The Simulation of the Urea Cycle: Correlation of Effects Due to Inborn Errors in the Catalytic Properties of the Enzymes With Clinical‐biochemical Observations

Abstract

Summary Steady‐state rate equations are written on the basis of information obtained from the literature describing the kinetics of the four enzyme‐catalysed reactions comprising the urea cycle. These equations are formulated into a set which also accounts for fluxes of input and output compounds external to the cycle. Numerical integration of this set of equations is performed employing parameters selected to approximate those pertaining to the operation of the urea cycle in normal liver. The result is a pattern of intermediate metabolite concentrations, which forms a basis for the comparison of patterns reflecting the effects of inborn errors of metabolism. The latter are calculated by varying specified kinetic parameters in the numerical integration. Each of the observed clinical syndromes, Hyperarginemia Types I and II, Hyperarginemia, Citrullinemia and Argininosuccinicaciduria, is discussed.

Mathematical modelling of the urea cycle

“…The method for deriving the rate equations and assigning values to rate constants is given in detail by Kuchel et al [10], and more recently using an automated procedure, by Mulquiney and Kuchel [15]. Briefly, for ornithine carbamoyltransferase (OTC), the rate equation for a reversible Bi Bi ordered sequential mechanism was assumed.…”

“…Other intracellular and mitochondrial metabolites were assigned a value of 1 lM. The unitary rate constants and rate equations for the four relevant enzymes, and their initial concentrations, were taken from the original urea cycle simulation [10] (Appendix, part 3). Rate constants for membrane exchange of metabolites were assigned values consistent with transport through the outer mitochondrial membrane and the plasma membrane being faster than transport through the inner mitochondrial membrane, and very rapid exchange across the cytoplasmic membrane.…”

“…Hence the ornithine would not have reached its equilibrium concentration by a large margin, and thus it would not have exerted its inhibitory effect. On the other hand, the computer simulation study of the urea cycle by Kuchel et al [10] showed that even if the ornithine in the cytoplasm had reached the concentrations used by Bach et al [8] the cycle flux would not have been affected. In other words, the flux control coefficient of arginase, even in the presence of high ornithine concentrations, was small compared with that of other enzymes in the cycle.…”

“…A similar protocol was used to demonstrate the preference of matrix ornithine carbamoyltransferase for endogenously formed carbamoyl phosphate [13]. In addition, immunocytochemical studies [14] support the hypothesis that some of the urea cycle enzymes are spatially organized in vivo.A detailed mechanistic-kinetic model of the urea cycle was previously written by one of us (P. W. Kuchel) [10], but aspects of channelling and the effects of subcompartmentation of the cycle were not explored. Hence, the aims of the current work were to: (a) extend this model in the widely available and readily modifiable program, Mathematica; (b) expand the model so that it could distinguish between events in subcellular compartments such as the mitochondria; and (c) include equations for additional, distinct radioactive, and exogenous substrates (Fig.…”

“…A detailed mechanistic-kinetic model of the urea cycle was previously written by one of us (P. W. Kuchel) [10], but aspects of channelling and the effects of subcompartmentation of the cycle were not explored. Hence, the aims of the current work were to: (a) extend this model in the widely available and readily modifiable program, Mathematica; (b) expand the model so that it could distinguish between events in subcellular compartments such as the mitochondria; and (c) include equations for additional, distinct radioactive, and exogenous substrates (Fig.…”