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National Yang Ming University

\frac{d[ethanol]}{dt}=Kpyruvateacetaldehyde\times{Kacetaldehydeethanol}\times\frac{[PDC]^{nPDC} }{ KdPDC^{nPDC}+[PDC]^{nPDC}}\times\frac{[ADH]^{nADH} }{ KdADH^{nADH}+[ADH]^{nADH}}-Km\times\frac{[ADH]^{nADH}}{ KdADH^{nADH}+[ADH]^{nADH}}\times[ethonal]

In this equation, the production rate of ethanol is composed of both synthesizing rate and degrading rate. Kpyruvateacetaldehyde represents reaction rate constant of pyruvate→acetaldehyde, while Kacetaldehydeethanol represents reaction rate constant of acetaldehyde→ethanol; \frac{ [PDC]^{nPDC} }{ KdPDC^{PDC}+[PDC]^{PDC} }represents hill effect of PDC to pyruvate→acetaldehyde reaction, while \frac{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} }represents hill effect of ADH to acetaldehyde→ethanol reaction; Km represents the rate constant of ethanol→acetaldehyde, a reverse reaction of the second process of ethanol synthesis. For the section of the equation, \times{ Kpyruvateacetaldehyde }{ Kacetaldehydeethanol }\frac{ [PDC]^{nPDC} }{ KdPDC^{PDC}+[PDC]^{PDC} }{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} } represents the synthesizing rate of ethanol from pyruvate to acetaldehyde to ethanol under the influence of enzymes ADH and PDC; \times{ -Km }{ Kacetaldehydeethanol }{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} }{[ethanol]} takes the reverse reaction of acetaldehyde to ethanol into consideration, which results in the decreasing of ethanol.

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