GENERAL MICROBIOLOGY - T.P. Pirog - 2004

6. MICROBIAL GROWTH

6.4. GROWTH PHYSIOLOGY

6.4.4. Exponential Growth

Bacteria reproduce by binary fission, which is why their population increases in a geometric progression: 2⁰ → 2¹ → 2² → 2³ →... 2ⁿ. If a growing batch culture contains N_n Cells per unit volume, then after n divisions, The Cell count will become N_n · 2ⁿ. Taking Logarithms, we obtain:

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from which the number of cell divisions is:

THE NUMBER OF CELL DIVISIONS per hour (division rate constant V) is determined by the formula

The time required for a single division cycle (generation time g) is determined by the formula

Example. If the cell count in a suspension increases from 10^a to 10® over 10 hours, the division rate constant is:

where lg 2 = 0.3010.

The generation time in minutes is:

Graphical representation of exponential growth. If we plot the number of cells in an exponentially growing population on the ordinate axis and the growth duration on the abscissa axis (both quantities on an arithmetic scale), we obtain an exponential growth curve (Fig. 6.6). However, this method of graphical representation is unsuitable for A large number of cell divisions because, depending on the chosen scale, it allows us to account for either only the early or only the late divisions. Therefore, a semi-logarithmic scale is used, where the logarithm of the cell count is plotted on the ordinate axis. With this type of graph construction, bacterial exponential growth is described by a straight line. The slope of the line characterizes the division rate: the steeper the slope, the higher the rate. Since exponential growth exhibits a linear relationship between the duration of growth and the logarithm of the cell count, such growth is also referred to as logarithmic growth. However, in recent scientific literature, preference is given to the term "exponential growth", while the term "logarithmic growth" is used very rarely and is considered obsolete.

Fig. 6.6. Exponential growth of unicellular organisms: cell count as a function of cultivation time

If the generation time is determined from the cell count using the method described above, we obtain an average value. However, a bacterial population always contains some proportion of defective cells incapable of division; consequently, for actively dividing cells, the true generation time will be slightly shorter than the calculated one. For this reason, when studying growth kinetics, individual cells are disregarded, and the bacterial population is treated as an autocatalytically reproducing system, basing calculations on the bacterial mass density (biomass). The rate of change of this bacterial mass density at any given moment is proportional to the density itself, meaning the change follows first-order reaction kinetics.

In the exponential growth phase, the specific growth rate constant is determined by the formula

.

where X is biomass and t is time

Integrating this equation, we obtain:

where X and X₀ are the final and initial biomass, respectively.

For the doubling of cellular biomass from which the doubling time t_d is:

Only for "standard cells" (under conditions where biomass growth is proportional to the increase in cell concentration):

The distinction between The concepts of "cell number" and "cell mass" is summarized in Table 6.6.

Table 6.6.

Differences between the concepts of "cell number" and "cell mass"