Optimal control strategy for the enhanced production of cellulase enzyme using the new mutant Trichoderma reesei E-12

Cellulase enzyme production was enhanced using the mutant strain Trichoderma reesei, E-12, which was shown to be partially resistant to catabolite repression. An optimal profile for pH, which was found to be the critical environmental parameter, was determined using a rigorous mathematical optimization procedure. Semi-empirical models were used to minimize complications in the computation. A 30% increase in enzyme activity and productivity was obtained using the optimal pH strategy as compared to the pH cycling strategy.List of Symbols a ₁ , a ₂ , a ₃ d^–1, d^–2, d^–3 coefficients of the polynomial in the generalized logistic growth model - a ₄, a ₅, a ₆ d^–1, d^–2, d^–3 coefficients of the polynomial in the generalized logistic product model - b ₁ d^–1 enzyme synthesis rate constant - b ₂ d ^–1 enzyme decay rate constant - b ₃ power coefficient in the polynomial model for enzyme synthesis - H Hamiltonian function - J Objective function of the maximization procedure - K ₁ kg/m³ limiting cell mass concentration in biomass logistic model - K _s kg/m³ saturation constant - K ^s kg/m³ saturation death rate constant - q power coefficient in polynomial model - s kg/m³ substrate concentration - t d fermentation time - T d total fermentation time (=7 d) - x ₁₀ kg/m³ initial biomass concentration - x ₁ kg/m³ biomass concentration at time t - x ₂ F.P.A enzyme activity at time t - x ₃ d state variable replacing time term on the right hand side of biomass equation - x _f kg/m³ final biomass concentration - z ₁, z ₂, z ₃ adjoint variable corresponding to state variable x ₁, x ₂, x ₃ - d^–1 specific death rate - d^–1 specific growth rate