Growth Kinetics :

Growth Kinetics :

The organisms growing by binary fission or budding in a particular set of growth conditions do not all have the same individual generation time.

The generation time can be used to describe the microbial population.For the populations the term doubling time (td, units -h) is takes for population to double in mass or numbers.

In terms of numbers, if there are No. cells at zero time, then after one doubling time there will be 2No. cells and these are given rise to 2²No. Cells after another doubling time.

The series of growth can be represented by 

2⁰ No.→ 2' No.→ 2² No.→ 2³ No.→- - - - 2ⁿ No.

Where,

'n' is the number of doubling times if the culture growing for time 't' then , 

n = t/td

The generation equation for the growth of cells can be written as ,

Nt = 2ⁿ No.

Where, 

Nt-No. of cells present at 't'.

This type of increase is known as "Exponential Growth".

Another way of expressing growth (its imp. in fermentation technology) is the rate at which the number (N) or Mass (X) of microorganisms per ml increase in a culture depends on the No. Present at any time (t).

i.e. dN/dt = YN 

                 or 

       dx/dt = μx

Where,

'Y' and 'μ' are specific growth rate constant for number or mass

∴ 'Y' is equivalent to 'μ' .

Xt = X₀eµt

Xt - mass/ml at time 't'

X₀ - mass/ml at zero time

Specific growth rate constant can be related to the mean generation time for population td , by sustituting Xt/X₀ = 2 and t = td in the exponential function.

td =1n2/μ 

td = 0.693/μ

                       Growth Kinetics

Example : 

Doubling time of some organisms are mentioned below ↓

1.E.coli - 20 minutes

2.S.aureus - 30 minutes

3.Cl.botulinum - 35 minutes

4.Ps.aeroginosa - 35 minutes

5.M.tuberculosis - 12 hrs.