Highly reliable computation of dynamic sensitivities in metabolic reaction systems by a variable-step Taylor series method

Dynamic sensitivities are useful to characterize time-varying systems efficiently. In metabolic reaction systems, however, analysis using these values is not so popular. This is mainly due to the following two reasons. One is that the calculation of dynamic sensitivities requires us to derive differential equations for sensitivities from those for metabolite concentrations by partial differentiation, and it is not easy for experimentalists to perform this mathematical operation. The other is that the metabolic reaction systems are mostly described by stiff differential equations, from which it may not be easy to obtain reliable numerical solutions. We have previously developed software for calculation of dynamic sensitivities (softcads), in which one can calculate dynamic sensitivities with high accuracy by setting only differential equations for metabolite concentrations. This paper further improves the algorithm of softcads to enhance its performance. The results clearly show that regardless of the degree of stiffness, the improved softcads provides dynamic sensitivities with the super high accuracy that is comparable to the machine accuracy and also completes the calculation in a shorter time.