  The presented previously indirect optimization method (IOM) developed within
biochemical systems theory (BST) provides a versatile and mathematically
tractable optimization strategy for biochemical systems. However, due to the
local approximations nature of the BST formalism, the iterative version of this
technique possibly does not yield the true optimum solution. In this work, an
algorithm is proposed to obtain the correct and consistent optimum steady-state
operating point of biochemical systems. The existing linear optimization
problem of the direct IOM approach is modified by adding an equality constraint
of describing the consistency of solutions between the S-system and the
original model. Lagrangian analysis is employed to derive the first order
necessary optimality conditions for the above modified optimization problem.
This leads to a procedure that may be regarded as a modified iterative IOM
approach in which the optimization objective function includes an extra linear
term. The extra term contains a comparison of metabolite concentration
derivatives with respect to the enzyme activities between the S-system and the
original model and ensures that the new algorithm is still carried out within
linear programming techniques. The presented framework is applied to several
biochemical systems and shown to the tractability and effectiveness of the
method. The simulation is also studied to investigate the convergence
properties of the algorithm and to give a performance comparison of standard
and modified iterative IOM approach.
