MtEis was expressed and purified as previously reported [4]. KAN, NEO, and AcCoA were purchased from Sigma-Aldrich (St. Louis, MO, USA) and used without any further purification.

Reactions were carried out in Tris buffer (50 mM, pH 8.0) using varying concentrations of KAN or NEO (0, 20, 50, 100, 250, 500, 1000, and 2000 µM) at several concentrations of AcCoA (25, 50, 100, 200, 300, and 500 µM) using constant concentrations of Eis (0.25 µM) and 5,5′-dithiobis-(2-nitrobenzoic acid) (DTNB, 2 mM). Reactions were monitored using a SpectraMax M5 multimode plate reader by taking absorbance measurements at 412 nm every 15 s for 15 min. Initial rates were calculated using the first 1.5 min of the reaction.

A random sequential rapid equilibrium bisubstrate mechanism is given by the following kinetic scheme [6]:(1)where E designates the enzyme, AG and AG-Ac is the aminoglycoside and its acetylated form, respectively, and AcCoA and CoA are acetyl coenzyme A and coenzyme A, respectively. Then, under pseudo-first order conditions (large excess of the two substrates over the enzyme), the apparent Michaelis-Menten parameters in terms of the microscopic mechanism parameters are:(2)(3)(4)(5)Here, the subscript “AG” for K_cat and K_m means that this constant is obtained from the dependence of the steady-state rate on the concentration of AG measured at a fixed concentration of AcCoA. The analogous nomenclature is used for AcCoA. For the subscript nomenclature of equilibrium binding constants K_d, for example, K_{d,AG(E•AcCoA)} is the equilibrium constant for binding of AG to E•AcCoA complex, etc; k_cat is the microscopic rate constant of the acetylation step (last equation in scheme (1)).

In the scheme for the ordered mechanism in which AcCoA must bind the enzyme first, the above parameters have the following functional form:(6)(7)(8)(9)The ordered mechanism is ruled out by the observed kinetics, as described in the Results and Discussion section. Because the kinetics were measured in sets of experiments at different fixed concentrations of AcCoA for each concentration of AcCoA varying the concentration of AG, a statistically rigorous way of determining the microscopic mechanism constants K_d and k_cat from the data is to determine the apparent Michaelis-Menten constants k_cat,AG and K_m,AG first. The next step is to fit dependence of k_cat,AG on [AcCoA] described by eq. (2) to the respective observed values, to obtain k_cat and K_{d,AcCoA(E•AG)}. These values are obtained for each AG independently. Finally, because K_d,AcCoA(E) is AG-independent, its value is determined by a nonlinear regression data fitting of eq. (3) to the observed K_m,AG dependence on [AcCoA] for KAN and NEO together. In the same fitting procedure two independent values K_{d,AG(E•AcCoA)} for KAN and NEO are obtained. This analysis was performed by nonlinear regression with SigmaPlot 11.0 (SysStat). We have observed a preparation-dependent activity of Eis, varying within a 4-fold range. For this reason, all experiments in this study were performed with the same preparation of MtEis. The differences in fraction of active MtEis translate in corresponding differences in values of k_cat reported in this and other studies. Values of K_m and K_d as well as the relative differences in k_cat values for different AGs are not affected by this variability.

In order to distinguish among the two ordered sequential mechanisms and a random sequential mechanism of binding of the AG and the AcCoA to MtEis to form a ternary acetylation complex, we performed a series of steady-state acetylation kinetic assays as a function of two independent variables, the concentrations of AG and AcCoA, both in large excess of the enzyme. These experiments were carried out with two AGs, KAN and NEO. For both KAN and NEO, the steady-state rate of acetylation by MtEis followed a hyperbolic dependence when plotted as a function of concentration of AG at a fixed concentration of AcCoA (Figures 1A and 2A for KAN and NEO, respectively) or as a function of concentration of AcCoA at a fixed concentration of AG (Figures 1B and 2B for KAN and NEO, respectively). Each of such hyperbolic dependences for KAN and NEO, where the concentration of AG is an independent variable (Figures 1A and 2A, respectively) yields apparent Michaelis-Menten constants, K_m,AG and k_cat,AG. Dependence of these constants on the concentration of AcCoA is also hyperbolic within the experimental uncertainty (Figures 1C, 1D for KAN and Figures 2C, 2D for NEO). We observe that K_m,AG increases with increasing concentration of AcCoA (Figures 1D and 2D) for both KAN and NEO; this is possible only for a random sequential mechanism (scheme (1), eq. (3)), where K_d,AcCoA(E)<K_{d,AcCoA(E•AG)}, i.e., AcCoA has a higher affinity towards free enzyme than towards AG bound enzyme. In other words, binding of AcCoA and AG is anti-cooperative. A similar observation was made recently about KAN acetylation by the Eis homolog from M. smegmatis based on a more limited set of experiments [6].

The rapid equilibrium mechanism of acetylation by MtEis makes physical sense, when one considers the ability of MtEis to efficiently acetylate AGs at multiple amino groups. This random sequential mechanism would allow an AG bound to MtEis to simply change its orientation in the active site after one acetylation, independently of dissociation of the CoA product and binding of another AcCoA for subsequent acetylation of the same AG. In contrast, if, for example, AG binding strictly followed AcCoA binding, the AG would need to dissociate after each acetylation event in order to rebind the same or another enzyme bound to AcCoA.

The quantitative analysis of these kinetic data in terms of the random sequential mechanism yields microscopic Michaelis-Menten parameter values for KAN and NEO. We obtain similar values of k_cat for KAN and NEO (k_cat = 0.68±0.15 s⁻¹ and 0.86±0.16 s⁻¹) (Figure 1A, 1C and Figure 2A, 2C) and a somewhat higher affinity of AcCoA to the KAN bound enzyme than to the NEO bound enzyme (K_{d,AcCoA(AG•E)} = 45±37 µM and 111±62 µM, for KAN and NEO, respectively). On the other hand, NEO binds the AcCoA bound enzyme with an approximately 3-fold higher affinity than KAN (Figures 1D and 2D); the values of the equilibrium binding constants obtained from the simultaneous fit of the KAN and NEO acetylation data (see Materials and Methods) are K_{d,AG(AcCoA•E)} = 439±52 µM and 135±53 µM for KAN and NEO, respectively. This analysis also yields the equilibrium constant for binding of AcCoA to MtEis, K_d,AcCoA(E) = 18±14 µM. It is to note that this value of K_d,AcCoA(E) is about 4-fold lower than that for AcCoA binding to Eis from M. smegmatis reported recently [6] and not equal to it, as it was assumed. Because the four equilibria in scheme (1) form a thermodynamic cycle, any three K_d values yield the fourth one, in this case the equilibrium constant for binding of AG to free enzyme, K_d,AG(E) = K_d,AcCoA(E)K_{d,AG(AcCoA•E)}/K_{d,AcCoA(AG•E)} = 176±144 µM and 22±17 µM for KAN and NEO, respectively. These results demonstrate quantitatively the anti-cooperativity of AcCoA and AG binding, as discussed above based on qualitative grounds. A different, four-ring structure of NEO from the three-ring structure of KAN may explain stronger binding of NEO to MtEis. In addition, NEO is tri-acetylated by MtEis while KAN is di-acetylated [3], [4], indicating that NEO binds MtEis in more orientations than KAN does, which may explain the higher affinity of NEO to MtEis.

The random sequential mechanism is more common among characterized AG acetyltransferases than the ordered sequential mechanism where AcCoA binds the enzyme first. The ability of either AG or AcCoA to bind the free enzyme raises a possibility that bisubstrate compounds combining the chemical features of both substrates can be developed as MtEis inhibitors, which would be more potent than respective substrate analog inhibitors individually or as a combination. The 4,5-disubstituted 2-deoxystreptamine four-ring scaffold of NEO appears to be more promising than the 4,6-disubstituted 2-deoxystreptamine three-ring scaffold of KAN for such design, based on the stronger affinity of NEO to MtEis. Bisubstrate inhibitors of GCN5-related N-acetyltransferases have been reported [16]–[21]. Blanchard and colleagues developed and elegantly applied analysis of the inhibition kinetics by such inhibitors to the dissection of the kinetic mechanism, an alternative to the analysis presented in this study [22]. Consistent with the thermodynamic argument made above, a bisubstrate inhibitor of the E. coli AAC(3)-IV acetyltransferase, which obeys the random sequential mechanism, is extremely strong, and its intrinsic K_i could be obtained only by extrapolation [22]. These examples demonstrate the power of bisubstrate inhibitors as chemical probes. Even though therapeutically useful bisubstrate inhibitors of acetyltransferase targets have not emerged yet, examples of bisubstrate inhibitors of other enzymes that are used in clinic exist [22]. Development of a potent bisubstrate inhibitor of MtEis as a selective probe or a pharmaceutical lead, based on its unique structure and catalytic properties, is an attractive direction for future studies. Studies focusing on the development of such bisubstrate inhibitors of MtEis are currently underway in our laboratories.