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Microbial kinetics of growth and substrate utilization.
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.
Slide2Growth of a typical microbial culture in batch conditions
Slide3The 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
Slide4On 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.
Slide5On taking natural logarithms of equation (2) we have :
In
Xt
= In
Xo
+
μ
t (3)
Slide6Therefore, 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.
Slide7Typical values of μmax for a range of microorganisms are given below in the Table.
Slide8FIG. 2. The effect of initial substrate concentration on the biomass concentration at the onset of stationary phase, in batch culture.
Effect of substrate concentration on microbial growth
Whether the organism is unicellular or mycelia the growth is influenced by consumption of nutrients and the excretion of products. The cessation
of growth may be due to the depletion
of essential
nutrient in the medium (substrate
limitatioln
), the
accumulation of some
autotoxic
product
of the organism
in the medium (toxin limitation) or
a combination
of the substrate
limitation and
toxin limitation
.
The
nature of the limitation of growth may
be discussed
by growing the organism in the
presence of a range of
substrate concentrations and plotting
the biomass concentration
at stationary phase against
the initial
substrate
concentration is shown given below in fig 2:
Slide9From 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
Slide10In 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
Slide11The 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 Monad in1942 is know as Monad equation.Based upon MichaelishMenten kinetics.According to Monad equation μ = μmax . S /Ks + S (4)Where,S is residual substrate concentration,Ks is substrate utilization constant, numerically equalto 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’.
Monad Equation
Slide12In the above figure
The zone A to B is equivalent to the exponential phase in batch culture where substrate concentration is in excess and growth is at μmax .The zone C to A is equivalent to the deceleration phase of batch culture where the growth of the organism is due to the depletion of substrate to a growthlimiting concentration which will not support μmax .
Fig: 3 The effect of residual limiting substrate concentration on specific growth rate of a hypothetical bacterium.
Slide13Some representative values of Ks for a range of microorganisms and substrates
Typical values of
K, for a range of organisms
and substrates are usually very small and therefore the affinity for substrate is high.
Slide14If 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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