Monod equation

The Monod kinetics is a mathematical model of theoretical biology, which allows predictions for the growth of microorganisms as a function of the concentration of the substrates. It was erected in 1949 found empirically by the French Nobel Prize winner Jacques Monod for modeling growth kinetics.

Monod equation

The equation based on the following model assumptions:

The specific growth rate (including specific growth rate ) μ of cells is related to the concentration of the limiting substrate S. If there is no inhibition and the substrate concentration is very large (S >> KS ), the maximum growth rate is achieved μmax. The saturation or affinity constant KS is the substrate concentration is in the μ = μmax. The smaller the value of KS is, the greater the affinity of the organism to the respective substrate.

The Monod equation is:

In a plot of μ against S can be seen that the growth rate increases already in the range of low substrate concentrations rapidly. However, at high substrate concentrations, the growth rate varies only very slightly.

The important for growth in culture sizes μmax and KS are characteristic of the particular organism. For small K the cultured organism needs only small amounts of substrate in order to achieve maximum growth μmax. In a linearized representation of the growth rate versus substrate concentration ( double - reciprocal plots similar to the Lineweaver- Burk plot for the determination of enzyme kinetics ), these two values ​​can be determined graphically.

The Monod equation is the Michaelis -Menten equation is very similar since the cell growth is dependent on the speed with which to build the enzymes of the organism biomass.

Limitations of the model

In the kinetic model by Monod specific substrate uptake rate is not considered. But where the real growth is a result of reaction of substrate uptake and thus dependent on this. More complex models are built on the model of Monod; they take into account additional effects, such as product or Substratinhibierungen.

In a set operation is a major part of the culture period S >> KS and thus the term S / (KS S ) equal to 1, this corresponds to a zero-order reaction; thus the model is hardly sensitive with p in this area