## Dpdt qpX26

where p is the concentration of product and qp is the specific rate of product formation (mg product g^1 biomass h~') Also, product formation is related to biomass production by the equation:

where Yp/X is the yield of product in terms of biomass

(g product g^1 biomass) Multiply equation (2.7) by dx/dt, then:

dx/dt • dp/dx = Yp/X ■ dx/dt and dp/dt = Yp/x ■ dx/dt.

dp/dt = Yp/X ■ tix and dp/dt = qp-x and therefore:

From equation (2.8) it may be seen that when product formation is growth associated the specific rate 0f product formation increases with specific growth rate Thus, productivity in batch culture will be greatest at Mmax and improved product output will be achieved by increasing both n and biomass concentration. Non. growth linked product formation is related to biomass concentration and, thus, increased productivity in batch culture should be associated with an increase in biomass. However, it should be remembered that non-growth related secondaiy metabolites are produced only under certain physiological conditions — primarily under limitation of a particular substrate so that the biomass must be in the correct 'physiological state' before production can be achieved. The elucidation of the environmental conditions which create the correct 'physiological state' is extremely difficult in batch culture and this aspect is developed in a later section.

Thus, batch fermentation may be used to produce biomass, primary metabolites and secondary metabolites. For biomass production, cultural conditions supporting the fastest growth rate and maximum cell population would be used; for primary metabolite production conditions to extend the exponential phase accompanied by product excretion and for secondary metabolite production, conditions giving a short exponential phase and an extended production phase, or conditions giving a decreased growth rate in the log phase resulting in earlier secondary metabolite formEtion.

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