General Microbiology - Schlegel, H. 1987

Microbial Growth
Physiology of Growth

Growth is defined as an irreversible increase in The amount of living matter, typically associated with Cell enlargement and division. In Multicellular Organisms, this manifests as an increase in body size, whereas in unicellular organisms, it leads to an increase in cell number. Even in unicellular forms, however, one must distinguish between an increase in cell count and an increase in total cell mass (Table 6.4).

To determine the number or mass of Bacteria, researchers typically prepare a homogeneous cell suspension in a liquid medium and measure either the bacterial concentration (number of Cells per mL) or the bacterial density (in mg/mL). Based on how these parameters increase in a growing bacterial culture, one can calculate the Cell Division rate constant (expressed as the number of cell concentration doublings per hour) and its reciprocal—the generation time (the time interval required for The Cell count to double).

Class="center">Table 6.4. Distinction between "bacterial number" and "bacterial mass"

6.5.1 Methods for determining Bacterial Number and Mass

During the growth of a batch (static)¹ bacterial culture, strict proportionality between the increase in cell number and the increase in bacterial mass may not always be maintained. Therefore, these two parameters must be assessed separately.

¹ A term used for microorganism cultures grown in a closed medium without replenishment. — Note of the Editor.

Determination of bacterial number. Not all cells in a bacterial population are viable. Viable cells are generally defined as those capable of forming colonies on (or within) an Agar medium or growing as a suspension in a nutrient broth. These viable cells are detected using specialized methods designed to enumerate living cells. By contrast, the Total Cell Count includes all visible or otherwise detectable cells, thereby encompassing dead or damaged cells as well.

Total cell count. 1. The most widespread METHOD FOR DETERMINING the total cell count is direct microscopic counting in a thin layer using a counting chamber (e.g., Neubauer, Thoma, or Petroff-Hausser). If the chamber depth is 0.02 mm and the side of the smallest grid square is 0.05 mm (giving a volume of 5 ∙ 10^-8 cm³), the number of cells per 1 mL is obtained by multiplying the counted value by 2∙10⁷. 2. One of the oldest methods involves comparing the bacterial count with a known concentration of other small particles, such as erythrocytes (approximately 5∙10⁶ erythrocytes per 1 mL). 3. Work is considerably facilitated by The Use of an electronic particle counter (Coulter counter), which operates on THE PRINCIPLE OF a temporary decrease in electrolyte conductivity as a single bacterium passes through a narrow aperture. 4. If a sample contains fewer than 10⁶ cells per mL, the Membrane filtration method is suitable. Sea Water, pond water, or drinking water is passed through a membrane filter, after which the filter is dried, stained, cleared, and examined microscopically for cell counting.

Viable cell count. This typically involves counting the colonies formed by viable cells under growth-favorable conditions. In the Koch pour-plate method, appropriate dilutions of a homogeneous cell suspension are mixed with molten agar medium (40–45 °C) and poured into Petri dishes. Alternatively, the suspension can be spread across the agar surface of a Petri dish using a Drigalski spatula, or cells can be collected by filtration onto an agar surface or nutrient-laden cardboard discs. In all cases, colonies are counted following appropriate incubation. While the Koch plate method and its various modifications are well suited for enumerating single species from homogeneous Suspensions, they are inadequate for counting different species within mixed populations.

Determination of bacterial mass. The choice of method for measuring bacterial mass depends on the specific research objective. To estimate yield, researchers usually weigh wet or dried centrifuged cells. When assessing metabolic intensity or enzymatic activity, measurements are typically based on cellular protein or nitrogen content. Practical considerations such as simplicity and speed often dictate the method of choice; thus, in routine practice, indirect methods (following proper calibration) are preferred over direct ones.

Direct methods. 1. Wet biomass is determined after pelleting cells via centrifugation. Following the centrifugation of washed cells, dry mass can also be measured. Both approaches are subject to substantial systematic errors. 2. Considerably higher precision is achieved by determining total nitrogen (via the micro-Kjeldahl method or microdiffusion ammonia analysis) or total carbon content (using the Van Slyke-Folch method). 3. In routine laboratory work, bacterial protein content is frequently measured. Reliable results are provided by modifications of the biuret reaction and other colorimetric assays. Micromethods rely on quantifying characteristic protein components such as Tyrosine and Tryptophan (using the Lowry or Folin Procedures).

Indirect methods. 1. Measuring the turbidity of cell suspensions is extremely useful for estimating cell mass. In practice, optical density is typically determined via extinction measurements or turbidimetry. For certain Applications, light scattering measurements (nephelometry) yield more precise results. However, a direct (linear) relationship between these optical readings and bacterial mass holds true only at very low cell densities. Because light scattering depends on the diameter, shape, and refractive index of the scattering particles (including intracellular inclusions), the correlation between optical values and more direct parameters—such as dry biomass, nitrogen content, or carbon content—must be verified empirically on a case-by-case basis. 2. Metabolic indicators directly coupled to growth (such as O₂ consumption, CO₂ production, or acid generation) can serve as reliable proxies for bacterial mass. Such measurements are particularly useful when other methods fail, such as with extremely sparse cell suspensions, and can be performed titrimetrically, manometrically, electrochemically, or through other analytical means.

6.5.2 Exponential Growth and Generation Time

Bacteria reproduce primarily by binary fission, causing their population to increase in a geometric progression: 2⁰ → 2¹ → 2² → 2³ → ... → 2ⁿ.

If a growing batch culture has an initial cell concentration of N₀ per unit volume, the number of cells after n divisions will be N₀ ∙ 2ⁿ. Taking Logarithms yields lgN = lgN₀ + nlg2, from which the number of cell divisions is derived as follows:

The number of cell divisions per hour, or the division rate constant v, is calculated using the formula:

The time required for a single division cycle, known as the generation time, is expressed as:

If the cell concentration in a suspension increases from 10³ to 10⁹ over a 10-hour period, the division rate constant is calculated as:

yielding a generation time of half an hour.

Plotting the cell count of an exponentially growing population on the ordinate against time on the abscissa (both on an arithmetic scale) produces an exponential growth curve (Fig. 6.5). However, this graphical representation is impractical for A large number of cell divisions because the chosen scale allows one to visualize either only the earliest or only the latest divisions. Therefore, it is preferable to use a semilogarithmic scale (Fig. 6.5), where the logarithm of the cell number is plotted on the vertical axis. In this type of graph, exponential bacterial growth is depicted as a straight line. The slope of this line reflects the division rate: the steeper the slope, the higher the rate. Because exponential growth exhibits a linear relationship between time and the logarithm of the cell number, this phase is also referred to as logarithmic growth.

Fig. 6.5. Exponential growth of unicellular organisms: cell number as a function of time.

If the generation time g is determined from the cell number using the method described above, we obtain its average value. It should be borne in mind, however, that a bacterial population always contains a certain number of defective cells incapable of division; therefore, the actual generation time of actively dividing Cells must be somewhat shorter. In many cases, when studying growth kinetics, individual cells are disregarded, and the growing bacterial population is treated as an autocatalytically reproducing system. Calculations are thus based on the density of the bacterial suspension. The rate of change in the density of such a suspension at any given moment is proportional to the density itself; that is, the change follows first-order reaction kinetics. During the exponential phase, the specific growth rate constant is defined as

Integrating this yields x = x_{0 ∙} e^μt, and for the doubling of cell mass 2х₀ = х_{0 ∙} е^μtd, from which the doubling time is

When comparing the growth rate constant (μ) with the division rate constant (v), one should bear in mind that cell number and cell mass are not identical concepts, and that the ratio between these two parameters changes during the growth of a batch culture. If, however, the determination and comparison of dry mass or cell number are carried out under conditions where cell mass growth is strictly proportional to the increase in cell number ("standard cells"), then μ = ln 2 ∙ v and t_d = g.

6.5.3 Bacterial growth in batch culture

When bacteria are introduced into a nutrient medium, they typically grow until the concentration of one of the essential medium components reaches a minimum, after which growth ceases. If no nutrients are added and no metabolic end-products are removed during this time, a so-called batch culture (a cell population in a limited living space) is obtained. Growth in such a "closed system" obeys regularities that hold true not only for unicellular, but also for multicellular organisms. A batch culture behaves like a multicellular Organism with genetically limited growth.

Fig. 6.6. Growth curve of a bacterial culture.

The curve describing the dependence of the logarithm of the Number of viable cells on time is called the growth curve. A typical growth curve (Fig. 6.6) is sigmoidal in shape and allows several growth phases to be distinguished, which succeed one another in a specific sequence and are expressed to a greater or lesser extent: the initial (or lag) phase, the exponential (or logarithmic) phase, the stationary phase, and the death phase.

Microbial growth on solid nutrient media proceeds in much the same way, although significantly higher cell densities are achieved.

Lag phase. This phase covers the time interval between inoculation and the attainment of the maximum division rate. Its duration depends mainly on the preceding cultivation conditions and the age of the inoculum, as well as on how well-suited the given medium is for growth. If the inoculum is taken from an old culture (in the stationary growth phase), the cells must first adapt to the new conditions through RNA Synthesis, ribosome formation, and enzyme synthesis. If the energy and carbon sources in the new medium differ from those in the previous culture, adaptation to the new conditions may involve the synthesis of new Enzymes that were previously unnecessary and thus not synthesized. The formation of these new enzymes is induced by the new substrate.

A good example of the substrate's influence on enzyme synthesis is the so-called diauxie (Fig. 6.7). This phenomenon of biphasic growth, or a double growth cycle, is observed in media containing a mixture of nutrients. For instance, out of a glucose and sorbitol mixture, Escherichia coli preferentially takes up glucose first. Glucose initially induces the synthesis of enzymes required for its utilization in the cells while simultaneously repressing the synthesis of enzymes necessary for sorbitol utilization. These latter enzymes are formed only after all the glucose has been depleted. Such regulatory processes adequately account for the presence of the two initial phases.

Fig. 6.7. Biphasic growth (diauxie) of Escherichia coli in nutrient media containing varying ratios of glucose and sorbitol. (Monod J., Recherches sur la croissance des cultures bacteriennes, Paris: Hermann, 1958.)

The quantitative change in the composition of a bacterial cell during the lag phase primarily affects ribonucleic acid: the RNA content increases 8- to 12-fold. This indicates the involvement of RNA and Ribosomes in the synthesis of enzyme Proteins.

Exponential phase. The exponential (logarithmic) growth phase is characterized by a constant maximum cell division rate. During this phase, the rate depends on the bacterial species and the medium. Enterobacteria divide every 15-30 min, while Escherichia coli divides approximately every 20 min at 37°C. In other bacteria, the generation time is considerably longer: in many soil species, it reaches 60-150 min, and in Nitrosomonas and Nitrobacter, even 5-10 h.

In many bacteria, Cell size and protein content also remain constant during the exponential phase. In a sense, it can be said that a bacterial culture under these conditions consists of "standard cells." Once it is firmly established that the cell count, protein content, and dry biomass increase at the same rate, any of these parameters can be used to monitor culture growth.

Frequently, however, even during the exponential growth phase, batch culture cells undergo changes as the medium gradually shifts: Substrate Concentration decreases, cell suspension density increases, and metabolic products accumulate. Because the cell division rate is relatively constant during the exponential phase, this phase is the most convenient for determining the division rate (and growth rate). When studying the Influence of Environmental factors (pH, redox potential, Temperature, aeration, etc.) as well as the suitability of various substrates, researchers track the increase in cell count or turbidity (optical density) of the cell suspension during exponential growth.

Stationary phase. The stationary phase begins when the cell count stops increasing. The growth rate depends on the substrate concentration; as this concentration decreases—even before the substrate is completely exhausted—the growth rate starts to decline. Consequently, the transition from the exponential phase to the stationary phase occurs gradually. The growth rate may drop not only due to substrate limitation but also because of a high bacterial population density, low partial pressure of O₂, or the accumulation of toxic metabolic byproducts; all these factors trigger the onset of the stationary phase. Even in the stationary phase, processes such as the utilization of reserve Materials, The breakdown of a fraction of ribosomes, and enzyme synthesis may still occur. The observed picture depends on which specific factor limits growth. Only highly sensitive cells die rapidly; others remain viable for a long time as long as they can obtain the energy required for this by oxidizing certain reserve materials or cellular proteins.

The amount of biomass reached in the stationary phase is referred to as the yield. The yield depends on The Nature and quantity of the nutrients used, as well as on the cultivation conditions.

Death phase. The death phase and the causes of bacterial cell death in standard nutrient media are insufficiently understood. Cases where acids accumulate in the medium (during the growth of Escherichia, Lactobacillus) are relatively easy to explain. The number of viable cells may decline exponentially. Sometimes cells undergo lysis through the action of their own enzymes (autolysis).

6.5.4 GROWTH CURVE PARAMETERS

When batch culture growth is monitored by the increase in dry bacterial mass, three growth metrics or parameters are of primary interest: cell yield, growth rate, and lag-phase duration (Fig. 6.8).

Yield. Yield is defined as the difference between the maximum and initial bacterial mass: X = Х_макс — Х₀. This value is expressed in grams of dry matter. Of particular importance is The ratio of cell yield to the amount of consumed substrate (X/S). If both values are expressed in weight units, the X/S ratio is referred to as the yield coefficient (or economic coefficient) and denoted as Y. If the yield in grams is instead normalized to the number of moles of substrate consumed, the resulting value is termed the molar growth yield and designated as Y. This coefficient correlates the yield with the amount of ATP synthesized via a specific energy source (substrate). Thus, the energy yield coefficient Y_AТР is obtained (expressed in grams of cell mass per mole of ATP); it can be calculated if the catabolic pathway of the given substrate and the energy yield of the process are known.

Fig. 6.8. Growth parameters: cell yield (A), growth rate (B), and lag-phase duration (C).

For anaerobic cultures of Escherichia coli and Klebsiella pneumoniae, whose growth rates were limited by the amount of added glucose, Y_AТР values of 12.4 and 14 g of biomass per mole of ATP equivalents were found, respectively. In anaerobic bacteria that derive energy through Fermentation, Y_AТР is largely a constant value. If a significantly higher coefficient is obtained for a new bacterial strain, it can be concluded that There is a "side income," i.e., an additional energy-yielding metabolic pathway. Y_AТР values have also been calculated and determined for cells growing under aerobic conditions; they depend on growth conditions and the required intensity of biosynthetic processes within the cells, i.e.,

for example, on whether ammonium ions, nitrate ions, or molecular nitrogen serves as the nitrogen source.

Exponential growth rate. This is a measure of the rate of cell growth during the exponential phase. It is calculated from the initial and final bacterial densities, x₀ and x_t, at times t₀ and t using the formula

where lg e = 0.43429. The doubling time is For "standard cells"

p = ln2 ∙ v and t_d = g (sec. 6.5.2).

Lag-phase duration (T_i). This parameter is crucial for assessing bacterial properties or medium suitability. It is defined as the time interval between the moment t_r at which the culture reaches a specific density x_r and the moment t_i at which it would have reached the same density had exponential growth begun immediately after inoculation (the subscript l denotes the lag phase, r denotes real growth, and i denotes ideal growth):

Since the parameter T_i is only suitable for comparing two cultures with identical exponential growth rates, it is recommended to measure lag-phase duration not in absolute units, but in physiological units (generation time g). The difference between the observed growth and the calculated ideal growth, expressed as a multiple of the generation time, is L = T_iv. Thus, the value L indicates how many doublings (generations) the real culture lags behind an ideal culture that would have grown exponentially from the very beginning. This value is commonly used when comparing data characterizing the effects of various nutrients, growth inhibitors, and cultivation conditions.

6.5.5 Growth in Continuous Culture

In batch culture, conditions are constantly changing; the bacterial population density increases while the substrate concentration decreases. In many physiological studies, however, it is desirable for cells to remain in the exponential growth phase for extended periods at a constant substrate concentration under unchanging conditions. To some extent, this state can be approximated by repeatedly and frequently transferring cells into fresh nutrient medium. Obviously, this goal could be more simply achieved by continuously supplying fresh nutrient solution into a vessel containing a population of growing bacteria while simultaneously removing a corresponding amount of the bacterial suspension. This very method forms The basis of continuous cultivation in chemostats and turbidostats.

Fig. 6.9. Principle of continuous culture in a chemostat. 1 - nutrient medium vessel equipped with a vent filter (VF) and refilling tube (R); 2 - peristaltic pump; 3 - chemostat with nutrient medium inflow (NM), stirrer (M), air filter (AF), and sampling port (SP); 4 - collection vessel with exhaust air filter (AF).

Growth in a chemostat. A chemostat (Fig. 6.9) consists of a culture vessel into which nutrient solution is fed at a constant rate from a dedicated reservoir. Aeration and mechanical stirring create optimal conditions within the culture vessel for supplying cells with oxygen and for faster, more uniform distribution of nutrients delivered with the fresh medium. As the nutrient solution flows into the culture vessel, an equivalent volume of bacterial suspension overflows.

Let us denote the vessel volume by V (in liters) and the feed rate of the nutrient solution—the dilution rate—by f (in liters per hour); then the dilution rate D will be equal to f/V. Thus, the value D reflects the volume of liquid exchanged per hour. If the bacteria inside the chemostat (x [g/L]) were not growing upon startup, they would be washed out of the vessel, and the washout rate would be equal to In this case, the density of the bacterial suspension in the vessel would decrease exponentially:

Bacteria in the culture vessel also grow exponentially. The growth rate is determined by the expression meaning that the density of the bacterial suspension also increases exponentially:

Consequently, the rate of change in suspension density within the vessel, dx/dt, is equal to the algebraic sum of μx and — Dx:

If the growth rate μ and the dilution rate D are equal, cell loss due to washout and biomass production balance each other out—that is, the rate of change is zero, and the bacterial suspension density x remains constant. The culture thus enters a steady state (dynamic equilibrium). Exponential cell multiplication is offset by another exponential process leading to a decrease in cell numbers.

Growth of a culture in a chemostat is controlled by substrate concentration. The Stability of the system relies on limiting the growth rate via the concentration of a single essential substrate (an electron donor, or a source of nitrogen, sulfur, or phosphorus). If, due to this limitation, the true growth rate μ turns out to be less than μ_макс (the maximum rate achievable under substrate saturation), the dilution rate D can be varied over a wide range without causing a drop in suspension density. However, the dilution rate must not exceed μ_макс.

The dependence of the growth rate constant μ on the substrate concentration c_s is described by a saturation curve (Fig. 6.10). Generally speaking, bacteria are capable of growing at their maximum rate even at very low substrate concentrations (e.g., 10 mg of glucose per liter). Only at even lower substrate amounts does the value of μ depend on its concentration. The substrate concentration at which the growth rate μ reaches half of its maximum value (μ = μ_Макс/2) is designated as K_S. Alongside Y and μ_макс, the K_S value is one of the most critical parameters characterizing bacterial growth in chemostats.

Fig. 6.11 illustrates The Effect of the dilution rate D on four parameters: bacterial suspension density, substrate concentration, doubling time, and cell yield. As the dilution rate D varies from zero to nearly the washout point D_c, the density of the bacterial suspension changes only slightly. In this range, bacteria respond to an increase in D with a decrease in doubling time. However, as the dilution rate increases (which also increases the inflow rate and decreases the doubling time), the cell yield goes up. It reaches a maximum at D_m, and drops sharply with any further increase in D.

Fig. 6.10. Dependence of the growth rate μ on the substrate concentration (c_s).

Fig. 6.11. Relationships between bacterial suspension density, substrate concentration, doubling time, and bacterial yield under steady-state conditions at various dilution rates (D) in a chemostat. Data for a bacterial culture with the following parameters: μ_макс = 1.0 h^-1; Y = 0.5; K_s = 0.2 g/l; substrate concentration in the incoming nutrient medium S_r = 10 g/l. On the ordinate axis: A – bacterial yield, g/(l ∙ h); B – doubling time t_d, h; C – substrate concentration in the culture vessel S, g/l. On the abscissa axis: dilution rate D, h^-1; D_m – dilution rate at maximum bacterial yield; D_c – washout point. (Herbert et al., J. Gen. Microbiol., 14 [1956] 601.)

At low dilution rates, the substrate concentration in the cultivator—and consequently in the outflowing suspension—remains close to zero over a fairly wide range. Only when the dilution rate approaches the value that ensures maximum growth does a noticeable fraction of the substrate begin to wash out along with the cells; eventually, the effluent substrate concentration equals its concentration in the incoming nutrient medium.

The stability of steady-state culture growth in a chemostat is due to the fact that its growth is limited by the concentration of a specific substrate. The value of μ is maintained at a low level. The chemostat is a self-regulating system that is simple to operate; if the inflow rate remains constant for a sufficiently long time, chemostat operation is regulated automatically.

Growth in a turbidostat. Continuous culture in a turbidostat differs significantly from the chemostat-based continuous culture described above. As the name implies, turbidostat operation is based on maintaining a constant bacterial suspension density, or constant turbidity. A turbidity sensor regulates the supply of nutrient medium through a control system. All nutrients are present in excess within the cultivation vessel, and the bacterial growth rate approaches its maximum. Working with turbidostats is technically more complex than with chemostats.

Fundamental differences. There are fundamental differences between classical batch culture and continuous culture in a chemostat, which should be re-emphasized in Conclusion.

Batch culture can be viewed as a closed system (somewhat akin to a multicellular organism) that passes through four phases in its development: lag, exponential, stationary, and death (youth, maturity, Aging, and death). The environmental conditions for the culture vary across all these phases. Automatic regulation in a batch culture is hardly feasible.

Continuous culture is an open system tending toward a steady state. The time factor is largely eliminated. Constant environmental conditions are provided for the organisms. The setup is easily amenable to automatic regulation.

6.5.6 Synchronization of Cell Division

Studying metabolic processes throughout the cell division cycle requires suspensions in which cells divide simultaneously (synchronously). To achieve this phase alignment among different cells, culture synchronization is employed. Division in a cell population can be synchronized using various artificial techniques, such as temperature shifts, light exposure, nutrient restriction, or passing microorganisms through a special filter to obtain cells of uniform size. Following a particular Treatment, a cell synchronized suspension gradually returns to asynchronous division after several simultaneous divisions, so that the cell number subsequently increases continuously rather than in a stepwise manner.