KINETICS OF SEQUENTIAL METABOLISM - CONTRIBUTION OF PARALLEL, PRIMARYMETABOLIC PATHWAYS TO THE FORMATION OF A COMMON, SECONDARY METABOLITE

Interpretation of rate constants in the sequential metabolism of two d ifferent primary metabolites (MIA and MIB) for formation of a common, secondary metabolite (MII) after drug administration requires theoreti cal development of formulations that govern mass transfer during intra venous and oral administrations. Two cases (a and b) were presently co nsidered for metabolism occurring only in the first-pass organs (intes tine and liver) for flow-limited drugs and primary and secondary metab olites: (case a) wherein drug formed only the two primary metabolites, with the fractions of total body clearance that formed MIA and MIB, b eing denoted by f(1) and f(2), respectively, and (case b) wherein othe r additional elimination pathways for drug were present. MIA and MIB o nly partially formed MII (denoted by f(MIA) and f(MIB), respectively), because provision was made for alternate elimination pathways; the fr actional clearance in the formation of MII from MIA and MIB were f(MIA ) and f(MIB), respectively. Drug was metabolized to MIA then MII withi n the gut lumen with oral drug administration; the MIA and MII formed were further absorbed. Triangular matrices were found to result from m ass transfer equations for first-order conditions with oral and intrav enous ad-ministrations. Upon inversion of the matrices, the areas unde r the curve for drug and metabolite species were obtained after multip lication by the administered dose and division by the volume of the sp ecies considered. However, the dose-corrected area under the curve was used as the basis for comparison. Case-independent solutions were obt ained for the fractions absorbed (F-a, F-aMIA, F-aMIB) and the availab ilities (F, F{MIA}, F{MIB} of drug and the primary metabolites, and fo r f(1), f(2), f(1)/f(2), f(MIA)/f(MIB), and (f(1)f(MIA))/(f(2)f(MIB)) ratio of effective clearances of MII formation from D via MIA and MIB) . Case-dependent solutions also existed. For case a (f(1) + f(2) = 1), the fraction of total body clearance that formed MIA (f(1)) or MIB (f (2)) was solved with the area under the curve of MII after intravenous D, MIA, and MIS administrations. For case b, however, the same consta nts were obtained after greater manipulation, and entailed oral admini stration of the metabolites. Although solutions for the ratios of f(1) /f(2) and (f(1)f(MIA))/(f(2)f(MIB)) were found, the fractional clearan ces in formation of MII from MIA (f(MIA)) and MIB (f(MIB)) were, howev er, not provided in both cases unless MII was completely absorbed.