Models of biochemical systems are typically formulated with kinetic data obtained from isolated enzymes studied in vitro, and one has always to question whether or not all the relevant metabolites, processes and regulatory interactions have been identified and whether the parameter values obtained in vitro reflect the actual intracellular environment. In this paper we extend and further test strategies for model assessment and refinement that take advantage of the power-law formalism, which provides the systematic structure underlying biochemical systems theory. Our purpose is three fold. First, we introduce an algorithm for systematically scanning a model for putative errors, which, if corrected, would reconcile its behavior with the experimental system. Second, we further test the working hypothesis that systems in nature are selected to be robust and, hence, that the profile of. parameter sensitivities can be used to identify poorly defined regions of a model. Third, we illustrate the use of these strategies within the context of a relatively large and realistic biochemical system - the metabolic pathways of the human red blood cell. Our results show that the reference model we have used is neither locally stable nor robust. The algorithm identifies a number of putative regulatory interactions that, when added to the model, are capable of stabilizing the nominal steady state. We include one of these, the feedback inhibition of hexokinase by fructose-6-phosphate, in a first refinement of the model because there is experimental support for it in the literature. Careful re-examination of the most sensitive section in this model, the pathways of nucleotide metabolism, reveals two mechanisms that were omitted from the reference model: membrane transport of adenosine and inosine, and regulation of phosphoribosyl pyrophosphate synthetase by adenosine diphosphate, 2,3 diphosphoglycerate and 5-phosphoribosyl-1-pyrophosphate. It was also found that the concentration of inorganic phosphate had been inappropriately assumed to be a constant. Modifications to correct these deficiencies produced a second refinement of the model whose parameter sensitivities are reduced on average by 10-fold. Although these refinements are modest and there is substantial room for further improvement, this application identified several biochemically relevant features of the model that had been overlooked. It also points to nucleotide metabolism as the area most in need of further experimental study. (C) 1996 Academic Press Limited
