Using dynamic sensitivities to characterize metabolic reaction systems

Metabolite concentrations in cells are governed by enzyme kinetics in the metabolic reaction system. One can analyze how these concentrations depend on system variables such as enzyme activities by computing system sensitivities, which generally vary with time. Dynamic sensitivities, i.e., time-varying sensitivities, reflect the time-dependent response of the metabolic reaction network to perturbations. Unfortunately, dynamic sensitivity profiles are not commonly used in the analysis of metabolic reaction systems. In the present study, we demonstrate the use of dynamic logarithmic gains, i.e., normalized time-varying sensitivities, to gain insights into the dynamic behavior of metabolic networks. A biosynthetic reaction model of aromatic amino acids proposed by other researchers is used as a case study. The model system is analyzed using the dynamic logarithmic gains in parallel with simulations of the time-transient behavior of metabolite concentrations and metabolic fluxes. The result indicates that the influences of independent variables are most pronounced just after perturbations and the effects of perturbations on metabolite concentration at early times can be larger than those at steady state. These findings suggest that it is important to perform dynamic sensitivity analysis in addition to steady-state analysis. Furthermore, the rankings of the bottleneck ranking indicators, defined as the product of dynamic logarithmic gain and metabolite concentration, for three desired amino acids reveal that the degree of bottleneck for each enzyme changes with time. In conclusion, the dynamic logarithmic gains are not only useful for analyzing metabolic reaction systems but also can offer additional insights on the transient behavior of the system over steady state sensitivities, leading to a proper design of metabolic systems.