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Unformatted text preview: CEE 266
ENVIRONMENTAL BIOTECHNOLOGY
Lecture 4
(Monod Growth and Chemostat Kinetics) Typical Growth Curve for a Bacterial Population Batch culture: a closedsystem microbial culture of fixed volume.
Figure 6.10 Exponential Phase Growth Log phase growth is first order
Growth rate ∝ to population size lnX vs. t is linear, slope = µ µ units are 1/t (i.e. hr1) Monod Growth Kinetics
Relates specific growth rate, µ, to substrate concentration
Empiricalno theoretical basis—it just “fits”!
Have to determine µmax and Ks in the lab
Each µ is determined for a different starting S µmax S
µ=
Ks + S € Monod Growth Kinetics Looks like MichaelisMenten,
but variable is different
Firstorder region,
S << KS, the equation can be
approximated as µ = µmaxS/Ks
Center region, Monod “mixed
order” kinetics must be used S << KS mixed order µmax
µ, 1/hr Zeroorder region,
S >> KS, the equation can be
approximated by µ = µmax S, mg/L S >> KS Michaelis Menten vs. Monod Michaelis Menten
Kinetic expression derived
(theoretical) Monod
Empirical expression
Enzyme concentration increases
with time Constant enzyme pool
Pure enzymes Growing microbes Nongrowing microbes Relates growth rate to S v vs. S where v is velocity µ vs S Km is half saturation constant Ks is half saturation constant Cell Growth and Binary Fission Figure 6.1 The Rate of Growth of a Microbial Culture Figure 6.8 Calculating Microbial Growth Parameters Figure 6.9 Doubling Time N0 initial population (@t=0) Nt = N0 x 2n Nt population at time t log Nt = log N0 + nlog 2 n number of generations n = (log Nt – log N0)/log 2 g generation (doubling) time = (log Nt – log N0)/log 2 K growth rate constant = 3.3 (log Ntlog N0) * g is measured only in exponential
phase! The Mathematics of Exponential Growth
Increase in cell number in an exponentially growing bacterial
culture is a geometric progression of the number 2
Relationship exists between the initial number of cells
present in a culture and the number present after a period of
exponential growth:
N = No2n
where N is the final cell number, No is the initial
cell number, and n is the number of generations
during the period of exponential growth The Mathematics of Exponential Growth Generation time (g) of the exponentially growing
population is g = t/n where t is the duration of exponential growth and n is
the number of generations during the period of exponential
growth Specific growth rate (k) is calculated as
k = 0.301/g Example Question You determine that a coconut cream pie has 1 million (106) Staphylococcus
aureus cells in it. You estimate that the food preparer did not wash hands and
probably inoculated the cream with 1000 S. aureus.
If the pie was made 5 hours ago, how many generations have occurred?
How long is each generation?
If the pie was refrigerated for the first 2 hours, how many cells would you
have counted? Solution
Without refrigeration: g = 0.5 hr
With refrigeration: N = 64,000 Continuous Culture: The Chemostat
Continuous culture: an opensystem microbial culture of
fixed volume
Chemostat: most common type of continuous culture
device
Both growth rate and population density of culture can be
controlled independently and simultaneously
Dilution rate: rate at which fresh medium is pumped in and
spent medium pumped out
Concentration of a limiting nutrient Schematic for Continuous Culture Device (Chemostat) Figure 6.11 Continuous Culture: The Chemostat In a chemostat
The growth rate is controlled by dilution rate
The growth yield (cell number/ml) is controlled by the
concentration of the limiting nutrient In a batch culture growth conditions are constantly
changing; it is impossible to independently control both
growth parameters The Effect of Nutrients on Growth Figure 6.12 Continuous Culture: The Chemostat Chemostat cultures are sensitive to the dilution rate and
limiting nutrient concentration
Too high a dilution rate, the organism is washed out
Too low a dilution rate, the cells may die from starvation
Increasing limiting nutrient concentration results in
greater biomass but same growth rate SteadyState Relationships in the Chemostat Figure 6.13 ...
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 Fall '11
 ShailyMahendra

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