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Escherichia coil. Rhodotorula rubra. Spirillum sp. Unidentified bacterium. NCIB 11083. NCIB 11083. NCIB 9399. B6/2, obligate methylotroph. DT26, facultative.
FEMS MicrobiologyReviews 46 (1987) 419-432 Published by Elsevier

419

FER 00081

Determination of the Monod substrate saturation constant for microbial growth J.D. Owens and J.D. Legan Department of Food Technology, University of Reading, Whiteknights, Reading RG6 2AP, ILK.

Received 3 February 1987 Revised received 5 May 1987 Accepted 27 May 1987 Key words: Growth; Saturation constant; Affinity constant

1. S U M M A R Y Methods used to determine the Monod substrate saturation constant for microbial growth are surveyed. The preferred and most accurate method is to assay the concentrations of growth rate-limiting nutrients in steady-state continuous cultures. But, this is not always possible due to the lack of sufficiently sensitive assay methods or due to high nutrient fluxes in rapidly growing cultures. It is suggested that an acceptable and simple alternative method for aerobic microorganisms is to measure initial oxygen uptake rates during growth in the presence of different initial concentrations of growth rate-limiting nutrient. It is important in this method that the microbial cells are taken from rapidly growing cultures and are suspended in a medium permitting growth. 2. I N T R O D U C T I O N Monod [1] introduced the use of an empirical equation to describe the relationship between Correspondence to: J.D. Owen, Department of Food Technology, University of Reading, Whiteknigbts, Reading RG6 2AP, U.K.

bacterial growth rate and the concentration of a single growth rate-limiting nutrient of the form (Fig. 1): tZ = l~mS/( Ks + s )

where # is the specific growth rate (h-~), #m is a constant, the maximum specific growth rate; K~ is a constant, called the substrate saturation constant or substrate affinity constant (g. 1-1 or mol • l-a), and equals the substrate concentration that supports a growth rate one half of the maximum; and s is the concentration (g. 1 i or mol. 1-1) of the growth rate-limiting nutrient. All other nutrients are presumed to be present in excess of the requirements for growth and, hence, their concentrations do not limit the growth rate. Experimental evidence suggests that the equation does not saturate fast enough at high nutrient concentrations and a variety of alternative equations have been suggested [2,3]. Nevertheless, the Monod equation has remained most widely used in microbiology because of its simplicity and its similarity to the familiar Michaelis-Menten equation for enzyme kinetics. In order to make use of the equation to predict microbial growth rates it is first necessary to determine the values of the two constants, tt m and

0168-6445/87/$03.50 © 1987 Federation of European Microbiological Societies

420 1.0 --

•/•Bacterium

A= Bacterium A

0.8

Bacterium B oJ

"~ 0.6 J~

o 0.4

Qu~

0.2

0

(a)

I 0 100

~

I

I

500

1000

Nutrient c o n c e n t r a t i o n

0

(b) I

I

20

40

(pmol,I-1)

Fig. 1. Relationship between specific growth rate and concentration of growth rate-limiting nutrient for two bacteria having different growth parameters. (Bacterium A: ~t,1, 1.0h 1; Ks , 10 ~ M and Bacterium B: /*m, 0 . 7 ' h 1; Ks ' 2 #M). Growth rates were calculated using the Monod equation. (a) shows the relationship over a wide range of nutrient concentrations and the rapid saturation that occurs at low concentrations; (b) shows crossing of the curves at low nutrient concentrations.

K~, the m a x i m u m specific growth rate and the substrate saturation constant. M a x i m u m specific growth rates are relatively easily determined under conditions of nutrient excess either in batch cultures or by the wash-out from continuous culture method [4,5]. But to determine K~ is far more difficult, largely due to the difficulties of estimating the low substrate concentrations at which growth rates become substrate-limited. This paper considers the approaches available for determining K S values and their applicability and usefulness. Especial attention is given to the respirometric method of Harrison [6].

3. I M P O R T A N C E OF K s Knowledge of K s values is required for modelling microbial cultures, and especially continuous cultures where K~ largely determines the steadystate concentration of unused growth rate-limiting nutrient. If this nutrient is the carbon and energy source, then the value of K~ is an important factor

in the efficiency of conversion of substrate to biomass [6]. K~ values also play an important role in determining the outcome of microbial competitions. Two main eco-physiological strategies can be recognised among microbes. These two microbial types are presently called copiotrophs and oligotrophs [7]. Copiotrophs are conceived as those organisms adapted to an opportunistic life-style, growing rapidly in the presence of occasional high nutrient concentrations. They are characterised by a high maximum growth rate and a high substrate saturation constant. Oligotrophs are considered as organisms adapted to life under continuous nutrient limitation and are characterised by a low maximum growth rate and a low substrate saturation constant. C o m m o n l y this leads to the curves of growth rate versus concentration for a particular nutrient crossing, as illustrated in Fig. 1. It is evident that at high nutrient concentrations, above the cross-over point on the curves, the high/*m-high K~ organism will grow faster than the low /*m-lOw K~ organism and will come to dominate mixed populations under constant conditions. At low nutrient concentrations the opposite applies and the low /*m-low K~ organism will predominate [8-10].

4. D E F I N I T I O N OF SUBSTRATE S A T U R A TION CONSTANT

If the specific growth rate is set equal to half the maximum specific growth rate in the Monod equation, the substrate saturation constant then equals the concentration of growth rate-limiting nutrient. Hence, the substrate saturation constant may be defined as the concentration of growth rate-limiting nutrient that supports half the maxim u m specific growth rate. Values of K~ reported for different organisms and nutrients are given in Table 1. It is noteworthy that K~ values have been relatively infrequently determined, and that mostreported values lack information on their precision or likely accuracy. Growth involves a great complex of reactions, including uptake processes and the subsequent

Table 1 Values of M o n o d s u b s t r a t e s a t u r a t i o n c o n s t a n t s for g r o w t h of m i c r o o r g a n i s m s Nutrient

Microorganism Species

Glucose

A chromobacter sp. Cytophaga johnsonae Escherichia coli

Pseudomonas sp. Pseudomonas sp. Streptococcus sanguis Streptococcus mutans Glucose

Vibrio sp. Unidentified bacterium Unidentified bacterium Saccharomyces cerevisiae Aspergillus nidulans Mucor hiemalis

Glycerol

Maltose

Enterobacter cloacae Candida utilis Candida utilis Escherichia coli

Strain/properties

208 C21 A t d i l u t i o n rate: 0.03- h 1 0 . 1 5 . h -1 M L 3 0 G , selected from ML30 (NCIB1000) b y long culture in glucose m i n i m a l medium M L 3 0 8 ( N C I B 9553) NB4, m e t h a z o t r o p h

M e t h o d of m e a s u r e m e n t

Refer. ences

30

Direct assay of s in c h e m o s t a t

[111

8.6 42 0.38

Direct assay of s in c h e m o s t a t Direct assay of s in c h e m o s t a t Initial /* in b a t c h culture

[12]

Substrate saturation constant (ttM)

[12] [131

Initial bt in b a t c h culture Direct assay of s in c h e m o s t a t Respirometry Direct assay of s in c h e m o s t a t

[14]

201

13 5.9_+1.6 ~ 6.1_+3.0 a 105

10558

110

I n d i r e c t assay of s in c h e m o s t a t

[161

2170

Indirect assay of s in c h e m o s t a t

[16]

Direct assay of s in c h e m o s t a t

[11]

2.5 _+0.35 a 2.7

Respirometry Direct assay of s in c h e m o s t a t

I151

1.2

Direct assay of s in c h e m o s t a t

[17]

Direct assay of s in c h e m o s t a t

[18]

R a d i a l g r o w t h rate R a d i a l g r o w t h rate

[19] [19]

N C Y C 321

135 49 50

Max. o u t p u t in c h e m o s t a t I n d i r e c t assay of s in c h e m o s t a t Direct assay of s in c h e m o s t a t

[20] [211 [39]

R V (lac )

25

Indirect assay of s in c h e m o s t a t

[22]

6715-15 2O4 DT26, facultative methylotroph Minimal medium M i n i m a l 4- a r g i n i n e medium N C Y C 229

55

139 28 24

N C T C 8197 ( N C I B 8271)

[151 [151 [111

[171

321 = RV, streptomycin resist, m u t a n t 322 = RV + lac 323 = 321 + lac 372 = 321 + constitutive lac o p e r o n

19 20 20_+11 a

Indirect assay of s in c h e m o s t a t Indirect assay of s in c h e m o s t a t I n d i r e c t assay of s in c h e m o s t a t

[221 [22] [221

22.5 + 7.0 a

I n d i r e c t assay of s in c h e m o s t a t

[22]

Lactose

Escherichia coli

322 323 372

59+0.9 a 58.5+0.9 a 34_+1.5 a

I n d i r e c t assay of s in c h e m o s t a t Indirect assay of s in c h e m o s t a t Indirect assay of s in c h e m o s t a t

[22] [22] [22]

Lactate

Achromobacter sp. Pseudomonas sp. Pseudomonas sp. Spirillum sp. Spirillum sp. Vibrio sp.

208 201 D S M 1110 101 D S M 1109 204

10 90 91 30 23 8

Direct Direct Direct Direct Direct Direct

[11] [111 [231 [111 [23]

assay assay assay assay assay assay

of of of of of of

s s s s s s

in in in in in in

chemostat chemostat chemostat chemostat chemostat chemostat

[111

Table 1 (continued) Nutrient

Methane

Methanol

Methylamine

Tryptophan

Strain/properties

Substrate saturation constant (/LM)

Method of measurement

Species

Microorganism

References

Methylococcus sp. Unidentified bacterium Unidentified bacterium

NCIB 11083

32

Respirometry

[24]

26

Respirometry

[6]

Hyphomicrobium sp. Methylococcus sp. Methylobacterium extorquens Unidentified bacterium Unidentified bacterium

Indirect assay of s in chemostat

[251

NCIB 11083

8.3 42

Respirometry Respirometry

[26] [24]

NCIB 9399

2O

Respirometry

[61

5O

Respirometry

[61

0.45

Unidentified bacterium Unidentified bacterium

B6/2, obligate methylotroph DT26, facultative methylotroph

Escherichia coli

B / l , tryptophan auxotroph B / I / f , mutant of B / 1 TS-701, tryptophan auxotroph from ML30G

Escherichia coli

Formaldehyde

1.7

Direct assay of s in chemostat

[25]

Respirometry

[15]

5.1+_1.2 ~

Respirometry

[151

0.005

Initial bt in batch culture

[271

0.001 b

Initial /~ in batch culture

[271

0.034

Initial p~ in batch culture

[13]

36+4.3 a

Methylobacterium extorquens

NCIB 9399

100

Respirometry

[61

Formate

M. extorquens

NCIB 9399

230

Respirometry

[61

Arginine

geurospora crassa

Arginine auxotroph

Thiamine

Crytococcus albidus

Oxygen

Candida utilis Candida utilis Candida utilis Sphaerotilus natans

Phosphate

Radial growth rate

[191

4.7-10 7

Indirect assay of s in chemostat

[281

1.3 b 2.6 14

Direct assay of s in chemostat Direct assay of s in chemostat Indirect assay of s in chemostat

[29] [39] [211

1.0

by washout from chemostat

[30]

0.44

~t by washout from chemostat

[30]

2.3

/~ by washout from chemostat

[3o1

1-3

[31] [32]

U nidentified bacterium

From activated sludge From activated sludge From activated sludge

Escherichia coli

A324

Klebsiella aerogenes

N C T C 418

23

Direct assay of s and bt in batch culture by wash-out from chemostat

Escherichia coil Rhodotorula rubra Spirillum sp. Unidentified bacterium

ML30G

17 0.012 0.066

Initial tL in batch culture Direct assay of s in chemostat Direct assay of s in chemostat

[13] [33] [551

0.027

Direct assay of s in chemostat

[551

Sphaerotilus sp.

Magnesium

N C Y C 321

2.8

423 Table 1 (continued) Nutrient

Microorganism Strain/properties

Substrate saturation constant (/~M)

Method of measurement

Species

References

Potassium

Klebsiella aerogenes

NCTC 418

10

/1 by wash-out from chemostat

[32]

Sulphate

Klebsiella aerogenes

NCTC 418

/t by wash-out from chemostat

[32]

2.8

a Standard deviation of mean. b Estimate from figure.

metabolism of nutrients involving many enzymic reactions. Hence, it is not generally possible to relate the substrate saturation constant, K S, to the Michaelis constant, K m , for any specific step or steps in the utilisation of a compound [34,35]. In particular, reported values of K s differ from those of the Michaelis constant for uptake of the same nutrient [36,37]. Thus, K S is analogous to what biochemists refer to as ' t h e apparent substrate saturation constant' for enzymic processes which are known to involve more than one enzyme and where it is not possible to relate measurements to the kinetic parameters of a specific enzymic reaction. True Michaelis-Menten substrate saturation constants refer, strictly, to enzymic reactions involving single enzyme species and even then only under restricted circumstances can K m be related to specific kinetic parameters [38]. It is a general assumption that K S for growth with a specific nutrient is a constant for a particular organism. But, it is not u n c o m m o n for microorganisms to have two separate uptake systems for a single nutrient, one of which predominates at high concentrations of the external nutrient and the other at low concentrations [36,40]. In such cases two distinct K S values may be exhibited for the one nutrient [37]. Law and Button [17] reported apparently different values for K S on glucose for a marine coryneform bacterium, depending on whether it was grown in mineral salts plus glucose medium or in the same medium supplemented with amino acids, and Wirsen and Jannasch [41,10] reported changes in K S with growth temperature. It is not clear why these changes occurred but they may be a consequence of the fact that growth rate is

influenced by a multiplicity of cellular processes [35], rather than by a single rate-determining step.

5. PRINCIPLES OF D E T E R M I N I N G STRATE S A T U R A T I O N C O N S T A N T S

SUB-

The Monod equation can be rearranged to give: K s =S(~

m-

~)/~

Thus the two basic approaches for determining K S are to measure growth rates in the presence of known concentrations of growth rate-limiting nutrient or to measure nutrient concentrations at known growth rates. The resultant data are then analysed to obtain a value for K S. Generally, linearised forms of the Monod equation are used, though it is also possible to fit data to the hyperbolic curve with computer techniques [2]. Commonly used linear equations are [42,43]: Lineweaver-Burke: 1//~ = 1//.t m + Ks/liras. A plot of 1 / > against 1 / s is linear with intercepts 1 / ~ m and - 1 / K S. Eadie-Hofstee: l~/S = I ~ m / K ~ - I ~ / K S. A plot of t~ against I z / s is linear with slope - 1 / K S and intercept is m / K s. Langmuir: s / l ~ = K J l ~ m + S/l~m. A plot of s against s / # is linear with intercept - K S. The Lineweaver-Burke plot, although widely used, is the least satisfactory of these three plots since the data points are compressed at one end (Fig. 2) and it yields a less precise determination of K s than alternative methods [42]. With the E a d i e - H o f s t e e plot the points are evenly distributed and it allows a very wide range of concentrations, from near zero to infinity, to be fitted on a

424 120

12

'~

lO

,"

8

100

9 ~

80

~'-

0

c

060

._o E 4

~2 ~ 40 8

2

c

o

_l/Ks

0

-0.1

I 0.2

I 0.4

I 0.6

1/nutrient

concentration

I 0.8

l 1.0

(I-pmo1-1)

Fig. 2. Determination of Monod substrate saturation constant for growth, K~, by the Lineweaver-Burke linearised plot of the M o n o d equation. Data is that for Bacterium A in Fig. 1. /Lm is m a x i m u m specific growth rate.

single plot (Fig. 3). Of these three equations the Langmuir plot (Fig. 4) is likely to yield the most reliable estimate of K S [42]. However, all three of these linearised equations are open to statistical objections to the ways in which the data are treated [43] and the best method of analysing /~ versus s data would currently appear to be the

F 001

-...

"R ,o

--... /

0

0

Specific

I 0.02 growth

I 0.04

rate/nutrient

I 0.06 concentration

I 0.08

"~J 0.10

(I.pmol-1.h-1)

Fig. 3. Determination of Monod substrate saturation constant for growth, K s, by the Eadie-Hofstee linearised plot of the Monod equation. Data is that for Bacterium A in Fig. 1. /~m is m a x i m u m specific growth rate.

20

-10

o

I 20 Nutrient

I I I 40 60 80 concentration (pmol.1-1)

I 1 O0

Fig. 4. Determination of Monod substrate saturation constant for growth, Ks, by the Langmuir linearised plot of the Monod equation. Data is that for Bacterium A in Fig. 1.

direct linear plot of Eisenthal and Cornish-Bowden [43,44]. Rearrangement of the Monod equation gives: I~m = i~ + K s l ~ / S

Thus, for any observation (/~, si), it is possible to plot ~m against K s as a straight line of slope i ~ / s , intercept -s~ on the K s axis and intercept /~ on the /~m axis [44]. The technique consists of plotting, for each observation (/~i, si), - s on the x axis and /~ on the y axis and drawing a line through the two points. When this is done for all observations the lines intersect at a common point whose co-ordinates provide the values of K S and /1,1 (Fig. 5). In practice, experimental error will ensure that there will usually be no unique intersection point for all the lines and the best estimate is taken as the median value for a series of intersections. Apart from being very simple to do, the method provides more information about the uncertainty in the values of K~ and /~m than other plots. Poor observations and errors in determinations are immediately demonstrated whereas with the other plots they may be quite inapparent. It is claimed [43] that this method is, in most cases. more reliable than other methods of analysing enzyme kinetic data and the same might be ex-

425

v= ~o~'0.814

-100

-80

-60

-40

-20

/ :

0

20

Substrate saturation constant (pmol,U 1)

Fig. 5. D e t e r m i n a t i o n of M o n o d s u b s t r a t e s a t u r a t i o n c o n s t a n t for growth, Ks, by the Eisenthal and C o r n i s h - B o w d e n direct l i n e a r plot m e t h o d [44]. Each line represents one o b s e r v a t i o n of s a n d /~, p l o t t e d as i n t e r c e p t - s on the K S axis a n d intercept /z on the /~m axis. The point of intersection of the lines gives the c o o r d i n a t e s for K~ and /~m"

pected for its use with microbial growth rate versus nutrient concentration data.

6. D E T E R M I N A T I O N OF K s F R O M D I R E C T MEASUREMENTS OF NUTRIENT CONCENTRATIONS IN C H E M O S T A T CULTURES In chemostat culture at steady state the specific growth rate equals the culture dilution rate. Hence, if the concentration of growth rate-limiting nutrient is measured, K~ can be calculated from:

K~=s(l~m- D)/D where D is the culture dilution rate. Determinations are made over a range of different dilution rates and the data plotted by one of the methods discussed previously. Microbes growing under steady-state conditions in continuous culture are in a well defined and readily reproduced physiological state, so this is the preferred method for determining substrate saturation constants. The ideal would be to measure the concentration of specific nutrients in situ but this is presently only possible for oxygen, using an oxygen electrode

[29], for oxygen, carbon dioxide, methane, hydrogen sulphide, hydrogen and other dissolved gases by membrane inlet mass spectrometry [45], and possibly some inorganic ions with ion-selective electrodes. Hence, it is normally necessary to remove samples from cultures for analysis, but the methodology suffers from two practical problems that may render it useless or inaccurate. The first of these is that measuring the very low nutrient concentrations is difficult and in many cases current analytical techniques are not sufficiently sensitive. The other practical difficulty is to halt microbial metabolism quickly enough so that the concentration of growth rate-limiting nutrient in culture samples remains representative of that in the culture. Often this has been attempted by rapid filtration to obtain a cell-free culture filtrate [15,17,23,25,55]. Reported times to obtain culture filtrates are 2 - 5 ml in less than 5 s [25], 2 ml in less than 10 s [15], 4 ml in 30-60 s [23], 3 ml in less than 60 s [17] and 50 ml in less than 60 s [55]. However, this approach is only practical with relatively low density and slowly growin~ cultures. For example, in a glucose-limited continuous culture containing 0.01 g dry biomass - 1-1 and growing at a dilution rate of 0 , 1 - h 1 the flux of glucose would be 3 n m o l . 1 - 1 - s - I (assuming a yield coefficient of 90 g dry biomass • m o l t ) . In a culture containing 10 g dry biomass. 1-1 growing at the same growth rate the glucose flux would be 3 /~mol-1-1- s 1. Glucose consumption in 5 s in the first culture would be up to 15 n m o l . 1 i and in the second, up to 15 /~mol.1-1. Thus, if the concentration of glucose in the cultures was in the range 1-10/~mol - 1-1 (i.e. of the same order as K s for many bacteria, Table 1) an acceptable representative sample could readily be obtained from the more dilute culture but certainly not from the denser one. With fast-growing dense cultures the filtration method becomes quite unusable because the high nutrient fluxes make it impossible to obtain a representative medium sample, The need for sensitive in situ sensors is obvious. Apart from the need for rapid filtration, it may also be advisable to treat filtrates to preclude changes due to the activities of extracellular en-

426

zymes that might possibly be present. Most authors do not mention what, if any, precautions they took, but Law and Button [17] acidified their filtrates at the time of collection, heated them to 95 o C, and then stored them frozen until analysed. In principle, it is possible to quickly inhibit metabolism in culture samples with metabolic inhibitors. This approach does not seem to have been used to determined residual substrate concentrations in chemostat cultures, presumably due to fears of materials leaking from the inhibited cells. Nevertheless, its use, possibly in combination with rapid filtration, would be worth investigating in cases where other methods are not available.

7. D E T E R M I N A T I O N OF K~ F R O M I N D I RECT ESTIMATES OF N U T R I E N T CONC E N T R A T I O N S IN C H E M O S T A T C U L TURES To avoid the difficulties inherent in the direct measurement of substrate concentrations in chemostat cultures, a number of indirect methods for estimating substrate levels have been devised. In steady-state continuous cultures, biomass concentration, x, is given by: x = r(Sr

Thus: x l = ( s t 1 - s)l X 2 =

-

s)Y

Since: Sr2 >> S, Y = x 2 / S r 2 And: x e S r l / S r 2 = x 1 - s Y The yield coefficient, I1, was measured in batch cultures and s calculated using the above equations. No correction for maintenance energy requirements was made on Y, but for relatively fast growing cultures the error introduced is small. An extension of this approach is to measure x for different values of Sr at a constant dilution rate (when s is also constant), then a plot of x versus S r is a straight line of gradient Y and intercept s on the substrate axis (Fig. 6). If such plots are repeated at different dilution rates estimates of s versus D can be obtained and K s determined as before. To avoid excessive extrapolation of the curves and, hence, inaccuracies in the estimations of s, it is necessary to use very low reservoir concentrations of growth rate-limiting nutrient and consequent low-culture densities. The method was used by Button and Garver [21] and Button [28] but is very laborious. Lamb and Garver [25] described an indirect

- s)

where Y is the yield coefficient, S~ is the concentration of growth rate-limiting nutrient in the reservoir, and s is the concentration of growth rate-limiting nutrient in the culture. Hence, s can be estimated if the other parameters are known. The method requires the use of low reservoir concentrations of growth-limiting nutrient (i.e. of the same order as Ks) and sensitive methods for determining the consequent low concentrations of biomass [47]. Dykhuizen and Davies [22] obtained a more precise estimate of s by comparing the cell population in a chemostat fed a low concentration of growth-limiting nutrient (Srl , approximately equal to K~) with the cell population in a chemostat operated at the same dilution rate but fed a higher concentration of growth-limiting nutrient (S~2).

(Sr2

20

2 8 '2

t~ -=_12 co '~

55 ~

8

~ E

m

0

40 80 120 160 Nutrient concentration (pmol-1-1)

200

Fig. 6. Estimation of concentration, s, of growth rate-limiting nutrient in steady-state chemostat cultures from plots of biomass concentration versus concentration of growth rate-limiting nutrient in the reservoir. Data illustrated is for Bacterium A (Fig. 1) with tLm, 1 . 0 ' h - l ; Ks, 10 /tmol-l-1; and yield coefficient, 90 g dry biomass.(mol nutrient) 1

427

technique for estimating the concentration of gaseous nutrients in chemostat cultures. They grew the organism in continuous culture at a constant dilution rate and supplied it with gas mixtures containing different amounts of methane. The concentration of methane in the culture medium was estimated as follows: The transient state mass balance equation for methane in the culture is: a

/d, =

-

) -

Ds

-

where KL~ is the overall volumetric mass transfer coefficient for methane (h 1), Sg is the concentration of dissolved methane in equilibrium with the gas phase ( g . l - l ) , s is the concentration of methane in the culture ( g - l - l ) , x is the concentration of biomass (g. l - l ) , and Y is the yield coefficient (g. g - i). At steady state, d s / d t is zero and /L equals D:

x = ( Y K t . J D ) S g - Y[(1 + K L a / D ) s ] and a plot of x versus S~ yields a straight line of slope Y K L J D and intercept on the Sg axis of (1 +

D/KLa)S.

Y was measured in batch cultures and Sg was calculated from

Sg = M P H where M is the percentage methane in the gas phase, P is the total pressure in the fermenter corrected for water vapour, and H is Henry's law constant for methane. KL~ could then be calculated from the slope, Y K L a / D of the graph. In these methane-using cultures, as will usually be the case, D/KLa is much less than unity and the intercept on the Sg axis equals s. K s is then obtained from K~ = s(# m -

D)/D.

This method would appear to offer an attractive approach to determining substrate saturation constants of gaseous nutrients, though it might be criticised for the use of a yield coefficient determined in batch culture. At growth rates substantially less than the maximum, cell yields are liable to be reduced due to the requirements for maintenance [4].

8. D E T E R M I N A T I O N OF K s F R O M I N I T I A L G R O W T H RATES I N B A T C H C U L T U R E S WITH KNOWN NUTRIENT CONCENTRATIONS An alternative approach to controlling the growth rate and attempting to measure nutrient concentration is to provide batch cultures with known, low concentrations of growth rate-limiting nutrient and an attempt to measure initial growth rates before the nutrient concentration is substantially reduced by microbial growth. The main difficulty with this approach is that of measuring growth rates over a short enough time period that the nutrient concentration does not change significantly. The use of low culture densities helps to minimise nutrient flux. Novick and Szilard [27] used inocula of about 100 cells. ml-1, followed growth by colony counts, and extrapolated the growth curves to zero time to obtain growth rates in the presence of initial concentrations of nutrient. Shehata and Marr [13] used an electronic particle counter to monitor the growth of cultures kept below a density of 105. m1-1 by periodic dilution. Koch [48] measured turbidity changes following the addition of small doses of nutrient to low density cultures in a 10-cm spectrophotometer cuvette. Computerized collection of the turbidity data allowed the determination of growth rates over periods as short as 200 s. At the cell densities and nutrient concentrations used, less than 10% of the growth rate-limiting nutrient was consumed in this time. It is an implicit assumption in this general method that microbial growth rate responds virtually instantly to the prevailing concentration of growth rate-limiting nutrient. G a u d y et al. [46] have presented and cited evidence to suggest that this may not always be the case. Hence, the method should be used with some caution, and with attention paid to the previous history of the cells and to the possibility that a period of adaptation to changes in nutrient concentration may occur.

428 9. D E T E R M I N A T I O N OF K~ BY M E A S U R E M E N T OF G R O W T H R A T E D U R I N G WASHO U T F R O M C O N T I N U O U S C U L T U R E IN T H E P R E S E N C E OF K N O W N N U T R I E N T CONCENTRATIONS When the dilution rate of a continuous culture is set to exceed the critical dilution rate, the rate of wash-out of the culture is given by: dx/dt=(>-

D)x

thus: x t = x o e ( " - D ) t a n d : l n x t -= l n x o + (t* -- D ) t where x t is concentration of biomass at time t and x 0 is biomass concentration at zero time. A plot of l n x t against t is a straight line of slope bt - D. At low cell densities the concentration of growth rate-limiting nutrient in the culture approaches that in the nutrient feed. Hence the technique can be used to measure microbial growth rates in the presence of known concentrations of limiting nutrients. With high concentrations of growth rate-limiting nutrient in the reservoir the method is commonly used to measure maximum growth rates [4]. But it can also be used to determine growth rates at low nutrient concentrations by using known, low reservoir concentrations of growth rate-limiting nutrients [30]. K,~ is then determined from the growth rate versus nutrient concentration data as before. As with all the techniques using reservoir c o n c e n t r a t i o n s of growth-rate limiting nutrient of the same order as Ks, precautions are necessary to avoid nutrient contamination and sensitive methods are needed to monitor the low microbial populations. Dean and Rogers [32] used a variant of this procedure in which they determined the critical dilution rate (De) at which a continuous culture just washes out. When the reservoir concentration, Sr, of growth rate-limiting nutrient is much greater than Ks, then Dc approximates to the maximum specific growth rate (/*m) for the organism [4]. If S r is close to K s then D c is less than /*,nIn continuous culture at steady-state the specific growth rate of the micro-organism (/~) equals the culture dilution rate (D) and it follows that: K S = s(Iz m - D)/D

where s is the steady-state concentration of growth

rate-limiting nutrient in the culture. When the culture washes out the nutrient concentration in the culture approximates to that in the nutrient reservoir and hence: K~= Sr(tZm-

Dc)/Dc

Thus if D~ is measured at known low concentrations of nutrient in the reservoir, K s can be estimated. But the technique leads to cultures of very low density and wash-out may be difficult to detect. Dean and Rogers [32] used this method to obtain saturation constants for potassium, magnesium and sulphate for E n t e r o b a c t e r a e r o g e n e s but gave no details of their methods. In general, it would seem easier to measure growth rate during wash-out at dilution rates greater than btm than to attempt to determine the critical dilution rate.

10. D E T E R M I N A T I O N OF K~ F R O M T H E DIL U T I O N RATE Y I E L D I N G M A X I M U M OUTP U T IN C O N T I N U O U S C U L T U R E The dilution rate, D m, at which output of biomass is at a maximum in a continuous culture is given by [4]:

D m : ~m[1 - ~ s / / ( K s

+ St) ]

Hence if Din, #m and S r are known, K~ can be calculated. Herbert et al. [20] used this method hut suggested that the value obtained may be subject to considerable error. The method is obviously too laborious if the aim is only to determine K S.

11. D E T E R M I N A T I O N ROMETRY

OF K~

BY RESPI-

This method is based on measurement of the rates of oxygen uptake in a culture sample supplied with different concentrations of substrate. The substrate concentration supporting an oxygen uptake rate of one half the maximum rate is presumed to equal K s. It has been used to determine saturation constants for methane [6,24], methanol [6,24,26] and glucose [15]. Lamb and Garver [25] stated that, in their opinion, the

429

method measured the saturation constant for respiration and not that for growth, but this is not necessarily so. In Harrison's original method [6], a sample was taken from a carbon-limited chemostat culture, diluted 1 to 5 or 1 to 10 with aerated basal medium lacking the nitrogen and the carbon components, and placed in the chamber of an oxygen electrode respirometer. Different concentrations of carbon substrate were added and the rates of oxygen uptake measured. The substrate saturation constant was obtained from a plot of 1/(initial rate of oxygen uptake, Vo) versus 1/(initial substrate concentration). Although a nitrogen-free diluent was used, almost certainly enough nitrogen would have been carried over with the carbon-limited culture sample to ensure that growth was not prevented by nitrogen limitation at the lowest concentrations of methanol supplied. The fact that the plots of 1 / V o versus 1 / s were linear over the whole range of substrate concentrations suggests that the cultures were not nitrogen limited at any of the concentrations of methanol supplied. Thus it seems likely that the respirometer cultures were able to grow when provided with methanol and that the rates of oxygen uptake would then have been proportional to the growth rates [49-51]. This conclusion is also supported by consideration of Harrison's data. Harrison noted that only 1 mol of oxygen was c o n s u m e d / m o l methanol supplied. The complete oxidation of methanol to carbon dioxide requires 1.5 tool o x y g e n / m o l methanol: C H 3 O H + 1 . 5 0 z ~ CO~ + 2 HzO Hence, Harrison suggested that the oxidation was incomplete and that formate accumulated. The presence of formate was not tested for. An alternative interpretation of the observed oxygen consumption is that the cells grew and assimilated some of the methanol. Methanol is assimilated at the oxidation level of formaldehyde [52] and its oxidation to this level requires 0.5 mol o x y g e n / t o o l methanol: C H 3 O H + 0.5 02 ~ H C H O + H 2 0 Hence, Harrison's observed oxygen consumption

of 1 m o l / m o l methanol may be explained if 50% of the methanol was oxidised to carbon dioxide and 50% was assimilated, as formaldehyde, into cell material. This figure of 50% assimilated is very similar to experimentally determined values [53]. Thus there is every reason for believing that the bacteria were actually growing during Harrison's respirometric determinations and that the method measures K S for growth rather than the apparent saturation constant for respiration of methanol to carbon dioxide. Harrison [6], making the assumption that the K s for growth was of the same order as the K m for respiration, calculated the concentrations of methanol in methanol-limited continuous cultures. The calculated values agreed well with experimental values and thus provide support either for Harrison's assumption or for the suggestion that the method actually measures K S. Legan and Owens [15] considered the theoretical basis for using respirometric data for the determination of K S for growth. They showed that, for a culture growing with a single growth ratelimiting carbon and energy source at a particular moment, the specific rate of oxygen consumption for generation of energy for growth, qo2, EG plus the specific rate of oxygen consumption for raising the oxidation level of the assimilated carbon source to that of biomass, qo2, is directly proportional to the specific growth rate. If it is assumed that the rate of oxygen consumption for generation of energy for maintenance, qoE~, is the same as the EE endogenous respiration rate, qo2, measured in the absence of added substrate, then: EG qo2 +qoC2 q~2 - -

EE qo2

where qT 2 is the total rate of oxygen consumption. Hence, these authors concluded that respiration rate measurements on growing cells may be used to determine K~ values for growth, with the suggested proviso that the cells should be taken from relatively rapidly growing cultures. It has been shown experimentally that the specific rate of oxygen consumption is directly proportional to the specific growth rate for carbon and energy source-limited, chemostat cultures of Klebsiella pneumoniae [49,50] and Enterobacter aerogenes [51]. In carbon- and energy-sufficient cultures, where growth rate was limited by am-

430

monium, sulphate or phosphate, linear relationships between specific rate of oxygen consumption and specific growth rate were still obtained but rates of oxygen consumption were higher at low growth rates than in the carbon and energy source-limited cultures [49]. It was suggested that this was due to the occurrence of uncoupling between energy generation and biosynthesis in the carbon-sufficient cultures. Hence, these observations lend support to the use of the respirometric method for determining K s for carbon and energy sources but it is not clear whether or not the method is suitable with other nutrients. If respirometry is to be used for estimating K~ for growth, then it is axiomatic that the microbial cells should be provided with a medium that allows growth. If a suspending medium which does not support growth is used, it is difficult to imagine the precise physiological state of the cells, which then have no outlet for generated ATP besides possible futile cycles. Additionally, it would seem desirable to take cells from cultures growing at relatively high growth rates (say, at least 70% of m a x i m u m [15,54]). The concentrations of rate-limiting nutrient they are exposed to in the respirometer are then of the same order or less than those previously experienced in the culture. The cells will also only be exposed to decreases in nutrient concentration and can be expected to respond immediately [40], whereas the same is not true for increases in nutrient concentration. Preferably, also, cells should come from chemostat cultures so that their physiological state is defined and reproducible. The question still remains as to whether the respirometric method, which uses cells whose composition is adapted to only one nutrient regime will, in all cases, yield a value for K s identical to that obtained from measurements in steadystate continuous cultures, where the cellular composition is adapted to the prevailing conditions. The only report, besides the data of Harrison mentioned above, of a comparison of K s values determined by respirometry and by direct assays of nutrient concentrations in chemostat cultures is that by Legan and Owens [15] for a single bacterial strain on glucose. They obtained very good agree-

ment between the two values (6.1 and 5.9 /~mol. 1-I). In conclusion, it seems that the respirometric method may offer a very simple means for determining K~ for growth, but it is not yet entirely clear whether the value obtained will always be identical to that obtained from direct assays of nutrient concentrations in steady-state continuous cultures. Perhaps values so determined might be referred to as ' a p p a r e n t K~' for growth until such time as their relationship to K s is established.

12. C O N C L U S I O N S It is clear that the preferred method of determining Monod substrate saturation constants for growth is by the direct assay of growth ratelimiting nutrient in steady-state continuous cultures. All the other methods that have been used are open to the objection that the cells are exposed to concentrations of nutrients to which their cellular composition is not adapted. Additionally, the assumption, inherent in these other methods, that cells respond immediately to the prevailing nutrient concentration is known not always to be true. Nevertheless, in view of the difficulty or impossibility at present of accurately determining concentrations of growth rate-limiting nutrients in chemostat cultures, we suggest that the respirometric technique may be an acceptable and easy method for determining substrate saturation constants for growth with aerobic microorganisms. The approach is readily adapted for use with anaerobic organisms by using some other suitable method to monitor metabolic activity.

ACKNOWLEDGEMENTS This work was supported by a contract for research from the Ministry of Agriculture, Fisheries and Food. REFERENCES [1] Monod, J. (1942) Rrcherches sur la Croissance des Cultures Bactrriennes. Herman & Cie, Paris.

431 [2] Moser, A. (1985) Kinetics of batch fermentations. In: Biotechnology, Vol. 2 (Brauer, H., Ed.), pp. 242 283. Verlag Chemie, Weinheim. [3] Koch, A.L. (1985) The macroeconomics of bacterial growth. In: Bacteria in Their Natural Environments (Fletcher, M. and Floodgate, G.D., Eds.), pp. 1-42. Academic Press, London. [4] Pirt, S.J. (1975) Principles of Microbe and Cell Cultivation. Blackwell, London. [5] Pirt, S.J. and Callow, D.S. (1960) Studies on the growth of Penicillium chrysogenum in continuous flow culture with reference to penicillin production. J. Appl. Bact. 23, 87-98. [6] Harrison, D.E.F. (1973) Studies on the affinity of methanol and methane-utilising bacteria for their carbon substrates. J. Appl. Bact. 36, 301-308. [7] Poindexter, J.S. (1981) Oligotrophy. Fast and famine existence. Adv. Microbial Ecol. 5, 63-89. [8] Jannasch, H.W. and Mateles, R.I. (1974) Experimental bacterial ecology studied in continuous culture. Adv. Microbial Physiol. 11, 165-212. [9] Veldkamp, H. (1976) Mixed culture studies with the chemostat. In: Continuous Culture, Vol. 6 (Applications and New Fields) (Dean, A.C.R., Ellwood, D.C., Evans, C.G.T. and Melling, J., Eds.), pp. 315-328. Chichester, Ellis Horwood. [10] Harder, W., Kuenen, J.G. and Matin, A. (1977) Microbial selection in continuous culture. J. Appl. Bact. 43, 1-24, [11] Jannasch, H.W. (1968) Growth characteristics of heterotrophic bacteria in seawater, J. Bacteriol. 95, 722 723. [12] HiSfle, M.G. (1982) Glucose uptake of Cytophagajohnsonae studied in batch and chemostat culture. Arch. Microbiol. 133, 289-294. [13] Shehata, T.E. and Marr, A.G. (1971) Effect of nutrient concentration on the growth of Escherichia coli. J. Bacteriol. 107, 210-216. [14] Koch, A.L. and Wang, C.H. (1982) How close to the theoretical diffusion limit do bacterial uptake systems function. Arch. Microbiol. 131, 36-42. [15] Legan, J.D. and Owens, J.D. (1987) Determination of growth parameters of methylamine-using bacteria. J. Gen. Microbiol. 133, 1075-1080. [16] Kemp, C.W., Robrish, S.A., Curtis, M.A., Sharer, S.A. and Bowen, W.H. (1983) Application of a competition model to the growth of Streptococcus mutans and Streptococcus sanguis in binary continuous culture. Appl. Environ. Microbiol. 45, 1277-1282. [17] Law, A.T. and Button, D.K. (1977) Multiple-carbonsource-limited growth kinetics of a marine coryneform organism. J. Bacteriol. 129, 115-123. [18] Pirt, S.J. and Kurowski, W.M. (1970) An extension of the theory of the chemostat with feedback of organisms. Its experimental realisation with a yeast culture. J. Gen. Microbiol. 63, 357-366. [19] Pirt, S.J. (1973) Estimation of substrate affinities ( K S values) of filamentous fungi from colony growth rates. J. Gen. Microbiol. 75, 245-247. [20] Herbert, D., Elsworth, R. and Telling, R.C. (1956) The

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34] [35]

[36] [37]

[38] [39]

continuous culture of bacteria: a theoretical and experimental study. J. Gen. Microbiol. 14, 601-622. Button, D.K. and Garver, J.C. (1966) Continuous culture of Torulopsis utilis: a kinetic study of oxygen limited growth. J. Gen. Microbiol. 45, 195-204. Dykhuizen, D. and Davies, M. (1980) An experimental model: bacterial specialists and generalists competing in chemostats. Ecology 61, 1213-1227. Matin, A. and Veldkamp, H. (1978) Physiological basis of the selective advantage of a Spirillum sp. in a carbonlimited environment. J. Gen. Microbiol. 105, 187-197. Linton, J.D. and Buckee, J.C. (1977) Interactions in a methane-utilising mixed bacterial culture in a chemostat. J. Gen. Microbiol. 101,219-225. Lamb, S.C. and Garver, J.C. (1980) Batch and continuous culture studies of a methane-utilising mixed culture. Biotech. Bioeng. 22, 2097-2118. Wilkinson, T.G. and Harrison, D.E.F. (1973) The affinity for methane and methanol of mixed cultures grown on methane in continuous culture. J. Appl. Bact. 36, 309-313. Novick, A. and Szilard, L. (1950) Experiments with the chemostat on spontaneous mutations of bacteria. Proc. Natl. Acad. Sci. U.S.A. 36, 708-719. Button, D.K. (1969) Thiamine limited steady state growth of the yeast Cryptococcus albidus. J. Gen. Microbiol. 58, 15-21. Borkowski, J.D. and Johnson, M.J. (1967) Experimental evaluation of liquid film resistance in oxygen transport to microbial cells. Appl. Microbiol. 15, 1483-1488. Hao, O.J., Richard, M.G., Jenkins, D. and Blanch, H.W. (1983) The half-saturation coefficient for dissolved oxygen: a dynamic method for its determination and its effect on dual species competition. Biotech. Bioeng. 25, 403-416. Lusk, J.E., Williams, R.J.P. and Kennedy, E.P. (1968) Magnesium and the growth of Escherichia colt'. J. Biol. Chem. 243, 2618-2624. Dean, A.C.R. and Rogers, P.L. (1967) The cell size and macromolecular composition of Aerobacter aerogenes in various systems of continuous culture. Biochim. Biophys. Acta 148, 267-279. Robertson, B.R. and Button, D.K. (1979) Phosphatelimited continuous culture of Rhodotorula rubra: kinetics of transport, leakage and growth. J. Bacteriol. 138, 884-895. Monod, J. (1949) The growth of bacterial cultures. Annu. Rev. Microbiol. 3, 371-394. Kell, D.B. and Westerhoff, H.V. (1986) Towards a rational approach to the optimisation of flux in Microbiol biotransformations. Tibtech June 1986, 137-142. Button, D.K. (1985) Kinetics of nutrient-limited transport and microbial growth. Microbiol. Rev. 49, 270-297. H~3fle, M.G. (1983) Long term changes in chemostat cultures of Cytophaga johnsonae. Appl. Environ. Microbiol, 46, 1045-1053. Metzler, D.E. (1977) Biochemistry. Academic Press, London. Sinclair, C.G. and Ryder, D.N. (1975) Models for the

432

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

continuous culture of microorganisms under both oxygen and carbon limiting conditions. Biotech. Bioeng. 17, 375-398. Ingraham, J.L., Maaloe, O. and Neidhardt, F.C. (1983) Growth of the Bacterial Cell. Sinauer Associates, Sunderland, MA. Wirsen, C.O. and Jannasch, H.W. (1970) Growth response of Spirosoma sp. to temperature shifts in continuous culture. Bacteriol. Proc. Gl18, 32. Moser, A. (1985) Rate equations for enzyme kinetics. In: Biotechnology, Vol. 2 (Brauer, H., Ed.), pp. 199-226. Verlag Chemie, Weinheim. Cornish-Bowden, A. and Eisenthal, R. (1974) Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot and other methods. Biochem. J. 139, 721-730. Eisenthal, R. and Cornish-Bowden, A. (1974) The direct linear plot; a new graphical procedure for estimating enzyme kinetic parameters. Biochem. J. 139, 715-720. Lloyd, D., Scott, R.I. and Williams, T.N. (1983) Membrane inlet mass spectrometry-measurement of dissolved gases in fermentation liquids. Trends Biotech. 1, 60-63. Gaudy, A.F., Obayashi, A. and Gaudy, E.T. (1971) Control of growth rate by initial substrate concentrations at values below maximum rate. Appl. Microbiol. 22, 1041 - 1047. Dykhuizen, D. (1978) Selection for tryptophan auxotrophs of Escherichia coli in glucose-limited chemostats as a test of the energy conservation hypothesis of evolution. Evolution 32, 125-150.

[48] Koch, A.L. (1979) Microbial growth in low concentrations of nutrients. In: Strategies of Microbial Life in Extreme Environments (Shilo, M., Ed.), pp. 261-279. Verlag Chemie, Weinheim. [49] Neijssel, O.M. and Tempest, D.W. (1976) Bioenergetic aspects of aerobic growth of Klebsiella aerogenes NCTC 418 in carbon-limited and carbon-sufficient chemostat culture. Arch. Microbiol. 107, 215-221. [50] Tempest, D.W. and Neijssel, O.M. (1978) Eco-physiological aspects of microbial growth in aerobic nutrient-limited environments. Adv. Microbial Ecol. 2, 105-153. [51] Stouthamer, A.H. and Bettenhaussen, C.W. (1975) Determination of the efficiency of oxidative phosphorylation in continuous cultures of Aerobacter aerogenes. Arch. Microbiol. 102, 187-192. [52] Anthony, C. (1982) The Biochemistry of Methylotrophs. Academic Press, London. [53] Atkinson, B. and Mavituna, F. (1983) Biochemical Engineering and Biotechnology Handbook, p. 144. MacMillan, London. [54] H~Sfle, M.G. (1984) Transient responses of glucose-limited cultures of Cytophaga johnsonae to nutrient excess and starvation. Appl. Environ. Microbiol. 47, 356-362. [55] Kuenen, J.G., Boonstra, J., Schr~Sder, H.G.J. and Veldkamp, H. (1977) Competition for inorganic substrates among chemoorganotrophic and chemolithotrophic bacteria. Microbial Ecol. 3, 119-130.