23 Kinetics of Yeast Growth and Metabolism in Beer Fermentation IVAN MARC and JEAN-MARC ENGASSER Institut National Polytechnique de Lorraine, Laboratoire des Sciences du Génie Chimque, CNRS-ENSIC, Nancy 54042 France
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MANFRED M O L L and BRUNO DUTEURTRE Centre de Recherche TEPRAL, Champigneulles 54250 France An experimental and t h e o r e t i c a l k i n e t i c study o f yeast growth and f l o c c u l a t i o n , sugar and amino a c i d uptake, ethanol, CO and other metabolite production during beer fermentation is presented. C e l l u l a r growth, and consequently amino a c i d s uptake and some metabolites production, stops a f t e r about 100 hours o f f e r mentation. Yeast f l o c c u l a t i o n , which s t a r t s when glucose is totally removed from the medium, then becomes a predominant phenomenon. Fermentable sugars are sequentially taken up, maltose and m a l t o t r i o s e being repressed by glucose. Ethanol and CO production r a t e remain e s s e n t i a l l y p r o p o r t i o n a l to the t o t a l r a t e o f sugar uptake both during the growth and f l o c c u l a t i o n phase. The increase with temperature o f s u b s t r a t e uptake, yeast growth and f l o c c u l a t i o n , and metabolite product i o n r a t e is simply described by Arrhenius type o f relationships. 2
2
The conversion by yeast o f sugars and amino a c i d s i n t o aromatic compounds represents a c e n t r a l process i n brewing. A q u a n t i t a t i v e understanding o f the m i c r o b i a l events t a k i n g p l a c e during the t r a n s f o r m a t i o n o f wort i n t o beer i s e s s e n t i a l when c o n s i d e r i n g the automatic c o n t r o l o f t h i s fermentation. A f i r s t k i n e t i c modeling o f yeast growth, sugar and amino a c i d uptake and aromatic m e t a b o l i t e p r o d u c t i o n was p r e v i o u s l y proposed (1,2). On the b a s i s o f recent experimental r e s u l t s we propose a new model which takes i n t o account the e v o l u t i o n o f the yeast v i a b i l i t y during the f e r m e n t a t i o n , and d e s c r i b e s i n g r e a t e r d e t a i l the f l o c c u l a t i o n phase and the p r o d u c t i o n o f CO2. The k i n e t i c study i s s p e c i a l l y aimed a t e s t a b l i s h i n g r e l a t i o n s p h i p s between the wort i n i t i a l composition, the f i n a l beer q u a l i t y and v a r i o u s process parameters, such as temperature, pressure and i n o cculum s i z e .
0097-6156/83/0207Ό489$06.00/0 ©
1983 American Chemical Society
In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
490
BIOCHEMICAL
ENGINEERING
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EXPERIMENTAL The experimental p a r t of t h i s work was performed at the TEPRAL Beer Research Center i n Champigneulles, France. Beer pro d u c t i o n was c a r r i e d out e i t h e r i n l a b o r a t o r y t u b u l a r fermentors, 1,80 m h e i g h t and 4,5 cm inner diameter, c o n t a i n i n g 2 l i t e r s of medium, or i n 1000 l i t e r s c y l i n d r o - c o n i c a l p i l o t p l a n t fermentors without mechanical a g i t a t i o n . Standart i n d u s t r i a l wort and yeast Saccharomyces uvarum 0019 were used. The i n i t i a l d i s s o l v e d oxygen c o n c e n t r a t i o n i n the wort was f i x e d at 8 ppm. The temperature was maintained constant at e i t h e r 10° C or 14° C during the whole f e r mentation. The overhead pressure was 1 atm w i t h the l a b o r a t o r y fermentor and 2,2 atm w i t h the p i l o t p l a n t . Samples of 80 cm^ and 4 l i t e r s were p e r i o d i c a l l y withdrawn from the l a b o r a t o r y and p i l o t v e s s e l , r e s p e c t i v e l y . Yeast concen t r a t i o n was determined e i t h e r from the dry weight or w i t h a Coul ter counter. The v a r i o u s sugars, glucose, f r u c t o s e , maltose, sac charose, m a l t o t r i o s e were analyzed by high pressure l i q u i d chroma tography. The c o n c e n t r a t i o n o f the twenty amino a c i d s were d e t e r mined by i o n exchange chromatography. Ethanol was assayed by microc a l o r i m e t r y and other m e t a b o l i t e s by gas chromatography.(3) THE KINETIC MODEL In c o n v e n t i o n a l fermentation models the c e n t r a l equation u s u a l l y expresses c e l l u l a r growth as a f u n c t i o n o f s u b s t r a t e , pro duct and c e l l u l a r c o n c e n t r a t i o n i n the medium. Product formation i s then r e l a t e d to c e l l growth or c e l l u l a r c o n c e n t r a t i o n , whereas s u b s t r a t e uptake r a t e may i n c l u d e s e v e r a l c o n t r i b u t i o n s from c e l l u l a r growth, maintenance and product formation. Moreover, these mo d e l s most o f t e n are based on constant y i e l d s . In view of the experimental r e s u l t s (4) i t i s c l e a r t h a t the c o n v e n t i o n a l approach cannot be used to model beer fermentation. F i r s t , the fermentation medium c o n t a i n s s e v e r a l sugars which are a s s i m i l a t e d at d i f f e r e n t r a t e s . The uptake of each sugar may be l i mited by i t s own c o n c e n t r a t i o n and i n h i b i t e d by the presence of others. Second, the i n v e s t i g a t e d beer fermentation from a k i n e t i c p o i n t of view i s complicated by yeast f l o c c u l a t i o n which becomes predominant during the second stage of the process, and which i s a f f e c t e d by one of the fermentable sugars, namely glucose. T h i r d , the v a r i o u s y i e l d s between fermentable sugars uptake, yeast growth, ethanol and CÛ2 formation are not constant during the course of the fermentation. F i n a l l y , the r a t e o f aromas production i s r e l a t e d to e i t h e r yeast growth r a t e or sugars uptake r a t e . In order to d e s c r i b e the i n f l u e n c e of the i n i t i a l wort compo s i t i o n on the fermentation process the proposed model i s based on separate r a t e equations f o r the v a r i o u s sugars uptake. Production of y e a s t , ethanol and carbon d i o x i d e i s then r e l a t e d to the t o t a l uptake of fermentable sugars w i t h v a r i a b l e y i e l d s . The r a t e of amino a c i d s uptake and other m e t a b o l i t e s production i s expressed as a f u n c t i o n of growth r a t e or sugars uptake r a t e w i t h constant or v a r i a b l e y i e l d s .
In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
23.
MARC ET AL.
Kinetics
in Beer
491
Fermentation
Y e a s t g r o w t h and f l o c c u l a t i o n . D i s t i n c t i o n i s made between t h e t o t a l y e a s t p r o d u c e d d u r i n g t h e g r o w t h p h a s e and t h e s u s p e n d e d y e a s t c o n c e n t r a t i o n i n t h e f e r m e n t a t i o n medium. The i n c r e a s e i n t o t a l yeast c o n c e n t r a t i o n i n the fermentor i s d i r e c t l y r e l a t e d t o the t o t a l r a t e o f fermentable sugar consumption. d(X ) T
= - R
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dt
X/S
d(TFS) dt
(1)
(Xy)
being the t o t a l yeast concentration
(TFS) R X/S
t h e t o t a l fermentable sugar c o n c e n t r a t i o n the yeast t o sugar y i e l d
The e x p e r i m e n t a l l y o b s e r v e d d e c r e a s e o f R x / s d u r i n g t h e f e r m e n t a t i o n h a s p r e v i o u s l y been a t t r i b u t e d t o t h e d e c r e a s e i n i n t r a c e l l u l a r s t e r o l c o n c e n t r a t i o n as a r e s u l t o f yeast growth i n t h e a b s e n c e o f o x y g e n . We f o u n d i t most c o n v e n i e n t t o m a t h e m a t i c a l l y r e l a t e t h e d e c r e a s e o f Rx/s t o t h e i n c r e a s e o f t h e e t h a n o l c o n c e n t r a t i o n i n t h e medium, ( E t h ) , a s : R
X/S
=
Y
(2)
X/S 1 +
with Y ^ g
(Eth)
4
t h e i n i t i a l yeast t o sugar the ethanol i n h i b i t i o n
yield
constant.
Y e a s t f l o c c u l a t i o n , an e s s e n t i a l phenomenon i n b e e r f e r m e n t a t i o n , i s i n f l u e n c e d by t h e medium c o m p o s i t i o n , e s p e c i a l l y by t h e g l u c o s e c o n c e n t r a t i o n , and i s d e l a y e d by t h e m i x i n g e f f e c t o f CO2 p r o d u c t i o n . The t i m e v a r i a t i o n o f t h e s u s p e n d e d y e a s t c o n c e n t r a t i o n i s t h u s t a k e n a s t h e d i f f e r e n c e between t h e g r o w t h and f l o c c u l a t i o n r a t e as : d(X ) T
dt
- k
dt K
CO,
(x )
(3)
s
G1
w i t h ( X ) t h e suspended y e a s t c o n c e n t r a t i o n 5
k
the yeast f l o c c u l a t i o n
f
constant
(Gl)
the glucose c o n c e n t r a t i o n
K
the i n h i b i t i o n constant o f f l o c c u l a t i o n
G1 k m d r
co
by g l u c o s e
t h e m i x i n g c o n s t a n t by CO^ t h e r a t e o f CO^ d e s o r p t i o n 2
In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
492
BIOCHEMICAL
ENGINEERING
Sugars consumption. Saccharose i s f i r s t hydrolysed i n t o g l u cose and f r u c t o s e a t the c e l l s u r f a c e , then the four fermentable sugars, glucose, f r u c t o s e , maltose and m a l t o t r i o s e are a s s i m i l a t e d at d i f f e r e n t r a t e s depending on the medium composition. Glucose i s taken up the f a s t e s t as the maltose, m a l t o t r i o s e and f r u c t o s e i n t r a c e l l u l a r t r a n s p o r t s are i n h i b i t e d by glucose. Assuming that the s u b s t r a t e s are mainly consumed by the suspended y e a s t s , the f o l l o wing r a t e expressions are proposed t o describe the time v a r i a t i o n of fermentable sugars : d(Gl) _ dt " " G1 K
(Gl) + (Gl)
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V
G 1
U
, S
γ ;
χ 180 d(Sac) " 342 d t
d(Mal) _ (Mal) dt " " Mal K + (Mal)
1 , (Gl) S
V
U
M a l
+
K
d(Sac) dt " * sac k
(
S
d(Mlt) .
c
)
(
J
, n ^ s
;
G1
(
(Mit)
- - Mit
χ
;
V 1
KMit Z T W- I
v
"dt
a
y
m K
V , , J
W
,
: 1— + (cry K G1
(
γ
6
)
χ
v
m (
7
)
1
K
d(Fr) _
~dF~~ " * F r K V
(Fr) 1 , . 180 d(Sac) + (Fr) ~ (GÎT V " 342 "dt Fr 1 + -prY
(
W
r
K
G1
with ( G l ) , (Mal), (Sac), ( M i t ) , ( F r ) the glucose, maltose, saccha rose, m a l t o t r i o s e and f r u c t o s e c o n c e n t r a t i o n . ^ G l ' ^Mal* ^ M l t ' V r ^ ^ ^ ^ °^ glucose, maltose, malto t r i o s e and f r u c t o s e consumption. i i i " ^Gl' ^ G l ' ^Gl 9 ^ i n h i b i t i o n constants n e m a x
m a
r a
e
f
u c o s e
k
K
K
K
K
k i n e t i c
c o n s t a n t s
s a c ' G1' M a l ' M l t ' F r The time v a r i a t i o n o f the t o t a l fermentable sugar concentra t i o n i s c a l c u l a t e d by adding the p r e v i o u s l y defined r a t e s o f v a r i a t i o n o f the c o n c e n t r a t i o n o f the i n d i v i d u a l sugars.
Amino a c i d s consumption. Two r a t e expressions were used. For threonine, s e r i n e , methionine, i s o l e u c i n e , l e u c i n e , l y s i n e , the r a t e o f consumption i s p r o p o r t i o n a l t o the r a t e o f yeast growth, but can be l i m i t e d by the amino a c i d c o n c e n t r a t i o n
In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
23.
MARC
ET
Kinetics
AL.
in Beer
493
Fermentation
(AA) being the amino a c i d c o n c e n t r a t i o n i n the medium the maximal r a t e of amino a c i d consumption a k i n e t i c constant. For other amino a c i d s , such as a s p a r t i c a c i d , glutamic a c i d , a l a n i n e , v a l i n e , t y r o s i n e , p h e n y l a l a n i n e , h i s t i d i n e , a r g i n i n e , an a d d i t i o n n a i i n h i b i t o r y e f f e c t of threonine demonstrated by expe riments w i t h threonine enriched wort, i s considered (AA)
d(AA) Downloaded by UNIV OF PITTSBURGH on August 13, 2015 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch023
dt
AA Κ
TThrT
+ (AA) ~
Δ
V
d (
1
n n ) v
dt
J
Thr w i t h K.^
the i n h i b i t i o n constant by threonine.
Ethanol p r o d u c t i o n . Ethanol production i s assumed d i r e c t l y r e l a t e d to the t o t a l r a t e of fermentable sugar consumption
Φ*
- - Vs
