Sensitivity constraints in a chemical/biochemical highly responsive system

Abstract

The sensitivity properties of a reaction scheme that can show highly sensitive responses is studied (see e.g. Okamoto, M., Sakai, T. and Hayashi, K., 1987, Biosystems 21, 1–11). This model was previously proposed to represent a ‘chemical diode’, a ‘chemical McCulloch Pitts neuron’, the cycling of a cofactor or the interconversion of a covalently modifiable enzyme. The sensitivity of the steady-state flux and concentrations with respect to changes in a rate is quantified by the control coefficient (CC). Two types of constraints reduce the sensitivity patterns that the model can exhibit: the structural and kinetic constraints. The existence of these constraints substantially reduces the number of CC that can show arbitrary values. For instance, under extreme kinetic constraints, the value of one CC suffices to determine the values of the other thirty nine. The dependent CC are obtained as a function of the independent CC in two particular cases: the chemical case, governed by simple mass action rate laws, and the biochemical case, catalyzed by saturable enzymes. It is shown that the biochemical case exhibits a qualitatively richer repertoire of sensitivity patterns than the chemical case. Although the strategy developed in this work is restricted to a particular model its application is general. The usefulness of this type of analysis in the solution of problems ranging from design of chemical/biochemical devices to evolution of metabolism is discussed.