Constrained optimization of L-lysine production based on metabolic flux using a mathematical programming method.

Constrained optimization for microbial fermentation was studied. For optimization, we used not the maximum principle but a nonlinear programming method because of the need to consider many metabolic reactions. In the case of L-lysine fermentation, the optimization problem in L-lysine production was formulated as a nonlinear programming problem. In general, the state equations based on material balances are represented as differential equations, but such equations which are dependent on time can not be applied to a nonlinear programming problem. Therefore, the state equations were made discrete in a time base, and a new single vector which is not dependent on time was substituted. From these formulae, the objective function and the constraints using nonlinear programming problem were defined as the amount of L-lysine produced, and as a metabolic reaction model and empirical equations, respectively. Computer program was developed to solve this constrained nonlinear programming problem. The applied algorithm of the computer programming was a sequential quadratic programming method (SQP method). When the constrained nonlinear programming problem is solved using the SQP method, the maximum amount of L-lysine produced and the optimal feeding rate of L-threonine could be calculated. From the calculated results, it was clear that introduction of the equality and inequality constraints was easy. L-Lysine at a concentration up to 75.3 g/l could be produced when the fermentation was carried out under optimal conditions.