Diffusion-limited component of reactions catalyzed by Bacillus cereus .beta.-lactamase I

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Abstract
The B. cereus .beta.-lactamase I catalyzes the hydrolysis of a wide variety of penicillins and cephalosporins with values of kcat/Km varying over several orders of magnitude. The values of this parameter for the most reactive of these compounds, benzylpenicillin, I, and furylacryloylpenicillin, II (kcat/Km = 2.43 .times. 107 M-1 s-1 and 2.35 .times. 107 M-1 s-1, respectively, at pH 7.0 in postassium phosphate buffer containing 0.17 M KCl, Ic = 0.63, 25.degree. C) are decreased markedly by increasing viscosity in sucrose- or glycerol-containing bufers. The relative sensitivities to viscosity of kcat/Km values for I and for cephaloridine, III, were virtually unchanged at pH 3.8 from those observed at pH 7.0. The differential effects of viscosity on the reactive vs. the sluggish [e.g., cephalothin (IV), kcat/Km = 1 .times. 104 M-1 s-1] substrates support the contention that the rates of reaction of the former with the enzyme are in part diffusion controlled. Quantitative analysis gives values for the association rate constants, k10, of 7.6 .times. 107 M-1 s-1, 4 .times. 107 M-1 s-1, and 1.1 .times. 107 M-1 s-1 for I, II, and III, respectively. As both reactive and sluggish substrates associate with the active site of the enzyme with relatively similar rate constants, the variation in kcat/Km values is primarily due to the variation in the partition ratios, k-10/k2, for the ES [enzyme-substrate] complex, which are 2.3, 0.77 and 30 for I, II and III, respectively. The preceding analysis is based on direct application of the Stokes-Einstein diffusion law to enzyme kinetics. The range applicability of this law to the diffusion of substrate size molecules and the mechanics of diffusion of ionic species through viscous solutions of sucrose vs. polymers are explored.