# Bacteria Specific Growth Rate Calculator

This online **Empirical Monod Equation** calculator is used to measure the dependence of the growth rate on the substrate concentration of bacteria or aerobic metabolism.

## 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} ( _{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 | μ_{max} (1/h) | K_{s} (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 |