**4.3 Rate Expression and Metabolic
Quotient**

We have already discussed rate expressions for cell growth, Eq
(4-1). Let us now examine rate expressions for other medium
components in the **growth reaction**, Eq (2-1). Consider the
growth reaction on the basis of __one g of substrate__ consumed.
It can be written as ,

The stoichiometric coefficients in growth reaction become yield coefficients on the basis of substrate. See Example 2-2. The general rate expression is then:

where ri is expressed in g of i L^{-1}
h^{-1}. Since r_{x} is the most fundamental of the
various rates, it is conventional to write the stoichiometric
coefficient in terms of it. That is

Following the examples above, the rate expression for species i can be written as

Metabolic quotients are rate expressions on the basis of unit mass of biomass. That is

The metabolic quotient for oxygen is of special interest. This single property determines the upper limit of cell concentration that can be achieved in many bacterial fermentation systems. We will see further analysis in the next chapter. Typical values of metabolic coefficients are given below.

Organism |
q |
q |

E. coli |
2.5 |
0.3 |

Yeast |
0.5 |
0.2 |

Hybridoma |
0.2 |
0.02 |

Example 4-0

If specific growth rate of a bacteria is 0.35 h

^{-1}and cell yield is 0.6, calculate glucose consumption rate.