Systemic properties of ensembles of metabolic networks: application of graphical and statistical methods to simple unbranched pathways

Motivation: Mathematical models are the only realistic method for represent ing the integrated dynamic behavior of complex biochemical networks. Howeve r it is difficult to obtain a consistent set of values for the parameters t hat characterize such a model. Even when a set of parameter values exists, the accuracy of the individual values is questionable. Therefore, we were m otivated to explore statistical techniques for analyzing the properties of a given model when knowledge of the actual parameter values is lacking. Results: The graphical and statistical methods presented in the previous pa per are applied here to simple unbranched biosynthetic pathways subject to control by feedback inhibition. We represent these pathways within a canoni cal nonlinear formalism that provides a regular structure that is convenien t for randomly sampling the parameter space. After constructing a large ens emble of randomly generated sets of parameter values, the structural and be havioral properties of the model with these parameter sets are examined sta tistically and classified The results of our analysis demonstrate that cert ain properties of these systems are strongly correlated thereby revealing a spects of organization that are highly probable independent of selection. F inally, we show how specification of a given behavior affects the distribut ion of acceptable parameter values.