Bioprocess Engineering
~ Springer-Verlag 1993
The effect of pH on kinetic and yield parameters during the ethanolic fermentation of D-xylose with Pachysolen tannophilus
V. Bravo, F. C a m a c h o , G r a n a d a , S. Sfinchez, E. C a s t r o , Jadn, S p a i n
Abstract. We have studied the ethanolic fermentation of D-xylose g ethanol with Pachysolen tannophilus in batch cultures. We propose a model Y~/s g xylose to predict variations in D-xylose consumed, and biomass and g biomass ethanol produced, in which we include parameters for the specific Yx/s
growth rate, for the consumption of D-xylose and production of g xylose
ethanol either related or not to growth, g xylitol
The ideal initial pH for ethanol production turned out to be 4.5.. fxi/$
At this pH value the net specific growth rate was 0.26 h 1, biomass g xylose yield was 0.16 g.g- 1, the cell-maintenance coefficient was
0.073 g.g-1.h-1, the parameter for ethanol production non-related to growth was 0.064 g.g- 1.h 1 and the maximum ethanol yield was 0.32 g . g - 1
Greek letters g ethanol c~ g biomass
c
E g/1
L f;
L, ka 1/h ME
Ms Mxi
g xylose rn
g biomass g xylose md g biomass
g ethanol qE g biomass.
s g/1
so g/1
t h
x g/l
Xo g/1
g ethanol Ye/s
g xylose -fe/~ g ethanol
g xylose g ethanol yT E/S
g xylose g ethanol Y*/$
g xylose
g ethanol
List of symbols fl
Ac Carbon atomic weight g biomass.h
aa 1/h Specific cell-maintenance rate defined in
g ethanol
Eq. (8) fie
Mass fraction of carbon in the biomass g biomass.h Ethanol concentration
Correction factor defined in Eq. (13) Correction factor defined in Eq. (13) Correction factor defined in Eq. (14) Death constant
Ethanol molecular weight Xylose molecular weight Xylitol molecular weight
Maintenance coefficient for substrate Maintenance coefficient when kd 4= 0 Specific ethanol production rate Residual xylose concentration Initial xylose concentration Time
Biomass concentration Initial biomass concentration Instantaneous ethanol yield Mean ethanol yield Theoretical ethanol yield
Corrected instantaneous ethanol yield
O h
/~ 1/h
/~,~ 1/h
Corrected mean ethanol yield Biomass yield
Mean xylitol yield
Growth-associated product formation parameter
Non-growth-associated product forma- tion parameter
Non-growth-associated product forma- tion parameter when kd # 0
Variable defined in Eq. (6) or Eq. (7) Specific growth rate
Maximum specific growth rate
1 Introduction
T h e c o n t i n u o u s c u l t u r e system is r e c o g n i s e d as being the ideal one for e s t a b l i s h i n g b o t h the kinetic a n d yield p a r a - m e t e r s of m i c r o o r g a n i s m s g r o w t h a n d d i s t i n g u i s h i n g between those p a r a m e t e r s related with processes which are d e p e n d e n t u p o n cell concentration, such as e n d o g e n o h s respiration, cell m a i n t e n a n c e a n d the f o r m a t i o n of p r o d u c t s u n a s s o c i a t e d with cell g r o w t h , a n d t h o s e p a r a - m e t e r s r e l a t e d w i t h p r o c e s s e s w h i c h d e p e n d u p o n g r o w t h rate, such as s u b s t r a t e m e t a b o l i s m to p r o d u c e b i o m a s s a n d the f o r m a t i o n of p r o d u c t s a s s o c i a t e d with cell growth.
I n b a t c h cultures these two t y p e s of p a r a m e t e r s are clearly i n c a l c u l a b l e d u r i n g the e x p o n e n t i a l g r o w t h p h a s e b e c a u s e the specific g r o w t h r a t e r e m a i n s c o n s t a n t at its m a x i m u m . O n l y at the e n d of the e x p o n e n t i a l p h a s e w h e n the c o n c e n - t r a t i o n of the l i m i t i n g n u t r i e n t has been sufficiently re-
duced can any useful information be obtained, and this with considerable experimental difficulty [1]
Nevertheless, the batch culture of certain microorga- nisms under determined environmental conditions can lead to a fairly short exponential growth phase, during which a relatively small amount of the initial nutrient stock in the medium is consumed, followed by a long non- exponential growth phase, which continues until all of the limiting nutrient is used up. This secondary growth phase can often be adjusted to a linear increase in cell concentra- tion versus time and thus be explained in terms of such natural physical phenomena as light intensity in photo- synthetic cultures or gas transference when this is needed for cell growth. The existence of a non-exponential growth phase, therefore, makes it feasible in principle to calculate in batch cultures the parameters related with both pro- cesses, those which depend upon cell concentration and those which are related to cell growth. This leads to the possibility of analysing more easily on a laboratory scale the influence of different variables upon the kinetic and yield parameters.
In this way it has been concluded that during ethanolic fermentation of xylose solutions with Pachysolen tan- nophilus the concentration of dissolved oxygen is elimi- nated rapidly, even when the culture medium is aerated, and thus cell growth becomes limited by the transference of oxygen within the cell suspension [2]; in the results of some authors [3, 4] long linear-growth phases during this fermentation process can be observed.
The study of ethanolic fermentation of xylose solu- tions is of particular interest because fuller use is made of the products deriving from the hydrolysis of cellulose residues, among which xylose can account for between 10% and 30% of the carbohydrates thus obtained [5].
Pachysolen tannophilus is one of the yeasts most widely assayed in this process because of its capacity to ferment monosaccharides (D-xylose I-2, 6], D-manose and D-ga- lactose [-7] and L-arabinose [8]) and even the disacchar- ide D-celobiose [8].
In previous papers [-9, 10] we have described the ethanolic fermentation of glucose solutions with Pachy- solen tannophilus and analysed the influence of the envi- ronmental conditions (pH, temperature and aeration) and the composition of the culture medium (concentration of glucose and yeast extract). We deduced that after the exponential growth phase there was always a stationary phase thus it was impossible in batch cultures to identify which processes were dependent upon cell growth and which were not. In this work we have set out to find out whether there is a non-exponential growth phase during the fermentation of xylose with Pachysolen tannophilus which would allow us to calculate the parameters related with those processes dependent upon cell concentration and those relying on cell growth rate. We also studied the possible effects that pH might have on the kinetic and yield parameters.
2 Theoretical background
To explain the variations in x, s and E versus time and to determine the kinetic and yield parameters during the fermentation of xylose by Pachysolen tannophilus we have employed the following model:
1 dx
x dt - # - ka , (1)
1 d(so - s) #
x d ~ - m + Y~/s (2)
1 dE
-
#
+ c ~ . # , (3)x dt
in which # represents the specific growth rate and ka death constant; the parameters for growth-related processes are biomass yield, Yx/s, and product formation, c~, and those for non-growth-related processes are the cell-maintenance coefficient, m, and product formation,/3.
In these equations it is evident that as # remains constant during the exponential growth phase in a batch culture and so too therefore the specific substrate con- sumption and product formation rates, Eqs. (2) and (3), it is thus impossible to distinguish between the parameters associated with growth and those which are not.
The combination of Eqs. (1) to (3) lead to:
d(s0 - s) 1 dx
- [ m + ( k a / I % s ) ] . x + - - - -
dt Y~/~ dt
1 dx
= me.x + - - - - (4)
Yx/s dt
d E d x d x
dt
(#
+ e . k e ) . x + ~ fia.x + c ~ (5)which, given that the parameters of the model are known, will provide the substrate consumption and product formation rates. Although these equations would be valid for the application of the differential method for the treat- ment of kinetic data, the difficulty in evaluating the deri- vatives involved with any degree of precision makes it advisable on the whole to apply the integral method, by which the following equations can be deduced from Eqs.
(4) and (5):
i x . d r
So - s o 1 1
- - - m a + - - = m a . O + - - ,
x - Xo x - Xo Yx/s Yx/s
i x . d t E
- - -
Be
o + ~ =#a.O
+ c~ ,X - - X 0 X - - X 0
(6)
(7)
in which we have defined a variable, O, with units of time, which would play the same role as the inverse of the dilution rate does when determining cell-maintenance co- efficients in continuous cultures [11] and for the calcu-
V. Bravo et al.: Effect of pH on kinetic and yield parameters lation of which the integral of biomass concentration throughout time must be determined. It is worth noting that if we were dealing with exponential growth then from the outset O would be constant and equal to the inverse of the specific growth rate, and thus once more it would be impossible to calculate the parameters of the model dur- ing this phase.
3 Experimental
All experiments were made in the same batch-culture unit as that described in a previous paper [12].
The growth medium composition in g'1-1 was:
M g S O , , 1; K H 2 P O 4 , 2; (NH4)2SOr 3; peptone, 3.6; yeast extract, 4 and D-xylose, 25. This medium was sterilized by filtration through 0.2 #m cellulose nitrate. Inocula were prepared by growing for 48 h to 60 h at 30 ~ in a culture medium containing 3 g.1-1 malt extract, 3 g'1-1 yeast extract, 5 g-l- ~ peptone and 10 g.1-1 D-xylose, solidified with 20 g ' l - a agar-agar. The biomass concentration in the fermentor after inoculation, Xo, was always kept at about 0.010-0.028 g ' l - 1.
Cell concentration was measured indirectly through absorbance at 620 nm, an absorbance versus dry weight calibration line having been obtained beforehand. The
[aJ I -
8 3
g/t .g/I
•
O- 0
a 0
o % ~ \ _ _ 0
" ~4Y fo-
~ t ~ / / o
J i (9- -- "-
%
~ . ~ . , > ~ . . . . , . . . , ,
LO 80 120 h 160
Time t
!-
1 5 3 g / l . g / t
10 - 2
W •
5- 1
O-
C
I l I I
x .
30 60 90 h 120
Time t
- ] ' I ' I ~ I ~ I
1.4- 1.5 f 1,',~,..._~..
g / [ . /t g _ / - ~ e / ~ 1 7 6 ~ ~ 1 7 6 o . . . o
1.0 - e _
0 . 7 - /
v'- /~
- - _ . _ _ " 0 .J.' i ,
O - n l , I I I
VO LO 80 120 h 160
e Time t
2L g/[
16
2L g/L
16
u]
2/-, g/t
16
uo
10 g/{
Ld
5
O
I I I I
LU
0 35 70 105 h
b Time t
_•5
---|2
0 I
\
A , -'.%O
16- L g/L g/L
x
8 - 2
O- 0 8
I 1 i I
"o
O.O
30 60 90 h 120
Time t
2/-, g/L
16
tn
2L g/[
16
Ul
Fig. la-e. Variations in biomass produced (O) (g/l), residual xylose (O) s (g/l) and ethanol produced (C)) (g/l) versus time for the experiments carried out at initial pH: a 2.5, b 3.5, c 4.5, d 5.5 and e 6.5.
Arrows indicate the time intervals of linear growth
concentration of the residual xylose and that of the ethanol produced were determined after dilution, using the DNS [13] and alcohol dehydrogenase [-14] methods.
In the experiments with initial pH's of 2.5 and 6.5 assays were carried out by the polyol dehydrogenase enzymatic method [-15] to determine the quantities of xylitol that appeared as subproduct.
F o r environmental conditions we chose T = 30 ~ and aeration through the stirring vortex alone, as these had proved to be optimum for the ethanolic fermentation of glucose [9]. The influence of the initial pH was studied by varying this condition from 1.5 to 6.5.
4 Results and discussion
i
' I I I I I
&4&..~...~... a
'" . . . . . 0 0 O--
i I , I , f , I ~ r
0 0 40 80 120 160 200
Time t
Fig. 2. Variation in pH during the course of the experiments The values obtained for the concentrations of biomass,
xylose and ethanol versus time in the experiments with
initial pH's of 2.5, 3.5, 4.5, 5.5 and 6.5 are set out in Fig. 1. s The data for the experiment with an initial pH of 1.5 are
not shown as the concentration of biomass diminished
from 0.041 to 0.018 g.1-1 and both xylose consumption s and ethanol production were negligible.
Changes in pH were also followed during all the ex- 4 periments. Thus it can be seen in Fig. 2 that there was
virtually no change when the initial value was 1.5, coincid-
ing with the negligible results in the other variables. In the "~o 3 other assays pH fell gradually to become more or less
v
constant during the stationary phase, and is thus seeming- s 2 ly related to cell growth. This may be put down to the
production of organic acids along with ethanol [2]. This is
of interest in the practical use of Pachysolen tannophilus 1 as many of the possible contaminating microorganisms
are inhibited at such low pH values.
0 4.1 Cell growth
A representation of the adimensional concentration of biomass versus time in semilogarithmic co-ordinates, of which those pertaining to initial pH values of 1.5 to 3.5 are set out in Fig. 3, shows that in none of the experiments was there a lag phase of any consideration. At initial pH 1.5 a decrease in biomass concentration occurred, growth being completely inhibited at such high acidity, and thus, taking # = 0 it can be determined that kd = 0.006 h-1.
With the other initial pH values any influence by cell death is clearly overcome by exponential growth and so net maximum specific growth rates, # , , - ke, are ob- tained. It can be seen in Table 1 that these values are fairly constant in the pH range of 3.5 to 5.5, whilst they are somewhat lower at the extremes of 2.5 and 6.5.
It is also clear from Fig. 3, however, that the exponen- tial growth phase is greatly reduced and that there is an intermediate phase before the stationary phase, which is reached when the xylose in the medium has been virtually
I I .I I I I I
-10
eee---~e___e_~
' 2'0 ' 4'0 ' ; o ' o ' lOO ' ' 12o ' 14o
Time t
Fig. 3. Growth curves for experiments with initial pH: (D 1.5, 9 2.5, O 3.5. Arrows indicate the end of the exponential growth
used up. During the intermediate phase, as can be seen in Fig. 1, the dependence of biomass concentration upon time is practically linear, which may be compatible with the restriction in the growth of Pachysolen tannophilus on xylose caused by the availability of oxygen in the medium, and thus both types of parameters can be calculated, those related with processes dependent upon cell concentration and those dependent on the growth rate. Furthermore, this linear dependence facilitates considerably the analyti- cal or numerical integration of the biomass concentration throughout time and thus the calculation of the values for O, which are necessary to apply Eqs. (6) and (7).
V. Bravo et al.: Effect of pH on kinetic and yield parameters 4 . 2 X y l o s e c o n s u m p t i o n
As regards xylose consumption, the application of the integral method to the proposed model leads to Eq. (6), using which the values of 1/Yx/~ and ma can be arrived at via representations of the quotient ( S o - s ) / ( x - Xo) versus O, as shown in Fig. 4 for an initial pH of 3.5. The values obtained by linear regression for biomass yield and specific cell-maintenance rate, defined by;
aa = ma" Y~l~ , (8)
are set out in Table 1. Biomass yield was found to be lowest at an initial pH of 4.5 and particularly high at 6.5. It is noteworthy that the yields here were higher than those with 25 g.1-1 glucose [9], which increased from 0.087 to 0.138 g biomass/g substrate on raising the pH from 2.5 to 6.5. This is despite the fact that the yields with glucose were obtained with 0.075 v/v/min aeration, a variable which was also shown to increase the value of Y~/~.
As far as the specific cell-maintenance rate is con- cerned, the minimum value was also found at an initial pH of 4.5, which coincides with the 0.012 h - 1 for Saccharo- myces cerevisiae when cultivated continuously on glucose [11]. The highest values for this parameter occur at the
Table 1. Kinetic and yield parameters
pHi ,u,,, - ka Yx/~ aa fla
[ 1/hi [g/g] [l/h] [g/(gh) ]
2.5 0.14 0.19 0.021 0.046
3.5 0.25 0.20 0.014 0.053
4.5 0.26 0.16 0.012 0.064
5.5 0.25 0,20 0.014 0.056
6.5 0.19 0.28 0.018 0.012
two extremes of pH (2.5 and 6.5), which would require a higher consumption of energy for cell-maintenance.
4.3 E t h a n o l p r o d u c t i o n r a t e
In accordance with Eq. (7), the representation of the quo- tient E / ( x - Xo) versus 69 leads to an intercept and slope which coincide respectively with the parameters of growth-related and non-growth-related ethanol forma- tion, c~ and fla. Fig. 5 shows the plot for the initial pH's of 4.5 and 6.5. We have deduced that these values always adjust to intercepts through zero, as can be seen in the examples in Fig. 5, which represent the minimum and maximum values of fla. It turns out, therefore, that ethanol production is not basically dependent on growth rate and so with the single parameter fla via Eq. (7) it is possible to describe the variations in ethanol concentration versus biomass production, and hence, with the known values of x, versus time.
In the same way variations in the substrate concentra- tion throughout time can be described by using Eq. (6) and the parameters Y~/s and rod. These predictions, which were arrived at using the values of the parameters in Table 1 for every initial pH, lead to the solid curves shown in Fig. 1, in which can be seen the acceptable fitting of both the values for E and for s.
With regard to non-growth-related ethanol produc- tion, the highest/~a values were obtained with an initial pH of 4.5, which coincides with minimum Y~/s and aa values in this experiment. Thus it may be concluded that, as far as ethanol production is concerned, this initial pH is the most favourable of those value of fla is equal to fl and represents the specific rate of ethanol production, qE, which thus remains constant throughout than those ob- tained with 25 g ' l - 1 glucose [9], which increase from 0.55 to 1.05 g- g - 1.15 - 1 concomitantly with a decrease in initial pH from 6.5 to 2.5, although it must be pointed out that
12
10
, 8
x
u~
bq
o
o o
1 I I I I I
15 30 /.5 60 75 h 90
VariabLe 0
% 3
x
1
1 I
0 60 h 80
-
| 0
|
20 /*0
VariabLe B
Fig. 4. (So - s)/(x - Xo) versus O for the experiment carried out at Fig. 5. E/(x - Xo) versus O for the experiments carried out at
pHi = 3.5 pHi = 4.5 (@) and pHi = 6.5 (0)
these qE values for glucose were obtained with 0.075 v/v/min aeration and also represent maximum values, as a significant variation for qE was determined.
4.4 Ethanol yield
The combination of Eqs. (6) and (7), bearing in mind that in this case e = 0 is admissible, leads to:
r~/s - E fie" o fie. r~/~. o
So -- S--(1/Yx/s) + m d . O -- 1 + ad.O ' (9) an equation that allows us to predict the variation of the mean ethanol yield, Ye/s, versus O, that is to say through- out the fermentation process, using the previously deter- mined parameters for the model, i.e. fie, Yx/~ and me or ad.
A comparison between the variations thus obtained and the experimental values, as shown in Fig. 6 for the initial pH of 3.5, reveals an acceptable fitting for the most significant values, when xylose consumption and ethanol production are high and thus O is also high. Both the predicted values and the experimental ones show that Y~/s grows with time but that the maximum values at- tained, about 0.32 g ethanol/g xylose at initial pH's of 4.5 and 5.5, are far below the theoretical yield, Y~/s = 5/3(Me/M~). They are also lower than the 0.36 g ethanol/g glucose obtained with 25 g.1 - t glucose in the pH range 2.5 to 6.5 [9], a value which remained constant throughout the experiments. They are, however, some- what higher than the values of 0.2, 0.22 and 0.08 g ethanol/g @lose obtained at pH's of 2.5, 4.5 and 6.5 with 50 g.1-1 xylose at 25 ~ and 0.075 v/v/rain aeration [-2].
As the mean ethanol yield increases with time it is of interest to be able to calculate the yield at any moment during the fermentation process, i.e. the instantaneous yield, Y~/s, in order to compare it with the theoretical yield. F r o m the definition of the average integral value,
9 1 0
s O ~ 6 YE/s.dO , (10)
it is possible to deduce the instantaneous yield according to:
O dfE/" (11)
Ye/s = f e/s + d O '
which, when applied to the expression for Ye/s in Eq. (9) leads to:
fie. Yx/s.O.(2 + ad.O)
YE/s = (1 + ae.O) 2 ' (12)
F r o m this equation and the values of the parameters in Table 1 the variation in instantaneous yield versus O can be calculated, although only the range of O values that correspond to the determination of these parameters should be used. As an example in Fig. 7 we show the variation obtained for with an initial pH of 2.5. It can be seen that Y*/s also increases with O, although obviously to a lesser degree than YE/s.
Although in the experiments with the most favourable pH's (3.5 to 5.5) the values for Y~/s, at the highest O values, are of the same order of magnitude as that for YrE/s in the experiments beginning with extreme pH's (2.5 and 6.5), they are still far removed from the theoretical value. Thus we have considered possible corrections to justify these discrepancies.
Firstly, to take into account the consumption of xylose destined towards the production of biomass and cell maintenance, (So - s)x, if we accept the hypothesis that xylose is the only carbon source, we can make a carbon atomic balance, in such a way that, using Eqs. (6) and (8), we get:
f~ (So -- s)x Ms Yx/s f "
- - - - c - - . -
(13)
(So -- s) 5.At(1 + ad.O) (1 + ad.O) '
where, to obtain a value forfx o r f ~ it is necessary to know the mass fraction of carbon in the biomass, c, which in this case turns out to be 0.446, as obtained by an elemental
I o t/i LU
0.3
0.2
0.1
I i I i I i I i
0 10 20 30 40 h 50
Variabl.e O
Fig. 6. Mean ethanol yield versus O for the experiment carried out at pH~ = 3.5
u)
>.-
1 . 0 r
0.8
0.6
0.4 i
10
I I ~ ] l I
(3)
(2)
I t I i I i I
20 30 &O 50
Variabte 0
I
h 6O
Fig. 7. Variation o f Y* i yr els/ EIs versus O for the experiment of pHi = 2.5:f' x =f~i O = (1),f' # 0 andfx i = 0 (2),f~ r 0 andfx i r 0 (3)
v. Bravo et al.: Effect of pH on kinetic and yield parameters
analysis which allowed us to determine
C H l . s l N o . 1 6 0 0 . 6 s as being the empirical f o r m u l a for the biomass.
Secondly, to take into a c c o u n t the c o n s u m p t i o n of xylose c o r r e s p o n d i n g to the f o r m a t i o n of xylitol (So - s)xi, a n o t h e r correction factor can be defined:
f,~, _ (So - S)x~ Ms ~ / ~ , (14)
(s O - s) Mxi
where we include the m e a n xylitol yield based on the total c o n s u m p t i o n of xylose, 'Z~vs, which, for the experiment with an initial p H of 2.5 has been calculated as 0.27 g xylitol/g xylose from experimental xylitol-concentration values of 1.45 a n d 6.5 g l - 1 o b t a i n e d for total xylose con- s u m p t i o n s of 4 a n d 24.8 g l - ~ respectively, accepting that Y~/s remains c o n s t a n t t h r o u g h o u t the fermentation pro- cess and that the xylitol c o n c e n t r a t i o n at the outset is nil.
T h e i n c o r p o r a t i o n of these correction factors into Eq. (9) provides the corrected m e a n ethanol yield:
E
?*/~ = (So - s).(1 --f~ - f ~ i ) fn. Y~/~. O
(15)
= (1 + an.O).{1 - [f'~/(1 -I- an.O)] - f ~ i } '
and thus, via Eq. (11), a corrected instantaneous ethanol yield with the equation:
y~/~ fie. Yv~.O.[2(1 - f ' ~ - f ~ i ) + (1 - f ~ , ) . a n . O ] (16)
= [(1 - f " - f x i ) -~ (1 -fxi).aa.(y)] 2 ' which can be reduced to Eq., (12) if the correction factors f ' a n d f x are annulled and also those with which the curves of YE/J YE/~ * r in Fig. 7 have been calculated for those cases where only the first correction, i.e. that related to the b i o m a s (fxi = 0), has been taken into account, a n d where b o t h corrections have been considered. It can be seen that in this latter case the values for Y~/s closely resemble the theoretical ethanol-yield value, a b o v e all if we bear in m i n d the m a r g i n of error to which the calculation of the parameters is subject and that it has n o t been possible to take into a c c o u n t other factors such as the metabolic c o n s u m p t i o n of ethanol a n d the f o r m a t i o n of s u b p r o d u c t s other t h a n xylitol.
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Received September 7, 1992 V. Bravo
F. Camacho
Universidad de Granada Facultad de Ciencias
Departmento de Ingenieria Quimica 18071 Granada
S. S/mchez (corresponding author) E. Castro
Universidad de Granada
Facultad de Ciencias Experimentales Departamento de Ingenieria Quimica 23071 Ja6n
Spain
