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Calorimetric investigations into enzyme catalysed glucose oxidation
Ther,nochimt'ca Acta, 217 (1993) 1 - 7 E l s e v i e r S c i e n c e P u b l i s h e r s B.V., A m s t e r d a m
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Calorimetric investigations into enzyme catalysed glucose oxidation K. B o h m h a m m e l , R. Hfittl *, K. Pritzkat and G. W o l f Institute of Physical Chemistry, Bergakademie Freiberg, Leipziger Sir., D-9200 Freiberg (Germany) ( R e c e i v e d 21 A u g u s t 1992; a c c e p t e d 6 S e p t e m b e r 1992)
Abstract T h e s t u d y p r e s e n t s t h e results o f c a l o r i m e t r i c i n v e s t i g a t i o n s into e n z y m e c a t a l y s e d g l u c o s e o x i d a t i o n . It w a s s h o w n t h a t t h e c o n v e r t i b l e a m o u n t o f g l u c o s e is l i m i t e d by the availability o f t h e o x i d a n t o r m e d i a t o r : O2, K.~[Fe(CN),] a n d b e n z o q u i n o n e w e r e u s e d as m e d i a t o r s . T h e m e a s u r a b l e g l u c o s e c o n c e n t r a t i o n r a n g e w a s m u c h e x p a n d e d b y using b e n z o q u i n o n e . I n d e p e n d e n t l y of t h e m e d i a t o r used; t h e e n t h a l p y value for t h e o x i d a t i o n of g l u c o s e in t h e p r e s e n c e o f t h e e n z y m e g l u c o s e o x i d a s e was f o u n d to be A R H - - - 1 2 5 ± 2 kJ t o o l - ' . INTRODUCTION
The analytical • determination of •glucose is based u p o n its enzymecatalysed oxidation to o-glucono,5-1actone or D-gluconic acid and hydrogen peroxide; only /3:D-glucose is capable of this reaction. Possible oxidants or mediators include b e n z o q u i n o n e and potassium hexacyanoferrate, ~ in addition t o oxygen. The reaction can be quantitatively •indicated i n three ways: amperometrically [1], calorimetrically [2], or by measuring t h e concentration of one reactant (usually by photometry) [3]. The accurate k n o w l e d g e of the reaction conditions and Parameters is an indispensable prerequisite for research activities ~such as the d e v e l o p m e n t of a g l U c o s e sensor.
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.... This s t u d y c o m m u n i c a t e s t h e r e s u l t s of c a l o r i m e t r i c m e a s u r e m e n t s a t n o r m a l t e m p e r a t u r e as a basis for t h e d e v e l o p m e n t of a t h e r m a l s e n s o n T h e •influence of various m e d i a t o r s , the p r e s e n c e of catalase in addition•t 0 t h e e n z y m e glucose o x i d a s e and t h e •equilibrium Of m u t a r 0 t a t i o n on the m o l a r reaction e n t h a l p y were investigated. Q u a l i t a t i v e s t a t e m e n t s a r e m a d e •With •
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K. Bohmhamnlel et aL/Thermochim. Acta 217 (1993) i - 7
.••respect to: the Conversion rate. A s u b s e q u e n t s t u d y [4] p r e s e n t s the results iof a q u a n t i t a t i v e t h e r m o k i n e t i c analysis. M A T E R I A L S AND EQUIPMENT
. T h e glucose .oxidase (E.C. 1.1.3.4) used was f r o m A s p e r g i l l u s niger (Serva),. a n d h a d a. specific activity of. 2 5 0 U m g - ' (foreign activities 5 U m g ~ l catalase; 0.05% a - a m y l a s e , 0.05% i n v e r t a s e a n d 0.05% m a l t a s e ) , T h e specific activity of t h e e m p l o y e d c a t a l a s e (E.C. 1.11.1.6) f r o m •A s p e r g i l l u s n i g e r ( S e r v a ) was 1950 U m g -1. R e a g e n t - g r a d e c h e m i c a l s w e r e u s e d f o r all m e a s u r e m e n t s . A t e s t c a l i b r a t i o n buffer of p H = 6.86 (0.25 M K H 2 P O 4 - 0 . 2 5 M Na2HPO4) was u s e d . . : . T h e c a l o r i m e t r i e m e a s u r e m e n t s w e r e c a r r i e d o u t in an isoperibolic r e a c t i o n c a l o r i m e t e r [5]. U s u a l l y a b o u t 6 2 m l of an a q u e o u s solution of g l u c o s e , the m e d i a t o r s u b s t a n c e in different c o n c e n t r a t i o n s a n d p h o s p h a t e buffer (c = 0.1 M, p H = 6.86) w e r e m i x e d in the c a l o r i m e t r i c cell. T h e •reaction was •initiated by b r e a k i n g • a n a m p o u l e filled .with e n z y m e s o l u t i o n . B e c a u s e a n e v a l u a t i o n o f t h e t e m p e r a t u r e - t i m e g r a p h s in a c c o r d a n c e with D i c k i n s o n involved a hig h d e g r e e of u n c e r t a i n t y , in view of t h e long r e a c t i o n times ( u p to 100 m i n ) , the h e a t flow to the e n v i r o n m e n t w a s first c o r r e c t e d o n t h e b a s i s of an electrical calibration (in a c c o r d a n c e with: R e g n a u l t - P f a u n d l e r [6]). T h e r e s u l t i n g a d i a b a t i c t e m p e r a t u r e ' t i m e g r a p h s allow the d e t e r m i n a t i o n of b o t h ATm°x as r e q u i r e d for the calculation of the.. r e a c t i o n e n t h a l p y a n d the functions A T = A T ( t ) or • (a A T ~ a t ) =(19 A T I ~ t ) ( t )
w h i c h are n e c e s s a r y for kinetic analysis. . It•holds t h a t x]c ° = AT/ATm.x.
••where c ° =.total glucose c o n c e n t r a t i o n , x = c o n v e r t e d glucose c o n c e n t r a •t i o n at t i m e t, a n d A T = a d i a b a t i c t e m p e r a t u r e difference at t i m e t so t h a t . A T at-•time, t is.a m e a s u r e for the c o n v e r s i o n or the r e a c t i o n rate. c~..Ax. ' c ° . # A T ...-AT. .... :ATma, At . . . . . . . . . . . . . . . . . . . . . • .- ....
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-i. :The object, q u a n t i t i e s w e r e • d e t e r m i n e d b y w e i g h i n g . All m e a s u r e m e n t s :"refer to .a ••thermostatic t e m p e r a t u r e of the c a l o r i m e t e r of 2 9 8 K . T h e : / g i u c 0 s e c o n c e n t r a t i o n w a s v a r i e d o v e r t h e r a n g e 0 . 9 - 1 8 m m o l -I corres. . p o n d i n g t o a AT,,.~, Value b e t w e e n a b o u t • 16 a n d .250inK:,. T h u s ; a t : a m a x i m u m • • • r e a c t i o n . t i m e o f i 100 rain u p to. c o m p l e t e c o n v e r s i o n a n d a ':"
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K. B o h m h a m m e i et al./Therrnochim. A c t a 2 i 7 (1993) 1 - 7
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Fig. 1. A T - t i m e graphs for glucose solution (--) and a-glucose ( - - - ) v = 62.15 ml).
(m = 100rag,
l o n g - t e r m stability of the c a l o r i m e t e r of ±0.1 m K h -~, the lowest glucose c o n c e n t r a t i o n was still far a b o v e the detection• limit, w h i c h was a s s u m e d a t s o m e 0 . 0 5 m m o l l -t f o r an a s s u m e d e r r o r of ± 2 % , OXygen, p o t a s s i u m h e x a c y a n o f e r r a t e a n d b e n z o q u i n o n e w e r e used as mediators. DISCUSSION
In a c c o r d a n c e with t h e m u t a r o t a t i o n equilibrium, a ' g l u c o s e ( 3 8 % ) m p r e s e n t in solutions in a d d i t i o n to /3-glucose ( 6 2 % ) . T h e r e f o r e the first q u e s t i o n to be a n s w e r e d was w h e t h e r only t h e / 3 - f r a c t i 0 n would r e a c t , or w h e t h e r the m u t a r o t a t i o n r a t e would be sufficient for a total c o n v e r s i o n of the glucose, In c o n t r a s t to a calorimetric m e a s u r e m e n t (solution of glucose (c = 8.9 m m o l 1-1), b e n z o q u i n o n e (c = 15.6 m m o l 1-1) and buffer + glucose• oxidase (god) solution, a m e a s u r e m e n t w a s c a r r i e d o u t in which s o l i d a - g l u c o s e was a d d e d to a solution of equal c o n c e n t r a t i o n s of buffer, b e n z o q u i n o n e a n d god. T h e resulting • e n d o t h e r m i c solution effect w a s d e t e r m i n e d s e p a r a t e l y in an e x p e r i m e n t w i t h o u t g o d ( A L H = 10.04kJ m o l - l ) ; the p r e v i o u s m e a s u r e m e n t was t h e n c o r r e c t e d t o the p u r e reaction effect. Figure 1 shows •the two calorimetric curves (for glucose solution and ,v-glucose), : : .... .... It is e v i d e n t that• the ATm"~ value, and thus the •molar reaction e n t h a l p y , i s i n d e p e n d e n t of t h e initial c o m p o s i t i o n (glucose solutio n o r a - g ! u c g s e ) , T h i s m e a n s t h a t the m u t a r o t a t i o n rate• is so high t h a t a - g l u c o s e is c o n v e r t e d a s well, so t h a t t h e r e a c t i o n e n t h a l p y m u s t be related• to the •entire •object q u a n t i t y of t h e glucose. T h e A T - t i m e g r a p h ( F i g . 1) for a - g l u c o s e s h o w s t h e typical s h a p e of t h a t for a s u c c e s s i v e reaction, especially in t h e s t a r t i n g p h a s e . O n the whole,: the c o n v e r s i o n r a t e o f a ' g l u c o s e w a s lower t h a n t h a t of g l u c o s e •solution,• which w a s e x p e c t e d . .... : .... .
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It i s known• [7], and will be c o n f i r m e d in t h e followingi that the convertible amount of glucose i s limited by the available amount o f oxidants or mediators. If o x y g e n is used as a mediator, the limit at 25°C (in d e p e n d e n c e on t h e oxygen c o n c e n t r a t i o n ) is 2.36 x 1 0 -4 mol 1-1 f o r air-saturated solutions a n d 1.22 x 10 -3 tool I-1 for oxygen-saturated solutions. A s can be seen from Fig. 2, these limits can be proved b e y o n d doubt f r o m the calorimetrie c u r v e s , Sharp breaks can be observed in either case. With minor deviations, the ATK values assigned to the break points exactly c o r r e l a t e w i t h the above o x y g e n concentrations: c•(air)2.29 x 1 0 - ' mol 1-';
c~:(O2) = 1.18 x 10 -3 mol 1-1;
c lc*=ar lar ... T h e constant increase of the AT-t curve after the break ( e q u i v a l e n t to a c o n s t a n t reaction rate) is i n d e p e n d e n t of the glucose concentration, and is obviously controlled by the diffusion o f the oxygen from the gas phase (air or oxygen) into the solution. It is understandable that in the case of an oxygen a t m o s p h e r e (curve b in Fig. 2) this increase is greater than in the case of air (curve a in Fig. 2). The ratio of the increases b/a is about 4.8, i.e. exactly the same as the ratio of the oxygen partial pressures p,(O2)/p.(Oa). •The high-resolution calorimeter used in the experiments allows a reliable determination Of the entire reaction effect and thus of ARH; nevertheless, t h e u p p e r limit for the thermometric determination of the glucose concentration appears to be the limit fixed by the oxygen concentration in the solution. A s discussed in refs. 8 and 9, this limit can be c o m p l e t e l y eliminated (1) for an addition of the e n z y m e catalase to the pair, or (2) for the use of a different mediator. A m o n g others, potassium hexacyanoferrate and b e n z o q u i n o n e [10, 11] are k n o w n as substitutes for oxygen. Calorimetric m e a s u r e m e n t s with K3[Fe(CN)~] as a mediator s h o w that a vast excess of K3[Fe(CN),] in .
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Fig. 3. C a l o r i m e t r i c curves, CG, " 1.34 m m o l i-r; c u r v e a, a i r - s a t u r a t e d solution; curve b, N2 a t m o s p h e r e , with n ( g l u c o s e ) : n(K.,[Fe(CN)~,])--1:55.
relation to stoichiometric conversion is n e e d e d t o obtain reaction rates allowing a n evaluation of the calorimetric curve. Figure 3 compares two calorimetric curves. It is evident that even for a vast excess of K.~[Fe(CN)~] the •attainable reaction rates are in the same range as for an air-saturated solution. H e n c e K3[Fe(CN)~] does not a p p e a r to be a suitable •mediator. A different situation is created when b e n z o q u i n o n e is used as a m e d i a t o r . For equal glucose concentrations below the s a t u r a t i o n concentration of oxygen, the calorimetric curves for oxygen and b : n z o q u i n o n e are absoI, utely identical within th e error limits, i.e. the same reaction rates as•with oxygen can be attained with benzoquinone. T h e s e are some further conclusions from this experiment: (1) the reaction rate is i n d e p e n d e n t of the m e d i a t o r concentration. This is also c o n f i r m e d by m e a s u r e m e n t s with different b e n z o q u i n o n e concentrations; (2) the conversion o f t h e reduced form • o f glucose oxidase t o t h e oxidized form by means of the m e d i a t o r is effected so rapidly t h a t this reaction stage does not exert any influence on the overall reaction •rate;• (3) for the given p H value of the solution (6.86), the oxidation potential of K3[Fe(CN)6] is greater than that of benzoquinone; therefore the unexpectedly small effect of K3[Fe(CN)6] can be explained only b y the reaction kinetics. It must b e assumed that t h e oxidation of the r e d u c e d glucose o x i d a s e is connected •with hydrogen transfer f a t h e r • t h a n electron transfer. H y d r o g e n transfer is excluded for Ka[Fe(CN)6], whereas it~is possible for oxygen and benzoquinone. ..... ~ Calorimetric m e a s u r e m e n t s with b e n z o q u i n o n e as a mediator•• were performed in the glucose concentration range b e t w e e n 0.8 and 1•8 m m o l 1-:!, A kinetic analysis allows statements •concerning••the r e a c t i o n order, t h e functional d e p e n d e n c e of~ t h e r e a c t i o n • rate o n : glucose and enzyme • concentration, the enzyme activity, a n d the determination of the Michaelis :.i i...' . .
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Acta217
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Number of
Mediator
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measurements god god
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127.1 -4- 4.3 123.3 -4- 5.6 •124.9 4- 4.0 125.3 -!- 1.8 127.4 4- 2.5 223.3 ± 1.9
10 10 4 4 7
K.~[Fe(CN),] ÷ Oa Benzoquinone
god + catalase
i24.0.4- 4
12 12
BenzoqUinone Oxygen K.a[Fe(CN),,] + air K~[Fe(CN),] + air K~[Fe(CN)~,] q- N:,
god,
constant KM. T h e s e questions will be discussed in detail in a subsequent study [4]. All m e a s u r e m e n t s were e v a l u a t e d with respect to the overall reaction e f f e c t •ARH. : A n overview• is g i v e n in Table 1. I n d e p e n d e n t l y of t h e mediator, the enthalpy v a l u e of the oxidation of glucose in the presence of t h e enzyme glucose oxydase was found to be A R H - --125 ± 2 kJ mol -~. As expected, :this Value was increased by some - 1 0 0 kJ mo1-1 in the presence of catalase. T h e difference is almost equal t o the r e a c t i o n entha!py of the decomposition r e a c t i o n . • H~O2(aq)
, H 2 0 + 0.502(g)
ARHe(298) = 100.06 kJ m o l - '
A l l l i t e r a t u r e data originate from the m e a s u r e m e n t s by Schmidt et al. [12]. Fo r the Oxidation of glucose in the presence of glucose oxidase and c a t a l a s e , a value of ARH = - 2 0 7 . 2 kJ mol -t is gl,/en, i.e. a value 7% below that m e a s u r e d by us. Since Schmidt et al. [12] u s e d immobilized enzymes, • an incomplete reaction•can be assumed, which would explain the lower value. .
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REFERENCES
1 T!Bayer, T. H.er0!d,R. Hiddessen and:K: SchUgell,Anal. Ch!m.. Act, 190 0986)213. .i. 2 H.G. Hundeck, A. Safierbrei, U . HUbner, T. Scheper, K. SchUgerl, R. Koch and G. ; i Antranikian, Anal.• .Chim: Acta, 238 (1990) 211 and references therein. 3 M . B . : G a r n , A,: S P i e ! m a n n , H. Lud i. and. . .H.M. . . . . . . . . .Widmer, . . . . . . . . . . . . .Proc, . . . . . . . .5th .. Eur. C o...... ngr. i-:- .... :iBiotechnol., Copenhagen, 1990, p. 1029. • 4 G. Wolf, K. B o h m h a m m e l , R. HUttl and K. Pritzkat, to b e published. 5 G, Wolf,: Nauchn. Apparat., 1 • ( 4 ) ( 1 9 8 6 ) 7 6 . " ....6 W . H e m m i n g e r and G.: H~Shne, Grundlagen der Kalorimetrie, A k a d e m i e - V e r i a g , ' Berlin; 1 9 7 9 , " ......... : : .... : ..... 7 M J . Muelbauer, EiJ. Guilbeau and B.C, Towe, Anal. C h e m . , 6 1 (!989) 77. . : 8 B.I Danielssoni K.L. Gadd, B. Mathiasson and K. Mosbach, Clin, Chim, Acta, 81 (1977) •:._ 163. " :: _: i . . . . :" ".
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N. Kiba and M. Furusawa, Methods Enzymol., 137 (188) 225. :, ..... G. Geppert and L. Asperger, Bioeleetrochem. Bioenerg., 17 (1987) 399. . . . . . . . . . . J.R. Mor and R. Guarnaecia, Anal. Bioehem., 79 (1977) 319. H.L. Sehmidt, G. Krisam and G. Grenner, Biochirn. Biophys. Aeta, 429 (1976) 283.
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Calorimetric investigations into enzyme catalysed glucose oxidation K. B o h m h a m m e l , R. Hfittl *, K. Pritzkat and G. W o l f Institute of Physical Chemistry, Bergakademie Freiberg, Leipziger Sir., D-9200 Freiberg (Germany) ( R e c e i v e d 21 A u g u s t 1992; a c c e p t e d 6 S e p t e m b e r 1992)
Abstract T h e s t u d y p r e s e n t s t h e results o f c a l o r i m e t r i c i n v e s t i g a t i o n s into e n z y m e c a t a l y s e d g l u c o s e o x i d a t i o n . It w a s s h o w n t h a t t h e c o n v e r t i b l e a m o u n t o f g l u c o s e is l i m i t e d by the availability o f t h e o x i d a n t o r m e d i a t o r : O2, K.~[Fe(CN),] a n d b e n z o q u i n o n e w e r e u s e d as m e d i a t o r s . T h e m e a s u r a b l e g l u c o s e c o n c e n t r a t i o n r a n g e w a s m u c h e x p a n d e d b y using b e n z o q u i n o n e . I n d e p e n d e n t l y of t h e m e d i a t o r used; t h e e n t h a l p y value for t h e o x i d a t i o n of g l u c o s e in t h e p r e s e n c e o f t h e e n z y m e g l u c o s e o x i d a s e was f o u n d to be A R H - - - 1 2 5 ± 2 kJ t o o l - ' . INTRODUCTION
The analytical • determination of •glucose is based u p o n its enzymecatalysed oxidation to o-glucono,5-1actone or D-gluconic acid and hydrogen peroxide; only /3:D-glucose is capable of this reaction. Possible oxidants or mediators include b e n z o q u i n o n e and potassium hexacyanoferrate, ~ in addition t o oxygen. The reaction can be quantitatively •indicated i n three ways: amperometrically [1], calorimetrically [2], or by measuring t h e concentration of one reactant (usually by photometry) [3]. The accurate k n o w l e d g e of the reaction conditions and Parameters is an indispensable prerequisite for research activities ~such as the d e v e l o p m e n t of a g l U c o s e sensor.
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.... This s t u d y c o m m u n i c a t e s t h e r e s u l t s of c a l o r i m e t r i c m e a s u r e m e n t s a t n o r m a l t e m p e r a t u r e as a basis for t h e d e v e l o p m e n t of a t h e r m a l s e n s o n T h e •influence of various m e d i a t o r s , the p r e s e n c e of catalase in addition•t 0 t h e e n z y m e glucose o x i d a s e and t h e •equilibrium Of m u t a r 0 t a t i o n on the m o l a r reaction e n t h a l p y were investigated. Q u a l i t a t i v e s t a t e m e n t s a r e m a d e •With •
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.••respect to: the Conversion rate. A s u b s e q u e n t s t u d y [4] p r e s e n t s the results iof a q u a n t i t a t i v e t h e r m o k i n e t i c analysis. M A T E R I A L S AND EQUIPMENT
. T h e glucose .oxidase (E.C. 1.1.3.4) used was f r o m A s p e r g i l l u s niger (Serva),. a n d h a d a. specific activity of. 2 5 0 U m g - ' (foreign activities 5 U m g ~ l catalase; 0.05% a - a m y l a s e , 0.05% i n v e r t a s e a n d 0.05% m a l t a s e ) , T h e specific activity of t h e e m p l o y e d c a t a l a s e (E.C. 1.11.1.6) f r o m •A s p e r g i l l u s n i g e r ( S e r v a ) was 1950 U m g -1. R e a g e n t - g r a d e c h e m i c a l s w e r e u s e d f o r all m e a s u r e m e n t s . A t e s t c a l i b r a t i o n buffer of p H = 6.86 (0.25 M K H 2 P O 4 - 0 . 2 5 M Na2HPO4) was u s e d . . : . T h e c a l o r i m e t r i e m e a s u r e m e n t s w e r e c a r r i e d o u t in an isoperibolic r e a c t i o n c a l o r i m e t e r [5]. U s u a l l y a b o u t 6 2 m l of an a q u e o u s solution of g l u c o s e , the m e d i a t o r s u b s t a n c e in different c o n c e n t r a t i o n s a n d p h o s p h a t e buffer (c = 0.1 M, p H = 6.86) w e r e m i x e d in the c a l o r i m e t r i c cell. T h e •reaction was •initiated by b r e a k i n g • a n a m p o u l e filled .with e n z y m e s o l u t i o n . B e c a u s e a n e v a l u a t i o n o f t h e t e m p e r a t u r e - t i m e g r a p h s in a c c o r d a n c e with D i c k i n s o n involved a hig h d e g r e e of u n c e r t a i n t y , in view of t h e long r e a c t i o n times ( u p to 100 m i n ) , the h e a t flow to the e n v i r o n m e n t w a s first c o r r e c t e d o n t h e b a s i s of an electrical calibration (in a c c o r d a n c e with: R e g n a u l t - P f a u n d l e r [6]). T h e r e s u l t i n g a d i a b a t i c t e m p e r a t u r e ' t i m e g r a p h s allow the d e t e r m i n a t i o n of b o t h ATm°x as r e q u i r e d for the calculation of the.. r e a c t i o n e n t h a l p y a n d the functions A T = A T ( t ) or • (a A T ~ a t ) =(19 A T I ~ t ) ( t )
w h i c h are n e c e s s a r y for kinetic analysis. . It•holds t h a t x]c ° = AT/ATm.x.
••where c ° =.total glucose c o n c e n t r a t i o n , x = c o n v e r t e d glucose c o n c e n t r a •t i o n at t i m e t, a n d A T = a d i a b a t i c t e m p e r a t u r e difference at t i m e t so t h a t . A T at-•time, t is.a m e a s u r e for the c o n v e r s i o n or the r e a c t i o n rate. c~..Ax. ' c ° . # A T ...-AT. .... :ATma, At . . . . . . . . . . . . . . . . . . . . . • .- ....
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(m = 100rag,
l o n g - t e r m stability of the c a l o r i m e t e r of ±0.1 m K h -~, the lowest glucose c o n c e n t r a t i o n was still far a b o v e the detection• limit, w h i c h was a s s u m e d a t s o m e 0 . 0 5 m m o l l -t f o r an a s s u m e d e r r o r of ± 2 % , OXygen, p o t a s s i u m h e x a c y a n o f e r r a t e a n d b e n z o q u i n o n e w e r e used as mediators. DISCUSSION
In a c c o r d a n c e with t h e m u t a r o t a t i o n equilibrium, a ' g l u c o s e ( 3 8 % ) m p r e s e n t in solutions in a d d i t i o n to /3-glucose ( 6 2 % ) . T h e r e f o r e the first q u e s t i o n to be a n s w e r e d was w h e t h e r only t h e / 3 - f r a c t i 0 n would r e a c t , or w h e t h e r the m u t a r o t a t i o n r a t e would be sufficient for a total c o n v e r s i o n of the glucose, In c o n t r a s t to a calorimetric m e a s u r e m e n t (solution of glucose (c = 8.9 m m o l 1-1), b e n z o q u i n o n e (c = 15.6 m m o l 1-1) and buffer + glucose• oxidase (god) solution, a m e a s u r e m e n t w a s c a r r i e d o u t in which s o l i d a - g l u c o s e was a d d e d to a solution of equal c o n c e n t r a t i o n s of buffer, b e n z o q u i n o n e a n d god. T h e resulting • e n d o t h e r m i c solution effect w a s d e t e r m i n e d s e p a r a t e l y in an e x p e r i m e n t w i t h o u t g o d ( A L H = 10.04kJ m o l - l ) ; the p r e v i o u s m e a s u r e m e n t was t h e n c o r r e c t e d t o the p u r e reaction effect. Figure 1 shows •the two calorimetric curves (for glucose solution and ,v-glucose), : : .... .... It is e v i d e n t that• the ATm"~ value, and thus the •molar reaction e n t h a l p y , i s i n d e p e n d e n t of t h e initial c o m p o s i t i o n (glucose solutio n o r a - g ! u c g s e ) , T h i s m e a n s t h a t the m u t a r o t a t i o n rate• is so high t h a t a - g l u c o s e is c o n v e r t e d a s well, so t h a t t h e r e a c t i o n e n t h a l p y m u s t be related• to the •entire •object q u a n t i t y of t h e glucose. T h e A T - t i m e g r a p h ( F i g . 1) for a - g l u c o s e s h o w s t h e typical s h a p e of t h a t for a s u c c e s s i v e reaction, especially in t h e s t a r t i n g p h a s e . O n the whole,: the c o n v e r s i o n r a t e o f a ' g l u c o s e w a s lower t h a n t h a t of g l u c o s e •solution,• which w a s e x p e c t e d . .... : .... .
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It i s known• [7], and will be c o n f i r m e d in t h e followingi that the convertible amount of glucose i s limited by the available amount o f oxidants or mediators. If o x y g e n is used as a mediator, the limit at 25°C (in d e p e n d e n c e on t h e oxygen c o n c e n t r a t i o n ) is 2.36 x 1 0 -4 mol 1-1 f o r air-saturated solutions a n d 1.22 x 10 -3 tool I-1 for oxygen-saturated solutions. A s can be seen from Fig. 2, these limits can be proved b e y o n d doubt f r o m the calorimetrie c u r v e s , Sharp breaks can be observed in either case. With minor deviations, the ATK values assigned to the break points exactly c o r r e l a t e w i t h the above o x y g e n concentrations: c•(air)2.29 x 1 0 - ' mol 1-';
c~:(O2) = 1.18 x 10 -3 mol 1-1;
c lc*=ar lar ... T h e constant increase of the AT-t curve after the break ( e q u i v a l e n t to a c o n s t a n t reaction rate) is i n d e p e n d e n t of the glucose concentration, and is obviously controlled by the diffusion o f the oxygen from the gas phase (air or oxygen) into the solution. It is understandable that in the case of an oxygen a t m o s p h e r e (curve b in Fig. 2) this increase is greater than in the case of air (curve a in Fig. 2). The ratio of the increases b/a is about 4.8, i.e. exactly the same as the ratio of the oxygen partial pressures p,(O2)/p.(Oa). •The high-resolution calorimeter used in the experiments allows a reliable determination Of the entire reaction effect and thus of ARH; nevertheless, t h e u p p e r limit for the thermometric determination of the glucose concentration appears to be the limit fixed by the oxygen concentration in the solution. A s discussed in refs. 8 and 9, this limit can be c o m p l e t e l y eliminated (1) for an addition of the e n z y m e catalase to the pair, or (2) for the use of a different mediator. A m o n g others, potassium hexacyanoferrate and b e n z o q u i n o n e [10, 11] are k n o w n as substitutes for oxygen. Calorimetric m e a s u r e m e n t s with K3[Fe(CN)~] as a mediator s h o w that a vast excess of K3[Fe(CN),] in .
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relation to stoichiometric conversion is n e e d e d t o obtain reaction rates allowing a n evaluation of the calorimetric curve. Figure 3 compares two calorimetric curves. It is evident that even for a vast excess of K.~[Fe(CN)~] the •attainable reaction rates are in the same range as for an air-saturated solution. H e n c e K3[Fe(CN)~] does not a p p e a r to be a suitable •mediator. A different situation is created when b e n z o q u i n o n e is used as a m e d i a t o r . For equal glucose concentrations below the s a t u r a t i o n concentration of oxygen, the calorimetric curves for oxygen and b : n z o q u i n o n e are absoI, utely identical within th e error limits, i.e. the same reaction rates as•with oxygen can be attained with benzoquinone. T h e s e are some further conclusions from this experiment: (1) the reaction rate is i n d e p e n d e n t of the m e d i a t o r concentration. This is also c o n f i r m e d by m e a s u r e m e n t s with different b e n z o q u i n o n e concentrations; (2) the conversion o f t h e reduced form • o f glucose oxidase t o t h e oxidized form by means of the m e d i a t o r is effected so rapidly t h a t this reaction stage does not exert any influence on the overall reaction •rate;• (3) for the given p H value of the solution (6.86), the oxidation potential of K3[Fe(CN)6] is greater than that of benzoquinone; therefore the unexpectedly small effect of K3[Fe(CN)6] can be explained only b y the reaction kinetics. It must b e assumed that t h e oxidation of the r e d u c e d glucose o x i d a s e is connected •with hydrogen transfer f a t h e r • t h a n electron transfer. H y d r o g e n transfer is excluded for Ka[Fe(CN)6], whereas it~is possible for oxygen and benzoquinone. ..... ~ Calorimetric m e a s u r e m e n t s with b e n z o q u i n o n e as a mediator•• were performed in the glucose concentration range b e t w e e n 0.8 and 1•8 m m o l 1-:!, A kinetic analysis allows statements •concerning••the r e a c t i o n order, t h e functional d e p e n d e n c e of~ t h e r e a c t i o n • rate o n : glucose and enzyme • concentration, the enzyme activity, a n d the determination of the Michaelis :.i i...' . .
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127.1 -4- 4.3 123.3 -4- 5.6 •124.9 4- 4.0 125.3 -!- 1.8 127.4 4- 2.5 223.3 ± 1.9
10 10 4 4 7
K.~[Fe(CN),] ÷ Oa Benzoquinone
god + catalase
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BenzoqUinone Oxygen K.a[Fe(CN),,] + air K~[Fe(CN),] + air K~[Fe(CN)~,] q- N:,
god,
constant KM. T h e s e questions will be discussed in detail in a subsequent study [4]. All m e a s u r e m e n t s were e v a l u a t e d with respect to the overall reaction e f f e c t •ARH. : A n overview• is g i v e n in Table 1. I n d e p e n d e n t l y of t h e mediator, the enthalpy v a l u e of the oxidation of glucose in the presence of t h e enzyme glucose oxydase was found to be A R H - --125 ± 2 kJ mol -~. As expected, :this Value was increased by some - 1 0 0 kJ mo1-1 in the presence of catalase. T h e difference is almost equal t o the r e a c t i o n entha!py of the decomposition r e a c t i o n . • H~O2(aq)
, H 2 0 + 0.502(g)
ARHe(298) = 100.06 kJ m o l - '
A l l l i t e r a t u r e data originate from the m e a s u r e m e n t s by Schmidt et al. [12]. Fo r the Oxidation of glucose in the presence of glucose oxidase and c a t a l a s e , a value of ARH = - 2 0 7 . 2 kJ mol -t is gl,/en, i.e. a value 7% below that m e a s u r e d by us. Since Schmidt et al. [12] u s e d immobilized enzymes, • an incomplete reaction•can be assumed, which would explain the lower value. .
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REFERENCES
1 T!Bayer, T. H.er0!d,R. Hiddessen and:K: SchUgell,Anal. Ch!m.. Act, 190 0986)213. .i. 2 H.G. Hundeck, A. Safierbrei, U . HUbner, T. Scheper, K. SchUgerl, R. Koch and G. ; i Antranikian, Anal.• .Chim: Acta, 238 (1990) 211 and references therein. 3 M . B . : G a r n , A,: S P i e ! m a n n , H. Lud i. and. . .H.M. . . . . . . . . .Widmer, . . . . . . . . . . . . .Proc, . . . . . . . .5th .. Eur. C o...... ngr. i-:- .... :iBiotechnol., Copenhagen, 1990, p. 1029. • 4 G. Wolf, K. B o h m h a m m e l , R. HUttl and K. Pritzkat, to b e published. 5 G, Wolf,: Nauchn. Apparat., 1 • ( 4 ) ( 1 9 8 6 ) 7 6 . " ....6 W . H e m m i n g e r and G.: H~Shne, Grundlagen der Kalorimetrie, A k a d e m i e - V e r i a g , ' Berlin; 1 9 7 9 , " ......... : : .... : ..... 7 M J . Muelbauer, EiJ. Guilbeau and B.C, Towe, Anal. C h e m . , 6 1 (!989) 77. . : 8 B.I Danielssoni K.L. Gadd, B. Mathiasson and K. Mosbach, Clin, Chim, Acta, 81 (1977) •:._ 163. " :: _: i . . . . :" ".
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