Figure 1

Summary of the hybrid method. (i) In the dynamic module (V₁, V₂, V₉, and V₁₀), the rate equations provide the reaction rates. (ii) In the static module, the reaction rate distribution (V₃, V₄, V₅, V₆, V₇, and V₈) is calculated from the matrix equation at the right, which corresponds to v = S^#b. S^# denotes the Moore-Penrose pseudo-inverse of S. (iii) Numerical integration of all the reaction rates (V₁-V₁₀) determines the concentrations of the metabolites (X₁-X₁₃). The metabolites X₅, X₇, and X₁₁ are at the boundary.