Where is the population size at stationary phase. From integrating equation (8), with Xm x = xo at as initial conditions: t = 0 (9) Equation (9), known as the logistic equation, gives a sigmoidal variation of biomass which empirically represents two phases of cell growth, the exponential and stationary phases, during which most PHB is produced. The biomass concentration depends on the initial and maximum attainable cell concentrations with respect to time, which varies with fermentation conditions and the microorganism used. The basic kinetic model for growth and non- growth associated PHB production under nitrogen limitation was proposed by Leudeking-Piret (Pazouki et al., 2008), where the product formation rate depends upon both the growth rate and biomass concentration in a linear fashion, equation 10: (10) where and are the associated and non-associated growth constants respectively. In order to α β evaluate the constants (α and we divide equation 9 by and assume yielding: x k =, β) When the experimental cell growth data are plotted as against the result is a straight line where k is equal to the slope while the is equal to the intercept (data not shown). and represent the P x α β PHB polymer and dry cell weight concentration. The biomass concentration with respect to time depends upon the initial and final biomass concentrations. Theoretically, this model is based on three assumptions: (a) is constant (b) death-rate of the cell is negligible, and (c) also, the lag phase period is negligible. In a batch culture, the combined of Monod and Luedeking–Piret model can be used to describe quite simply, with three set of mass balance equations, the cell mass (equation 7), product concentration (equation 10) and the limiting substrate (equation 12) with respect to time (t): (12) , the rate specific substrate consumption, is related toµ according to: where known as substrate yield coefficient which is defined as: (14)
Where Xm is the population size at stationary phase. From integrating equation (8), with x = xo at t = 0 as initial conditions: (9) Equation (9), known as the logistic equation, gives a sigmoidal variation of biomass which empirically represents two phases of cell growth, the exponential and stationary phases, during which most PHB is produced. The biomass concentration depends on the initial and maximum attainable cell concentrations with respect to time, which varies with fermentation conditions and the microorganism used. The basic kinetic model for growth and non- growth associated PHB production under nitrogen limitation was proposed by Leudeking-Piret (Pazouki et al., 2008), where the product formation rate depends upon both the growth rate and biomass concentration in a linear fashion, equation 10: (10) where α and β are the associated and non-associated growth constants respectively. In order to evaluate the constants (α and β) we divide equation 9 by x and assume k =, yielding: When the experimental cell growth data are plotted as against k the result is a straight line where α is equal to the slope while the β is equal to the intercept (data not shown). P and x represent the PHB polymer and dry cell weight concentration. The biomass concentration with respect to time depends upon the initial and final biomass concentrations. Theoretically, this model is based on three assumptions: (a) is constant (b) death-rate of the cell is negligible, and (c) also, the lag phase period is negligible. In a batch culture, the combined of Monod and Luedeking–Piret model can be used to describe quite simply, with three set of mass balance equations, the cell mass (equation 7), product concentration (equation 10) and the limiting substrate (equation 12) with respect to time (t): (12) , the rate specific substrate consumption, is related toµ according to: (14) where known as substrate yield coefficient which is defined as:
Date_Seed_Waste_PHB_Paper_JBW_27_09_16.docx