Bteen 67#6

Fermentation Process Kinetics*
Elmer L. Gaden, Jr.
Department of Chemical Engineering, Columbia University,New York 27, N.Y.
Abstract: Information on fermentation process kinetics is
especially true for kinetics. Although the study of fermen- potentially valuable for the improvement of batch pro- tation rates is relatively new, it promises much for the fuller cess performance; it is essential for continuous process and more efficient exploitation of biochemical reaction sys- design. An empirical examination of rate patterns in vari-ous fermentations discloses three basic types: (1) ‘growth associated' products arising directly from the en-ergy metabolism of carbohydrates supplied, (2) indirect Development of Fermentation Kinetics
products of carbohydrate metabolism and (3) productsapparently unrelated to carbohydrate oxidation. Effects Final product yields and substrate conversions were the only of operating variables on the primary kinetic processes, criteria of performance in early commercial fermentations.
growth, sugar utilization and antibiotic formation, in the As the technology developed, however, greater attention penicillin process, illustrate the special nature of thistype.
was paid to time factors; ‘productivity', the average rate ofproduct formation (Fig. 1), soon became popular as a basisfor comparison. On the other hand, instantaneous rates were largely ignored until the studies of gluconic acid production In the design of any chemical, or biochemical, process one by Wells, Moyer, Gastrock et al.12,19,20,26 in the late 1930's.
must consider two more or less distinct aspects. First, there They were among the first to report rates of sugar utilization are the chemical reactions themselves and secondly, the and acid formation in detail.
numerous physical processes which precede, accompany The introduction of antibiotic fermentations greatly and follow them. Some of these physical processes are quite stimulated interest in fermentation rates. It was recognized clearly separate, like the purification of raw materials and from the first that these processes were markedly different products. Others, like the transport of materials to and from from most earlier fermentations. Studies of the chemical the surface of a solid catalyst, are intimately bound up with changes in penicillin biosynthesis required frequent analysis the reactions themselves.
of carbohydrate and nitrogen levels, cell weight and antibi- For a long time, methods available for dealing with the otic titre. From these, general rate patterns could be dis- physical aspects of chemical processes were better devel- cerned and it was soon noted that the process comprised two oped than those for handling the chemical changes them- more or less distinct phases; growth and antibiotic produc- selves. This was largely the result of empirical simplifica- tions offered by the ‘unit operations' concept in chemical Dulaney et al.,8 noticed the same general behaviour in engineering. With the rapid development of chemical kinet- streptomycin fermentations. They defined an initial ‘growth ics and, equally important, methods for applying kinetic phase' in which mycelium was rapidly generated, accom- relationships to process design, this disparity has been over- panied by a reduction in soluble medium constituents (car- bon, nitrogen, phosphorous), rapid sugar utilization and Kinetics is concerned with reaction rates in general; ‘pro- high oxygen demand. Virtually no streptomycin was pro- cess kinetics' simply suggests a primary concern with the duced. Following this was an ‘autolytic phase', character- rates of commercially practised reactions and, particularly, ized by a marked drop in mycelial weight, release of nitro- with the effects of process variables on them.
gen and inorganic phosphorous to the medium, low oxygen Since fermentation is only another type of chemical pro- demand and rapid antibiotic synthesis. All strains examined cess, albeit a special and complex one, possibilities for ap- exhibited the same basic pattern and gross medium changes plying ideas and techniques developed for more conven- had little effect on it.
tional chemical systems should always be sought. This is Calam, Driver and Bowers6 were among the first to sup- port these general observations with specific experiments.
Penicillin fermentations were carried out at several tempera- * Presented at the 134th National Meeting of the American Chemical tures between 12° and 32°C and average rates of growth, Society, Chicago, September 1958.
respiration and penicillin synthesis noted. By plotting the Re-typeset from the original.
Reprinted from Journal of Biochemical and Microbiological Technology observed rates in the Arrhenius manner (logarithm of rate and Engineering Vol. 1, No. 4. Pages 413–429 (1959).
versus reciprocal absolute temperature) it was possible to 2000 John Wiley & Sons, Inc.
similation, do so indirectly and accumulate only underconditions of restricted or abnormal metabolism.
(3) Processes in which product formation has no apparent association with carbohydrate oxidation (penicillin andmany other antibiotics are examples of this type).
It must be recognized that a classification of this sort is based on purely empirical examination of batch fermenta-tion results, not on a full and complete understanding of theindividual mechanisms involved and their relationships toone another. Still, until such understanding has beenachieved, empirical analysis is a powerful and useful tool— Figure 1.
Fermentation rates and productivity.
so long as its limitations are kept constantly in mind.
More recently Luedeking16 investigated the kinetics of the lactic acid fermentation using a batch process at con- characterize each process by the slope of the line obtained, trolled pH. He showed that rate of product formation is the ‘thermal increment'. Since these three rates all exhibited indeed proportional to the rate of substrate utilization as significantly different thermal increments, the authors con- expected. Furthermore, rates of acid production could be cluded that the ‘pace-setting enzyme-systems' involved are related to rates of growth by a simple expression involving two constants dependent on the pH of the fermentation.
Any survey of the literature on fermentation rates under- Subsequently, the performance of single or multi-stage scores the dearth of direct kinetic studies of this type. One continuous lactic acid processes were predicted from these cardinal reason for this is the matter of experimental pro- batch results by analytical and graphical methods.17 Equa- cedure itself. Rate information can best be obtained in tions for both transient and steady-state operations of the steady-state (continuous) systems with automatic control of continuous-system have been developed.
process variables.
In an excellent example of this approach, Kempe, Gillies and West15 studied rates of acid production by Lactobacil- Kinetic Phenomena in Fermentation
lus delbrueckii at controlled pH. Rates were determined by The first problems in studying fermentation kinetics are (1) differentiating the automatically recorded curve of alkali the establishment of consistent rate expressions, and (2) the addition. Steady-state operation at various temperatures selection of meaningful rate processes to be measured.
provided values for an Arrhenius-type plot which gave anactivation energy of 17 kcal/g mole, a value in the rangecharacteristic of many chemical reactions.
Rates and Productivity For one reason or another satisfactory methods for auto- matic regulation and control in fermentation studies have To avoid confusion, the term ‘productivity' has been rec- only recently been introduced and most experiments so far ommended for the time-average output of a process.9 The reported involve the classical batch technique. Data which expression ‘fermentation rate' can then be reserved for the permit the computation of rates are rare—and often inad- instantaneous rate of change of any concentration factor— equate because of the absence of key values. Of course the sugar, product, cell weight, etc. These distinctions are aim of these experiments was yield improvement in batch shown graphically in Fig. 1.
processes, not the gathering of kinetic data. Still, despite the Productivity is defined as the final product concentration inherent limitations of the unsteady-state, batch technique, a divided by the time from inoculation to delivery of the surprising amount of information has been accumulated and batch. It might seem more reasonable to divide by the total a great deal has been learned about the general kinetic as- process time from delivery of one batch to delivery of the pects of various fermentation processes.
next. This would include many operational factors involved From an analysis of the rate patterns in batch alcohol, in turnover of a tank, like cleaning, batching and filling, citric acid and penicillin fermentations, for example, which have little or nothing to do with the actual fermen- Gaden9 distinguished between three broad kinetic groups.
tation system. While it is essential for proper economicanalysis of the plant, such an overall productivity has little (1) Processes in which the desired products (ethanol, glu- use in analyzing the fermentation process itself.
conic and lactic acids, for example) arise directly from Two bases for expressing fermentation rates have been oxidation of the primary carbohydrate.
(2) Processes in which the products (citric acid, for ex- ample), though also resulting from carbohydrate dis- (1) The volumetric rate, or the rate of change of concen- JOURNAL OF BIOCHEMICAL AND MICROBIOLOGICAL TECHNOLOGY AND ENGINEERING VOL. 1, NO. 4 ARTICLE REPRINTED IN: BIOTECHNOLOGY AND BIOENGINEERING, VOL. 67, NO. 6, MARCH 20, 2000 tration with time; its units are mass/unit time (unit vol-ume).
(2) The specific rate, or the volumetric rate divided by cell concentration; its units are mass/unit time (unit cellmass).
The first is the preferred form for process design, especiallyfor continuous systems, because it includes a volume term.
The second is best for kinetic analysis because it puts ev-erything on a comparable basis—unit mass of tissue. It doesnot follow, of course, that this unit tissue mass is physi-ologically identical throughout the fermentation process.
Rate process in fermentation Rate measurements may be applied to an almost infinitenumber of factors in a fermentation system. Three of thesehowever, have been consistently singled out for study—growth, sugar utilization and product formation.
Growth is taken as a rough expression of the total cata- lytic activity in the system. Admittedly, tissue accumulationis only the crudest expression of the true levels of activity ofthe various enzyme systems involved. Until these can actu-ally be determined, however, it is the best measure we have.
Figure 2.
Streptomycin fermentation rates.
Synthetic processes require the metabolic energy released by oxidation of primary carbon sources and sugar utilization environment, as opposed to the concentration of specific is generally taken as an indication of the rate of energy components (sugar, nitrogen sources, etc.), is not included.
release to the system. While it is true that proteins and fats This is considered an inherent feature of the process system are similarly degraded, with accompanying energy release, and not a ‘process variable' in the usual sense. While this carbohydrate sources are ordinarily the major energy sup- view is reasonable for most other chemical reaction sys- pliers. At the same time these materials are frequently the tems, it may not be so for fermentation. One cannot syn- substrates from which specific products are formed. The key thesize ammonia unless the reaction mixture contains both rate, product formation needs no further elaboration.
nitrogen and hydrogen (the mole ratio of these reactants is Perhaps the greatest difficulty encountered in the exami- the ‘process variable') but tetracycline can be produced in a nation of any complex fermentation process is the lack of wide variety of nutrient media.
any stoichiometric relationship between reactants and prod-ucts. Lacking this, measurements of the three basic ratesdefined above may still be made. They offer the singular Fermentation Process Types
advantage of being determined directly from the measure-ments most commonly made in fermentation process stud- Fermentation processes may be classified in a number of ies, tissue mass, sugar and product concentrations.
different ways. The first systematic approach was proposed Complete rate patterns, on both volumetric and specific by Gale11 who grouped microbiological processes in a se- bases for a typical complex fermentation (streptomycin bio- ries of type groups, oxidation, reduction, hydrolysis, etc.
synthesis) are shown in Fig. 2. They were calculated from Such an arrangement though fundamentally attractive, is data of Sikyta et al., in the manner previously described.9 only suitable for specific reactions operating on specificsubstrates to yield specific products. Unfortunately, manycommercially important fermentation processes cannot be Fermentation process variables so neatly described.
Primary process variables in fermentation are: (1) tempera- Gale's classification scheme has recently been extended ture, (2) pH, and (3) nutrient (or reactant) concentration by Stodola24 and others,25 who have proposed a more de- (including oxygen). In addition, certain conditions of the tailed breakdown of ‘type reactions'. In this scheme, micro- physical environment, like fluid turbulence and equipment organisms, or more specifically their enzyme complements, design features which effect mass transfer in the reaction are looked at as added means for controlled organic synthe- zone, must be considered.
sis. Again, this concept is not applicable to most of the Note that the fundamental composition of the nutrient fermentation processes now practised commercially—at ELMER L. GADEN, JR.
GADEN, JR., ET AL.: FERMENTATION PROCESS KINETICS least at the present level of knowledge regarding mecha- Fermentation process types.
Dissimilation reactions A different approach was proposed by Gaden.10 It is sum- ⌬F ⳱ − ⌬F ⳱ + marized in modified form in Table I. Here fermentationprocesses rather than specific reactions are grouped together Type III. Biosynthesis of complex A → products and the overall free energy change involved is the basis for A B C → products Type II. Complex: The primary advantage of this scheme is technological; it A B C → Antibiotics, vitamins, etc.
coincides with the general classification of fermentation rate patterns suggested earlier.9 Experience has shown that fer-mentation processes fall more or less into three kinetic groups, which may be designated ‘types I to III' for conve-nience. Their relationship to the general reaction types isshown in Table I and summarized below: Type I: processes in which the main product appears as a tically over and product accumulation is maximum. Both result of primary energy metabolism. Examples of this type penicillin and streptomycin (Fig. 2) fermentations are ex- of system are most common in the older branches of fer- cellent examples of the Type III kinetic pattern.
mentation technology, for instance: (1) aerobic yeast propa- It must be emphasized that these are only generalizations gation (mass propagation of cells in general), (2) alcoholic for technological convenience. They are neither perfect nor fermentation, (3) oxidation of glucose to gluconic acid, and comprehensive and great variations may occur. A particular (4) dissimilation of sugar to lactic acid.
fermentation type may exhibit widely different behaviour Type II: processes in which the main product arises in- with major changes in medium composition and process directly from reactions of energy metabolism. In systems of conditions. Strain variations, on the other hand, seem to this type the product is not a direct residue of oxidation of have little effect on the general rate patterns.
the carbon source but the result of some side-reaction or Exceptions are found in all groups, especially Type III. In subsequent interaction between these direct metabolic prod- fact it may prove necessary to subdivide this group further ucts. Examples are: (1) formation of citric and itaconic ac- as more kinetic information on complex processes becomes ids, and (2) formation of certain amino acids.
Type III: processes in which the main product does not One apparent exception is the production of oxytetracy- arise from energy metabolism at all but is independently cline. Doskocˇil et al.7 have presented a very complete study elaborated or accumulated by the cells. It is perfectly truethat carbon, nitrogen, etc., provided in essential metabolitesappear in product molecules but the major products of en-ergy metabolism are CO and water. Antibiotic synthesis (Fig. 2) is a prime example of this type.
Each of these types demonstrates a fairly distinctive rate pattern. These are shown schematically in Fig. 3. The TypeI processes show only one maximum for each of the rateprocesses and these are virtually coincident, hence the term‘growth-associated' often used for products of this processtype.
In the Type II process two rate maxima are distinguish- able. In the first phase tissue is produced with little productformation; in the second product formation rate is maxi-mized. Rapid carbohydrate utilization is common to both.
Unfortunately, very few kinetic data are available for thisgroup. In fact, until the recent development of microbio-logical processes for amino acids (probably Type II), thecitric acid fermentation was the only example for which rateinformation had been published.
Type III processes again show two distinct phases. In the first tissue accumulation and all aspects of energy metabo-lism are maximized with virtually no accumulation of thedesired product, in the second oxidative metabolism is prac- Figure 3.
Fermentation rate patterns.
JOURNAL OF BIOCHEMICAL AND MICROBIOLOGICAL TECHNOLOGY AND ENGINEERING VOL. 1, NO. 4 ARTICLE REPRINTED IN: BIOTECHNOLOGY AND BIOENGINEERING, VOL. 67, NO. 6, MARCH 20, 2000 of metabolic changes observed during this fermentation.
Rate curves calculated from these are shown in Fig. 4.
These authors7 did not attempt any detailed analysis of rates, but they did suggest a multiphase nature for this pro-cess. Specifically they proposed five periods as follows: (1) Lag: virtually no metabolic activity.
(2) Growth of primary mycelium: very high level of me- tabolism (respiration, nucleic acid synthesis, etc.), noantibiotic formation.
(3) Fragmentation of primary mycelium: respiration and nucleic acid synthesis fall, antibiotic synthesis is juststarting.
(4) Growth of secondary mycelium: rapid antibiotic pro- duction, renewal of nucleic acid synthesis, further de-crease in respiration.
(5) Stationary phase: no further growth, metabolic activity low but antibiotic synthesis continues.
Another process which one would expect to fall in Type III is the chloramphenicol (chloromycetin) fermentation. Onthe basis of very scanty data, however, it too appears to be Figure 4.
Oxytetracycline fermentation rates.
an exception to the general pattern. If it is in fact, then thetwo processes which give a typical behaviour both involveorganisms which normally fragment during growth. This batch data is theoretically possible.13,17,18 Furthermore, this may well lead to a characteristic kinetic behaviour different type of process can be operated satisfactorily in a single from that for streptomycin; unfortunately, the information stage system, although additional stages may be added to available is not sufficiently complete to permit any firm ensure economical utilization of nutrients supplied. Both these points have been demonstrated experimentally in a A generous amount of sub-classification would undoubt- number of cases.5,13,17 edly remove most discrepancies. At the same time, how- On the other hand, kinetic considerations alone demand ever, it would make void the primary purpose of this ap- at least two stages for satisfactory operation of the more proach—the establishment of certain reasonably reliable complex process types (II and III). In the first, conditions generalizations about fermentation rate patterns which can will be adjusted to provide maximum rates of growth, and serve as a basis for further kinetic studies.
energy metabolism, in the second, for maximum productformation. Kinetic studies for continuous process design Fermentation Kinetics and Continuous Processes
should therefore be aimed primarily at elucidating the rela-tionships between these various rates and the major, con- Many reasons, both practically useful and intellectually sat- trollable process variables.
isfying, can be offered to justify more intensive study of The only complex fermentation process for which studies fermentation kinetics but one outweighs all others: we can- of this sort have been made is the biosynthesis of penicillin.
not hope to operate continuous processes at a predictable In the final section of this paper, that information will be steady state unless the relationships between major rate pro- collected and related to illustrate the kinetic nature of the cesses and the effects of process variables on them are Type III process.
The reactor system which is apparently best adapted to Penicillin Process Kinetics
continuous fermentation is the homogeneous, overflowtype, with virtually complete backmixing. To establish an Early attempts to clarify the effects of process variables on overflow reactor at steady state all rate processes must be in the two phases of the penicillin fermentation were seriously balance. It is possible to achieve this by simply letting the handicapped by the inadequacies of available experimental system hunt for such a point, but no one can predict in techniques. Even so a general picture was obtained. With advance where this point will be. Such a procedure is hardly improved procedures this has been greatly amplified over an adequate basis for plant operation.
the last decade until the effects of major process variables For the ‘kinetically simple' Type I fermentations, predic- on growth and antibiotic formation are reasonably under- tion of continuous steady state operating conditions from stood. Temperature and pH are the best examples.
ELMER L. GADEN, JR.
GADEN, JR., ET AL.: FERMENTATION PROCESS KINETICS Stefaniak et al.23 found no effect on overall penicillin yieldsbetween 20° and 29°C with an early culture (X–1612). At32°C, however, antibiotic yields fell while oxidative meta-bolic processes (sugar utilization, etc.) were more rapid.
In the work previously cited, Calam, Driver and Bowers6 set the optimum temperatures for growth and penicillin for-mation at 30° and 25°C, respectively. These conclusionswere arrived at rather indirectly because they did not, infact, separate the two phases of the process experimentally.
This was done by Owens and Johnson21 who showed that growth rates were highest around 30°C while penicillin syn-thesis proceeded most rapidly near 20°C. A two-stage fer-mentation with the temperature reduced from 30° to 20°Cafter 40 h gave the highest penicillin titre.
The importance of pH in the penicillin fermentation wasearly recognized. Lacking reliable means for external con- Figure 6.
Penicillin fermentation rates with pH control.
trol, most processes employed medium formulations whichprovided a degree of internal buffering. A number of labo-ratory studies with externally controlled pH have been re- a medium which tended to become alkaline. After 30 h, the ported,2,3,14 however, and the results are plotted on a com- pH was adjusted to 7.0 with acid and held there (approxi- mon basis in Fig. 5. Note that the rates indicated are average mately) by controlled acid addition. Volumetric and specific rather than instantaneous. This does not alter the fundamen- rate patterns calculated from their results are shown in Fig.
tal relationships shown.
6. Since no determinations of mycelial nitrogen were made From these experiments it is clear that the growth phase before the 30-h point, specific rates (based on mycelial ni- of the penicillin fermentation should be operated at a pH trogen, not dry tissue in this case) cannot be computed for value around 4.5–5 while antibiotic formation will be maxi- the early hours.
mized around 7–7.5.
With pH control, constant rates of metabolism and prod- It is also interesting to note the effect of external pH uct formation may be sustained for a long time, even in the control on rate patterns in a penicillin fermentation. Brown unsteady-state batch process. Extended batch processes of and Peterson4 have reported batch fermentations employing this type may very well be practical competitors of continu-ous operations, particularly if the operating problems whichhave often been encountered in continuous systems provedifficult to overcome. The limit on such a process, assumingcontinuous nutrient addition as well as pH control, willpresumably be imposed by the accumulation of productstoxic to the organism or inhibitory to its enzyme systems.
Acknowledgment. This study was aided by a grant from the Na-tional Science Foundation, whose support is gratefully acknowl-edged.
1 Adams, S. L. and Hungate, R. E. Industr. Engng. Chem. (Industr.), 42 2 Bautz, M. Antibiotics Research, Report No. 10, University of Wisconsin 3 Brown, W. E. Antibiotics Research, Report No. 11, University of Wis- consin (August 1, 1949) 4 Brown, W. E. and Peterson, W. H. Industr. Engng. Chem. (Industr.), 42 Figure 5.
pH effects in penicillin biosynthesis.
JOURNAL OF BIOCHEMICAL AND MICROBIOLOGICAL TECHNOLOGY AND ENGINEERING VOL. 1, NO. 4 ARTICLE REPRINTED IN: BIOTECHNOLOGY AND BIOENGINEERING, VOL. 67, NO. 6, MARCH 20, 2000 5 Butlin, K. R. Continuous Culture of Microorganisms, Czechoslovak 16 Luedeking, R., Ph.D. Thesis, Dept. of Chemical Engineering, University Academy of Science, Prague (1958) of Minnesota (1956) 6 Calam, C. T., Driver, N. and Bowers, R. H. J. Appl. Chem., 1 (1959), 17 Luedeking, R. and Pivet, E. L. This Journal, 1 (1959), 393 18 Maxon, W. D. Appl. Microbiol., 3 (1955), 110 7 Doskocˇil, J., Sikyta, B., Kasˇparova´, J., Doskocˇilova´, D. and Zajicˇek, J.
19 Moyer, A. J., Wells, P. A., Stubbs, J. J., Herrick, H. T. and May, O. E.
J. Gen. Microbiol. 18 (1958), 302 Industr. Engng. Chem. (Industr.), 29 (1937), 777 8 Dulaney, E. L., Hodges, A. B. and Perlman, D. J. Bact., 54 (1947), 1 20 Moyer, A. J., Umberger, A. J. and Stubbs, J. J. Industr. Engng. Chem. 9 Gaden, E. L., Jr. Chem. & Ind. (Rev.) (1955), 154 (Industr.), 32 (1940), 1379 10 Gaden, E. L., Jr. Chem. Engng. (April, 1956), 159 21 Owens, S. P. and Johnson, M. J. Appl. Microbiol., 3 (1955), 375 11 Gale, E. F. Chemical Activities of the Bacteria. (1947). New York: Aca- 22 Sikyta, B., Doskocˇil, J. and Kasˇparova´, J. This Journal, 1 (1959), 379 12 Gastrock, E. A., Porges, N., Wells, P. A. and Moyer, A. J. Industr. En- Stefaniak, J. J., Gailey, F. B., Jarvis, F. G. and Johnson, M. J. J. Bact., 52 gng. Chem. (Industr.), 30 (1938), 782 Herbert, D., Elsworth, R. and Telling, R. C. J. Gen. Microbiol., 14 Stodola, F. H. Chemical Transformations by Microorganisms. (1958).
14 Hosler, P. and Johnson, M. J. Industr. Engng. Chem. (Industr.), 45 25 Wallen, L. L., Stodola, F. H. and Jackson, R. W. Type Reactions in Fermentation Chemistry. (1959). U.S. Dept. of Agriculture 15 Kempe, L. L., Gillies, R. A. and West, R. E. Appl. Microbiol., 4 (1956), 26 Wells, P. A., Moyer, A. J., Stubbs, J. J., Herrick, H. T. and May, O. E.
Industr. Engng. Chem. (Industr.), 29 (1937), 653 ELMER L. GADEN, JR.
GADEN, JR., ET AL.: FERMENTATION PROCESS KINETICS

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