Desulfovibrio vulgaris (Hildenborough) cells catalyzed the oxidation of hydrogen with several quinone compounds as exogenous electron accepters, in which hydrogenase existing in the periplasmic space of the bacterial cells functioned as the enzyme to catalyze the reaction. The rates of the hydrogen oxidation and quinone reduction were analyzed by a Michaelis-Menten type equation to yield the values of the catalytic constant of a D. vulgaris cell, k(B,cat), and the bimolecular reaction rate constants for hydrogen, k(B,cat)/K-B,K-H, and for quinone, k(B,cat)/K-B,K-Q. They were in the ranges of k(B,cat) = (1.1-5.3) x 10(7) s(-1), k(B,cat)/K-B,K-H = (1.8-2.2) x 10(12) M-1 s(-1) and k(B,cat)/K-B,K-Q = (0.97-10) x 10(10) M-1 s(-1) for the reactions with four kinds of quinone compounds. The mass transfer process involved in the bacterial cell-catalyzed reaction was considered by a model taking account of the substrate diffusion to and through the cross-membrane channels (composed of proteins called porins) distributed in the bacterial outer membrane to reach the periplasmic space. The rate of diffusion of the substrates toward the whole cell surface was also calculated on the basis of the model of spherical diffusion and compared with the rate of the diffusion through the cross-membrane channels. Calculation based on the model has revealed that the diffusion toward the cell surface is the slowest step of the mass transfer processes and that the rates of the catalytic reaction are large enough to be close to the rates of the substrate diffusion.