B American Society for Mass Spectrometry, 2014
J. Am. Soc. Mass Spectrom. (2014) 25:439Y443 DOI: 10.1007/s13361-013-0793-8
RESEARCH ARTICLE
Activation Energies of Fragmentations of Disaccharides by Tandem Mass Spectrometry Ákos Kuki, Lajos Nagy, Katalin E. Szabó, Borbála Antal, Miklós Zsuga, Sándor Kéki Department of Applied Chemistry, University of Debrecen, 4010 Debrecen, Hungary
Abstract. A simple multiple collision model for collision induced dissociation (CID) in quadrupole was applied for the estimation of the activation energy (Eo) of the SY fragmentation processes for lithiated and trifluoroacetated disaccharides, such as maltose, cellobiose, isomaltose, gentiobiose, and trehalose. The internal energy0.5 dependent rate constants k(Eint) were calculated using the Rice-RamspergerKassel-Marcus (RRKM) or the Rice-Ramsperger-Kassel (RRK) theory. The Eo values were estimated by fitting the calculated survival yield (SY) curves to the 0 experimental ones. The calculated Eo values of the fragmentation processes for 10 30 50 lithiated disaccharides were in the range of 1.4–1.7 eV, and were found to Collision Energy (eV) increase in the order trehalose G maltose G isomaltose G cellobiose G gentiobiose. Key words: Multiple collisions, Tandem mass spectrometry, Collision-induced dissociation, RRK and RRKM model, Disaccharides 1
Received: 14 October 2013/Revised: 12 November 2013/Accepted: 17 November 2013/Published o nline: 14 January 2014
Introduction
C
arbohydrates represent one of the most important classes of biological molecules and play important roles in a wide range of biological processes [1–3]. Tandem mass spectrometry, on the basis of collision induced dissociation (CID) fragmentation experiments, is an essential tool for the structural characterization of carbohydrates [4– 7]. Exploring the mass spectrometric behavior and the basic parameters of the fragmentation processes is of crucial importance for the development of tandem mass spectrometric methodologies. Modeling techniques can help describe these mechanisms. The extent of fragmentation obtained from CID depends, among many other factors, on the activation energy (Eo) of the fragmentation processes. Very recently, our research group reported a simple collision model of multiple collisions occurring in quadrupole type mass spectrometers for the description of the energetics of the fragmentations. The model was used for the estimation of Eo of lithiated polyethers from the survival yield (SY) versus laboratory collision energy curves [8]. In this article, we report an application of our collision model for the estimation of Eo of lithiated
Electronic supplementary material The online version of this article (doi:10.1007/s13361-013-0793-8) contains supplementary material, which is available to authorized users. Correspondence to: Sándor Kéki; e-mail: [email protected]
disaccharides, such as maltose, cellobiose, isomaltose, gentiobiose, and trehalose. The energetics of fragmentation of the disaccharides ionized with trifluoroacetate ion was also studied.
Experimental Chemicals HPLC grade methanol (VWR International, Leuven, Belgium) were used without further purification. Water was purified by a Direct-Q water system (Millipore, Molsheim, France). LiCl, sodium trifluoroacetate (NaTFA), polyethylene glycol (PEG), and all disaccharides were received from Aldrich (Steinheim, Germany). The disaccharides were dissolved in methanol/water (4/1 vol/vol) at a concentration of 0.1 mg/mL. To obtain lithiated and trifluoroacetated adducts, LiCl and NaTFA were added to the disaccharide solutions to obtain 0.1 mM concentration of the salts. PEG with Mn of 400 g/mol was used for the experiments. To obtain lithiated adducts of PEG in ESI, a solution of LiCl in methanol was added to the PEG solution (in methanol) to obtain 1 mM concentration of the PEG and LiCl.
Electrospray Quadrupole Time-of-Flight MS/MS (ESI-Q-TOF) The MS/MS measurements were performed with a MicroTOFQ type Qq-TOF MS instrument (Bruker Daltoniks, Bremen,
440
Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
Germany) using an ESI source with positive ion mode. The sample solutions were introduced directly into the ESI source with a syringe pump (Cole-Parmer Ins. Co., Vernon Hills, IL, USA) at a flow rate of 3 μL/min. The spray voltage was set to 4 kV. The temperature of the drying gas (N2) was kept at 180 °C. For the MS/MS experiments, nitrogen was used as the collision gas and the collision energies were varied in the range of 1– 60 eV (in the laboratory frame). The pressure in the collision cell was determined to be 8×10–3 mbar. The precursor ions for MS/ MS were selected with an isolation width of 1–4m/z units.
Determination of the Survival Yield (SY) The SY values were calculated according to Equation 1 SY ¼
Ip þ
Ip X
I F;i
ð1Þ
where Ip is the intensity of the precursor ion, and ΣΙF,i is the sum of all fragment ion intensities. The laboratory collision energy (CE50) at which the intensity of the precursor ion is equal to that of all fragment ions (i.e., at 50 % fragmentation (SY = 0.5)) was determined with appropriate accuracy by a linear two-point interpolation.
Results and Discussion In our previous study [8], a simple collision model was developed for the calculation of the precursor ion internal energy increase due to multiply collisions and for the computation of the time intervals between collisions (τ) in quadrupole-type instruments. The internal energy-dependent rate constant k(E int ) was calculated using the RiceRamsperger-Kassel-Marcus (RRKM) or the RiceRamsperger-Kassel (RRK) theory. The survival yield (SY) can be determined from the k(Eint) and (τ) values after each collisions. Implementing our model and the unimolecular dissociation theory (RRKM or RRK) in a spreadsheet software the survival yield versus laboratory collision energy
curve can be constructed and the activation energy of the fragmentation can be estimated by fitting the calculated SY curve to the experimental one. As an extension of our work this simple collision model was applied for the estimation of Eo for five disaccharides. Figure 1 shows the MS/MS spectra of the [M + Li]+ ion of maltose recorded at 32 eV laboratory collision energy. This laboratory collision energy was chosen as it provided informative fragmentation pattern with sufficient precursor and product ion intensities. Additional MS/MS spectra of lithiated cellobiose, isomaltose, gentiobiose and trehalose are presented as Supplementary Figures S1–S4. The breakdown curves (i.e., the relative intensities of product ions versus laboratory collision energy) are plotted in Supplementary Figures S5–S9. Although the decomposition process is the result of competitive reactions, the product ions arising from the cleavage of the glycosidic bond of the lithiated adduct ion at m/z 169 and 187 are dominant in the laboratory collision energy range of 10–50 eV, as the product ion spectra and the breakdown plots show. Therefore, our model is capable of estimating the average activation energy of the decomposition reaction, which can mainly be attributed to the glycosidic bond cleavage.
Estimating the Eo Values for the Disaccharides Using the Collision Model and RRK Algorithm In the first step, the parameters of the collision model were determined for the lithiated disaccharides using leucine enkephaline as a “calibrant.” The collision cross-sections (σ) [9] were estimated scaling it by the mass ratio of the disaccharides to Leucine enkephaline. The numbers of effective oscillators (Seff, see Equation 2), which were determined for leucine enkephaline by our model [8], was proportioned by the degrees of freedom. The energy transfer efficiency (η) was kept constant as obtained for leucine enkephaline [8]. The initial internal energies (Eint,o) [10] were calculated as detailed in our previous report [8]. Using formulas of our collision model [8], the SY values were calculated. The energy-dependent rate constant k(Eint) was calculated using the RRK approximation (Equation 2) for
Figure 1. Product ion spectra (ESI- Qq-TOF) of the lithiated adduct of maltose (Glcα1-4Glc) recorded at 32 eV laboratory frame collision energy
Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
1 Maltose
0.9
Cellobiose
0.8
Isomaltose
0.7
Gentiobiose Trehalose
SY
0.6
PEG6
0.5 0.4
0.3 0.2 0.1 0 10
20
30
40
50
60
Collision Energy (eV)
Figure 2. The SY values for lithiated disaccharides and PEG as a function of the laboratory collision energy measured by quadrupole-time-of-flight (Q-TOF) instrument. Parameters for Q-TOF: collision gas, N2; collision cell length, 0.08 m; collision cell pressure, 0.8 Pa. The solid lines represent the calculated curves using our collision model with RRK equation. Calculation parameters: Eint,o = 1.2 eV, Tcoll = 293 K, σ = 1.02 × 10–18 m2, η = 0.43, Seff = 25. The Eo and A values providing the best fit between the experimental and calculated plots are compiled in Table 1
each collision Eo Seff kðEint Þ ¼ A 1 ‐ Eint
ð2Þ
where A is the pre-exponential factor. Figure 2 shows the SY versus laboratory collision energy curve for the lithiated disaccharides determined by the QTOF instrument together with the fitted curves calculated by our collision model with the RRK theory. The experimental SY curves were fitted to calculated SY curves varying Eo and A to get the best possible match. The same A value was used for all the disaccharides; hence, the reaction enthalpy differences between the disaccharides contributed to the differences of the estimated Eo values. As seen in Figure 2, excellent agreement can be achieved between the experimental and the fitted curves. The Eo and A values together with the CE50 values (see Experimental section) for the lithiated disaccharides are compiled in Table 1. The activation energies were found to increase in the order trehalose Gmaltose Gisomaltose Gcellobiose G
441
gentiobiose, which coincides with the order of the corresponding CE50 values, and reflected by the slight shift of the SY curves in Figure 2. The following relations can be recognized for the Eo values in Table 1: maltose (α 1-4)Gcellobiose (β 1-4) and isomaltose (α 1-6)Ggentiobiose (β 1-6), that is the axial glycosidic bond in the α isomers are more easily cleaved than the equatorial glycosidic bond in the corresponding β isomers, as it was anticipated from the results in [11]. The difference between the 1→4 or 1→1 and the 1→6 linkages can be explained by that the 6-linkage has 3-bond rotation and it is more flexible than the 2-bond 1→4 and 1→1 linkage. The more rotational freedom should make the 1→6 bonds more resistant to decomposition [12]. In our previous study [8] using the collision model and RRK algorithm with the suggested value of Eo (1.05 eV) [9], logA = 7.90 was obtained for the pre-exponential factor for the reference compound leucine enkephalin, which is close to the logA value (7.33) estimated for the disaccharides. This suggests that the activation entropy is quite similar for leucine enkephalin and the disaccharides, and the difference in the energetics of the fragmentation process of leucine enkephalin and the disaccharides can be expressed by the different Eo values. As a test of our simple collision model, we estimated the critical energy of lithiated polyethylene glycol (PEG) with degrees of freedom (DOF) similar to that of the disaccharides. The experimental and the calculated SY curves for PEG with six repeat units are also presented in Figure 2. The critical energy Eo = 2.24 eV obtained by our model for the lithiated PEG6 is very close to that obtained by high-level quantum chemical calculations for PEG6 (2.28 eV at the levels of theory B3LYP for the main fragmentation pathway) [13]. This very good agreement validates our collision model for the estimation of the activation energy of decomposition. In further experiments, the decomposition of disaccharides ionized by trifluoroacetate was also investigated and the activation energy of the fragmentation process was determined. The dissociation of the trifluoroacetated disaccharides yielded a neutral disaccharide and a trifluoroacetate anion without the formation of other product ions. The trifluoroacetated parent ions suffer only one decomposition reaction, and no competitive reactions are present. Hence, the decomposition process can be characterized by one critical energy. The MS/MS spectra of trifluoroacetated maltose, cellobiose, isomaltose, gentiobiose, and trehalose
Table 1. The Estimated Eo and A Values from the RRK Fitting for the Lithiated (Li+) and Trifuoroacetated (TFA–) Disaccharides and PEG. The CE50 Values of the Lithiated Disaccharides and PEG Determined from the SY Plots
Li+ TFA+
Eo (eV) logA CE50 Eo (eV) logA
Maltose α 1→4
Cellobiose β 1→4
Isomaltose α 1→6
1.50 7.33 27.1 0.55 6.51
1.59 7.33 29.3 0.54 6.51
1.55 7.33 28.4 0.54 6.51
Gentiobiose β 1→6 1.65 7.33 30.8 0.54 6.51
Trehalose α 1→1 1.43 7.33 25.4 0.57 6.51
PEG 2.24 7.48 39.5
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Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
1 0.9 0.8 0.7
SY
0.6 0.5 0.4
0.3 0.2 0.1 0 0
10
20
30
40
50
Collision Energy (eV)
Figure 3. The SY values for lithiated cellobiose as a function of the laboratory collision energy measured by quadrupoletime-of-flight (Q-TOF) instrument. Parameters for Q-TOF: collision gas, N2; collision cell length, 0.08 m; collision cell pressure, 0.8 Pa. The solid line represents the calculated curve using our collision model with RRKM theory. Calculation parameters: Eint,o = 1.2 eV, Tcoll = 293 K, σ = 1.02 × 10–18 m2, η = 0.43. The fitting values providing the best fit between the experimental and calculated plots are Eo = 1.50 eV and S = 2.6
are presented as Supplementary Figures S10–S14. The Eo values for the dissociation of the trifluoroacetate ion from disaccharides are also collected in Table 1. The experimental and the calculated SY versus laboratory collision energy curves for the trifluoroacetated disaccharides are shown in Supplementary Figure S15. As seen in Supplementary Figure S10, the SY plots of maltose, cellobiose, isomaltose, and gentiobiose coincide with each other, while the SY plot of trehalose is slightly shifted to higher energies with about 1 eV characteristic energy increase. This shift is reflected also in the slighty higher activation energy of trifluoroacetated trehalose (Table 1).
The RRKM approximation [14] (Equation 3) more accurately describes the rates of unimolecular reactions than the RRK equation does, σW≠ ðEint − Eo Þ hρðEint Þ
Conclusions Our simple collision model [8] was successfully applied for the estimation of the activation energy (Eo) of disaccharides. Very good fitting was achieved between the calculated and the experimental SY versus laboratory collision energy curves by varying the pre-exponential factor and Eo in the RRK equation. Using the more sophisticated RRKM theory for the calculation of the internal energy dependent rate constant is not straightforward because of the lack of vibrational frequency data. The collision model with the RRK formalism provided critical energy for fragmentation for PEG very close to that calculated by high-level quantum chemical calculations. Our model is based on simple approximations, the numerical results are tentative estimations of the activation energy, nevertheless, the calculated Eo values can be used as a comparison for other carbohydrate fragmentations or testing new methodologies.
Acknowledgment
Estimating the Eo Value for Cellobiose Using the Collision Model and RRKM Algorithm
kðEint Þ ¼
frequencies of cellobiose were obtained from [15]. The transition state frequencies were estimated from the reactant frequencies by deleting the vibration assumed to be the reaction coordinate (1080 cm–1) and scaling five from the lowest frequencies by a factor S [14]. The unknown Eo and S can be obtained experimentally [16]. The SY values of lithiated cellobiose calculated by our collision model and RRKM theory were fitted to the experimental SY versus laboratory collision energy curve by varying the value of Eo and S until the best fit was obtained. The experimental and the calculated plots are shown in Figure 3. The reason for the deviation between the fitted and the experimental curves may be the lack of the accurate transition state vibrational frequencies. The Eo = 1.59 eV estimated by our model using the RRK equation for cellobiose (Table 1) agrees well with the Eo = 1.50 eV (Figure 3) calculated by our model and the RRKM theory.
The authors acknowledge financial support for this work by the grant K-101850 given by OTKA (National Found for Scientific Research Development, Hungary), and the grant TÁMOP-4.2.2.A-11/1/KONV-2012-0036 by the European Union and co-funded by the European Social Fund.
ð3Þ
where ρ(Eint) is the density of states of the reactant and W≠ (Eint - Eo) is the sum of states of the transition state, Eo is the critical energy for fragmentation, σ is the reaction path degeneracy and h is the Planck’s constant. The calculation of the k(Eint) by the RRKM model for disaccharides requires the knowledge of the reactant and transition state vibrational frequencies, which are only partially known for the disaccharides. The ground state
References 1. Taylor, M.E., Drickamer, K.: Introduction to Glycobiology, pp. 123– 266. Oxford University Press, Oxford (2006) 2. Varki, A., Cummings, R.D., Esko, J.D., Freeze, H.H., Stanley, P., Bertozzi, C.R., Hart, G.W., Etzler, M.E.: Essentials of Glycobiology, pp. 75–89. Cold Spring Harbor Laboratory Press, Cold Spring Harbor (2009) 3. Muthana, S.M., Campbell, C.T., Gildersleeve, J.C.: Modifications of glycans: biological significance and therapeutic opportunities. ACS Chem. Biol. 7, 31–43 (2012) 4. Hofmeister, G.E., Zhou, Z., Leary, J.A.: Linkage position determination in lithium-cationized disaccharides: tandem mass spectrom-
Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
5. 6.
7.
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9. 10.
etry and semi-empirical calculations. J. Am. Chem. Soc. 113, 5964–5970 (1991) Asam, M.R., Glish, G.L.: Tandem mass spectrometry of alkali cationized polysaccharides in a quadrupole ion trap. J. Am. Soc. Mass Spectrom. 8, 987–995 (1997) Simões, J., Domingues, P., Reis, A., Nunes, F.M., Coimbra, M.A., Domingues, M.R.M.: Identification of anomeric configuration of underivatized reducing glucopyranosyl-glucose disaccharides by tandem mass spectrometry and multivariate analysis. Anal. Chem. 79, 5896–5905 (2007) Azenha, C.S.R., Coimbra, M.A., Moreira, A.S.P., Domingues, P., Domingues, M.R.M.: Differentiation of isomeric β-(1–4) hexose disaccharides by positive electrospray tandem mass spectrometry. J. Mass Spectrom. 48, 548–552 (2013) Kuki, Á., Shemirani, G., Nagy, L., Antal, B., Zsuga, M., Kéki, S.: Estimation of activation energy from the survival yields: fragmentation study of leucine enkephalin and polyethers by tandem mass spectrometry. J. Am. Soc. Mass Spectrom. 24, 1064–1071 (2013) Sztáray, J., Memboeuf, A., Drahos, L., Vékey, K.: Leucine enkephalin—a mass spectrometry standard. Mass Spectrom. Rev. 30, 298–320 (2011) Drahos, L., Vékey, K.: Determination of the thermal energy and its distribution in peptides. J. Am. Soc. Mass Spectrom. 10, 323–328 (1999)
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11. Fangmark, I., Jansson, A., Nilsson, B.: Determination of linkage position and anomeric configuration in glucose-containing disaccharide alditols by multivariate analysis of data from mass spectrometry. Anal. Chem. 71, 1105–1110 (1999) 12. Laine, R.A., Yoon, E., Mahier, T.J., Abbas, S.A., de Lappe, B., Jain, R.K., Matta, K.L.: Non-reducing terminal linkage position determination in intact and permethylated synthetic oligosaccharides having a penultimate amino sugar: fast atom bombardment ionization, collisional-induced dissociation and tandem mass spectrometry. Biol. Mass Spectrom. 20, 505–514 (1991) 13. Memboeuf, A., Drahos, L., Vékey, K., Lendvay, G.: Energetics of fragmentation for cationized poly(ethylene glycol) oligomers. Rapid Commun. Mass Spectrom. 24, 2471–2473 (2010) 14. Baer, T., Mayer, P.M.: Statistical Rice-Ramsperger-Kassel-Marcus quasi-equilibrium theory calculations in mass spectrometry. J. Am. Soc. Mass Spectrom. 8, 103–115 (1997) 15. Andrianov, V.M., Zhbankov, R.G., Dashevskii, V.G.: A theoretical study of the vibrational spectrum of cellobiose within the framework of the additive model of interatomic interactions. J. Struct. Chem. 21, 320– 324 (1980) 16. Laskin, J., Denisov, E., Futrell, J.: A comparative study of collisioninduced and surface-induced dissociation. 1. Fragmentation of protonated dialanine. J. Am. Chem. Soc. 122, 9703–9714 (2000)
J. Am. Soc. Mass Spectrom. (2014) 25:439Y443 DOI: 10.1007/s13361-013-0793-8
RESEARCH ARTICLE
Activation Energies of Fragmentations of Disaccharides by Tandem Mass Spectrometry Ákos Kuki, Lajos Nagy, Katalin E. Szabó, Borbála Antal, Miklós Zsuga, Sándor Kéki Department of Applied Chemistry, University of Debrecen, 4010 Debrecen, Hungary
Abstract. A simple multiple collision model for collision induced dissociation (CID) in quadrupole was applied for the estimation of the activation energy (Eo) of the SY fragmentation processes for lithiated and trifluoroacetated disaccharides, such as maltose, cellobiose, isomaltose, gentiobiose, and trehalose. The internal energy0.5 dependent rate constants k(Eint) were calculated using the Rice-RamspergerKassel-Marcus (RRKM) or the Rice-Ramsperger-Kassel (RRK) theory. The Eo values were estimated by fitting the calculated survival yield (SY) curves to the 0 experimental ones. The calculated Eo values of the fragmentation processes for 10 30 50 lithiated disaccharides were in the range of 1.4–1.7 eV, and were found to Collision Energy (eV) increase in the order trehalose G maltose G isomaltose G cellobiose G gentiobiose. Key words: Multiple collisions, Tandem mass spectrometry, Collision-induced dissociation, RRK and RRKM model, Disaccharides 1
Received: 14 October 2013/Revised: 12 November 2013/Accepted: 17 November 2013/Published o nline: 14 January 2014
Introduction
C
arbohydrates represent one of the most important classes of biological molecules and play important roles in a wide range of biological processes [1–3]. Tandem mass spectrometry, on the basis of collision induced dissociation (CID) fragmentation experiments, is an essential tool for the structural characterization of carbohydrates [4– 7]. Exploring the mass spectrometric behavior and the basic parameters of the fragmentation processes is of crucial importance for the development of tandem mass spectrometric methodologies. Modeling techniques can help describe these mechanisms. The extent of fragmentation obtained from CID depends, among many other factors, on the activation energy (Eo) of the fragmentation processes. Very recently, our research group reported a simple collision model of multiple collisions occurring in quadrupole type mass spectrometers for the description of the energetics of the fragmentations. The model was used for the estimation of Eo of lithiated polyethers from the survival yield (SY) versus laboratory collision energy curves [8]. In this article, we report an application of our collision model for the estimation of Eo of lithiated
Electronic supplementary material The online version of this article (doi:10.1007/s13361-013-0793-8) contains supplementary material, which is available to authorized users. Correspondence to: Sándor Kéki; e-mail: [email protected]
disaccharides, such as maltose, cellobiose, isomaltose, gentiobiose, and trehalose. The energetics of fragmentation of the disaccharides ionized with trifluoroacetate ion was also studied.
Experimental Chemicals HPLC grade methanol (VWR International, Leuven, Belgium) were used without further purification. Water was purified by a Direct-Q water system (Millipore, Molsheim, France). LiCl, sodium trifluoroacetate (NaTFA), polyethylene glycol (PEG), and all disaccharides were received from Aldrich (Steinheim, Germany). The disaccharides were dissolved in methanol/water (4/1 vol/vol) at a concentration of 0.1 mg/mL. To obtain lithiated and trifluoroacetated adducts, LiCl and NaTFA were added to the disaccharide solutions to obtain 0.1 mM concentration of the salts. PEG with Mn of 400 g/mol was used for the experiments. To obtain lithiated adducts of PEG in ESI, a solution of LiCl in methanol was added to the PEG solution (in methanol) to obtain 1 mM concentration of the PEG and LiCl.
Electrospray Quadrupole Time-of-Flight MS/MS (ESI-Q-TOF) The MS/MS measurements were performed with a MicroTOFQ type Qq-TOF MS instrument (Bruker Daltoniks, Bremen,
440
Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
Germany) using an ESI source with positive ion mode. The sample solutions were introduced directly into the ESI source with a syringe pump (Cole-Parmer Ins. Co., Vernon Hills, IL, USA) at a flow rate of 3 μL/min. The spray voltage was set to 4 kV. The temperature of the drying gas (N2) was kept at 180 °C. For the MS/MS experiments, nitrogen was used as the collision gas and the collision energies were varied in the range of 1– 60 eV (in the laboratory frame). The pressure in the collision cell was determined to be 8×10–3 mbar. The precursor ions for MS/ MS were selected with an isolation width of 1–4m/z units.
Determination of the Survival Yield (SY) The SY values were calculated according to Equation 1 SY ¼
Ip þ
Ip X
I F;i
ð1Þ
where Ip is the intensity of the precursor ion, and ΣΙF,i is the sum of all fragment ion intensities. The laboratory collision energy (CE50) at which the intensity of the precursor ion is equal to that of all fragment ions (i.e., at 50 % fragmentation (SY = 0.5)) was determined with appropriate accuracy by a linear two-point interpolation.
Results and Discussion In our previous study [8], a simple collision model was developed for the calculation of the precursor ion internal energy increase due to multiply collisions and for the computation of the time intervals between collisions (τ) in quadrupole-type instruments. The internal energy-dependent rate constant k(E int ) was calculated using the RiceRamsperger-Kassel-Marcus (RRKM) or the RiceRamsperger-Kassel (RRK) theory. The survival yield (SY) can be determined from the k(Eint) and (τ) values after each collisions. Implementing our model and the unimolecular dissociation theory (RRKM or RRK) in a spreadsheet software the survival yield versus laboratory collision energy
curve can be constructed and the activation energy of the fragmentation can be estimated by fitting the calculated SY curve to the experimental one. As an extension of our work this simple collision model was applied for the estimation of Eo for five disaccharides. Figure 1 shows the MS/MS spectra of the [M + Li]+ ion of maltose recorded at 32 eV laboratory collision energy. This laboratory collision energy was chosen as it provided informative fragmentation pattern with sufficient precursor and product ion intensities. Additional MS/MS spectra of lithiated cellobiose, isomaltose, gentiobiose and trehalose are presented as Supplementary Figures S1–S4. The breakdown curves (i.e., the relative intensities of product ions versus laboratory collision energy) are plotted in Supplementary Figures S5–S9. Although the decomposition process is the result of competitive reactions, the product ions arising from the cleavage of the glycosidic bond of the lithiated adduct ion at m/z 169 and 187 are dominant in the laboratory collision energy range of 10–50 eV, as the product ion spectra and the breakdown plots show. Therefore, our model is capable of estimating the average activation energy of the decomposition reaction, which can mainly be attributed to the glycosidic bond cleavage.
Estimating the Eo Values for the Disaccharides Using the Collision Model and RRK Algorithm In the first step, the parameters of the collision model were determined for the lithiated disaccharides using leucine enkephaline as a “calibrant.” The collision cross-sections (σ) [9] were estimated scaling it by the mass ratio of the disaccharides to Leucine enkephaline. The numbers of effective oscillators (Seff, see Equation 2), which were determined for leucine enkephaline by our model [8], was proportioned by the degrees of freedom. The energy transfer efficiency (η) was kept constant as obtained for leucine enkephaline [8]. The initial internal energies (Eint,o) [10] were calculated as detailed in our previous report [8]. Using formulas of our collision model [8], the SY values were calculated. The energy-dependent rate constant k(Eint) was calculated using the RRK approximation (Equation 2) for
Figure 1. Product ion spectra (ESI- Qq-TOF) of the lithiated adduct of maltose (Glcα1-4Glc) recorded at 32 eV laboratory frame collision energy
Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
1 Maltose
0.9
Cellobiose
0.8
Isomaltose
0.7
Gentiobiose Trehalose
SY
0.6
PEG6
0.5 0.4
0.3 0.2 0.1 0 10
20
30
40
50
60
Collision Energy (eV)
Figure 2. The SY values for lithiated disaccharides and PEG as a function of the laboratory collision energy measured by quadrupole-time-of-flight (Q-TOF) instrument. Parameters for Q-TOF: collision gas, N2; collision cell length, 0.08 m; collision cell pressure, 0.8 Pa. The solid lines represent the calculated curves using our collision model with RRK equation. Calculation parameters: Eint,o = 1.2 eV, Tcoll = 293 K, σ = 1.02 × 10–18 m2, η = 0.43, Seff = 25. The Eo and A values providing the best fit between the experimental and calculated plots are compiled in Table 1
each collision Eo Seff kðEint Þ ¼ A 1 ‐ Eint
ð2Þ
where A is the pre-exponential factor. Figure 2 shows the SY versus laboratory collision energy curve for the lithiated disaccharides determined by the QTOF instrument together with the fitted curves calculated by our collision model with the RRK theory. The experimental SY curves were fitted to calculated SY curves varying Eo and A to get the best possible match. The same A value was used for all the disaccharides; hence, the reaction enthalpy differences between the disaccharides contributed to the differences of the estimated Eo values. As seen in Figure 2, excellent agreement can be achieved between the experimental and the fitted curves. The Eo and A values together with the CE50 values (see Experimental section) for the lithiated disaccharides are compiled in Table 1. The activation energies were found to increase in the order trehalose Gmaltose Gisomaltose Gcellobiose G
441
gentiobiose, which coincides with the order of the corresponding CE50 values, and reflected by the slight shift of the SY curves in Figure 2. The following relations can be recognized for the Eo values in Table 1: maltose (α 1-4)Gcellobiose (β 1-4) and isomaltose (α 1-6)Ggentiobiose (β 1-6), that is the axial glycosidic bond in the α isomers are more easily cleaved than the equatorial glycosidic bond in the corresponding β isomers, as it was anticipated from the results in [11]. The difference between the 1→4 or 1→1 and the 1→6 linkages can be explained by that the 6-linkage has 3-bond rotation and it is more flexible than the 2-bond 1→4 and 1→1 linkage. The more rotational freedom should make the 1→6 bonds more resistant to decomposition [12]. In our previous study [8] using the collision model and RRK algorithm with the suggested value of Eo (1.05 eV) [9], logA = 7.90 was obtained for the pre-exponential factor for the reference compound leucine enkephalin, which is close to the logA value (7.33) estimated for the disaccharides. This suggests that the activation entropy is quite similar for leucine enkephalin and the disaccharides, and the difference in the energetics of the fragmentation process of leucine enkephalin and the disaccharides can be expressed by the different Eo values. As a test of our simple collision model, we estimated the critical energy of lithiated polyethylene glycol (PEG) with degrees of freedom (DOF) similar to that of the disaccharides. The experimental and the calculated SY curves for PEG with six repeat units are also presented in Figure 2. The critical energy Eo = 2.24 eV obtained by our model for the lithiated PEG6 is very close to that obtained by high-level quantum chemical calculations for PEG6 (2.28 eV at the levels of theory B3LYP for the main fragmentation pathway) [13]. This very good agreement validates our collision model for the estimation of the activation energy of decomposition. In further experiments, the decomposition of disaccharides ionized by trifluoroacetate was also investigated and the activation energy of the fragmentation process was determined. The dissociation of the trifluoroacetated disaccharides yielded a neutral disaccharide and a trifluoroacetate anion without the formation of other product ions. The trifluoroacetated parent ions suffer only one decomposition reaction, and no competitive reactions are present. Hence, the decomposition process can be characterized by one critical energy. The MS/MS spectra of trifluoroacetated maltose, cellobiose, isomaltose, gentiobiose, and trehalose
Table 1. The Estimated Eo and A Values from the RRK Fitting for the Lithiated (Li+) and Trifuoroacetated (TFA–) Disaccharides and PEG. The CE50 Values of the Lithiated Disaccharides and PEG Determined from the SY Plots
Li+ TFA+
Eo (eV) logA CE50 Eo (eV) logA
Maltose α 1→4
Cellobiose β 1→4
Isomaltose α 1→6
1.50 7.33 27.1 0.55 6.51
1.59 7.33 29.3 0.54 6.51
1.55 7.33 28.4 0.54 6.51
Gentiobiose β 1→6 1.65 7.33 30.8 0.54 6.51
Trehalose α 1→1 1.43 7.33 25.4 0.57 6.51
PEG 2.24 7.48 39.5
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Á. Kuki et al.: Activation Energies of Disaccharides by MS/MS
1 0.9 0.8 0.7
SY
0.6 0.5 0.4
0.3 0.2 0.1 0 0
10
20
30
40
50
Collision Energy (eV)
Figure 3. The SY values for lithiated cellobiose as a function of the laboratory collision energy measured by quadrupoletime-of-flight (Q-TOF) instrument. Parameters for Q-TOF: collision gas, N2; collision cell length, 0.08 m; collision cell pressure, 0.8 Pa. The solid line represents the calculated curve using our collision model with RRKM theory. Calculation parameters: Eint,o = 1.2 eV, Tcoll = 293 K, σ = 1.02 × 10–18 m2, η = 0.43. The fitting values providing the best fit between the experimental and calculated plots are Eo = 1.50 eV and S = 2.6
are presented as Supplementary Figures S10–S14. The Eo values for the dissociation of the trifluoroacetate ion from disaccharides are also collected in Table 1. The experimental and the calculated SY versus laboratory collision energy curves for the trifluoroacetated disaccharides are shown in Supplementary Figure S15. As seen in Supplementary Figure S10, the SY plots of maltose, cellobiose, isomaltose, and gentiobiose coincide with each other, while the SY plot of trehalose is slightly shifted to higher energies with about 1 eV characteristic energy increase. This shift is reflected also in the slighty higher activation energy of trifluoroacetated trehalose (Table 1).
The RRKM approximation [14] (Equation 3) more accurately describes the rates of unimolecular reactions than the RRK equation does, σW≠ ðEint − Eo Þ hρðEint Þ
Conclusions Our simple collision model [8] was successfully applied for the estimation of the activation energy (Eo) of disaccharides. Very good fitting was achieved between the calculated and the experimental SY versus laboratory collision energy curves by varying the pre-exponential factor and Eo in the RRK equation. Using the more sophisticated RRKM theory for the calculation of the internal energy dependent rate constant is not straightforward because of the lack of vibrational frequency data. The collision model with the RRK formalism provided critical energy for fragmentation for PEG very close to that calculated by high-level quantum chemical calculations. Our model is based on simple approximations, the numerical results are tentative estimations of the activation energy, nevertheless, the calculated Eo values can be used as a comparison for other carbohydrate fragmentations or testing new methodologies.
Acknowledgment
Estimating the Eo Value for Cellobiose Using the Collision Model and RRKM Algorithm
kðEint Þ ¼
frequencies of cellobiose were obtained from [15]. The transition state frequencies were estimated from the reactant frequencies by deleting the vibration assumed to be the reaction coordinate (1080 cm–1) and scaling five from the lowest frequencies by a factor S [14]. The unknown Eo and S can be obtained experimentally [16]. The SY values of lithiated cellobiose calculated by our collision model and RRKM theory were fitted to the experimental SY versus laboratory collision energy curve by varying the value of Eo and S until the best fit was obtained. The experimental and the calculated plots are shown in Figure 3. The reason for the deviation between the fitted and the experimental curves may be the lack of the accurate transition state vibrational frequencies. The Eo = 1.59 eV estimated by our model using the RRK equation for cellobiose (Table 1) agrees well with the Eo = 1.50 eV (Figure 3) calculated by our model and the RRKM theory.
The authors acknowledge financial support for this work by the grant K-101850 given by OTKA (National Found for Scientific Research Development, Hungary), and the grant TÁMOP-4.2.2.A-11/1/KONV-2012-0036 by the European Union and co-funded by the European Social Fund.
ð3Þ
where ρ(Eint) is the density of states of the reactant and W≠ (Eint - Eo) is the sum of states of the transition state, Eo is the critical energy for fragmentation, σ is the reaction path degeneracy and h is the Planck’s constant. The calculation of the k(Eint) by the RRKM model for disaccharides requires the knowledge of the reactant and transition state vibrational frequencies, which are only partially known for the disaccharides. The ground state
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