Calorimetric Studies on the Mutarotation of D-Galactose and D

J. Biochem., 73, 763-770 (1973)

Calorimetric Studies on the Mutarotation of

Katsutada TAKAHASHI** and Sozaburo ONO Laboratory of BiophysicalChemistry, College of Agriculture, University of Osaka Prefecture, Sakai

Receivedfor publication, September 11, 1972

1. Calorimetric measurements were made on the heat change accompanying the mutarotation on D-galactose and D-mannose to evaluate quantitatively the anomeric stability of the two sugars in aqueous solution. 2. It was found that in D-galactose the ƒÀ-anomer is 1,300•}50 J mol-1*** energetically more stable than the ƒ¿-anomer, while in D-mannose the a-anomer is 1,900•}80 J mol-1 more stable than the ƒÀ-anomer at 25•Ž. 3. From stereochemical considerations regarding D-mannose, D-galactose, D-glucose, and D-xylose, it was assumed that the hydroxyl group on C2 in the pyranose ring

plays a major role in determining the preferred form of the anomeric pairs. 4. By combining the data with those reported for the isomerization of eq-D-glucose to eq-D-mannose, the energies required for the conversion of a hydroxyl group on C2 of a-D-glucose and ƒÀ-D-glucose in chair-1 form from equatorial to axial were esti- mated to be 7,950 J mol-1 and 10,880 J mol-1, respectively.

Conformational stability of pyranose rings has for each a-ƒÀ anomer pair the predominant been considered by Reeves (2) on the basis component in an equilibrium mixture can be of substituent effects. He concluded that any deduced from weighing the above instability substituent other than hydrogen oriented per- factors. In this connection, Sundararajan pendicular to the pyranose ring, introduces and Rao (3) made a potential energy calcu- an instability into the conformation, and that lation for various hexo-, and pentopyranoses in gaseous molecular models using the Kitay- * Presented in part at the 2nd Japanese Calorimetry gorodsky functions ( 4 ). Conference, Tokyo, November 1966 and in part at However, it seems that changes in the the 20th Annual Meeting of the Chemical Society relative position of substituents in pyranose of Japan, Tokyo, April 1967. ** To whom corre- rings have not yet been quantitatively related spondence should be sent. *** In accordance with the decision of IUPAC (International Union of Pure and to the stability of anomers in solution. Applied Chemistry) in 1969 concerning the use of One of the most common experimental symbols, terminology and units ( 1 ), all the thermo- approaches to this problem is obviously the dynamic quantities are given in Joule units, J, in investigation of differences in the ther- this article. For conversion from Joules to calories, modynamic quantities of the anomers. the coefficient 4.184 J cal-1 may be used. For some sugars it is possible to determine

Vol.73, No.4, 1973 763 764 K. TAKAHASHI and S. ONO, the thermodynamic quantities ; while free ed polarimetrically by using the following energy difference between ƒ¿- and ƒÀ-anomers values for optical rotation in water at 20•Ž in solution may be calculated from the con- (8, 9); centration ratio of a to ƒÀ in the equilibrium α一D-galactose 【α】D=十144 mixture, enthalpy change can be obtained β一D-galactose [α]D=十52 most accurately by direct calorimetric meas- α-D-mannose [α]D=十30 urement of the heat changes during the β一D-mannose [α]D=-17 mutarotation process.* Direct calorimetric measurements of mu- It was found that the composition of the tarotation have been made on D-glucose by D-mannose sample was 83% a-anomer and 17 Sturtevant (5) and on D-glucose, D-xylose, % ƒÀ-anomer, * while that of D-galactose sample: cellobiose, lactose, and maltose by Kabayama was 100% pure a-anomer, both within the. et al. (6). limits of analysis. In the present study, measurements were Apparatus and Procedure-The calori- calorimetrically attempted on the mutarota- meter used was essentially of a constant-tem- tion process of D-galactose and D-mannose to perature environment type (isoperibol type) obtain further information about the stability with a thermistor as the temperature sensor. of pyranose rings in aqueous solution. The structure of calorimeter is shown in Fig. 1. A Dewar vessel (D) , about 50 cm3 in vol- EXPERIMENTAL ume, provided with a bakelite lid(L) having Materials-Both the sugars studied were a thermistor(T), a heater(H), and a stirrer(S), of the purest grade, purchased from Wako served as a reaction cell. Pure Chemicals, Osaka (D-galactose, mp The thermistor(T) (CS 503, TOA Electro- 167•Ž) and from Shimakyu Pure Chemicals, nics Ltd., Tokyo) with B-values of 3,200 •‹K. Osaka (D-mannose, mp 132•Ž). They were and resistance of 52.41 kƒ¶,at 25•Ž was con- used after vacuum drying at 80•Ž for three nected to a certified DC-Wheatstone bridge:

days. The anomer compositions were examin- placed in an air-thermostat. The potential. derived from the bridge was amplified and . continuously recorded. The sensitivity was. 28.65 mV•EK-1 at 25•Ž. As the temperature change is small (several hundredths of a de-

gree), a linear relationship between the temperature rise and the bridge potential has been assumed. The heater (H) made from platinum wire: having a resistance of 24.509 ƒ¶ at 25•Ž was used for calibration, i.e., determination of the heat capacity. The heater was also used for compensation of the large endothermic heat of sample dissolution, which should be dis- tinguished from the heat change due to mutarotation.

Fig.1. Calorimeter structure. * Because of technical reason in doing calorimetry , a material which shows the highest dissolution rate * In some cases it is also possible to deduce the at the mixing with buffer solution was chosen out enthalpy values from the temperature dependence of several specimens. In the case of D-mannose of the equilibrium constant by using the van't Hoff study, however, the sample chosen was unfortunately relation. Such data, that are less reliable, are given not in a pure anomer form but was a mixture of in the review of Isbell and Pigman ( 7 ). α-and β-anomers.

J. Biochem. CALORIMETRY ON MUTAROTATION OF SUGARS 765

The stirrer(S) was a glass propeller con- tion was durated for 5 min* and the rotation nected to a synchronous motor. Its rotation rate was then reduced to 300 rpm. The bridge speed could be adjusted in two steps; 300 and output voltage was recorded for 40 min and 2,000 rpm. The higher rate was employed the temperature-time curve, which was due only for sample dissolution at the initiation to mutarotation alone, was analyzed by apply- of the calorimetric run. ing the kinetic equation, including the mu- An accurately weighed sample (2 to 5 g) tarotation rate constant described later. was placed in the Dewar vessel(D). The buffer Mutarotation Rate Constants-There seems solution (20 cm3, 0.025 M acetate buffer, pH to be some evidence that the mutarotation of 4.5) was held in a cylindrical buffer holder certain sugars does not follow simple first- (B) which was suspended from the lid(L) by order kinetics (10). Isbell and Pigman (11) a control shaft(C). The holder had a thin reported in their study on sugar mutarota- rubber film(R) at its bottom which was broken tions made in 1937 that both D-galactose and by a needle tip(N) when the holder was raised D-mannose show a complex mutarotation in up via the control shaft(C). Because of the water. However, in the present study we tensile force of the rubber film, the bottom have carefully performed measurements on of the cylindrical holder(B) was fully opened these two sugars in buffered solutions of at the instant of film breakage so that the various pH values using an advanced recording

buffer solution was allowed to contact quickly polarimeter, and we found that their mutarota- the whole of the sugar. tions obey a first-order law over a pH range Since the rate of mutarotation was de- from 3 to 7 and show the minimum rate at

pendent upon pH, measurements were per- pH 4.5. formed with a buffered solution at pH 4.5, The polarimeter used was a Yanagimoto where the mutarotation obeyed first-order ORD-185 spectropolarimeter with a quartz kinetics with the minimum rate constant. cuvette of 1 cm optical path. The change in After the whole assembly was put in place, optical rotation with time was recorded at the the calorimeter was submerged in a water fixed wavelength of 370 nm and was analyzed thermostat at 25•}0.001•Ž and left for three by the Guggenheim method (12), which is to four hours. commonly used for the analysis of reaction When thermal equilibrium had been kinetics. From a Guggenheim plot of the reached, as judged from the recorder chart, the optical rotation curve, the rate constants of rotation rate of the stirrer was raised to 2,000 mutarotation in buffered solution at pH 4.5 rpm and electrical heating was started by were obtained as 0.03205 min-1 and 0.06496 sending a known amount of electric current min-1 for D-galactose and D-mannose, respec-

(273 mA). Five seconds later the control shaft tively, at 25•Ž. (C) was raised to break the rubber film for sample dissolution. THEORY Electrical heating to compensate for the endothermic dissolution heat was durated for Kinetic Analysis of the Temperature-time 12 to 23 sec. The compensation was control- Curve-If one defines g(t) as the observed tem- led almost empirically by watching the am- perature change at time t in the calorimeter,

plifier scale in such a manner that the bridge the true temperature change of a thermal output voltage finally attained nearly zero. process corrected for the heat exchange Stirring at 2,000 rpm for sample dissolu- through the calorimeter wall, f(t), which is re- garded as a hypothetical adiabatic change, is given by the following equation (13); * In a separate dissolution test , the apparent first- order rate constant of dissolution in the present (1) system was found to be 2.1 min-1. This indicates that sample dissolution is achieved to the extent of 99.9985% in 5 min. where K is a constant termed the"cooling

Vol.73, No.4, 1973 766 K. TAKAHASHI and S. ONO

constant" or "heat conductivity constant" of The validity of this kinetic analysis of the the system. temperature-time curve was checked using If there is a temperature difference, Td, the hydrolytic reaction of sucrose. Since the between the calorimeter and its surroundings acid hydrolysis of sucrose, whose reaction heat at the instant when the thermal process starts is well established (14-16), is known to obey and if the system involves any source of heat first-order kinetics, the temperature-time curve evolution, w, such as heat of stirring, other observed by calorimetry on this reaction was than the thermal process to be studied, the analyzed to evaluate the reaction heat ac- equation is revised as follows ; cording to the theory described above. The result was obtained that the enthalpy of. (2) sucrose hydrolysis is ƒ¢K=-15,820•}=170 J mol-1 which is in good agreement with the reported. value, ƒ¢H=-14,910•}280 J mo1-1 (15). Methods of computing the heat exchange

term, •çg(t)dt, and obtaining the hypothetical RESULTS

adiabatic change of the system, f(t), have Figure 2 shows typical examples of chart re- been described previously (13). cordings observed during calorimetric runs on If the reaction to be studied follows first- the mutarotation of (a) D-galactose and (b) D order kinetics with a rate constant of k min-1 mannose , respectively. and is accompanied by a heat evolution of q It is obvious that the heat change due to joule per gram of reactant, then the thermal mutarotation of D-galactose to give anomeric process, f(t), will be expressed in kinetic terms equilibrium is exothermic, while that of D- by the equation; mannose is endothermic. At the points in dicated by arrows, the reading of the recorder (3) chart was taken as g(t)=0 at t=0; the devia- tions from this scale were taken as apparent temperature changes due to mutarotation, where m is the amount of reactant in grams and C is the heat capacity of the whole system g(t), and were analyzed by Eq. 5. in J K-1.* Two typical Plots of (g(t)+K∫9(t)dt)/Kt Substituting Eq. 3 into Eq. 2, one obtains, against (1-e-t-kt)/Kt are shown in Fig. 3 ((a) D-galactose; (b) D-mannose). The plots give a straight line with a slope of qm/C, from (4) which the heat evolution per gram of the. or sample, q, can be calculated. The values of q thus obtained for total: runs are summarized in Table I (third column). Since during measurement the reading of the recorder chart was initiated some time (5) after sample dissolution (ts min, as indicated Thus, if the first-order rate constant, k, in the fourth column of Table I), the correc- is known, the heat evolution, q, can be ob- tion for heat evolution due to mutarotation tained from the above equation by plotting during the period is was made using the following equation;

(g(t)+K∫g(t)dt)/Kt against(1-e-kt)/Kt. (6)

* J K-1=1/4 .184 cal/•Ž as a heat capacity unit. K The fifth column of Table 1 gives thus

is the temperature unit on the Kelvin scale, read as corrected values for each calorimetric run. "degree kelvin ." The heat evolution due to mutarotation

J. Biochem_ CALORIMETRY ON MUTAROTATION OF SUGARS 767

(a) D-galactose (100%a-form)

(b) D-mannose (83%a-form)

Fig. 2. Chart recordings during mutarotation calorimetry of (a) D-

galactose and (b) D-mannose in buffered solution of pH 4.5 at 25•Ž.

for D-galactose and D-mannose, respectively. (a) D-galactose (100%a-form) The heat evolutions of the anomeric conversion from a to 13 were derived from the above values by using the percent compositions of a- and ƒÀ-anomers in the starting and final (equilibrium) solutions. The results are

given in Table II. The molar enthalpy changes for the conversion from ƒ¿- to j3-anomers were found to be ƒ¢H=- 1,300•}50 J mo1-1* and ƒ¢H=+1,900 ±80 J mol-1* for D-galactose and D-mannose (b) D-mannose (83%a-form) at 25•Ž, respectively.

DISCUSSION

The percentages of ƒÀ-anomer in the equilibrium solutions are reported to be 73 and 33 for D-galactose and D-mannose, respectively (17). Using these values and the molar enthalpy changes determined calorimetrically, the free energy and entropy changes, ƒ¢G and ƒ¢S, can Fig. 3. Plots of (g(t)+K•çg(t)dt)/Kt against(1-e-kt)/ be calculated using the following equations : kt for the mutarotation of (a) D-galactose and (b) D-mannose; (a) m=1.9778g, k=0.03205 min-1, K= (7) 0.02605 min-1, C=0.2155 JK-1.* (b) m=5.0736g, k= (8) 0.06496 min-1, K=0.02605 min, C=0.2360 JK-1.* * JK-1=1/4 .184 cal/•Ž as heat capacity unit. K is the * Regarding the accuracy of the data , the error in temperature scale unit," degree kelvin." the enthalpy value for D-mannose is expected to be

larger than that described here. Since the sample per gram of sample was thus determined to used was a mixture of ƒ¿-and ƒÀ-anomers, this would

be + 5.260 •}0.222 J g-1 and -1.640•}0.071 J g-1 introduce an uncertainty in the enthalpy evaluation.

Vol.73, No.4, 1973 768 K. TAKAHASHI and S. ONO

TABLE I. Calorimetric data for the mutarotation of sugars.

†Standar ddeviation.

TABLE II. Enthalpies for conversion from ƒ¿- to ƒÀ-anomers.

†Standard deviation.

where Keq is the composition ratio of ƒÀ- to ity and that the contribution of entropy to a-anomer in equilibrium solution and R and the stability of anomers is comparatively T are the gas constant and the absolute minor. temperature, respectively. In D-mannose the ƒ¿-anomer is more stable The thermodynamic quantities thus ob- than the ƒÀ-anomer, while in D-glucose, D- tained are summarized in Table III together xylose, and D-galactose the more stable anomer with the values for some other isomerization is the ƒÀ-form. Figure 4 shows the structures processes reported previously. The magni- of a-D-glucose, ƒ¿-D-galactose, and ƒÀ-D-man- tude of enthalpy changes in all the anomeriza- nose, that are less stable in the anomer pairs tion processes is close to that of free energy for each respective sugar. changes. This indicates that the anomeric As shown in Fig. 4, the configuration of forms are affected mainly by energetic stabil- the two hydroxyl groups on C1 and C2 of the

J. Biochem. CALORIMETRY ON MUTAROTATION OF SUGARS 769

TABLE III. Thermodynamic quantities for isomerization of sugars in aqueous solution at 25•Ž.

and showed that the enthalpy of eq-D-mannose is 9,290 J mo1-1 greater than that of eq- D-glucose. Using this value, together with the value for anomerization of D-glucose and D-mannose, ƒ¿- D-glucose ƒ¿- D-galactose β-D-mannose the enthalpy differences between a-D-glucose Fig.4. Structure of a-D-glucose, a-D-galactose, and and a-D-mannose and between P-D-glucose -D-mannose . ƒÀ and ƒÀ-D-mannose in aqueous solution can be obtained by weighing the known percentage pyranose ring* is cis in these less stable anomers. From this fact, it may be assumed composition of a-and ƒÀ-anomers for both that the cis-interaction of the two hydroxyl sugars.* Thus the energies required for the conversion of a hydroxyl group on C2 of a- groups on C1 and C2 introduces an instability into the conformation and that the stability D-glucose and ƒÀ-D-glucose from equatorial to of anomers depends on the relative configura- axial in Cl form** were found to be 7,950 tion of the hydroxyl group on the anomeric J mo1-1 and 10,880 J mol-1, respectively. The carbon, C1, to that on C2. In other words, corresponding entropy changes were calculated in any pyranose sugar the situation of the in the same way and were found to be 19.7 hydroxyl group on C2 plays a major role in J for both cases. The thermodynamic determining the preferred form of the anomer quantities thus determined are also included in Table III for comparison. In Fig. 5 the pair. Takasaki ( 19 ) studied the temperature enthalpy relationship among the sugars is dependence of equilibrium constants for the schematically illustrated. enzymatic isomerization of eq-D-glucose It is obvious that the instabilities both in eq-D-fructose and eq-D-mannose eq-D- energy and entropy terms produced by the fructose. He derived thermodynamic quanti- conversion of a hydroxyl group on C2 are ties for a hypothetical reaction, considerably greater than those produced by

* For the calculation eq-D-glucose•àeq-D-mannose , the enthalpy difference between a- and ƒÀ-D-glucose, ƒ¢H= -1,160 J mo1-1, ob- * NMR study of the conformation of hexoses in tatined by Sturtevant (5) was employed. ** It is

aqueous solution revealed that in D-mannose and generally believed that most hexopyranoses and

D-glucose, no furanose-type structure is present and pentopyranoses are in chair-1 form rather than boat that in D-galactose only a trace of furanose-type forms both in the solid state (3, 20, 21) and in structure is involved (18), aqueous solution (22-24).

Vol.73, No.4, 1973 770 K. TAKAHASHI and S. ONO

Fig. 5. Enthalpy relationship between sugars in aqueous solution.

the anomeric conversion. By a NMR study 9. R.M.C. Dawson, D.C. Elliott, W.H. Elliott, and of the conformation of sugars in aqueous solu- K.M. Jones (eds.), "Data for Biochemical Re- tion it has been demonstrated that, while D- search," Oxford at the Clarendon Press, p. 236, glucose is in a perfect chair form, D-mannose (1969). 10. H.S. Isbell and W. Pigman, AdƒÒan. Carbohyd. takes rather distorted structure (22). The Chem., 23, 11 (1968). large enthalpy and entropy changes obtained 11. H.S. Isbell and W. Pigman, J. Res. Natl. Bur. in the present calculation may be attributed Std., 18, 141 (1937).

to this distorted conformation of the pyranose 12. E.A. Guggenheim, Phil. Mag., 2, 538 (1926). ring in D-mannose. It seems that the con- 13. S. Ono, K. Hiromi, and K. Takahashi, J. Bio- version of a hydroxyl group on C2 brings about chem., 57, 799 (1965). a major change in the molecular structure of 14. T. Kozaki, Rev. Phys. Chem. Japan, 9, 64 (1935). the pyranose ring and produces a large change 15. J.M. Sturtevant, J. Am. Chem. Soc., 59, 1528. in both the enthalpy and entropy values. (1937). 16. M. Lazniewski, Bull. Acad. Polon. Soc., Ser.

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