Kinetics of Fast Tetramerization of the Huntingtin Exon 1 Protein Probed by Concentration-Dependent On-Resonance R_1ρ Measurements

Abstract

An approach for the quantitative description of the kinetics of very fast exchange processes (τ_ex < 50–100 μs) associated with transient, reversible protein oligomerization, is presented. We show that on-resonance ¹⁵N-R_1ρ measurements conducted as a function of protein concentration at several spin-lock radio frequency field strengths are indispensable for unambiguous determination of the rate constants for interconversion between monomeric and higher order oligomeric species. The approach is experimentally demonstrated on the study of fast, reversible tetramerization of the full-length Huntingtin exon 1 protein, htt^ex1, responsible for Huntington’s disease. Incorporation of concentration-dependent ¹⁵N-R_2,eff data, obtained from on-resonance R_1ρ measurements performed at three spin-lock field strengths, into analysis of the kinetic scheme describing reversible tetramerization of htt^ex1 allowed us to uniquely determine the rate constants of interconversion between the various species. This approach serves as a valuable complement to the existing array of NMR techniques for studying early, transient oligomerization events in protein aggregation pathways.

Graphical Abstract

Dynamic processes in proteins occurring on a wide range of time scales in general,^1,2 and those associated with reversible protein oligomerization events in particular,^3,4 can be studied using a variety of solution NMR techniques. Characterization, however, of exchange processes involving protein oligomerization occurring on time scales <50–100 μs by solution NMR may be challenging for several reasons. This exchange regime falls outside the window of applicability of conventional Carr–Purcell–Meiboom–Gill (CPMG)^5,6 relaxation dispersion methods.⁷ However, the chemical shifts induced by exchange (δ_ex)^8,9 in this regime report on the equilibrium parameters of exchange (equilibrium constants/populations) and do not bear information on the rates of interconversion. In principle, R_1ρ relaxation dispersion experiments,^10-12 where spin relaxation rates of the magnetization aligned along the effective radiofrequency (RF) field are recorded in the rotating frame as a function of effective RF field strength, cover a range of exchange rates between ~10 000 and ~100 000 s⁻¹ (10 μs < τ_ex < 100 μs). However, in systems undergoing fast (homo)-oligomerization processes, where the rate constants of interconversion between monomeric and one or more oligomeric species (and, consequently, overall exchange rates) depend on the concentration of the main, observable species (monomers),^3,4 neither on-resonance R_1ρ dispersion obtained at a single protein concentration, nor on-resonance R_1ρ (R₂,_eff) rates acquired at a series of concentrations but a single RF field strength, contain sufficient information to uniquely determine the rate constants of the reversible oligomerization process. In this Letter, we show that a combination of (1) on-resonance R_1ρ (R_2,eff) rates obtained at a series of protein concentrations and several RF field strengths and (2) exchange-induced shifts δ_ex measured at a series of concentrations allows one to accurately define the kinetic rate constants of the fast, reversible tetramerization of the full-length Huntingtin exon 1 protein, htt^ex1. Polyglutamine expansion within Huntingtin exon-1 is responsible for Huntington’s disease, a fatal autosomal dominant neurodegenerative condition.¹³

Recently, we reported a detailed kinetic investigation of the prenucleation, transient oligomerization events involving htt^ex1 using a combination of exchange NMR techniques suitable for the study of reversible oligomerization processes.¹⁴ The htt^ex1 construct comprised a 16-residue amphiphilic N-terminal sequence (NT), a seven-residue polyglutamine tract (polyQ), and a proline-rich domain (PRD) containing two polyproline repeats separated by a 17-residue linker. Transient tetramerization of htt^ex1 is an early stage event^4,14 in the pathogenic pathway leading to the formation of neuronal inclusion bodies comprising polymorphic aggregates of oligomers and fibers.^15,16 This study relied on the kinetic scheme (Figure 1A) developed earlier for the transient, reversible oligomerization of a shorter, minimalistic construct, htt^NTQ₇, lacking the PRD domain.⁴ The kinetic model of oligomerization that satisfied all the experimental data obtained for htt^ex1 and htt^NTQ₇ (with only slightly different exchange parameters) consists of two branches: an “on-pathway” branch involving self-association of the monomeric species, E, to form a tetrameric helical bundle (E₄) via a helical coiled-coil dimer intermediate (E₂) (shown in black in Figure 1A), and an “off-pathway” branch leading to formation of “nonproductive” dimeric species, E₂*, that cannot oligomerize further (shown in gray in Figure 1A). The interconversion between the monomeric species E and the “off-pathway” dimer E₂* occurs on a relatively slow time-scale (τ_ex ~ 750 μs), making it amenable to analysis by CPMG relaxation dispersion techniques. In contrast, the overall exchange between the monomer and the tetramer E₄ occurs very fast on the chemical shift time scale (τ_ex ~ 50 μs) and is monitored primarily by changes in exchange-induced shifts, δ_ex, as a function of protein concentration. The minimal set of experimental NMR observables needed for analysis of the scheme in Figure 1A, included amide ¹⁵N- and ¹³Cα-CPMG relaxation dispersion profiles acquired at three protein concentrations and ¹⁵N/¹³Cα–δ_ex values measured at a series of concentrations ranging from 100 μM to 1.2 mM.^4,14 Even though the equilibrium parameters (i.e. equilibrium dissociation constants and populations) of each species of the on-pathway branch could be determined (listed in Figure 1A for full-length htt^ex1) under the assumption that the ¹⁵N/¹³Cα chemical shifts of species E₂ and E₄ are the same, neither in the case of htt^NTQ₇⁴ nor in that of the full-length htt^{ex1 14} was it possible to establish unequivocally the kinetic rate constants (k₂ and k₋₂) for the interconversion between dimer and tetramer. As confirmed by numerical simulations using synthetic data sets and observed in practice, inclusion of on-resonance ¹⁵N-R_1ρ dispersion data obtained at a single (typically, the highest) concentration of the protein and/or on-resonance ¹⁵N-R_1ρ (¹⁵N-R_2,eff) relaxation rates acquired at a series of concentrations but a single spin-lock RF field strength in the analysis, does not affect this result appreciably. Extensive grid searches performed over a wide range of k₋₂ values (which defines the overall exchange rate between monomer and tetramer at low concentrations⁴), while optimizing all of the remaining rate constants, allowed us, nevertheless, to estimate approximate lower bounds for k₋₂ (~20 000 s⁻¹ and ~40 000 s⁻¹ for full-length htt^ex1 and htt^NTQ₇, respectively).

Figure 1.

Kinetic model of prenucleation, transient htt^ex1 oligomerization. (A) Kinetic scheme: the “on-pathway” fast branch (τ_ex < 50 μs) leading to the formation of the tetramer E₄ via the dimer E₂ is shown in black, while the slow “off-pathway” process (τ_ex ~ 750 μs) leading to the formation of the “nonproductive” dimer, E₂*, is shown in gray. The equilibirum dissociation constants, as well as the expressions for the pseudo-first-order, apparent association rate constants, are shown beneath the scheme. The fractional populations of each species indicated above the scheme correspond to [htt^ex1] = 1.2 mM. (B) ¹⁵N exchange-induced chemical shifts (¹⁵N-δ_ex) and (C) ¹⁵N transverse spin relaxation rates (¹⁵N-R_2,eff) calculated for the “off-pathway” (gray) and “on-pathway” (red) branches and the full 4-state scheme of htt^ex1 oligomerization (black) as a function of htt^ex1 concentration. ¹⁵N-R_2,eff values were obtained from on-resonance R_1ρ rates calculated for a spin-lock RF field strength of 1 kHz. Dashed horizontal lines are drawn at zero for comparison. The following set of exchange parameters derived from our previous study of htt^ex1 oligomerization,¹⁴ was used in all simulations: k₁ = 5.8 × 10⁵ M⁻¹ s⁻¹, k₋₁ = 4.1 × 10⁴ s⁻¹, k₂ = 8.5 × 10⁸ M⁻¹ s⁻¹, k₋₂ = 2.0 × 10⁴ s⁻¹, k₃ = 5.9 × 10³ M⁻¹ s⁻¹, k₋₃ = 1350 s⁻¹; ^1SN-Δω = −1.1 ppm for the “off-pathway” dimer and −3.1 ppm for the “on-pathway” dimer E₂ and tetramer E₄ (assumed the same); and ¹⁵N-R₂ = 5.0 s⁻¹, while the R₂ of the dimeric and tetrameric species were assumed to be 2R₂ and 4R₂, respectively.

The scheme in Figure 1A can be simplified to include only the “on-pathway” process describing the tetramerization of htt^ex1, the main focus of the present study. Panels B and C of Figure 1 show that the concentration series of ¹⁵N-δ_ex and ¹⁵N-R_2,eff values (where R_2,eff is calculated from R_1ρ with a 1 kHz spin-lock RF field) simulated for the full scheme (black curves) are practically indistinguishable from those obtained using the “on-pathway” branch only (red curves), whereas the contribution of the “off-pathway” dimerization process (gray curves) to these NMR observables is clearly negligible. The large separation of time scales of the two branches of exchange in Figure 1A allows for such simplification to be achieved with a minimal loss of information content. Note that the “on-pathway” branch of htt^ex1 oligomerization is experimentally probed primarily by ¹⁵N/¹³Cα-δ_ex and ¹⁵N-R_2,eff data and is responsible for the characteristic curvature of their concentration dependence due to formation of higher-order (tetrameric) oligomers (Figures 1B,C). “Off-pathway” dimerization, however, is ¹⁵N/¹³Cα CPMG profiles (not considered here) up to CPMG fields of 500 Hz.¹⁴ The ¹⁵N/¹³Cα CPMG profiles from 500 Hz to the highest CPMG fields attainable in practice (1 kHz for ¹⁵N and 2 kHz for ¹³Cα) decay almost monotonically and therefore bear limited information on the kinetics of the “on-pathway” tetramerization process (i.e., insensitive to the value of k₋₂ above a lower bound). In the following, only the “on-pathway” branch is considered in the analysis of ¹⁵N/¹³Cα–δ_ex and ¹⁵N-R_2,eff data of htt^ex1.

It is instructive to consider some salient features of the two-step tetramerization scheme, E ⇌ E₂ ⇌ E₄, with respect to its dependence on protein concentration and its relationship to simpler models of exchange. Figure 2A shows plots of the overall exchange rate, $k_{\text{ex}}^{\text{overall}}$, that describes the total rate of exchange between the end species of a kinetic scheme, as a function of htt^ex1 concentration simulated for three different cases of exchange: (i) concentration-independent (green horizontal line), such as would be observed, for example, for a 2-state folding-unfolding equilibrium, U ⇌ F, where $k_{\text{ex}}^{\text{overall}}=k_{\mathrm{U}}+k_{\mathrm{F}}$, the sum of folding (k_F) and unfolding (k_U) rate constants; (ii) a linearly concentration-dependent apparent association rate constant (blue line), such as would be observed for a dimerization process, E ⇌ E₂, with $k_{\text{ex}}^{\text{overall}}=2k_1[{\text{htt}}^{\text{exl}}]+k_{-1}$, where the same notation as in Figure 1A is used, and (iii) tetramerization via a dimer intermediate, E ⇌ E₂ ⇌ E₄ (red curve), where the overall process E ⇌ E₄ is characterized by an overall exchange rate of $k_{\text{ex}}^{\text{overall}}=({k_{-1}}^2{k}_{-2}+4k_1^2{k}_2[{\text{htt}}^{\text{exl}}{]}^3)∕(k_{-1}^2+2k_1{k}_2[[{\text{htt}}^{\text{exl}}{]}^2)$ using the notation of Figure 1A. While the exchange rate of dimerization (E ⇌ E₂) only weakly and linearly depends on protein concentration (at least for the range of concentrations and low populations of the dimeric species considered here), the overall rate of tetramerization (E ⇌ E₄) is predicted to decrease almost 2-fold at higher protein concentrations (Figure 2A), a unique property of this kinetic scheme that arises from the concomitant concentration dependence of the overall reverse process (E₄ → E) as well. This decrease in the overall exchange rate is predicted to be manifested in the relationship between ¹⁵N-R_2,eff and ¹⁵N-δ_ex values, the two experimental observables that we focus on here, as we describe in more detail below.

Figure 2.

Simulations of the concentration dependence of various kinetic and experimental parameters for “on-pathway” tetramerization. (A) Dependence of the overall exchange rate, $k_{\text{ex}}^{\text{overall}}$, on protein concentration simulated for three different cases of exchange: (i) concentration-independent (green), (ii) linearly concentration-dependent apparent association rate constant (dimerization; blue), and (iii) tetramerization via a dimer intermediate according to the scheme shown in black in Figure 1A. (B) Simulated dependence of ¹⁵N-δ_ex values on protein concentration calculated for a series of k₋₂ values as indicated on the plot. (C) Simulated dependence of ¹⁵N-R_2,eff rates on protein concentration calculated for k₋₂ = 20 000 s⁻¹ (dashed lines) and 50 000 s⁻¹ (continuous lines). ¹⁵N-R_2,eff values calculated at the spin-lock field strengths of 750, 1500, and 3000 Hz, are shown in red, green, and blue, respectively. (D) Simulated values of ¹⁵N-R_2,eff plotted versus the absolute values of ¹⁵N-δ_ex for the same range of protein concentrations as in (A)–(C) (0–1.2 mM). The values calculated at the spin-lock field strengths of 750, 1500, and 3000 Hz, are shown with continuous, dash-dotted, and dashed red curves, respectively, with the rest of the color coding as in (A). All calculations were performed using the simplified, three-state model of exchange shown in black in Figure 1A. The same parameters of exchange as listed in Figure 1 were used in all simulations. In all the instances where k₋₂ is varied (as in (B) and (C)), $K_2^{\text{diss}}$ was kept fixed at 24 μM to leave the dimer–tetramer equilibrium unperturbed.

Panels B and C of Figure 2 show simulation plots of ¹⁵N-δ_ex and ¹⁵N-R_2,eff values, respectively, as a function of protein concentration, calculated with a typical set of exchange parameters obtained in our previous study of this system.¹⁴ The values of ¹⁵N-δ_ex (Figure 2B) are predicted to be sensitive to the rate constant k₋₂, which, at low htt^ex1 concentrations, determines the overall exchange rate for tetramerization (E ⇌ E₄)⁴ up to a limit of ~5000 s⁻¹. Beyond this limit, the values of ¹⁵N-δ_ex lose sensitivity to the rate(s) of species’ interconversion. Conversely, the concentration dependence of ¹⁵N-R_2,eff (Figure 2C) retains sensitivity to k₋₂ even for very fast rates of exchange (≥20 000 s⁻¹), especially so at the two extreme RF field strengths (0.75 and 3 kHz) of the applied spin-lock. When ¹⁵N-R_2,eff values are plotted versus absolute ¹⁵N-δ_ex (Figure 2D) for the same three scenarios of exchange as in Figure 2A, the characteristic curvature of the plot can be observed for the tetramerization scheme, E ⇌ E₂ ⇌ E₄, at low spin-lock RF field strengths applied in R_1ρ measurements (red solid curve). To obtain a more quantitative description of the relationship between R_2,eff and δ_ex, we draw analogies with a two-state exchange process, as the existing analytical expressions for the three-site exchange¹⁷ are too bulky to provide immediate insights. It is straightforward to show that for two-site exchange in the presence of an on-resonance RF field (as in R_1ρ measurements), R_2,eff depends linearly on δ_ex, with a slope that can be approximated by (Δω/k_ex)(k_ex² + Δω²)/(k_ex² + ω₁²), where Δω is the difference in chemical shifts between the exchanging sites, and ω₁ is the strength of the applied on-resonance RF field; here the simplest expression for R_1ρ in the limit of fast exchange^18,19 is used, and the intrinsic R₂ rates for the two sites are assumed to be the same. Clearly, if k_ex remains invariant with concentration ($k_{-1}\gg k_1^{\text{app}}$), as is almost the case for the dimerization process, E ⇌ E₂, the slope remains almost constant (blue line in Figure 2D), whereas a gradual increase in the slope with concentration will be observed in the case of the tetramerization scheme for low RF field strengths (red solid curve, Figure 2D). The resulting curvature of the plot is the direct consequence of the decrease in the overall exchange rate at higher protein concentrations for tetramerization via a dimer intermediate as discussed above. Note that for larger RF field strengths, when the RF field (ω₁) starts to “compete” with exchange (k_ex), the curvature of the R_2,eff vs δ_ex plot almost disappears (dashed-dotted and dashed red curves in Figure 2D).

Exploiting the sensitivity of the concentration dependence of ¹⁵N-R_2,eff rates to both the rate of exchange and the strength of the applied spin-lock RF field illustrated in Figure 2C, we globally fit the ¹⁵N/¹³Cα-δ_ex and ¹⁵N-R_2,eff data, acquired for full-length htt^ex1 over a concentration range from 0.1 to 1.4 mM, to the three-state tetramerization model E ⇌ E₂ ⇌ E₄ (see Supporting Information, “Materials and Methods” for details of NMR sample preparation, NMR experiments, and procedures of data analysis). The ¹⁵N-R_2,eff data were obtained from on-resonance ¹⁵N-R_1ρ experiments at three spin-lock RF field strengths (750, 1500, and 3000 Hz). This analysis yielded robust estimates of the optimized exchange parameters: the equilibrium dissociation constants, $K_1^{\text{diss}}=65\pm 2\text{mM}$ and $K_2^{\text{diss}}=34\pm 2\mu \mathrm{M}$; the dissociation rate constants, k₋₁ = 4.4(±0.4) × 10⁴ s⁻¹ and k₋₂ = 2.3(±0.2) × 10⁴ s⁻¹; and the derived second-order association rate constants, k₁= 6.8(±0.5) × 10⁵ M⁻¹ s⁻¹ and k2 = 6.7(±0.8) × 10⁸ M⁻¹ s⁻¹ (Figure 3A). While the value of $K_1^{\text{diss}}$ compares well with that from our previous study (~70 μM), the value of $K_2^{\text{diss}}$ is ~40% higher than that reported earlier (~24 μM).¹⁴ We attribute this discrepancy to slight variations in preparation of (aggregation-prone) NMR samples that are beyond our control. Note that the 40% increase in the value of $K_2^{\text{diss}}$ corresponds to a decrease in the tetramer population of only ~0.8% at a concentration of 1.2 mM. Selected examples of ¹⁵N-/¹³Cα-δ_ex and ¹⁵N-R_2,eff concentration profiles for Lys5, Lys8, and Glu11 are shown in Figure 3B,C, respectively, while the fits to all the experimental data included in analysis are shown in the Supporting Information (Figures S1 and S2, respectively). It is important to note that the equilibrium parameters ($K_1^{\text{diss}}$, $K_2^{\text{diss}}$ and the fractional populations of E₂ and E₄), as well as the differences in chemical shifts, Δω, can be extracted with a high level of confidence from analysis of the ¹⁵N/¹³Cα δ_ex data alone (Figure S3), albeit with uncertainties in their values higher by almost an order of magnitude compared to those obtained from the analysis of the combined δ_ex and R_2,eff data set. The ¹⁵N-R_2,eff concentration series obtained with several spin-lock RF field strengths are, however, indispensable for reliable determination of the exchange rate constants.

Figure 3.

Global analysis of concentration-dependent ¹⁵N-R_2,eff and ¹⁵N/¹³C_α-δ_ex values obtained for htt^ex1. (A) The simplified kinetic model of “on-pathway” oligomerization of htt^ex1. The optimized values of the equilibrium dissociation constants ($K_1^{\text{diss}}$, $K_2^{\text{diss}}$) and dissociation rate constants (k₋₁ k₋₂), together with the derived values of the second-order association rate constants (k₁, k₂) obtained from the global fit are indicated beneath the scheme. The populations of each species indicated above the scheme correspond to those at [htt^ex1] = 1.2 mM. Examples of (B) ¹⁵N/¹³C_α-δ_ex and (C) ¹⁵N-R_2,eff values obtained over the range of htt^ex1 concentrations between 0.1 and 1.4 mM (800 MHz, 5 °C). ¹⁵N-R_2,eff values obtained at RF spin-lock field strengths of 750, 1500, and 3000 Hz are shown in red, green, and blue, respectively. The experimental data are shown as circles; the continuous lines represent the best global fit to the kinetic model shown in (A). The full δ_ex and ¹⁵N-R_2,eff experimental data sets (and best fit curves) are provided in the Supporting Information (Figures S1 and S2, respectively). The overall reduced χ² of the global fit is 2.25 with errors of 0.5 Hz for δ_ex and 0.5 s⁻¹ for R_2,eff. See the Supporting Information, “Materials and Methods” for experimental details and a description of the fitting procedure.

Panels A and B of Figure 4 show correlation plots comparing the ¹⁵N- and ¹³Cα-Δω values extracted from the fit of the combined δ_ex/R_2,eff data set (y-axis) versus the values reported previously (x-axis).¹⁴ There is good agreement between the two sets of Δω values but the uncertainties are reduced ~2-fold for the combined δ_ex/R_2,eff fit, validating the approach described here (see Supporting Information, Table S1, for the full list of optimized ¹⁵N/¹³Cα-Δω values). Note the assumption that ¹⁵N/¹³Cα chemical shifts for the dimer E₂ and tetramer E₄ are the same, used in this work as well as in the previous studies,^4,14 is fully justified as secondary ¹⁵N/¹³Cα backbone shifts, occurring as a result of the transition from an intrinsically disordered monomer to a coiled-coil helical dimer/tetramer, are the main determinants of Δω. Figure 4B shows the experimental concentration series of ¹⁵N-R_2,eff rates plotted versus the absolute values of ¹⁵N-δ_ex, for Glu4, the residue with the largest ¹⁵N-∣Δω∣ value. The predicted curvature of the plot is clearly observed for the two lower spin-lock RF field strengths (750 and 1500 Hz) reflecting the interesting inherent property of two-step tetramerization kinetics (see Figure 2).

Figure 4.

Correlation plots comparing (A) ¹⁵N-Δω and ¹³Cα-Δω values (ppm) between the oligomeric (E₂/E₄) and monomeric (E) species of htt^ex1 obtained in this work (y-axis) with those obtained previously using the full four-state model of exchange, x-axis.¹⁴ The correlation coefficients are indicated in the right lower corner of the plots. Error bars (±1 SD) for the x and y axes are shown in blue and red, respectively. (B) Experimental ¹⁵N-R_2,eff values obtained for htt^ex1 concentrations from 0.1 to 1.4 mM plotted versus the absolute values of ^1SN-δ_ex for Glu4 of htt^ex1. Experimental curves corresponding to RF spin-lock field strengths of 750, 1500, and 3000 Hz are shown in red, green, and blue, respectively.

The optimized values of the kinetic and equilibrium parameters of htt^ex1 tetramerization are robust with respect to the number of spin-lock RF field strengths employed (a minimum two is recommended; see Table S2), as well as the range of protein concentrations used, as long as a substantial concentration dependence of R_2,eff relaxation rates is present in the data (see Table S3).

Numerical simulations consisting of global fits of sets of synthetic R_1ρ relaxation dispersion data at a small number (2 or 3) of htt^ex1 concentrations in conjunction with experimental ¹⁵N/¹³Cα δ_ex concentration profiles, indicate that the approach described here (namely, a small number of spin-lock RF field strengths employed for R_1ρ measurements together with extensive sampling of concentrations) is more robust and efficient for extracting reliable kinetic parameters of exchange. As might be expected, extensive sampling of effective RF fields to generate R_1ρ relaxation dispersion profiles with reduced sampling of concentrations is not as informative and time efficient in fast exchange processes with strongly concentration-dependent kinetics.

In conclusion, we have described a NMR approach for obtaining a quantitative description of the kinetics of very fast exchange processes (τ_ex < 50–100 μs) associated with transient, reversible protein oligomerization and demonstrated its utility with regard to the tetramerization of Huntingtin exon 1. While the equilibrium parameters describing oligomerization can be established from the concentration dependence of exchange-induced chemical shifts alone (Figure S3), on-resonance R_1ρ measurements conducted as a function of protein concentration at several RF field strengths are indispensable for determining the rate constants of interconversion between the monomeric species and higher order oligomers (Figure 3).

The approach described here should serve as an important complement to the pool of available NMR techniques for characterizing early transient events in protein aggregation pathways. Although analysis is restricted here to ¹⁵N R_1ρ relaxation, it can be extended to higher gyromagnetic-ratio (γ) nuclei. As higher RF field frequencies are accessible for higher γ nuclei, it can be expected that even faster oligomerization processes can be characterized via concentration-dependent ¹³Cα or amide ¹H R_1ρ measurements.²⁰