Biochemistry - The Chemical Reactions of Living Cells, Volume 2 - D. Metzler 1980

Enzymes: The Protein Catalysts of Cells
Cell Growth Rate

How can The rate of Cell growth be described? Let us consider a bacterial culture in the logarithmic growth phase. Each cell in the culture divides after a specific time interval (the generation time), which in some cases, such as in E. coli, is only 20 min¹⁾. If a given volume of culture contains an initial number of N₀ Bacteria, then after n cell divisions, the number of bacteria will be    

Class="center">N_n = 2nN₀.       (6-59)

¹⁾ At Cytology/cytology/16.html">Early stages of growth, the generation time can be as short as 17 min, but growth subsequently slows down. The average generation time for E. coli at 37 °C is typically about 26 min, whereas for mammalian tissue culture Cells it is about 1 day.

Thus, a single bacterium with a generation time of 20 min can produce 2¹⁴⁴ cells after 48 h of exponential growth.

The rate constant k for exponential growth equals the number of doublings occurring per unit time, meaning that k is the reciprocal of the generation time. It is easy to show that the number of bacteria at time t is

N_t = 2^ktN₀.       (6-60)

It follows from this that

k_t = log₂ (N_t/N₀) = lg (N_t/N₀)/0.301.       (6-61)

This equation can be used to determine the value of k by measuring the number of bacteria at the initial time and at time t.

Bacterial culture growth can also be described in another way. The rate of increase in the number of bacteria is equal to the product of the specific growth rate constant μ and the current number of bacteria:

dN/d_t = μN.       (6-62)

This is the general equation for an autocatalytic reaction, in which N can be replaced by concentration (for example, the total amount of cellular material per 1 L of medium). It follows from equations (6-61) and (6-62) that

μ = k ln 2 = 0.696.       (6-63)

When bacteria are transferred to a fresh medium, exponential growth is typically preceded by a lag phase. Over time, exponential growth ceases, and the culture enters a stationary phase, which is generally followed by relatively rapid cell death.

Cell cultures are frequently grown under conditions where the generation time is kept constant while The Cell density in the medium does not increase. A simple device called a chemostat has been designed for this purpose. The medium in the culture vessel, containing a specific number of bacteria, is continuously stirred. Fresh culture medium is constantly fed into this vessel from a special reservoir, while a portion of the contents, along with the suspended bacteria, is continuously withdrawn into another vessel. The population size of the bacteria in the vessel reaches a steady state that can be maintained for a relatively long time.