Structure-Reactivity Relationships for β-Galactosidase (Escherichia coli, lac Z). 1. Brpnsted Parameters for Cleavage of Alkyl β-D-Galactopyranosides

Seven substituted alkyl β-D-galactopyranosides 1-OR have been prepared and shown to be fair to excellent substrates for hydrolysis catalyzed by β-galactosidase (Escherichia coli, lac Z). Brønsted parameters of (β_1g)_k3 = -0.49 ±0.13 and (β_1g)_kcat/km = -0.75 ±0.14, respectively, were determined at pH 8.6 for k₃ (s^-1), the first-order rate constant for cleavage of enzyme-bound 1-OR, and k_cat/K_m (M^-1 s^-1), the second-order rate constant for reaction of the free enzyme and 1-OR. There is a weak correlation between log k_m and the pK_a of the alkyl alcohol leaving group, which is attributed to stabilization of the Michaelis complex by hydrophobic interactions between the enzyme and electron-withdrawing halogen substituents at the alkoxy leaving group. These binding interactions are probably both productive and expressed in the value of k_cat/K_m and nonproductive and expressed in the value of k₃. The negative values of β_1g are inconsistent with enzymatic catalysis of endocyclic cleavage of the glycosidic bond. The values of β_1g for enzyme-catalyzed cleavage of alkyl β-D-galactopyranosides lie between those observed for the spontaneous (β_1g ≈ -1.25) and specific-acid-catalyzed (β_1g ≈ 0) cleavage of acetals, and these pathways are therefore excluded for the enzyme-catalyzed reaction. Removal of the metal cofactor Mg²⁺ from the enzyme causes a ~0.2 unit decrease in (β_1g)_k3 for β-galactosidase-catalyzed cleavage of 1-OR. The interpretation of this change in β_1g is unclear. The Brpnsted coefficients for the β-galactosidase-catalyzed reaction are consistent with participation by an essential catalytic residue in concerted general-acid catalysis of cleavage of the glycosidic bond of 1-OR and/or stabilization of developing negative charge at the alkoxy oxygen by interaction with the magnesium ion cofactor.