Application of 2D-ITC to the Elucidation of the Enzymatic Mechanism of N-Acetylmuramic Acid/N-Acetylglucosamine Kinase (AmgK) from Pseudomonas aeruginosa

Abstract

Characterization of the turnover mechanism of bisubstrate enzymes is a tedious task. Molecular tools for studying the enzymatic mechanism are not readily available for all enzymes (e.g., radioactive substrates, substrate-competitive inhibitors, etc.). Wang and Mittermaier recently introduced two-dimensional isothermal titration calorimetry (2D-ITC) for determining the bisubstrate mechanism at high resolution while simultaneously quantifying the kinetic parameters for substrate turnover in a single reporter-free experiment. We demonstrate the utility of 2D-ITC in studying N-acetylmuramic acid/N-acetylglucosamine kinase (AmgK) from Pseudomonas aeruginosa. This enzyme is involved in cytoplasmic cell-wall-recycling events as a step in the peptidoglycan salvage pathway. Furthermore, AmgK phosphorylates N-acetylglucosamine and N-acetylmuramic acid, linking the recycling events to de novo cell-wall synthesis. We document in a 2D-ITC experiment that AmgK follows an ordered-sequential mechanism, where ATP binds first and ADP is released last. We also show that classical enzyme kinetic methods support the results of 2D-ITC and that 2D-ITC could overcome the shortcomings of these classical methodologies. We provide evidence for inhibition of AmgK by the catalytic product ADP, but not by the phosphorylated sugar product. These results provide a full kinetic characterization of the bacterial kinase AmgK. This work highlights 2D-ITC as a versatile tool for the mechanistic evaluation of bisubstrate enzymes, as an alternative for classical methods.

The peptidoglycan is the major constituent of the bacterial cell wall, which encases the entire bacterium and is critical for its survival.^1,2 The cell wall is dynamically recycled during homeostasis as well as in response to damage inflicted by antibiotics that inhibit cell-wall biosynthesis. Peptidoglycan recycling is initiated by the catalytic action of lytic transglycosylases (LTs).^3,4 The reaction products of LTs progressively undergo additional transformations to the ultimate smallest fragment, N-acetylglucosamine-1,6-anhydro-N-acetylmuramylpeptides [NAG-anhNAM-peptides; compound 1 (Figure 1)].⁵ Compound 1 and related compounds are internalized by the permease AmpG.^6,7 Once in the cytoplasm, compound 1 undergoes a series of transformations that culminate in the formation of Lipid II, which is transported to the outer leaflet of the cytoplasmic membrane, where it serves as a substrate for the biosynthesis of peptidoglycan (Figure 1).⁶ Metabolites 1‒3 are important inducers of the AmpR signaling pathway, which activates expression of the ampC gene for a class C β-lactamase (AmpC), a resistance determinant to β-lactam antibiotics.^8-10

Figure 1.

Cell-wall-recycling events in Pseudomonas aeruginosa.

The first six reactions of the cytoplasmic cell-wall-recycling events are shown in Figure 1 (transformations of compound 2 to 7). The conversion of N-acetylmuramate (5) to N-acetylmuramate-1-phosphate (NAM-1-P; 6), the subject of this study, is catalyzed by AmgK.¹¹ AmgK is particularly important in the context of cell-wall recycling as it is the key enzyme for linking the cytoplasmic recycling events to the de novo synthesis of cell-wall building blocks (8 → 9 → 7). As such, AmgK also contributes to the N-acetylglucosamine-1-phosphate 9) pool (Figure 1).^6,11 This apparent substrate promiscuity of AmgK has been exploited in producing synthetic photoaffinity probes for metabolic labeling and probing of the bacterial peptidoglycan.^12,13 In the interest of catalytic characterization of this enzyme, we utilize a recently reported two-dimensional isothermal titration calorimetry (2D-ITC) method.¹⁴ A single 2D-ITC experiment furnishes the full set of steady-state kinetic parameters for a bisubstrate enzyme. The validation of these results is provided by standard methodologies.

We cloned the amgK gene (PA0596) and a GAGAG linker-encoding sequence at its N-terminus into a pMAL-c6T plasmid to express it as the fusion protein 6×His-MBP-TEV-GAGAG-AmgK. Incubation with TEV protease and a series of affinity chromatography steps produced the purified GAGAG-AmgK (Supporting Information) as a homogeneous protein as determined by sodium dodecyl sulfate–polyacrylamide gel electrophoresis (Figure S1). Sedimentation velocity analytical ultracentrifugation (SV-AUC) of this protein revealed two protein species with apparent molar masses of ~37 kDa (~98%) and ~79 kDa (~2%) corresponding to monomeric and dimeric AmgK, respectively (Figure S2).

AmgK is a kinase that utilizes ATP to phosphorylate NAM and NAG at position C1.^11,12 This allows the utilization of pyruvate kinase/lactate dehydrogenase-coupled ATP recycling to monitor the rate of turnover of the substrate by AmgK by measuring the consumption of NADH at 340 nm.^11,15 A control experiment containing all assay components except one substrate was performed to account for background oxidation of NADH, the rate of which was subtracted from the measured rates in the presence of both substrates. The data were fit to the Michaelis–Menten equation, and the turnover parameters by AmgK are given in Table 1 and Figure S3. Turnover parameters of NAM and NAG were obtained at the saturating concentration of ATP (3.1 mM), while the parameters of ATP turnover were obtained at the saturating concentration of NAG (4 mM). Over the course of monitoring the reaction at the saturating NAG concentration, the reaction rate did not change (Figure S4). This observation is important for the regulation of AmgK catalysis. Under the conditions of the assay, ADP is recycled into ATP, resulting in a fixed ATP concentration and essentially the absence of appreciable ADP. However, NAG-1-P/NAM-1-P accumulates in the reaction mixture. The lack of a change in the catalysis rate, despite the accumulation of NAG-1-P/NAM-1-P, indicates that NAG-1-P/NAM-1-P does not inhibit AmgK. The same cannot be concluded for ADP.

Table 1.

Kinetic Parameters Determined by 2D-ITC and by ATP-Recycling Methods^a

	2D-ITC	ATP recycling
$k_{\text{cat}}^{\text{NAM}}$ (s−1)	12 ± 0.4	18 ± 3
$k_{\text{cat}}^{\text{NAG}}$ (s−1)	72 ± 7	48 ± 13
$K_{\mathrm{M}}^{\text{NAM}}$ (μM)	757 ± 132	171 ± 15
$K_{\mathrm{M}}^{\text{NAG}}$ (μM)	550 ± 71	264 ± 30
$K_{\mathrm{M}}^{\text{ATP}}$ (μM)	550 ± 78b	70 ± 12
$K_{\mathrm{i}}^{\text{ADP}}$ (μM)	694 ± 128	NDc
$K_{\mathrm{i}}^{\text{AMP}-\text{PNP}}$ (μM)	NDc	471 ± 169
$K_{\mathrm{S}}^{\text{ATP}}$ (μM)	444 ± 245	NDc

^aAll values are presented as means ± the standard deviation. 2D-ITC experiments were performed in duplicate, and ATP-recycling runs were performed in triplicate.

^bValue obtained from the 2D-ITC experiments in which NAG was injected.

^cNot determined.

Wang and Mittermaier recently described the use of ITC for the extraction of enzymatic kinetic parameters in a single experiment.¹⁴ This versatile 2D-ITC method allowed us to obtain steady-state kinetic parameters of AmgK from a recurring single-injection pattern. Eighteen consecutive 1 μL injections of either NAM or NAG (160 mM) were introduced into a calorimetry cell containing AmgK (650 nM in the case of NAM or 300 nM in the case of NAG) and ATP (13.5 mM). The interval between the consecutive injections was at least 1200 s to allow complete consumption of the sugar substrate, which was indicated by the return of the thermogram to the baseline. The initial concentration of the sugar substrate at the beginning of each injection was ~800 μM. The initial concentration of ATP was chosen to allow complete consumption of ATP over the course of the 18 injections. Finally, the concentration of AmgK was adjusted to allow the evolution of quantifiable heat during catalysis within the limits of the instrument detection.

As the reaction progressed, the reaction rate decreased and the thermogram slowly returned to the baseline upon complete substrate consumption. At the end of each injection, ADP and NAG-1-P/NAM-1-P were being formed in concentrations equimolar to that of the initial sugar substrate. The resulting thermogram pattern reveals a decrease in peak height with an attendant increase in peak width, upon comparison of consecutive injections (Figure 2A). This indicates that the catalytic reaction becomes slower over time. From one injection to the next, the sugar substrate concentration decreases from ~800 μM to zero while the ATP concentration decreases by an equimolar amount to the initial sugar substrate concentration. This is important to consider as products are accumulating and the concentrations of both substrates are varying simultaneously. The concentration of ATP decreases by ~6% in a single injection, and it is completely depleted by the 17th injection. Because we had already established that NAG-1-P/NAM-1-P does not inhibit AmgK, the observed progressive decrease in catalytic rate can be attributed to AmgK inhibition by the second product, ADP.

Figure 2.

(A) Schematic for the setup of the 2D-ITC experiment. Either NAM or NAG is titrated to produce the thermogram that demonstrates a reduced peak height and an increased peak width. (B) Workflow of the analysis of 2D-ITC data. Raw data of each peak are analyzed individually to extract the reaction enthalpy, reaction rate, and substrate concentration using eqs 1-3, respectively. Three-dimensional data sets are fitted to eq 4 for the ordered-sequential mechanism to produce the best-fit surface. Finally, the mechanism of AmgK is represented in Cleland notation.

The traces from the 2D-ITC experiment were mathematically treated to extract three-dimensional (3D) data sets of the reaction rate versus ATP concentration versus NAG/NAM concentration, V([ATP], [NAG/NAM]) (Figure 2B). Individual peaks were mathematically deconvoluted using reference injections of CaCl₂/EDTA to eliminate the effect of instrument delay.¹⁶ The deconvoluted peaks were used to extract the enthalpy of the reaction (ΔH) from the total peak area. The ΔH and instantaneous value of the ITC signal ${(\frac{\mathrm{d}Q}{\mathrm{d}t})}_t$ were then used to calculate reaction rate v at time point t. Concurrently, the instantaneous concentration of the sugar substrate ([S]_t) can be calculated using the partial integrals of the injection peak with respect to time and to the initial substrate concentration [S]₀. Concentrations of products ADP and NAG-1-P/NAM-1-P could then be determined by the difference [ATP]_o – [ATP]_t. The extracted V([ATP], [NAG/NAM]) data sets were fit to the kinetic equations for ordered, random, and ping-pong mechanisms. We note that four different permutations of the ordered-sequential mechanism rate equation were used, where [ATP] and [NAM]/[NAG] were assigned to A and B while [ADP] and [NAM-1-P]/[NAG-1-P] were assigned to P or Q with different orders (Table 2). The mechanism of AmgK was assessed on the basis of the goodness of fit for the data using sum-of-squared errors (SSE).

Table 2.

Goodness of Fit of 2D-ITC Data to Rate Equations of Different Kinetic Mechanisms

mechanism	SSE
random-sequential mechanism	113
ping-pong mechanism	221
ordered-sequential mechanism: A = ATP, B = sugar, P = sugar-1-P, Q = ADP	70
ordered-sequential mechanism: A = ATP, B = sugar, P = ADP, Q = sugar-1-P	167
ordered-sequential mechanism: A = sugar, B = ATP, P = ADP, Q = sugar-1-P	116
ordered-sequential mechanism: A = sugar, B = ATP, P = sugar-1-P, Q = ADP	204

On the basis of this analysis, AmgK follows an ordered-sequential mechanism, in which ATP binding is followed by NAM/NAG binding for the onset of catalysis. Once the products are formed, NAG-1-P/NAM-1-P dissociates first, followed by ADP. The data fit to this model best with an SSE of 70 with more than 23 000 degrees of freedom (DF). This large number of DF is due to the numerous measurements performed each second over an 8–10 h experiment. As the degrees of freedom increase, the difference between the SSE required for ascertaining better data fitness to one model over the other decreases, because $\frac{{\text{SSE}}_1\times {\text{DF}}_2}{{\text{SSE}}_2\times {\text{DF}}_1}$ follows an F-distribution. For DFs on the order of 23 000, the critical F value is 1.042, meaning that any difference in SSE of >4.2% is enough to deem the fits significantly different at a p-value of 0.001.^14,17 In our case, the difference between the best-fitting mechanism (SSE = 70) and the closest contender (random-sequential; SSE = 113) is >60%. Thus, the enzyme mechanism is elucidated with a high degree of confidence. We hasten to add that the data fitting was done while setting the value of [NAM-1-P] or [NAG-1-P] to zero, because we know from our experimental results that these products do not inhibit AmgK. Finally, fitting the 3D data sets V([ATP], [NAG/NAM]) to the rate equation of the ordered-sequential mechanism allowed the extraction of kinetic parameters for the turnover process (Table 1). Moreover, 2D-ITC data fitting allowed us to calculate the K_i of ADP to be 694 ± 128 μM. Inhibition by ADP has been documented previously in bacterial kinases by ITC.¹⁸ In terms of k_cat/K_M values, a mere 2- to 8-fold difference in turnover of NAM and NAG (in favor of NAG) exists between the two methods. The difference is not significant in terms of substrate preference. The differences between the parameters extracted from 2D-ITC and those from standard ATP recycling can be attributed to several factors. (1) In 2D-ITC, a coupling of the AmgK reaction to the recycling of ADP does not exist, but direct measurements of the heat of transformation are made. (2) The 2D-ITC method is performed over ~8–10 h with stirring, while ATP-recycling reactions are monitored for only 10 min without stirring. (3) There is a concentration difference between the two methods for substrates, the enzyme, and accumulated products. These factors collectively account for the 2- to 8-fold difference between the rate parameters determined by 2D-ITC compared to the standard method. Nonetheless, as the overall effects reflect ΔΔG < 1 kcal/mol in each case, we do not consider the differences significant.¹⁹

To confirm the 2D-ITC mechanistic result, we performed an analysis of the Lineweaver–Burk plot intersection pattern using the ATP-recycling methodology. AmgK was incubated with five different concentrations of ATP and a serial dilution of NAG (0.03–2 mM), and each reaction was monitored for 10 min. The intersection pattern on the Lineweaver–Burk plot is clearly above the abscissa (Figure 3A), which agrees with the ordered-sequential mechanism determined by 2D-ITC.^20,21 However, this method does not enable the determination of the order of substrate binding and product dissociation.

Figure 3.

(A) Intersection pattern on the Lineweaver–Burk plot at different ATP concentrations and varied NAG concentrations demonstrating an ordered-sequential mechanism. (B) Competitive and noncompetitive inhibition of AMP-PNP at variable ATP and NAG concentrations.

The pattern of enzyme inhibition can be utilized to determine the exact mechanism of bisubstrate catalysis.²² For this purpose, we utilized the nonhydrolyzable ATP analogue adenosine 5′-(β,γ-imido)triphosphate (AMP-PNP) as an inhibitor using the same coupled ATP-recycling assay.²³ AMP-PNP showed competitive inhibition (K_i = 471 ± 169 μM) of AmgK with varied ATP and fixed NAG concentrations (Figure S5). When the NAG concentration was varied and the ATP concentration was fixed, AMP-PNP inhibited AmgK noncompetitively, as demonstrated by Lineweaver–Burk plots (Figure 3B). This inhibition pattern is typical of either a random-sequential mechanism or an ordered-sequential mechanism, in which ATP binding is followed by NAM/NAG binding.²² For the counterpart inhibition of sugar–substrate binding, we screened 11 related carbohydrates (Figure S6). Unfortunately, none of these compounds showed AmgK inhibition. Hence, the full inhibition pattern for AmgK could not be established by the standard methodology. The lack of a NAG/NAM-competitive inhibitor represents an obstacle to the full mechanistic characterization of AmgK using the classical enzyme inhibition method. This shortcoming documents the challenge with the standard methods, which is not the case with the 2D-ITC approach employed here for AmgK.

In summary, these results document the utility of the 2D-ITC method for analysis of steady-state kinetics. We document an ordered-sequential mechanism for AmgK as supported by three orthogonal methods. In light of the fact that a majority of enzymes are bisubstrate enzymes, the benefit of the method is self-evident. The limitations of the method are few. Certainly, the transformation should generate sufficient heat for detection by the instrument. Additionally, were there no product inhibition for the enzyme in question, the exact sequential mechanism would not be discerned. Finally, if the resulting product inhibits the enzyme rather effectively, the thermogram patterns fade rapidly, leaving a small set of data points for analysis.