Dynamics of GCN4 Facilitate DNA Interaction: A Model-Free Analysis of an Intrinsically Disordered Region
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\xe2\x80\x932146] and correlate well with molecular dynamics simulations [Robustelli, et al. (2013) J. Chem. Theory Comput., 9, 5190\xe2\x80\x935200]. 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 (\xcf\x84s \xe2\x89\x88 1.4\xe2\x80\x932.5 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<!>Sample preparation<!>NMR spectroscopy<!>Data processing and analysis<!>Determination of relaxation parameters<!>Spectral density mapping<!>Model-free analysis<!>Assignment of GCN4 amide resonances<!>Fast timescale dynamics of GCN4<!>Reduced spectral density analysis of GCN4<!>Model-free analysis of GCN4<!>Comparison of spectral density and Model-free analysis results<!>Consistency with previous studies of GCN4 dynamics<!>Biological implications of structural fluctuations and dynamical rates<!>Conclusions
<p>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.</p><p>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.</p><p>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.</p><p>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.</p><p>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.</p><p>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.</p><!><p>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.</p><!><p>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.</p><p>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.</p><p>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.</p><!><p>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.</p><!><p>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.</p><p>The 10% trimmed mean correlation time (τM) 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 (τM), 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 τM according to the following equations: 
1R1=R10(τM/τM0)(1+ωN2τM02)/(1+ωN2τM2)R2=(R20-0.5R10)(τM/τM0)+0.5R1 where ωN is the 15N frequency at 16.45 T. R10, R20, and τM0 are the respective original R1 and R2 relaxation rates and correlation time, and R1, R2, and τM 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 Γauto vs (3d2 + 4c2)/6, J(ωN) vs ωN−2, and J(0.870ωH ) vs (0.870ωH) −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.</p><!><p>The 15N relaxation rate constants are given by: 
2R1=(d2/4){J(ωH-ωN)+3J(ωN)+6J(ωH+ωN)}+c2J(ωN)R2=(d2/8){4J(0)+J(ωH-ωN)+3J(ωN)+6J(ωH)+6J(ωH+ωN)}+(c2/6){4J(0)+3J(ωN)}σNH=(d2/4){-J(ωH-ωN)+6J(ωH+ωN)}=R1(NOE-1)γN/γH in which the dipolar coupling constant is 
d=(μ0hγHγN/8π2)rNH-3, μ0 is the permeability of free space, h is Planck's constant, rNH is the average amide bond length (1.02 Å), the CSA coupling constant is c = ΔσωN/31/2, Δσ is the amide CSA (−172 ppm), ωN and ωH 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(ωN) (at each static field) and J(0.870ωH) (at each static field): 
3Γauto=R2-0.5R1-0.454σNH=J(0)(3d2+4c2)/6J(ωN)={R1-1.249σNH}/(3d2/4+c2)J(0.870ωH)=4σNH/(5d2)</p><p>The value of J(0) was obtained from the slope of a linear fit through the origin of Γauto vs. (3d2 + 4c2)/6 for all four static fields.</p><p>The most complex spectral density function consistent with the acquired data is an extended version of the Model-free spectral density function 57: 
4J(ω)=25{S2τM1+ω2τM2+(Sf2-S2)τs′1+ω2τs′2+(1-Sf2)τf′1+ω2τf′2} in which S2 is the square of the generalized order parameter and τM is the (effective) overall rotational correlation time for a given N-H bond vector. Ss2 = S2/Sf2, and Sf2 are the squares of the generalized order parameters for intramolecular motions with slow, τs, and fast, τf, correlation times, respectively. τs′, and τf′ are the inverse sums of the respective correlation time with τm: 
τs′=(1/τM+1/τs)-1 and 
τf′=(1/τM+1/τf)-1. This equation assumes that the stochastic processes governing τM, τs, and τf are statistically independent, which approximately holds if the processes are time-scale separated τM ≫ τs ≫ τf). If 
(0.870ωHτf′)2≪1 and 
(ωNτs′)2≫1, then the spectral density function becomes a linear function of (0.870ωH)−2 58: 
5J(0.870ωH)=mH(0.870ωH)-2+bH in which: 
6mH=25{S2/τM+(Sf2-S2)/τs′}bH=25(1-Sf2)τf′</p><p>Similarly, if 
(ωNτs′)2≪1 and (ωNτM)2 ≫ 1, then the spectral density function becomes a linear function of ωN−2: 
7J(ωN)=mNωN-2+bN in which: 
8mN=25S2/τMbN=25{(Sf2-S2)τs′+(1-Sf2)τf′}</p><p>If the linear relationships hold for a given set of field-dependent relaxation measurements, then the values mN, bN, mH, and bH, together with</p><p>
9J(0)=25{S2τM+(Sf2-S2)τs′+(1-Sf2)τf′} are sufficient to determine the five parameters in Equation 4: 
10S2=52[{J(0)-bN}mN]1/2τM=[{J(0)-bN}/mN]1/2Sf2=S2+52[{bN-bH}{mH-mN}]1/2τf′=52bH/(1-Sf2)τs′=[{bN-bH}/{mH-mN}]1/2</p><p>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.</p><!><p>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 τM). 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 τM). For residues located in or near the disordered region (residues 3–27 and 54–58), the correlation time was fixed to the average τM 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: 
11Model0:J(ω)=25τmModel1:J(ω)=25τm[S21+(ωτm)2]Model2:J(ω)=25τm[S21+(ωτm)2+(1-S2)(τe+τm)τe(τe+τm)2+(ωτeτm)2]Model5:J(ω)=25τm[S21+(ωτm)2+(Sf2-S2)(τs+τm)τs(τs+τm)2+(ωτsτm)2]Model6:J(ω)=25τm[S21+(ωτm)2+(1-Sf2)(τf+τm)τf(τf+τm)2+(ωτfτm)2+(Sf2-S2)(τs+τm)τs(τs+τm)2+(ωτsτm)2]</p><p>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.</p><!><p>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).</p><!><p>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).</p><p>Plots of Γauto vs. (3d2 + 4c2)/6, J(ωN) vs. ωN−2, and J(0.870ωH) vs. (0.870ωH)−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 Γauto 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 Γauto vs. B02 performed with Rex = 0 and with Rex 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 τM, τs, and τe represent effective fits to a more complex distribution of correlation times.</p><!><p>The values of S2τM, S2/τM, 
(Sf2-S2)τs′,(Sf2-S2)/τs′, and 
(Sf2-S2)τs′ 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 
(Sf2-S2)τs′ vs. S2τM, 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 τf and τs with extremely large uncertainties, because the corresponding Sf2 or Ss2 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 τM 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 S2τM, S2, and τM for all residues using the two analyses.</p><!><p>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 (τM), and then the mean τM 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 τM values. Based on the modest diffusion tensor anisotropy 2Dzz/(Dxx+Dyy) = 1.25 determined from the local τM 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 (τM) 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 (τe, model 2). When τe < 100 ps, the internal motion was classified as fast (τf), otherwise it was slow (τs). 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 τf and Sf2 and the slower by τs and Ss2, which are determined as described above. Given the lack of evidence for chemical exchange, as determined by analysis of Γauto, additional models containing an Rex term were not considered.</p><p>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 τM 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 τM 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.</p><p>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 τM 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.</p><p>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 τf ≈ 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 Ss2 (lower order parameters imply a larger degree of conformational variability), relative to the higher values of Sf2 (Figure 7E). These slower internal motions have a correlation time τs ≈ 1.4–2.5 ns (Figure 7D).</p><!><p>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, Sf2 decreases to a plateau value (~0.6 in Figures 7E and S3E), while Ss2 decreases dramatically to very low values at the N-terminus (Figures 7C and S3C). Values of Sf2 (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 τM 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 τf = 48.9 ps and τs = 1.6 ns for the analysis with fixed τM. (Again, the same qualitative behavior is observed if local overall correlation times are utilized, albeit with somewhat different correlation times.) The local correlation times (τM) 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 τM, thus demonstrating the feasibility of using Model-free analysis to study IDPs in some cases.</p><!><p>The τM 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 τM = 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 τM 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.</p><p>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).</p><!><p>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.</p><p>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 (τs) ranges between 1.4 and 2.5 ns, which is faster than both the binding rate of GCN4 to DNA (kon ~106–1010 M−1s−1 65,66, which gives kon[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.</p><!><p>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 (τs ≈ 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.</p>