The Growth of Bacterial Populations (page 3)

(This chapter has 4 pages)

© Kenneth Todar, PhD

**The Bacterial Growth Curve**
In the laboratory, under favorable conditions, a growing bacterial
population
doubles at regular intervals. Growth is by geometric progression: 1, 2,
4, 8, etc. or 2^{0}, 2^{1}, 2^{2}, 2^{3}.........2^{n}
(where n = the number of generations). This is called **exponential
growth**.
In reality, exponential growth is only part of the bacterial life
cycle,
and not representative of the normal pattern of growth of bacteria in
Nature.

When a fresh medium is inoculated with a given number of cells, and
the population growth is monitored over a period of time, plotting the
data will yield a **typical bacterial growth curve** (Figure 3
below).

**Figure 3. The typical
bacterial
growth curve. When bacteria are grown in a closed system (also called a
batch culture), like a test tube, the population of cells almost always
exhibits these growth dynamics: cells initially adjust to the new
medium (lag phase) until they can start dividing regularly by the
process
of binary fission (exponential phase). When their growth becomes
limited, the cells stop dividing (stationary phase), until eventually
they
show loss of viability (death phase). Note the parameters of the
x and y axes. Growth is expressed as change in the number viable
cells vs time. Generation times are calculated during the
exponential
phase of growth. Time measurements are in hours for bacteria with
short generation times.**

Four characteristic phases of the growth cycle are recognized.

1. **Lag Phase**. Immediately after inoculation of the cells
into
fresh medium, the population remains temporarily unchanged. Although
there
is no apparent cell division occurring, the cells may be growing in
volume
or mass, synthesizing enzymes, proteins, RNA, etc., and increasing in
metabolic
activity.

The length of the lag phase is apparently dependent on a wide
variety
of factors including the size of the inoculum; time necessary to
recover
from physical damage or shock in the transfer; time required for
synthesis
of essential coenzymes or division factors; and time required for
synthesis
of new (inducible) enzymes that are necessary to metabolize the
substrates
present in the medium.

2. **Exponential (log) Phase**. The exponential phase of growth
is
a pattern of balanced growth wherein all the cells are dividing
regularly
by binary fission, and are growing by geometric progression. The cells
divide at a constant rate depending upon the composition of the growth
medium and the conditions of incubation. The rate of exponential growth
of a bacterial culture is expressed as **generation time**, also
the
**doubling
time **of the bacterial population. Generation time (G) is defined
as
the time (t) per generation (n = number of generations). Hence, G=t/n
is
the equation from which calculations of generation time (below) derive.

3. **Stationary Phase**. Exponential growth cannot be continued
forever
in a **batch culture** (e.g. a closed system such as a test tube or
flask). Population growth is limited by one of three factors: 1.
exhaustion
of available nutrients; 2. accumulation of inhibitory metabolites or
end
products; 3. exhaustion of space, in this case called a lack of
"biological
space".

During the stationary phase, if viable cells are being counted, it
cannot
be determined whether some cells are dying and an equal number of cells
are dividing, or the population of cells has simply stopped growing and
dividing. The stationary phase, like the lag phase, is not necessarily
a period of quiescence. Bacteria that produce **secondary metabolites**,
such as antibiotics, do so during the stationary phase of the growth
cycle
(Secondary metabolites are defined as metabolites produced after the
active
stage of growth). It is during the stationary phase that spore-forming
bacteria have to induce or unmask the activity of dozens of genes that
may be involved in sporulation process.

4. **Death Phase**. If incubation continues after the population
reaches stationary phase, a death phase follows, in which the viable
cell
population declines. (Note, if counting by turbidimetric measurements
or
microscopic counts, the death phase cannot be observed.). During the
death
phase, the number of viable cells decreases geometrically
(exponentially),
essentially the reverse of growth during the log phase.

**Growth Rate and Generation Time**

As mentioned above, bacterial growth rates during the phase of
exponential
growth, under standard nutritional conditions (culture medium,
temperature,
pH, etc.), define the bacterium's generation time. Generation times for
bacteria vary from about 12 minutes to 24 hours or more. The generation
time for *E. coli* in the laboratory is 15-20 minutes, but in the
intestinal tract, the coliform's generation time is estimated to be
12-24
hours. For most known bacteria that can be cultured, generation
times
range from about 15 minutes to 1 hour. Symbionts such as *Rhizobium *tend
to have longer generation times. Many lithotrophs, such as the
nitrifying
bacteria, also have long generation times. Some bacteria that are
pathogens,
such as *Mycobacterium tuberculosis* and *Treponema pallidum*,
have especially long generation times, and this is thought to be an
advantage
in their virulence. Generation times for a few bacteria are are shown
in
Table 2.

**Table 2. Generation times
for
some common bacteria under optimal conditions of growth.**

**Bacterium** |
**Medium** |
**Generation Time (minutes)** |

*Escherichia coli* |
Glucose-salts |
17 |

*Bacillus megaterium* |
Sucrose-salts |
25 |

*Streptococcus lactis* |
Milk |
26 |

*Streptococcus lactis* |
Lactose broth |
48 |

*Staphylococcus aureus* |
Heart infusion broth |
27-30 |

*Lactobacillus acidophilus* |
Milk |
66-87 |

*Rhizobium japonicum* |
Mannitol-salts-yeast extract |
344-461 |

*Mycobacterium tuberculosis* |
Synthetic |
792-932 |

*Treponema pallidum* |
Rabbit testes |
1980 |

**Calculation of Generation Time**

When growing exponentially by binary fission, the increase in a
bacterial
population is by geometric progression. If we start with one
cell,
when it divides, there are 2 cells in the first generation, 4 cells in
the second generation, 8 cells in the third generation, and so on. The
**generation
time** is the time interval required for the cells (or population) to
divide.

G (generation time) = (time, in minutes or hours)/n(number of
generations)

G = t/n

t = time interval in hours or minutes

B = number of bacteria at the beginning of a time interval

b = number of bacteria at the end of the time interval

n = number of generations (number of times the cell population
doubles
during the time interval)

b = B x 2^{n} (This equation is an expression of growth by
binary
fission)

Solve for n:

logb = logB + nlog2

n = __logb - logB__

log2

n = __logb - logB__

.301

n = 3.3 logb/B

G = t/n

Solve for G

G = __ t__

3.3 log b/B

**Example: What is the
generation
time of a bacterial population that increases from 10,000 cells to
10,000,000
cells in four hours of growth?**

G = __ t_______

3.3 log b/B

G = __ 240 minutes__

3.3 log 10^{7}/10^{4}

G = __ 240 minutes__

3.3 x
3

G = 24 minutes

chapter continued

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