Notes, lecture 8, BIOL401 – 2/10/10
Growth of Bacterial Populations
Length of time it takes for the formation of 2 cells from 1
generation time
(
doubling time)
•
Generation time can vary widely among different types of bacteria
•
Dependent on growth conditions
Exponential Growth:
n
N
N
2
0
=
where
n
= number of doublings
N
= number of bacteria after
n
doublings
N
0
= starting number of bacteria
)
log
(log
3
.
3
301
.
0
log
log
2
log
log
log
2
log
log
log
2
0
0
0
0
0
N
N
N
N
n
n
N
N
n
N
N
N
N
n

=

=
=

+
=
=
Determination of growth parameters:
•
Semilogarithmic graph
of Cell#
vs
Time yields straight line during exponential growth
(since cells double in a constant period of time)
o
Such graphs can be used to estimate doubling times (see Fig 6.7)
Related Growth Parameters
Generation Time
(
a.k.a.

doubling time
): time required for cell population to double
time/doubling
•
also time needed for single cell to divide by binary fission
•
g=t/n,
also,
•
g = 0.301/slope
Division Rate:
# of generations per unit time
•
v = 1/g,
where
g
= generation time
Specific Growth Rate
:
•
k
= 0.301
n/t,
where
n=
# of doublings, and,
t =
time
•
note that n/t = 1/g so k=0.301/g
•
g
= 0.301/
k
Generation time is also equal to 0.301/slope as described below:
•
For cells that are in the exponential phase of growth, we can plot the number of cells per
ml
vs
time on a semilog graph and we observe a straight line.
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The slope of a straight line is defined as:
X
Y
slope
∆
∆
=
•
By definition, when
Δ
X
=
g
(generation, or, doubling time),
Δ
Y
= 2
•
However, we only get a straight line when we plot the number of cells/ml
vs
time on
semilog paper (
i.e.
when we are actually plotting time
vs
the
log
of the # of cells per ml).
•
Therefore the linear relationship holds, when Δ
X
=
g,
and,
Δ
Y
=
log
2
•
So,
k
g
g
X
Y
slope
=
=
=
∆
∆
=
301
.
0
2
log
(
specific growth rate)
•
Given
g
slope
301
.
0
=
we can multiply both sides of the equation by
slope
g
to obtain:
slope
g
301
.
0
=
The Growth Cycle
Batch
culture – closed system
•
lag phase – cells adjust to new conditions; length variable depending on history of culture
and growth conditions
•
exponential phase – cells in healthiest state, rate influenced by environmental conditions
•
stationary phase – exponential growth limited in batch culture, growth limited by variety
of factors including, depletion of essential nutrient(s) and accumulation of waste products
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 Spring '09
 Microbiology, Bacteria, generation time, specific growth rate

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