Mechanisms of Allosteric Gene Regulation by NMR Quantification of μs-ms Protein Dynamics

Abstract

The trp RNA-binding attenuation protein (TRAP) is a paradigmatic allosteric protein that regulates the tryptophan biosynthetic genes associated with the trp operon in Bacilli. The ring-shaped 11-mer TRAP is activated for recognition of a specific trp-mRNA target by binding up to 11 tryptophan molecules. To characterize the mechanisms of tryptophan-induced TRAP activation we have performed methyl relaxation dispersion (MRD) nuclear magnetic resonance (NMR) experiments that probe the time-dependent structure of TRAP in the microsecond to millisecond “chemical exchange” time window. We find significant side chain flexibility localized to the RNA and tryptophan binding sites of the apo protein, and that these dynamics are dramatically reduced upon ligand binding. Analysis of the MRD NMR data provides insights into the structural nature of transiently populated conformations sampled in solution by apo TRAP. The MRD data are inconsistent with global two-state exchange, indicating that conformational sampling in apo TRAP is asynchronous. These findings imply a temporally heterogeneous population of structures that are incompatible with RNA binding, and substantiate the study of TRAP as a paradigm for probing and understanding essential dynamics in allosteric, regulatory proteins.

Introduction

Allosteric effects are pervasive in cellular mechanisms for regulating gene expression. The undecameric (11-mer) trp RNA-binding attenuation protein (TRAP) is a paradigmatic allosteric protein that regulates production of enzymes involved in biosynthesis of the amino acid tryptophan (Trp) in bacilli¹ via transcription attenuation and translation inhibition². When the cellular concentration of Trp is low, TRAP remains in its apo state, and an anti-terminator hairpin is formed in nascent trp-mRNA transcripts that enables transcription and translation of the encoded enzymes, and hence production of Trp (Fig. S1). As cellular concentration of Trp increases, the amino acid binds to TRAP, thus activating it for high-affinity binding to trp-mRNA. The interaction of holo (Trp-bound) TRAP with nascent RNA transcripts leads to formation of a transcriptional terminator, thus precluding downstream production of Trp. In some bacilli, binding of Trp-activated TRAP to RNA can be prevented through prior interaction with the Anti-TRAP protein, thus favoring Trp production³.

Qualitative solution NMR studies of this 91 kDa oligomer⁴, and quantitative thermodynamic studies⁵ suggest that TRAP activation involves changes in both structure and dynamics, such that the flexibility exclusive to the apo protein masks its RNA-binding surface. In turn, this localized disorder hinders detailed structural insights from crystallographic studies of apo TRAP⁶, whereas the structure of the Trp-bound state has been defined⁷. In the holo TRAP structure, the Trp ligand is completely buried and secluded from solvent; thus, in order for bound Trp to be released, thereby deactivating TRAP, holo TRAP must also be somewhat flexible (albeit in a manner distinct from apo TRAP, such that RNA and Anti-TRAP can bind). Moreover, the structure of holo TRAP appears nearly unchanged when bound to RNA^8-10, or to Anti-TRAP³, underscoring the importance of Trp binding to the mechanism of TRAP activation.

Severe line broadening in previous ¹⁵N-edited NMR studies of TRAP⁵ provided limited quantitative insights into the mechanism of TRAP activation. Here, we have used quantitative methyl-directed NMR-based chemical shift and relaxation dispersion methods to study the solution structure and dynamics of TRAP in its inactive apo and Trp-activated holo states. Experiments that focus on the sidechain methyl groups of Ile, Leu, and Val^{11, 12} reveal both structural differences between apo and holo TRAP, and a high degree of flexibility only in the apo protein. NMR experiments probing single- and multiple-quantum coherences, both acquired at two magnetic field strengths, enable both kinetic and structural insight into the conformational exchange processes exhibited by apo TRAP. Importantly, asynchrony in the detected dynamic processes reveals an underlying temporally heterogeneous population of structures that differ from the RNA binding, Trp-activated conformation, and underscores the role of protein dynamics in gene regulation by TRAP.

Results

Tryptophan binding alters the structure of TRAP: NMR CSPs (Δδ_H, Δδ_C)

Bacillus stearothermophilus TRAP is a 74-residue protein that adopts a beta sandwich fold with seven strands (A-G), and assembles into an axially-symmetric undecameric ring, with binding sites for Trp between adjacent protomers^{8, 13}. To study the structure and dynamics of TRAP sidechains, we prepared samples in which the methyl groups of Ile, Leu, and Val were isotopically labeled with ¹³C and ¹H, while other carbons were unlabeled and their attached hydrogens were deuterated. In addition, we substituted Ala 28 with Ile in order to probe the Trp-binding loop between strands B and C. (This point mutant binds both Trp and RNA with near-WT affinity, and exhibits similar structure and dynamics, (Figs. S2 and S3), and is hereafter referred to as “TRAP.” Residue numbers correspond to those of B. subtilis TRAP, matching the scheme used in the crystal structure of B. stearothermophilus TRAP, 1C9S.)

To monitor Trp-induced conformational changes in TRAP, ¹H-¹³C two-dimensional correlation spectra of the protein were acquired in its apo and Trp-bound holo states. These are of high quality (Fig. 1a), reflecting the eleven-fold symmetry of the molecule, and enable resolution and stereospecific assignment of all 29 labeled methyl groups in apo and holo TRAP. Upon binding Trp, the chemical shift perturbations (CSPs) for ¹H and ¹³C, Δδ_H and Δδ_C, provide a site-specific metric for the structural changes coincident with activation¹⁴ (Figs. 1a, S5); the magnitude of the CSPs are mapped to the structure of TRAP as observed in ternary complex with Trp and RNA (1C9S⁸). The largest CSPs map to the methyl probes nearest the Trp-binding site, including those in the inter-protomer interface, the BC loop and the RNA-binding surface (Fig. 2a). The core of the beta sandwich fold and base of the oligomeric ring exhibit no significant CSPs and thus appear structurally insensitive to Trp. These observations are consistent with the allosteric function of TRAP: Trp binding induces structural changes that propagate to the RNA-binding sites of the protein.

Fig. 1.

Chemical shift perturbations and methyl relaxation dispersion demonstrate site-specific changes in the structure and μs-ms dynamics of TRAP upon binding Trp. (a) ¹H-¹³C correlation spectra of apo TRAP (blue) and holo TRAP (red) at 25°C. Lines connect the apo and holo signals for each of 29 methyl probes. The signal for *Ile 28δ₁ at δ_C = 13.5 ppm in holo TRAP suggests this methyl group samples a minor state, which may reflect flexibility at the supra-ms timescale. (Inset in a) A single protomer from the 11-mer is shown in blue, with 11 bound Trp molecules in gold. (b) Medium to large dispersions exclusively in apo TRAP, but not holo TRAP, for Ile 22δ₁ and Leu 24δ₁ from ¹³C-SQ MRD at 25°C. Solid lines are fits to the site-specific two-state exchange model and dashed lines are fits to the no-exchange model. Uncertainties in the R ^Eff₂ values (see methods) were generally on the order of 1-3 Hz and smaller than symbols shown. For Leu 24δ₁, the double-headed arrow illustrates that the value of R_ex corresponds to the height of the dispersion curve.

Fig. 2.

Chemical shift perturbations and R_ex values mapped to 29 methyl probes in a model based on the crystal structure of holo TRAP. One TRAP protomer is shown in blue, neighboring protomers in black, bound Trp molecules in gold, and RNA shown in green spheres only in the inset figure. (a) ¹H and ¹³C CSPs upon Trp binding, Δδ_H and Δδ_C, indicate the largest structural differences between apo and holo TRAP are at the Trp-binding loop, the inter-protomer interface and regions of the core near the Trp pocket and RNA surface. The color scale ranges from white (0 ppm) to red (0.37 ppm for ¹H and 1.3 ppm for ¹³C). (b) Exchange broadening, R_ex, is largest in the Trp binding loop, the inter-protomer interface and regions of the core beneath the Trp pocket and the RNA surface. In contrast, methyls at the base report R_ex near zero. The color scale ranges from white (0 /s) to red (73 /s). (Inset) The RNA-binding surface coincides with regions of large apo-holo CSPs and apo R_ex.

Tryptophan binding eliminates the flexibility of apo TRAP: MRD exchange-broadening (R_ex)

To examine the hypothesis that protein dynamics is important for the function of TRAP, we investigated the dynamics of apo and holo TRAP in the μs-ms time window by performing ¹³C single quantum methyl relaxation dispersion NMR experiments (¹³C-SQ MRD¹⁵). The resulting “relaxation dispersion curves,” $R_2^{Eff}\left({\nu }_{\mathrm{CPMG}}\right)=R_2^0+R_{ex}\left({\nu }_{\mathrm{CPMG}}\right)$, encapsulate effects from dynamic processes that enable the protein to transiently populate alternative conformations with different chemical shifts. Fitting each curve reliably yields the dynamic metric R_ex, the contribution of exchange to the transverse relaxation rate (Fig. 1b)¹⁶. We found apo TRAP to be remarkably flexible in the μs-ms time window, with 23 of 29 methyl probes yielding non-zero R_ex (Figs. 2b, S4, and S5). These values are largest in the Trp-binding loop, the inter-protomer interface, and regions of the core beneath the Trp pocket and the RNA surface, whereas R_ex vanishes near the base (Fig. 2b). This localized flexibility may both permit Trp-binding and prevent RNA-binding, thus enabling the functions of apo TRAP without disrupting the integrity of its oligomeric structure. Upon binding Trp, R_ex is reduced significantly from an average of 14±18 /s for 29 apo signals to 1±2 /s for 30 holo signals (Figs. 1b, S4, and S5). It is worth noting that methyl groups experiencing conformational exchange may nevertheless exhibit zero R_ex if the processes are too fast or slow and/or involve alternative states that are not sufficiently populated or distinguished via chemical shift¹⁶. However, the multitude of NMR probes provides confidence in the conclusion that μs-ms dynamics present in apo TRAP are almost entirely eliminated in holo TRAP, in response to Trp binding and activation.

Describing apo TRAP dynamics: evidence for independent motions

The observed values of R_ex suggest important μs-ms dynamics that are unique to the inactive apo state of TRAP (Figs. 1b, 2b, S4, S5). To understand how these dynamics affect the function of apo TRAP, we sought to address the extent to which these motions reflect a “global” dynamic process involving all methyl probes moving in synchrony, versus set of “site-specific” motions wherein different parts of the protein move independently of one another¹⁶. Hence, additional MRD data were acquired and analyzed using a site-specific two-state exchange model A↔B, which comprises the kinetics (k_ex = k_A + k_B), thermodynamics (P_A = k_B / k_ex) and structural changes (|Δω_H|, |Δω_C|), for each methyl probe in apo TRAP. In this way, the presence of global motions can be evidenced by the uniformity of site-specific k_ex and P_A values.

A rigorous fitting procedure applied to signal intensities from the 29 methyl probes reveals that 18 of 29 exhibit exchange (R_ex > 0 and therefore k_ex > 0), 13 of 18 yield reliable k_ex, and 5 of 13 also yield reliable P_A, |Δω_H|, and |Δω_C|, in part because they are not in the fast-exchange regime (Table S2). These fitted parameters suggest that some TRAP side chains undergo independent motions, as evidenced by non-uniform k_ex values (Fig. 3), which range from ~1000 /s at Leu 24δ₂ at the inter-protomer interface to ~2400 /s at Ile 28δ₁ in the Trp-binding loop (average 1629±366 /s; N = 13). The P_A values corroborate this result by a similarly wide distribution (Fig. 4a), from 87.3±2.5% at Leu 24δ₂ to 98.6±0.62% at Ile 22δ₁ at the RNA surface (average 94.8±4.4%; N = 5). Moreover, some probes which appear dynamically similar by values of k_ex, such as Ile 22δ₁, Leu 24δ₁, and Leu 24δ₂, are shown to be different by values of P_A, which quantifies the energetic preference of their respective A states.

Fig. 3.

Site-specific exchange rate constants, k_ex, suggest dynamics in apo TRAP is asynchronous, not a “global” exchange process. (a) MRD data for Leu 24δ₂ and Ile 28δ₁ illustrate the difference between the slowest and fastest exchanging probes, at 1047±104 /s and 2391±238 /s, respectively. (b) Of the 29 methyl probes, 11 exhibit zero R_ex (black rectangles at k_ex = 0), 13 of 29 exhibit exchange from which site-specific k_ex can be determined (black squares, with error bars obtained from standard deviations from Monte Carlo error analysis), and 5 of 29 exhibit exchange with ill-defined k_ex, due to poor signal to noise (magenta circles at k_ex = average(k_ex) with error bars spanning min(k_ex) to max(k_ex)). Because some pairs of probes correspond to the same residue number, the second probe is offset by 0.5 residue units (e.g., Val 10γ₁ and Val 10γ₂ are shown at Residue = 10 and 10.5, respectively). (c) k_ex values mapped to the structure of holo TRAP, with a color scale ranging from white (0 /s) to red (2400 /s); magenta designates k_ex > 0, but undefined.

Fig. 4.

Exchange kinetics and chemical shift differences obtained from relaxation dispersion data for methyl probes in apo TRAP. (a) For the 5 methyl probes that are not in the fast-exchange regime, the fits to RD data yield the population fraction, P_A. The spread in these values quantitatively illustrates the extent to which these probes independently sample their alternate local conformations. In addition to site-specific fits (black), to consider the effect of a hypothetical concerted motion in TRAP, a global fit was performed that imposes a uniform k_ex and P_A for all probes, each fixed to the average value (red circle). (b) Site-specific chemical shift differences from MRD, |Δω_C|, compared to the Trp-induced CSP |Δδ_C| (Figs. 1a and S5) for methyls analyzed site-specifically (black square), or globally (red circles). The observation that most data lie above the diagonal (i.e., |Δω_C| > |Δδ_C|) suggests that apo TRAP samples conformations that exceed the structural differences between the apo and holo forms of the protein. All error bars are standard deviations from Monte Carlo error analysis, except for the “Global fit” errors in (a), which correspond to standard deviations from site-specific k_ex and P_A, and for the Δδ_C errors in (b), which correspond to the line width of each NMR signal. The curved dotted line indicates the difference in |Δω_C| values between the global fit and site-specific fit, for both Ile 22δ₁ and Ile 28δ_1.

Considering the sparse data and the simplifying advantages to detailed analysis by assuming global two-state exchange, we examined whether the data could be reasonably explained by a global dynamic process by two fitting procedures. First, a global fit which fixes k_ex and P_A to their average values, while optimizing site-specific |Δω_H|, |Δω_C|, and $R_2^0$, is unable to adequately fit several signals whose site-specific fits are far from this average, as evidenced by non-random residuals (Fig. S8). Second, a global fit of the fastest-exchanging probe, Ile 28δ₁, with either of the two slowest-exchanging probes, Leu 24δ₁ or Leu 24δ₂, also appears inadequate, even when the shared k_ex and P_A values are variable fitting parameters (Fig. S9). Finally, although these data could be fit using more complex models of exchange such as global three-state or two-state and a local jump, the additional model parameters would increase uncertainty in the fitted parameters with only modest improvements in the residuals. Hence, these simple two-state analyses are consistent with the interpretation that μs-ms dynamics in apo TRAP is asynchronous, at least in part, with different methyl groups experiencing different exchange processes. By comparison, holo TRAP exhibits more conformational coherence in this time window, as per the small values of R_ex (Figs. S4, S5).

Apo TRAP samples divergent structures: MRD chemical shifts (Δω)

The magnitude of chemical shift differences between exchanging A and B states, |Δω_H| and |Δω_C|, were obtained from fits to the MRD data for the five methyl probes. Here, we focus on |Δω_C| because it is a more robust indicator of sidechain conformational change than its ¹H counterpart, which is strongly influenced by through-space effects^{14, 17}. Although the magnitude of a chemical shift change is not a perfect metric for the magnitude of structural change, the finding that |Δω_C| for these methyl probes exceeds the magnitude of the shift perturbations induced by Trp binding, |Δδ_C|, suggests that these methyl probes in apo TRAP exhibit structural excursions in excess of the differences between the apo and Trp-bound states (Fig. 4b). For example, Ile 22δ₁ exhibits a mere |Δδ_C| = 0.1 ppm shift upon Trp-binding, but in the apo state, the sampled orientations differ by |Δω_C| = 1.5 ppm! This structural interpretation holds even if exchange kinetics are considered globally uniform, wherein |Δω| values can be extracted for more than five probes (Figs. 3 and 4a). Hence, the inferred high degree of conformational sampling, which is exclusive to the apo state, is consistent with the dynamics of apo TRAP both masking the RNA binding site and making the otherwise-secluded Trp-pocket accessible for ligand entry.

Discussion

Solution structure of apo TRAP

Trp-induced activation of TRAP likely requires changes in both structure and dynamics^4,5. In order to understand the unique structural features of apo TRAP that preclude RNA binding, we interpret the CSPs (Table S1) as perturbations to the holo TRAP crystal structure (1C9S⁸). In general, the ¹H shift δ_H is strongly dependent on through-space effects from electron-rich functional groups, whereas the ¹³C shift δ_C encapsulates through-bond effects from side chain structure^{14, 17}. In other words, δ_C reports methyl orientation relative to its side chain, whereas δ_H reports methyl orientation relative to its local environment, and therefore, reports the conformations of adjacent residues. Although we note that the magnitude of chemical shift changes need not necessarily be linearly correlated to a unique conformational coordinate, this analysis (detailed in Table S1) forms the basis for the following structural hypotheses describing the inactive apo state of TRAP.

1. The observation that CSPs are localized to the vicinity of the Trp-binding pocket and RNA-binding site (Fig 2a) suggest that RNA binding to apo TRAP is precluded by only a sparse set of highly localized uniquely-apo side chain conformations; this implies that the structural component of the TRAP activation requires only a few key intramolecular interactions.

2. The small Δδ_H and Δδ_C from Val 21γ₁, which is proximal to bound Trp (Fig. 2a), might be explained by a conformational change that allows either His 33 or His 34¹³ to occupy the empty pocket in apo TRAP. Such a conformational change could conceivably replace the effects on δ_H from the Trp ring current with those from the His sidechain, yet without facilitating other intramolecular contacts that stabilize the activated conformation of TRAP. Notably, mutation of each of these conserved histidines to Ala results in binding defects to both Trp and RNA¹⁸. (In the crystallographic model of apo TRAP, the sidechain of Arg 31 is modeled in the Trp-binding pocket, albeit with weak electron density⁶.)

3. Methyl CSPs suggest that the conserved Phe 32¹³, which contacts both RNA^{8, 18} and Anti-TRAP³ in their respective complexes, adopts a different orientation in apo TRAP. This hypothesis is primarily evidenced by the adjacent Ile 22δ₁, which reports only a small change in sidechain structure upon Trp binding, via Δδ_C, but a large change in local magnetic field, via Δδ_H (Fig 2a). This pattern implies that Phe 32 has reoriented upon Trp binding because it is the only proximal functional group that could magnetically shield the structurally-undisturbed Ile 22. Additional support for this hypothesis arises via large Δδ_H in Leu 24δ₁ and Leu 24δ₂, but is confounded by their proximity to His 34 and the Trp ligand, both of which may contribute to the observed Δδ_H.

Dynamic conformational sampling by apo TRAP

In order to synthesize our knowledge regarding the role of dynamics in the functions of apo TRAP, we interpret the two-state exchange parameters k_ex, P_A, |Δω_H|, and |Δω_C| from the MRD experiments (Tables S1 and S2). The observation of pervasive μs-ms dynamics via k_ex (Fig. 3c) indicates that the side chains of apo TRAP are nearly uniformly flexible, except near the base of the ring, and suggests that TRAP activation involves a relatively global restriction in protein dynamics (as opposed to the sparse set of structural changes induced by Trp binding, as reported by CSPs, Fig. 2).

Furthermore, based on site-specific differences in k_ex and/or P_A (Figs. 3b, 4a), there appear to be multiple independent modes of motion in apo TRAP, which are reported on by methyl side chains at the Trp binding loop, at the inter-protomer interface, and at the core of each protomer (n.b., this independence is amplified in the context of the TRAP 11-mer, which is relevant for RNA binding, if each protomer is independently flexible). Interestingly, the Leu 24 methyl groups, δ₁ and δ₂, report different dynamic experiences (Fig 4a), presumably because they probe distinct structural locations of TRAP. Specifically, Leu 24δ₁ is pointed toward the protomer core in holo TRAP, and reports a large |Δω_H| of 0.1±0.02 ppm in apo TRAP, which likely results from the aromatic sidechain of Phe 32. In contrast, Leu 24δ₂ is pointed toward the inter-protomer interface in holo TRAP, and reports a near-zero |Δω_H| of 0±0.02 ppm. This result makes it unlikely that the dynamics of apo TRAP involve coherent sampling of a B state structure with a particular function (e.g., a holo-like state). Instead, we suggest that dynamic incoherence in apo TRAP ensures structural heterogeneity between adjacent protomers, thereby preventing population of conformations of the TRAP ring that are active for binding to RNA or Anti-TRAP; the dynamics likely also function locally to permit binding and dissociation of Trp.

Finally, the magnitude of conformational sampling in apo TRAP is relatively large, as indicated by the site-specific values of |Δω_C| (Fig 4b). This result underscores the importance of the observed dynamic excursions (i.e., they should not be ignored in a mechanistic description of TRAP), and clarifies the magnitude of conformational restriction that is coincident with Trp-binding and subsequent activation.

Dynamics of holo TRAP

Holo TRAP exhibits only minor flexibility in the μs-ms time window, most apparent under the RNA-binding surface and inter-protomer interface via Ile 22δ₁ and Ile 45δ₁ (Figs. 1b and S4). Exchange at these sites is slower and of smaller magnitude than its apo counterpart, consistent with activation via altered dynamics. Moreover, slower dynamics in the BC loop may allow sampling a conformation that permits release of bound Trp (Fig. 1a).

Mechanism for allosteric activation of TRAP

Protein dynamics are becoming broadly understood as necessary for enabling the allosteric behavior of macromolecules^19-21, whether allostery occurs through induced fit²² or conformational sampling²³ mechanisms. In the case of TRAP, the data suggest the undecameric ring exhibits both types of behaviors. Asynchronous conformational sampling at the protomer level makes it unlikely that multiple adjacent protomers will adopt a holo-like conformation, though such conformations can be stabilized in apo TRAP at reduced temperatures⁶. The conformational sampling likely also involves conformations that enable binding of Trp to an otherwise solvent-secluded site. Upon binding of Trp to one or multiple binding sites, the energetics of the conformational landscape are likely dramatically shifted in an induced-fit manner²⁴ that favors structural, if not dynamic, synchrony between adjacent protomers, thereby favoring the activated state of TRAP.

In addition to supporting this general premise for the role of dynamics in allostery, the findings reported here move beyond this broader perspective to provide site-specific insight into the manner by which protein dynamics enable the function of apo TRAP. Analysis of methyl chemical shift perturbations and relaxation dispersion suggests that apo TRAP is characterized by incoherent μs-ms dynamic motions (Figs. 3 and 4a) that may both enable Trp binding and prevent RNA binding in the absence of adequate amounts of Trp. In contrast, Trp-activated holo TRAP is characterized by a discontinuous set of structural adjustments (Fig. 2a), and broader attenuation of μs-ms dynamics (Figs 1b and 5) that accommodate binding to RNA. Moreover, this extensive conformational restriction has been corroborated by a large negative heat capacity change ΔC_p upon Trp binding⁵. Thus, allosteric activation of TRAP occurs via (1) a sparse set of localized, structural changes, and (2) a global change in incoherent protein dynamics. This finding underscores the importance of dynamics in TRAP function and suggests that attenuation of TRAP dynamics may be sufficient to enable RNA binding, whether induced by Trp binding, mutagenesis^{25, 26} or reduced temperatures⁶. This study substantiates the role of TRAP as a paradigm for probing and understanding essential dynamics in allosteric, regulatory proteins.

Fig. 5.

Tryptophan binding alters the conformational landscape of TRAP, which permits distinct functions of the apo and holo states. Apo TRAP dynamics permit binding to Trp, yet not to trp-mRNA. Hypothetically, this requires flexibility in the Trp loop and the core, which links the Trp pocket and RNA surface. As these motions are incoherent, the inactive protein is characterized by a “rugged” distribution of conformations in the μs-ms time window. In contrast, holo TRAP functions to bind trp-mRNA, and to release bound Trp. Activation by Trp attenuates the μs-ms flexibility, thus focusing the distribution of conformations and imparting a large negative heat capacity change ΔC_p⁵, which may introduce the RNA scaffold. The μs-ms dynamics are quantified via R_ex from ¹³C-SQ MRD at 25°C, and are color-mapped to 29 sites in each of 11 protomers of the apo and holo donuts. The color scales range from white (0 /sec, more rigid) to red (73 /sec, more flexible).

Materials and Methods

Sample preparation

TRAP mutagenesis, expression, and purification protocols were described previously⁴, with minor alterations. Mutagenesis was performed using the Stratagene QuikChange method using the WT B. stearothermophilus gene as the template and oligonucleotide primers designed to change Ala 28 to Ile. Candidate clones were sequenced by the Roswell Park Biopolymers sequencing facility and a clone with the desired substitutions was transformed into E. coli BL21(DE3). Three isotope labeling schemes were used: (1) U-[²H, ¹³C, ¹⁵N], ILV-[¹³CH₃]²⁷ for total correlation spectroscopy (TOCSY) and out-and-back spectra, (2) 10%-[¹³C] for stereo-assignments²⁸, and (3) U-[²H, ¹⁵N], ILV-[¹³CH₃] for relaxation measurements²⁹. Samples for resonance assignments were 600-900 μM TRAP (11-mer) in H₂O NMR buffer (100 mM NaCl, 50 mM NaPO₄, pH 8.0 at 25°C, 0.02% NaN₃), while MRD spectra were recorded with 130-145 μM TRAP 11-mer in D₂O NMR buffer.

Molecular visualization

Pymol (http://pymol.sourceforge.net) was used to generate figures and introduce the A28I in silico mutation to 1C9S⁸.

NMR spectroscopy

Apo and holo WT TRAP methyl signals were assigned using several experiments, NMR samples (1) and (2), and backbone assignments⁴, all at 50-55°C. Assignments were transferred from WT to A28I TRAP by spectral comparison (Fig. S2). Apo TRAP was assigned from six NMR spectra: (1) 3D C(CO)NH-TOCSY, (2) 3D H(CCO)NH-TOCSY, (3, 4, 5) 2D methyl “out and back” experiments²⁷ correlating (C^m−x, H^m) where x = {0, 1, 2} is the number of C-C magnetization-transfers from methyl carbon towards backbone, and (6) a 2D ¹³C-edited ¹H-¹H NOESY. Holo TRAP was assigned from five NMR spectra: (1) 3D C(CO)NH-TOCSY, (2) 3D H(CCO)NH-TOCSY and the methyl “out and back” experiments. Stereo-specific assignments for apo and holo TRAP were obtained from a 2D non-decoupled ¹H, ¹³C-HSQC²⁸.

Dispersion curves for each of 4 MRD conditions were obtained by recording 12 2D spectra: one reference spectrum with T = ν_CPMG = 0, and 11 CPMG spectra with T = 20 ms acquired in random order using ν_CPMG = 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1000 Hz. The 4 MRD conditions consisted of ¹H,¹³C-MQ³⁰, acquired twice with different ¹³C carrier frequencies³⁰, or ¹³C-SQ¹⁵: (1) 25°C, 800 MHz, MQ, (2) 25°C, 800 MHz, SQ (apo and holo), (3) 25°C, 600 MHz, MQ, and (4) 25°C, 600 MHz, SQ. Processing, assignment, and analysis were conducted with NMRPipe³¹ and NMRViewJ³². Temperatures were calibrated with ethylene glycol, and chemical shifts were referenced with DSS.

MRD analysis

Dispersions were calculated via $R_2^{Eff}=\ln (I\left({\nu }_{\text{CPMG}}\right)∕I_0)∕T_{CPMG}$, where I(ν_CPMG) is the signal intensity in the spectrum with refocusing duration T_CPMG at frequency ν_CPMG, and I₀ is the intensity in the spectrum with no refocusing block. Intensities were extracted using NMRPipe³¹, with errors via standard deviation from repeat experiments. Each dispersion curve was fit with a custom software package, GUARDD (Kleckner, et al., in press; http://code.google.com/p/guardd/), programmed in-house using MATLAB (The Mathworks, Inc.). Dispersion curves were fit to Carver-Richards-style formulae that describe two-site exchange A↔B for MQ or SQ dispersions^{30, 33}. Each curve requires specification of 5 types of parameters: (1, 2) |Δω_H| and |Δω_C|, the ppm magnitude of ¹H and ¹³C chemical shift differences between states A and B (note: |Δω_H| is fixed to zero only for ¹³C-SQ curves), (3) P_A, the equilibrium population fraction of state A, (4) k_ex = k_A + k_B,, the rate of exchange between states A and B. k_A and k_B are the rates of exchange from A→B and B→A, respectively, with k_A = (1-P_A)k_ex and k_B = P_Ak_ex. (5) $R_2^0$, the transverse relaxation rate in the absence of exchange assuming $R_2^0=R_{2\mathrm{A}}^0\approx R_{2\mathrm{B}}^0$^{33, 34}. When fitting multiple dispersion curves, these 5 parameters were shared by way of three different models. (A) The site-specific model aggregates up to all four curves from a single NMR probe into a group (e.g., Ile 28δ₁), and optimizes shared values of |Δω_H|, |Δω_C|, P, and k_ex for all curves, as well as one $R_2^0$ for each curve. (B) The group-optimized model aggregates curves from multiple NMR probes into a group (e.g., two probes: Ile 28δ₁ + Leu 24δ₁), with variable P_A and k_ex used for all curves in the group, and variable |Δω_H| and |Δω_C| for each set of curves from the same NMR probe, and one variable $R_2^0$ for each curve. (C) The group-fixed model is the same as (B) except that P_A and k_ex are fixed for all curves in the group, instead of being variable fitted parameters (because for large groups, varying P_A and k_ex in addition to site-specific |Δω| makes it difficult to find the global best fit). In general, RD data can be challenging to interpret because of their multivariate nature^{35, 36}, and because P_A and Δω are unknown if the NMR probe is in the fast-exchange regime (k_ex >> Δω, or α→2.0, where α = d(ln(R_ex )) d(ln(Δω)) ³⁷). Hence, to assess the sensitivity of the final fit to the initial conditions, the data in each group for models (A) and (B) were fit multiple times using a grid search over 4D parameter space which varied |Δω_H| from [0.01, 0.1] ppm in 2 steps, |Δω_C| from [0.1, 2.0] ppm in 3 steps, P_A from [0.8, 0.999] in 4 steps and k_ex from [500, 3,500] /s in 4 steps. Each grid point specified initial conditions for the fit optimization, which minimized the sum of fitted residuals, χ², via MATLAB’s fmincon function. For each group, a χ² map was produced and visually inspected to either (a) select the best fit, or (b) conclude that the data cannot be fit accurately (e.g., due to multiple apparently-reasonable fitting solutions). If a single reasonable fit was obtained, 100 iterations of Monte Carlo error estimation was used to assess the sensitivity of the final fit to noise in the data³⁸. For many probes, fast-exchange precluded knowledge of P_A, |Δω_H|, and |Δω_C|, as evidenced by a wide range in parameter values that yield an equivalent quality of fit, assessed via χ², as well as the calculated value of α which approached 2.

Abbreviations

TRAP

trp RNA-binding attenuation protein

Trp

tryptophan

NMR

nuclear magnetic resonance

CSP

chemical shift perturbation

MRD

methyl relaxation dispersion

SQ

single quantum

MQ

multiple quantum

R_ex

NMR exchange broadening

sec

second

s

second

ms

millisecond (10⁻³ s)

μs

microsecond (10⁻⁶ s)

Δδ

chemical shift difference upon binding tryptophan

Δω

chemical shift difference upon exchange from A state to B state

P_A

population of A state

k_ex

total exchange rate between A and B states

k_A

exchange rate from A to B

k_B

exchange rate from B to A

α

scaling parameter for timescale of chemical exchange