# Generation Time of Bacteria

Flagella Animation Study | BiologyI...
Flagella Animation Study | BiologyIdeas.com

## Generation Time of Bacteria

During the exponential growth phase, each organism is dividing at constant intervals of time. Thus the population will double in number during a specific length of time called the generation time or doubling time.

The mathematics of growth can be shown as below:

Suppose,

N0= Initial population number

Nt = Population number at time t

n = Number of generations in time t

Formula : Nt = N0 x Nn

Growth rate studies contribute to basic physiological and ecological research and the solution of applied problems in the industry.

During the exponential phase, each microorganism is dividing at constant intervals.

The population will double in number during a specific length of time called the generation time or doubling time.

Because the population is doubling every generation, the increase in population is always 2n where n is the number of generations.

The resulting population increase is exponential or logarithmic.

These observations can be expressed as equations for the generation time.

Let No be the initial population number; Nt be the population at time t; n be the number of generations in time t.

Nt = N0 x 2n

Solving for n, the number of generations, where all logarithms are to the base 10,

log Nt = log No + n (log 2)

n = log Nt – log No / log 2

= log Nt – log No / 0.301

The rate of growth during the exponential phase in batch culture can be expressed in terms of the mean growth rate constant (k).

This is the number of generations per unit time, often expressed as the generations per hour.

k = n/t

= log Nt – log No / 0.301 (t)

The time it takes a population to double in size—that is, the mean generation time or mean doubling time (g), can now be calculated.

If the population doubles (t =g), then,

log Nt = 2 (log No)

Substitute 2No into the mean growth rate equation and solve for k.

k = log (2 No) – log No / 0.301 (g)

= log 2 + log No – log No / 0.301 (g)

= 0.301 / 0.301 (g)

= 1/g

∴ k = 1/g

The mean generation time is the reciprocal of the mean growth rate constant.

k = 1/g

The mean generation time (g) can be determined directly from a semilogarithmic plot of the growth data and the growth rate constant calculated from the g value.

Solving for n, the number of generations, where all logarithms are to the base 10,

Log Nt = Log N0 + n Log 2

n = ( Log Nt- Log N0) / Log 2

= ( Log Nt – Log N0 ) / 0.301

The rate of growth in batch culture can be expressed in terms of mean growth rate
constant (k). This is the number of generations per unit time and expressed as the generations
per hour.

k = n / t

= ( Log Nt- Log N0) / 0.301t

The time it takes for a population to double in size, that is the mean generation time or
mean doubling time (g). If the population doubles (t = g);

then, Nt = 2 × N0

Substituting 2N0 into the mean growth rate equation and solving for k, we get;

k = (Log 2N0 – Log N0 ) / 0.301g

= (Log 2 + LogN0 – LogN0 ) / 0.301g

= 1 / g

g = 1 / k

The mean generation time is the reciprocal of the mean growth rate constant. The mean generation time (g) can be determined directly from a semi-logarithmic plot of growth data and the growth constant calculated from the ‘g’ value. The generation time may also be calculated directly from the equations derived above.

### Example of calculation

Q. A bacterial population increases from 103 cells to 109 cells in 10 hours.

k = (Log 109 – Log103) / [ (0.301) × 10]

=2.0 generations/hour

∴ g = 1/k

= 1/2

= 0.5 hour/ generation or 30 minutes per generation.

Generation time varies markedly with the species of microorganism and environmental conditions.

## Generation Time of Some Organisms

Generation time varies markedly with the species of microorganism and environmental conditions.

In Microbiology, the Generation time of an organism is also known as the doubling time of an organism.

Generation time may vary from organism to organism.

### Generation Time of Some Bacteria

MicroorganismTemperature (°C)Generation time (Hours)
Beneekea natriegens370.16
Escherichia coli400.35
Bacillus subtilis400.43
Clostridium botulinum370.58
Anacystisnidulans412.0
Rhodospirillumrubrum254.6 – 5.3
Anabaena cylindrical2510.6
Mycobacterium tuberculosis3712

### Generation Time of Some Algae

MicroorganismTemperature (°C)Generation time
(Hours)
Chorellapyrenoidosa257.5
Asterionella Formosa209.6
Euglena gracilis2510.9
Skeltonemacostatum1813.1
Ceretiumtripum2082.8

### Generation Time of Some Protozoa

MicroorganismTemperature
(°C)
Generation time
(Hours)
Tetrahymena geleii242.2 – 4.2
Paramecium caudatum2610.4
Acanthomoebacastellanii3011 – 12
Giardia lambila3718

## References

https://www.biologydiscussion.com/bacteria/generation-time-of-bacteria-with-mathematical-expression/55137

## FAQs : Generation time of bacteria

### Q1. What is meant by generation time of bacteria?

Ans: The population of bacteria will double in number during a specific length of time called the generation time.

### Q2. What is meant by doubling time of bacteria?

Ans: The population of bacteria will double in number during a specific length of time called the doubling time.

### Q3. Why is generation time of bacteria important?

Ans: The generation time of bacteria is important because during laboratory practical cell counting is very important for us. Thus, for counting the cell number, the generation time of bacteria is important.

Automated page speed optimizations for fast site performance