Conformational heterogeneity in the Hsp70 chaperone‐substrate ensemble identified from analysis of NMR‐detected titration data

Classification of the observed titration profiles

In order the quantify the interactions between hTRF1 and DnaK we performed a titration experiment using highly deuterated proteins, labeled as Ileδ1‐¹³CH₃, Met‐¹³CH₃ (IM‐¹³CH₃) and Ileγ2‐¹³CH₃, Leu,Val‐¹³CH₃/¹²CD₃ (Iγ‐LV‐¹³CH₃) for DnaK and hTRF1, respectively. A ¹H‐¹³C HMQC spectrum of 440 μM Iγ‐LV‐¹³CH₃ hTRF1, 570 μM IM‐¹³CH₃ DnaK is shown in Figure 2 and the intensities of (A) correlations arising from free hTRFI and DnaK‐bound hTRF1 in the LV and Iγ regions and (B) hTRF1‐bound DnaK peaks derived from Ile 401 and Ile 438, can all be quantified independently in such spectra. While the intensities of a number of other DnaK peaks can also be measured reliably, these derive from both unbound and hTRF1‐bound DnaK molecules (degenerate shifts in free and bound states) and hence provide less useful information because they report only on the total concentration of DnaK. As described previously,11 there are at least four very slowly exchanging conformations of the hTRF1‐DnaK complex, referred to as states “a,” “b,” “c,” and “d,” which arise because of the recognition of four distinct sites of hTRF1 by DnaK, centred at Leu 31, Leu 30, Val 41, and Val 18 respectively. These four amino acids occupy the central position in the binding groove of DnaK in each of the respective states “a”–“d” and have distinct chemical shifts because of their proximity to hydrophobic residues lining the binding groove such as Ile 401 and Ile 438. Cross peak intensities derived from states “a,” “b,” and “c,” but not “d,” can be robustly obtained from ¹H‐¹³C HMQC spectra and have been used to formulate the binding model presented below.

Figure 3(A) outlines the approach used to generate the titration profiles, whereby a sample for titration point j was prepared by removing a calculated volume (V ₁) from sample j‐1 and adding an equivalent volume of a stock DnaK solution of concentration L ₀ [Fig. 3(A)] so that the total volume of the solution, V _o, remains constant. Thus, starting from an initial sample with an hTRF1 concentration of P ₀ (600 μM) without any DnaK, the total concentration of hTRF1 (P _T) in subsequent samples decreases linearly with increasing total DnaK concentration (L _T) [Fig. 3(B)], as shown in Supporting Information, since the total concentrations of hTRF1 and DnaK at the n ^th titration point are given by $P_{\mathrm{T}}(n)=P_0{r}^n$ and $L_{\mathrm{T}}(n)=L_0(1-r^n)$ respectively, where $r=\left(\frac{V_o-V_1}{V_o}\right)$. At each titration point, a ¹H‐¹³C HMQC spectrum of the sample was acquired and peak intensities measured. Titration profiles were then quantified as peak intensities as a function of the L _T/P _T (=[DnaK]_T/[hTRF1]_T) ratio. Although we have assumed for the purpose of illustration in Figure 3 that equivalent volumes of sample are removed in successive titration points (V ₁), this is not a requirement and indeed the results discussed below hold even when different volumes are removed, so long as the total sample volume remains constant (see Supporting Information). In fact, in practice, we have not used constant volumes V ₁ during the titration. Instead, L _T/P _T ratios were chosen to adequately sample the titration profile and the volume removed from a given sample to obtain a particular L _T/P _T ratio in the successive sample was calculated based on L ₀ as well as L _T and P _T values from the current sample. We have adopted this particular mode of titration whereby V _o is kept constant instead of keeping the hTRF1 concentration constant during the titration, because this method results in maxima for peak intensities [Fig. 3(C)] which are easier to detect than plateaus that arise when the hTRF1 concentration is kept constant.

An examination of the 21 profiles that could be reliably measured shows that they can be broadly classified into three types, representative examples of which are depicted in Figure 3(C). For the eight native state resonances of hTRF1 (i.e., in what follows, we refer to native as being folded and unbound), intensities decrease with [DnaK]_T/[hTRF1]_T, consistent with DnaK binding to hTRF1 and shifting the equilibrium away from the native state. Conversely, bound state resonances from states “a” (6 peaks), “b” (4 peaks) and “c” (3 peaks) increase initially with L _T/P _T because of an increase in the population of the bound state, and subsequently decrease because the overall concentration of hTRF1 decreases during the titration. Profiles from states “a” and “b” appear identical except for a scaling factor and have a maximum when [DnaK]_T/[hTRF1]_T = 1, while profiles from state “c” maximize at a [DnaK]_T/[hTRF1]_T value of 2. It is worth emphasizing that in a system comprising multiple simultaneous binding equilibria, the equilibrium populations of species with the same stoichiometry are directly related by their equilibrium constants at all titration points. Consequently, the resulting titration profiles will be related by a scaling factor and hence must maximize at the same value of [DnaK]_T/[hTRF1]_T. For example, consider two species of the type $U_{\mathrm{n}}{K}_{\mathrm{m}}$, $U_{\mathrm{n}}{K}_{\mathrm{m}}^{\mathrm{p}}$ _, and $U_{\mathrm{n}}{K}_{\mathrm{m}}^{\mathrm{q}}$, where U and K refer to hTRF1 and DnaK, and n and m are the respective stoichiometries of U and K in the complex. The association constants are given by

for states “p” and “q,” respectively, so that

Conversely, the titration profiles of species with different stoichiometries will not be related by a simple constant factor, as the ratios of concentrations of these species at every titration point will depend on at least one of $[U]$ or $[K]$. It follows, then, that the distinct titration profiles for states “a”/“b” vs “c” which maximize at different [DnaK]_T/[hTRF1]_T ratios indicate a different stoichiometry of DnaK and hTRF1 for state “c” compared to states “a” or “b” (see below).

Fitting native state titration profiles

As a first step towards modeling the titration data, we fit the eight native state profiles to a 1:1 binding model. The resulting fits were very poor and the underlying reason is illustrated in Figure 4 showing normalized peak intensity ratios as a function of [DnaK]_T/[hTRF1]_T for a number of residues in hTRF1. The solid curve in Figure 4 is the result of fitting the data to a single exponential function and does not derive from a specific binding model (see below). Notably, the initial rate of decrease of the native state population is much greater than expected from the amount of DnaK added, even assuming all the DnaK has bound to hTRF1 to form a 1:1 complex. More native hTRF1 is consumed than the amount of added DnaK, suggesting that a species of the form U _n K _m (n/m > 1) forms during the initial stages of the titration.

To obtain the value of n/m, we performed an analysis of the initial slopes of the native state profiles. The titration profile of each residue was normalized by its peak intensity in the absence of DnaK, which is proportional to the total hTRF1 concentration in the sample lacking DnaK (P ₀). After the addition of the first aliquot of DnaK the concentrations of hTRF1 and DnaK are given by $P_{\mathrm{T}}(1)=P_{0}r$ and $L_{\mathrm{T}}(1)=L_0(1-r)$, respectively, and if all the added DnaK binds to form a complex of the form U _n K _m, the amount of free hTRF1 will be

so that the decrease in free hTRF1, ΔP, is given by

The initial slope (S) in the normalized titration profile of the native state is thus

where L _T(0) = 0 and P _T(0) = P ₀ are the concentrations of DnaK and hTRF1 in the starting sample, respectively, before addition of DnaK. Substituting from above gives,

As the initial slope is measured in the limit of $r\to 1$ we obtain that $S=-\left(\frac{n}{m}+\frac{P_0}{L_0}\right)$. In the titration analyzed here P ₀ = 0.6 mM and L ₀ = 2.1 mM, so that P ₀/L ₀ = 0.28. If DnaK is only partly bound, ΔP _p < ΔP, and consequently, the initial slope, S _p, measured will be smaller than the slope expected for the case of a fully bound species of the same stoichiometry. If there are a number of species with varying stoichiometries and concentrations at equilibrium, the value of the initial slope will be dictated by the species with the largest n/m ratio.

An initial slope, B, was calculated by fitting the profiles globally to a single exponential function of the form $y=A\exp (-Bx)$ (Fig. 4). The numerical value of B from the global fit, and hence the experimental initial slope, is 3.05. The expected slope for n/m = 3 is 3.28, strongly suggesting that an hTRF1‐DnaK complex with 3:1 stoichiometry forms in solution; the slightly smaller than expected value (3.05 vs 3.28) likely reflects incomplete binding of the added DnaK. Assuming that there is one molecule of DnaK in the complex, our results indicate that a species of the type U ₃ K is formed in solution, though the existence of species of the form U ₆ K ₂ or U ₉ K ₃ cannot be ruled out.

To further probe the stoichiometry of the hTRF1‐DnaK complex formed during the initial stages of the titration, we fit residue specific titration profiles to models assuming that species of the type U _n K are formed, with n ranging from one through five. The quality of the fits and the magnitude of the residuals, as well as a prominent minimum in the ${\chi }_{\text{red}}^2$ metric as a function of n at n = 3 (Fig. 5), demonstrate that hTRF1₃‐DnaK (U ₃ K) is the most probable species initially detected in the titration profiles of native state hTRF1 peaks, consistent with the fitted initial slopes of the native state titration profiles.

Fitting the titration profiles from DnaK‐bound peaks

Having elucidated the stoichiometry of one of the chaperone‐substrate complexes that evolves during the titration, through modeling of native state profiles, we next examined the titration profiles from hTRF1 and DnaK peaks reporting on complexes “a” and “b” which have a maximum at a [DnaK]_T/[hTRF1]_T ratio of 1, as well as profiles from state “c” which maximize at a ratio of 2. We have shown earlier using numerical simulations11 that hTRF1‐DnaK complexes of 1:1 and 1:2 stoichiometry are maximally populated at [DnaK]_T/[hTRF1]_T values of 1 and 2, respectively, under conditions of tight binding. In Supporting Information, we derive analytical expressions for the maximal populations of 1:1 and 1:2 complexes in the strong binding limit (see Supporting Information) as a function of L _T/P _T that support the simulations. Titration profiles of states “a” and “b” thus report on 1:1 complexes, while state “c” reports on a 1:2 complex.

Assembling the final model for global analysis of the titration profiles

As discussed above, the titration data demonstrate a mixture of hTRF1‐DnaK complexes with stoichiometries of 3:1, 1:1 and 1:2 at equilibrium and, accordingly, all these complexes were included in the binding model of Figure 6. The model includes 1:1 complexes UKa, UKb and UKc corresponding to binding of DnaK at hTRF1 residues L31 (state “a”), L30 (state “b”) and V41 (state “c”), one 1:2 complex resulting from binding to V41 (UK2) and three 3:1 complexes U3Ka, U3Kb and U3Kc whose generation is contingent upon previous formation of UKa, UKb and UKc. The equilibrium constants for the formation of U3Ka, U3Kb and U3Kc from UKa, UKb and UKc, respectively, were set to be identical. In the model of Figure 6 DnaK is assumed to bind the unfolded and not the native state, though we do not have direct evidence for such a conformational‐selection mode of binding presently. However, this assumption is not required to obtain high quality fits of the data. E.coli DnaK is known to oligomerize18 through the binding of the linker of one monomer to the SBD of a second;19, 20 we have included this process in a simplistic manner by the DnaK dimerization scheme of Figure 6 (right) where the dimer is assumed not to bind client. It is possible that one of the monomers in a DnaK dimer (or several monomers in a DnaK oligomer) retains the ability to bind client protein. However, we do not have NMR spectral probes that can distinguish DnaK molecules based on their oligomerization status. To account for a fraction of DnaK molecules that are incapable of client binding in the oligomeric form of DnaK, we have employed an approximate model of DnaK dimerization where neither DnaK molecule in the dimer can interact with substrate.

Having constructed a binding model, we postulated that the intensities of correlations in the titration profiles are related to concentrations via

where i ∈ (a,b) and c ₀, c ₁, c ₂, and c ₃ are residue‐specific parameters accounting for noise in NMR spectra (c ₀) and the proportionality between intensity and protein concentration (c ₁,c ₂,c ₃), that additionally takes into account spin relaxation. Note that I _1i (states “a” and “b”) and I ₂ (state “c”) include contributions from both UKi and U3Ki. Additionally, because the chemical shifts of V41c, I401c and I438c are assumed to be unchanged in monomeric (UKc) and dimeric (UK2) forms of the complex where V41 is centered at the DnaK binding site, the intensities of the peaks derived from state “c” (I ₂) include a contribution from UK2. Note also that the concentration of the unbound, unfolded state is not relevant for the calculation of I_i values, above, because only the intensities of hTRF1 peaks far removed from the random coil region of the HMQC are included in the analysis. Finally, it is expected that the chemical shifts of methyl groups in any of the complexes will be different from those of N and thus I_N values were calculated from a dependence on the concentration of N only.

Global analysis of titration profiles

Using the model depicted in Figure 6, the titration profiles were analyzed globally with fits shown in Figure 7(A–D) and the changes in concentrations of key molecular species during the course of the titration are illustrated in Figure 7(E). The model reproduces the data well; the best fit χ2 _red value of 3.6 likely reflects underestimates in the errors associated with measurement of the intensities. To estimate the reliability of the parameters resulting from the fit we constructed 1D χ2 _red plots generated by keeping one of the six equilibrium constants fixed at a particular value during the fitting procedure (Fig. 8). Because of the difficulties with minimization of such a high dimensional target function a 6D χ2 _red surface was initially constructed comprising 10⁶ points by evaluating the χ2 _red value at each point of a grid consisting of 10 values for each equilibrium constant (see Materials and Methods). Then in each 1D plot for which K_i was varied the remaining {K_j} j ≠ i values were minimized starting from initial values that produced the minimum in the 6D χ2 _red surface for the chosen K_i value.

The χ2 _red plots are flat for most of the equilibrium constants, implying that the values from the fit are not robust. However, a pronounced minimum in the χ2 _red surface at a value of ∼10,000 mM⁻² can be observed for K ₄, the equilibrium constant for the formation of U3Ki from UKi. A lower bound can also be obtained for the sum of the association constants, K ₁ + K ₂ + K ₃ (panel G of Fig. 8), ∼7000 mM⁻¹. Assuming naively that K ₁ $\approx$ K ₂ $\approx$ K ₃, the equilibrium constants for the dissociation of hTRF1 from DnaK are smaller than ∼0.5 μM. Given that the NMR titrations are performed at concentrations of hTRF1 and DnaK that are much larger than the involved dissociation constants, it is reasonable to expect that only a lower bound can be recovered for the affinity (K_i).

Although it is not possible to obtain individual K_i values from fits of the titration profiles, qualitative estimates for the ratio K ₁/K ₂ can nevertheless be obtained from inspection of the curves, under the assumption that the reporter spins in question have similar relaxation rates.11 From Eq. (2) above it follows that an estimate for K ₁/K ₂ ranges between ∼ 1.5 to ∼ 3, obtained by comparing maxima for profiles L31δ1a and L30δ1b; I401δ1a and I401δ1b; and I438δ1a and I438δ1b in Figure 7.

One of the important results from this study is the presence of additional structures beyond UKi and UK2, namely the 3:1 hTRF1‐DnaK complexes, as described above in the context of fits of the initial decay of hTRF1 N state peaks (Fig. 4). To assess whether the goodness of fit of the titration data (Fig. 7) is consistent with this interpretation we reanalyzed titration profiles from peaks reporting on states “a” and “b,” neglecting contributions from U3Ki,

As can be seen in Figure 9 the fits underestimate the experimental intensities at small [DnaK]_T/[hTRF1]_T ratios (black solid curves) suggesting the presence of other molecular species that are reporting on binding to states “a” and “b.” Notably, when the U3Ki species is included the fits become noticeably improved (red and orange solid curves).

In addition to the titration data obtained using hTRF1 as a DnaK substrate we have also recorded similar experiments with a small peptide, hTRF1_23–38, that includes Leu 30 and Leu 31 that are positioned centrally in the DnaK binding site (Fig. 10, Supporting Information Fig. S2). Notably, the decay of free peptide peaks with added DnaK is more gradual and in a manner that is now consistent with 1:1 binding (Fig. 10). Normalized intensity ratios for a pair of peaks derived from the unbound state as a function of [DnaK]_T/[hTRF1]_T, one for each of hTRF1 (blue) and hTRF1_23–38 (red), are shown (circles), along with curves based on fits using the model of Figure 6 (hTFR1) and a simplified model where N, UK2 and U3Ki are not included (hTRF1_23–38,), described in the legend to Figure 10. The excellent fits for data involving hTRF1 (blue) and hTRF1_23–38 (red), as well as the difference in the response of hTRF1 and hTRF1_23–38 to added DnaK, that is expected (see below), provide confidence in the model used for analysis and indicate that the peptide is incapable of forming complexes of the type U3Ki.

Sample preparation

Protein samples of hTRF1 and of E. coli DnaK were prepared as detailed previously.9 Overexpression was performed in BL21(DE3) cells grown in M9 D₂O‐based minimal media supplemented with 1 g/L 15NH₄Cl and 3 g/L [²H,12C]‐glucose as the only sources of nitrogen and carbon respectively. U‐²H, Ileδ1‐¹³CH₃, Leu/Val‐¹³CH₃/¹²CD₃, Met‐¹³CH₃‐ (ILVM‐¹³CH₃‐) labeling was achieved following the procedures of Tugarinov et al.12 and Gelis et al.33 ¹³CH₃‐labeling at the Ileγ2 position was obtained following the protocol of Ruschak et al.34 NMR samples were 100% (vol/vol) D₂O buffer (pH 8) containing 50 mM HEPES, 50 mM KCl, 5 mM MgCl₂, 1 mM TCEP, 1 mM EDTA, 0.03% NaN₃, and 5 mM ADP.

NMR spectroscopy and data analysis

All NMR spectra were acquired at 35°C using a Bruker Avance III HD 18.8 T (800 MHz ¹H Larmor frequency) spectrometer equipped with a cryogenically cooled triple‐resonance probe. Spectra were processed using the NMRPipe35 software suite and visualized with Sparky.36 NMR titrations were performed as described in Results and intensities at each titration point were obtained by fitting peak lineshapes globally across all titration points using the software package FuDA (http://www.biochem.ucl.ac.uk/hansen/programs.html). Titration profiles were fit globally to various models of binding using an in‐house written software program (available upon request) that numerically solves the equilibrium and mass‐balance equations for a given model to arrive at concentrations of various molecular species at each titration point based on total DnaK ([DnaK]_T) and hTRF1 ([hTRF1]_T) concentrations. The folding equilibrium constant K_UN = [N]/[U] was fixed at a value of 22.7 for all the fits based on previous measurements at 35°C.

Constructing a six‐dimensional χ2 _red surface

A 6D χ2 _red surface was constructed based on the final model shown in Figure 6. The grid for generating the surface comprised 10⁶ points with 10 values for each of the six equilibrium association constants in the model, logarithmically spaced between the following ranges: K ₁: (100–1,968,300) mM⁻¹, K ₂: (100–1,968,300) mM⁻¹, K ₃: (10–196,830) mM⁻¹, K ₄: (5000–53,022.5) mM⁻², K ₅: (1–19,683) mM⁻¹, and K ₆: (10–196,830) mM⁻¹. At each point in the grid, titration profiles were fit to the model keeping all 6 equilibrium constants fixed to values at that grid point and floating only the residue‐specific parameters to obtain a χ2 _red value.