MATHEMATICAL-MODELS OF PURINE METABOLISM IN MAN

Experimental and clinical data on purine metabolism are collated and a nalyzed with three mathematical models. The first model is the result of an attempt to construct a traditional kinetic model based on Michae lis-Menten rate laws. This attempt is only partially successful, since kinetic information, while extensive, is not complete, and since qual itative information is difficult to incorporate into this type of mode l. The data gaps necessitate the complementation of the Michaelis-Ment en model with other functional forms that can incorporate different ty pes of data. The most convenient and established representations for t his purpose are rate laws formulated as power-law functions, and these are used to construct a Complemented Michaelis-Menten (CMM) model. Th e other two models are pure power-law representations, one in the form of a Generalized Mass Action (GMA) system, and the other one in the f orm of an S-system. The first part of the paper contains a compendium of experimental data necessary for any model of purine metabolism. Thi s is followed by the formulation of the three models and a comparative analysis, For physiological and moderately pathological perturbations in metabolites or enzymes, the results of the three models are very s imilar and consistent with clinical findings. This is an encouraging r esult since the three models have different structures and data requir ements and are based on different mathematical assumptions. Significan t enzyme deficiencies are not so well modeled by the S-system model. T he CMM model captures the dynamics better, but judging by comparisons with clinical observations, the best model in this case is the GMA mod el. The model results are discussed in some detail, along with advanta ges and disadvantages of each modeling strategy. (C) 1998 Elsevier Sci ence Inc. All rights reserved.