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Microbial Growth Kinetics describe how the microbe grows in the fermenter.
This information is important to determine optimal batch times.
The growth of microbes in a fermenter can be broken down into four stages: Lag Phase
Exponential Phase
Stationary Phase
Death Phase
Apparatus
Bioreactor
pH meter
Sampling
device
Mixer
Temperature
sensor
YSI 2700
Biochemistry
Analyzer
pH probe
D-oxygen
probe
Using Biochemistry Analyzer and Spectrophotometer to measure and make calibration curves for sugar and yeast cell concentrations
Reactant initial concentration
dextrose/or sucrose 25 g/L
yeast 3 g/L
volume reactant solution 2 L
Lag Phase
This is the first phase in the fermentation process
The cells have just been injected into a new environment and they need time to adjust accordingly
Cell growth is minimal in this phase.
Exponential Phase
The second phase in the fermentation process
The cells have adjusted to their environment and rapid growth takes place
Cell growth rate is highest in this phase
Stationary phase
This is the third phase in the fermentation process
The cell growth rate has leveled off and become constant
The number of cells multiplying equals the number of cells dying
Death phase
The fourth phase in the fermentation process
The number of cells dying is greater than the number of cells multiplying
Growth Can be represented by:
Considering primary constituents:
Generalized substrate consumption and biomass growth with time.
Experimental observation ; Cell mass is proportional to available substrate
Concept : Cell Yield
Xdt
dX
• Growth rate to population size
• units are 1/t (i.e. h-1 1/h)
Cell Growth - Kinetics
X = concentration of
microorganisms at time t (g/l) t = time (h) = proportionality constant or specific growth rate, [h-1] dX/dt = microbial growth rate, [mass/volume time]
Generation time or doubling time is the time
required for the population to double.
The calculation is: td = ln(2)/
Doubling Time
Classified based on the relationship between product synthesis and energy generation in the cell
Growth associated
Non-growth associated
Mixed-growth associated
Growth-associated produced at the same time as cell growth
▪ metabolic intermediates ▪ pyruvate, citrate, acetate
Non-growth-associated takes place during the stationary phase (=0)
▪ secondary metabolites ▪ antibiotics
Mixed - growth associated takes place during growth and stationary phases
▪ metabolic byproducts ▪ lactate, ethanol
▪ secondary metabolites
Growth-associated Non growth-associated Mixed-growth-associated
Rate per microbe, which depends on
Species
Substrates
Environmental factors
Total numbers of microbes
Product yield is defined as:
dS
dXY s/x
Cell Yield is:
ConsumedSubstrate
MassCellinChangeY s/x
dS
dPY S/P
Batch Growth Kinetics
Growth Yield, Yield Coefficient
• Growth yield = microorganisms
produced per unit substrate utilized.
• Other yield coefficients.
ΔS
ΔXYX/S
YP / S
P
SYX / O2
X
O2
time (hr) X (g/L) S (g/L)
0 0.34 19.38
2 0.36 19.34
4 0.52 19.05
8 1.67 16.86
10 3.01 14.28
12 5.44 9.66
14 9.52 1.93
16 10.46 0.16
18 10.54 0.00
Find…
•Maximum growth rate
• Yield on substrate
• doubling time
•specific growth rate at
12 hr
Example Problem Solution
max
Integrate
ln(X) – ln(Xo) = t
plot ln(X) vs. t
Slope (largest) = max
1
X
dX
dtXdt
dX
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20
Time (hr)
ln(X
)
experimental data
regression
slope=u max=0.292
Maximum doubling time will occur in
exponential growth, when = max
td = ln 2/
substrategcellg
0.52
Lsubstrateg
19.38)(0
Lcellg
0.34)(10.54
ΔS
ΔXYX/S
Example Problem Solution
YP/S
Temperature
effects
on growth
rate.
Classifications of microbes according to temperature optima.
Classification
of microbes
according
to tolerance
of pH
extremes
Classification
of microbes
according to
their oxygen
responses.
a. Aerobic
b. Anaerobic
c. Facultative
d. Microaerobic
e. Aerotolerant