Monod kinetics

The Monod equation is a mathematical model of theoretical biology , predicting the growth of microorganisms depending on the concentration of substrates allows. It was set up in 1949 by the French Nobel Prize winner Jacques Monod to model empirically found growth kinetics.

Monod equation

The equation is 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 high ( S >> K _S ), the maximum growth rate μ _{max is} achieved. The saturation or affinity constant K _S is the substrate concentration at which µ = µ _max . The smaller the value of K _S , the greater the affinity of the organism for the respective substrate. ${\displaystyle 1/2}$

The Monod equation is: ${\displaystyle \mu ={\mu _{max}[S] \over K_{S}+[S]}}$

The specific growth rate µ as a function of the substrate concentration S according to the Monod model

A plot of µ against S shows that the growth rate increases rapidly even in the range of low substrate concentrations. At high substrate concentrations, however, the growth rate changes only very slightly.

The variables µ _max and K _{S which} are important for growth in culture are characteristic of the respective organism. With a small K _s , the cultivated organism only needs small amounts of substrate in order to achieve its maximum growth μ _max . These two values ​​can be determined graphically in a linearized representation of the growth rate against the substrate concentration (double-reciprocal plot similar to the Lineweaver-Burk diagram for determining enzyme kinetics).

The Monod equation is very similar to the Michaelis-Menten equation in that cell growth depends on the rate at which the organisms' enzymes build biomass.

Limits of the model

In the kinetic model according to Monod, the specific substrate uptake speed is not considered. However, the actual growth is a subsequent reaction to the uptake of the substrate and is therefore dependent on it. More complex models build on the Monod model; they take into account additional effects such as product or substrate inhibitions.

In a record mode , S >> K _S and thus the term S / ( K _S + S ) is equal to 1 for a large part of the cultivation time. This corresponds to a zero order reaction; thus the model is hardly sensitive to S in this area .

literature

• Hans G. Schlegel: General microbiology. 7th, revised edition. Thieme-Verlag, 1992, ISBN 3-13-444607-3 .
• J. Murray: Mathematical Biology. Volume 1, Springer, 2002, ISBN 0-387-95223-3

Individual evidence

1. ↑ Jacques Monod. The Growth of Bacterial Cultures . Annual Review of Microbiology, 1949, v. 3, p. 371
2. ^ Horst Chmiel: Bioprozesstechnik. 2nd edition, Elsevier, Munich 2006, ISBN 3-8274-1607-8 , pp. 106-109.