Bacteria Specific Growth Rate(Monod Equation) works

Monod equation, which was developed by Jacques Monod in the 1940s.

The empirical Monod equation is the most common rate expression to describe the growth of microorganisms in general and hydrogen-producing bacteria in particular.

Formula :

Bacteria Specific Growth Rate (μ) = μ_max ( SK_s - S )

Where,

μ - Specific growth rate in time ^-1

μ_max - Maximum specific growth rate (time^-1)

S - concentration of subrate in solution (mass/unit volumn).It is also known as affinity constant.

K_s - Half velocity constant (mass/unit volumn)

This Monod formula to describe the relationship between the specific growth rate and the substrate concentration.

There are 2 constants in this equation, μ_max, the maximum specific growth rate, and K_s , the half-saturation constant, which is defined as the substrate concentration at which growth occurs at one half the value of μ_max.

Both μ_max and K_s reflect intrinsic physiological properties of a particular type of microorganism.

Monod assumed that no nutrients other than the substrate are limiting and that no toxic by-products of metabolism build up.

The Monod Growth Constants

Both μ_max and K_s are constants that reflect:

i) The intrinsic properties of the degrading microorganism.

ii) The limiting substrate

iii) The temperature of growth

The following table provides representative values of μ_max and K_s for growth of different microorganisms on a variety of sub-strates at different temperatures and for oligotrophs and copiotrophs in soil.

Organism	Growth temperature (°C)	Limiting nutrient	μmax (1/h)	Ks (mg/l)
Escherichia coli	37	Glucose	0.8-1.4	2-4
Escherichia coli	37	Lactose	0.8	20
Saccharomyces cerevisiae	30	Glucose	0.5-0.6	25
Pseudomonas sp.	25	Succinate	0.38	80
Pseudomonas sp.	34	Succinate	0.47	13
Oligotrophs in soil			0.01	0.01
Copiotrophs in soil			0.045	3

Source: Adapted from Blanch and Clark (1996), Miller and Bartha (1989), Zelenev et al. (2005)