**An apparatus (see illustration) for the continuous cultivation of microorganisms, such as bacteria, yeasts, molds, and algae, or for the cultivation of plant cells.** The nutrients required for cell growth are supplied continuously to the culture vessel by a pump connected to a medium reservoir. The cells in the vessel grow continuously on these nutrients. Residual nutrients and cells are removed from the vessel (fermenter) at the same rate by an overflow, thus maintaining the culture in the fermenter at a constant volume.

#### Parameters

An important feature of chemostat cultivation is the dilution rate, defined as the volume of nutrient medium supplied per hour divided by the volume of the culture. During chemostat cultivation, an equilibrium is established (steady state) at which the growth rate of the cells equals the dilution rate. The higher the dilution rate, the faster the organisms are allowed to grow. Above a given dilution rate, the cells will not be able to grow any faster, and the culture will be washed out of the fermenter. The chemostat thus offers the opportunity to study the properties of organisms at selected growth rates. This is particularly important because in their natural environment microorganisms seldom grow at their maximum rate. Under nutrient limitation, cells may display properties which also are of great importance in a number of applications, such as industrial fermentation and wastewater treatment. * See also: ***Fermentation**; **Water treatment**

The nutrient medium which is fed to the fermenter contains an excess of all growth factors except one, the growth-limiting nutrient. The concentration of the cells (biomass) in the fermenter is dependent on the concentration of the growth-limiting nutrient in the medium feed. Upon entering the fermenter, the growth-limiting nutrient is consumed almost to completion, and only minute amounts of it may be found in the culture and the effluent. Initially, when few cells have been inoculated in the growth vessel, even the growth-limiting nutrient is in excess. Therefore, the microorganisms can grow at a rate exceeding their rate of removal. This growth of cells causes a fall in the level of the growth-limiting nutrient, gradually leading to a lower specific growth rate of the microorganisms. Once the specific rate of growth balances the removal of cells by dilution, a steady state is established in which both the cell density and the concentration of the growth-limiting nutrient remain constant. Thus, the chemostat is a tool for the cultivation of microorganisms almost indefinitely in a constant physiological state.

To achieve a steady state, parameters other than the dilution rate and culture volume must be kept constant (for example, temperature and pH). The fermenter is stirred to provide a homogeneous suspension in which all individual cells in the culture come into contact with the growth-limiting nutrient immediately. Furthermore, stirring is also required to achieve optimal distribution of air (oxygen) in the fermenter when aerobic cultures are in use.

Laboratory chemostats usually contain 0.5 to 10.5 quarts (0.5 to 10 liters) of culture, but industrial chemostat cultivation can involve volumes up to 343,000 gal (1300 m^{3}) for the continuous production of microbial biomass.

#### Advantages

The chemostat offers a number of advantages for the cultivation of cells as compared with growth in a batch culture. In the latter, a closed system, organisms grow in excess nutrients at their maximum rate, and the nutrient concentration, products, and biomass change continuously. When a nutrient becomes depleted, a rapid fall in the growth rate takes place. This often leads to the death of cells. In the chemostat, however, the constancy of all parameters allows accurate and reproducible experiments. By varying the dilution rate, within limits, the rate of growth of the organisms can be changed at will. The density of cells in the cultures can be chosen by the appropriate concentration of the growth-limiting nutrient in the medium reservoir. Depending on the question to be answered, the type of growth-limiting nutrient can be selected. Of course, possible choices are limited by the nature and capabilities of the organisms studied.

The chemostat can be used to grow microorganisms on very toxic nutrients since, when kept growth-limiting, the nutrient concentration in the culture is very low. The chemostat can be used to select mutants with a higher affinity to the growth-limiting nutrient or, in the case of a mixed population, to select the species that are optimally adapted to the growth limitation and culture conditions. The chemostat is of great use in such fields of study as physiology, ecology, and genetics of microorganisms. * See also: ***Bacterial genetics**; **Bacterial physiology and metabolism**; **Microbiology**

#### Mathematical description

The operation of a chemostat can also be described in mathematical terms. Growth of a microorganism can be described by the empirical formula of J. Monod (1942) as a function of the growth-limiting substrate, Eq. (1),

in which μ is the specific growth rate (h^{−1}), μ_{max
} is the maximum specific growth rate, *C*_{s} is the concentration of the growth-limiting substrate, and *K*_{s} is a Monod saturation constant, numerically equal to the substrate concentration at which μ = (½)μ_{max
}. The relationship between *C*_{s} and μ is a typical saturation curve. When an organism is grown in a closed system (batch culture) with, initially, excess substrate, it will grow at μ_{max
}. During growth, its environment will constantly change; however, if the conditions remain favorable, growth will continue until the growth-limiting compound is depleted. Near the end of growth, μ will fall because of the factors described by Eq. (1), and will finally become zero.

The chemostat can be considered as an open culture system in which fresh (sterilized) medium is introduced at a constant flow rate ϕ, and from which the culture fluid emerges at the same flow rate. At a constant volume *V* and an in-flow rate ϕ, the dilution rate *D* is defined by Eq. (2), in which the dilution rate is expressed in h^{−1}.

Monod demonstrated that over a large range of growth rates a fixed relationship exists between the amount of (growth-limiting) substrate consumed and the amount of biomass produced, Eq. (3),

in which *C*_{x} is the biomass concentration and *t* is time. *Y* ″_{sx} is the yield factor and is defined as the amount (weight) of cell material produced per amount (weight, or mole) of substrate consumed. *Y* ″_{sx} is not always a constant.

If the medium in the fermenter is inoculated (for example, with bacteria), the culture will grow at a given rate. At the same time, a quantity of bacteria will be washed out because the culture is continuously fed and diluted with fresh medium. It thus follows that accumulation of biomass in the culture is equal to growth minus washout.

The balance equation is Eq. (4).

Hence if μ is greater than *D*, *C*_{x} will increase; while if μ is less than *D*, *C*_{x} will decrease. If μ equals *D*, Eq. (4) will be zero and an equilibrium will exist.

It can be shown mathematically that, irrespective of the starting conditions, a steady state, with μ equal to *D*, must inevitably be reached, provided that *D* does not exceed a critical value.

In order to calculate the steady-state concentrations of biomass and the growth-limiting nutrient in the culture, mass balance equations similar to Eq. (4) for the nutrients entering, being consumed, and leaving the culture must also be made. In Eq. (5), *C*_{s} is the substrate concentration in the culture,

and *C*_{si} is the concentration of the substrate entering the vessel. The net change in *C*_{si} per unit of time is equal to the dilution rate multiplied by the difference in substrate concentration entering and leaving the culture, minus the substrate consumed. The substrate consumed is expressed as the growth divided by the yield, Eq. (3). At steady state, both Eqs. (4) and (5) are zero. This, when combined with Eq. (1), will lead to the equilibrium concentrations *$\stackrel{\u2015}{\text{C}}$*_{x} for biomass [Eq. (7)] and *$\stackrel{\u2015}{\text{C}}$*_{s} for the substrate [Eq. (6)].

Here *K*_{s}, μ_{max
}, and *Y* ″_{sx} are constants for a microorganism under the specified conditions of temperature, medium composition, and the nature of the growth-limiting substrate. For *C*_{si} and *D*, any realistic constant value can be chosen. From Eq. (6), it appears that *$\stackrel{\u2015}{\text{C}}$*_{s} solely depends on *D*. Equation (7) shows that *$\stackrel{\u2015}{\text{C}}$*_{x} depends on *D* and *C*_{si} and is proportional to *C*_{si} if *$\stackrel{\u2015}{\text{C}}$*_{s} \mmll *C*_{si}, which is usually the case. If *K*_{s}, μ_{max
}, and *Y* ″_{sx} are known for a given microorganism, the relationship between *C*_{x} or *C*_{s} and *D* can be predicted at a chosen *C*_{si}.