Kinetics of product inhibition in alcohol fermentation

The inhibitory effect of ethanol concentration p in a medium on the specific rates of growth mu and ethanol production nu of a specific strain of baker's yeast was studied in a chemostat, where except for ethanol as the product, only the concentration of glucose S was controlled to limit the metabolic activity of the yeast. This was designed to supplement the previous findings from the batch experiment, in which ethanol was added artificially and no substrate components were limiting the metabolism of the same yeast, that mu = mu(0)e(-k(1)p) and nu = nu(0)e(-k(1)p), where k(1) and k(2) are empirical constants and subscript the 0 denotes respective values at p = 0. The effects of p on the values of mu and nu were confirmed by the Line-weaver-Burk plot to belong to noncompetitive inhibition. The formulas here for mu and nu as affected by p, if extrapolated to the case of no limiting substrates, were in good agreement in respective forms with those derived previously from the batch experiment, though the values of corresponding coefficients in these formulas were different. The differential equations for mu and nu as functions of both p and S and, in addition for the rate of glucose consumption as correlated by the yield factors either with the cell growth rate or the rate of ethanol production, were solved properly with a digital computer. A kinetic pattern calculated so far was discussed with reference to the data obtained in the batch experiment and those relevant to actual "sake" brewing.