During cultivation of microorganisms, they grow by both increase in the size (volume), and by increase in number. The increase in cell size is more significant for filamentous cells such as fungi. In this case, the spores germinate into young hyphae, which then grow by increase in size. In the case of unicellular microorganisms, increase in cell size is limited since unlike other living organisms, the difference in the sizes of young and old cells is not much. This means that the high increase in cell concentration achieved during cultivation of microorganisms is mainly due to increase in the number of cells. However, significant increase in the size is also observed in some unicellular microorganisms. For example, cyst of Haematococcus pluvialis can be more than ten times larger than the vegetative cell.

Methods by which microorganisms increase their cell numbers

Some microorganisms such as yeast cells increase in number by a process of budding. In this case, a small bud develops at one end of the cell. This bud enlarges gradually until it is almost as big as the parent cell. It then separates from the parent cell. Most other unicellular microorganisms increase their cell number by transverse binary fission. In this case, a single cell divides after developing a septum (cross wall).

For example, the cells grow by increasing the length either unidirectional or bi-directional followed by septation and eventually division into two cells. In some cells such as Streptococci, the successive cell division is in the same plane leading to formation of chains of cells. In other strains such as Micrococci, successive plane of division is at right-angle to the previous one, leading to formation of cluster of cells.

Factors Affecting cell growth

Temperature

Growth of microorganisms involves a series of chemical reactions catalyzed by various enzymes. Unlike warm-blooded animals, the internal temperatures of microorganisms are the same as that of the environment. Therefore, the growth rates of microorganisms are dependent on temperature. Temperature affects membrane fluidity (membrane phospholipids), membrane stability, as well as DNA expression. For each microorganism, there are

(i) a minimum temperature below which the growth rate is zero,

(ii) an optimum temperature at which the growth rate is highest (this means the temperature that support the most rapid growth of microorganism during a short period (12 to 24 hours), and

(iii) a maximum temperature above which there is no cell growth.

Figure Schematic representation of microbial growth response to temperature. A: Minimum temperature for growth, B: Optimum temterature for growth, C: Maximum temperature for growth.

Even within temperature ranges that support cell growth, cell metabolism may change depending on the temperature. For example, at 25 ℃ Lactobacillus plantarum does not require phenylanine but requires it at 37℃. Microorganisms differ greatly on their response to temperature. In other words, the optima temperature for growth varies from strain to strain. On the basis of their response to temperature, microorganisms can be classified into

(a) Psychrophiles (those that grow at very low temperatures, even below zero ℃). The Psychrophiles cannot grow at high temperatures because their ribosomes and other enzymes are unstable at such high temperatures.

(b) Mesophiles (those that grow at moderate temperatures). Their optimum temperature is usually between 20 and 40 ℃.

(c) Thermophiles (those that grow at very high temperatures, as high as 90 ℃). Their optimum temperature is usually above 60℃. They have thermostable ribosomes, membranes, and various enzymes. At low temperatures, they loose membrane fluidity, and thus are unable to grow.

No microorganism is known to grow below zero degree and above 90℃. Generally, at low temperatures, the growth rate of microorganisms decreases because of reduced rate of enzymatic reactions. At high temperatures, the growth rate decreases due to metabolic disruption and due to cell death. There are thermal denaturation of proteins, and breakdown of important cell structures, such as cell membrane fluidity. The yields from carbohydrate/energy source are lower at higher temperature because of increased maintenance demand. Temperature also affects product formation, especially for non- growth associated products. For Penicillium chrysogenum, the optimum temperature for growth is 30℃ but that for penicillin production is 20℃.

Hydrogen ion concentration (pH)

The chemistry of any solution depends to a large extent on the pH value. It affects the redox potential of the solution. pH affects both the K_m and V_m of enzymatic reactions. pH affects membrane functions, and substrate uptake. This is because pH affects ionization of polar substrates, and thus their passive diffusion. It also affects extra-cellular enzyme-dependent uptake of some substrates. Cells protect the vital cell reaction by excluding the hydrogen ions. The intracellular pH of most cells (even acidophiles and alkalophiles) is very close to neutral pH.

During the cultivation, pH of the broth changes because of the following.

i) Production of some acid products such as citric acid and acetic acid, or production of basic products such as lysine, arginine, or release of ammonia

ii) Uptake of some basic nutrients such as ammonia leads to pH decrease while uptake of acidic substrates such as acetic acid leads to pH increase

iii) Change in the buffering capacity of the broth. For example, uptake of phosphate or citrate will lead to decrease in the buffering capacity of the broth.

As in the case of temperature, there are minimum, optimum and maximum pH values for cell growth. Some microorganisms such as Thiobacillus thioxidant are acidophiles with optimum pH of between 2 and 3.5 while others such as Bacillus alcalophilus are alkalophiles with optimum pH of between 10 and 11.5. Generally, the optima pH for growth range from 4 to 8 for bacteria; 3 to 6 for yeast cells; 3 to 7 for fungi, and 6.5 to 7.5 for most Eucaryotic cells. It should be noted that the optima pH for growth rate may differ from that for growth yield, and from that of product formation. pH also affects product formation. Yeast produces ethanol at low pH but glycerol or acetic acid under alkaline condition. The optima pH may vary depending on the culture stage. For example, the pH may be regulated to increase cell growth, enzyme induction, product formation, product secretion, and finally to flocculate the cells at the end of the culture.

Control of pH during cultivation

During the cultivation, various methods can be used to control the pH of the broth. These include

i) Buffering: Many media components such as citrate and phosphate are added in excess of cell requirement in order to increase the buffering capacity of the system.

ii) Balancing metabolisms: A balanced medium where the effects of substrate utilization and product formation balance out, resulting in no change in the pH of the broth. For example, uptake of ammonia leads to pH decrease but uptake of nitrate leads to pH increase. Thus, when ammonia and nitrate are simultaneously used as nitrogen source in a nitrogen – limited culture, there will be no net change in the pH during the culture.

iii) Addition of CaCO₃ to the culture. In this case, when the pH decreases below 5.4, CaCO₃ dissociates to produce CO₃^2-, which pushes the pH up.

CaCO₃        Ca²⁺ + CO₃^2-

iv)Feedback control: In this case, the pH of the broth is monitored (for example, by using pH electrodes) and either acid or base is added in response to pH change. NaOH, KOH or Ca(OH)₂ can be added in response to decrease in the pH value. However, KOH is relatively expensive. Also although Ca(OH)₂ is relatively cheap, its use can lead to precipitation of CaCO₃ at high pH values or precipitation of Calcium salts of organic acids at low pH values. Ammonia is also a good base for pH control. When used, it serves a dual role of controlling the pH and serving as a nitrogen source. HCl and H₂SO4 are the most frequently used acids for pH control. However, depending on the fermentor material, HCl can lead to corrosion of equipment. Phosphoric acid is relatively expensive. Some organic acids such as acetic acid can be used as both carbon source and pH controller.

Oxygen

Oxygen serves as terminal electron acceptor for oxidative reactions, which provide energy for cellular activities. Most of the required oxygen is not incorporated into the cells or metabolites. However, depending on the strain and culture condition (especially the nature of carbon source), a part of the oxygen may be incorporated into cell biomass. In this case, fixation of the oxygen is catalyzed by oxygenase enzymes. Most of the incorporated oxygen is derived from water or carbon source, and only a very small percentage is derived from molecular oxygen. Higher percentage of incorporated oxygen may come from molecular oxygen if hydrocarbons such as methane are used as the sole carbon source.

Classification of microorganisms on the basis of oxygen requirement

On the basis of oxygen requirement, microorganisms are classified into

i) Aerobic microorganisms: Those that require oxygen and can grow under atmospheric air containing 21% oxygen.

ii) Anaerobic microorganisms: Those that do not use oxygen to obtain energy and cannot grow when exposed to atmospheric air.

iii)Facultative anaerobic microorganisms which do not require oxygen but may use it to produce energy if it is available.

iv)Microaerophilic microorganisms which require very low level of oxygen but cannot grow when exposed to atmospheric air (21% oxygen).

Oxygen may be inhibitory to the cells (especially anaerobic, facultative anaerobic and microphilic strains) because it inactivates some groups of enzymes such as the thiol (-SH). For example, nitrogenase is irreversibly destroyed by even small amount of oxygen. Furthermore, super oxide radicals, peroxides, and hydroxide radicals are produced under certain culture conditions (such as under illumination) and these are toxic to the cells.

Control of dissolved oxygen concentration during cultivation

Even for aerobic microorganisms, there are optima dissolved oxygen concentrations for cell growth and product formation and other metabolic activities. In other words, there may be a need to vary the dissolved oxygen concentrations to suite the stage of the culture. Oxygen is supplied to the culture by aeration (sparging with air). The dissolved oxygen concentration is monitored by using dissolved oxygen electrodes and the level can be controlled by varying:

a) the aeration rate (the air flow rate)

b) the sparger pore sizes,

c) the type of impeller

d) the agitation speed (mixing intensity)

e) the oxygen partial pressure in the air (this is achieved by using mixtures of air, pure oxygen, and nitrogen in various combinations).

Nutrients

Microorganisms require various essential nutrients for growth. They cannot grow at all in the absence of some nutrients while their growth is greatly reduced in the absence of some of them (See Chapter 3 for details). Also, excess supply of some of the nutrients can lead to growth inhibition. The inhibitory effects of high substrate concentration may be due to direct toxic effect of the substrate or indirectly through its effects on pH, water activity and other properties of the broth. Thus there are minimum and maximum concentrations for each media components. Even when high concentration of nutrient does not produce significant inhibitory effect, economic considerations dictate the maximum concentration to be used. The dependency of cell growth on the limiting substrate concentration has been described by Monod equation and its modifications (See Chapters 9 and 10 for details). In the case of photosynthetic microorganisms, light is used as the energy source. In photoautotrophic cultures, there is a critical light intensity below which cell growth does not occur. Above this light intensity, the growth rate increases with light intensity until saturation light intensity is reached. Light intensities above the saturation light intensity inhibit cell growth and in some cases product formation.

Water activity

Osmotic stress affects the growth of microorganisms. Because of the process of osmosis and plasmolysis, (movement of water into, or out of the cells depending on the tonicity of the medium) there should not be much difference in the osmotic pressure between the cells and the environment. In other words, the culture medium/broth should be isotonic to the cells. This is very important in solid-state cultures, and in cultures where polysaccharides are produced. Some microorganisms can grow well at low water activity and are called osmophiles. For example, Saccharomyces rouxii can grow at high osmotic pressure and is one of the important contaminants of sugar syrups. They are able to grow at such high sugar concentration because they accumulate polyols such as arabitols, which increase the intracellular concentration of bound water and thus lowers the osmotic pressure difference between the cell and the environment. Also extreme halophiles can grow even at very low water activity (2.5 M NaCl), while some can grow at a very wide salt concentration range. For example, Dunaliella viridis can grow at various concentrations of NaCl by accumulating corresponding concentrations of glycerol.

Hydrodynamic (Shear) stress

The force, which brings about relative movement of fluid molecules is known as shear stress. This is another important factor that affects cell growth during cultivation. Culture agitation, sparging, broth circulation and other devices used to mix culture and thus prevent cell sedimentation and facilitate mass and heat transfer produce some stress that affect cell growth and other metabolic activities. In the case of agitation, the magnitude of the stress depends on the type of impeller, the size (diameter of the impeller), the shape of the impeller, as well as on the tip velocity. The shear stress also increases with increase in the broth circulation rate (type of pump and rate of pumping) and on the aeration rate (air flow rate, pore size of the sparger). Microorganisms vary in their response to hydrodynamic stress. The susceptibility of microorganisms to hydrodynamic stress depends on the presence or absence of cell wall, the nature of the cell wall, the size of the cell(the smaller, the more resistant), and the shape of the cell. Some microorganisms such as unicellular bacteria are very resistant to shear stress while animal cells, without cellulose cell wall, are very susceptible. Also plant cells, and microorganisms without cellulose cell was (e.g. Euglena) are very susceptible to hydrodynamic stress. Hydrodynamic stress also affects the shape of the cells (example Euglena, and filamentous cells), the size of pellets, and the metabolic activities (the nature of products formed) of the cells.

Measurement of cell growth in microbial cell cultures

Introduction

During cultivation of microorganisms, it is very necessary to determine the cell concentration in the culture broth. This is a very good indication of the progress of the process. Moreover, in some processes, biomass is the product and it is important to know how much of the cell biomass is produced under a given culture condition.

Methods used to measure cell growth

There are many different methods of determining cell concentration in a culture broth. Some of these methods are discussed below. It is important to note that each of these methods has merits and de-merits and the choice depends on the type of the cell, the culture condition (characteristics of the culture broth), as well as on the purpose for which the cell concentration is being measured.

 Enumeration of cell number

There are three methods of enumerating cell number. These are microscopic method using counting chambers, biological techniques of counting the number of colonies formed after plating in a petri-dish, and automatic methods.

(a)Microscopic method: Various counting chambers are used to directly count the number of cells using microscopes. The most common types of counting chambers are the Thoma Haemocytometer and the Petroff-Hausser counting chambers.

Each well in the Thoma Haemocytometer used for counting microorganisms is 50 x 50 x 100 μm. Thus, the volume of the well is 250,000μm ³ (2.5 x 10^-7 ml). In order to obtain accurate results, it is necessary to count the number of cells in at least 50 wells and the sample should be diluted so as to have about 3~5 cells per well. The cell concentration in the sample (X) is then calculated as: X = n x 4 x 10⁶ (cells/ml), where X is the cell concentration (number/mL), and n is the number of cells per well.

  An advantage of this microscopic enumeration method is that cell morphology, contamination, cell aggregation, cell viability (if appropriately stained) and other physical properties of the cells can be simultaneously observed. It is also relatively fast.

b) Colony counting: In this method, the cells are appropriately diluted and a known volume (usually about 0.1 ml, depending on the diameter of the petri dish) plated on a solid medium such as 2% agar medium. It is then incubated at an optimum temperature for 24 to 72 h (depending on the growth rate of the cell). Each cell grows and develops into a colony. Thus, the number of colonies corresponds to the number of the cells in the volume of the cell suspension plated. If the volume of the suspension plated is too much, there will be overflow of the suspension with resultant clustering of some cells at the edge of the petri dish. On the other hand, if the volume is too small, it will not be possible to spread it over the whole surface of the plate. This can also lead to clustering of the cells. The number of colonies per plate (diameter = 9 cm) should be between 30 and 300. A modification of this method is the pour plate method. In this case, a known volume (0.1 ~ 1 mL) of an appropriately diluted culture broth is added into a sterilized agar medium in a test tube (10 ~ 15 mL) at about 40~50^OC (depending on the type and concentration of the agar). If the temperature is too high, some cells will be killed, leading to under estimation of cell concentration but when the temperature decreases below the gelling temperature for the agar, the agar will start to gel and it will be difficult to get a homogenous distribution of the cells in the agar. The test tube is then properly mixed and poured into a pre-sterilized petri-dish where it is allowed to solidify. It is then incubated at the desired temperature until colonies are formed. 

The advantage of this method is that it gives the number of viable cells since dead cells will not grow to form colonies. However, the disadvantage is that it is time consuming. It can take more than a day before the results are obtained (depending on the growth rate of the cells).

c) Automated method: This is also called an electronic method. Large number of cells can be counted within a very short time. An example is the coulter counter, which is based on the resistance that occurs when a suspension of microorganisms in saline solution passes through an orifice. The rate of counting can be as high as 3~5 x 10³ cells per second. The main advantages are that large number of cells can be counted within a very short time and it also gives information on size distribution of the cells. The major disadvantages include:

1. Dead cells and non-cell particles of the same size as the cells are also counted

    ii) Clumps, cell floccs and un-separated cells are counted as a single large cell.

Another example of an electronic counter is the microfluorometer, which is based on fluorescence of a stained cell as it flows pass an exciting laser beam. An advantage of this method is that by using some specific stains, non-biological particles are not counted. An example of such a stain is fluorescein isothiocyanate, which is specific for protein, and propidium iodide, which is specific for nucleic acids.

Packed cell volume

This is a measure of the volume of tightly packed cells with little or no intercellular spaces. It is mainly used for plant and animal cells. The packed cells are obtained by centrifuging a given volume of culture broth in a graduated centrifuge tube. After centrifugation, the volume of the sedimented cells is read and the unit is expressed as the volume of cells per volume of the culture broth. An advantage of this method is that it is non destructive. In other words, if the measurement is done under aseptic condition, the cells can be returned to the culture after the measurement. It is also relatively easy and fast. The main disadvantages are that the accuracy of the data is influenced by many factors such as the centrifugation conditions (the speed and length of time), the size and morphology of the cells (which affect the intercellular spaces), and the tonicity of the broth (which can lead to swelling or shrinking of the cells).

Wet weight

This is a measure of the weight of cells after removing the intercellular water. A given volume of the culture broth is filtered or centrifuged to remove the bounding water. It is then washed to remove salts and then weighed. An advantage of wet weight method is that it is relatively fast and non-destructive. However, the accuracy of the data depends on both the shape and size of the cells since these factors affect the amount of water bound to the cells. Also the water content of the cells depends on the strain, growth condition (especially on the tonicity of the medium), as well as on the age of the cells. For most microorganisms, the wet weight of the cells varies between 4 and 10 times the dry weight. In other words, cells contain 80 to 90 % water.

 Dry weight

This is the most reliable and accurate method for quantitative measurement of cell growth. After centrifuging or filtering the culture broth, the cells are washed and dried to a constant weight. Mild acid can be used for the washing to ensure complete removal of precipitated salts. However, strong acid can lead to leaching or lyses of the cells. Constant weight is usually achieved by drying at 80℃ for 24 hours, or drying at 110℃ for 8 hours. Drying at lower temperature can lead to incomplete drying while higher temperatures can lead to biomass loss through volatilization or oxidation. Furthermore, the size/density of the cells should be taken into consideration while choosing the centrifugation conditions. Incomplete sedimentation of the cells can lead to cell loss during decantation. Although this method is accurate, it is very slow, it is destructive and both dead and non-cell particles are also measured.

Turbidometric method (Optical density)

This is based on light absorption by suspended cells. Within a given cell concentration, there is a linear relationship between the cell concentration and light absorption by the cells (Figure 8-1). A spectrophotometer is used to measure the optical density of an appropriately diluted cell suspension. The relationship between the optical density (OD) and the cell concentration (X) can be expressed as in Eq 8-1

                              Eq 8-1

Where Io is the incident light intensity, I is the transmitted light intensity, a is the light absorption coefficient, l is the light path (the diameter of the curvet). The value of a depends on the wavelength of the light source. Selection of the wavelength is based on the light absorption characteristics (the size, shape and colour) of the cells. The wavelength that gives the maximum light absorption is used. For the measurement of concentration of microbial cells, wavelengths between 420 and 660 nm are most widely used.

   If the cell concentration is too high, there will be no more linear relationship and the above equation does not hold. Thus, the culture broth must be appropriately diluted before measurement. It is advisable to pre-determine the critical cell concentration above which Eq 8-1 does not hold. This value depends on the cell and the type of photometer used. In some spetrophotometers, it is easier to read the values of light transmitted (transmittance). In such a case, the transmittance values are converted to the optical density (OD), using Eq 8-2.

                                                           Eq 8-2

where T is the transmittance.

The turbidometric method is a very fast, simple and convenient method for measuring the concentrations of unicellular cells with sizes between 0.4 ~ 2 x 10^-18 m³. However, it has the following disadvantages:

1. It is not good for virus (too small) or filamentous cells (no good dispersion).
2. Non-cell particles are also measured
3. The colour of the culture broth affects the readings. Thus, depending on the colour of the broth and the dilution factor, it is advisable to used filtered (or supernatant after centrifugation) broth as the reference standard.
4. Measurement should be done quickly to avoid cell sedimentation.

Expression of Cell growth

Introduction

During cultivation of cells for various purposes, it is usually very necessary to monitor cell growth. The cell growth rate can be expressed in various ways.

Growth rate (dx/dt)

The cell growth rate is usually expressed as an increase in cell concentration over a given period of time. The cell growth rate between the time t₁ and t₂ is calculated as

 

                                            Eq 9-1

Where X₁ is the cell concentration at the time t₁, and X₂ is the cell concentration at time t₂. This is usually denoted as dx/dt. The unit depends on the unit used for cell concentration. Since the dry cell weight is the most accurate unit for cell concentration, the cell growth rate is usually expressed as g/L.h.

Specific growth rate ()

  The specific growth rate is the growth rate per unit cell. It is the most important parameter used for kinetic analysis of cell growth. It is calculated as the cell growth rate divided by the cell concentration as shown in Eq. 9-2.

                                                    Eq 9-2

The specific growth rate between t₁ and t₂ can then be calculated as shown in Eq 9-3 

                                         Eq 9-3

where  is the average cell concentration between t₁ and t₂. Alternatively, can be defined as the cell concentration at t_1.5 (the mid time between t₁ and t₂) as illustrated in the Figure below

Figure  Graphical method of estimating the specific growth rate of cells

During the cultivation, the specific growth rate () usually varies as the cultivation progresses due to various reasons such as depletion of the nutrients, accumulation of products, and changes in the culture pH and other culture conditions. It is therefore more accurate to talk of average specific growth rates over a period of cultivation. In other words,  should be calculated at very short time intervals (when it can be assumed that the change in the value of  is not significant), and the specific growth rate during the cultivation is then expressed as the average of these individual values. Regardless of the definition of  in Eq 9-3, the shorter the time interval, the more accurate will be the estimated value of  .

If is assumed to be constant as observed during the log phase, then Eq 9-4 holds.

                                                  Eq 9-4

In a batch culture, the specific growth rate during the log phase (between time t₁ and t₂) can be calculated from Eq 9-5.

Specific growth rate           Eq 9-5

If the specific growth rate of the microorganism under the culture condition (medium, temperature, DO etc) is known, the cell concentration in the broth after cultivating the cell for a given period of time (t), can be calculated from Eq 9-6

                                                 Eq 9-6

where X is the final cell concentration and X₀ is the initial cell concentration. This equation implies that the cells were growing through out the cultivation period (t). In batch culture systems where the cell may require some time to adapt to the new condition before growing (lag phase), the length of the lag phase must be subtracted from the total cultivation time. In that case, Eq 9-7 is used to estimate the final cell concentration.

                                             Eq 9-7

where l is the length of the lag phase.

Generation time (g)

The generation time is defined as the length of time taken for a cell to divide to produce daughter cell(s). A schematic representation of how cell can grow in generations is shown in Figure 9-2. The generation time (g) can thus be simply represented by Eq 9-8

                                                                       Eq 9-8

where t is the cultivation time and n is the number of generations.

The number of cells (X) after n generations can then be calculated from Eq 9-9.

                                                              Eq 9-9

Eq 9-10 is derived from Eq 9-8,

                                                                          Eq 9-10

Thus Eq 9-9 can be transformed into Eq 9-11

                                                              Eq 9-11

Taking log in both sides,

Thus after cultivating Cells with intial concentration of X₀, the final cell concentration X is measured and the generation time can be calculated from either Eq 9-12 or Eq 9-13.

                            Eq 9-12

                                    Eq 9-13

Doubling time (t_D)

Doubling time is defined as the time taken for the cell concentration to double. From Eq 9-4, the cultivation time can be expressed as shown in Eq 9-14

                                          Eq 9-14

By definition, t = t_D when X = 2X₀, therefore

and the doubling time can be calculated from Eq 9-15.

                                                                    Eq 9-15

Batch cultures

Basic characteristics of batch cultures

This is a type of culture where a fixed volume of medium is inoculated with cells and incubated (cultivated) for a given period of time. It is the simplest and most widely used culture system. It is regarded as a closed system since during the cultivation, nothing is added to, and nothing is removed from the culture except for sampling. In other words, the nutrients for the cell growth and product formation come solely from the nutrients originally present in the medium.

After inoculation of the cells, the substrate start to decrease while the cells and the product concentrations increase until the nutrients in the culture vessel are completely exhausted (Figure 10-2). Thus, cells grown in batch culture are exposed to a continually changing environment due to continuous depletion of nutrients and accumulation of various metabolites.

The main advantage of batch culture is that it is very simple. However, it has the following disadvantages

1. The cell growth rate is low since the optima concentrations of the substrates, products and by-products cannot be maintained for a long period of time.

2. The productivity, especially of the growth associated products is comparatively low.

3. Time is wasted between batches. There is startup time for each batch (the time used to empty the vessel, wash the vessel, prepare and sterilize the medium). This results in decrease in the overall productivity.

Figure Changes in substrate, cell and product concentrations during a typical batch culture

Growth phases in batch cultures

 As a result of the continuous changes in the composition of the culture broth during batch cultivation, the cell growth passes through various phases as shown in Figure 10-3. These are the lag phase, the log phase, the stationary phase, and the death phase.

Figure Growth phases during batch cultivation of microorganisms

Lag phase

This is the period for cell adaptation. The cells do not grow, rather, they adapt to the new environment. This phase is usually characterized by enzyme production. The length of the lag phase depends on many factors such as the cell strain, the history of the culture, the age of the culture, and the differences between the conditions of the seed and the main cultures. It is desirable to reduce the length of the lag phase to maximize productivity. This can be achieved by using young and active cells, and by minimizing the differences between the seed and the main cultures.

Log phase

After the cell adaptation (the lag phase), the cells start to grow. The growth rate continues to increase gradually until it reaches a maximum constant value. At this stage, the culture is said to be in the logarithmic growth phase. This phase is also called an exponential growth phase because the cell number (biomass) increases exponentially with time. For growth associated products, it is desirable to maintain the cells in this phase over a long period of time (example by using a continuous culture).

Declining growth phase

During this phase, the cells continue to grow but the growth rate is relatively lower that the one observed during the log phase. The cells are under growth limited condition. The growth may be limited by substrate (substrate concentration is lower than the saturation constant), or by other nutrients in the medium. It can also be limited by physical or chemical conditions in the medium such as sub-optimal temperature, pH, or high concentration of inhibitory products and by-products. Nevertheless, the cell growth rate is still higher than the cell death rate so that there is a net increase in biomass concentration.

Stationary growth phase

As the cultivation continues, the growth rate starts to decrease while the death rate continues to increase until there is no more net increase in the cell concentration. During this stage, the cells are still growing but the growth rate is equal to the death rate. This happens due to various factors such as depletion of the nutrients, and accumulation of inhibitory metabolites. This is called the stationary growth phase. For growth associated products, the culture is terminated once the stationary growth phase is attained. However, in the case of non-growth associated products, product formation continues even when the cells growth has stopped.

Death phase

In this phase, the cell concentration starts to decline because the death rate is now higher than the growth rate. This can be attributed to various reasons which include

1. Cell starvation: This leads to decrease in cell mass since the cells may start to metabolite the intracellularly stored carbohydrate and other cell materials.
2. Some toxic substances produced by the cells can lead to cell death and cell lysis.

Kinetics of cell growth in batch cultures

Cell growth rate in a batch culture is calculated as

                                         Eq 10-1

Where  is the specific growth rate (h^-1) and X is the cell concentration. Under optimum culture conditions, μis approaches μ_m but usuallyμis lower thanμ_m because of either high or low substrate concentration, due to product inhibition or because other culture conditions are hardly optimum. Under substrate-limited condition, the dependence of cell growth on substrate concentration can be expressed by the Monod equation (Eq 10-2). This is very similar to Michael Menten equation in enzyme kinetics.

                                                    Eq 10-2

where μm is the maximum specific growth rate, S is the substrate concentration, and K_S is the saturation constant. The K_S is a measure of the affinity between the cells and the substrate. As shown in Figure 10-4, it is the substrate concentration at which the specific growth rate is half of the maximum specific growth rate.

Figure　 Schematic representation of substrate saturation constant (Ks)

Estimation of kinetic parameters

Estimation of the maximum specific growth rate and the saturation constant from the Monod equation

Eq10-1 can be transformed into a straight line equation as shown in Eq10-3

                       Eq 10-3

This means that plotting (1/) against (1/S) will result in a straight line whose intersept at y-axis is  and the slope is equal to

This is graphically represented in Figure 10-5.

Figure Graphic representation of the graphical method of calculating the kinetic parameters

This requires that the substrate concentration (S) is varied and the resulting specific growth rate is recorded. However, as explained before, it is not possible to keep the substrate concentration constant in a batch culture. From Eq 10-2, the specific growth rate can be constant only when the substrate concentration is constant. Thus accurate determination of  and K_S requires a continuous culture. Nevertheless, a batch culture can be used to estimate the parameters by conducting the experiments at low substrate concentrations so that KS >>>>S, and small change in S has little effect on the specific growth rate.

In practice, this is possible only if the K_S value is high otherwise the working substrate concentration range will be too narrow. With a batch culture, the initial rate kinetics (Eq 10-4) is employed and the initial growth rates are measured before the substrate concentration changes significantly. Lineweaver plot is then used as shown in Figure 10-6

                               Eq 10-4

Figure Graphic representation of how to calculate the kinetic parameters using initial rate kinetics

To get reliable data from this method,

1. Low initial substrate concentrations must be used

2. Low initial concentration of active cells must be used for inoculation

3. Sensitive and accurate analytical techniques must be used to measure both the substrate and cell concentrations.

Limitation by more than one substrate

If cell growth is limited by more than one substrate, then the specific growth rate is cualcuated from Eq 10-5.

                                      Eq 10-5

Eq 10-5 assumes that consumption of each substrate is not affected by consumption of the other substrate. Thus, if one of the substrate becomes saturated, Eq 10-5 reduces to Eq 10-2. If consumption of one substrate affects consumption of the others, then Eq 10-6 is used.

                                   Eq10-6

Substrate inhibition kinetics

The above Monod equation assumes that the cell growth is limited only by substrate concentration. In other words, that high substrate concentration does not inhibit cell growth. However, it is known that high concentration of substrates inhibit cell growth. The nature of inhibition depends on the type of substrate used. The inhibition may be due to direct effects on the cells or due to their effects on the physical and chemical characteristics of the culture broth. Such characteristics include the pH, the ionic strength and the viscosity of the medium. Many models have been used to describe how high substrate concentration inhibits cell growth. Typical examples are shown in Eq. 10-7 and Eq 10-8

                                                               Eq 10-7

                                                                                Eq 10-8

Here, Ki is the substrate inhibition coefficient (g/L).

Product inhibition

High concentration of products also inhibit cell growth. This is especially true when the product is alcohol, acidic or basic substance. For example, during ethanol production, cell growth rate typically starts to decrease when the concentration of ethanol increases above 90 g/L. In such cases, it is desirable to keep the concentration of the product below the inhibitory level. This can be achieved by using initial low substrate concentration, using membrane (dialysis) bioreactor to remove the products as they are formed, circulating the broth through adsorption column so that the products are adsorbed in the column and product-free broth is returned to the bioreactor, or using continuous culture systems where the steady state product concentration is kept low by adjusting the feed rate or the feed substrate concentration. Several equations have been used to describe product inhibition. Examples are shown in Eqs 10-9 ~ 10-11

                                                           Eq 10-9

                                                           Eq 10-10

                                               Eq 10-11

where K_P is the product inhibition coefficient, P is the product concentration, P_m is the maximum product concentration above which there will be no cell growth, and n is a constant. Typically the value of n ranges from 0.2 to 3. It is important to point out that these equations used to describe substrate or product inhibition are experimental equations developed using some specific microorganisms and culture conditions. Thus each may fit one culture very well but may not be appropriate for another culture. Again the K_S, K_i, and K_P all represent inhibition constants but their physical and biological meaning may vary from one equation to the other.

Substrate consumption in batch cultures

During cell cultivation, a part of the consumed substrate is used for cell growth, a part for product formation, and a part for cell maintenance. This is represented by Eq. 10-12

                                                  Eq 10-12

Here

 represents the part of the consumed substrate used for cell growth.

 represents the part of the consumed substrate used for product formation.

  represents the part of the consumed substrate used for cell maintenance.

 is the biomass yield coefficient, Y_P/S is the product yield coefficient, q_P is the specific rate of product formation, and m is the maintenance coefficient. The biomass yield coefficient can be calculated from Eq 10-13

                                                       Eq 10-13

where X₀ and X_f are the initial and final cell concentrations respectively, while S₀ and S_f are the initial and final substrate concentrations. In a batch culture, several initial substrate concentrations (S₀) are used and the resulting final cell concentration is measured for each initial substrate concentration. The Y_X/S is then obtained as slope of a plot of dX=(X_f-X₀) against dS=(S₀-S_f) as shown in Figure 10-7.

Figure Graphical method of determining the biomass yield coefficient (Y_X/S)

Similarly, the product yield coefficient can be expressed as shown in Eq 10-14 and Y_P/S can be experimentally determined as described for Y_X/S  (Figure 10-8).

                                                                      Eq 10-14

Figure Graphical method of determining the product yield coefficient (Y_P/S)

The specific rate of product formation is expressed as in Eq 10-15

                                                                           Eq 10-15

When no product is formed in the culture then the consumed substrate is used only for cell growth and cell maintenance as represented in Eq 10-16.

                                        Eq 10-16

Dividing through by .X will result in Eq 10-17.

                                                                                   Eq 10-17

where Y_G is the theoretical biomass yield coefficient. The maintenance coefficient is thus obtained as the slope of a plot of 1/Y_X/S against  as shown in Figure 10-9

Figure Graphical method of determining the maintenace coefficient (m)

The specific rate of substrate consumption is given in Eq 10-18.

                                              Eq 10-18.

It is important to note that when maintenance energy is negligibly small, the change in substrate concentration can be represented by Eq 10-19

                                                  Eq 10-19

Also, when product formation is considered negligible, as in the case of Bakers’s yeast production where excess nitrogen is supplied and under high dissolved oxygen concentration, the substrate consumption rate can be expressed as

                                                     Eq 10-20

and when both product formation and maintenance energy are neglected, then Eq 10-21 applies.

                                                                 Eq 10-21.