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

Constrained optimization for microbial fermentation was studied. For optimi zation, we used not the maximum principle but a nonlinear programming metho d 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 equati ons based on material balances are represented as differential equations, b ut such equations which are dependent on time can not be applied to a nonli near 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 constrain ts using nonlinear programming problem were defined as the amount of L-lysi ne produced, and as a metabolic reaction model and empirical equations, res pectively. Computer program was developed to solve this constrained nonline ar programming problem. The applied algorithm of the computer programming w as a sequential quadratic programming method (SQP method). When the constra ined nonlinear programming problem is solved using the SQP method, the maxi mum amount of L-lysine produced and the optimal feeding rate of L-threonine could be calculated. From the calculated results, it was clear that introd uction of the equality and inequality constraints was easy. L-Lysine at a c oncentration up to 75.3 g/l could be produced when the fermentation was car ried out under optimal conditions.