Mathematical modelling of dynamics and control in metabolic networks. III. Linear reaction sequences

Kinetics of linear sequences of enzymatic reactions converting a single substrate into a single product are examined with emphasis on obtaining the relationship between the individual kinetic parameters and overall dynamic behavior. Chains of reactions exhibiting irreversible Michaelis-Menten kinetics are examined via scaling, linearization and modal analysis. The modal analysis gives the conditions under which the quasi-steady state assumption is applicable for one reaction relative to another in such a reaction sequence. The linearized description permits characterization of the transient response in terms of temporal moments. The moments provide useful physical insight and also provide a basis for systematic model reduction.