A mathematical model of kinetics of the biosynthesis of tetracyclines

Summary A mathematical model simulating the behaviour or Streptomyces aureofaciens in batch culture under conditions when tetracyclines are synthesized in excessive amounts has been formulated. The response of the mathematical model to the experimental conditions applied corresponds with data obtained in the experiments. The mathematical model demonstrated that the level of tetracycline production is determined during the period of culture growth beginning with exhaustion of inorganic phosphate from the medium and ending with inhibition of the synthesis of enzymes caused by the synthesized tetracyclines. Further tetracycline synthesis is then proportional to the amount of enzymes synthesized in this interval.List of symbols E Activity of ACT-oxygenase (10×nkat/g) - P Product concentration (mg/l) - k ₁-k ₆ Rate constants - K _S Saturation constant (g sugar/l) - K _I1 Inhibition constant (mg product/l) - K _I2 Inhibition constant (mM phosphate/l) - K _I3 Inhibition constant (mg product/l) - S ₁ Substrate sucrose (g sugar/l) - S ₂ Substrate concentration — phosphate (mM/l) - r _P Specific rate of product formation (mg product/g · h) - r _E Specific rate of enzyme synthesis (10×nkat/g² · h), Expressed by activity units - t Cultivation time (hour) - X Biomass dry weight (g/l) - Y _S/X Yield coefficient - Specific growth rate (h^-1)