I
Evelyn Nobles Drake and Charles Eric Brown1 Department of Biochemistly and Molecular Biolow Northwestern University Evanston, Illinois 60201
I
Application of NMR lo. A laboratory experiment in physical biochemistry
Recent advances in nuclear magnetic resonance (nmr) technology have improved the sensitivity, stability, and resolution of commerciallv available instruments to such a demee that nmr spectromet"ry is being applied to complex ibiochemical oroblems a t an ever increasine rate (1-8). . . This has created a need for experiments which teach to beginning hiochemistry students the practical and theoretical aspects of this powerful technique. The following laboratory experiment which involves the application of nmr to hiochemical kinetics has been designed to fulfill this need. I t teaches students how to perform an nrnr experiment and allows them to compare in aiahoratory setting the capabilities of nmr spectrometry with those of another technique used routinely in biochemistry. In addition, this experiment prepares students to read and understand the evolving literature concerning the aoolication of nmr to enzvme kinetics (9. and to other . . 10) ~,~ topics of biological and chemical interest. 'HMR spectrometry and polarimetry are used in this experiment to measure the mutarotation of freshly prepared solutions of a-and B-D-elucose. As illustrated in Fieure 1.the mutarotation of D-glu&ne involves the intercon;ersion of these two anomeric rine isomers. Thev exhibit different initial specific rotations, and-the a-and p-komeric protons can be resolved by nmr. The mutarotation process obeys reversible equilibrium kinetics (11) and is independent of sugar concentration over a wide range (12). At room temperature the mutarotation of freshly prepared solutions of e&her anomer occurs over a period of several hours until an equilibrium composition is approached. These properties allow convenient measurement of kinetics by continuous-wave nmr techniques
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~~.~. ~~~
~
~
H
Figure 1. Interconversion of
the anomeric f
124 1 Journal of Chemical Education
m s of
Dglucoee
as well as by polarimetry. The experiment described requires only an inenpensive ' ~ m spec&ometer r such as the ~ a r i a n T-60 and a Rudolph polarimeter. However, a wide range of additional experiments is passihle with the availability of more versatile equipment. Conformatlonal Analysls of Sugars by NMR The structure and conformation of sugars in solution bas been a subject of intense investigation for many years. While polarimetry has been responsihle primarily for elucidating the kinetic features of mutarotation, nuclear magnetic resonance techniques have played the major role in establishing conformations and tautomeric equilibria in solution (13, 14). Conformational analysis of sugars is based on the assumption that the geometries of pyranases and furanoses in solution are essentially those of cyclohexane and cyclopentane, respectively (15). This assumption, in conjunction with 'Hmr spectrometry, has been used to predict the conformations shown for a-and 8-D-glucose in Figure 1. Two kinds of data provided by 'Hmr spectrometrv yield information on the co~formatiotkof sugars in soluti& the shielding from the external mametic field experienced by a proton due t o its environment;and the extent of spin-spin coupling between adjacent, nonequivalent protons. Shielding is measured in chemical shift units of parts-per-million (ppm) relative to a standard proton resonance. Theshielding experienced hv the anomeric protons of D-ducose is due a t least to the following two factors. First, the additional oxygen atom bonded to the anomeric carbon. throueh an inductive effect. causes the a-and &protons to r;sonateUat lower field than the other sugar protons. Second, equatorial protons generally resonate at lower field than do chemically similar axial protons of anomers in the same conformationsil6). Hence the resonances corresponding to the a- and J-anomeric protons of D-glucose canbe resdved in nrnr spectra and are assigned as indicated in Figure 2. Spin-spin coupling refers to the fact that spins of protons on adjacent, nonequivalent carbon atoms will interact and therebv cause the resonances of each of the noneauivalent to he split into multiple peaks (17). In thesimplest case onlv one proton is bonded to each of two adiacent carbon atoms, and thk resonance of each peak is split into a doublet. This is the situation which causes the a- and B-protons of D-glucose to he split into doublets. The extent of Eoupling is designated by the coupling constant, JH-H,which by definitionis the separationin hertz between the two peaks of the doublet. The magnitude of the coupling constant can be ap.
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1 Present mailing address: Roche Institute of Molecular Biology, Nutley, New Jersey 07110.
If a and 8 are the concentrations of the a - and p-anomers a t time t, respectively, then doldt = Kl(ao - P) - K28
(2)
where a 0 is the value of a at t = 0. A similar equation can be written if it is assumed that the reaction starts with the 8anomer. Integration of this equation followed by conversion to decimal logarithms yields log [K,ao
-Klao
+
K2)P] = 0.4343(K1 + K d t
(3)
At equilibrium dpldt equals zero, and equals &., Solving for Klao in eqn. (2) and substituting this result into eqn. (3) yields
[+] 8 -0
lag
Figwe 2. The 'HMR specfa d Dglat We indicatedtime intervals following dismlutim of We a-anin D a at 34.Z°C. The r a m of We b m m mWmm iS 2.75-7.60 w m downfield horn 2.2.3.3.lebadaI*(~WuimSmy riiyl)popmic acid IOdium MR. The chsm ea shin of Mch pnan rewnarra remalns mnstant with time, but the anomeric composition of t k sample changes.
proximately related to the dihedral angle between the two protons hy the Karplus equation
= 0.4343(K1
+ Kz)t
(4)
This equation is used directly for analysis of the nmr data hut must he converted in the following manner for use with the polarimetric data. Define ro and r, to he the observed rotations a t zero time and a t time t, respectively, and r, to be the observed rotation a t equilibrium. Then ro = [a]J1bao
(5)
rt = [ a l ~ ~ b ( u o8) + [Blr'bP
(6)
r., = [ali'b(ao
- Pes) + [ 8 1 ~ ' b P ~ ~
(7)
where [aIAtand [f31Atare the specific rotations of a- and pD-glucose and b is the pathlength. Solving eqns. (6) and (7) for 13 and p., yields
JH-H= Jocos2$ + K
in which Ju-u is the observed counline constant. 6 is the dicharactkistic of the hedral angie, i d Joand K are con&& system under consideration (18, 19). A modified Karplus equation is available which makes corrections for deviations that arise from the electronegativity of adjacent suhstituents it is possible (20). With this equation and the observed JH-H to estimate the conformation of the Dvranose rine and to assign the downfield proton r e ~ o n a n c e ~the t o indkdual anomers (21). For example, if two adjacent hydrogen atoms in a six-membered ring are trans (i.e. diaxial) a value of 7-10 Hz should he observed for JH-H, but a value of only U Hz should be observed if the hydrogen atoms are gauche (i.e. axial-equatorial) (14). These values are in agreement with the for the anomeric experimentally observed values of JH-H protons of a - and 8-D-glucose (See Fig. 2) and are the same as would be predicted for the conformations shown in Figure 1. However, the coupling constants of the anomeric proton resonances alone do-notconfirm these conformations. One must measure the relevant coupling constants of all the protons bonded to the carbon atomsof the ring in the &me manner as was used recently to analyze the nmr spectrum of a glucose derivative (22). Unfortunately, this can not be done with D-glucose on a 60 MHz spectrometer because the resonances of these Drotons are not resolved sufficientlv (See Fie. 2), and we must'accept the conformation assignm&s in t c e literature (14). I t should be remembered that this technique, like any other, has its weaknesses. Information concerning values is a t best molecular conformation obtained from JH-H only qualitative (19,23). Also, nmr spectrometers generally can not detect compounds which correspond to only 5% or less of a mixture. Therefore one can not rule out the possibility that two conformations exist in equilibrium with only 10%or less of each anomer in the undetected conformation.. Mutarotation Klnetlcs I t is assumed that a reversible equilibrium exists between a- and 0-D-glucose and that only one anomer, m-D-glucose, is present a t zero time.
Substitution of eqns. (8) into eqn. (4) yields log
[=I TO
- r0
= 0.4343(K1
+K z ) ~
(9)
When either log [p.,I(p,, - p)] or log [(ro- r,)/(rt - r-)] is plotted versus t in min, the slope is called the mutarotation constant (24) and is equal to 0.4343(K1+ K2). The equilibration constant for the reaction in eqn. (1)can be expressed as K = -K1- - oes KP
aeq
(10)
where a.q = ao - Pes
(11)
The values of a,, and p,, can he measured directly from the corrected nmr spectral integration or from the polarimetric data with eqns. (7) and (11). Therefore, the forward and reverse rate constants for the mutarotation of a-D-glucose, K I and K2, can he calculated by simultaneous solution of eqns. (4) and (10) or eqns. (9) and (10). Experimental Anhydrous a - and p-D-glucose in powdered form were purchased from Siema Chemical Company. Mutarotation was initiated by dissd\.ing samples of sugar in known volumes of H90 or D,O at the desired temperature. Hnpid dissolutiun was a i e d by the use of a vortex mixer, and zero time for each kinetic run was taken after approximately half of a sugar sample had dissolved. Final volui& were noted prior to transfer of solutions to either nmr tubes or polarimetric cells. Kinetic measurements were begun as soon thereafter as possible with a Varian T-60 nmr spectrometer, a Rudolph polarimeter, and a Cay-60 spectropolarimeter in the ORD mode. The elapsed time between sample dissolution and the first kinetic measurement in all cases was less than 5 min. Mutarotation kinetics were measured with 'Hmr specVolume 54, Number .Z February 1977 / 125
I-
sm O.D.
NmR tube
t
g l ~ ~ o ssolution e
I t
silicone stopcock grease
5 0 p l n i c m e a p Pillmd w i t h CHC13 minutes
a i l i m n a atopcock g n m n
Figure 4. Characteristic data obtained for the mutarotationof freshly prepared solutions of a-Dglucase by nmr (0)at 34.Z°C and by polarimetry ( 0 )at 25°C.
Figure 3. D-glucose so~utionand reference capillary in s 5-mm nmr sample tuoa. me reterence capo1my u It rtam mncenbicalhl on the bntom ot the nmr tube when the tube is spinning in the spectrometer pmbe.
trometry by periodically taking an integration of that part of the glucose snectrum conesoondiw to the a-anomeric nroton ove;a time span of approximately fhr. In order to standardize the spectral integrations over this rather long time period, a resonanre corresponding to a fixed proton co&entr.&ion was needed. This was produced by adding a capillary containinp; CHC13 to the nm; sample tube as di&ra&ed-in Figure 3 Students made this reference capillary by cutting a l-in. piece from a 50-pl microcap (Drummond Scientific Co.), filling i t with CHCIs, and sealing the ends with silicone stopcock mease. In order to calculate the molar conrentration ofi-anomer as a function of time, the apparent molar concentration of CHCI? in this reference canill& had to be measured. This value differs from the concent;ation of neat CHC13 because the cross-sectional area of the reference capillary is only a small fraction of that of the nmr tube, and because the contents of a reference ca~illarvaenerallv are not coupled to a spectrometer recei;er coil to the same extent as the bulk sample solution. The value was measured experimentally by placing an identical reference capillary into an nmr tube filled with an aqueous solution of methanol of known concentration and taking spectral integrations of the two resonances. The quotient of these two values ~rovidesa measure of the " a ~ ~ a r e n t " molar chlon)form conce&ration. The molar concent&tion of a-1)-nlucose at each time point then was determined by com&ng the integration ofthe a-anomeric proton resonance to that of CHC13. The caiculation may be expressed by
where a and [CHaOHJ are the molar concentrations of a-DICH~OH, and Ia-~.glumM are glucose and methanol, and ICHCL~, the spectral integration values of the resonances of CHCL, the methyl protons of methanol, and the anomeric proton of aD-elucose.. resnectivelv. The chemicd shifts of the anomeric proton resonances were measured relative I(, the external CHCl7 during the mutaro. tation reaction. After the sample reached equilibrium a small amount of 2.2.3.3-tetradeutero-9-(trimethvlsilvl)oro~ionic . . acid sodium salt &as added to the sample to permit accurate measurement of the chemical shift values. In this wav the internal reference compound could not interfere with the kinetin of the reaction. lt was found that the chemical shifts did
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126 I
.
Journal of Chemical Education
not change appreciably during mutarotation. The exact ronditions under which this experiment should be run are controlled hy the sensitivity and ksolution of the snectrometer available for student use. The spectra shown in figure 2 were taken by dissolving 0.3 g of &hydrous a-Dglucose in 99.9% isotopically enriched DzO and collecting spectra a t the times indicated on a 60-MHz instrument. The greatest complication with this procedure is due to the large HOD peak which arises from rapid exchange of the protons on the sugar hydroxyl groups with solvent (25). This problem usually can be alleviated by lyophilizing a sample from D20 several times to substitute deuterons for all the exchangeable protons, but this procedure can not be used with ease in this case because mutarotation of the sugar occurs during the exchange. This undesired mutarotati6n can be kept to a minimum by dissolvingthe sugar in cold D20 and lyophilizing the resultine solution immediatelv. However. the nmr spectra of these d e k r a t e d sugars did n i t change appreciably G t h time because the initial mutarotation, which produces the greatest spectral changes, had occurred before the kinetic measurement was begun. The experiment provides more useful data if the sample is not exchangedwithD20, but this requires one to take certain precautions when the spectra are obtained. If the resolution of the instrument to be used for this experiment is insufficient to separate the H; and HOD resonances, or if the HOD spinning side bands are too large, the concentration of a-D-glucose in solution should be reduced. A spinning rate for the sample tube should be chosen so that spinning side bands do not coincide with the chemical shifts of resonances of interest. If the presence of the HOD peak or spinning side bands makes electronic intamation difficult, the areas of the a-anomerir protons ran he measured by "counting squares." It is recommended that twoor more spectral integrations he taken in ranid succession and averaged for each data ooint. ~ a m ~ l e s ' fpolarimetry or were pre&ed as described above, and chanees " in ontical rotation were measured for -3 hr a t room temperature. Final "equilibrium" rotation values were measured at least 8 hr after mutarotation was initiated. Standard glass cells with a pathlength of 1dm were used in a Rudolph polarimeter equipped with a sodium vapor lamp (5896 A, 5890 A). Sample concentrations of approximately 0.2 elm1 resulted in adeauate rotations for observation with this & u m e n t . cylindrical Pyrex samplecells with a pathlength of 0.1 dm were used in the Cary-60 spectropolarimeter. Since the maximum rotation that can be measured by the Cary-60 is lo,sugar concentrations of 0.1 glml or less were used.
Results and Discussion We report the results obtained only at the ambient temperatures of the nmr spectrometer and of the polarimeter used in this investigation (i.e. 34.Z°C and 25'C, respectively). If temperature controls are not used in the preliminary experiments, the technical problems are decreased, and the students can more easily master the unfamiliar instrumentation. One should keep in mind that this experiment can be performed on inexpensive instruments which may not be supplied with temperature controllers. A series of nmr spectra taken during the course of a-Dglucose mutarotation at 34.Z°C are presented in Figure 2. The anomeric protons of n- and 0-D-glucose are labelled H; and Hf and occur a t 5.22 and 4.65 ppm downfield from 2,2,3,3tetradeutero-3-(trirnethvlsilvl)prodonic acid sodium salt. . . . . re.ipectively. The H;' resonance is a douhlet with JH-H equal to 2.5 Hz as described previously. Although the H; resonance is not comnletelv resolved from the HOI) oeak. it is nossihle to show th& t h e " J ~ - is ~ roughly equal to &e p"hlish'ed value of 7.5 Hz (26). The Hp resonance decreases in intensity, and, simultaneously, the Hf resonance increases as the a-D-glucose is converted to the 0-anomer by mutarotation. The molar concentration of a-anomer a t time t was measured by nmr snectral inteeration as described above. and the concentration o ~ 0 - ~ - ~ lwas u ccalculated ~e by diffeience (i.e. 0 = a 0 - a). Values for (3 were substituted into eqn. (4) and produced the data plotted as open circles in Figure 4. The slope of the associated line is 0.0120 min-'. For the mutarotation of a-Dglucose in Hz0 at 34.Z°C, a value of 0.0262 min-I was predicted bv the Arrhenius equation (12). However. the mutarotation-of glucose is slower in DzO than in HzO due to a combination of solvent and kinetic isotope effects (27). I t was found that the experimental results were in agreement with the calculated value if a correction was made to account for these effects. The students can this and investigate the isotope effect quantitatively by measuring mutarotation in D20with both nmr spectrometry and larimetry and comparing the results obtained with those obtained by polarimetry in H20. The polarimetry data ohtained from the mutarotation of u-D-gluchsein at 250C was substituted into eqn' (')' The results are plotted as open squares in Figure 4. The initial specific rotation, ro, of a-D-glucose was assumed to he 112.Z0 (28), The slope of this plot is 0,0100 min-l which favorably with the literature value, 0.0105 min-I (12). Virtually identical results were obtained with the Cary.60 and the Rudolph polarimeter. It is of interest that although the Cary-60 provided increased sensitivity, automatic of optical rotation data, and the opportunity to vary wavelength, the students preferred the Rudolph polarimeter hecause they could better visualize the physical significance of the measurements they made with this instrument. Additional information pertaining to the kinetics of mutarotation can be obtained with these techniques as time and student interest permit. The use of the Karplus equation for determination of the configurations and conformations of sugars in solution he validated (14,15). The effe& of solvent, pH, and temperature on mutarotation rate constants and the equilibrium compositions of a variety of sugars can be investigated 7,28),~ ~mutarotation ~ behavior, ~ in which aninitial rapid equilibration between pyranose and furanose forms is followed by a slower equilibration between the a- and 0-isomers of each, can be measured with polar/-
metry, and the lifetime of each intermediate can be determined bv 'Hmr svectrometw (14.15). ~ p p l i i a t i o nof nmr spectrometry to enzyme kinetics requires an instrument which is capable of detectinn very small concentrations of substrates and products and of cofiecting and storing spectra at a rapid rate. Spectrometers of this type are beine develoned (9.10). but it is unlikelv that one would be available forhteachingpurposes. HoweGer, the students should realize that the basic theow and teclmiaues which thev use in this experiment are directiy applicahle'to the study 01 enzvme kinetics. and thev should he encouraeed to write protocols for studying mitarotation in the presence of enzymes such as mutarotase and glucose oxidase (29,30). Conclusion This experiment was used in a laboratory course offered to juniors, seniors, and graduate students with majors in biology, biochemistry, and chemistry. Working in groups of two or three, the students gained enouch experience to become conversant hoth in IH& spectrom&y&d polarimetry. Some students were sufficiently interested in the experiment to study the theory of nmr in greater detail. On the basis of the data in Figure 4, the students concluded that polarimetry is the preferred technique for measurement of mutarotation kinetics hut that nmr provides a rapid, non-destmrtive means for identitiration of the structures of reactants and products. One can not characterize the reaction completely hy using only one techniuue t t ~the exrlusion of the other. Followine completion of ihe course, these students tended to appiy nmr techniques to a greater extent in their own research. Cited 111 ~ h i l l iW~ .~D.., in " ~ ~ t h in o ~d ~ ~ IEdirora: H ~ ~ ~ ~H, cw.. .~ and~imasheff, ~ S. N~1,AcademicPress.New Yark, 1973, Vul. 27.p.825. (21 Gurd, F. R.N.,and Keim. P.. in "Methods in Enzym~,loyy."(Edilorr:Hirs,C. H. W.. and T ~ ~ ~S.~N.),P ~ E , ~ P F ~ S S ,N ~~ WY W ~1973, d, VOI. 27. ~ p. 8x6. ~ i 13) Meadow. D. H..in " M e t h d h Enzymoloiy." IEdilors: Him. C. H. W.,and mmasheff, S. N.1, Academic Press. New Yurk. 197Z.VoI. 26.p.618. (41 M ~ I ~ V ~A. " s.. . and E"@, J. L., in " ~ ~ t in h ~ ~n ~dy m ~ ~ ~ o i~ditora: g y . " ~ i r sC. . H. W . ,and Timashoff, S. N.1, Aesdemie Prau, New York, 1972, Voi. 26, p. 654. 151 Anet. F.A. L..andLpvy,G.C.,Scienca, 180.141 (19731. 161 B~OW", C. E.. K ~ L ZJ.. J., and shemi", D., PPX. N.L A F . ~ .sci. US.. 69,2585
~
119121. 119731. (7) Brown.C. E., Shemin. D., and Katz. J. J., J . Bid. Chem.. 248, (8) sudmeir, J ~ . , * " dp e s e k , ~J. . , A ~ ~ I .i ~ h4 1~ , ~119711. ~ . . 19) patt,s. L . , D o I ~D~. ~. ~~ , ~ ~ s ~ D ~ .~, A s ,~ B~ .. NA. YC ~S C~ ~. . 222,211 (1975). 1101 Grimsldi. J..J.,snd Syken,B. D.. J. Amer. Chrm S a c , 97,273119751. I l l ) Lowry,T. M.. J. Chem.Suc.. 76.211 11899). 1 1 2 ~~ ~ d ~ o n , c . s . , aDale, n d J. K., J . ~ m e Chem.Soc., r 39,320 119171. 113) Lemieux. R. U...md Stevens. J. D.. Con. J. Ch~m.,44.249 113661. (14) Angyal,S.J.,Angeu~.Chsm.. 8,157119691. 1151 EM. E. ~ . . - ~ ~Analyak: ~ f ~~ i ~ ~ ~ ~ ~ ~ t NEW - i ~yo.k, ~ ~ ~ 1965. f ~ eP. 351. ~ ~ ~ i 1161 Lemieux, R. U.,Kullnig, R K., Bernstein, H. L a n d Sehneidcr. W .G.. J . Amcr Cham. Sur., 80,6098 119581. (171 D,., J. R,, l l ~ p p ~ i c a t i . of n ~ ~ b e ~ spectrascopy ~ ~ t i to~ organic ~ compound.,^^ p r e n t i c e - ~ d iN
