Industrial Microbiology INDM 4005 Lecture 8 200204

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Industrial Microbiology INDM 4005 Lecture
820/02/04
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Lecture 8

• Biotechnological Processing
• Bacterial Kinetics

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Questions for today

• 1. What is meant by doubling time of a bacterial
  culture?
• 2. What is specific growth rate?
• 2. What is the Monod equation?
• 3. What is a chemostat?
• 4. What is dilution rate?
• 5. What is the relationship between substrate
  concentration and specific growth rate?

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Overview (Lecture Objectives)

• (a) Bacterial growth
• (b) Growth kinetics and equations
• (c) Batch and continuous growth kinetics

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Growth in batch culture

• Growth in batch cultures is split into several
  distinct phases
• E.g of a closed culture system

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Bacterial growth

• Most bacterial cells reproduce asexually by
  binary fission. This involves several stages
• (i) increasing cell size (growth)
• (ii) DNA replication, and
• (iii) division (septum formation)

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Generation Time Time required for a cell
population to double
DNA DNA Replication Cell Elongation Septum
Formation Cell Separation
One generation
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3
9
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Generation time
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Bacterial growth

• The time taken for a microbial population to
  double in number is called the doubling time. The
  time taken for a single cell to divide is called
  the generation time
• The mean generation time of a population is equal
  to the doubling time.
• Doubling time is a measure of growth rate
• a short doubling time implies a fast growth rate.

DT
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Use of generation time to compare growth of
different bacteria
Microorganism Temp oC Generation Time B.
stearothermophilus 40 11 min Escherichia
coli 40 20 min S. aureus 37 28 min P.
aeroginosa 37 36 min Lactobacillus
acidophilus 37 75 min M. tuberculosis 37 720
min
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Stationary Phase
Death Phase
Exponential Phase
Lag Phase
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For a batch process, the rate of cell growth in
the exponential phase is given by dx
µx dt x is the concentration of cells
(biomass in g/L) µ is the specific growth rate
of the cells t time in hrs This equation is
valid under conditions of balanced growth, which
is when the cell composition remains constant.
During the exponential growth phase, cell growth
is not limited by nutrient concentrations and µ
equals µmax. However, during the deceleration
phase the specific growth rate of the cells
depend on the concentration of limiting
substrate. In this case, µ can be calculated
using the Monod expression
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On Integration xt x0emt x0 original biomass
concentration xt biomass concentration after
time t e base of the natural logarithm On
taking natural logarithms ln xt ln x0 mt
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Bacterial growth

• If we consider a bacterium growing under ideal
  conditions in which the numbers of cells exactly
  doubles in every generation, the population size
  after a known number of generations can be
  calculated...
• When the initial population size is N0
• after one generation N1 2 x N0
• after two generations N2 2 x 2 N0 22N0
• after three generations N3 2 x 22N0 23N0
  etc
• . after n-generations Nn 2n N0

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Geometric progression
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2
4
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The Mathematics of Growth

• No the initial population number
• Nt the population at time t
• n the number of generations at time t
• Nt No x 2n
• There is a direct relationship between the number
  of cells originally in a culture and the number
  present after exponential growth.

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Growth starting with a single cell
Time Generation 2n Population Nt log10
Nt number (No x 2n)
0 0 20 1 1 0.000 20 1 21 2
2 0.301 40 2 22 4 4 0.602 60 3 23
8 8 0.903 80 4 24 16 16 1.204 100 5
25 32 32 1.505 120 6 26 64 64 1.806
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The Mathematics of Growth

• Nt N0 x 2n
• Expressed as n
• n logNt - logN0
• log 2
• n 3.3(logNt - logN0)
• If you know the initial (No) and final (Nt)
  number of cells then you can calculate n, the
  number of generations.

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The Mathematics of Growth

• n 3.3 (log Nt - log N0)
• Example Nt 107, N0 103
• n 3.3 (7-3)
• n 13.2 generations
• If you know n, the number of generations, and t,
  the growth time, then you can calculate td, the
  generation time.

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The Mathematics of Growth

• The generation time (td) is calculated as
• td t
• n
• t number of hours of exponential growth
• n number of generations
• If n 15.5 and t 31 then td 2 hours

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Estimation of generation time from a bacterial
growth curve
1 x 108 8 x 107 5 x 107 4 x 107 2 x
107 1 x 107
Population Doubles in 2 hrs
T 2 n 1 td t/n 2hrs
Slope 0.15
Cells /ml
2 hours Generation time
1 2 3 4 5
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Gradient m
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Growth Rate Constant K

• Growth rate is often expressed as a value (k),
  equivalent to the number of doublings per unit
  time.
• k is usually expressed as generations per hour
• If t/d 2 hours then K 0.5 generations per hr
• k LogNt - LogN0 / 0.301 t

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Monod Equation

• The decrease in growth rate and cessation of
  growth may be described by the relationship
  between m and the residual growth limiting
  substrate
• m max S
• m Ks s
• s residual substrate concentration (g/L)
• Ks substrate utilisation constant when m is
  half m max (g/L)
• m max maximum specific growth per hour

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The relationship between substrate concentration
and specific growth rate
m max
1/2 mmax
SgtgtKs then m m max
Ks 1.0 g/L
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ks

• Bacteria with a high affinity for substrate has a
  low Ks and vice versa
• The higher the affinity the less growth is
  affected until substrate levels are very low

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Yield Coefficient

• Important in optimising batch fermentations
• Defined as
• x Yx/ s(S- Sr)
• x biomass concentration (g/L)
• Yx/ s yield coefficient (g biomass/g substrate
  utilised)
• S initial substrate concentration (g/L)
• Sr residual substrate concentration (g/L)

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Continuous Growth Kinetics

• Start as batch fermentations but exponential
  growth can be extended by addition of fresh broth
• Reactor is continuously stirred and constant
  volume is maintained
• Steady state conditions exist
• The rate of addition of fresh broth controls
  growth

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Continuous Growth Kinetics

• D F
• V
• D dilution rate (per hour)
• F flow (L/h)
• V reactor volume (L)

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Continuous Growth Kinetics

• Under steady state conditions
• dx rate of growth rate of loss
• dt in reactor from reactor (washout)
• or
• dx
• dt

-

Under steady state conditions rate of growth
rate of loss hence dx/dt 0 therefore mx
Dx and m D
mx - Dx
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Continuous Growth Kinetics

• At fixed flow rates and dilution rates the
  specific growth rate is dependant on the
  operating dilution rate
• For any given dilution rate under steady-state
  conditions the residual substrate concentration
  in the reactor can be predicted by substituting D
  for m in the Monod equation
• mmaxSr
• D Ks sr
• where Sr is the steady-state residual
  concentration in the reactor at a fixed dilution
  rate

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Critical dilution rate

• The dilution rate at which x zero is termed the
  critical dilution rate Dcrit
• Dcrit is affected by the constants mmax and Ks
  and the variable Sr,
• the larger Sr the closer Dcrit to mmax

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Growth of a microorganism in continuous chemostat
culture
Low Ks value
Dcrit critical dilution rate
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Growth of a microorganism in continuous chemostat
culture
High Ks value
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Effect of increased initial substrate
concentration on the steady-state biomass and
residual substrate concentrations in a chemostat
x at Sr3 x at Sr2 x at Sr1
Sr3 Sr2 Sr1
Steady state residual substrate concentration
X steady state cell concentration s steady
state residual substrate concentration Sr
Initial substrate concentration
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mmaxSr D Ks sr

• Rearranging gives
• D (Ks Sr) mmax Sr
• dividing by Sr then gives
• DKs D mmax
• Sr
• Hence DKs
• mmax - D

Consequently, the residual substrate
concentration in the reactor is controlled by the
dilution rate
Sr
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Chemostat / Turbidostat

• Chemostat Device for maintaining a bacterial
  population in the exponential growth phase by
  controlling nutrient input and cell removal.
• Turbidostat The concentration of cells is kept
  constant by controlling the flow of medium such
  that the turbidity of the culture is kept within
  certain limits

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Summary

• Bacterial kinetics
• 1. We have looked at the growth kinetics of
  homogeneous unicellular suspension cultures
• 2. We have examined growth in batch and
  continuous cultures
• 3. Examined how cell growth is controlled by
  substrate levels
• 4. Monod showed that growth rate is a hyperbolic
  function of the concentration of rate limiting
  substrate
• 5. Understand the relationship between substrate
  concentration and specific growth rate
• 6. How Ks the saturation constant effects cell
  growth

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Conclusion

• This lecture introduced bacterial growth kinetics
  in relation to fermentation
• It outlined how bacterial growth and fermentation
  efficiency are controlled