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ESM 219
Lecture 4:
Growth and Kinetics
Concepts
• Concerned with populations of cells and
population numbers and characteristics
• Various ways to report population sizes
• Unrestricted cellular division is well
understood
• Mass transferlimited growth models,
including on solid media, involve more
terms
Unrestricted Cell division =
population growth
X = 2
n
X = number of cells
n = number of division events (doublings)
At the beginning, X = 2
0
= 1
2
1
= 2
2
2
= 4, etc…….
Population growth, X = 2
n
(cont.)
Let
n = (# doublings / time) * t
= growth rate constant * t
=
μ
*t
where
μ
= “specific growth rate”
Notice that equation is exponential,
so can express as X = e
μ
t
Note that starting concentration is not 1,
So X = X
o
e
μ
t
where X
o
is the initial concentration.
Unrestricted cell division is a “first
order” rate process
• Unrestricted cell
division is a first order
rate process.
()
)
e
X
(
dt
d
X
dt
d
t
0
μ
=
X
dt
dX
μ
=
So, ….
.
X
dt
dX
μ
=
∫∫
=
=
=
=
=
=
t
t
t
t
t
t
dt
X
dX
dt
X
dX
00
μ
e
X
X
X
X
t
t
t
t
0
0
ln
=
=
Now let’s go the other direction….
.
Separate variables.
Integrate over the interval 0 to t.
The result is a straight line equation….
t
X
X
+
=
0
ln
ln
And if we raised e to both sides, we’d be
back where we started…
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During
exponential
phase growth, a
loglinear plot
produces a
straight line,
because
t
X
X
μ
+
=
)
ln(
)
ln(
0
Microbial Laboratory Culture
Wellmixed liquid
(flask or culture tube
or chemostat)
Solid media culture
(agar or sand culture)
In all cases
• Prepare media with nutrients, and establish
conditions required for growth
• Inoculate
– With a small amount of known cells for pure culture
– With an environmental sample for enrichment culture
• Monitor over time
– Quantify population size at various time points
– Or measure / observe beginning and end.
How to measure cell concentration
1. Direct counts with a microscope
How to measure cell concentration
2. Culturable counts
With or without a dilution series.
3
How to measure cell concentrations
3. Flow cytometry
one might also measure proxies for
biomass
•
Biochemically (DNA, protein, etc.)
•
Absorbance, reported as optical density or
OD (indirect based on turbidity)
Microbial Growth
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This note was uploaded on 08/06/2008 for the course ESM 219 taught by Professor Holden during the Fall '07 term at UCSB.
 Fall '07
 Holden

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