# Microbial Kinetics and Substrate utilization in Fermentation

**Batch culture and Kinetics of Microbial growth in batch culture**

# After inoculation the growth rate of the cells gradually increases.

# The cells grow at a constant, maximum, rate and this period is known as the *log or exponential, phase.*

# Growth of a typical microbial culture in batch conditions

# The rate of growth is directly proportional to cell concentration or biomass-

# i.e. *dx/dt **α** **X ** *

* dx/dt = **μ**X ———-1*

* Where,*

* X *is the concentration of microbial biomass,

* t *is time, in hours

* **μ* is the specific growth rate, in hours -1

# On integration of equation (1) from t=0 to t=t ,we have:

* **x**t* = *x**o* e *μ**t** ——— **2*

*Where,*

*Xo *is the original biomass concentration,

*Xt* is the biomass concentration after the time interval, *t *hours,

# e is the base of the natural logarithm.

# On taking natural logarithms of equation (2) we have :

# In *Xt *= In *Xo *+ *μ**t (3)*

# Therefore, a plot of the natural logarithm of biomass concentration against time should yield a straight line, the slope of which would equal to *μ**. *

# During the exponential phase nutrients are in excess and the organism is growing at its maximum specific growth rate, ‘*μ**max *‘ for the prevailing conditions.

# Typical values of *μ**max* for a range of microorganisms are given below in the Table.

# From figure 2 it may be seen that over the zone A to B due to an increase in initial substrate concentration gives a proportional increase in the biomass occur at stationary phase. This relation between increase in initial substrate concentration and proportional increase in the biomass may be described by equation:

* X *= *Y(S**R* – s) ———(3)

# Where,

* X –*is the concentration of biomass produced,

* Y –*is the yield factor (g biomass produced g-1 substrate consumed),

* S**R** –*is the initial substrate concentration, and

# s -is the residual substrate concentration.

# Thus, equation (3) may be used to predict the production of biomass from a certain amount of substrate

# In Fig. 2:-

# Over the zone A to B: s = 0; at the point of cessation of growth.

# Over the zone C to D an increase in the initial substrate concentration does give a proportional increase in biomass due to the exhaustion of another substrate or the accumulation of toxic products

# The decrease in growth rate and the cessation of growth due to the depletion of substrate, may be described by the relationship between μ and the residual growth limiting substrate.

# This relationship is represented by a equation given by Monod in1942 is know as Monod equation.

# Based upon Michaelish-Menten kinetics.

# According to Monad equation-

# μ = μmax . S /Ks + S (4)

# Where,

# S is residual substrate concentration,

# Ks is substrate utilization constant, numerically equal

# to substrate concentration when μ is half of μmax.

# Ks s a measure of the affinity of the organism with substrate

# It tell about the relationship between specific growth rate ‘μ’ and growth limiting substrate concentration ‘S’.

# If the organism has a very high affinity for the limiting substrate (a low *Ks value) the growth rate will *not be affected until the substrate concentration has declined to a very low level. Thus, the deceleration phase for such a culture would be short.

# However, if the organism has a low affinity for the substrate (a high *Ks value) the growth rate will be deleteriously affected *at a relatively high substrate concentration. Thus, the deceleration phase for such a culture would be relatively long.

# The biomass concentration at the end of the exponential phase is at its highest level. Therefore the decline in substrate concentration will be very rapid so that the time period during which the substrate concentration is close to *Ks is very short.*

# The stationary phase in batch culture is that point where the growth rate has declined to zero. This phase is also known as the maximum population phase.

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