A heuristic approach to fed-batch optimisation of streptokinase fermentation

Previous studies have shown that the rate of formation of streptokinase, a secondary metabolite, in batch fermentation is proportional to the specific growth rate of the biomass, which in turn is inhibited by its substrate and the primary product (lactic acid). These kinetics suggest the suitability of fed-batch operation to increase the yield of streptokinase. A near-optimal feed policy has been calculated by the chemotaxis algorithm, and it shows a substrate feed rate decreasing nonlinearly and vanishing after 11 hours. This is followed by batch fermentation for a further 8 hours, at the end of which 12% more streptokinase is generated than by purely batch fermentation. Further improvements in productivity are possible.List of Symbols k _dh^–1 decay constant for active cells - k _ph^–1 decay constant for streptokinase - K _Igl^–1 inhibition constant for lactic acid - K_S gl^–1 inhibition constant for substrate - M gl^–1 lactic acid concentration - P gl^–1 streptokinase concentration - Q 1h^–1 substrate feed rate - S gl^–1 substrate concentration - S _ingl^–1 inlet concentration of substrate - t h time - t _bh end-point of batch fermentation - t _fh end-point of fed-batch fermentation - V l volume of broth in fermenter - V ₀ l initial value of V (at t=0) - V _ml maximum value of V - X gl^–1 total biomass concentration - X _agl^–1 concentration of active biomass - Y _MX yield coefficient for lactic acid from biomass - Y _PX yield coefficient for streptokinase from biomass - Y _XS yield coefficient for biomass from substrate Greek Letters h^–1 specific growth rate of biomass - _mh^–1 maximum specific growth rate