A mathematical model was constructed to define the dynamics of incorporation of radioactivity into urea carbon and the guanidine carbon of arginine in plasma albumin after the rapid intraportal-venous administration of Na214CO3 in the isolated perfused rat liver. 2. The model was formulated in terms of compartmental analysis and additional experiments were designed to provide further information on subsystem dynamics and to discriminate between alternative model structures. 3. Evidence for the rapid-time-constant of labelling of intracellular arginine was provided by precursor-product analysis of precursor [14C]carboante and product [14C]urea in the perfusate. 4. Compartmental analysis of the dynamics of newly synthesized urea was based on the fate of exogenous [13C]urea, endogenous [14C]urea and the accumulation of [12C]urea in perfusate water, confirming the early completion of urea carbon labelling, the absence of continuing synthesis of labelled urea, and the presence of a small intrahepatic urea-delay pool. 5. Analysis of the perfusate dynamics of endogenously synthesized and exogenously administered [6-14C]arginine indicated that although the capacity for extrahepatic formation of [14C]-urea exists, little or no arginine formed within the intrahepatic urea cycle was transported out of the liver. However, the presence of a rapidly turning-over intrahepatic arginine pool was confirmed. 6. On the basis of these subsystem analyses it was possible to offer feasible estimations for the parameters of the mathematical model. However, it was not possible to stimulate the form and magnitude of the dynamics of newly synthesized labelled urea and albumin which were simultaneously observed after administration of [14C]carbonate on the basis of a preliminary model which postulated that both products were derived from a single hepatic pool of [16-14C]arginine. On the other hand these observed dynamics could be satisfied to a two-compartment arginine model, which also provided an explanation for discrepancies observed between albumin synthesis measured radioisotopically and immunologically. This was based on a relative overestimation of [14C]urea specific radioactivity resulting from the rapid dynamics of [14C]carbonate and the [14C]urea subsystem relative to the labelled albumin subsystem. The effects of arginine compartmentalization could be minimized in the model by minor slowing of the rate of [14C]carbonate turnover or by constant infusion of [14C]carbonate, both of which permitted valid determination of albumin-synthesis rates.

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