Mycobacterium tuberculosis d-alanine:d-alanine ligase as a case study in the measurement of competitive kinetic isotope effects for dimerization reactions

The small magnitudes of some kinetic isotope effects (KIEs), including those associated with ¹³C, necessitate a highly precise experimental approach involving the competition of light and heavy substrates. Provided the reaction is first order in the labeled substrate, the product isotopologue ratio converges to the initial reactant isotopologue ratio at completion, but the same is not true for dimerization reactions simply because the product diverges into four distinct isotopologues. The relative populations of these dimers deviate from the statistical distribution under the influence of a KIE. Accordingly, the current study aims to demonstrate this concept by analyzing the relative ¹³C placement in d-alanine:d-alanine-d-alanine:d-alanine at reaction completion for the dimerization of D-[1-¹³C]alanine catalyzed by Mycobacterium tuberculosis d-alanine:d-alanine ligase (Ddl). Using ¹³C NMR spectroscopy and Fourier-transform ion cyclotron mass spectrometry, the relative distributions of the four dimer isotopologues were determined. The ratio of the mono-labeled dimers with ¹³C at the C-terminus to that with ¹³C at the N-terminus yielded a relative KIE of 1.011 ± 0.004 for the acyl carbon. This result suggests that the rate-limiting step of the Ddl-catalyzed reaction involves peptide bond formation—either nucleophilic attack by the amino group or collapse of the resulting tetrahedral intermediate. This method of analysis, to the best of our knowledge, is the first of its kind for obtaining competitive KIEs in enzyme-catalyzed dimerization reactions.