Kinetics of yeast growth and enzyme syntheses in a phosphate-limited continuous culture

Summary The effect of a deficiency of inorganic phosphate on the growth rate and on the invertase and phosphatase activities inSaccharomyces carlsbergensis was studied in a chemostat culture using a synthetic medium in which ethanol was the sole carbon source.The kinetic relationship between the growth rate and both the rates of phosphate uptake and the ethanol consumption agreed well with the threshold model but not the multicative model. The invertase activity of the yeast increased as the dilution rate decreased. As the phosphate concentration in the feed was reduced, the enzyme synthesis increased remarkably. Acid phosphatase activity was repressed completely above a critical molecular ratio, 0.015, of monopotassium phosphate to ethanol in the feed medium. As the phosphate concentration in the feed decreased, the maximum specific enzyme activity increased and the corresponding optimum dilution rate decreased. These experimental changes in enzyme synthesis were expressed mathematically using the modified operon models for enzyme regulation in terms of two fractions of limited inorganic phosphate; one which affects growth and the other which is incorporated in excess by the cells.Nomenclature A ethanol concentration in the culture (mM) - a, b, c, d exponents in the operon model - D dilution rate (h^–1) - E enzyme concentration in the culture (enzyme unit l^–1) - K_a, K_b, K_c, K_d, k equilibrium constants used in the operon model, see Toda (1976b) - o operator gene - P inorganic phosphate concentration in the culture (mM) - Pi limited inorganic phosphate concentration in the cells (mmole inorganic phosphate/g dry weight of cell) - Q specific enzyme activity, no units: (E/X)/(E/X)_max - Q_c, Q_d as defined in Eq. 12 - R repressor - r regulator gene - X cell concentration in the culture (dry cell weight l^–1) Greek Letters molecular ratio of inorganic phosphate to ethanol in the feed medium (mole/mole) - specific growth rate (h^–1) - A specific uptake rate of ethanol (mmole/g cell·h) - P specific uptake rate of inorganic phosphate (mmole/g cell·h) Suffix crit critical value - f feed - max maximum - min minimum - t total - 1, 2 number of species Superfix eff effective for cell growth - exc excess - str structural