Dynamics of GCN4 Facilitate DNA Interaction: A Model-Free Analysis of an Intrinsically Disordered Region

Abstract

Intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered regions (IDRs) are known to play important roles in regulatory and signaling pathways. A critical aspect of these functions is the ability of IDP/IDRs to form highly specific complexes with target molecules. However, elucidation of the contributions of conformational dynamics to function has been limited by challenges associated with structural heterogeneity of IDP/IDRs. Using NMR spin relaxation parameters (¹⁵N R₁, ¹⁵N R₂, and {¹H}-¹⁵N heteronuclear NOE) collected at four static magnetic fields ranging from 14.1 to 21.1 T, we have analyzed the backbone dynamics of the basic leucine-zipper (bZip) domain of the Saccharomyces cerevisiae transcription factor GCN4, whose DNA binding domain is intrinsically disordered in the absence of DNA substrate. We demonstrate that the extended Model-free analysis can be applied to proteins with IDRs such as apo GCN4 and that these results significantly extend previous NMR studies of GCN4 dynamics performed using a single static magnetic field of 11.74 T [Bracken, et al. (1999) J. Mol. Biol., 285, 2133–2146] and correlate well with molecular dynamics simulations [Robustelli, et al. (2013) J. Chem. Theory Comput., 9, 5190–5200]. In contrast to the earlier work, data at multiple static fields allows the time scales of internal dynamics of GCN4 to be reliably quantified. Large amplitude dynamic fluctuations in the DNA-binding region have correlation times (τ_s ≈ 1.4–2.5 ns) consistent with a two-step mechanism in which partially ordered bZip conformations of GCN4 form initial encounter complexes with DNA and then rapidly rearrange to the high affinity state with fully formed basic region recognition helices.

Introduction

The discovery of intrinsically disordered proteins (IDPs) and proteins with extensive intrinsically disordered regions (IDRs), collectively referred to as IDPs herein, challenged the structure-function paradigm by demonstrating that biological activity is possible in the absence of well-defined tertiary structure ^1,2. In the time since this discovery, sequence analyses have led to the realization that IDPs are widely distributed: recent estimates suggest that over 100,000 disordered regions are located throughout ~40% of the mammalian proteome ^1,3,4. Moreover, IDPs are associated with crucial but diverse roles in cellular function, including signaling pathways ^5,6, cell cycle regulation ^5,7, and control of both transcription and translation ^2,8,9.

The mechanisms by which IDPs recognize and bind to their substrates or interaction partners are central to their biochemical properties. Two limiting paradigms have been proposed. The first, conformational selection, posits that more-ordered, binding-competent structures exist among an ensemble of conformations and that these conformers are selected during the binding process ^10,11. The second, induced fit, posits that binding-competent structures are induced by interactions with the target ^2,12. Biochemical, theoretical, and computational evidence suggests these two alternatives are the extremes of a spectrum of behavior, rather than independent dichotomies ^13–15.

Structural variability and dynamic substrate interaction mechanisms make IDPs well-suited to rapid control of cellular processes. For example, the extremely fast (often diffusion-limited) association rates for transcription factors enables fast activation of the signaling response ^6,16. Likewise, the tendency of IDPs to bind partners or ligands with high specificity but modest affinity leads to rapid dissociation, and thus signal termination ^17,18.

The transient and flexible (structurally heterogeneous) nature of IDPs creates challenges for their study by techniques of structural biology. Crystallization of IDPs, particularly in their unbound (disordered) states, often is not possible. Considerable success has been reported using NMR methods to study IDPs ^19,20, but the absence of a single, global correlation time hinders application of approaches such as the Model-free formalism ^21,22 as a method for analyzing otherwise powerful NMR spin relaxation measurements. We demonstrate herein that an extended protocol and analysis can overcome these limitations and provide a general approach for the detailed examination of internal dynamics in IDPs.

The Saccharomyces cerevisiae protein GCN4, which has homologs in mammals ²³, is a prototypical example of a transcription factor that binds DNA target sequences using IDRs. The DNA-binding domain of GCN4, termed the bZip domain, contains an N-terminal highly basic helical region that inserts into the DNA major groove and a C-terminal region that dimerizes to form a leucine zipper (Figure 1A) ^24,25. In the absence of DNA substrate, the N-terminal region consists of a (partially) disordered ensemble (Figure 1B) that contains significant residual helicity ^26–29, while the C-terminal leucine zipper remains ordered and dimeric under the solution conditions used in the present work. The presence of both a flexible and an ordered region makes GCN4 an ideal model for demonstration of the proposed formalism.

Figure 1.

(A) The bZip region of GCN4 contains a C-terminal coiled-coil region (blue) that forms a leucine zipper, while the N-terminal basic region (red) interacts with DNA substrate (gray). Crystallographic coordinates are from PDB 1YSA ²⁴. (B) The inverse of the order parameters (S²) determined by Bracken and coworkers ²⁶ are mapped onto the width and color of the bZip domain. Narrow regions that are colored blue are the most rigid (highest S²), while wider regions that are colored red are the most dynamic (lowest S²).

Using NMR spin relaxation measurements (¹⁵N R₁, ¹⁵N R₂, and {¹H}-¹⁵N heteronuclear NOE) for backbone amide moieties, collected at four static magnetic fields, we have performed spectral density mapping and Model-free analysis on the apo (substrate-free) form of the GCN4 bZip domain. The order parameters (S²) are consistent with previous studies, including an analysis of ¹⁵N spin relaxation data from a single static field ²⁶ and recent molecular dynamics simulations ³⁰. Significantly, the use of multiple static fields allowed internal motions to be resolved on ps and ns timescales, which was not possible previously. The disordered basic domain contains regions with motions whose correlation times are consistent with structural pre-organization in advance of DNA substrate binding followed by rapid stabilization within the DNA encounter complex. Thus, the GCN4 bZip domain utilizes aspects of both selected- and induced-fit binding mechanisms. This may be a common paradigm for IDPs, which can now be investigated in detail using the strategy described herein.

Methods

Sample preparation

The DNA binding domain of Saccharomyces cerevisiae GCN4 was expressed and purified as described previously ²⁶. Briefly, BL21(DE3)-pLysS cells were transformed and grown in 1–2 L of M9 minimal media with 1 g/L ¹⁵NH₄Cl and either 4 g/L of unlabeled glucose in 98% ²H₂O or 4 g/L ¹³C₆-glucose in H₂O at 37 °C to an optical density (OD₆₀₀) of 0.7. Protein expression was induced with 1 mM IPTG and allowed to proceed for approximately 2 hrs. The protein was purified on an SP sepharose column with 25 mM HEPES, pH 7.5, and 1 mM EDTA with a gradient of 0.2–1 M NaCl followed by HPLC purification using a C18 reverse phase column with starting buffer of 10% acetonitrile/0.1% trifluroacetic acid (TFA) and final buffer of 90% acetonitrile/0.1 % TFA. Eluted fractions were lyophilized and then reconstituted into a pH 4.5 buffer that contained 50 mM sodium acetate-d₆, and 75 mM KCl in 90%H₂O/10% ²H₂O ²⁶. Final GCN4 sample concentrations were 1 mM U-[¹⁵N, ¹³C] and 800 μM U-[¹⁵N, ²H], respectively. Protein concentrations are defined with respect to a single monomer.

NMR spectroscopy

NMR experiments were conducted on Bruker Avance spectrometers operating at 14.1, 16.45, 18.8, and 21.1 T. The spectrometer operating at 16.45 T was equipped with a triple resonance, triple-axis gradient room temperature probe. All other spectrometers were equipped with triple resonance z-axis gradient TCI cryoprobes. Sample temperature was calibrated at 300 K with 98% ²H₄-methanol as described previously ³¹.

Resonance assignments ²⁶ were confirmed using HNCA ^32–34 and HN(CO)CA spectra ^32,34 with 12.6 × 2.9 × 7.3 kHz spectral widths and 1024 × 30 × 64 complex points (t₃ × t₂ × t₁), and a 3D (¹H, ¹⁵N, ¹⁵N) HSQC-NOESY-HSQC ^35,36 with 10.8 × 2.1 × 2.4 kHz spectral widths, 1024 × 64 × 64 complex points, and 600 ms mixing time. All assignment experiments were collected with 16 scans at 21.1 T.

R₁, R₂, and {¹H}-¹⁵N heteronuclear NOE experiments ^37,38 were recorded with spectral widths of 7.2 × 1.6, 8.4 × 1.8, 9.6 × 2.1, and 10.8 × 2.4 kHz for 14.1, 16.45, 18.8 and 21.1 T, respectively, and contained 1024 × 300 complex points. Relaxation delays for the R₁ and R₂ experiments ranged from 0.02–1.75 and 0.004–0.208 s, respectively, and are listed for each static magnetic field in Table S1. For the R₂ experiment, the phase cycle of Yip and Zuiderweg ³⁹ was incorporated in the CPMG train for improved off-resonance compensation and the spacing between 180° pulses was 500 μs. The R₁ and R₂ experiments were collected with 8 scans per FID. The heteronuclear NOE experiment was collected with 32 scans, and the t₁ points of the Boltzmann and saturation experiments were interleaved during acquisition. The R₁ and R₂ experiments used the Rance-Kay protocol and the NOE experiments used the States-TPPI protocol for quadrature detection ^40–43.

Data processing and analysis

All data were processed in NMRPipe ⁴⁴. The two indirect dimensions of the HNCA, HN(CO)CA, and HSQC-NOESY-HSQC experiments were processed with linear prediction and a Kaiser window (θ = π) in the two indirect dimensions. The relaxation data were processed using a Kaiser window (θ = π) for t₁ and linear prediction with 3 Hz exponential line broadening for t₂. Resonance assignments and quantitation of peak intensities were performed in Sparky ⁴⁵. Additional data processing and visualization was performed using the Python scientific libraries ^46–52.

Determination of relaxation parameters

The program relax ^53,54, version 3.2.3, was used for determination of relaxation parameters. Errors in R₁ and R₂ rate constants were determined from 500 Monte Carlo simulations, while those for the heteronuclear NOE were calculated from the noise floor. Due to large variations in peak intensities between disordered and coiled-coil regions, relaxation parameters were analyzed in two separate groups (residues 1–12 and 56–58 for disordered residues and 13–55 for ordered residues), as determined by k-means clustering of initial R₁ and R₂ peak intensities. Five residues were omitted from analysis due to spectral overlap (31, 33, 34, 36, 40, and 47), residue 2 was not quantified because its extremely narrow resonance lineshape was not well-digitized, and residue 4 is a proline. The resulting R₂ rates were corrected for R₁ contribution as described by Yip and Zuiderweg ³⁹.

The 10% trimmed mean correlation time (τ_M) and diffusion tensor anisotropy for the coiled-coil region were calculated at each static field from the ratio R₂/R₁ and Model-free local correlation times (τ_M), respectively, using the program quadric ^55,56. The mean correlation time for data recorded at 16.45 T was 15.6 ns, lower than the mean value of 16.9 ns for the other fields (14.1, 18.8, and 21.1 T). This difference likely reflects a slightly elevated sample temperature for the 16.45 T (700 MHz) NMR spectrometer, as it was the only instrument with a room-temperature probe. To account for this difference, R₁ and R₂ relaxation rates recorded at 16.45 T were adjusted for the difference in τ_M according to the following equations:

$$\begin{array}{l}{R}_1=R_{10}({\tau }_M/{\tau }_{M0})(1+{\omega }_N^2{\tau }_{M0}^2)/(1+{\omega }_N^2{\tau }_M^2)\\ R_2=(R_{20}-0.5R_{10})({\tau }_M/{\tau }_{M0})+0.5R_1\end{array}$$ 1

where ω_N is the ¹⁵N frequency at 16.45 T. R₁₀, R₂₀, and τ_M0 are the respective original R₁ and R₂ relaxation rates and correlation time, and R₁, R₂, and τ_M are the adjusted versions. In addition, the uncertainties in R₁, R₂, and heteronuclear NOE data were rescaled by an empirical factor of 1.38 so the median χ² of the combined linear regressions of Γ_auto vs (3d² + 4c²)/6, J(ω_N) vs ωN⁻², and J(0.870ω_H ) vs (0.870ω_H) ⁻² was equal to 1.0 (vide infra). These two adjustments reduced the χ² values in subsequent Model-free analyses of the relaxation data but did not significantly change the fitted parameter values or selected models.

Spectral density mapping

The ¹⁵N relaxation rate constants are given by:

$$\begin{array}{l}{R}_1=(d^2/4)\{J({\omega }_H-{\omega }_N)+3J({\omega }_N)+6J({\omega }_H+{\omega }_N)\}+c^{2}J({\omega }_N)\\ R_2=(d^2/8)\{4J(0)+J({\omega }_H-{\omega }_N)+3J({\omega }_N)+6J({\omega }_H)+6J({\omega }_H+{\omega }_N)\}+(c^2/6)\{4J(0)+3J({\omega }_N)\}\\ {\sigma }_{NH}=(d^2/4)\{-J({\omega }_H-{\omega }_N)+6J({\omega }_H+{\omega }_N)\}=R_1(\mathit{NOE}-1){\gamma }_N/{\gamma }_H\end{array}$$ 2

in which the dipolar coupling constant is $d=({\mu }_{0}h{\gamma }_H{\gamma }_N/8{\pi }^2)r_{NH}^{-3}$, μ₀ is the permeability of free space, h is Planck’s constant, r_NH is the average amide bond length (1.02 Å), the CSA coupling constant is c = Δσω_N/3^1/2, Δσ is the amide CSA (−172 ppm), ω_N and ω_H are the ¹⁵N and ¹H frequencies at the respective static field, and J(ω) is the spectral density function. Using the reduced spectral density mapping approach, the above expressions can be converted to expressions for J(0), J(ω_N) (at each static field) and J(0.870ω_H) (at each static field):

$$\begin{array}{l}{\mathrm{\Gamma }}_{\mathit{auto}}=R_2-0.5R_1-0.454{\sigma }_{NH}=J(0)(3d^2+4c^2)/6\\ J({\omega }_N)=\{R_1-1.249{\sigma }_{NH}\}/(3d^2/4+c^2)\\ J(0.870{\omega }_H)=4{\sigma }_{NH}/(5d^2)\end{array}$$ 3

The value of J(0) was obtained from the slope of a linear fit through the origin of Γ_auto vs. (3d² + 4c²)/6 for all four static fields.

The most complex spectral density function consistent with the acquired data is an extended version of the Model-free spectral density function ⁵⁷:

$$J(\omega )=\frac{2}{5}\left\{\frac{S^2{\tau }_M}{1+{\omega }^2{\tau }_M^2}+\frac{(S_f^2-S^2){\tau }_s^{\prime }}{1+{\omega }^2{\tau }_s^{\prime 2}}+\frac{(1-S_f^2){\tau }_f^{\prime }}{1+{\omega }^2{\tau }_f^{\prime 2}}\right\}$$ 4

in which S² is the square of the generalized order parameter and τ_M is the (effective) overall rotational correlation time for a given N-H bond vector. S_s² = S²/S_f², and S_f² are the squares of the generalized order parameters for intramolecular motions with slow, τ_s, and fast, τ_f, correlation times, respectively. τ_s′, and τ_f′ are the inverse sums of the respective correlation time with τ_m: ${\tau }_s^{\prime }={(1/{\tau }_M+1/{\tau }_s)}^{-1}$ and ${\tau }_f^{\prime }={(1/{\tau }_M+1/{\tau }_f)}^{-1}$. This equation assumes that the stochastic processes governing τ_M, τ_s, and τ_f are statistically independent, which approximately holds if the processes are time-scale separated τ_M ≫ τ_s ≫ τ_f). If ${(0.870{\omega }_H{\tau }_f^{\prime })}^2\ll 1$ and ${({\omega }_N{\tau }_s^{\prime })}^2\gg 1$, then the spectral density function becomes a linear function of (0.870ω_H)^{−2 58}:

$$J(0.870{\omega }_H)=m_H{(0.870{\omega }_H)}^{-2}+b_H$$ 5

in which:

$$\begin{array}{l}{m}_H=\frac{2}{5}\left\{S^2/{\tau }_M+(S_f^2-S^2)/{\tau }_s^{\prime }\right\}\\ b_H=\frac{2}{5}(1-S_f^2){\tau }_f^{\prime }\end{array}$$ 6

Similarly, if ${({\omega }_N{\tau }_s^{\prime })}^2\ll 1$ and (ω_Nτ_M)² ≫ 1, then the spectral density function becomes a linear function of ω_N⁻²:

$$J({\omega }_N)=m_N{\omega }_N^{-2}+b_N$$ 7

in which:

$$\begin{array}{l}{m}_N=\frac{2}{5}{S}^2/{\tau }_M\\ b_N=\frac{2}{5}\left\{(S_f^2-S^2){\tau }_s^{\prime }+(1-S_f^2){\tau }_f^{\prime }\right\}\end{array}$$ 8

If the linear relationships hold for a given set of field-dependent relaxation measurements, then the values m_N, b_N, m_H, and b_H, together with

$$J(0)=\frac{2}{5}\left\{S^2{\tau }_M+(S_f^2-S^2){\tau }_s^{\prime }+(1-S_f^2){\tau }_f^{\prime }\right\}$$ 9

are sufficient to determine the five parameters in Equation 4:

$$\begin{array}{l}{S}^2=\frac{5}{2}{\left[\{J(0)-b_N\}{m}_N\right]}^{1/2}\\ {\tau }_M={\left[\{J(0)-b_N\}/m_N\right]}^{1/2}\\ S_f^2=S^2+\frac{5}{2}{\left[\{b_N-b_H\}\{m_H-m_N\}\right]}^{1/2}\\ {\tau }_f^{\prime }=\frac{5}{2}{b}_H/(1-S_f^2)\\ {\tau }_s^{\prime }={\left[\{b_N-b_H\}/\{m_H-m_N\}\right]}^{1/2}\end{array}$$ 10

Fitted slopes and intercepts in Equation 4 were determined by linear least squares regression, and errors in the Model-free parameters were propagated by Monte Carlo simulations.

Model-free analysis

Model-free analysis was performed with relax ^53,54. During analysis, relaxation parameters were entered in duplicate for each residue to account for the homodimeric structure of GCN4. In the first analysis, for comparison with spectral density mapping, an individual overall correlation time was fit for each residue (local τ_M). In the second analysis, for comparison with previous NMR ²⁶ and molecular dynamics ³⁰ results, fitting was performed first for residues located in or near the coiled-coil region (residues 25–58) using an individual correlation time for each residue (local τ_M). For residues located in or near the disordered region (residues 3–27 and 54–58), the correlation time was fixed to the average τ_M of the coiled-coil region, with the resulting χ² values being used to determine the classification of residues located at the interface of the disordered and ordered regions (25–27 and 54–58). Parameters of the following models, enumerated in the relax documentation, were fit to the data:

$$\begin{array}{ll}\text{Model}0:\hfill & J(\omega )=\frac{2}{5}{\tau }_m\hfill \\ \text{Model}1:\hfill & J(\omega )=\frac{2}{5}{\tau }_m[\frac{S^2}{1+{(\omega {\tau }_m)}^2}]\hfill \\ \text{Model}2:\hfill & J(\omega )=\frac{2}{5}{\tau }_m[\frac{S^2}{1+{(\omega {\tau }_m)}^2}+\frac{(1-S^2)({\tau }_e+{\tau }_m){\tau }_e}{{({\tau }_e+{\tau }_m)}^2+{(\omega {\tau }_e{\tau }_m)}^2}]\hfill \\ \text{Model}5:\hfill & J(\omega )=\frac{2}{5}{\tau }_m[\frac{S^2}{1+{(\omega {\tau }_m)}^2}+\frac{(S_f^2-S^2)({\tau }_s+{\tau }_m){\tau }_s}{{({\tau }_s+{\tau }_m)}^2+{(\omega {\tau }_s{\tau }_m)}^2}]\hfill \\ \text{Model}6:\hfill & J(\omega )=\frac{2}{5}{\tau }_m[\frac{S^2}{1+{(\omega {\tau }_m)}^2}+\frac{(1-S_f^2)({\tau }_f+{\tau }_m){\tau }_f}{{({\tau }_f+{\tau }_m)}^2+{(\omega {\tau }_f{\tau }_m)}^2}+\frac{(S_f^2-S^2)({\tau }_s+{\tau }_m){\tau }_s}{{({\tau }_s+{\tau }_m)}^2+{(\omega {\tau }_s{\tau }_m)}^2}]\hfill \end{array}$$ 11

Model-free analysis was performed using only models that lack contribution from conformational exchange (0, 1, 2, 5, and 6, Equation 11) ^21,22,57. Best fit models were selected using the Bayesian Information Criterion (BIC) ⁵⁹. Errors for the Model-free parameters were determined from 500 Monte Carlo simulations.

Results

Assignment of GCN4 amide resonances

The assignment of U-[¹⁵N, ²H] GCN4 chemical shifts utilized a ¹H,¹⁵N,¹⁵N HSQC-NOESY-HSQC with 600 ms mixing time ⁶⁰. In the coiled-coil region, NOE connectivities were observed for residues ranging from i₋₃ to i₊₃ (Figure S1A), whereas connectivities for i₋₂ to i₊₂ were generally observed in the disordered basic region (Figure S1B). The amide chemical shift assignments are listed in Table S2. The exclusive use of amides for resonance assignments is advantageous because an additional ¹³C-labeled sample is not required and because the indirect dimensions can be acquired with very high resolution due to the narrow ¹⁵N chemical shift range and the absence of constant-time pulse sequence elements. In the case of GCN4, this strategy also enabled resonance assignment and spin relaxation experiments to be conducted on the same sample. Amide chemical shift assignments (Figure S2 and Table S2) were further confirmed using those reported by Bracken, et. al ²⁶ and with an HNCA and HN(CO)CA collected on U-[¹⁵N, ¹³C] GCN4 (data not shown).

Fast timescale dynamics of GCN4

Established amide spin relaxation experiments were performed to measure the ¹⁵N R₁, ¹⁵N R₂, and {¹H}-¹⁵N heteronuclear NOE spin relaxation rate constants of U-[¹⁵N, ²H] GCN4 (Table S3) at four static fields (14.1, 16.45, 18.8, and 21.1 T). The structurally heterogeneous nature of GCN4 leads to significantly different peak intensities in the disordered and coiled-coil regions, creating additional considerations for the acquisition and analysis of quantitative NMR experiments. An increased number of t₁ increments and additional relaxation time points were collected to ensure accurate digitization. To ensure accurate error estimation during Monte Carlo analysis, residues were analyzed in two groups based on initial peak intensities. The relaxation rate constants are consistent with a disordered basic region, having elevated R₁ relaxation rates, reduced R₂ relaxation rates, and reduced heteronuclear NOE values, relative to those of the coiled-coil region (Figure 2).

Figure 2.

Relaxation measurements for (A) R₁, (B) R₂, and (C) {¹H}-¹⁵N heteronuclear NOE experiments performed on GCN4. Data for 14.1, 16.45, 18.8, and 21.1 T are black, blue, orange, and green, respectively. Error bars are the result of Monte Carlo simulations for the R₁ and R₂ measurements and based on the noise floor for the heteronuclear NOE.

Plots of Γ_auto vs. (3d² + 4c²)/6, J(ω_N) vs. ω_N⁻², and J(0.870ω_H) vs. (0.870ω_H)⁻² were well-fit by the linear equations 3, 5, and 7, respectively. Examples of the fitted data are shown in Figure 3A–C for residue 14. The excellent fits of Γ_auto vs. (3d² +4c²)/6 for the assumed value of Δσ = −172 ppm indicate chemical exchange does not contribute significantly to the measured R₂ values. The absence of exchange contributions was also confirmed by comparing fits of Γ_auto vs. B₀² performed with R_ex = 0 and with R_ex as a fitted parameter, which was assumed to scale with B₀² (data not shown). The linearity of the graphs of these three sets of data implies that only five independent parameters are needed to describe the data and therefore Equation 4 is the most complex spectral density function supported. Motions may be distributed over multiple time scales so that τ_M, τ_s, and τ_e represent effective fits to a more complex distribution of correlation times.

Figure 3.

Spectral density mapping for residue 14 of the GCN4 bZip domain. (A) Γ_auto at 14.1, 16.45, 18.8, and 21.1 T plotted vs. (3d² + 4c²)/6 (Equation 3). The solid line is the best fit through the origin to determine J(0) from the slope. (B) J(ω_N) and (C) J(0.870ω_H) are plotted vs. ω⁻². Solid lines are the best linear fits to the data. (D) Reduced spectral density values J(ω) plotted vs. ω. The solid line is determined from the Model-free parameters obtained from the spectral density mapping protocol (Equation 10); the dashed line is calculated from Model-free parameters determined from full analysis using the relax program assuming a local overall rotational correlation time τ_M for each residue.

Reduced spectral density analysis of GCN4

The values of S²τ_M, S²/τ_M, $(S_f^2-S^2){\tau }_s^{\prime },(S_f^2-S^2)/{\tau }_s^{\prime }$, and $(S_f^2-S^2){\tau }_s^{\prime }$ obtained from Equations 6, 8, and 9 are shown in Figure 4A–E. The lack of mobility for the coiled coil and the extensive mobility of the basic region are evident directly from these plots. Figure 4F plots $(S_f^2-S^2){\tau }_s^{\prime }$ vs. S²τ_M, showing that four clusters of residues with related properties are evident: 3–12 (pink), 13–25 (green), 26–55 (black), and 56–58 (orange). The values of the Model-free parameters determined from the data in Figure 4 using Equation 10 are shown in Figure 5; values of τ_f and τ_s with extremely large uncertainties, because the corresponding S_f² or S_s² approaches unity, are not displayed for clarity. To test the accuracy of the assumptions used to obtain the Model-free parameters from the above equations, the relaxation data also were analyzed conventionally using the program relax and assuming a local τ_M for each residue. Figure 3D shows fitted spectral density values for residue 14 determined from the spectral density mapping and conventional analyses. Figure 6 compares S²τ_M, S², and τ_M for all residues using the two analyses.

Figure 4.

Aggregate Model-free parameters from field-dependent spectral density mapping. The values of (A) S²τ_M, (B) S²/τ_M, (C) $(S_f^2-S^2){\tau }_s^{\prime }$, (D) $(S_f^2-S^2)/{\tau }_s^{\prime }$, and (E) $(S_f^2-S^2){\tau }_s^{\prime }$ obtained from Equations 6–9 are shown. (F) $(S_f^2-S^2){\tau }_s^{\prime }$ is plotted vs. S²τ_M. Regions of the protein are colored as follows: region 1 on bZip (residues 3–12): pink; region 2 of bZip (residues 13–25): green; coiled-coil (residues 26–55): black; disordered C-term (residues 56–58): orange.

Figure 5.

Model-free parameters from field-dependent spectral density mapping. Values of (A) S², (B) τ_M, (C) S_s², (D) τ_s, (E) S_f², and (F) τ_f are plotted vs. residue number. Values not statistically different from zero are not shown. Colors are as in Figure 4.

Figure 6.

Comparison of Model-free parameters (A) S²τ_M, (B) S², and (C) τ_M from field-dependent spectral density mapping and the full analysis in which local τ_M values were fit using the relax program. The correlation coefficients are 0.999, 0.964, and 0.964, respectively. Colors are as in Figure 4.

Model-free analysis of GCN4

Treatment of the basic region, coiled coil, and C-terminal region during Model-free analysis of GCN4 was similar to the method used by Bracken and coworkers ²⁶. Briefly, the coiled-coil residues were first analyzed using a local correlation time (τ_M), and then the mean τ_M from this analysis was fixed for the basic region. The fitted Model-free parameters for residues in the coiled-coil incorporate the effects of diffusion anisotropy through the local τ_M values. Based on the modest diffusion tensor anisotropy 2D_zz/(D_xx+D_yy) = 1.25 determined from the local τ_M for residues in the coiled-coil region, further treatment of the global diffusion tensor is unlikely to significantly effect results for the residues in the basic region: a root-mean-square error of ~4% in S2 would arise from different (unknown) average orientations of N-H bond vectors for these residues ⁶¹. In the current study, a more detailed analysis, including the fitting of internal correlation times, was possible using spin relaxation data acquired at multiple static fields. Three of the models were originally described by Lipari and Szabo ^21,22 and have Brownian rotational diffusion characterized by a correlation time (τ_M) and the following dynamic properties: no dynamics (model 0), internal motion that can be characterized by a single order parameter (S², model 1), or an order parameter plus an effective internal correlation time (τ_e, model 2). When τ_e < 100 ps, the internal motion was classified as fast (τ_f), otherwise it was slow (τ_s). Two additional models (5 and 6) developed by Clore, et. al ⁵⁷ include internal motions on two timescales, the faster of which is described by τ_f and S_f² and the slower by τ_s and S_s², which are determined as described above. Given the lack of evidence for chemical exchange, as determined by analysis of Γ_auto, additional models containing an R_ex term were not considered.

The selected model, as determined by the Bayesian information criterion (BIC) ⁵⁹, is shown for reach residue in Table S4. Models 2 and 5 were chosen for the coiled-coil region indicating simpler dynamics, while model 6 was chosen for all of the disordered residues. The model selected for the disordered residues does not change in most cases when a local τ_M was assumed (see above) indicating the selection of a more complicated model in this region is not merely reflective of the reduced degree of freedom. The χ² values (Table S4) observed for the basic region are slightly higher than those of the coiled-coil region, but considerably less than those observed for the extreme N- and C-terminal residues. Based on the lowest χ² value from analyses where τ_M was either fit as a parameter or held constant, residues at the ordered-disordered interface were classified as follows: residues 26, 27, and 54 were considered part of the coiled-coil region while residues 25 and 55–58 were considered disordered.

The resulting Model-free parameters are plotted in Figure 7. The trends in parameters are similar to those obtained in the current study from reduced spectral density mapping (Figure 5), although the order parameters in the basic region are reduced because the global value of τ_M assumed in Model-free analysis (16.9 ns) is larger than the local overall correlation times determined by reduced spectral density mapping. The order parameter (S²) has a mean value of 0.91 for the coiled-coil region (Table S4 and Figure 7A) and the value of this parameter decreases gradually along the basic region.

Figure 7.

Model-free from field-dependent analysis using full analysis with relax. Values of (A) S², (B) τ_M, (C) S_s², (D) τ_s, (E) S_f², and (F) τ_f are plotted vs. residue number. Overall correlation times (τ_M) were determined individually for residues in the coiled-coil region. τ_M was fixed at 16.9 ns for residues in the basic region and C-terminal residues, as denoted by the horizontal line in (B). Colors are as in Figure 4.

The acquisition of relaxation parameters at multiple static fields enables the study of multiple (fast and/or slow) internal motions ⁵⁷. The basic region of GCN4 has a fast internal process (Table S4 and Figure 7F) with a correlation time τ_f ≈ 40–70 ps. There is also evidence for motions with correlation times in this range in the coiled-coil region, although the uncertainty on these values is much greater. The motions that dominate the internal order parameter for the basic region actually have a slower correlation time, as shown in Figure 7C by the lower values of S_s² (lower order parameters imply a larger degree of conformational variability), relative to the higher values of S_f² (Figure 7E). These slower internal motions have a correlation time τ_s ≈ 1.4–2.5 ns (Figure 7D).

Discussion

Comparison of spectral density and Model-free analysis results

The Model-free parameters determined from spectral density mapping bear a strong similarity to those determined from full analysis with relax (Figure S3). The order parameters (S², Figures 5A, 7A, and S3A) are large in the coiled-coil region and decrease dramatically in the basic region toward the N-terminus. The values of S² in the basic region are somewhat larger if local overall correlation times are assumed in the model spectral density function, compared to values obtained when the overall rotational correlation time is fixed at the mean value for the coiled-coil domain. This reflects different averaging of effective correlation times in the two analyses. Strikingly, S_f² decreases to a plateau value (~0.6 in Figures 7E and S3E), while S_s² decreases dramatically to very low values at the N-terminus (Figures 7C and S3C). Values of S_f² (and consequently S²) are elevated around residues 14–20 and, to a slightly lesser extent, residues 5–9, although the overall magnitude is reduced when τ_M was fixed (Figures 5E, 7E, and S3E). The presence of such local regions of elevated order parameters independent of calculation method indicates they likely adopt transiently ordered conformations. The effective internal correlation times for residues in the basic region have narrow distributions, with average values of τ_f = 48.9 ps and τ_s = 1.6 ns for the analysis with fixed τ_M. (Again, the same qualitative behavior is observed if local overall correlation times are utilized, albeit with somewhat different correlation times.) The local correlation times (τ_M) determined from spectral density calculations and full Model-free analysis also are nearly identical in the coiled-coil region (Figures 5B, 7B, and S3B). These findings demonstrate that spectral density mapping using at least three static magnetic fields can generate effective local correlation times in the absence of assumptions about a global τ_M, thus demonstrating the feasibility of using Model-free analysis to study IDPs in some cases.

Consistency with previous studies of GCN4 dynamics

The τ_M of the coiled-coil residues determined by Model-free analysis has a mean value of 16.9 ns (Figure 7B). This value is lower than that determined previously ²⁶ (mean τ_M = 18.9 ns), which is likely due to transient aggregation at the higher sample concentration used in the earlier study ²⁶. In both this and the previous study, determination of dynamical parameters for the disordered region is enabled by the assumption that a single τ_M dominates global motions. Though the dynamics of intrinsically disordered proteins is a topic of ongoing study, molecular dynamics simulations do support this assumption ^30,62.

The Model-free derived order parameters determined using a fixed overall correlation time for the basic region (Figure 8, black) are in excellent agreement with those determined previously by NMR at a single static magnetic field of 11.7 T ²⁶ (Pearson’s r = 0.997 and Figure 8, blue) and by Robustelli, et. al ²⁷ (see trajectory 2, Figure 4 in the reference) using molecular dynamics simulations (r = 0.982 and Figure 8, orange). In particular, elevated order parameters are noted for two parts of the disordered region, referred to as helix 1 (H1, residues A5–R9) and helix 2 (H2, residues Q14–R20), believed to form transient helices which may help pre-order this region for binding of DNA substrate ³⁰. Similar elevations are observed for the multi-field NMR data, particularly for H2 (Figure 8 and Table S4).

Figure 8.

Comparison of order parameters (S²) for GCN4 as determined in the current study (black) to those determined by previously at a single static field of 11.7 T by Bracken, et. al ²⁶ (blue) and by Robustelli, et al. ³⁰ (orange) using a series of 100 ns molecular dynamics simulations.

Biological implications of structural fluctuations and dynamical rates

The binding of GCN4 to DNA requires the formation of the basic region helices that insert into the DNA major groove, potentially incurring a large entropic cost. The magnitude of this penalty is considerably reduced by the presence of helix-capping sequences, such as the one prior to H1, which nucleate transient helix formation ⁶³. The observed regions of elevated order parameters (H1 and H2), which are corroborated by previous NMR ²⁶ and molecular dynamics ³⁰ studies, are consistent with the formation of these structures. Estimates of conformational entropy derived from S² are generally consistent with estimates of conformational entropy derived from calorimetric measurements ²⁶.

The existence of such transient helices may also enable GCN4 to bind DNA with on-rates at or near that of the diffusion limit (~10¹⁰ M⁻¹s^{−1 64}) by pre-organizing the DNA binding domain. The correlation time of slow internal motions (τ_s) ranges between 1.4 and 2.5 ns, which is faster than both the binding rate of GCN4 to DNA (k_on ~10⁶–10¹⁰ M⁻¹s^{−1 65,66}, which gives k_on[DNA] ~10² s⁻¹, assuming μM ligand concentration) and the off rate (~10⁵–10⁶ s^{−1 67,68}). Thus, these large amplitude motions could facilitate formation and rearrangement of transient encounter complexes to yield the well-ordered protein-DNA complex structure. Collectively, these observations lend further evidence to the combined and subsequent roles of conformational selection and induced fit in GCN4 binding to DNA and for IDP target recognition, in general.

Conclusions

We have measured the backbone ¹⁵N spin relaxation rate constants of apo GCN4 bZip DNA-binding domain at four static magnetic fields and demonstrated that both reduced spectral density mapping and the Model-free formalism can be used to analyze the dynamics of an intrinsically disordered region. The order parameters (S²) obtained from Model-free analysis are highly similar to those obtained from spectral density mapping of GCN4 at a single static field ²⁶ and to molecular dynamics simulations ³⁰, while the internal dynamics parameters determined in the current study provide additional insight. Local regions with elevated order parameters in the basic region ^26,30 are consistent with structural pre-organization of nascent helices prior to binding of DNA substrate. Additionally, we are able to determine the internal correlation times for conformational dynamics of the basic region and find that the basic region undergoes large amplitude internal motions whose correlation time (τ_s ≈ 1.4–2.5 ns) would allow induced formation of the fully helical basic region within the lifetime of a protein-DNA encounter complex. Thus, binding of the GCN4 bZip domain to DNA involves the, possibly correlated, steps of selected-fit and induced-fit interactions.