PART 1 Introduction
6.2. BATCH GROWTH
6.2.3. How Environmental Conditions Affect Growth Kinetics
6.2.3. How Environmental Conditions
maintain intracellular pH at a relatively constant level in the presence of fluctuations in environmental pH. When pH differs from the optimal value, the maintenance-energy re- quirements increase. One consequence of different pH optima is that the pH of the medium can be used to select one organism over another.
In most fermentations, pH can vary substantially. Often the nature of the nitrogen source can be important. If ammonium is the sole nitrogen source, hydrogen ions are re- leased into the medium as a result of the microbial utilization of ammonia, resulting in a decrease in pH. If nitrate is the sole nitrogen source, hydrogen ions are removed from the medium to reduce nitrate to ammonia, resulting in an increase in pH. Also, pH can change because of the production of organic acids, the utilization of acids (particularly amino acids), or the production of bases. The evolution or supply of CO2can alter pH greatly in some systems (e.g., seawater or animal cell culture). Thus, pH control by means of a buffer or an active pH control system is important. Variation of specific growth rate with pH is depicted in Fig. 6.8, indicating a pH optimum.
Dissolved oxygen(DO) is an important substrate in aerobic fermentations and may be a limiting substrate, since oxygen gas is sparingly soluble in water. At high cell con- centrations, the rate of oxygen consumption may exceed the rate of oxygen supply, lead- ing to oxygen limitations. When oxygen is the rate-limiting factor, specific growth rate varies with dissolved-oxygen concentration according to saturation kinetics; below a criti- cal concentration, growth or respiration approaches a first-order rate dependence on the dissolved-oxygen concentration.
Above a critical oxygen concentration, the growth rate becomes independent of the dissolved-oxygen concentration. Figure 6.9 depicts the variation of specific growth rate with dissolved-oxygen concentration. Oxygen is a growth-rate-limiting factor when the
Figure 6.7. Arrhenius plot of growth rate of E. coliB/r. Individual data points are marked with corresponding degrees Celsius.
E. coliB/r was grown in a rich complex medium () and a glucose-mineral salts medium (). (With permission, after S. L.
Herendeen, R. A. VanBogelen, and F. C.
Neidhardt, “Levels of Major Protein of Es- cherichia coliduring Growth at Different Temperatures,” J. Bacteriol. 139:195, 1979, as drawn in R. Y. Stanier and others, The Mi- crobial World, 5th ed., Pearson Education, Upper Saddle River, NJ, 1986, 207.)
170 How Cells Grow Chap. 6
DO level is below the critical DO concentration. In this case, another medium component (e.g., glucose, ammonium) becomes growth-extent limiting. For example, with Azotobac- ter vinelandiiat a DO =0.05 mg/l, the growth rate is about 50% of maximum even if a large amount of glucose is present. However, the maximum amount of cells formed is not determined by the DO, as oxygen is continually resupplied. If glucose were totally con- sumed, growth would cease even if DO =0.05 mg/l. Thus, the extent of growth (mass of cells formed) would depend on glucose, while the growth rate for most of the culture pe- riod would depend on the value of DO.
The critical oxygen concentration is about 5% to 10% of the saturated DO concen- tration for bacteria and yeast and about 10% to 50% of the saturated DO concentration for mold cultures, depending on the pellet size of molds. Saturated DO concentration in water at 25∞C and 1 atm pressure is about 7 ppm. The presence of dissolved salts and organics can alter the saturation value, while increasingly high temperatures decrease the saturation value.
Oxygen is usually introduced to fermentation broth by sparging air through the broth. Oxygen transfer from gas bubbles to cells is usually limited by oxygen transfer through the liquid film surrounding the gas bubbles. The rate of oxygen transfer from the gas to liquid phase is given by
(6.21) where kL is the oxygen transfer coefficient (cm/h), ais the gas–liquid interfacial area (cm2/cm3), kLais the volumetric oxygen transfer coefficient (h-1), C* is saturated DO
NO k a CL CL OTR
2= ( *- )=
Figure 6.8. Typical variation of specific growth rate with pH. The units are arbitrary.
With some microbial cultures, it is possible to adapt cultures to a wider range of pH val- ues if pH changes are made in small increments from culture transfer to transfer.
Figure 6.9. Growth-rate dependence on DO for (a) Azotobacter vinelandii, a strictly aerobic organism, and (b) E. coli, which is faculative. E. coligrows anaerobically at a rate of about 70% of its aerobic growth in minimal medium.
(With permission, from J. Chen, A. L. Tan- nahill, and M. L. Shuler, Biotechnol. Bioeng.
27: 151, 1985, and John Wiley & Sons, Inc., New York.)
m m m
m m
*= -
-
m
m m
anaerobic aerobic anaerobic
concentration (mg/l), CLis the actual DO concentration in the broth (mg/l), and the NO2is the rate of oxygen transfer (mg O2/l◊h). Also, the term oxygen transfer rate(OTR) is used.
The rate of oxygen uptake is denoted as OUR(oxygen uptake rate) and
(6.22) where qO2is the specific rate of oxygen consumption (mg O2/g dw cells◊h), Y
X/O2is the yield coefficient on oxygen (g dw cells/g O2), and Xis cell concentration (g dw cells/l).
When oxygen transfer is the rate-limiting step, the rate of oxygen consumption is equal to the rate of oxygen transfer. If the maintenance requirement of O2is negligible compared to growth, then
(6.23) or
(6.24) dX
dt =YX/O k a CL ( *-CL)
2
mg
/O2
X
Y k a C C
X
L L
= ( *- )
OUR O g
O /
=q X= X YX
2
2
m
172 How Cells Grow Chap. 6
Growth rate varies nearly linearly with the oxygen transfer rate under oxygen-transfer limitations. Among the various methods used to overcome DO limitations are the use of oxygen-enriched air or pure oxygen and operation under high atmospheric pressure (2 to 3 atm). Oxygen transfer has a big impact on reactor design (see Chapter 10).
The redox potential is an important parameter that affects the rate and extent of many oxidative–reductive reactions. In a fermentation medium, the redox potential is a complex function of DO, pH, and other ion concentrations, such as reducing and oxidiz- ing agents. The electrochemical potential of a fermentation medium can be expressed by the following equation:
(6.25) where the electrochemical potential is measured in millivolts by a pH/voltmeter and PO2is in atmospheres.
The redox potential of a fermentation media can be reduced by passing nitrogen gas or by the addition of reducing agents such as cysteine HCl or Na2S. Oxygen gas can be passed or some oxidizing agents can be added to the fermentation media to increase the redox potential.
Dissolved carbon dioxide (DCO2) concentration may have a profound effect on per- formance of organisms. Very high DCO2concentrations may be toxic to some cells. On the other hand, cells require a certain DCO2level for proper metabolic functions. The dis- solved carbon dioxide concentration can be controlled by changing the CO2content of the air supply and the agitation speed.
The ionic strength of the fermentation media affects the transport of certain nutri- ents in and out of cells, the metabolic functions of cells, and the solubility of certain nutri- ents, such as dissolved oxygen. The ionic strength is given by the following equation:
(6.26) where Cis the concentration of an ion, Ziis its charge, and Iis the ionic strength of the medium.
High substrate concentrations that are significantly above stoichiometric require- ments are inhibitory to cellular functions. Inhibitory levels of substrates vary depending on the type of cells and substrate. Glucose may be inhibitory at concentrations above 200 g/l (e.g., ethanol fermentation by yeast), probably due to a reduction in water activity.
Certain salts such as NaCl may be inhibitory at concentrations above 40 g/l due to high osmotic pressure. Some refractory compounds, such as phenol, toluene, and methanol, are inhibitory at much lower concentrations (e.g., 1 g/l). Typical maximum noninhibitory con- centrations of some nutrients are glucose, 100 g/l; ethanol, 50 g/l for yeast, much less for most organisms; ammonium, 5 g/l; phosphate, 10 g/l; and nitrate, 5 g/l. Substrate inhibi- tion can be overcome by intermittent addition of the substrate to the medium.