Existence of a scaling relation in continuous cultures of Scheffersomyces stipitis : the steady states are completely determined by the ratio of carbon and oxygen uptake rates.

Background: Recently, we showed that steady-state continuous cultures of S.   stipitis follow the principles of growth on mixture of two complementary substrates. More precisely, when such cultures are fed with progressively higher concentrations of glucose s f at fixed dilution rate D  = 0.1 h-1 , oxygen mass-transfer coefficient k l a  = 50 h-1 , and oxygen solubility c o ∗ , they transition from glucose- to oxygen-limited growth through an intermediate dual-limited regime in which both glucose and oxygen are limiting, and ethanol is produced without loss of glucose. It is, therefore, of considerable interest to characterize the dual-limited regime. We found that the dual-limited regime occurs precisely when the operating parameters D , s f , k l a, and c o ∗ satisfy the relation Y os < D s f / k l a · c o ∗ < Y os ' , where Y os and Y os ' denote g of glucose consumed per g of oxygen consumed in the carbon- and oxygen-limited regimes. In this work, our goal was to determine if the above characterization of the dual-limited regime holds over a wider range of D , k l a , and to understand why the dual-limited regime is determined by the dimensionless ratio D s f / k l a · c o ∗ .

Results: To this end, we performed the foregoing experiments at three additional dilution rates ( D  = 0.07, 0.15, and 0.20 h-1 ) and one additional mass-transfer coefficient ( k l a  = 100 h-1 ). We find that the above characterization of the dual-limited regime is valid for these conditions as well. Furthermore, the boundaries of the dual-limited regime are determined by the dimensionless ratio D s f / k l a · c o ∗ , because the steady-state concentrations are completely determined by this ratio. More precisely, if the steady-state concentrations of biomass, glucose, oxygen, and ethanol are suitably scaled, they collapse into a single curve with D s f / k l a · c o ∗ as the independent variable.

Conclusion: The dual-limited regime is characterized by the relation Y os < D s f / k l a · c o ∗ < Y os ' over the entire range of operating condition 0.07 h-1  ≤  D  ≤ 0.20 h-1 and 50 h - 1 ≤ k l a ≤ 100 h - 1 . Since the effect of all operating parameters is embedded in the single parameter D s f / k l a · c o ∗ , the dimensionless plot provides a powerful tool to compare, with only a handful of data, various ethanol-producing strains over a wide range of operating conditions.