor. Upon further examination of the PRE profiles, however, it is apparent that the Γ₂ rates for residues 24–33 and 41–42 are 30–100% larger for sample 2 than those for sample 1, whereas those for the N-terminal arm region are the same. The larger PRE values for a limited region of the protein in sample 2 are directly attributable to intramolecular translocation which gives rise to bias arising from the fact that the orientation of the protein bound to the specific site is favored as the protein slides along the DNA (35). Thus, as the protein slides away from the specific site, residues 24–33 and 41–42 can readily come into very close proximity to the paramagnetic center; the N-terminal tail, however, can only approach the paramagnetic center following an intermolecular translocation event resulting in a 180° flip in the binding orientation of the protein along the DNA duplex.

Fig. 6.

Intra- and intermolecular translocation in the HoxD9/DNA system. (a) PRE data were collected on HoxD9 in the presence of equal mixture of two DNA duplexes, one with and the other without the specific site (indicated in blue). In sample 1, the non-specific DNA bears the paramagnetic center and PREs only arise from intermolecular translocation; in sample 2, the specific DNA has the paramagnetic center and PREs can arise from both inter- and intra-molecular translocation. (b) Observed PRE profiles. (c) Schematic representation of sliding along the DNA with HoxD9 color coded according to the Γ₂(sample 2)/Γ₂(sample 1) ratio. Adapted from ref. 35.

Transient encounter complexes in protein-protein recognition

Kinetic studies on many protein-protein associations suggest the formation of a pre-equilibrium encounter complex that subsequently relaxes to the stereospecific complex. Further, site-specific mutagenesis studies and Brownian dynamics simulations have provided evidence of modulation of association rate constants via perturbations involving charged residues located outside the specific interaction surfaces (49–52). This suggests that non-specific encounter complexes may facilitate protein-protein recognition either by a reduction in dimensionality, in this instance from a three- to a two-dimensional search process (53), or by the presence of a short-range, non-specific attractive potential (47). We set out to detect such encounter complexes by means of PRE measurements using a relatively weak complex (K_diss ∼10 μM) comprising the N-terminal domain of enzyme I (EIN) and HPr. The 40 kDa EIN/HPr complex had previously been solved by NMR on the basis of extensive NOE and dipolar coupling measurements (54). This complex catalyses the transfer of a phosphoryl group from His189 of EIN to His15 of HPr, and the NMR structure of the complex is fully consistent with the formation of a pentacoordinate phosphoryl transition state intermediate without requiring any significant structural perturbation (54). EDTA-Mn²⁺ was introduced at three separate sites (E5C, E25C and E32C) on HPr, and intra and intermolecular PRE data were measured (37). The intramolecular PRE data observed for HPr are fully consistent with the X-ray structure of HPr with an overall intramolecular PRE Q-factor of 0.18 (Fig. 7a). Although the intermolecular PRE profiles observed on EIN display features that clearly arise from the stereospecific complex, other features are present indicative of the presence of alternative modes of binding involving non-specific encounter complexes (Fig. 7c). As a result the overall intermolecular PRE Q-factor calculated from the stereospecific complex is 0.61 and the correlation between observed and calculated Γ₂ rates is poor (Fig. 7b).

Fig. 7.

Intermolecular PREs for the EIN-HPr complex. EDTA-Mn²⁺ was conjugated to an engineered surface cysteine at 3 sites (E5C, E25C and E32C). (a) Correlation between observed and calculated intramolecular Γ ₂ rates for HPr. (b) Correlation between observed and calculated intermolecular Γ₂ rates measured on EIN and arising from paramagnetically labeled HPr. (c) Intermolecular PRE profiles observed for the 3 sites, with experimental Γ₂ rates denoted by the red circles, and the theoretical Γ₂ rates calculated from the structure of the stereospecific complex by the black line. Adapted from ref. 37.

A semi-quantitative description of the observed intermolecular PRE data for the EIN-HPr complex can be obtained by direct rigid body simulated annealing refinement (55) of a system comprising the stereospecific complex (whose structure is fixed) with population λ in rapid exchange with an ensemble of encounter complexes comprising N states with overall population (1 − λ) (Fig. 8) (37). Complete cross-validation indicates that the encounter complexes is best represented by an ensemble of size N = 10–20 at a population of ∼10%. The resulting intermolecular PRE Q-factor is 0.21.When the distribution of the non-specific encounter complexes is examined, there appears to be a qualitative correlation with electrostatic potential, with the positively charged face of HPr populating regions of EIN with highly negative electrostatic potentials (Fig. 9). Interestingly, the region occupied by the stereospecific complex is only minimally populated by non-specific encounter complexes suggesting that once HPr reaches this region, formation of the stereospecific complex occurs with high probability (37). The characteristics of the non-specific encounter complexes are quite distinct from the stereospecific complex that possesses a well-defined array of complementary van der Waals and electrostatic interactions (54). The buried accessible surface area at the protein-protein interface is on average an order of magnitude smaller, the gap index is much larger (i.e. the interface is less well packed), and the interfacial composition of charged residues is increased for the non-specific encounter complexes relative to the stereopecific complex (37).

Fig. 8.

Ensemble refinement of intermolecular PRE data for the EIN-HPR complex. (a) The observed Γ₂ rates in the fast exchange regime are a weighted average of the Γ₂ rates for the specific complex and an encounter complex ensemble comprising N species. (b) Dependence of working (Q_e and Q_ee) and complete cross-validated (Q_free) Q-factors on ensemble size N. (c) Dependence of working Q factors on population of the encounter complex ensemble. (d) Correlation between observed and calculated Γ₂ rates obtained with a population of 10% for the encounter complex species represented by an ensemble of size N = 20. (Q_e and Q_ee are the average Q-factor <Q> for all 100 calculated ensembles, and Q_ee is the ensemble of ensembles average Q-factor. Adapted from ref. 37.

Fig. 9.

Three views of a reweighted atomic probability map illustrating the distribution of HPr molecules on the surface of EIN that make up the ensemble of encounter complexes. The encounter complex probability map (green mesh plotted at a threshold of 20% maximum) is calculated from 100 independent calculations of ensemble size N = 20 at a population of 10%; the molecular surface of EIN is color coded by electrostatic potential (± 8 kT); and the location of HPr in the steterospecific complex is shown as a blue ribbon. Adapted from ref. 37.

The direct detection of non-specific encounter complexes by PRE is quite general for systems with relatively weak affinity. We observed similar phenomena for two other complexes involving HPr and the proteins IIA^Mannitol and IIA^Mannose (37) Contemporaneously, similar observations have been made for the interaction of cytochrome c and cytochrome c peroxidase (38). These findings probably reflect a general principle of steered macromolecular diffusion and protein-protein association whereby weak, transient, non-specific encounter complexes are formed, presumably via long-range non-specific electrostatic interactions supplemented by short range van der Waals ones, thereby facilitating the rapid formation of the stereospecific complex (37). The non-specific encounter complexes are sufficiently long-lived to permit a two-dimensional search on the surface of the proteins, until the region of the specific interaction surfaces is reached and the complex falls into a narrow energy funnel that leads rapidly and directly to the formation of the stereospecific complex. Very recently, using chemical shift mapping and NMR relaxation dispersion measurements, non-specific encounter complex formation has also been shown to play a key role in coupled folding and binding of an intrinsically disordered peptide to its target protein (56).

Concluding remarks

The PRE provides a very powerful tool for studying both structure and large scale dynamic phenomena in solution. In terms of structure, the PRE is particularly useful since Γ₂ rates are measured from through-bond correlation spectra and hence the effects can be unambiguously assigned to specific paramagnetic center-proton interactions with little effort. Unlike FRET measurements where only a single distance between two fluorescent labels can be measured from a single sample (57), the PRE affords the simultaneous measurements of hundreds of paramagnetic center-proton distances. For direct refinement against PRE data it is critical that accurate Γ₂ rates be obtained and that the extrinsic paramagnetic center be represented by an ensemble. The application of the PRE for structure determination of complexes, however, must be restricted to systems in slow exchange, since the presence of transient intermediates in fast exchange with the major species may significantly impact the observed PREs, particularly when the paramagnetic center-proton distances are shorter in the minor species than the major one. This is due to the fact the magnitude of the PRE is proportional to <r⁻⁶> and hence heavily weighted by shorter paramagnetic center-proton distances. Although this represents a caveat in the use of the PRE for structure determination of complexes, it affords a unique tool to easily detect, visualize and characterize transient, low population intermediates or species at equilibrium. Even if the population of the intermediate species is a low as 1%, the PRE permits structural information relating to such species to be obtained. The effect, of course, depends critically on time scale and the intermediates can only be detected in the fast exchange regime. We foresee that the PRE will yield unique insights into large-scale domain motions, the recognition processes involved in macromolecular interactions, and the formation of higher order complexes.

Abbreviations

NMR

nuclear magnetic resonance

PRE

paramagnetic relaxation enhancement

NOE

nuclear Overhauser effect

HSQC

heteronuclear single quantum coherence

FRET

fluorescence energy transfer