MODELLING OF ANAEROBIC MICROBIAL FERMENTATIONS
The production of alcohols by Zymomonas mobilis and Closiridium beijerinckii
MODELLING OF ANAEROBIC MICROBIAL
FERMENTATIONS
The production of alcohols by
Zymomonas mobilis and Clostridium beijerinckii
PROEFSCHRIFT
ter verkrijging van de graad van doctor in de technische wetenschappen aan de Technische Hogeschool Delft, op gezag van de Rector Magnificus, prof. dr. J. M. Dirken, in het openbaarte verdedigen ten overstaan van het College van Dekanen op 1 mei 1986 te 16.00 uur
door
Isabella Maria Leonarda Jöbses
geboren te Wittemkrips repro meppel
TR diss
1 4 8 1
Errata
- L e g e n d s f i g u r e 2 , p a g e 6 9 :
f igu/ic 2. Jo-cned con/üdtna* ie.gion.4 o£ if and m at dj././t*.*nJ. fxiAUMX. t£-A A i^tA* t*L *j*a Ltd from conLUnMOut CMLLUAA. 4.C4U-LL4 at aHiuCion 4aLa *.ang-Lng Letux-tsx 0.02 and O.U A* „'
3
Ö o n> o Er3 a
•t) o 2, CL ^ _ 'T* 5
■ a . O a. 3- o o> l
?■ XIr 3
= 3
S-2
a> o 30°Ct 46 g/L etAanol (LaLU 1, frg.1) )0°C, 2J g/L ethanol (adopted from **/.U)?5°C, 2) g/L ethanol (adopUd from A*£. H) — Legends figure 3, page 95 additional text:
Arrows indicate theoretical time interval for achieving 95% (left) and 99% (right) of the final biomass concentration at zero growth rate, calculated using equation 14.
- page 8, eqn. 1: change + signs for - signs
add to page end: r = FLOW. - FLOW ,-.
r ö a in out (2)
conserved quantities are not converted (r = 0) and the balance a
equation reads:
- page 17, line 26 should read: Also, non-energy limited growth will elevate m , whereas energy limited growth will decrease Y
s oj o sx
- page 45, line 37 should read: If C >>K , .... , s s - page 81, eigenvalues should read: s
"Here is an anecdote about my brother, which, with minor variations could be told truthfully about me:
Bernard worked for the General Electric Research Laboratory in Schenectady, New York, for a while, where he discovered that silver iodide could precipitate certain sorts of clouds as snow or rain. laboratory was a sensational mess, however, where a clumsy stranger could die in a thousand different ways, depending on where he stumbled.
The company had a safety officer who nearly swooned v/hen he saw this jungle of deadfalls and snares and hair-trigger booby traps. He bawled out my brother.
My brother said this to him, tapping his own forehead with his fingertips: 'If you think this laboratory is bad, you should see what it's like in here! '"
From: Kurt Vonnegut, 'Slapstick or Lonesome No Morel'
Voorwoord
Dit boekje is een bundelina van artikelen, die voor de kenner hopenlijk interessant en voor de leek waarschijnlijk saai zijn. Ik bespaar ben dan ook bet ongemak van bet lezen en mij de moeite van bet opschrijven van een "begrijpelijke" samenvatting.
In plaats daarvan wil ik graag iedereen bedanken die aan dit onderzoek heeft meegewerkt en degenen die de werksfeer veraangenaamd en/of verlevendigd hebben. Ik ben altijd met plezier naar bet lab gegaan en heb me geen moment verveeld.
Allereerst wil ik Joop Roels bedanken; ik heb veel van hem en het onderzoek geleerd en heb zijn vertrouwen in mij zeer gewaardeerd. Vervolgens gaat mijn dank uit naar de Steunpilaren van het onderzoek, die ondanks hun gering aantal toch dankzij hun inzet een grote bijdrage aan het onderzoek hebben geleverd: Ton van Baaien, Ger Egberts, Marijke van Benschop en Henk Hiemstra. Wie gaat promoveren leert studenten waarderen. Dick Reuvers bedank ik voor de talloze analyses die ze met een onbedwingbare werklust heeft uitgevoerd en voor haar hoede over de hinders.
Mijn kamergenoten Jacques Teven, Wxm Groot en Gerda Scboutens bedank ik voor de diskussies, bun morele steun en voor hun geduld. Verder bedank ik John Metselaar, Leo Janse, Cees van Houwelingen, Theo Geurts, Bas van Kleeff, Jaques Potters, Jan Woudwijk, Bart Kerkdijk, Arie, Nico en Max en niet te vergeten Sjaak Lispet voor hun bijdragen en gezelligheid. Tot slot wil ik Karel Luyben bedanken voor zijn stimulans om orde in de chaos te scheppen.
En als beste afsluiting bedank ik mijn ouders voor hun goede zorgen en de periodieke bevoorrading met heerlijke vlaaien.
Chapter 1.
Introduction. I
Chapter 2.
Unstructured models. 8
Chapter 3.
Mathematical modelling of growth and substrate conversion 21 of Zym.omon.a-i> moHJJLL/i at 30 and 35°C.
Chapter 4.
The inhibition of the maximum specific growth and 42 fermentation rate of Zymom.ona-6 moLULlA by ethanol.
Chapter 5.
Fermentation kinetics of Zym.omon.a4 mo£J.£ió at high ethanol 62
concentrations; oscillations in continuous cultures.
Chapter 6.
Fermentation kinetics of Zymomonaé mo&UJLió near zero growth 84
rate.
Chapter 7.
Experience with solvent production by 105
CÉo-itvUrlium ILeJ-jeAJJickil in continuous culture.
Summary. 113
Chapter 3, "Mathematical modelling of growth and substrate conversion of Zymomonas mobilis at 30 and 35 C " , I . M. L. Jöbses , G.T.C.Egberts, ft. van Baaien and J.fl.Roels, Copyright Biotechnol.Bioeng. 1985 (Wiley & Sons) and Chanter 7, "Experience with solvent production by Clostridiurn bei jermckii in continuous culture", I.H. L. Jöbses and J.A.Roels, Copyright Biotechnol.Eioeng. 1982 (J.Wiley & Sons) are reprinted by kind permission of John Wiley & Sons Inc.
Chapter 4, 5 and 6 : Hot for general distribution; for use only by I.M.L.Jöbses in connection with this doctoral thesis. These are prepublication prints of material to appear in Biotechnology and Bioengineering, to be published by John Wiley 8 Sons Inc. Copyright reserved.
CHAPTKR 1
I ■- I
Biotechnology covers a large field of biological and technical sciences. In fermentation technology, all activities are focussed to or based on biological units ranging from single enzymes to complete micro-organisms. The aim of all effort is to use these biological units as a catalyst in the degradation of unwanted or toxic compounds or in the synthesis of more or less specific organic compounds, including biomass. The type of biological unit which can be used in a process is primarily determined by the desired product or conversion. Single enzymes can catalyze highly specific reactions yielding very valuable products. But as they will gradually loose their activity, they need to be replaced in time. Complete organisms on the other hand are super-catalytic: besides catalyzing a desired process they can also replicate themselves, providing a steady replenashment of the catalyst and offering the basis for long term continuous processes. In contrast to enzymes, however, the range of products is much smaller. Although the same specific products as with isolated enzymes can be formed, these products are often metabolized further to less valuable compounds.
The subject in this thesis is the modelling of end-product formation by microorganisms under anaerobic conditions.
Like all living material, microorganisms need a suurce of energy to stay alive and to multiply. Apart from photosynthetic organisms which can utilize light as a source of energy, most bacteria obtain energy from converting energy-rich chemical compounds to relatively energy-poor compounds in a series of reactions called (catabolic) metabolism. Two types of metabolism can be distinguished; respiratory metabolism and fermentative metabolism. In respiratory metabolism, the substrates are completely oxidized by oxidants like oxygen, sulfates and nitrates to water, hydrogensulfide ammonia and carbondioxyde. In fermentative metabolism, substrates are converted to a mixture of only organic compounds, which contains often carbondioxyde and alcohols or organic acids. The energy yield per unit substrate converted is 10 to 20 times lower in fermentative metabolism compared to respiratory metabolism. As a consequence, ca. 10-20 times as much substrate is converted in fermentative metabolism as in respiratory metabolism for sustaining or growing equal amounts of biomass. Consequently, large amounts of product are formed per unit biomass, which make microbial fermentations an attractive process for the production of bulk-chemicals.
Bulk-chemicals are used as fuels, solvents, chemical starting material and food additives. For the first three purposes, fermentation products can hardly compete at the moment with chemicals obtained by petro-chemical processes. The costs of fermentation and product recovery are about 0.15 $/kg
-product for ethanol and isopropanol/butanol/ethanol mixtures. Considering the market prices * of ethanol (0,60 - 0.70 $/kg) and of raw materials like molasses, glucose syrup and starch (ca. 0=35 $/kg ethanol produced.), a profit margin of 0.10 - 0.20 $/kg would be left. The raw materials price can be reduced by using waste materials such as rrom food and diary industries. Liquid waststreams are, however, often very diluted and transport costs will be high. The butanol/isopropanol/ethanol mixtures obtained from Clostridial fermentations can be used as a fuel and is comparable with gasoline, which has a market price of ca. 0.30 $/kg. Substraction of the fermentation and recovery costs leaves maximally 0.J5 $/kg product for transport and nutrient costs. This price level is exceeded for transport distances larger than 400 km, calculated for 27.5 % whey
2
permeate"". Even if the process is not economically profitable in itself, it might be favourable as it removes organic waste material. However, serious competition can be expected then from the classical anaerobic waste water treatment. This process has no demands for sterile equipment and processing and yields methane as end-product, which is relatively easy recovered. Up to nowi even anaerobic waste water treatment is not a profitable process in itself5.
Anaerobic fermentation processes can, however, be economically feasible in the food-industry for the production of additives or complete products. For this purpose biological processes are often required by law (for example alcoholic beverages) or are simply the most efficient processes (citric and lactic acid production) or yield a special complex and final, product (beer, wine, yoghurt).
MODELS
The need for modelling microbial growth and product formation comes from the whish to understand, describe and ultimately control these processes. Modelling starts in general with a verbal description of the process, offering plausible cause-effect relationships based on experimental observations. Verbal models are inherently of a qualitative character, predicting all or none effects or subjective qualifications of responses like much, low, some etc, Recently • , fuzzy mathematics has gained interest as a means of integrating verbal statements or qualitative data into computerprograms for fermentation control. These models offer a valuable tool in situations where a lack of quantitative knowledge exists. For a more accurate process control and optimization of the process design, quantitative mathematical models are desirable.
A useful mathematical model should satisfy the following demands: - adequate description of the features of interest
- correlation of observable quantities to eachother by mathematical functions - the mathematical functions with their parameters must be experimentally verifiable and determinable.
- 2 ~
From the last constraint and in the context of process control, it is obvious that a model should be as simple as possible, thus containing a minimal number of parameters and constants. So far, a purely mathematical model lacking any physiological basis can do as well or sometimes better as a model based on detailed biochemical knowledge of the constituting sub-processes. A good model, however, predicts the systems behaviour also (qualitatively) outside the conditions it was constructed and tested for. This is the point, where general knowledge about biochemical processes comes into the picture. The more realistic a mathematical model is, what means that it is a reflection of suspected important biochemi cal sub-processes, the greater chance it has to predict new experimental results. Mathematical, models of this type are not only a tool for controlling and optimizing processes, but provide also a guideline for experimental strategies which differ from "normal" biochemistry. Often, in normal biochemistry, very detailed information on various sub-processes is gathered, from which it is difficult to say what processes are relevant for the behaviour of the total organism. The approach from the modelling side is mostly the other way around. First, the behaviour of the total organism is described with kinetic equations, which are in general determined empirically. These kinetic equations contain time constants which should reflect the response of the organisms to changes in environmental conditions. Then, the rate determining processes are searched for on basis of these time constants: If the response of the biomass to environmental changes is slow, the responsible mechanism for this response must have a large time constant.
Mathematical models can be classified according to their description of or assumptions on biomass. Segregated (or corpuscular) models regard biomass as a population of individual cells. Consequently, the applied mathematics are based on statistical equations. These models are valuable for describing variations in a given population, like for instance the age distribution amongst the cells. This type of models is also useful for the descriDtion of stochastic events, in which case probability statistics are applied. The fission of cells is a suitable example of such events. A disadvantage is of course the fact, that the variation in the population has to be determined experimentally in order to provide the parameters for the statistical models.
If there is no need for the description of variations in the biomass population or stochastic events, and provided that the number of cells under consideration is large, continuum models are more convenient. Continuum models regard biomass as a chemical complex in solution, or as a multiphase system without concentration gradients within the separate phases. This last assumption is based on the fact that the size of microorganisms is so small that internal concentration gradients are not likely to occur. Now there is no need to be concerned about variations from the mean, and all
-experimentally determined features are ascribed to the biomass as a whole. In fact, the description of non-stochastic interactions between the biomass and its environment by continuum models equals the description by segregated models in the case of large populations with a normal variance distribution ' .
Continuum models can be subdivided in unstructured and structured models. Unstructured models regard biomass as one compound which does not vary in composition upon environmental changes. Structured models regard biomass as consisting of at lenst two different compounds, and describe the interactions between the constituting compounds and between the biomass and the environment. In contrast to unstructured models, the biomass composition can change with changing conditions. It is obvious, that the more biomass constituents are described, the more complex the model will be, containing at least one extra equation and parameter per additional compound.
EXPERIMENTAL APPROACH
The development and verification of mathematical models relies entirely on experimental observations. The experimental results are however restricted by the type of experiments: if an experiment is performed under constant conditions one cannot expect to get reliable information about the response time of the system to environmental changes. Generally, models relate several variables to eachother like for instance product concentration and growth rate by means of mathematical equations which contain constants or parameters. Estimation of these parameters occurs preferrably under well defined, constant conditions. In this case, the relation between one control variable, like for instance temperature, and the value of a model parameter can be estimated unambiguously if the other control parameters are kept constant. These constraints are met by continuous cultures. Continuous cultures are systems which can reach steady states, i.e. all the variables of the system are constant in time. The time constants of the system are, however, determined by the combined mathematical functions and cannot always be deduced from the parameter values only. For the verification of the predicted time constants, dynamic experiments have to be performed in which the response of the system to changing environmental conditions can be estimated. Examples of dynamic experiments are batch and fed-batch cultures, where the concentrations of all participating compounds change in time. Also pulse or step changes in continuous culture can give valuable information, especially as the change can be applied to a single process variable and the initial and final situations are well defined.
SELECTION
Another characteristic of continuous cultures is the selective pressure on microorganisms. Dykhuizen and Hartl presented an extensive review on
- h
-observed selections and the underlying theory and applications. The explanation for occurence of selections is based on the evolution theory; survival of the fittest. As the environmental conditions in steady state continuous cultures do not change in time, organisms which have more favourable properties for the given situation will grow faster than organisms with less favourable properties. In time, the "fittest" organisms will overgrow the original population. This can be a disadvantage if continuous cultures are used for parameter estimation of the original population. On the other hand it can be an advantage as it provides a tool for selecting more suitable organisms. The type of selection depends on the growth limiting factor: if growth is limited by an Inhibiting product, organisms which are more resistant to this product can be selected. If growth is limited by a nutrient, organisms which use this nutrient most efficiently can be selected. Under energy limitation, for example, organisms can increase their efficency of substrate utilization in several ways. One way is to increase their substrate conversion rate. Another way is to increase the energy yield from substrate conversion. In both cases the energy production rate is increased, allowing a higher growth rate.
SURVEY OF THIS STUDY
In this study, the growth and fermentation characteristics of the anaerobic bacteria Zymomonas mobilis and Clostridium beijerinckii were investigated. Z.mobilis ferments sugars almost quantitatively to ethanol and carbondioxyde by the Entner Douderoff route as shown in figure 1. In contrast to glycolysis, conversion of 1 mol glucose yields only 1 mol ATP. This inefficient catabolism is one of the main reasons that Z.mobilis has a high specific substrate conversion rate compared to other microorganisms. The low level of by-product formation and the high product formation rate make Z.mobilis strongly competing with conventional organisms like yeasts for the production of ethanol. A disadvantage is however the substrate specificity of Z.mobilis; it can only convert glucose, fructose and polymers of these sugars like starch and molasses. Because of the relative simple metabolism and the high product formation rates, this organism is very suitable for testing and developing mathematical models. Furthermore, a large part of the metabolic energy is not used for growth of the biomass, but is obviously spent in maintenance processes. The mathematical equations for the description of maintenance substrate conversion and the physiological underlying mechanisms have been subject to much debate in literature.
Therefore, fermentations with Z.mobilis were used as the experimental model system for studying the influence of process conditions on this maintenance metabolism. A general introduction to mathematical modelling of anaerobic fermentations is given in chapter 2. The validity of an unstructured and structured model are tested and compared to eachother in chapter 3. In chapter 4, steady state kinetics of growth inhibition by
-ethanol is investigated in turbidostat cultures. Furthermore the time constants of the bior.iass response to stepwise changed ethanol concentrations in these cultures is estimated. In chapter 5 a model is developed, based on the ethanol inhibition kinetics, which Ls able to describe observed oscillations in continuous cultures. A more detailed study of the effect ol ethanol on the growth rate Independent product formation and a correspondingly extended model is presented in chapter 6.
1 glucose f ATP ^NAD(P)+ 2 2-keto,3-deoxy-gluconate-6-P 1 pyruvate ^» 1 pyruvate
uco-is m&ta(LoJU.óm o/i ^t/,'aomcn--i j ;;;ou LL-L J. Cy the.
Cl.bei lerinckii* is a strict anaerobe and has a more complicated and flexible metabolism as shown in figure 2. This organism can convert a large variety of sugars including pentoses. The most valuable products are butanol and isopropanol. The energy yield per mol glucose is higher when acetic and butyric acids are formed compared to the formation of butanol and isopropanol. Because of the ability to produce molecular hydrogen, all end-products can be formed independently of eachother, giving the organism a high flexibility in product formation which is indeed observed in practice. In batch fermentations, the metabolism switches from acid production to alcohol production. This switch is at least partly induced by the accumulation of the acids, which become inhibitory at high levels. The opposite behaviour is often observed in continuous cultures. After producing mainly alcohols for several generation times, the product pattern changes to acids. How the product formation is regulated is not fully understood yet, but the
6
-differences in energy obtained by the formation of the different products is probably an important factor. As mentioned before, a higher energy yield can give a selective advantage in energy-limited continuous cultures. The switch from alcohol to acid production after a long period of continuous growth might therefore be the result of selection of an acid producing species.
Modelling of the regulation of product formation is still in the verbal stage. The research on Cl.bei jerinckii described in chapter 7 is focussed on conditions affecting alcohol formation in long tern continuous cultures.
1 butanol 1 isopropanol
Py/iuuaie -CO £o/im&d ty the. ytyaolytic paihuxiy.
B.L.Maiorella, H.V.Blanch, C.R.Wilke, Biotechnol.Bioeng. 26 (1984) 1003. G.II.Schoutens, V.'.J. Groot, Process Biochem. 2Ü. (1985) 117.
JA Koels and J.de Klines, 3rd Eur.Congr.Biotechnol., Munchen, Proceed. 4_ (1984) 73.
Chemical Marketing Reporter, 2 Bee. (1985). L.H.A.Habets and J.H. Knelissen, \\nQ \J_ (1984) 626.
M.Dohnal, Biotechnol.Bioeng. 21_ (1985) 1146.
T.Nakamura, T.Kuratani, Y.Morita, in: Modelling and Control Biotechnol. Processes, 1st Il-AC Symp. (1985) Noordwijkerhout, The X'ethelands, (A.Johnson ed.) Pergamon Press, preprints p.211
J.A.Roels, Energetics and Kinetics in Biotechnol. (1983), Elsevier Biomed. Press, Amsterdam, New York.
D.Ramkrishna, Adv.Biochem.Eng. 11 (1979) 2. D.Dykhuizen, D.E.Hartl, Microbiol.Rev. (1983) 150. J.Swings and J.de Ley, Bacteriol. Rev. Ul_ (1977) 1.
E.E.Bruchman, Angewandte Biochemie (1975) Verlag Eugen Ulmer, Stuttgart.
CHAPTER 2
UNSTRUCTURED MOMELS
In this chapter, the development of unstructured models for anaerobic fermentations based on widely used equations is presented and some theoretical considerations with regard to experimental set up and data evaluation are discussed. A more profound and comprehensive treatment of mathematical models in biotechnology is presented by Roels .
Unstructured continuum models regard biomass not as a particulate with very complex internal structures and functions, but as a chemical compound in solution with an average chemical formula. This is of course far from reality, but it serves well as a starting point for modelling. In general it deserves preference to extend a (over)simplificated model if necessary, than to use a highly complicated model able to describe any feature but which cannot be falsified experimentally.
Regarding fermentations as chemical conversion processes, they can be described by mathematical models based on balance equations and kinetic equations.(see ref.2-4),
In microbial fermentations, biomass serves on one hand as the catalyst for substrate conversion and is on the other hand a product of this conversion. The catalyst properties are reflected in the kinetic equations by the growth and product formation constants. Biomass as a fermentation product appears as a simple chemical compound in the balance equations.
BALANCE EQUATIONS
Balance equations can be made up for all quantities which have the property to be additive for parts of the system, so called conservative quantities. Examples are the amounts of chemical compounds, volume, mass and energy. Kinetic equations are empirically derived or postulated equations, which describe a relationship between a reaction or transport velocity and the state of one or more components of the system. Balance equations show the following general structure:
ACCUMULATION FLOW FLOW CONVERSION (1) RATE IN OUT RATE
For a system in steady state, the net accumulation of a quantity (dC /dt) is zero, and the conversion rate (r ) is equal to the difference between the in- and outcoming flows.
8
-FLOW IN - -FLOW OUT (3)
The f low sheet for anaerobic fermentations consists of 6 main compounds, which the organisms exchange with the environment as illustrated in figure 1.
Tl quM.<i 1. TIÜIÜ óheet lot ana&Aotic £e./imeniatU.otn,
Flow products represents the flow of one product or the flow of a known constant ratio of products. Since the elements C, H, 0 and N account for about 90% of the biomass and in general for a higher percentage of the substrate and products, only these elemental flows are considered. When the C, H, 0 and N content of the compound flows are known, the elemental balances provide 4 equations between the 6 compound flows. Hence, whenever 2 flows are known, the remaining flows are determined and can be calculated.
By adjudging degrees of reduction , g, to the elements and summation of the 4 elemental balances, 1 degree of reduction balance is obtained * . For a fermentation system in steady state, or when the system considered is the biomass (in which accumulation is negligible) the net flows are equal to the conversion rates (eqn.2). The degree of reduction balance reads:
8srs + 8nrn + Snr„ §xrx + 8H20rH20 + §C02rC02 " ° (4)
Production rates have a positive sign and consumption rates have a negative sign in this balance equation, g is a constant for compound a and is calculated from the elemental composition and the degree of reduction of the elements (see table 1 ) . In this equation, the degree of reduction of the elements need not to be equal to the chemical valencies of the ionic forms of the elements, but can be chosen arbitrarely . It is convenient to choose g of the elements in such a way, that flows in which one is not interested are eliminated from the degree of reduction balance. The generalized degree of reduction balance is the reduction balance normalized to carbon equivalents and reads:
Y»r«
V P
-
V x
(5)-In whichy is the degree of reduction of the compound per Oequivalent. In
this case the flows are of course also expressed in C-equivalents per unit time. In table 1, an example of the values of the degrees of reduction is given for a fermentation for which the HgO, COo and N'-source flow are eliminated from the degree of reduction balance.
Again it is clear, that whenever two conversion rates are known, say ry and r , the remainder r is determined and can be calculated.
TABLE 1. Some examples of reduction degrees (g) for elements and compounds. The generalized degree of reduction ( Y ) of a compound is the reduction degree per carbon equivalent.
elements: g compound H20
co
2 NH3 glucose ethanol biomass C H A 1 formula CaHb°cNd H,0co
2 NH3 C6H12°6 C2H60 CH1.8°0.5N0 0 -2 .2 a c N* -3 g gc + b.gH + 80 + d- 8N 0 0 0 24 12 4.2 g Y compound'a 0 0 0 4 6 4.2* gn-jtr0oen c a n D e chosen in a way that the reduction degree of the nitrogen source used in the fermentation is zero .
KINETIC EQUATIONS
Biomass growth is a first order reaction with respect to biomass:
rx = , CX (6)
in which p is the specific growth rate.
The equation for substrate consumption, r , was derived for aerobic fermentations by extending • ~ the linear equation for substrate consumption (eqn.10)
rs - ^ s x ' ^ x +™ s 'Cx+ W V ' p ( 7 )
in which Y ', m ' and Y are constants. Y ' relates rs to growth
10
-of the biomass (r ) and m relates r to maintenance -of the biomass. These constants will be discussed later. Equation 7 states, that product formation is independent of biomass formation and maintenance. This is not correct for anaerobic fermentations, for both, physiological and mathematical reasons, as will be shown: For anaerobic fermentations, eqn.7 is overdetermined0' , which follows from rearranging eqn.5 :
r = ^r_Yr ) / V (8)
o ' s s ' x x/n p K '
v y p -
1 / Y° * ' „ .
f^ i , c (9)
Since all terms between parentheses are constants, r can be written as:
(10)
in which the constants Y and m are called the true yield constant and the maintenance factor respectively. The expression for r becomes by substitution of eqn.10 in eqn.7:
rp - (Ys/Ys xYp ~ YX/ Vp) rx + (Ysms/Yp)Cx (11)
Since again all terms between parentheses are constants, eqn.11 can be written as:
r
p " d / V
rx
+>
Cx
(12)In „nich Yp x = YpYs x/ ( Ys - Yxïs x) (13)
and mp = Ysms/ Yp ( H )
Y is the true yield of biomass based on product and ni is the
rA P
maintenance factor based on product.
From the foregoing it is evident that product formation in anaerobic fermentations is directly linked to biomass formation and maintenance. If only one product is formed, it has to be directly linked to both, biomass growth and maintenance. When more products are formed, all products together are linked to growth and maintenance, but one particular product can be linked to biomass growth or to biomass maintenance or to both. From the physiological point of view it is obvious that the formation of end products of the energy providing catabolism (primary products) must be directly coupled to the energy demanding anabolism (biomass formation) and other
energy consuming processes like maintaining proton gradients, turnover of macromolecules and transport processes.
The linear equation for substrate conversion (eqn.10) was postulated to account for the feature that part of the substrate consumed is not related to biomass growth but is obviously used for other energy demanding processes. There are two approaches to the concept of non-growth associated energy demand, which appear to be mathematically equivalent:
ENDOGENOUS METABOLISM
When microorganisms are deprived of substrate, respiration or fermentation will continue to some extent. In this case, intracellular molecules in stead of substrate are metabolized to yield energy, i.e. negative growth occurs, until death. Apparently microorganisms are forced to utilize energy even when they do not grow. From the observation of Herbert , that in continuous cultures lower yields of biomass on substrate were obtained than expected, it can be concluded that this non-growth associated energy consumption also occurs during growth. The specific CO2 evolution was linear with the growth rate but when extrapolated to zero growth rate, it was greater than zero. Mathematically he described this metabolism by a negative growth rateU ■
rx = ( Ub- Ue) Cx (15)
in which V is a constant. U K is the bruto growth rate and depends of
i_ 11
the substrate concentration as given by the Monod equation :
Kb = (um a x bCs)/(Ks + Cs) (16)
i! . is the maximum growth rate when no endogenous metabolism occurs and
^maxb ö °
K is the Monod constant. The substrate consumption is linear dependent of the bruto growth rate by the yield constant Ys x:
r
s
= ^ W V x <
1 7)
MAINTENANCE MODEL
Another approach is the maintenance energy concept, first postulated by
revalued this concept and continuous cultures data showed that the maintenance substrate utilization was constant at different growth rates. Equation 10 is the mathematical expression which accounts for the maintenance energy demand, and is further called the linear equation for substrate
12
-consumption. For biomass growth, the Monod equation is taken:
rx "" raaxCsV<Ks+Cs) (18)
\imax is the maximum growth rate which is observed experimentally. Both approaches are mathematically practically equivalent and can be converted in one another. Combining eqn.18,15 and 16 gives:
Umaxb "Wmax + Ysxms^i (s+ Cs) / Cs (19)
and combining eqn.10 and 17 results in:
v e " Ysxms (20)
Of course, U m a x t ) is a constant and is therefore independent of C . Under circumstances where U b is valid, K will be ignorable with regard to c so
'3 s
% a x b =u. a x + Ysxms (21)
Both models predict a linear relation between the specific substrate consumption or product formation and the growth rate. The specific substrate consumption rate q equals:
Is = rs/ Cx (22)
For the endogenous model by combining oqn 15 and 17, q is:
(23) and for the maintenance model:
«s ■ U ^ s x » " ms (24)
A difference between the models appears when growth under substrate limited conditions is described as for example growth in continuous cultures at D < Umax' 0 f c°urse, rx is for both models equal to the dilution rate D, and rs is also equal in both models. Deviations appear in the predicted steady state values of Cx and Cs' For the maintenance model they are given b y
Cs " W s ^ m a x - D ) (25)
Cx " D Cs i/ ( D / Y s x + -.) <26>
and for the endogenous model:
Cs " VD + Y a x ms » < max"D) (27)
An example of the magnitude of deviations is shown in Table 2.
The deviation in Cx is negligible but the deviation in Cg is at low growth rates considerable with regard to its absolute values. It will be difficult however to discriminate between these two models experimentally by measuring C , since rs is high with regard to Cs (table 2 ) , so that within 1 minute sampling time a significant decrease in Cs will occur.
In growing systems where substrate is fed to the biomass, the maintenance model seems preferable. In this case it is more logical to assume that part of the substrate is converted for non-growth energy demand, than to assume that substrate is first converted to biomass whereafter the biomass is degraded for the non-growth energy demand.
TABLE 2. Comparison I) e t we en trie endogenous metabolism mode I and the maintenance energy model for steady state continuous culture concentrations and r The steady state concentrations are calculated from eqns.25-28. R is equal for both models and can be calculated from eqn.9 or 16. In continuous cultures r equals D. Applied parameters: Um a x - 0.3 hr , Y
-0 . -0 5 g / g , D ( h r "1) 0 . 0 1 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 5 ms = 2 C End. 0 . 0 3 8 0 . 1 0 0 . 1 7 0 . 3 0 0 . 7 0 g / g h r , Ks = 0 . 1 g / 1 ,
. Cs/»
M a i n t . 0.0036 0.U5 0 . 1 0 0 . 2 0 0 . 5 0 C X End. 0 . 2 2 7 1.25 1.50 1.66 1.77 Cs i = 5° g / D Maint 0 . 2 2 7 1.25 1.50 1.66 1.77 g / 1 . rs ( g / L . m l n ) 0 . 0 0 8 3 0 . 0 8 3 0 . 1 2 5 0 . 1 6 6 0 . 2 0 7 MICROSCOPIC MODELThe macroscopic modeling described above, based on elemental balances and empirical equations for conversion rates can be extended to a microscopic m o d e l1'1^ . ATP can be regarded as the universal energy carrier in microbial metabolism since it is in direct or indirect connection with other energy rich compounds (like GTP) or systems (membrane p o t e n t i a l s ) . The net synthesis of ATP is assumed to be z e r o , considering that ATP leakage out of the cells is negligeable and variation in the intracellular ATP levels can be neglected with regard to the ATP turnover. S o , a s an intermediate, the production of ATP in energy yielding reactions must equal the ATP consumption. ATP consuming secondary product formation is for simplicity not considered here. Stouthamer et al1'4'-'-5 translated the maintenance model to a microscopic m o d e l , describing the fate of ATP by transforming the linear equation of
14
-substrate consumption (eqn.10) to a linear equation for ATP consumption:
rA T P ( l / YA T p) r NIATP' ■Cv (29)
in which YATD is the true yield of biomass on ATP and ™ A T U growth associated or maintenance ATP consumption rate. The schematically represented in figure 2.
is the non-fate of ATP is
substrate > intermediates ^ product(s)
maintenance
/•' iga/ie. 2. A7P psiQdu.ciU.on and utilization in anae./io&ic
f-&/u?iesii ation-j.
In this scheme, ATP production only occurs directly linked to product formation and not with intermediate formation.
In fact, ATP formation will occur during intermediate formation during growth on energy rich substrates like fatty acids. In this case figure 2 represents the net ATP requirement for biomass formation. ATP formation is now directly linked to product formation by the stoechiometric constants of the particular fermentative pathways used by the organisms:
rATP " a rp (30)
Since the ATP consumption must equal the ATP production:
a rp " (i/ÏATP^x + mATPCx ( 3 D
substitution of eqn 12, 13 and 14 yields:
YATP = Yp x/ c !
YA T P = ( Y pYs x )/ a( Y s - Y xYs x )
mA T p = a mp
m
ATP " « V V V p
(32)
Note that if intermediates are regarded as biomass, figure 2 repesents the endogenous metabolism model and the macroscopic parameters can be converted
to the microscopic parameters in the same way.
Differences in Y and m caused by differences in product formation and cocurrent ATP generation can be accounted for by basing the yield and maintenance constants on the ATP yield. However, Yvj«p and m^-pp appear not to be constant for all organisms
THE CONSTANCY OF THE GROWTH PARAMETERS.
Extensive reviews on this subject can be found in literature ' J and only a short summary is presented here. Y.pp and nupp are not universal constants for all microorganisms as formerly hoped for. All external factors which affect metabolism appear to influence these growth parameters. Examples of these factors are: kind of substrate, kind of products, nature of nitrogen source, complex or minimal medium and vitamin concentration , pH, temperature and the nature of the growth limitation (energy limitation, C-, N-, P-limitation) and so on.
Comparing for example Zymomonas mobilis with Saccharomyces cerevisiac shows, that even when both organisms are grown on the same substrate and form the same product, Y.pp and m^pp differ largely . Furthermore, ^ A T P and mATP a r e no*- constant for an organism grown on different substrates '"tfJ. The latter is probably partly due to the assumption made earlier that no ATP is produced in intermediate formation and hence Yftrp is the net yield of biomass on ATP starting from substrate. The growth constants for energy limited cultures differ significantly from growth constants of cultures limited in carbon, nitrogen or other element supply. Carbon limitation occurs during growth on substrates with a high energy content per carbon equivalent ' . Under energy limitation Y A T P and mATP aP Pe a r t 0 be lower. Other growth conditions as mentioned above also affect the values of the growth constants. For example vitamin deprivation , or addition of uncouplers elevates the maintenance factor.
Stouthamer discossed the term maintenance of the biomass in a physiological way. Since the maintenance factor is also affected by energy spilling reactions caused by, for example, uncouplers, which he considers as not belonging to the maintenance of the organism, he regards the term maintenance factor incorrect in this sense. Mathematically, the maintenance terms in the expressions for substrate and ATP consumption (eqn.10 and 30) stands for nothing more or less than non-growth energy demand, whatever the biochemical processes are.
Apart from external factors influencing the growth parameters, there is some evidence that the growth constants are not constant for varying growth rates ~ . The cause for this variation is searched in the macromolecular composition of the biomass and viability, which are both reported to vary with the growth rate ~~ . The change in viability can up to now not fully account for the observed deviation , and the macromolecular composition seems to change linearly with the growth rate . Structured models *
-
16
-accounting for the change in biomass composition, offer in this regard a better description than the unstructured models discussed here (see chapter 3)
PRACTICAL CONSEQSNCES OF THE MODEL
In industrial fermentations for bulk chemical production, a high conversion efficiency of substrate into product is desired. The conversion efficiency
Substitution of eqns.10, 11 and 13 yields:
(Yn/Y„)( ) (34)
pathways is required for calculating the maximum attainable conversion efficiency. The efficiency is high when Ys x is low and mg is high5,,J. This result is obvious regarding eqn.5: all of the substrate which is not converted in biomass is converted in product.
The efficiency of product formation can be improved in several ways. First an organism can be chosen or selected which produces no or little
unwanted byproducts and which has favourable growth constants. Fermentation technology provides further tools for realization of favourable fermentation conditions as given by eqn.34, i.e. low growth rate and low Ys x and high ms factors. Low growth rates and high productivities are achieved in cell-retaining or cell-recycle systems. Yg x and mg can be influenced as discussed earlier by growing the organisms under conditions which are energy spilling from the viewpoint of the organisms. Examples are: Growth under high osmotic pressure J, growth at superoptimal temperatures27 (see ref. 14), or at high product concentrations27'28. Also non energy limited growth will elevate m and decrease Y
EXPERIMENTAL APPROACH
Estimation of the parameters of a model and testing the validity of a model requires in general a different approach. For the estimation of the growth constants, continuous culture (C.S.T.R., chemostat) experiments are most suitable. In chemostats, the process conditions are kept constant and when steady state is reached there will be no influence of adaptation or lag times on the experimental data. However, long-term adaptation might occur29. lesting the model for consistancy with regard to these constants is thus
preferably done in chemostats.
Testing a model in terms of kinetics, requires experiments with changing conditions to verifiate the descriptive ability which is highly dependent on the time constants . Las times or growth hysteresis are in general not included in simple models. For example, Um a x and K from Monod's equation (eqn.18) can be estimated from steady state continuous culture data, but these parameters have no effect on the actual growth rate since the growth rate will be equal to the dilution rate Ü. In batch culture however, these constants will influence the fate of concentration of substrate, biomass and
24 products .
Furthermore, during so called transition states, in which quick changes from say excess substrate during the exponential phase to substrate limitation during the early stationary phase of a batch culture occurs, most simple models appear to be inable to describe the process adequately. This feature is called growth rate hysteresis. An explanation for this inability lies in the fact, that growth and hence product formation is supposed to be ruled by one rate limiting reaction step. When the process conditions are changed, however, another reaction in the metabolic chain may become rate limiting and the kinetic characteristics of this reaction become expressed in the course of the fermentation. Mathematical models describing growth rate hysteresis are called bottleneck kinetics 'u'J .
Of course it depends on the application of the model and the magnitude of the discrepancy between model and experiment whether extensions and refinements of simple mathematical models are necessary. Extending a model and introducing new parameters obliges to estimate these parameters and test the extended model.
DATA EVALUATION.
Statistical evaluation of the experimental data and the estimated parameters can give some insight in the accuracy of the experimental data and moreover in the precision with which parameters can be estimated. Especially when the influence of environmental conditions on a parameter is investigated, it is important to know the confidence limits of the estimation in order to decide whether the value of the parameter has significantly changed.
Normal statistics puts several constraints on the experimental results: The data should be normally distributed, independent of eachother, as numerous as possible and systematic errors are not allowed. When statistics are used to discriminate between models, the magnitude of the random errors has to be known, which means that repeated experiments are required. For continuous culture experiments it means that idependent steady state results are only achieved after subsequent disturbations of the steady state. At low
growth rates this procedure will be very time consuming considering that
18
-steady state is reached after at least five volume changes.
Since in practice it is generally not possible to know wether all statistical requests are fulfilled, statistics should be handled with care. As pointed out by Oner and Erickson , both, the statistical method of estimation and the forms of the equations from which the parameters are estimated, influence che values of the estimates and the confidence limits. Their conclusion is, that for parameter estimation application of several equation forms and estimation methods is desirable. Their result also indicates, that a 95/o confidence limit of an estimate according to one approach can be a 907.
confidence limit according to another estimation method.
SYMBOLS
a stoechiometric constant (-) CJ concentration of compound i (g/L) $. flow rate of compound i (g/hr)
conversion rate of compound i (C-/nr) degree of reduction of compound i (-)
Y-L generalized degree of reduction of compound i (-) Yg x yield factor of biomass on substrate (g/g) YA T p yield factor of biomass on ATP (g/mol)
ms maintenance factor based on substrate requirement (g /g.hr) mATP maintenance factor based on ATP requirement (mmol/g.hr) D dilution rate (hr )
u specific growth rate (hr^1) umax maxim,ini specific growth rate (hr-1) Ujj bruto specific growth rate (hr-1) Mmaxb b r u C o maximum specific growth rate (hr-1) Ue endogenous biomass degradation (hr-1) qs specific substrate consumption (g/g.hr) Ks Monod constant (g/L) subscripts: substrate influent substrate biomass product(s) - 19
LITERATURE
1. J.A.Roels, Energetics and Kinetics in Biotechnology, Elsevier Biomedical Press, Amsterdam, Oxford, New York (1983)
2. L.E.Erickson, I.G.Minkevich, V.K.Eroshin, Biotechn.Bioeng. 213 (1978) 1595 3. J.A.Roels, Biotechn.Bioeng. 22_, (1980), 2457.
4. Roels J.A.,Kossen N.W.F. in: Progr. in Ind. Microbiol. (ed. M.J. Bull) 1_4 (1978) 95.
5. J.A.Roels, Ann N.York Acad. Sci. 369 (1981) 113.
6. A.E.Humphrey, P.K.Jefferis, G.I.A.M. meeting Sao Paulo 4. (1973) 767. 7. M.D.Oner, L.E.Erickson, Biotechn.Bioeng. 25 (1983) 631.
8. A.v.Baaien, I.M.L.Jö'bses, J.A.Roels in: Energie durch Biotechnologie (H. Dellweg ed.), Verlag Versuchslehranstalt Spir. Fabr. Ferm. Technol. Berlin (1982) 221.
9. A.A.Esener, J.A.Roels, N.W.F.Kossen, Biotechnol.Lett. 3_ (1981), 15. 10. D.Herbert in: Recent Progr. in Microbiol., 7th Symp.Int. Congr.
Microbiol. 6_, (G.Tunevall ed.) Almqvist Uppsala (1959) 381.
11. J.Monod, Recherches sur la Croissance Bacteriennes. Paris Masson (1942). 12. E.Ducleaux, Traite de Microbiol. l_ (1898) 208, Paris:Masson
13. S.J.Pirt.Proc.Roy.Soc. B163 (1965) 224-231. 14. A.H.Stouthamer, Microb.Blochem. 21 (1979) 1.
15. A.H.Stouthamer, C.W.Bettenhausen,Arch.Microbiol. J_13 (1977) 185. 16. Tempest D.W., Neyssel O.M., Ann.Rev.Microbiol. 38_ (1984) 459. 17. Lazdunski A., Belaich J.P., J.Gen.Microbiol. 70 (1972) 187.
18. N.S.Panikov, A.G.Dorofee, D.G.Zvyagintsev, Microbiologya 51_ (1983) 581. 19. M.Arbige, W.R.Chesbro, Arch.Microbiol.1^ (1982) 338.
20. S.J.Chapman,T.R.G.Gray, Soil Biol.Biochem. 13. (1981) 13. 21. W.Chesbro, T.Evans, R.Eifert,J.Bacteriol.139. (1979) 625.
22. D.W.Tempest, D.Herbert and P.J.Phipps, in: Micr. Physiol. Cont. Cult., Proc. 3rd Int. Symp. (eds. E.0. Powell, C.C.T. Evans, R.E.Strange and D.W.Tempest), Porton Down, Salisbury, Wiltshire, (1967) 240. 23. D.W.Tempest, J.W.Dicks in: Micr. Physiol. Cont. Cult., Proc. 3rd Int.
Symp. (eds. E.0. Powell, C.G.T. Evans, R.E.Strange and D.W.Tempest), Porton Down, Salisbury, Wiltshire, (1967) 140.
24. A.A.Esener, J.A.Roels, N.W.F.Kossen, Biotechn.Bioeng. 25_ (1983) 2803. 25. Harder A., Roels J.A., Adv.Biochem.Eng. 21_ (1982) 55.
26. A.A.Esener, N.W.F.Kossen, J.A.Roels, 2nd. Int. Symp. Waste Treatment and Utilization, Waterloo, Canada (1980).
27. J.Fieschko and A.E.Humphrey, Biotechn.Bioeng. 25 (1983) 1655.
28. K.J.Lee, M.L.Skotnicki, D.E.Tribe, P.L.Rogers, Biotechnol.Lett. 2. (1980) 339
29. M.G.Hofle, Appl.Env.Microbiol. 46 (1983) 1045.
30. E.O.Powell in: Cont.Cult.Microorg., Proc. 4th Symp. Prague 1968, (I.Malek et al. eds.) Acad. Press, N.Y. (1969) 275.
31. P.Agrawal, H.C.Lim, D.Ramkrishna, J.Chem.Techn.Biotechn. 33B (1983) 155.
20
-CHAPTER 3
MATHEMATICAL MODELLING OF GROWTH AND SUBSTRATE CONVERSION OF Zymomonas mobilis AT 30 AND 35°C.
I.M.L.Jobses, G.T.C.Egberts, A.van Baaien, J.A.Roels"
Laboratory of Bioengineering, Department of Chemistry and Chemical Engineering, Delft University of Technology, Delft, The Netherlands.
* Present address: Gist-Brocades N.V., Research and Development, Delft, The Netherlands.
Published in: Biotechnology and Bioengineering, Vol.27 (1985), pp 984-995
ABSTRACT
Zymomonas mobilis was grown in continuous cultures at 30 and 35°C. The specific substrate consumption rates at 35°C were higher compared to those at 30°C. An unstructured mathematical model based on the linear equation for substrate consumption provided a statistically adequate description for cultures grown at 35°C but not for cultures grown at 30°C. A structured two compartment model described growth and substrate consumption well at both temperatures. Some theoretical and practical aspects of the two-compartment model are discussed.
INTRODUCTION
Zymomonas mobilis has interesting characteristics for application in the large scale fermentation of glucose to ethanol. Especially its high specific rate of glucose consumption and its ability to grow strictly anaerobically1 would lead to a preference for the bacterium over the commonly used yeast species. Furthermore, Z .mobilis shows a higher conversion efficiency of glucose into ethanol, '3 which is the result of the low level of by-product formation* and the low yield of biomass on substrate.5,6 The physiological properties of the bacterium Zymomonas mobilis are extensively reviewed by Swings and de Ley.7
Mathematical models of fermentations are generally based on kinetic equations and balance equations. The unstructured model used here, is based on a kinetic equation for growth, Monod's equation8, and on a kinetic equation for substrate conversion; the linear equation for substrate consumption.11,12 For anaerobic fermentations, the rate of product formation can be
calculated from these equations and the elemental b a l a n c e s .5 , 6 , 9 , 1 0
The linear equation for substrate consumption was first postulated in 1898 by
-1 3
metabolism, as proposed by Herbert , is mathematically equivalent to the linear equation for substrate consumption.
The linear equation states that part of the substrate is consumed for maintenance of the existing biomass (growth rate independent), and that the remaining part is consumed for production of new biomass (growth rate dependent):
( i ) The independency of the maintenance energy requirement (ms) of the growth
rate (u) has been subject to much debate (see ref.14). Neyssel and Tempest concluded from their results of continuous cultures grown under different kinds of limitation (substrate, nitrogen source, phosphate and sulphate) that the maintenance energy requirement must be growth rate dependent in a linear way. Hellingwerf and Westerhoff et al. provided a model based on non-equilibrium thermodynamics, which is able to describe at least qualitatively the observed differences in the maintenance factors found for different nutrient limitations. Furthermore, this model also contains a maintenance factor which is linearly dependent on the growth rate. From the experimentalists point of view, however, a linearly growth rate dependent maintenance factor cannot be distinguished from a constant one on the basis of steady state continuous culture experiments alone.
Other literature reports that the maintenance substrate requirement is dependent on the growth rate in a non-linear way; the maintenance factor seems to decrease progressively with decreasing growth rate. To account for this feature, the linear equation for substrate consumption has to be modified or a structured model for growth and fermentation should be applied. '
High product specificity, in that glucose is almost quantitatively converted to ethanol and carbondioxide, make Z.mobilis a suitable organism for studying various mathematical models, in which mass and elemental balances play an important role. Also, the high maintenance energy requirement is very advantageous for modelling studies: it can be expected that the experimental determination is more accurate for high than for low maintenance energy requirements. Consequently, the effects of process conditions, such as the growth rate and temperature, on the maintenance energy demand can be detected more clearly.
THEORY
This section gives a description of the kinetic equations of the unstructured and structured models which were used in the interpretation of the results. In steady state continuous cultures, the net formation of any compound i will be equal to its washout:
rx = DC i ( 2)
When this equation is applied to the rate of biomass formation, it becomes apparent that the specific growth rate, U, equals the dilution rate, D.
The unstructured model, or maintenance model is based on the linear equation for substrate consumption, ' *■* eq. 1.
The specific substrate consumption rate q (q =rs/C ) is given by:
Is ■ d / W1 5 + ras (3)
The endogenuous metabolism mode]. i s mathematically equivalent to the maintenance model. The maintenance energy requirement of the biomass i s in t h i s model provided by an endogeneous biomass degradation:
rx - UmaxCsCx/(Ks+Cs) -"eCx W
and the substrate consumption i s given by:
rs = 0 / Ys x) rx ( 5)
In the endogenuous model, Um a x and Ks are contrary to Ys x numerically not equal to their counterparts in the maintenance model. By comparison, it follows that the maintenance model and the endogenuous metabolism model are equivalent, if the following expression holds:
»e " Ysxms (6)
The structured two-compartment model as introduced by Roels et a l .6 , 2 3"2 5 is schematically represented in figure 1. The model divides biomass in a K- and a G-compartment. Physiologically, it can be regarded as an extension of the endogenuous metabolism model (eqn.4). The maintenance energy requirements are explained in terms of a non-zero rate of G-compartment turnover. Generally, the K-compartment is interpreted to exist of RNA, carbohydrates and monomers of macromolecules. The G-compartment is identified with protein, DNA and lipids. The maintenance energy demand will increase with increasing turnover rates of G-compartment and decreasing values of the yield factors of K on G or G on K. The model is based on the following equations:
rs = u « s k > l W CsCx/ ( Ks +Cs)
For the net formation of K-compartraent:
'K " W V W < y " V G C
x +k
gG C
x(V)
( 3 )
atlc te.pAje.AejdaiU.on 0/ the tLoo-cxnupaAimeitt /nodal. Ihe
tiomaii exliti 0/ two compaJiJjnejiti, a and a g-compcvitment. /he K-flQlME. 7. Schemed.
compartment Li directly iyntheiized fiicm the iulttnate S. The Q-compaJltmenl Li synthesized piom and depolymeMZed to the
K-compayitment. Ton anaejioiic {j-Amentatloni, the metaiollc end-product formation (not ihown) can lie calculated piom the degiee. of. -leducUon ialance (njef. 5, 6, 9, 10).
The conversion of K- into G-compartment i s assumed to be proportional to the biomass K-content as the r e a c t a n t , and proportional to the G-content as the compartment containing the enzymes for the conversion. The conversion of G-i n t o the K-compartment G-i s regarded as a depolymerG-izatG-ion r e a c t G-i o n , whG-ich G-i s only proportional to the G-fration of the biomass. The y i e l d of K on G can be expected to be high, and i s in t h i s model put equal to 1.
The net formation of G-compartment i s :
(9)
The net formation of total biomass is:
rK (10)
Of course, the K- and G-compartment together make up the total biomass: K + G - 1. For steady state continuous culture growth the specific substrate consumption can be calculated by combination of eqns
results in eqn.11: 2, 6, 7 and 9 which (11)
is - ! /
Ys k f y
kk
+ kg - w
/ ( kk V -
kg
+ (2k ♦ kk - 2kg/Yk )/(kkYkg) D- i i \ -
1 ) , (W
B lNote that there are three seperate terms: the first is growth rate independent, the second is linear dependent of u (D) and the third is a nonlinear second order function of u .
By applying eqn.2 to the steady-state G-compartment biomass and substituting into eqn.9, the steady-state [(-fraction of the biomass is calculated to be:
K - (D + kg)/(kkYk g) (12)
MATERIALS AND METHODS
Zymomonas mobilis sLrain L.M.D. 29.34 f obtained from the Laboratory of Microbiology, Delft University of Technology) which is also known as strain ATCC 10988: was used. The strain was kept on agar slants containing 20 g/L glucose, 10 g/L yeast extract and 20 g/L CaCO^ at room temperature and was transferred every 1-2 months.
The cultivation medium consisted of glucose 50 g/1, KH^PO/ 1 g/1, NH4C1 2 g/1, MgS04.7H20 0.49 g/1, Ca-panthothenate 5 rag/1, FeS04.7H20 5 mg/L, ZnS0A.7II20 7.2 mg/L, CaCl2.2H20 1.5 mg/L, MnS04.H20 4.2 mg/L, CuS0A.5H20 2.0 mg/L, CoS04.7H20 1.6 mg/L, NaCl 50 mg/L, KC1 50 mg/L, concentrated HC1 0.25mL/L. Glucose was sterilized by autoclaving at 110°C. Salt solutions were sterilized by filtration. Cultures were grown in 2L fermenters with a working volume of 1-1.5 L, except the experiment at D 0.0077 hr"1 at 30°C which was performed in a 15 L fermenter with 8 L working volume. The medium of the inoculum consisted of 20 g/L glucose and 10 g/L yeast extract. The cultures were seeded with 60 mL inoculum and the culture pH was kept at pH 5 by an automatic pH controller using NaOH. Steady states in continuous cultures were assumed to be established after 5 times the residence time.During 5-10 residence times after this period, 4-8 samples of 40 mL were taken.
Ethanol and acetealdehyde were determined by GLC using a Porapack QS column. Acetealdehyde in the gasphase was determined by bubbling the gas leaving the fermentor through a solution containing a complex forming hydrazon . Acetic acid, formic acid, succinic acid, acetoin, lactate, formiate and glycerol were determined by HPLC on a Biorad HPx column. Glycerol and succinic acid were detected by refraction and the other components by UV-absorption.
Glucose was determined with a glucose oxidase kit (Boehringer) or by HPLC on a mu-Bondapack/carbohydrates column (Waters). C 02 production was determined volumetrically with a callibrated wet gas meter (Schlumberger, Dordrecht). Dissolved C 02 was calculated according to Stumm and Morgan28.
Dry weight of the biomass was determined by centrifugation or filtration. The biomass was washed twice with demineralized water and dried at 85°C until constant weight. Ash content was determined by heating dried biomass to 650°C until constant weight. C, H and N contents were determined with a CHN auto-analyzer (Perkin Elmer). Oxygen content was calculated from the
-difference between dry weight and the ash-,C-,H-, and N-weights.
RNA, total carbohydrate, protein and phosphorous content were determined in freeze dried biomass: the biomass was obtained by centrifugation of the total fermenter content at 4°C and washed twice with demineralized water. RNA was determined in an acid extract by the orcinol method . E.coli RNA (Calbiochem) was used as standard. Protein was determined by the biuret method with bovine serum albumine (Merck) as standard. Total carbohydrate
The methylene blue test for staining dead cells was performed as follows: a sample of the culture was diluted with fresh medium water and suspended in 0.01% w/v methylene blue and after 10 minutes incubation examined by phase contrast or light microscopy. Cell division ability was measured by the slide culture technique : Slides contained 50 g/L glucose, 10 g/L yeast extract and lOg/L agar and were incubated anaerobically (under Ni gas) for 24-48 ours at 30°C. Since Z.mobilis often occurs in pairs, only groups of more than 2 bacteria and the increment of the percentage of pairs were regarded as viable. For the methylene blue test and slide test duplicate counts of 300 subjects were made. Polyphosphate staining was employed according to Laybourn .
For the calculation of the carbon and generalized degree of reduction balances, the concentrations of the compounds were expressed in C-equivalents/L and the CO2 gas flow in Cequivalents/hr.
carbon balance
C + * Cx + * CC 0 2 + C02-gas flow
CC
S, -
c
s)
The generalized degree of reduction T of a compound was defined according to Roels36:
Y CaHb0cNd = (a YC + b YH + c Y0 + d YN)/a YC = 4, YH = 1, Y0 - - 2 , YN - - 3 .
The degree of reduction balance was calculated as follows:
gree of reduction balance = — y,!100 ^
TABLE 1■ CONTINUOUS CULTURE DATA OP Z.iiQBILIS AT 30°C AND 35°C. q AND Cx ARE BASED ON ASH-FREE BIOMASS. FIGURES BETWEEN PARENTHESES REPRESENT 95 % CONFIDENCE INTERVALS. THE DECREE OP REDUCTION, 7, IS DEFINED ACCORDING TO REF. 36: YgiUcose " 4' Ybiomass r 4 •2 • ''ethanol " 5 A H D •rC02 » 0. MEAN VALUES FOR THE BALANCES ARE: AT 30°C, THE C-BALANCE IS 92.44 (2.7%], THE Y-BALANCE IS 9 3.4% (2.81), -f-GhP IS 4.5 (0.6). At 35°, C-BALAHCE
0.001) (0.36) n.d.;not detectable (<0.01g/L).
-RESULTS
Two series of continuous cultures were run at 30°C and 35°C at dilution rates varying from D=0.008 hr to D=0.24 hr~ . The results are shown in table 1. In all runs, the influent glucose (50 g/L) was converted quantitatively as it was not detectable in the effluent (less than 0.01 g/L), except for the run at D=0.24 hr , 35°C, whore the mean effluent glucose concentration was 1.8 g/L. Biomass and ethanol yields are shown in figure 2. The biomass yield at 30°C is for all dilution rates except D=0.02 hr~ higher than at 35°C, the difference being largest at low and high dilution rates. Note that the yield is strongly dependent on the growth rate as a result of high maintenance energy requirements. The efficiency of glucose conversion into ethanol was high at all growth rates and showed a slight downward trend with increasing growth rate as can be expected on the basis of the unstructured model ' .
0.1 DlVhr)
• x • .
D(Vhr)
TlQUTtt 2. {j-Uld o/ Liomass and ethanol on glucose in continuous cultures at 30 and 35°. Cuttun.es wesie tun at pH.5. Ike influent glucose. (50 g/L) was connected quantilatluely, exce.pt at D=0,24 at 35°C. Othen. data asm shown in table. 1, 7 he mean p/ioduct yield was £ =0.46 g/g (95% confidence, limits: 0.4-5-0.47). 7he sywlols show (A) yield o£ ilomass, (B) yield o/ etjianol, (x)
30°C, and (•} 35°C.
- 28
The mean e for all data was e =0.46 g ethanol/g glucose which is 90% of the theoretical maximum (0.51 g/g). Since the carbon and degree of reduction balances (see the materials and Methods section) calculated from the glucose, ethanol, biomass and C02 flows closed for only 92%, we searched for several possible by-products. The results are shown in table 2. The total amount of by products accounted for 2-3% of the total carbon, which is comparable with results of Amin and coworkers . We found, however, less glycerol and acetoin, which might be correlated with the ethanol level in the culture fluid; in our experiments ethanol concentrations were about 23 g/L in contrast to 70 g/L in their experiments.
TABLE 2. By-product formation in continuous cultures at 30 and 35°C. Influent glucose concentration was 50 g/L. Other data are reported in table 1. For determinations see Materials and Methods section. Due to the low
concentrations of the compounds, the figures only represent a global estimate. The generalized degree of reduction y is defined according to ref. 36. temperature Dilution rate 1/hr acetate (g/L) lactate succinate acetoin Propionate " formiate glycerol acetealdehyde " 0.01 0.5 0.05 0.06 < 0.05' < 0.05 < 0.05 < 0.05 < 0.1 30°C 0.13 0.1 0.05 0.14 0.24 0.4 0.04 0.24 0.01 0.4 0.4 0.05 35°C 0.13 0.25 0.1 0.14 0.24 0.5 0.09 0.28 Y 4.0 4.0 3.5 5.0 4.7 2.0 4.67 5.0 the values for the following compounds are equal for all dilution rates and both temperatures.
From the by-products, succinate increases with increasing growth rate or biomass concentration, whereas lactate is relatively high at low growth rates. Acetealdehyde accounted in the fermentation broth for only 0.3% and in the gasphase for only 0.004% of the total in-going carbon. The latter value seems very low, considering that the boiling point of acetealdehyde is 21°C. However, theoretically the acetealdehyde content in the gasphase would amount to 0.001% of the carbon balance, when calculated from its concentration in the liquid phase, its vapor pressure and its activity coefficient in water37. When the by-products are taken into account, the carbon and degree of reduction balances close for about 95% (tables 1 and 2 ) , leaving a gap of 5% for some unknown product(s) with a generalized degree of reduction of 4-4.5. There are many biological compounds in this range of generalized degree of reduction, including carbohydrates. From this class of compounds, levan and sorbltol are reported as by-products in sucrose fermentations38.
The growth constants Ys x and ms of the unstructured model can be estimated by plotting the specific glucose consumption rate q versus the specific growth rate U, which equals D in continuous cultures. According to eqn.2 this should yield a straight line with slope l/Tsx and intercept m , From the experimental results, shown in figure 3, it is obvious, that the relationship between q and Ü at 30°C is not linear. The datapoints at D=-0»008 and D O . 0 2 hr~ are statistical outliers from the linear regression line on all datapoints . Allthough a slight deflection of q versus Ü at 35°C can be noticed, a linear relationship between these variables can not be rejected statistically.
i+l
TLQdRt 3. Q, v&. D plot 0/ continuous cwttun&A gioim at 35 and
30UC. Data one shown hiith the.il 95%u confidence. Limits
calculated fofi D and a 4e.peytate.Jly. /he. tejnpeiatuies wei€ (A) 30°C and (B) 35°C.
In spite of the fact that the unstructured model does not provide an adequate description of the experimental results, at least at 30°C, it was applied to the nearly linear part of the curve for comparison with literature. Linear regression was applied to the data at 30°C and 35°C, both between D=0.02 and D=0.0l4hr_l. In figure 3 the data points are shown with their 957.
confidence limits in qs and D seperately. Since these variances are obtained from replicate samples (see the Matrials and Methods section) of one particular steady state, they represent the minimum real variance. As the
variances differ mutually, weighted linear regression was used. After
transformation of the variance of the "independent" variable D to the "dependent" variable qs, standard linear regression weighted to the variance in qs was applied . This method yielded essentially the same results as methods in which the variances of both variables were taken in account seperately ' . Consequently, the joint confidence regions of the estimated parameters were also calculated by standard methodsJ The result is show in figure A. The estimated parameters with their seperate 95% confidence interval are:
30
-TABLE 3. Comparison of Y and m values with the literature The presented figures are based on ash-containing dry weights. temperature medium ethanol
g/L
V
8/8 g/g-hr complex"
"
minimal"
"
45 40 50 27 23 23 0.06 -0.03 0.01 0.035 0.03 2.9 1.6 1.6 2.1 2.7 2.8 3 66 69 45 this work this work * complex refers to a medium containing yeast extract, minimalrefers to a medium without yeast extract.
025 1 2 3 4
m . ( % . h r ] _
TICjWL /,. Estimation op" the pajiametens IJ and m and theisi joint confidence, legion ty ucighted lineoji negiession: In (A), lineayi legiession weighted to the .summed variance in D and q has applied to the datapoints letueen U - 0.02 and 0.14 hi'1 Ion toth tempesi.atunes. I he estimates) paiameteis a/ie:
(X) at 35°C: m - 3.06 q/g.hn (95% conJUden.ee. limit of 2.24-3.88)
1'ViK = 40.0 g/g (95% confidence. IJmit of. 29.7-50.3)
I») at 30 c - m = 2.98 g/g.hn (95% confidence limit of 2.27-3.69)
1'lh,* = 3!-6 9/g (95% confidence, limit of 25.3-38.0) in (ll), the joint, confidence legion of m and WJA„ asie shown: fon.
