Michaelis-Menten Kinetics in a Chemostat

The concentration of an organism culture grows in the presence of nutrient concentration at a rate described by the Michaelis–Menten scheme. In dimensionless form the kinetic equations are: , . The time evolution of the two concentrations is presented as a function of the growth constant , the nutrient flux, , and the initial concentration, . The phase plane map of these equations is shown simultaneously.



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Varying the three parameters permits the study of such features as stable versus unstable equilibrium, steady state, and threshold concentration. Viewing the phase plane map simultaneously permits correlating these with features such as condensation points and nullclines.
[1] A. Novick and L. Szilard, "Description of the Chemostat," Science, 112, 1950 pp. 715–716.
[2] L. Michaelis and M. L. Menten, "Die Kinetik der Invertinwirkung," Biochem. Z., 49, 1913 pp. 333–369.
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