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The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910–1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient.
Bacterial growth curve\Kinetic Curve. In autecological studies, the growth of bacteria (or other microorganisms, as protozoa, microalgae or yeasts) in batch culture can be modeled with four different phases: lag phase (A), log phase or exponential phase (B), stationary phase (C), and death phase (D).
Figure 1: A bi-phasic bacterial growth curve.. A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), individual body height or biomass (in physiology, for growth analysis of individuals).
One of the most important features of chemostats is that microorganisms can be grown in a physiological steady state under constant environmental conditions. In this steady state, growth occurs at a constant specific growth rate and all culture parameters remain constant (culture volume, dissolved oxygen concentration, nutrient and product concentrations, pH, cell density, etc.).
If an enzyme that is part of a rate-limiting step of microbial growth is substrate inhibited, then the cell growth will be inhibited in the same manner. However, the mechanisms are often more complex, and parameters for a model equation need to be estimated from experimental data. [ 1 ]
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period.
As resources become more limited, the growth rate tapers off, and eventually, once growth rates are at the carrying capacity of the environment, the population size will taper off. [6] This S-shaped curve observed in logistic growth is a more accurate model than exponential growth for observing real-life population growth of organisms. [8]
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.