Differentiation of Underivatized Diastereomeric Hexosamine

in a Mixture Using the Kinetic Method under Electrospray Ionization Conditions ... to quantify these hexosamines in a mixture following the three-...
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Anal. Chem. 2004, 76, 3505-3509

Differentiation of Underivatized Diastereomeric Hexosamine Monosaccharides and Their Quantification in a Mixture Using the Kinetic Method under Electrospray Ionization Conditions V. Nagaveni, S. Prabhakar, and M. Vairamani*

National Center for Mass Spectrometry, Indian Institute of Chemical Technology, Hyderabad-500 007, India

A simple method to differentiate underivatized diastereomeric hexosamine monosaccharides, glucosamine, galactosamine, and mannosamine is reported by applying the kinetic method using N-acetylhexosamines or naturally occurring amino acids as reference bases under electrospray ionization conditions. The observed differences to distinguish the diastereomeric hexosamines are found mainly due to the proton affinity (PA) differences between the analyte and the reference base. The PA values of the hexosamines are not available in the literature, and hence, we estimated them by the kinetic method using N-acetylhexosamines as reference bases. The determined PA values are 223.97 kcal/mol for glucosamine, 224.99 kcal/mol for mannosamine, and 224.71 kcal/mol for galactosamine. The similar PA values were also obtained by using amino acids as reference bases. We have applied the same methodology to quantify these hexosamines in a mixture following the three-point calibration method suggested in the literature. Differentiation of isomeric sugars is often difficult when using mass spectrometry as a tool because structural isomers of sugars hardly show distinctive fragmentations. Several groups have reported structural elucidation of isomeric sugars by mass spectrometry.1-12 One way of doing this is to apply the kinetic method developed by Cooks et al. that has been found to be highly reliable and useful in differentiating diastereomers and diastereomeric complexes formed in the gas phase.13,14 This method correlates the relative abundance of the ions formed from the * To whom correspondence should be addressed. E-mail: [email protected]. Telephone: +91-40-27193482. Fax: +91-40-27160387 (or) +91-40-27160757. (1) Fournie, J. J.; Prome, J. C.; Puzo, G. Anal. Chem. 1985, 57, 892-894. (2) Wang, G.; Sha, Y.; Xu, X.; Pan, J. Anal. Chem. 1985, 57, 2283-2286. (3) Fournie, J. J.; Puzo, G. Anal. Chem. 1985, 57, 2287-2289. (4) Meyerhoffer, W. J.; Bursey, M. M. Biomed. Environ. Mass Spectrom. 1989, 18, 801-808. (5) Smith, G.; Leary, J. A. J. Am. Chem. Soc. 1996, 118, 3293-3294. (6) Smith, G.; Pedersen, S. F.; Leary, J. A. J. Org. Chem. 1997, 62, 2152-2154. (7) Smith, G.; Leary, J. A. J. Am. Chem. Soc. 1998, 120, 13046-13056. (8) Gaucher, S. P.; Leary, J. A. Anal. Chem. 1998, 70, 3009-3014. (9) Desaire, H.; Leary, J. A. Anal. Chem. 1999, 71, 1997-2002. (10) Desaire, H.; Leary J. A. J. Am. Soc. Mass Spectrom. 2000, 11, 1086-1094. (11) Young, M. K.; Dinh, N.; Williams, D. Rapid Commun. Mass Spectrom. 2000, 14, 1462-1467. (12) Carlesso, V.; Fournier, F.; Tabet, J. C. Eur. J. Mass. Spectrom. 2000, 6, 421-428. 10.1021/ac049829c CCC: $27.50 Published on Web 05/19/2004

© 2004 American Chemical Society

decomposition of a proton-bound dimer or a complex in two similar pathways with the decomposition kinetics of the same system. It is very sensitive to small energy differences in thermodynamic properties such as proton affinity (PA) and, hence, applied successfully to a very many systems. In a recent study, we used the kinetic method to differentiate three isomeric N-acetylhexosamines by studying the decomposition of protonbound heterodimers formed between N-acetylhexosamines and amino acids.15 We also utilized the same methodology to measure the PAs of N-acetylhexosamines. Further extension of this method has shown that we can also differentiate the hexosamines, i.e., glucosamine, galactosamine, and mannosamine, which are biologically important compounds. Hexosamines are constituents of structures found in tissues and on cell surfaces and membranes, which cover them. These compounds appear in biologically significant glycosaminoglycans, such as heparin.16 Identification and quantification of these biologically important compounds by mass spectrometry is a challenging problem. In a recent report, differentiation and quantification of these isomeric hexosamines in a mixture was achieved by Desaire and Leary.17 Their method involves prior derivatization with metal complexes. Herein, we report a simple method to differentiate diastereomeric hexosamines without derivatization. This involves the decomposition of proton-bound heterodimers formed between hexosamines and two groups of compounds, namely, N-acetylhexosamines and amino acids under electrospray ionization mass spectrometry. We applied the kinetic method for the estimation of the PA values of hexosamines, which are hitherto unknown. By the same strategy, we have also quantified hexosamines in a mixture without prior separation or derivatization using two amino acids as references. EXPERIMENTAL SECTION All the chemicals used in the present work were purchased from Sigma-Aldrich (Steinheim, Germany) and were used without further purification. All the HPLC-grade solvents were purchased (13) Cooks, R. G.; Patrick, J. S.; Kotiaho, T.; McLuckey, S. A. Mass Spectrom. Rev. 1994, 13, 287-339. (14) Shen, W.; Wong, P. S. H.; Cooks, R. G. Rapid Commun. Mass Spectrom. 1997, 11, 71-74. (15) Nagaveni, V.; Vairamani, M. Rapid Commun. Mass Spectrom. 2003, 17, 1089-1091. (16) Chaplin, M. F., Kennedy, J. F., Eds. Carbohydrate Analysis; Oxford: New York, 1994. (17) Desaire, H.; Leary, J. A. Anal. Chem. 1999, 71, 4142-4147.

Analytical Chemistry, Vol. 76, No. 13, July 1, 2004 3505

Figure 1. Isomeric amino sugars (hexosamines and N-acetylhexosamines).

from Merck (Mumbai, India). Stock solutions (1 mM) of hexosamines (glucosamine, galactosamine, mannosamine) and Nacetylhexosamines (N-acetyl-D-glucosamine, N-acetyl-D-galactosamine) were made in water, and that of amino acids, methionine, asparagine, glutamic acid, proline, and tryptophan were made in water/methanol (50:50, v/v). The sample solutions were prepared by mixing N-acetylhexosamine or amino acid with hexosamine in equimolar ratios and further diluted in 1:1 water/methanol (v/ v) to get a final concentration of 100 µM. The samples for quantification experiments were made by mixing appropriate volumes of hexosamines and amino acid to make equimolar concentrations (100 µM each) of hexosamine and amino acid. Mass spectra were obtained under ESI conditions using a Quattro LC (Micromass, Manchester, U.K.) mass spectrometer with Mass Lynx software (version 3.2). Samples were introduced into the source by an infusion pump (Harvard Apparatus, Holliston, MA) at a flow rate of 10 µL/min. Capillary and cone voltages were kept at 3.5 kV and 10 V, respectively. The collision-induced dissociation (CID) spectra were obtained by selecting the precursor ion of interest with MS1 and scanning MS2. Argon was used as the collision gas, and the pressure in the collision cell was maintained at (1.7-2.0) × 10-4 mbar. All the CID spectra were recorded at 2, 4, 6, and 8 eV collision energies, unless otherwise stated, and the spectra presented here are an average of 30 scans. RESULTS AND DISCUSSION Structural differences among the three biologically relevant hexosamines (HexNH2), namely, glucosamine (GlcNH2), galactosamine (GalNH2), and mannosamine (ManNH2), occur at the C2 and C4 positions (Figure 1). With a view to differentiate them we selected the corresponding N-acetylhexosamines (HexNAc), (Figure 1), namely, N-acetylglucosamine (GlcNAc), N-acetylgalactosamine (GalNAc), and N-acetylmannosamine (ManNAc), as tools for forming noncovalent adducts under electrospray ionization and studied their decomposition. The ESI mass spectra of an equimolar mixture of the HexNH2 and HexNAc for all the possible combinations show the expected proton-bound heterodimers, and the spectrum of ManNH2 in the presence of ManNAc is given in Figure 2 as an example. All the spectra showed the [HexNH2 + H]+ ion at m/z 180 as the base peak, and the [HexNAc + H]+ ion (m/z 222) is negligible in the spectra. The predominance of protonated HexNH2 compared to protonated HexNAc is due to the higher PA of HexNH2 when compared to that of HexNAc. The proton-bound heterodimer [HexNH2 + HexNAc + H]+ ion (m/z 401) is prominent in the spectra when compared to the homodimer [(HexNH2)2 + H]+ at m/z 359. In addition, there are other minor peaks corresponding to heterotrimers, [(HexNH2)2 + (HexNAc) + H]+ and [(HexNH2) + (HexNAc)2 + H]+ 3506 Analytical Chemistry, Vol. 76, No. 13, July 1, 2004

Figure 2. ESI mass spectrum of an equimolar mixture of ManNH2 and ManNAc.

ions at m/z 580 and 622, respectively (Figure 2). The obtained ESI mass spectra are very much dependent upon experimental conditions, and consequently, the relative abundances are not diagnostic to be useful for distinguishing diastereomeric hexosamines. Hence, we performed CID studies on the proton-bound heterodimer [HexNH2 + HexNAc + H]+ ion at m/z 401. All the CID spectra of the ion at m/z 401 generated from each of the hexosamines in the presence of any of the N-acetylhexosamines used resulted in two fragment ions at m/z 180 and 222 that correspond to [HexNH2 + H]+ (a) and [HexNAc + H]+ (b), respectively. The ions a and b are formed by the competitive dissociation of proton-bound heterodimer, [HexNH2...H+... HexNAc]. The relative abundances of the ions a and b are found to be characteristic to both hexosamine and N-acetylhexosamine involved in the formation of heterodimer. The relative abundance ratio of ion a to b (a/b) can be taken as a measure to differentiate the isomeric hexosamines under study. The a/b values thus obtained from the averages of three sets of experiments performed on different days at the collision energy of 4 eV are given in Table 1. The values obtained from all the experiments are highly reproducible under the experimental conditions used. From Table 1, it is very much evident that all the diastereomeric hexosamines can be differentiated by any of the three N-acetylhexosamines and vice versa. It is well known from the kinetic method experiments that the abundances of the product ions (protonated monomer) formed during the decomposition of protonated heterodimer essentially depend on the PA of the individual monomer. The PA values of N-acetylhexosamines were reported in our earlier study by applying the kinetic method, and the values for GalNAc, ManNAc, and GlcNAc are 223.4, 222.9, and 222.8 kcal/mol, respectively.15,18-20 Since the a/b values for all the three hexosamines are >1, the PA of hexosamines used can be presumed to be higher than that of the N-acetylhexosamines used. And this (18) Bojesen, G.; Breindahl, T. J. Chem. Soc., Perkin Trans. 2 1994, 1029-1037. (19) Hunter, E. P. L.; Lias, S. G. J. Phys. Chem. Ref. Data. 1998, 3, 413-656. (20) These are the corrected values. The amino acid PA values given in ref 18 were revised as per the new Lias scale,19 and the revised values were used to correct our earlier reported value.15

Table 1. Relative Abundance of the Ions, a/b in the CID Spectra of [HexNH2 + HexNAc + H]+ Ions and That of c/d in the CID Spectra of [HexNH2 + AA + H]+ Ions at the Collision Energy of 4 eV relative abundance ratio (a/b)

relative abundance ratio (c/d)

hexosamine

GlcNAc

ManNAc

GalNAc

Met

Asn

Glu

Pro

Trp

mannosamine galactosamine glucosamine

14.9 8.6 4.3

13.3 8.2 3.7

7.1 4.4 2.1

18.2 11.0 4.4

3.7 2.5 1.2

2.7 2.0 0.86

2.3 1.8 0.6

2.2 1.4 0.5

Table 2. GBapp and Teff Values of Isomeric Hexosamines at Different Collision Energies Using Amino Acids or N-Acetylhexosamines as Reference Basesa N-acetyhexosamines as reference bases CE (eV) 2 4 6 8 av

amino acids as reference bases

mannosamine

galactosamine

glucosamine

mannosamine

galactosamine

GBapp

GBapp

GBapp

GBapp

GBapp

(kcal/mol) 224.89 224.99 225.03 225.08 224.99 ((0.2)

Teff (K) 379 403 412 421 404

(kcal/mol) 224.68 224.71 224.70 224.74 224.71 ((0.2)

Teff (K) 435 439 440 454 442

(kcal/mol) 223.94 223.95 223.97 224.0 223.97 ((0.1)

Teff (K) 387 388 401 412 397

Teff (K)

(kcal/mol) 224.95 224.99 225.12 224.99 225.01 ((0.2)

(kcal/mol)

472 454 440 437 451

224.71 224.74 224.74 224.70 224.72 ((0.2)

glucosamine

Teff (K)

GBapp (kcal/mol)

Teff (K)

413 414 417 445 422

223.94 223.98 224.05 224.09 224.02 ((0.2)

446 454 466 464 458

a CE, collision energy. The values are an average from triplicate measurements performed on different days. The values in parentheses indicate error from three sets.

fact is already reflected in the aforementioned source spectra. Further, it is interesting to note from Table 1 that the a/b values of all hexosamines are higher when GlcNAc was used and it decreased from GlcNAc to ManNAc and to GalNAc. Also, the higher the value of a/b, the larger will be the difference between the PA of hexosamine and N-acetylhexosamine. Among the hexosamines, the a/b value is higher for ManNH2 followed by GalNH2 and GlcNH2. From these results, the relative PA order for hexosamines can be predicted as ManNH2 > GalNH2 > GlcNH2. The PA values of hexosamine are not reported in the literature, and hence, we decided to measure the PA value of hexosamines to demonstrate its role in distinguishing isomers and also to explain the effect of substitution (acetylation) on PA of hexosamines. We decided to measure the PA values of hexosamines using N-acetylhexosamines as reference bases because the use of reference bases that are structurally similar to target compounds minimizes the entropy changes. Estimation of PA Values for Hexosamines Using NAcetylhexosamines as Reference Bases. We have used Nacetylhexosamines (GlcNAc, ManNAc, GalNAc) as reference bases to measure PA values for the three hexosamines by the kinetic method. The proton-bound heterodimers of HexNH2 (GalNH2, GlcNH2, ManNH2) with each of the HexNAc were generated under ESI conditions. The CID spectra of the [HexNH2 + HexNAc + H]+ ions are recorded at different collision energies (0, 2, 4, 6, 8, 10 eV, etc.), and we found that the decomposition of selected ion is not significant at a collision energy below 2 eV, and above 8 eV, the primary fragment ions are further undergoing fragmentation. Hence, the spectra recorded at the collision energies of 2, 4, 6, and 8 eV were used for the estimation of PA values. All the spectra resulted in two fragment ions a and b, and hence, the selected ion is proved to be a simple proton-bound dimer, [HexNH2...H+...HexNAc]+. The natural logarithm of the abundance values of ions a and b, ln(a/b), is plotted against the

PA values of the reference N-acetylhexosamines to measure the apparent gas-phase basicity (GBapp) for hexosamines and the effective temperature Teff using eq 1.21

ln

GB a ) b

()

app

(HexNH2) PA(ref) RTeff RTeff

(1)

The plots give a linear relationship with slope -1/RTeff, and the Y-intercept is interpreted as y′ ) GBapp/RTeff (plots not shown), where R is the ideal gas constant. Since GBapp and Teff values at different collision energies do not change significantly, no corrections for entropy change were made as suggested by Hahn and Wesdemiotis.21 Hence, we did not apply the modified kinetic method for this work and instead used the simple kinetic method. In this way, the values of the GBapp of the three hexosamines were calculated at different collision energies and are given in Table 2. PA values taken as the averages of GBapp at four different collision energies are 223.97 kcal/mol for GlcNH2, 224.71 kcal/mol for GalNH2, and 224.99 kcal/mol for ManNH2. These values are in good agreement with the proposed relative PA order for the hexosamines. The PA differences among the hexosamines could be due to site of protonation and the stability of protonated species. It is reasonable to expect the amino group as the favored protonation site rather than the hydroxy group of hexosamines. The higher PA for ManNH2 as compared to GalNH2 and GlcNH2 can be attributed to the effective stabilization of protonated site (NH3+), which is in the axial position, through the ring oxygen, and hydroxyl oxygens at C6 and C1. On the other hand, in the case of GlcNH2, the protonated species is in the equatorial position, which cannot be stabilized effectively as the stabilizing oxygens of the other functional groups are also in the equatorial (21) Hahn, I.; Wesdemiotis, C. Int. J. Mass Spectrom. 2003, 222, 465-479.

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position and hence the PA is lower for GlcNH2. The amino group is in the equatorial position for both GlcNH2 and GalNH2, but the PA of GalNH2 is marginally higher than GlcNH2. The higher PA for GalNH2 over GlcNH2 could be due to additional protonation of the hydroxy group at C4 that is in axial position, which can be stabilized through the ring oxygen and hydroxyl oxygen of C6. The decrease in PA value from hexosamines to N-acetylhexosamines is expected because the lone pair on the nitrogen of the free amino group is delocalized when it is acetylated. The decreases in PA values are 1.2, 1.3, and 2.1 kcal/mol for GlcNAc, GalNAc, and ManNAc, respectively, from their respective unsubstituted hexosamine. Though the PA value obtained for ManNH2 is higher than that of GalNH2, the order is reversed for their corresponding N-acetyl derivatives. The higher decrease in PA value from ManNH2 to ManNAc can be attributed to the protonation of the carbonyl of the acetyl group in ManNAc, in which the protonated site is not in the proximity to get stabilized by the other functional groups. These observations show the importance of the proton affinities of both hexosamines and their N-acetylated derivatives for understanding their gas-phase behavior and its use in the present study for differentiating isomers. To counter check the PA values for hexosamines, we decided to measure the PA values using a different set of reference bases, i.e., amino acids. Estimation of PA Values for Hexosamines Using Amino Acids as Reference Bases. We used methionine (Met), asparagine (Asn), glutamic acid (Glu), proline (Pro), and tryptophan (Trp) as reference bases. The proton-bound heterodimers of hexosamines (GalNH2, GlcNH2, ManNH2) with each of the naturally occurring amino acids (AA) were generated under ESI conditions, and CID spectra were recorded for the adduct ion that corresponds to [HexNH2 + AA + H]+ at the collision energies of 2, 4, 6, and 8 eV. All the spectra resulted in two fragment ions corresponding to [HexNH2 + H]+ (c) and [AA + H]+ (d). The relative abundances of the ions c and d are also found to be very characteristic of the hexosamines under study, and thus, the relative abundance values of ions c to d (c/d) can also be taken as the measure to differentiate hexosamines. The c/d values obtained from the averages of three sets of experiments performed on different days at the collision energy of 4 eV are given in Table 1. Amino acids showed trends in differentiating the hexosamines similar to those found with N-acetylhexosamines. A plot of the natural logarithm of the abundance values c and d, ln(c/d), against the PA value of the reference base, amino acids, gives a linear relationship with slope 1/RTeff and intercept [GBapp]/RTeff (plots not shown). The GBapp and Teff values of the three hexosamines were calculated at the different collision energies used, and it was found that they do not change significantly (Table 2), as observed in the case of N-acetylhexosamines as reference bases. Hence, in this case also, we used the simple kinetic method to obtain the PA values for hexosamines. The PA value was taken as the average of GBapp values at four different collision energies, and the values are 224.02 kcal/mol for GlcNH2, 224.72 kcal/mol for GalNH2, and 225.01 kcal/mol for ManNH2. These PA values of hexosamines match fairly well with the values that are obtained using Nacetylhexosamines as reference bases. Obtaining the same PA values for the target compounds with two different kinds of reference base reflects the accuracy of the method used. Quantification of Hexosamines in a Three-Component Mixture. In the present study, we have shown the successful 3508

Analytical Chemistry, Vol. 76, No. 13, July 1, 2004

identification of isomeric hexosamines by using the kinetic method. Since the results are prominent and consistent, we extended the method to quantify the three hexosamines present in a mixture. Desaire and Leary reported quantification of hexosamine monosaccharides in a mixture. In their study, hexosamines were derivatized with a metal-ligand complex, [Co(DAP)2Cl2]Cl, and the ESI spectrum of the resulting complex, [Co(DAP)2(HexNH2)]Cl, resulted in the ion at m/z 384 corresponding to [Co(DAP)2(HexNH2)]+ ion, and this ion upon CID gave fragment ions specific to each diastereomer. Depending on the presence or absence of these specific ions, they could easily differentiate hexosamines and quantify hexosamines when present in a two- or three-component mixture. In the present study, we selected proton-bound heterodimers [HexNH2 + AA + H]+ or [HexNH2 + HexNAc + H]+ ions for CID experiments to differentiate hexosamines, and all the spectra of isomeric hexosamines resulted in only two fragment ions corresponding to the protonated monomers of different relative abundances, rather than specific fragment ions as observed by Desaire and Leary. To solve a system of three unknowns, we need three equations, but that is not possible with our present system, as there are only two variables (two fragment ions). However, Cooks et al.22 recently reported a three-point calibration method to quantify a ternary mixture of D-, L-, and meso-tartaric acids. In this method, a solution composed of the analyte, a chiral reference ligand (N-acetyl-Lphenylalanine or L-DOPA), and a transition metal chloride (NiCl2 or CoCl2) was electrosprayed to form in situ metal complex of the analyte [MII(chiral ligand)2(analyte) - H]+ ion. The CID experiments were performed on the formed metal-complex ions using two different chiral ligands, and then two equations were derived to quantify three components in a system (D-, L-, and meso isomers) wherein the mole fraction of the third component was treated as (1 - x - y), where x and y represent the mole fractions of the other two isomeric components. Similarly in the present study, the ternary mixture contains three isomeric hexosamines, and if the mole fraction of mannosamine is taken as Rman and that of galactosamine as Rgal, then the mole fraction of glucosamine can be derived as (1 - Rman - Rgal). By applying the kinetic method then it is possible to correlate the logarithmic value of abundance ratio, ln R, with the concentration of hexosamines in a mixture of any combination as given in eq 1. where Rman ) [M + H]+ ion of

ln R ) Rman ln Rman + Rgal ln Rgal + (1 - Rman - Rgal) ln Rglc (1) mannosamine/[M + H]+ ion of reference base, Rgal ) [M + H]+ ion of galactosamine/[M + H]+ ion of reference base, and Rglc ) [M + H]+ ion of glucosamine/[M + H]+ ion of reference base. If the target analyte is measured under two sets of conditions, two equations are obtained by which the system of two unknowns can be solved and that of third can be easily obtained from any one of the equation. Any two amino acids or N-acetylhexosamines used for estimation of PA values of hexosamines can be used for quantification purposes. We selected two amino acids, namely, tryptophan and proline, as reference bases to make two sets of data for quantifying the ternary mixture of hexosamines. The reason to select Trp and Pro for these experiments is that the (22) Lianming, W.; Rebecca, L.; Clark, Cooks, R. G. Chem. Commun. 2003, 1, 136-137.

shown in eqs 2 and 3 when substituted by the actual measured

ln R(i) ) (0.79)Rman + (0.35)Rgal + (-0.68)(1 - Rman - Rgal) (2) ln R(ii) ) (0.84)Rman + (0.61)Rgal + (-0.45)(1 - Rman - Rgal) (3)

Figure 3. CID spectra of [HexNH2 + Pro + H]+ (a-c) and of [HexNH2 + Trp + H]+ (d-f): HexNH2 ) (a)/(d) GlcNH2, (b)/(e) GalNH2, and (c)/(f) ManNH2.

Figure 4. Three-point calibration diagram for quantification of ternary mixture of diastereomeric hexosamine monosaccharides using two separate systems: (1) tryptophan as reference amino acid (2) proline as reference amino acid. Values corresponding to each point are averages based on triplicate measurements made on separate days. Table 3. Quantification of a Ternary Mixture of Hexosaminesa measd ln R entry 1 2 3 4 5 a

Trp

Pro

-0.31 -0.11 0.31 0.46 0.19 0.39 -0.17 0.03 0.27 0.51

actual

exptl

% Man % Gal % Glc % Man % Gal % Glc 20 50 25 20 10

10 25 50 20 80

70 25 25 60 10

18.3 48.8 24.8 20.1 7.9

9.8 26.4 49.0 20.8 80.9

71.9 24.7 26.1 59.1 11.2

ln R values are rounded off to the second decimal.

c/d ratio (Table 1) for glucosamine is less than unity (0.5 and 0.6) when these two amino acids are used; hence, the error in the measurement of peak heights gets reduced in the mixture analysis. The typical mass spectra showing the differentiation of isomeric hexosamines are illustrated in Figure 3. We have measured the ln R values for pure glucosamine, mannosamine, and galactosamine, and the values obtained when tryptophan is used as reference base are -0.68, 0.79, and 0.35, respectively, system i; and the values are -0.45, 0.84, and 0.61, respectively, when proline is used as reference base for system ii. Based on these ln R values, three-point calibration curves for the two systems were constructed and are given in Figure 4. For all possible combinations, the logarithmic value of each measured ratio, ln R, will fall into the area of the triangle for system i (dotted line) or for system ii (soild line). This three-point calibration relationship is already described in eq 1, which takes the forms

values of Rman, Rgal, and Rglc for systems i and ii. Ternary mixtures of hexosamines with several representative compositions were made to quantify the mole fractions of hexosamines from the measured ln R values using the aforementioned equations, and the results are summarized in Table 3. The results presented in this table are an average of triplicate measurements of data performed on different days, and the data are quite reproducible. The experimentally measured molar fractions are comparable to the actual compositions. The experimental error value in determination of mole fractions of hexosamines is quite small, generally