Propagation of the Allosteric Signal in Phosphofructokinase from Bacillus stearothermophilus Examined by Methyl-Transverse Relaxation-Optimized Spectroscopy Nuclear Magnetic Resonance

Abstract

Phosphofructokinase from Bacillus stearothermophilus (BsPFK) is a 136 kDa homotetromeric enzyme. Binding of the substrate, fructose 6-phosphate (Fru-6-P), is allosterically regulated by the K-type inhibitor phosphoenolpyruvate (PEP). The allosteric coupling between the substrate and inhibitor is quantified by a standard coupling free energy that defines an equilibrium with the Fru-6-P-bound and PEP-bound complexes on one side and the apo form and ternary complex on the other. Methyl-transverse relaxation-optimized spectroscopy (Me-TROSY) nuclear magnetic resonance was employed to gain structural information about BsPFK in all four states of ligation relevant to the allosteric coupling. BsPFK was uniformly labeled with ¹⁵N and ²H and specifically labeled with δ-[¹³CH₃]-isoleucine utilizing an isotopically labeled α-keto acid isoleucine precursor. Me-TROSY experiments were conducted on all four ligation states, and all 30 isoleucines, which are well dispersed throughout each subunit of the enzyme, are well-resolved in chemical shift correlation maps of ¹³C and ¹H. Assignments for 17 isoleucines were determined through three-dimensional HMQC-NOESY experiments with [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK and complementary HNCA and HNCOCA experiments with [U-²H,¹⁵N,¹³C]-BsPFK. The assignments allowed for the mapping of resonances representing isoleucine residues to a previously determined X-ray crystallography structure. This analysis, performed for all four states of ligation, has allowed specific regions of the enzyme influenced by the binding of allosteric ligands and those involved in the propagation of the allosteric effect to be identified and distinguished from one another.

Allosteric inhibition of enzyme activity can involve substantial conformational changes that relate to the basis of inhibition such as that exhibited by the classical allosteric enzyme aspartate transcarbamoylase. The large conformational change this enzyme undergoes has been studied extensively with biophysical techniques ranging from analytical ultracentrifugation¹ to X-ray crystallography² and nuclear magnetic resonance (NMR).^3,4 However, some allosteric modifications of enzyme activity seem to occur without obvious causal structural perturbations. A case in point is phosphofructokinase from Bacillus stearothermophilus (BsPFK, UnitProt entry A7ZUC9), the enzyme that catalyzes the phosphorylation of fructose 6-phosphate (Fru-6-P) by MgATP to produce fructose 1,6-bisphosphate. BsPFK exhibits a decrease of >2 orders of magnitude in the binding affinity of Fru-6-P upon the binding of the strictly K-type allosteric inhibitor phosphoenolpyruvate (PEP), yet the two most obvious structural consequences of PEP binding, the positioning of the negative charge carried by Glu161 in the Fru-6-P binding site prior to Fru-6-P binding and a 7° twist along a dimer–dimer interface, have been shown to be responsible for no more than a small percentage of the ensuing binding antagonism between PEP and Fru-6-P.^5,6 Of course, structural perturbations need not be dramatic in scale to be consequential in influencing functionality. Cooper and Dryden⁷ have calculated that perturbations of only 1–2% in high-frequency dynamics, if distributed uniformly over all of the atoms of the protein, could lead to allosteric effects with typically observed magnitudes. In such a scenario, the perturbations would be virtually impossible to detect experimentally. In addition, not all structural changes that result from ligand binding may be consequential to the structural conflict that needs to occur to create an allosteric inhibitory response. The challenge in these cases is therefore twofold: (1) to assess whether there are observable conformational “hot spots” of perturbations that are large enough that they that can be experimentally observed to arise as a consequence of ligand binding and (2) to distinguish between those observable structural changes that are important to the binding antagonism between allosteric and substrate ligands and those that occur merely in response to ligand binding but are inconsequential to the allosteric communication. This investigation was undertaken in an effort to identify regions within the structure of BsPFK where observable structural perturbations might be particularly important for the transmission of the allosteric antagonism between the binding of PEP and Fru-6-P despite being unexceptional when compared to other structural changes.

To recognize regions and residues of BsPFK that are involved in the propagation of the inhibitory allosteric signal, we employed linkage analysis and methyl-transverse relaxation-optimized spectroscopy (Me-TROSY) NMR. Chemical shift changes of the relevant resonance frequencies were analyzed in response to ligand binding and the formation of the ternary complex containing both PEP and Fru-6-P bound. These resonance frequencies vary in response to changes in the local magnetic environment of the nuclei, and therefore, small changes in the structure and dynamics of a particular nucleus can be readily detected by monitoring the change in chemical shift.⁸ This sensitivity of the nuclei to its local magnetic environment has led to the frequent use of two-dimensional (2D) heteronuclear experiments to generate “fingerprints” by which protein conformational changes and ligand binding can be studied.⁹ Unfortunately, the utility of these traditional experiments is limited to proteins with a molecular weight of <50 kDa. BsPFK is a fairly large enzyme with a subunit molecular weight of 34 kDa. In its active form, the subunits form a homotetramer composed of a dimer of dimers in which inter- and intradimer interfaces form the active and allosteric binding sites, respectively, with a total molecular weight of 136 kDa.

The development of NMR experiments that enable the preservation of NMR signals that would otherwise rapidly decay for large protein systems,^10,11 including transverse relaxation-optimized spectroscopy (TROSY) coupled with selective isotope labeling strategies,^12,13 has allowed for the study of increasingly larger proteins by NMR spectroscopy, approaches that have been particularly useful in studying allosteric proteins, such as protein kinase,^14,15 glucokinase,^16,17 glycerol phosphate synthase,¹⁸ and aspartate transcarbamoylase,^3,4 that are often large, oligomeric structures. Aspartate transcarbamoylase in particular is quite large, and Me-TROSY has been used effectively to study the conformational transition that enzyme experiences.

The general approach that extends Me-TROSY utility to high-molecular weight proteins, such as BsPFK, involves the use of ¹³C and protonated methyl group probes on alanine, methionine, isoleucine, leucine, and/or valine residues in an otherwise highly deuterated environment.^4,13,19,20 Selection of this labeling scheme is motivated first by the fact that methyl groups are prevalent throughout the enzyme, including in hydrophobic cores and at molecular interfaces, thereby serving as well-distributed internal reporters of dynamics and structure.²¹ Second, the exceptional spectral sensitivity results from the three equivalent protons in each methyl group, combined with the rapid rotation of the methyl about its 3-fold symmetry axis and its localization to flexible ends of side chains. Furthermore, the inherent spin physics of a methyl group enables the preservation of NMR signals, even in large biomolecular systems, via a Me-TROSY effect that manifests in ¹³C–¹H heteronuclear multiple-quantum correlation (HMQC) spectra.¹⁰

This investigation utilizes Me-TROSY NMR to examine the four enzyme species involved in PEP inhibition of BsPFK. The labeling strategy incorporated isoleucines that were selectively labeled with ¹³C and protonated at the δ-methyl group in an otherwise ¹²C-labeled, deuterated, and ¹⁵N-labeled enzyme. The labeling was accomplished by adding isotopically labeled α-ketobutyrate, a metabolic precursor to isoleucine biosynthesis, to the cell culture prior to induction.¹⁹ Figure 1 shows the overall reaction by which 2-keto-3-d₂-4-¹³C-butyrate, [¹²C,²H]-D-glucose, ¹⁵NH₄Cl, and D₂O are incorporated into the isoleucine residues of BsPFK as carried out by Escherichia coli metabolism.

Figure 1.

Fate of isotopic labels when isoleucine is metabolically synthesized from 2-keto-3-d₂-4-¹³C-butyrate in isotopically labeled minimal medium producing [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK. The precursor was synthesized from 2-keto-4-¹³C-butyrate as described in Materials and Methods.

By measuring the perturbations in NMR chemical shifts upon substrate and inhibitor binding, we found the ¹³C-labeled methyl groups can serve as local reporters on the allosteric coupling, the functionality of which is quantitatively measured by the coupling free energy between Fru-6-P and PEP.^22,23

This study attempts to identify regions of the enzyme that likely contribute most strongly to the coupling free energy. More specifically, Me-TROSY HMQC experiments were conducted with [U-²H,¹⁵N]-BsPFK specifically labeled with Ileδ1-[¹³C,¹H₃] to gain structural information about BsPFK in all four states of ligation relevant to the inhibitory allosteric response. As a result of these experiments, specific residues of the enzyme in which structural conflicts arise upon the binding of both ligands simultaneously were identified. Mapping these residues back to the crystal structure has allowed specific regions of the enzyme likely involved in the propagation of the allosteric signal to be localized.

MATERIALS AND METHODS

Materials.

All chemical reagents used in buffers for protein purification, enzymatic assays, and NMR experiments were of analytical grade and were purchased from Sigma-Aldrich (St. Louis, MO), Fisher Scientific (Fair Lawn, NJ), or Research Products International (Mt. Prospect, IL) unless otherwise noted. Lyophilized creatine kinase, the ammonium sulfate suspension of glycerol-3-phosphate dehydrogenase, and the potassium salt of phosphoenolpyruvate were purchased from Roche (Indianapolis, IN). The ammonium sulfate suspensions of aldolase and triosephosphate isomerase, the disodium salt of fructose 6-phosphate, and the disodium salt of phosphocreatine were purchased from Sigma-Aldrich. The coupling enzymes were extensively dialyzed against 50 mM EPPS (pH 8.0), 100 mM KCl, 5 mM MgCl₂, and 0.1 mM EDTA before use. NADH and DTT were purchased from Research Products International. Mimetic Blue 1 A6XL resin used in protein purification was purchased from Promatic BioSciences (Rockville, MD). The Mono-Q HR anion exchange column used in protein purification was purchased prepacked for FPLC use from Pharmacia (currently GE Healthcare, Uppsala, Sweden). Amicon ultracentrifugal filter units (spin concentrators) were from Millipore Corp. (Billerica, MA), and poly(ethylene glycol)-3000 was from Sigma-Aldrich. Minimal medium was made using potassium phosphate, monobasic, and sodium phosphate, dibasic, from EMD Chemicals (Gibbstown, NJ). Additional components of the minimal medium included d-glucose from Macron Chemicals (Center Valley, PA), magnesium sulfate and ferrous sulfate from Fisher Scientific, thiamine hydrochloride and calcium chloride dihydrate from Sigma-Aldrich, and ammonium chloride from Acros Organics. Deuterated MES-d₁₃ was from Sigma-Aldrich. Ammonium chloride (¹⁵N, 99%), l-isoleucine (¹⁵N, 98%), l-isoleucine (¹³C₆, 99%; ¹⁵N, 99%), α-ketobutyric acid, sodium salt (CH₃-¹³C, 99%), d-glucose (1,2,3,4,5,6,6-d₇, 97–98%), d-glucose (U-¹³C₆, 99%; 1,2,3,4,5,6,6-d₇, 97–98%), and deuterium oxide (D, 99.9%) are from Cambridge Isotope Laboratories, Inc. (Andover, MA). Shigemi NMR tubes were purchased from Shigemi, Inc. (Allison Park, PA), and used for all NMR experiments.

Synthesis of 2-Keto-3-d₂-4-¹³C-butyrate.

2-Keto-3-d₂-4-¹³C-butyrate was synthesized from 2-keto-4-¹³C-butyrate by proton/deuterium exchange of C3 through incubation at pH 10.2 in 99.5% D₂O for 12–14 h.¹⁶

Protein Expression and Purification of Isotopically Labeled Wild-Type BsPFK.

Plasmid pBR322/BsPFK²⁴ contains the gene for BsPFK behind the native B. stearothermophilus promoter. This plasmid was modified to place the BsPFK gene behind an inducible lac promoter in pALTER-1. An inducible plasmid was necessary to express the enzyme in minimal medium. BsPFK was expressed in E. coli RL257A cells, which are a T1 bacteriophage resistant derivation of RL257 cells.²⁵ RL257 cells lack both the pfkA and pfkB genes. RL259A cells were made by P1 transduction²⁶ using RL257 cells as the recipient strain and RY12459 cells as a donor strain. RY12459 cells were obtained from Ryland Young (Texas A&M University) and are a derivative of MC4100b²⁷ that contain a tonA gene disruption within a kanamycin cassette.

Protein expression of the [U-¹⁵N,²H];Ileδ1-[¹³C¹H₃]-BsPFK was performed as described previously by Tugarinov et al.,¹³ with a few minor modifications. Following heat shock transformation, cells were picked from a single bacterial colony that was grown on solid lysogeny broth (LB)/tet/H₂O medium (10 g/L tryptone, 5 g/L yeast extract, 10 g/L sodium chloride, and 15 μg/mL tetracycline). These cells were transferred to a 5 mL culture of LB/tet/H₂O medium and allowed to grow in a shaking incubator at 37 °C until the cell density reached an OD₆₀₀ of 0.7–0.8 (4–6 h). The 5 mL culture was centrifuged at 1200g and room temperature, and the pellet was gently resuspended in 1 mL of M9/H₂O medium (0.048 M Na₂HPO₄, 0.022 M KH₂PO₄, 9 mM NaCl, 19 mM NH₄Cl, 0.2% glucose, 2 mM MgSO₄, 100 μM CaCl₂, 10 μg/mL thiamine, 10 μg/mL FeSO₄, and 15 μg/mL tetracycline) that contained unlabeled glucose and NH₄Cl. Aliquots of the resuspension were added to 20 mL of the unlabeled M9/H₂O medium until the starting OD₆₀₀ was between 0.05 and 0.1. The culture was grown until the OD₆₀₀ reached 0.6, which took 8–10 h. The culture was then centrifuged and resuspended in 100 mL of labeled M9/D₂O medium (containing [²H,¹²C]-glucose and ¹⁵NH₄Cl) so that the beginning OD₆₀₀ was 0.1. These cells were grown until the OD₆₀₀ was between 0.4 and 0.5 (8–10 h), and then the cells were diluted to 200 mL by the addition of 100 mL of labeled M9/D₂O medium and were again grown until the OD₆₀₀ reached 0.4–0.5 (4–6 h). At this time, the culture was diluted with labeled M9/D₂O medium to a volume that equaled 1 L once the α-ketobutyrate was added and allowed to grow until the OD₆₀₀ was 0.25 (4–6 h). At this time, 70 mg/L 2-keto-3-d₂-4-¹³C-butyrate was added to the culture. The culture was allowed to grow for approximately 1 h until the OD₆₀₀ was between 0.3 and 0.4. Protein expression was induced with the addition of 1 mM isopropyl β-d-1-thiogalactopyranoside, and the cells were allowed to grow for 8 h. The final OD₆₀₀ ranged between 0.7 and 1.0.

For [U-²H];Ile-[¹⁵N]-BsPFK, the same procedure was followed with the following exceptions. Minimal medium was prepared with ¹⁴NH₄Cl instead of ¹⁵NH₄Cl, and Ile-[¹⁵N] was added to the medium instead of the α-ketobutyrate precursor. For [U-¹⁵N,²H,];Ile-[¹⁵N,¹³C]-BsPFK, the same procedure was followed except Ile-[¹⁵N,¹³C] was added to the medium instead of the α-ketobutyrate precursor. For [U-²H,¹⁵N,¹³C]-BsPFK, minimal medium was prepared with D-[²H,¹³C]-glucose and ¹⁵NH₄Cl and no selective labeling of isoleucine methyl groups was performed.

Upon completion of growth, cells were harvested from the medium by centrifugation and frozen at −20 °C for at least 12 h before resuspension in purification buffer [10 mM Tris-HCl (pH 8.0) and 1 mM EDTA] and sonication in a Fisher 550 Sonic Dismembrator at 0 °C in 15 s pulses at setting 6 for 12 min or until the OD₆₀₀ was no longer decreasing. The crude lysate was centrifuged at 22500g for 30 min at 4 °C. The clarified supernatant was incubated in a water bath at 70 °C for 15 min, cooled on ice for 15 min, and centrifuged again for 30 min at 4 °C. The BsPFK supernatant was diluted to 1 L and loaded onto a Mimetic Blue 1 A6XL column that was equilibrated with purification buffer. The column was washed with 1 L of purification buffer, and the enzyme was eluted with a 600 mL 0 to 1.5 M NaCl gradient. Enzyme-containing fractions were pooled and dialyzed into 20 mM Tris-HCl (pH 8.5) and loaded onto a Pharmacia Mono-Q HR anion exchange column that had been equilibrated with the same buffer. The enzymes were eluted with a 200 mL 0 to 1 M NaCl gradient, and PFK-containing fractions were combined, concentrated, and dialyzed into MES buffer [10 mM MES (pH 6.0)]. The concentrated enzyme was further dialyzed and stored in MES-d₁₃/D₂O buffer [10 mM deuterated MES (pH 6.0) and 0.02% NaN₃] at 4 °C. The final enzyme was determined to be pure by sodium dodecyl sulfate–polyacrylamide gel electrophoresis, and the concentration was ascertained using the absorbance at 280 nm (ε = 18910 M⁻¹ cm⁻¹). The final enzyme concentration achieved for NMR experiments ranged between 0.4 and 0.5 mM in monomer. Approximately 325 μL of protein was added to a Shigemi NMR tube.

Me-TROSY NMR Spectroscopy.

The temperature was set to 37 °C, and the pH was adjusted to 6.0 for all NMR experiments. Me-TROSY experiments were performed on a Bruker 600 or 800 MHz spectrometer, each instrument equipped with a cryo-probe. Two-dimensional ¹H–¹³C HMQC methyl correlation experiments were performed on samples of [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK using the pulse schemes described previously.¹⁰ NMR data were processed and analyzed with TopSpin (Bruker, Inc.) and analyzed using Sparky 3 (T. D. Goddard and D. G. Kneller, University of California, San Francisco).

Resonance Assignments.

Isoleucine assignments were determined through three-dimensional (3D) HMQC-NOESY experiments with [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK and complementary HNCA and HNCOCA experiments with [U-²H,¹⁵N,¹³C]-BsPFK. In addition, a 2D ¹H–¹⁵N TROSY spectrum of [U-²H];Ile-[¹⁵N]-BsPFK and triple-resonance experiments with [U-¹⁵N,²H];Ile-[¹⁵N,¹³C]-BsPFK confirmed the assignments.

Generation of the Four Enzyme–Ligand Species.

To generate the PEP–BsPFK species, PEP was added to BsPFK to a final concentration of 50 mM. For the generation of the substrate-bound complex, Fru-6-P was added to BsPFK to a final concentration of 10 mM. The ternary complex (PEP–BsPFK–Fru-6-P) required BsPFK to be mixed with final concentrations of 10 mM Fru-6-P and 50 mM PEP. On the basis of the ligand dissociation constants and the allosteric coupling constant at 37 °C and pH 6.0, <2% of other species were present. The ligand dissociation constants were determined using steady-state fluorescence assays with a tryptophan-shifted mutant. These assays were performed in the absence of the second substrate, MgATP, and hence turnover to match the conditions of the enzyme during the NMR experiments (data not shown). In addition, NMR titrations confirmed that spectra represent saturated complexes where indicated.

Steady-State Kinetic Assays.

Activity measurements for BsPFK were carried out using a coupled enzyme system²⁸ in a 0.6 mL reaction volume of either 50 mM EPPS buffer (pH 8.0, 25 °C) or 10 mM MES buffer (pH 6.0, 37 °C), additionally containing 5 mM MgCl₂, 100 mM KCl, 0.1 mM EDTA, 2 mM DTT, 0.2 mM NADH, 3 mM ATP, 250 μg of aldolase, 50 μg of glycerol-3-phosphate dehydrogenase, and 5 μg of triosephosphate isomerase. Then, 40 μg/mL creatine kinase and 4 mM phosphocreatine were added as an ATP regenerating system to prevent the accumulation of MgADP, which is an activator. The temperature was controlled using a NESLab RTE-111 circulating water bath. Fru-6-P and PEP were added at varied concentrations as indicated. Assays were started by the addition of 10 μL of appropriately diluted PFK. The rate of the reaction was measured on Beckman Series 600 spectrophotometers using a linear regression calculation to convert the change in absorbance at 340 nm to PFK activity. One unit of PFK activity is described as the amount of enzyme needed to produce 1 μmol of fructose 1,6-bisphosphate per minute.

Kinetic Data Analysis.

Data were fit using the nonlinear least-squares fitting analysis of Kaleidagraph software version 4.5 (Synergy). For the steady-state kinetic assays, the initial velocity data were plotted against the concentration of Fru-6-P and fit to the Hill equation:²⁹

$$v=\frac{V{[\text{A}]}^{n_{\text{H}}}}{{K_{\text{a}}}^{n_{\text{H}}}+{[\text{A}]}^{n_{\text{H}}}}$$ (1)

where v is the initial velocity, [A] is the concentration of the substrate Fru-6-P, V is the maximal velocity, and n_H is the Hill coefficient. K_a is defined as the concentration of Fru-6-P at which the enzyme’s activity is half-maximal. Assuming that Fru-6-P achieves a rapid binding equilibrium, which was shown to be valid in EcPFK using a steady-state kinetic method,³⁰ K_a is equivalent to the dissociation constant for Fru-6-P from the binary enzyme–substrate complex.^22,23 Values of K_a obtained from the initial velocity experiments were plotted against the concentration of the opposing ligand and fit according to

$$K_{\text{a}}=K_{\text{ia}}^{\text{o}}\left(\frac{K_{\text{iy}}^{\text{o}}+[\text{Y}]}{K_{\text{iy}}^{\text{o}}+Q_{\text{ay}}[\text{Y}]}\right)$$ (2)

where $K_{\text{ia}}^{\text{o}}$ is the dissociation constant for Fru-6-P in the absence of PEP, $K_{\text{iy}}^{\text{o}}$ is the dissociation constant for PEP in the absence of Fru-6-P, and Q_ay is the coupling coefficient.^22,23 Q_ay describes the effect of the allosteric effector on the binding of the substrate and is defined in eq 3.

Analysis of Allosteric Interactions.

The effect the inhibitor PEP has on the subsequent binding of substrate Fru-6-P to BsPFK, and the equivalent reciprocal effect of Fru-6-P on the binding of PEP, can be quantified by the coupling constant, Q_ay, which is defined by a ratio of thermodynamic dissociation constants for Fru-6-P and PEP using the following equation:²³

$$Q_{\text{ay}}=\frac{K_{\text{ia}}^{\mathrm{o}}}{K_{\text{ia}}^{\infty }}=\frac{K_{\text{iy}}^{\mathrm{o}}}{K_{\text{iy}}^{\infty }}$$ (3)

where $K_{\text{ia}}^{\text{o}}$ and $K_{\text{ia}}^{\infty }$ are the dissociation constants for Fru-6-P (A) in the absence and saturating presence of PEP (Y), respectively. Analogously, $K_{\text{iy}}^{\text{o}}$ and $K_{\text{iy}}^{\infty }$ are the dissociation constants for PEP in the absence and saturating presence of Fru-6-P, respectively.

When describing the nature and magnitude of the allosteric effect between the two ligands Fru-6-P and PEP, one must consider all possible ligation states of the enzyme. BsPFK (E) is the free enzyme. BsPFK–F6P (EA) and PEP–BsPFK (YE) are the two binary complexes, and PEP–BsPFK–F6P (YEA) is the ternary complex. By substituting the definitions for the dissociation constants into eq 3, we can show that the coupling constant serves as an equilibrium constant among the four species as they appear in the following disproportionation reaction:

$$[\text{EA}]+[\text{YE}]\stackrel{Q_{\text{ay}}}{\leftrightarrow }[\text{E}]+[\text{YEA}]$$ (4)

where the left side of the equilibrium contains the two binary complexes and the right side consists of the free enzyme and the ternary complex. For this reaction, the standard allosteric coupling free energy (ΔG_ay) is related to the coupling constant and its associated enthalpy and entropy components as follows:

$$\mathrm{\Delta }{G}_{\text{ay}}=-RT\ln \left(Q_{\text{ay}}\right)=\mathrm{\Delta }{H}_{\text{ay}}-T\mathrm{\Delta }{S}_{\text{ay}}$$ (5)

where R is the gas constant and T is the absolute temperature in kelvin. (By past convention, the superscript “o” is usually included to denote a standard free energy is omitted to avoid confusion with the meaning of the superscripts appearing in eq 3.²³) In an effort to ascertain the molecular basis for the inhibition by PEP, for which ΔG_ay > 0 by definition, one must consider the four enzyme species depicted in eq 4 and how their differences might ultimately generate the thermodynamic values of ΔH_ay and ΔS_ay as shown in eq 5.

A useful way in this context to consider these ideas further is to recognize that the coupling free energy value associated with that equilibrium can be described in terms of the free energy of formation for the products minus the free energy of formation for the reactants:²³

$$\mathrm{\Delta }{G}_{\text{ay}}=G_{\text{YEA}}+G_{\text{E}}-\left(G_{\text{EA}}+G_{\text{YE}}\right)$$ (6)

Equation 6 can be rearranged to emphasize the changes introduced by the binding of ligands as follows:

$$\mathrm{\Delta }{G}_{\text{ay}}=\partial G_{\text{YEA}}-\left(\partial G_{\text{EA}}+\partial G_{\text{YE}}\right)$$ (7)

where $\partial G_{\text{EA}}=G_{\text{EA}}-G_{\text{E}},\partial G_{\text{YE}}=G_{\text{YE}}-G_{\text{E}}$, and $\partial G_{\text{YEA}}=G_{\text{YEA}}-G_{\text{E}}$.

For example, the perturbations in free energy of formation arising from the binding of both A and Y simultaneously to previously unligated enzyme are described by ∂G_YEA. When this value is equal to the sum of the perturbations that occur when the ligands bind individually, ΔG_ay equals zero and by definition there is no allosteric effect. Inhibition or activation occurs when ∂G_YEA and the quantity ∂G_YEA + ∂G_YEA are not equal to each other. In other words, there must be an energetic conflict arising from the binding of both ligands simultaneously that leads to the allosteric effect. If the ternary complex can accommodate simultaneously the free energy changes introduced by each ligand binding individually, then there is no conflict and hence no allosteric effect.

These energetic conflicts can be manifested in ΔH_ay and/or ΔS_ay:

$$\mathrm{\Delta }{H}_{\text{ay}}=\partial H_{\text{YEA}}-\left(\partial H_{\text{EA}}+\partial H_{\text{YE}}\right)$$ (8)

$$\mathrm{\Delta }{S}_{\text{ay}}=\partial S_{\text{YEA}}-\left(\partial S_{\text{EA}}+\partial S_{\text{YE}}\right)$$ (9)

RESULTS

Me-TROSY Assignments.

As a result of the selective labeling, all 30 of the isoleucine residues per monomer of [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK contain one methyl group that can be viewed by NMR. As shown in Figure 2A, the isoleucine residues in BsPFK are all well-dispersed throughout each subunit, providing excellent coverage of the enzyme structure. This includes many residues between the allosteric sites and the active sites in a BsPFK subunit. In Me-TROSY chemical shift correlation maps of ¹³C and ¹H, all 30 isoleucines are well resolved (Figure 2B). In addition, the amide backbones of all 320 amino acids are labeled with ¹⁵N in [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK, and Figure 2C shows a ¹H–¹⁵N TROSY spectrum with good dispersion of resonances. However, because the entire backbone is labeled with ¹⁵N, there is quite a bit of crowding in the ¹H–¹⁵N TROSY spectrum.

Figure 2.

[U-¹⁵N,²H];Ileδ1-[¹³CH₃] labeling of BsPFK provided excellent coverage of the enzyme and well-resolved 2D spectra. (A) X-ray crystal structure of the BsPFK monomer (Protein Data Bank entry 4PFK) with all 30 isoleucine residues represented by spheres. Yellow spheres are isoleucines we were able to assign, and black spheres are isoleucines that remain unassigned. ADP in the allosteric site is colored blue, and Fru-6-P in the active site is colored red. Lines depict the four unique pairwise heterotropic allosteric interactions that can occur within each subunit. (B) Me-TROSY spectrum (37 °C, pH 6.0, 600 MHz, 10% D₂O/90% H₂O). (C) ¹H–¹⁵N TROSY spectrum (37 °C, pH 6.0, 800 MHz, 10% D₂O/90% H₂O).

Both 2D spectra indicate the enzyme is well folded under the conditions of the experiments, which was confirmed by the sample remaining fully enzymatically active throughout the experiments. The specific activity (data not shown), apparent ligand dissociation constants, and allosteric coupling parameters for the isotopically labeled enzymes were comparable to those of their unlabeled counterparts, as shown in Tables 1 and 2. These parameters were assessed at pH 8 and 25 °C (Table 1) to be consistent with other similar characterizations in the literature and at 37 °C and pH 6 because those conditions were optimal for performing the NMR studies reported herein. The similar values for the apparent dissociation constants and the allosteric coupling parameters indicate that the isotopic labeling did not disrupt the structure or function of the enzyme in any appreciable way.

Table 1.

Allosteric Coupling Parameters for Unlabeled and Isotopically Labeled BsPFK at 25 °C and pH 8.0

BsPFK labeling	$K_{\text{ia}}^{\text{o}}$ (μM)	$K_{\text{iy}}^{\text{o}}$ (μM)	Q ay	ΔGay (kcal/mol)
unlabeled	39 ± 2	63 ± 4	0.0021 ± 0.0002	3.65 ± 0.06
[U-15N,2H];Ileδ1-[13CH3]	34 ± 2	40 ± 2	0.0022 ± 0.0002	3.63 ± 0.06
[U-2H,15N,13C]	44 ± 3	49 ± 4	0.0021 ± 0.0003	3.65 ± 0.08
[U-2H];Ile-[15N]	30 ± 2	33 ± 2	0.0021 ± 0.0001	3.65 ± 0.03
[U-2H,15N];Ile-[13C]	41 ± 1	56 ± 2	0.0022 ± 0.0002	3.63 ± 0.06

Table 2.

Allosteric Coupling Parameters for Unlabeled and Isotopically Labeled BsPFK at 37 °C and pH 6.0

BsPFK labeling	$K_{\text{ia}}^{\text{o}}$ (μM)	$K_{\text{iy}}^{\text{o}}$ (μM)	Q ay	ΔGay (kcal/mol)
unlabeled	35 ± 2	48 ± 7	0.010 ± 0.002	2.73 ± 0.12
[U-1sN,2H];Ileδ1-[13CH3]	32 ± 1	55 ± 4	0.008 ± 0.001	2.86 ± 0.07
[U-2H,15N,13C]	35 ± 4	42 ± 7	0.012 ± 0.002	2.62 ± 0.10
[U-2H];Ile-[15N]	35 ± 4	82 ± 14	0.011 ± 0.001	2.67 ± 0.06
[U-2H,15N];Ile-[13C]	31 ± 1	50 ± 3	0.011 ± 0.001	2.67 ± 0.06

Me-TROSY spectral maps reveal several cross peaks with chemical shifts unique to each state of ligation indicating unique structures for each of the enzyme forms appearing in eq 4. Apo BsPFK and F6P-bound BsPFK spectra have several overlapping resonances, whereas the PEP-bound BsPFK spectrum has numerous dissimilar peaks. Distinct peaks, not seen in any other spectra, are present in the spectrum of the ternary complex (BsPFK with both Fru-6-P and PEP bound). Complementary HNCA and HN(CO)CA experiments with [U-²H,¹⁵N,¹³C]-BsPFK were used to assign the resonances corresponding to the isoleucines in the ¹H–¹⁵N TROSY spectrum. To transfer these assignments to the Me-TROSY spectrum, both ¹⁵N-edited and ¹³C-edited 3D HMQC NOESY experiments were performed with [U-¹⁵N,²H];Ileδ1-[¹³CH₃]-BsPFK. We were able to unambiguously assign 17 of the 30 isoleucine residues. One residue, Ile-61, was assigned in the ¹H–¹⁵N TROSY spectrum but was unable to be transferred to the Me-TROSY spectrum. Of the 12 remaining unassigned isoleucines, at least eight appear to be buried and were likely unable to undergo the H/D exchange with solvent required to be NMR visible in ¹H–¹⁵N TROSY experiments.

Fortunately, the Fru-6-P binding process and the formation of the ternary complex by either order of ligand addition are in the fast exchange regime, allowing us to see resonances move across the magnetic field in response to an increase in ligand concentration. Resonance assignments were transferred to the ligated forms of the enzyme using these titrations as demonstrated in Figure 3 with the binding of Fru-6-P. This behavior facilitated the assignments of the Fru-6-P-bound binary and ternary complexes.

Figure 3.

(A) Overlay of Me-TROSY spectra (37 °C, pH 6.0, 800 MHz, 10% D₂O/90% H₂O) with Fru-6-P concentrations ranging from 0 (red) to 10 mM (purple). (B) Close-up of the boxed region of panel A. Arrows indicate the direction of chemical shift perturbation in response to increasing ligand concentrations.

Perturbations Relevant to Allosteric Communication.

To identify chemical shift changes that reflect conformational perturbations involved in the allosteric inhibition of BsPFK, it was essential to first determine those residues for which the chemical shift values for each ligation state differ from those of the apoenzyme to a significant extent. We assessed this criterion by evaluating the chemical shift changes due to ligand binding in the ¹³C and ¹H dimensions. The chemical shift changes due to the binding of Fru-6-P (δ[EA]), PEP (δ[XE]), or both ligands (δ[XEA]), relative to apoenzyme, of all assigned isoleucine residues in the ¹³C and ¹H dimensions are listed in Table 3. The largest observed ¹H shift is 0.209 ppm upfield in Ile-67 when either Fru-6-P or both ligands bind. The largest ¹³C shift is the 1.364 ppm upfield shift observed with Ile-28 when PEP binds. We have selected for further scrutiny those residues for which the absolute values of the ¹³C or ¹H chemical shift perturbations, relative to apoenzyme, are equal to at least 20% of either of these maximum (absolute value) chemical shift perturbations to focus attention on those residues that exhibit the most substantial effects from ligand binding. Applying this criterion results in 10 residues of particular interest that are highlighted in Table 3 in boldface font, and they are the residues shown in Figure 4.

Table 3.

Chemical Shifts δ[EA], δ[YE], and δ[YEA] and the Net Values of δ[YEA] – (δ[EA] + δ[YE]) in the ¹H and ¹³C Dimensions for Assigned Ile Residues^a

Residue	1H (ppm)				13C (ppm)
	δ[EA]	δ[YE]	δ[YEA]	δ[YEA] − (δ[EA] + δ[YE])	δ[EA]	δ[YE]	δ[YEA]	δ[YEA] − (δ[EA] + δ[YE])
Ile-4	−0.004	−0.001	0.001	0.006	0.005	0.018	0.020	−0.003
Ile-20	0.008	0.028	0.019	−0.017	0.025	−0.398	0.022	0.395
Ile-28	−0.010	0.169	−0.049	−0.208	0.243	1.364	0.287	−1.320
Ile-49	0.002	0.010	0.039	0.027	0.030	−0.210	−0.170	0.010
Ile-67	−0.008	0.209	0.209	0.008	0.015	0.136	0.286	0.135
Ile-86	0.014	0.010	0.011	−0.013	−0.003	0.002	0.011	0.012
Ile-94	0.000	0.010	0.016	0.006	0.028	0.116	0.139	−0.005
Ile-126	−0.016	−0.059	−0.005	0.070	0.065	−0.444	0.215	0.594
Ile-130	−0.012	−0.029	−0.019	0.022	0.015	−0.120	−0.164	−0.059
Ile-137	−0.030	0.014	−0.003	0.013	−0.273	0.691	0.002	−0.416
Ile-147	−0.034	0.012	−0.033	−0.011	−0.046	−0.160	−0.272	−0.066
Ile-150	−0.003	−0.154	−0.157	0.000	0.032	0.320	0.158	−0.194
Ile-153	−0.007	−0.015	−0.010	0.012	−0.021	0.031	0.080	0.070
Ile-166	−0.005	−0.041	0.007	0.053	0.024	−0.366	0.020	0.362
Ile-176	−0.037	−0.025	−0.002	0.060	0.077	0.491	0.240	−0.328
Ile-202	−0.019	0.006	−0.022	−0.009	−0.135	−0.161	−0.192	0.104
Ile-286	−0.024	−0.077	−0.065	0.036	−0.059	−0.312	−0.376	−0.005

^aBold numbers are those shifts that are >20% of the maximum observed for either nucleus. Green rows denote net values that are greater than 2 standard deviations away from the 10% trimmed mean of all values for either nucleus.

Figure 4.

(A) ¹³C and (B) ¹H chemical shift perturbations of Ile methyl groups of BsPFK in response to the binding of Fru-6-P (red), PEP (blue), and both simultaneously (purple) for those residues that had at least one chemical shift perturbation that was >20% of the maximum perturbation. Residues identified in green exhibit a marked distinction between the purple bar and the sum of the red and blue bars in the ¹H or ¹³C chemical shift (see the explanation in the text).

Second, the residues involved in the energetic conflict that leads to the allosteric inhibition were identified by examining the nature and magnitude of these chemical shift changes in these 10 residues deemed to have substantial perturbations from ligand binding as just described. If we presume that the magnitude of the chemical shifts due to the binding of either ligend or both ligands roughly relates to the magnitude of the energetic perturbation introduced by that ligand, we can make this assessment as follows. The issue becomes whether the chemical shift change when both ligands bind is comparable to the sum of the chemical shift changes introduced by the binding of each ligand alone. These comparisons can be visualized in Figure 4 for the 10 residues most influenced by ligand binding.

A more quantitative way to make this comparison is by calculating the net values of the chemical shifts that occur upon the binding of both ligands (δ[YEA]) less the sum of the chemical shifts obtained for each binary complex individually (δ[EA] + δ[YE]). These values are given for each residue for both ¹³C and ¹H dimensions in Table 3. The residues predicted to be involved in the allosteric communication are those for which this difference is significantly different from zero. We can assess this significance by seeing for which residues this net difference in either ¹H or ¹³C chemical shift perturbations is more than two standard deviations from the 10% trimmed mean of values for all 17 residues appearing in Table 3 (Figure 5). On the basis of this analysis, we conclude that although isoleucine residues 67, 147, 150, and 286 exhibit substantial individual chemical shift perturbations in response to ligand binding, those perturbations seem to suggest only a minor, if any, contribution to the overall coupling that defines the allosteric communication between Fru-6-P and PEP binding sites. By contrast, six residues meet this criterion in the ¹³C dimension, and four of these six also meet this criterion in the ¹H dimension. These six isoleucine residues are in positions 20, 28, 126, 137, 166, and 176 and are denoted in green in Table 3 and Figure 4.

Figure 5.

Changes in ¹H (black) and ¹³C (red) chemical shifts introduced by the binding of both Fru-6-P and PEP simultaneously minus the sum of the shifts associated with the respective binary complexes. Solid horizontal lines indicate two standard deviations above and below the respective means, which are near zero in each case. Those residues producing the net values outside of these two standard deviations are labeled.

Figure 6 shows an X-ray crystallography structure of the BsPFK tetramer with the residues color-coded to distinguish among all three categories of chemical shift changes in response to ligand binding. Positions Ile-4, Ile-49, Ile-86, Ile-94, Ile-130, Ile-153, and Ile-202 show no substantial changes in chemical shift upon ligand binding and are colored pink. Therefore, we predict that these resonances do not detect structural changes that directly contribute to the coupling free energy that defines the inhibition of BsPFK by PEP. Positions Ile-67, Ile-147, Ile-150, and Ile-286, colored yellow, show substantial changes in chemical shift upon ligand binding, but the ternary complex appears to be able to accommodate the perturbations caused by the ligands at these locations, indicating a lack of structural conflicts at these sites. We interpret this behavior as suggesting that these residues are also not likely to be involved in the structural conflict that gives rise to allosteric inhibition of BsPFK.

Figure 6.

Two views of the BsPFK homotetramer (Protein Data Bank entry 4PFK) displaying the locations of isoleucine residues with no shifts (pink spheres), additive shifts (yellow spheres), and non-additive shifts (green spheres). Positions previously identified by fluorescence spectroscopy to play a role in allosteric coupling are shown with orange spheres. ADP in the allosteric site is colored blue, and Fru-6-P in the active site is colored red. Three subunits of the homotetramer are represented as gray ribbons, and one is shown in cyan spacefill for the sake of clarity.

By contrast, positions Ile-20, Ile-28, Ile-126, Ile-137, Ile-166, and Ile-176, colored green, possess the greatest difference between the chemical shifts of the ternary complex and the sum of the chemical shifts resulting from the binary complexes. We feel that these residues, where a conflict is reported in response to the binding of both ligands simultaneously, mark regions crucial to the transmission of the allosteric signal for inhibition. These residues are located generally in the regions near the two interfaces and directly between the substrate and effector binding sites. Four isoleucines (Ile-20, Ile-28, Ile-126, and Ile-137) lie between Fru-6-P and PEP binding sites that are 30 Å from each other. The other two isoleucine residues (Ile-166 and Ile-176) both fall between another pair of binding sites that are located 32 Å apart. This implies the lack of a single discrete structural pathway by which the allosteric signal is propagated.

Ile-153 is located between the binding sites 22 Å apart, which we have previously determined is the strongest pairwise inhibitory coupling,³¹ and it does not seem to experience structural changes involved in the propagation of the allosteric signal on the basis of these NMR data. However, the conservative mutation of Ile-153 to valine has an almost 4-fold effect on allosteric inhibition,³² suggesting that this residue is involved in a way not accounted for by this NMR analysis. In addition, previous studies identified regions of the BsPFK enzyme that likely contribute to the entropy component of the coupling free energy.^33,34 This was accomplished by measuring the rotational correlation time of engineered fluorescent tryptophan probes throughout the enzyme in all four ligation states. The positions identified were Y164 and F240, and they are mapped as orange residues onto the structure in Figure 6. It is clear that a more thorough assessment of the changes in dynamics will be required to obtain a fuller picture of the nature, and locations, of all of the conflicts that give rise to the allosteric inhibition of BsPFK by PEP.

DISCUSSION

The essential challenge and promise of structural biology is to relate structure to function. In the case of K-type allosteric behavior, where “function” involves the perturbation of ligand (including substrate) binding affinities, the issue is how structural perturbations relate to free energy changes resulting from ligand binding. We propose that perturbations to the enzyme reported by chemical shifts can be qualitatively related to the energetics of allosteric coupling between Fru-6-P and PEP in the broadest possible terms by elaborating on ΔG_ay as described previously²³ and summarized in eqs 6 and 7. This restatement of the disproportionation equilibrium reaction given in eq 4 emphasizes the contrast between the summation of chemical potentials associated with the binary complexes and the chemical potential of the ternary complex, each normalized to free enzyme, as the determinant of the value of ΔG_ay. This formulation demonstrates the need to include structural information about all four species, with a focus on changes introduced into free enzyme, to interpret any structural changes even in the context of allosteric inhibition. In particular, we note that the consideration of only substrate-bound and inhibitor-bound forms is insufficient.

It is useful to consider how this analysis compares with other uses of NMR to study allosteric behavior. For example, in the case of V-type allosteric activation, an analysis similar to that performed here has been utilized to study the activation of imidazole glycerol phosphate synthase by N′-[(5′-phosphoribulosyl)formimino]-5-aminoimidazole-4-carboxamide-ribonucleotide.³⁵ The differences between the changes in chemical shift of the ternary complex and the sum of the chemical shifts for the binary complexes were assessed as done here, and unique features of the ternary complex were deduced from the fact that several residues produced a net value significantly different from zero. Consequently, even in the case of activation, where a ternary complex must form, evidence of a mechanism for allosteric behavior more complex than that predicted by a two-state model was obtained.

Most structural studies of K-type allosteric inhibition using NMR have focused on differences in the structure of the protein introduced by the binding of an allosteric inhibitor compared to a form considered to be active.^3,4,14–18 A particular strength of NMR in these studies is that it can reveal changes in dynamics as well as static conformations introduced by the allosteric ligand binding. In the case of an allosteric K-type inhibitor, however, for these changes to explain the reason for inhibition one must presume the nature of the binding interaction of the substrate while the inhibitor remains bound (and vice versa). It is important to appreciate that an allosteric K-type inhibitor may not (and certainly in the case of BsPFK does not) function as a pure competitive inhibitor, which by definition totally prevents the binding of the substrate unless the inhibitor first dissociates. In the case of allosteric inhibition by PEP of BsPFK, both PEP and the substrate can bind simultaneously at high concentrations of both ligands. The resulting ternary complex exhibits an enhanced dissociation proclivity for both the inhibitor and the substrate when compared to either singly ligated species. The ternary complex is therefore neither the “inhibited” form nor the “active” form but rather a unique form that uniquely manifests the mutual antagonism between the bound ligands that underlies the basis for the inhibition.

When a single ligand binds, the resulting protein component of the binary complex usually differs in various respects from the apoprotein as a consequence of the free energy of binding that has been introduced into the system. It is not surprising when these perturbations are localized in the vicinity of the now-occupied binding site. In the case of allosteric proteins in particular, these perturbations can also extend to regions far removed from the active site. The same is true for the second ligand (or substrate) binding to a spatially distinct (i.e., allosteric) site. If a residue perturbed by the binding of the first ligand is in a region unaffected when the second residue binds, one would expect that that region would retain the perturbations associated with the first ligand when the ternary complex is formed.

Several residues examined in BsPFK behave in this manner. For example, the proton chemical shift change exhibited by the ternary complex is comparable to that of the binary PEP-bound complex for residues Ile-67 and Ile-150, while the proton chemical shift change associated with the ternary complex is virtually identical to that of the Fru-6-P binary complex for Ile-147. Similar patterns can be seen in the ¹³C chemical shifts of residues (e.g., Ile-286). While these changes might be interpreted as identifying residues sensitive to unique attributes of two hypothetical allosteric states, we prefer an alternative interpretation that expands on our view of the conformational changes introduced by the ligands of this enzyme in a way that is complementary to the analysis presented above.

We feel that the real source of the energetic impact of the binding of one ligand on the binding of the other arises from the regions, suggested by the non-additive chemical shift changes, in which the structural, and hence energetic, conflict occurs. Schematically, we have represented this idea in Figure 7B, where we contrast it with the more conventional model in Figure 7A. Although this idea has been discussed previously,³⁶ we believe the analysis we have performed points to where the regions of potential conflict are in BsPFK, as well as those that are dominated by the binding of one ligand or another.

Figure 7.

Alternative models illustrating contrasting expectations regarding the structural influence of binding of either the substrate, Fru-6-P, or the allosteric inhibitor, PEP, to BsPFK. The regions where the structure is predominantly influenced by Fru-6-P are colored blue, and those predominantly influenced by PEP are colored red. (A) Result anticipated by a typical two-state model where subsequent to ligand binding a protein would adopt either an active (blue) or an inhibited (red) configuration. (B) Model that accommodates regions dominated by either Fru-6-P or PEP to varying extents across the protein with a region in which the structural perturbations of both ligands cannot be accommodated when bound simultaneously depicted in purple.

It is of interest to use the methyl probes and the power of NMR spectroscopy to further explore the dynamics and more fully characterize all of the regions and interactions of the enzyme that contribute to the entropy component of the coupling free energy. Changes in the line width and intensities are seen between the ligation states for several of the isoleucine residues in our study, indicating that dynamics may be present on the millisecond to microsecond time scale. Relaxation dispersion experiments need to be performed to further probe these internal dynamics involved in propagating the allosteric signal between binding sites in BsPFK. In addition, experiments probing side chain dynamics on a faster time scale may also provide additional information about how the allosteric effect is propagated in BsPFK.

ABBREVIATIONS

BsPFK

B. stearothermophilus phosphofructokinase

Fru-6-P

fructose 6-phosphate

PEP

phosphoenolpyruvate