Doubling Time Calculations

Doubling (generation) time is the time it takes a bacterial population to double. Generation time expresses in summary the rate of exponential growth of a bacterial culture as it is obtainable in the growth curve of bacteria. Bacterial growth usually occurs by geometric progression pattern i.e., 1, 2, 4, 8, 16 e.t.c. (or 20, 21, 22, 23, 24………2n); and this indicates a scenario in the growth medium when the bacterial population doubles at regular intervals. It is noteworthy that generation times vary significantly across the different microbial cells. For example, the generation time of Staphylococcus aureus, a Gram positive bacterium is 30 mins (i.e. S. aureus divides every half an hour) while the doubling time of Escherichia coli, a Gram negative bacterium is 20 mins and lesser than the former. The formular for calculating the generation time is given thus:

G = Generation time

t = time per generation (mins or hrs)

n = number of generations

Calculations for calculating the generation time of a bacterial growth is usually derived from the above formular.

Bacterial cells divide at constant intervals during the exponential growth phase. Growth rate is zero at the stationary phase of bacterial growth. If a microbial cell divides every 10 mins for example; after 10 mins, 2 daughter cells will be produced. How many cells will be produced after one hour if the bacterial cell divides every 10 mins? The answer is 12 cells i.e. 12 daughter cells shall be produced after 1 hr for a bacterial cell that divides every 10 mins. The 12 cells generated are produced at the 6th generation of doubling. The population increase during growth is expressed in an exponential or logarithmic value because the microbial cell or population is doubling in every subsequent generation produced. Thus, increase in cell population is mathematically expressed as 2n; where n = number of generations yielded, and 2 = indicate the doubling i.e. expression of growth by binary fission.

This relationship that exist between the initial number of microbial cells present in the growth medium and the number of cells that result after a certain stage of exponential growth can further be expressed mathematically as:

No = initial cell or population number (i.e. number of bacteria @ the beginning of a time interval)

N = final population number (i.e. number of bacteria @ the end of the time interval)

n = number of generations (doubling) in time during exponential growth.

Taking logarithm of both sides of the above expression (equation 2), we have:

Taking like terms of equation 3 together, we have:

Make “n” the subject of the formular by dividing both sides of equation 4 by log2, we have:

Finally, equations 1 & 8 can be used to evaluate the doubling (generation) time of the exponential growth of a bacterial cell.   

To calculate for the mean growth rate constant (k) and mean generation time or mean doubling time (g), the following applies:

Mean growth rate constant (k) is the number of generations per unit time. And this is mathematically expressed as:

Mean generation time or mean doubling time (g) is defined as the time it takes the bacterial cell to double its size in a growth medium. And this is mathematically expressed as:

Substitute equation 11 into equation 10:

Note: t = g since the population doubles



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