Metabolic regulation inferred from Jacobian and Hessian matrices of metabolic functions

Quantitative analysis of experimental metabolic data is frequently challenged by non-intuitive, complex patterns which emerge from regulatory networks. Quantitative output of metabolic regulation can be summarised by metabolic functions which comprise information about dynamics of metabolite concentrations. They reflect the sum of biochemical reactions which affect a metabolite concentration. Derivatives of metabolic functions provide essential information about system dynamics. The Jacobian matrix of a reaction network summarises first-order partial derivatives of metabolic functions with respect to metabolite concentrations while Hessian matrices summarise second-order partial derivatives. Here, a simple model of invertase-driven sucrose hydrolysis is simulated and both Jacobian and Hessian matrices of metabolic functions are derived for quantitative analysis of kinetic regulation of sucrose metabolism. Based on previous experimental observations, metabolite dynamics are quantitatively explained in context of underlying metabolic functions. Their potential regulatory role during plant cold acclimation is derived from Jacobian and Hessian matrices.