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.
Growth of a typical microbial culture in
batch conditions
The rate of growth is directly proportional to cell
concentration or biomassi.e.
dx/dt = μX
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
xt = xo e μt
--------- 2
• 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 + μt
• Therefore, a plot of the natural logarithm of
biomass concentration against time should yield
a straight line, the slope of which would equal to
• During the exponential phase nutrients are in
excess and the organism is growing at its
maximum specific growth rate, ‘μmax ‘ for the
prevailing conditions.
• Typical values of μmax for a range of microorganisms are
given below in the Table.
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:
FIG. 2. The effect of initial substrate concentration on the biomass concentration at the
onset of stationary phase, in batch culture.
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(SR - s) ---------(3)
X -is the concentration of biomass produced,
Y -is the yield factor (g biomass produced g-1 substrate consumed),
SR -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
Monad Equation
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 Monad in1942 is
know as Monad equation.
Based upon Michaelish-Menten kinetics.
According to Monad equation-
μ = μmax . S /Ks + S
• 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’.
Fig: 3 The effect of residual limiting substrate concentration on specific growth rate of a
hypothetical bacterium.
In 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 growth-limiting
concentration which will not support μmax .
Some representative values of Ks for a range of micro-organisms 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.
• 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
• 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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