Microbiology and Biotechnology

Lessons

Senior 4 · Biology

Microbiology and Biotechnology

5 lessons

Lesson 4 of 5

Population growth of bacteria and the roles of bacteria

25 min

A billion by bedtime

In a warm, rich broth, a single E. coli cell can divide every 20 minutes or so. After one hour there are 8 cells; after ten hours, if every cell kept dividing, there would be $2^{30}$ , more than a thousand million. A spoonful of milk left on a warm table, or a cut that is not cleaned, gives bacteria exactly this chance. Yet the world is not buried in bacteria. Something always stops the growth, and understanding what, and when, is central to food safety, medicine and every industry that uses microbes.

Definition

Binary fission: asexual reproduction of a prokaryote: the DNA is copied and the cell divides into two identical cells.

Generation time (doubling time), $g$ : the time taken for a population of cells to double in number.

Exponential (logarithmic) growth: growth in which the population doubles in each equal time interval, so the number multiplies rather than adds.

Viable count: the number of living cells able to form colonies, given as colony-forming units (CFU) per cm³. Total count: all cells, living and dead, counted under the microscope in a counting chamber (haemocytometer).

Serial dilution: a series of stepwise dilutions, each by the same factor (often 10), used to reduce a dense culture to a countable number of cells.

Calculating growth

If a population starts with $N_{0}$ cells and passes through $n$ generations, each doubling the number:

N = N_0 \times 2^{n} \qquad \text{where} \qquad n = \frac{t}{g}

Taking logarithms gives the number of generations from two counts:

n = \frac{\log N - \log N_0}{\log 2} = \frac{\log N - \log N_0}{0.301}

Worked example 1: finding the generation time

During the log phase, a culture grew from $1.0 \times 10^{3}$ to $6.4 \times 10^{4}$ cells per cm³ in 2 hours. Calculate (a) the number of generations and (b) the generation time. (c) How many cells per cm³ would there be after another hour, if growth continued at the same rate?

(a) $n = \frac{\log (6.4 \times 10^{4}) - \log (1.0 \times 10^{3})}{\log 2} = \frac{\log 64}{\log 2} = \frac{1.806}{0.301} = 6$
(b) $g = \frac{t}{n} = \frac{120\ \text{min}}{6} = 20\ \text{min}$ .
(c) One more hour is $\frac{60}{20} = 3$ generations: $6.4 \times 10^{4} \times 2^{3} = 5.1 \times 10^{5}$ cells per cm³.

The growth curve

In a closed container (a batch culture) nutrients are not replaced and wastes are not removed, so the population passes through four phases. Because numbers change by many powers of ten, they are plotted on a logarithmic scale, on which exponential growth appears as a straight line.

Phase	What happens	Why
Lag	Little or no increase in number	Cells adjust to the new medium: they take up water, make enzymes for the nutrients present and copy their DNA
Log (exponential)	Numbers double every generation; a straight line on a log scale	Nutrients plentiful, little waste; division as fast as conditions allow. Cells are most sensitive to antibiotics now
Stationary	Number of living cells stays constant	Nutrients run short and toxic wastes (acids, alcohol) build up: new cells are formed only as fast as others die. Some bacteria form spores
Death (decline)	Number of living cells falls, often exponentially	Nutrients exhausted and wastes toxic: more cells die than are formed

Counting bacteria: serial dilution and plate counts

A culture may hold millions of cells per cm³, far too many to count. It is diluted step by step, and a known volume of each high dilution is spread on agar. Each living cell grows into one colony, so the colonies can be counted and multiplied back up.

Worked example 2: a viable count

Use Figure 2. Calculate the number of living bacteria per cm³ in the original culture.

Choose the plate with between 30 and 300 colonies: the $10^{-5}$ plate, with 63 colonies. (Fewer than 30 gives a large error; more than 300 and colonies merge.)
The 0.1 cm³ spread from the $10^{-5}$ tube contained 63 living cells, so $\text{CFU per cm}^3 = \frac{\text{colonies}}{\text{volume plated} \times \text{dilution}} = \frac{63}{0.1 \times 10^{-5}} = 6.3 \times 10^{7}$
Check with the $10^{-6}$ plate: $\frac{7}{0.1 \times 10^{-6}} = 7 \times 10^{7}$ , close agreement. A viable count misses cells that stick together in clumps (each clump makes one colony), so it is usually an underestimate of the living cells.

The roles of bacteria

Role	Bacteria and what they do
Decomposition and recycling	Saprotrophic bacteria break down dead organisms and wastes, releasing carbon dioxide, ammonium and minerals for plants (S3 Unit 3, nutrient cycles)
Nitrogen fixation	Rhizobium in the root nodules of beans, peas and other legumes turns nitrogen gas into ammonium for the plant, in exchange for sugars; this is why beans enrich the soil for the next crop
Nitrification	Nitrosomonas oxidises ammonium to nitrite and Nitrobacter oxidises nitrite to nitrate, the form most plants absorb
Digestion in animals	Bacteria in the rumen of cattle and goats digest cellulose, which the animals cannot digest themselves; gut bacteria in humans make vitamin K
Food production	Lactic acid bacteria (Lactobacillus, Lactococcus) ferment the lactose in milk to lactic acid in ikivuguto, yoghurt and cheese; Acetobacter makes vinegar
Biotechnology and medicine	Genetically modified E. coli makes insulin; Streptomyces makes antibiotics such as streptomycin; bacteria make enzymes for industry (Lesson 5)
Sewage treatment and clean-up	Bacteria digest organic waste in sewage works and can break down oil and other pollutants (bioremediation)
Harmful roles	Disease in people, animals and crops (cholera, TB, bacterial wilt of potato); food spoilage; denitrifying bacteria return soil nitrate to nitrogen gas, lowering soil fertility

Worked example 3: how long does milk stay safe?

Fresh milk contains $2 \times 10^{5}$ bacteria per cm³. It is regarded as spoiled at $5 \times 10^{8}$ per cm³. At 30 °C the bacteria double every 30 minutes; in a refrigerator at 5 °C, every 8 hours (illustrative values; ignore the lag phase). How long does the milk last at each temperature?

Number of generations needed: $n = \frac{\log (5 \times 10^{8}) - \log (2 \times 10^{5})}{\log 2} = \frac{8.699 - 5.301}{0.301} = \frac{3.398}{0.301} = 11.3$
At 30 °C: $t = n \times g = 11.3 \times 30\ \text{min} = 339\ \text{min}$ , about 5.6 hours.
At 5 °C: $t = 11.3 \times 8\ \text{h} = 90\ \text{h}$ , almost 4 days. Cooling does not kill the bacteria; it slows their enzymes and so lengthens the generation time.

Bio-Rad Laboratories: "Serial Dilution and Plate Counts". Watch how each tube is mixed before the next transfer, why a fresh sterile pipette tip is used each time, and how the count is multiplied back up by the dilution.

Warning

Common mistakes

Adding instead of multiplying: after 3 generations, 100 cells become $100 \times 2^{3} = 800$ , not 106.
Forgetting that the log scale compresses numbers: a rise of 1 on the axis means ten times more cells.
Using a plate with too many colonies, or forgetting to divide by the volume plated as well as the dilution.
Saying cells stop dividing in the stationary phase. Division continues but is balanced by death.
In practical work, count colonies through the closed lid; never open an incubated plate.

Tip

Memory hook. The growth curve is a day in the life of a crowded city: "Late start, Lots of births, Stuck at full, Declining" (Lag, Log, Stationary, Death). For counts: "CFU = colonies ÷ (volume × dilution)".

✦

Practice: bacterial growth and the roles of bacteria

A bacterium has a generation time of 25 minutes. Starting with 500 cells, how many will there be after 2 hours 30 minutes?
A population grew from $3.0 \times 10^{2}$ to $7.68 \times 10^{4}$ cells in 4 hours. Calculate the number of generations and the generation time.
Explain the shape of each phase of the growth curve of a batch culture.
Explain why bacterial numbers are plotted on a logarithmic scale.
In a viable count, 0.1 cm³ of a $10^{-4}$ dilution gave 142 colonies. Calculate the CFU per cm³ in the original sample.
Explain why a viable count is usually lower than a total count made with a haemocytometer.
Describe two beneficial and two harmful roles of bacteria in Rwandan agriculture.

Show answersHide answers

$n = \frac{150}{25} = 6$ ; $N = 500 \times 2^{6} = 500 \times 64 = 32\,000$ cells.
$n = \frac{\log (7.68 \times 10^{4}) - \log (3.0 \times 10^{2})}{0.301} = \frac{\log 256}{0.301} = \frac{2.408}{0.301} = 8$ generations; $g = \frac{240}{8} = 30$ minutes.
Lag: cells adapt, making enzymes and copying DNA, so numbers barely rise. Log: plentiful nutrients, every cell divides each generation, so numbers double at a constant rate. Stationary: nutrients run short and toxic wastes build up, so births equal deaths. Death: nutrients exhausted and wastes toxic, so deaths exceed births and numbers fall.
Numbers range over many powers of ten (for example $10^{3}$ to $10^{9}$ ), which cannot be shown clearly on an ordinary scale; on a log scale exponential growth becomes a straight line, so the growth rate and generation time are easy to read.
$\frac{142}{0.1 \times 10^{-4}} = 1.42 \times 10^{7}$ CFU per cm³.
A total count includes dead cells, which cannot form colonies; and in a viable count clumps or chains of cells each give only one colony. So the viable count is lower.
Beneficial: Rhizobium in bean root nodules fixes nitrogen and improves soil fertility; decomposers recycle crop waste and manure into nutrients; rumen bacteria let cattle digest grass; lactic acid bacteria make ikivuguto. Harmful: bacterial wilt diseases of crops such as potato and banana; denitrifying bacteria in waterlogged soils remove nitrate; spoilage of milk and stored food.

Quick check

Put the phases of a batch culture's growth curve in order.

Tap the cards in the right order.

Key points

Bacteria reproduce by binary fission: $N = N_0 \times 2^{n}$ , $n = \frac{t}{g}$ , and $n = \frac{\log N - \log N_0}{\log 2}$ .
A batch culture shows lag, log, stationary and death phases, plotted on a log scale; limits come from nutrients running out and toxic wastes building up.
Viable count: serial dilution, plate 0.1 cm³, count a plate with 30–300 colonies; CFU per cm³ = colonies ÷ (volume × dilution).
Bacteria recycle nutrients, fix nitrogen, help animals digest cellulose, make foods, medicines and enzymes and clean waste; others cause disease, spoilage and loss of soil nitrogen.

Sources and credits

9.1: How Microbes Grow and 4.1: Prokaryote Habitats, Relationships, and Microbiomes, from Microbiology by OpenStax (Nina Parker, Mark Schneegurt, Anh-Hue Thi Tu, Philip Lister, Brian M. Forster), via LibreTexts Biology, licensed under CC BY 4.0. Used for binary fission, generation time, the growth curve, counting methods and the roles of bacteria. Adapted by Ganzaa.
Figures 1 and 2 (illustrative data), the tables, worked examples (the milk figures are illustrative), practice and quick check: written by Ganzaa.
Photo: Ninjatacoshell, CC BY-SA 3.0, via Wikimedia Commons.
Video: "Serial Dilution and Plate Counts", Bio-Rad Laboratories, embedded from YouTube.

1A billion by bedtime

2Calculating growth

3The growth curve

4Counting bacteria: serial dilution and plate counts

5The roles of bacteria

A billion by bedtime

Calculating growth

The growth curve

Counting bacteria: serial dilution and plate counts

The roles of bacteria