Anal. Chem. 2008, 80, 1385-1393
Accelerated Articles
Dynamic Titration: Determination of Dissociation Constants for Noncovalent Complexes in Multiplexed Format Using HPLC-ESI-MS Petr Frycˇa´k† and Kevin A. Schug*
Department of Chemistry and Biochemistry, The University of Texas at Arlington, 700 Planetarium Place, Arlington, Texas 76019-0065
With recent growth in fields such as life sciences and supramolecular chemistry, there has been an ever increasing need for high-throughput methods that would permit determination of binding affinities for noncovalent complexes of various host-guest systems. These are traditionally measured by titration experiments where concentration-dependent signals of species participating in solution-based binding equilibria are monitored by methods such as UV-vis spectrophotometry, calorimetry, or nuclear magnetic resonance spectrometry. Here we present a new titration technique that unifies and allows chromatographic separation of guests with determination of dissociation constants by electrospray mass spectrometry in a multiplexed format. A theoretical model has been derived that describes the complex formation for the guests eluted from a chromatographic column when hosts are admixed postcolumn. The model takes possible competition equilibria into account; i.e., it can deal with unresolved peaks of guests with the possible addition of multiple hosts in one experiment. This on-line workflow makes determination of binding affinities for large libraries of compounds possible. The potential of the method is demonstrated on the determination of dissociation constants for complexes of β- and γ-cyclodextrins with nonsteroidal antiinflammatory drugs ibuprofen, naproxen, and flurbiprofen. Weak noncovalent interactions play an important role in nature. They keep molecules in aggregate states and are also responsible for organizing molecules into higher order structures. Insight into * To whom correspondence should be addressed: Phone: +1-817-272-3541. Fax: +1-817-272-3808. E-mail:
[email protected]. † On leave from: Department of Analytical Chemistry, Faculty of Science, Palacky University, Olomouc, Czech Republic. 10.1021/ac7024078 CCC: $40.75 Published on Web 02/01/2008
© 2008 American Chemical Society
the intricate network of noncovalent interactions between the building blocks of every organism (proteins, nucleic acids) is necessary for understanding how organisms operate at the molecular level.1-4 To affect or mimic such processes, chemists try to design artificial molecular systems that exhibit similar or enhanced binding affinity and specificity compared to their natural counterparts, an area known as supramolecular chemistry.5 The specific noncovalent binding of two or more molecules is sometimes referred to as molecular recognition and is driven by the complementarity in terms of shape and type of interacting structural motifs of the binding partners (ion-ion, van der Waals, hydrogen bonding, π-π stacking, or solvophobic interaction). Specificity is brought about by multipoint contact of the binding molecules that often involves concerted actions of multiple noncovalent forces. On the macroscopic scale, interactions are described by the free energy change ∆G that consists of the enthalpic contribution ∆H and the entropic contribution T∆S (T is temperature; ∆G ) ∆H - T∆S). Although, from the thermodynamical point of view, the binding must be assessed as a whole, it can be said that some types of interactions contribute more to the enthalpic term (e.g., ion-ion interactions) while others contribute more to the entropic term (typically, solvophobic interactions). The ∆G as a measure of binding strength is directly associated with the dissociation constant Kd of a complex (∆G ) RT lnKd). Hence, measurement of Kd gives useful quantitative information about the binding affinity and is necessary in determining the thermodynamic quantities ∆G, ∆H, and ∆S, which in turn may help to explain the mechanism of interaction. UV-vis spectro(1) (2) (3) (4) (5)
Stelzl, U.; Wanker, E. E. Curr. Opin. Chem. Biol. 2006, 10, 551-558. Vasilescu, J.; Figeys, D. Curr. Opin. Biotechnol. 2006, 17, 394-399. Hanson, C. L.; Robinson, C. V. J. Biol. Chem. 2004, 279, 24907-24910. Kim, T. H.; Ren, B. Annu. Rev. Genomics Hum. Genet. 2006, 7, 81-102. Lehn, J.-M. Supramolecular Chemistry; Wiley-VCH: Weinheim, 1995.
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photometry,6 calorimetry,7 and NMR spectrometry6,8,9 have been widely used for measuring dissociation constants. All of these are solution-based methods and therefore allow for studying interactions in their native environment (most interactions interesting in supramolecular chemistry and life science research occur in a solvent medium). However, there are also factors that limit their use. The noncovalent complexes are not observed directly, which complicates determination of the stoichiometry of the complexes and, in the case of more complicated mixtures, also convolutes identification of the interacting partners. Often, sensitivity is an issue for rare compounds since milligram quantities are usually needed in calorimetric and NMR experiments. Last, it would be problematic to use these methods as a basis for high-throughput measurements. Mass spectrometry (MS), on the other hand, is free of the aforementioned shortcomings. It was the introduction of electrospray ionization10,11 (ESI) that enabled routine direct observation of noncovalent complexes.12-27 ESI-MS is a fast and sensitive technique, which allows direct and continuous introduction of liquid samples. A notable difference from solution-phase methods is, however, that analytes must be charged and then transferred to the gas phase prior to their detection. The dissociation constant determination must therefore involve correlation of gas-phase ion abundances with solution-phase equilibrium concentrations. Nevertheless, the resulting value can still well reflect the solutionphase conditions if the equilibrium established between the unbound fractions of interacting molecules and their complex is not disturbed; if all involved species yield gas-phase ions with (6) Hirose, K. J. Inclusion Phenom. Macrocyclic Chem. 2001, 39, 193-209. (7) Lohner, K.; Prenner, E. J. Biochim. Biophys. Acta:Biomembr. 1999, 1462, 141-156. (8) Bagno, A.; Rastrelli, F.; Saielli, G. Prog. Nucl. Magn. Reson. Spectrosc. 2005, 47, 41-93. (9) Schade, M.; Oschkinat, H. Curr. Opin. Drug Discovery Dev. 2005, 8, 365373. (10) Whitehouse, C. M.; Dreyer, R. N.; Yamashita, M.; Fenn, J. B. Anal. Chem. 1985, 57, 675-679. (11) Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Science 1989, 246, 64-71. (12) Baca, M.; Kent, S. B. H. J. Am. Chem. Soc. 1992, 114, 3992-3993. (13) Ganem, B.; Li, Y. T.; Henion, J. D. J. Am. Chem. Soc. 1991, 113, 62946296. (14) Yu, Y. H.; Kirkup, C. E.; Pi, N.; Leary, J. A. J. Am. Soc. Mass Spectrom. 2004, 15, 1400-1407. (15) Yu, Y. H.; Sweeney, M. D.; Saad, O. M.; Leary, J. A. J. Am. Soc. Mass Spectrom. 2006, 17, 524-535. (16) Li, H. H.; Yuan, G. Rapid Commun. Mass Spectrom. 2006, 20, 1736-1740. (17) Bazoti, F. N.; Bergquist, J.; Markides, K. E.; Tsarbopoulos, A. J. Am. Soc. Mass Spectrom. 2006, 17, 568-575. (18) Andersen, U. N.; Seeber, G.; Fiedler, D.; Raymond, K. N.; Lin, D.; Harris, D. J. Am. Soc. Mass Spectrom. 2006, 17, 292-296. (19) Zhang, H. R.; Chen, G.; Wang, L.; Ding, L.; Tian, Y.; Jin, W. Q.; Zhang, H. Q. Int. J. Mass Spectrom. 2006, 252, 1-10. (20) Zhou, J.; Yuan, G. Chem.-Eur. J. 2005, 11, 1157-1162. (21) Sherman, C. L.; Brodbelt, J. S.; Srinivas, G.; Sivappa, R.; Marchand, A. P. Arkivoc 2005, 5-11. (22) Sherman, C. L.; Brodbelt, J. S. J. Am. Soc. Mass Spectrom. 2005, 16, 11621171. (23) Chevreux, G.; Potier, N.; Van Dorsselaer, A.; Bahloul, A.; Houdusse, A.; Wells, A.; Sweeney, H. L. J. Am. Soc. Mass Spectrom. 2005, 16, 13671376. (24) Bazoti, F. N.; Tsarbopoulos, A.; Markides, K. E.; Bergquist, J. J. Mass Spectrom. 2005, 40, 182-192. (25) Pinkse, M. W. H.; Heck, A. J. R.; Rumpel, K.; Pullen, F. J. Am. Soc. Mass Spectrom. 2004, 15, 1392-1399. (26) Brodbelt, J. S. Int. J. Mass Spectrom. 2000, 200, 57-69. (27) Daniel, J. M.; Friess, S. D.; Rajagopalan, S.; Wendt, S.; Zenobi, R. Int. J. Mass Spectrom. 2002, 216, 1-27.
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equal efficiency and the observed complex is not partly or fully formed by nonspecific binding during the electrospray process. These requirements are briefly discussed in the following paragraph. Due to the solvent evaporation from the electrospray droplets, an increase in analyte concentration concomitant with a shift of equilibrium toward greater binding might be expected. However, it has been demonstrated recently that, at least for some hostguest systems, the time frame of electrospray ionization (milliseconds) is sufficiently short to prevent any equilibrium shift during the ionization process.28 The ion formation efficiency is related to the physicochemical properties of an analyte. Experimentally, this is expressed by response factors f (fX ) IX/[X]; IX is absolute ionic intensity of species X and [X] its equilibrium concentration in solution). Response factors cannot be readily measured for noncovalent complexes and are therefore often considered to be equal to those of corresponding hosts.29,30 This is easily justifiable when a large host (typically a protein) binds a small guest (e.g., a small molecule substrate, coenzyme, inhibitor, or drug) because the physicochemical properties of the resulting complex are not expected to be much different from the free host itself. In the case where binding partners are of comparable size, this assumption is less reliable and can be a source of systematic experimental error. Last, if nonspecific binding is suspected, a variety of approaches can be employed to either rule out or prove its existence.27 Advanced procedures designed to correct for partially nonspecific binding have also been developed.31-33 If the gas-phase abundances are found to be very different from the situation in solution, additional procedures are also available. Such methods may use mass spectrometric detection, but the determination of dissociation constant is based on correlating the degree of binding with other phenomena occurring in the solution phase, e.g., diffusion.34 Despite the fact that the debate regarding possible equilibrium shift and response factor disparities in ESI-MS has not yet come to an end, the technique has been already proven to yield valuable information about binding affinities of selected host-guest systems.26,27,35 The dissociation constant is most often measured by a titration experiment where the equilibrium population of relevant species is monitored in a series of solutions incorporating a constant concentration of host and increasing concentrations of guest. There are different approaches for processing results of titrations. Older ones like those of Scatchard,36 Benesi-Hildebrand,37 and Scott38 use linearization procedures where the dis(28) Wortmann, A.; Kistler-Momotova, A.; Zenobi, R.; Heine, M. C.; Wilhelm, O.; Pratsinis, S. E. J. Am. Soc. Mass Spectrom. 2007, 18, 385-393. (29) Jorgensen, T. J. D.; Roepstorff, P.; Heck, A. J. R. Anal. Chem. 1998, 70, 4427-4432. (30) Sannes-Lowery, K. A.; Griffey, R. H.; Hofstadler, S. A. Anal. Biochem. 2000, 280, 264-271. (31) Wang, W. J.; Kitova, E. N.; Sun, J. X.; Klassen, J. S. J. Am. Soc. Mass Spectrom. 2005, 16, 1583-1594. (32) Sun, J. X.; Kitova, E. N.; Wang, W. J.; Klassen, J. S. Anal. Chem. 2006, 78, 3010-3018. (33) Daubenfeld, T.; Bouin, A. P.; van der Rest, G. J. Am. Soc. Mass Spectrom. 2006, 17, 1239-1248. (34) Clark, S. M.; Konermann, L. Anal. Chem. 2004, 76, 7077-7083. (35) Schug, K. A. Comb. Chem. High Throughput Screening 2007, 10, 301316. (36) Scatchard, G. Ann. N. Y. Acad. Sci. 1949, 49, 660-672. (37) Benesi, H. A.; Hildebrand, J. A. J. Am. Chem. Soc. 1949, 71, 2703-2707. (38) Scott, R. L. Recl. Trav. Chim. 1956, 75, 787-789.
sociation constant can be retrieved from the slope or intercept of a line representing the relationship between quantities derived from experimental observables. More recent procedures obtain the dissociation constant as a parameter of curve fit into the titration data using a nonlinear model relating experimentally observed intensities and total concentrations of the host and the guest.39-42 Recently we introduced a new format of titration experiments designed to reduce the time and labor needed both for sample preparation and for the analysis itself.43 Instead of analyzing a series of solutions with increasing concentration of guest, we injected a single solution of guest with known concentration into solvent delivered by an LC pump and flowed through capillary tubing. A Gaussian concentration profile of guest is formed to which the host can be admixed at a steady concentration. Since the concentration of guest in the solution entering the MS detector was changing in time from zero to a maximum concentration and then back to zero, this novel experimental setup was denoted a dynamic titration, to distinguish it from the traditional setup using a set of discrete solutions (here termed a static titration experiment). It should be emphasized that thermodynamic equilibrium at every individual point of the guest concentration distribution is assumed in dynamic titration. The time and labor for sample preparation is reduced because only one solution of host and one solution of guest are needed. The new technique allows one to perform titrations rapidly, using common LC-MS instrumentation and greatly enhances the throughput. In this report, we take the concept of dynamic titration a step further and make it a much more general and effective technique. First, the retrieval of dissociation constants is now independent of the distribution of guest concentrations; i.e., the Gaussian distribution is no longer necessary.43 Next, more than one guest and more than one host can enter the mass spectrometer at the same time. This makes the method compatible with liquid chromatography, where non-Gaussian and unresolved, or partly resolved, peaks are commonly encoutered. The potential of the method is demonstrated here by the determination of dissociation constants for complexes of three nonsteroidal anti-inflammatory drugs with cyclodextrins, including separation of guests on an HPLC column. THEORETICAL BASIS Determination of Dissociation Constants from Dynamic Titration Data. The dynamic titration procedure is derived here focusing specifically on the evaluation of 1:1 binding events (it would be possible, however, to extend the mathematical model to include 1:2 and higher binding stoichiometries). The dissociation constant for 1:1 binding is defined by eq 1:
Kd ) [H][G]/[HG]
(1)
(39) Dotsikas, Y.; Loukas, Y. L. J. Am. Soc. Mass Spectrom. 2003, 14, 11231129. (40) Gabelica, V.; Galic, N.; Rosu, F.; Houssier, C.; De Pauw, E. J. Mass Spectrom. 2003, 38, 491-501. (41) Schug, K.; Frycak, P.; Maier, N. M.; Lindner, W. Anal. Chem. 2005, 77, 3660-3670. (42) Wortmann, A.; Rossi, F.; Lelais, G.; Zenobi, R. J. Mass Spectrom. 2005, 40, 777-784. (43) Frycak, P.; Schug, K. A. Anal. Chem. 2007, 79, 5407-5413.
where [H], [G], and [HG] denote equilibrium concentrations of the free host, the free guest, and their complex, respectively (for simplicity, concentrations are assumed here to be equal to activities). The relationship of equilibrium solution concentrations to total host and guest concentrations (cH and cG) is given by a set of mass balance equations:
cH ) [H] + [HG]
(2a)
cG ) [G] + [HG]
(2b)
The equilibrium concentration of complex can be determined from the mass spectrum in terms of association degree R, defined as the concentration of complex divided by the total concentration of host:
R ) [HG]/cH
(3a)
By substituting for cH in eq 3a, using eq 2a
R)
[HG] [H] + [HG]
(3b)
This equation can be used to determine the association degree directly from a mass spectrum, assuming equal response factors of the host and the complex:
R)
intHG intH + intHG
(3c)
where intH and intHG are the mass spectral intensities of the host and the complex. By substitution for [H] and [G] using eqs 2a, 2b, and subsequently 3a, one obtains
Kd )
(cH - [HG])(cG - [HG]) [HG]
)
(cH - cHR)(cG - cHR) ) cHR (1 - R)(cG - cHR) (4) R
Up to this point, a single solution with given total concentrations of host and guest has been considered. In the dynamic titration experiment, however, only the host concentration is fixed, while the total guest concentration is continuously changing over time (hence the designation dynamic) as the zone in which the injected amount of guest is distributed enters the ESI source. See Figure 1 for possible experimental setups. We can deal with this situation by treating each individual point in time using the approach described above, while linking them together with a logical assumption that the integral of the guest concentration with respect to the volume (V) over which it is distributed must yield the total amount of guest that was injected N0,G (eq 5):
∫
+∞
-∞
cG dV ) N0,G
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
(5) 1387
guest Gj (j ∈ 〈1, 2, ..., n〉), the mass balance equations are as follows: n
∑ [H G ]
cHi ) [Hi] +
i
(10a)
x
x)1 m
∑ [H G ]
cGj ) [Gj] +
x
(10b)
j
x)1
The dissociation constant Kd,ij of complex HiGj (note here that i and j are not stoichiometric coefficients but are indices specifying of which host and guest the complex consists) is defined as
Kd,ij ) [Hi][Gj]/[HiGj]
Figure 1. Experimental setups used for dynamic titration. Key: iv, injection valve (drawn in the load position); sl, sample loop (200 µL in (a) and 20 µL in (b), 10 µL was injected in both cases); gs, 25-µL syringe for the injection of guest solution; hs, syringe pump (equipped with 2.5-mL syringe) pumping solution of host; sp, solvent pump; col, chromatographic column; mx, mixer.
where cG is the total guest concentration at each specific point of the distribution. Because the flow rate Q is constant and known, dV in eq 5 can be replaced with Q dt (t is time) to transform it from a volume to a (more useful) time coordinate:
∫
+∞
-∞
cG dt )
N0,G Q
R + cHR 1-R
The equilibrium concentrations of Hi and Gj can be expressed from eqs 10a and 10b. Substituting into eq 11 yields n
(cHi -
∑ [H G ])(c i
x
m
Gj
-
x)1
Kd,ij )
∑ [H G ]) x
j
x)1
(12)
[HiGj]
The equilibrium concentrations of complexes involved in eq 12 can be retrieved from experimental data using their respective association degrees defined previously in eq 3a:
Rij ) [HiGj]/cHi
(6)
(13a)
The analogies of eqs 3b and 3c in the multicomponent system are then
The guest concentration is expressed from eq 4:
cG ) Kd
(11)
[HiGj]
Rij )
(7)
(13b)
n
∑ [H G ]
[Hi] +
i
x
x)1
and substituted into eq 6, one obtains
∫
+∞
-∞
(
Kd
N0,G R + cHR dt ) 1-R Q
)
intHiGj
Rij ) (8)
(13c)
n
intHi +
∑ int
HiGx
x)1
Now, the desired Kd can be expressed from eq 8 to yield
Kd )
N0,G - cH Q
∫
+∞
-∞
∫
+∞
-∞
R dt
R dt 1-R
(9)
The latter equation is used to determine the association degrees from spectral intensities under the assumption of equal response factors of host and its complexes. The equilibrium concentrations of complexes can then be expressed from eq 13a and substituted into eq 12: n
The derivation is only slightly more complicated when more than one guest or more than one host are involved. This can occur when guests are coeluting or multiple hosts are deliberately used in one experiment (multiplexing). Both of these cases are demonstrated in this study. In a system with m hosts and n guests, m × n complexes characterized by the same number of dissociation constants are present. For host Hi (i ∈ 〈1, 2, ..., m〉) and 1388
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
(cHi - cHi Kd,ij )
∑
m
Rix)(cGj -
x)1
∑c
HxRxj)
x)1
)
cHiRij n
(1 -
∑ R )(c ix
m
Gj
x)1
Rij
-
∑c x)1
HxRxj)
(14)
As in the case of a single host-single guest system, the cGj is expressed from eq 14:
Rij
cGj ) Kd,ij
m
+
n
∑R
1-
∑c
HxRxj
(15)
x)1
ix
x)1
and Kd,ij can then be calculated from the integral of cGj with respect to time (eq 16, analogous to eq 6)
∫
+∞
-∞
(
Rij
Kd,ij
m
+
n
1-
∑R
∑c
HxRxj
x)1
ix
x)1
)
dt )
N0,Gj Q
(16)
Kd characterizing the equilibrium is then evaluated as that which returns a minimum value of ∆.
yielding the final equation for Kd determination in a multicomponent dynamic titration:
N0,Gj Kd,ij )
-
Q
m
∫ (∑ c +∞
-∞
HxRxj)
dt
x)1
∫
(17)
Rij
+∞
-∞
dt
n
1-
∑R
ix
x)1
Determination of Dissociation Constant from Static Titration Data. In static titration, the dissociation constant can be theoretically calculated for each experimental point separately (i.e., for each solution with its cH and cG), using eq 4 in which the association degree is obtained from the mass spectrum using eq 3c. However, the result of a titration experiment is a set of association degreessone for every combination of cH and cG. Since it is preferable to get the dissociation constant from the data at once rather then calculating them for each titration point (and then taking their average, for example), we instead generate sets of association degrees for different values of Kd and pick that dissociation constant which yields theoretical data points as close to the experimental data points as possible. The calculation of association degrees is based on eq 4:
cH + cG + Kd - x(cH + cG + Kd)2 - 4cHcG R) (18) 2cH To quantify the degree of agreement between generated and experimental sets of association degrees, the sum of differences between generated and experimental values across all N experimental points, according to the following equation, is used: N
∆)
∑ i)1
(
|Ri,gen - Ri,ex| Ri,ex
+
Figure 2. Structures of cyclodextrins (m ) 7 for β-CD; m ) 8 for γ-CD), ibuprofen (IBP) naproxen (NPX), and flurbiprofen (FBP).
)
|Ri,gen - Ri,ex| 1 - Ri,ex
(19)
The reason behind dividing the absolute differences by both R and (1 - R) is to give each of them equal significance regardless of the actual value of R, which may be anywhere from 0 to 1. The
EXPERIMENTAL SECTION Chemicals. LC-MS grade water was supplied by J.T. Baker (Phillipsburg, NJ). Acetonitrile (ACN) and hydrochloric acid were obtained from EMD Chemicals (Gibbstown, NJ). Racemic ibuprofen (IBP; M.W. 206.3) was purchased from Biomol International (Plymouth Meeting, PA), (S)-naproxen (NPX; MW 230.3) and racemic flurbiprofen (FBP; MW 244.3) were from Cayman Chemical Co. (Ann Arbor, MI), β-cyclodextrin (β-CD; MW 1135.0) was from EMD Biosciences (La Jolla, CA), and γ-cyclodextrin (γCD, MW 1297.1) was from TCI America (Portland, OR). Structures are shown in Figure 2. Instrumentation and Methods. All measurements were carried out using an LCQ Deca XP ion trap mass spectrometer (Thermo Electron Corp., West Palm Beach, FL) equipped with an electrospray ion source operated in the negative ionization mode. The ion optic elements were tuned for the β-CD•NPX complex (the • character denotes a noncovalent complex throughout this report) using the automatic tuning feature. Ion source parameters were as follows: spraying voltage 3 kV, sheath gas flow rate 15 arbitrary units, heated capillary temperature 200 °C, capillary voltage 43 V, and tube lens offset 30 V. Spectra were taken from 200 to 2000 Th (1 Th ) 1 atomic mass unit per one elementary charge (m/z)), and each scan consisted of three microscans. The acquisition of one spectrum took ∼1.5 s. The automatic gain control feature was set to On. Two sets of experiments were done. In the first one, a solution containing the guest was injected into the flow of water (20 µL/min) provided by a Surveyor MS pump (Thermo Electron Corp.). Downstream from the injector, 10 µL/min 150 µM β-CD in 30 mM aqueous HCl from a KDS100 syringe pump (KD Scientific, Holliston, MA) with a 2.5-mL syringe (Hamilton, Reno, NV) was admixed using a “T” mixer (Upchurch Scientific, Oak Harbor, WA). The resulting flow of 30 µL/min containing the broadened guest band together with 50 µM β-CD in 10 mM HCl was introduced into the ion source. The injections were performed using the standard injection valve on the LCQ system equipped with a 200-µL loop (Upchurch Scientific). The valve was plumbed so that the injected solutions (10-µL aliquots of 250 µM guests in water) must have gone through the remaining volume of the loop (to achieve the desired band broadening) before leaving the injector and entering the ion source. The experimental setup is shown in Figure 1a. Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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The dynamic titrations of the second experimental set were performed after on-line HPLC separation of the guests. A 50 × 1.0 mm Zorbax SB-C8 column with 3.5-µm particles (Agilent Technologies, Santa Clara, CA) and isocratic elution with a mixture of ACN and 1 mM aqueous HCl (75:25 v/v) at a flow rate of 20 µL/min were used. In this case, the injection valve was equipped with a 20-µL loop and 10-µL aliquots of guest solutions were injected. The guests were dissolved at a concentration of 250 µM in water/ACN 50:50 mixtures, either individually or in combinations. The effluent was then mixed with 10 µL/min 150 µM host (β-CD or γ-CD) or 75 µM concentrations of both in 30 mM aqueous HCl delivered by the syringe pump. The resulting flow (30 µL/min) containing the guest bands together with 50 µM β-CD or γ-CD or 25 µM concentrations of both and 10 mM HCl in water/ACN 50:50 was introduced into the ion source. This experimental setup is depicted in Figure 1b. Static titrations were performed in both solvent systems (water with 10 mM HCl and water/ACN 50:50 with 10 mM HCl) for comparison. The concentration of cyclodextrin host was held fixed at 50 µM, and the concentration of guest was varied (5, 10, 20, 50, 100, and 200 µM) in discrete sample solutions. The titrations were performed by sequentially measuring solutions with only one host and one guest at a time. Each solution was measured in triplicate, and average values of ionic intensities obtained from 50 scans were used in the calculation of Kd. The solutions were infused directly into the ion source with the syringe pump at a flow rate of 30 µL/min. RESULTS AND DISCUSSION Cyclodextrins are cyclic oligosaccharides composed of R-Dglucopyranose units connected by ether linkages from carbon 1 of one monomeric ring to carbon 4 of the adjacent ring. Cyclodextrins assume the shape of a truncated cone in aqueous environment, exposing their hydroxyl groups to the solvent while the relatively more hydrophobic remainder of the molecule forms an internal cavity. Properly sized and shaped guests can enter the cavity, creating inclusion complexes, which can be stabilized by (in addition to hydrophobic interactions) van der Waals forces and hydrogen bonds. A large amount of data regarding binding of organic molecules to cyclodextrins exists in the literature.44 Nonsteroidal anti-inflammatory drugs IBP, NPX, and FBP that we have chosen as guests can form such inclusion complexes and their dissociation constants have been measured previously by solution-phase methods.45-51 The majority of published data has been obtained in purely aqueous solutions. Although the main goal of this study is to demonstrate the applicability of dynamic titration for chromato(44) Rekharsky, M. V.; Inoue, Y. Chem. Rev. 1998, 98, 1875-1917. (45) Nunez-Aguero, C. J.; Escobar-Llanos, C. M.; Diaz, D.; Jaime, C.; GardunoJuarez, R. Tetrahedron 2006, 62, 4162-4172. (46) Mura, P.; Bettinetti, G. P.; Manderioli, A.; Faucci, M. T.; Bramanti, G.; Sorrenti, M. Int. J. Pharm. 1998, 166, 189-203. (47) Manzoori, J. L.; Amjadi, M. Spectroc. Acta, Part A:Mol. Biomol. Spectrom. 2003, 59, 909-916. (48) Orienti, I.; Fini, A.; Bertasi, V.; Zecchi, V. Eur. J. Pharm. Biopharm. 1991, 37, 110-112. (49) Bettinetti, G.; Melani, F.; Mura, P.; Monnanni, R.; Giordano, F. J. Pharm. Sci. 1991, 80, 1162-1170. (50) Ueda, H.; Perrin, J. H. J. Pharm. Biomed. Anal. 1986, 4, 107-110. (51) Cirri, M.; Maestrelli, F.; Orlandini, S.; Furlanetto, S.; Pinzauti, S.; Mura, P. J. Pharm. Biomed. Anal. 2005, 37, 995-1002.
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Figure 3. Spectrum of 50 µM β-CD with 50 µM NPX in water with 10 mM HCl.
graphic separations, it is impossible to run the reversed-phase separations most commonly used in conjunction with MS in a purely aqueous medium. Therefore, to obtain data directly comparable to the literature, we carried out an initial set of experiments in aqueous solution utilizing broadening of the guest band in open tubing (more specifically, in the injection loop). Attention was paid to the selection of an additive to the solvent as it often has a profound effect on the electrospray process. Hydrochloric acid at a concentration of 10 mM was ultimately chosen. The reason for the selection of this rather unusual component in ESI-MS was 2-fold: The literature value of dissociation constant for the β-CD•NPX complex48 was acquired at pH 2; and clean negative ion spectra containing sufficiently high intensities of the cyclodextrins and the 1:1 complexes were observed under these conditions. In the positive mode, in plain water and in a basic environment of 0.01% triethylamine, for example, doubly charged 2:1 and 3:2 complexes were observed (data not shown), indicating the probable presence of nonspecific binding. A typical spectrum of a β-CD and NPX mixture is shown in Figure 3. The cyclodextrin was present predominantly as a chloride-attached species ([β-CD + Cl]-) with minor contributions from deprotonated and doubly chloride-adducted ions ([β-CD H]- and [β-CD + 2Cl]2-, respectively). The complex was present exclusively as a deprotonated species ([β-CD•NPX - H]-). Similar spectra were obtained for IBP and FBP as guests, with the exception that FBP yielded a substantial amount of chlorideadducted ions [FBP + Cl]-. The question can therefore arise concerning whether the guests and chloride ions compete for binding with β-CD, a situation that would have complicated the determination of Kd by introducing another equilibrium into the system. Some insight into this may be provided by the possible mechanism of ion formation. In 10 mM HCl, H+ ions are expected to be the species reduced at the electrospray capillary tip in the negative ionization mode. The observed electric current of 30 µA and the flow rate of 30 µL/min suggest that the H+ concentration drops by only 0.6 mM. The pH in the droplets is thus still fairly acidic to prevent the carboxylic groups of the guests from deprotonating (the pKa values are 4.40, 4.41, and 4.13 for IBP,47 NPX,48 and FBP,50 respectively). Evaporation of the solvent as the droplets travel through the ion source can only decrease the pH. The observation of the deprotonated species can thus be potentially attributed to their formation in the gas phase where the acido-basic properties often substantially differ from the solution. We hypothesize that both the cyclodextrin and the complex are
Figure 4. Titration of β-CD with NPX in aqueous environment. Top trace, β-CD; bottom trace, β-CD•NPX complex. Arrows mark the intervals where integration according to eq 9 was applied (signal) and from where the level of noise was taken (noise).
initially charged by chloride attachment, but in the latter case, the chloride is lost in the form of HCl in the gas phase (probably in the capillary-skimmer region), leaving a deprotonated complex. Although our measurements do not provide unambiguous evidence for this hypothesis, the chloride was considered to not be in competition with the guests in this work. Figure 4 shows traces of β-CD and β-CD•NPX complex for one injection of NPX. The intensities were obtained by integration across whole isotopic envelopes of all quasimolecular ions pertaining to host or complex. The time interval where the integration according to eq 9 was applied is marked, as well as the interval from which the level of noise for the complex intensity was assessed (the noise was subtracted from the signal before calculating the association degree R). The resulting Kd for this particular injection was determined to be 469 µM. In Figure 5, data obtained in static titration experiment with the same hostguest system are shown as a graph of association degrees versus the concentration of guest. Using the fitting procedure described in the Theoretical Basis section, a Kd of 428 µM was obtained, showing excellent agreement between the two titration procedures. Dissociation constants for all three guests measured in the aqueous environment are summarized in the first section of Table 1, together with values from the literature.45-51 Comparison of the data reveals that the Kd values obtained by dynamic and static titrations agree reasonably well; particularly in the context of the respective RSD values (for static titration of the β-CD-NPX system in the water/ACN solvent, the RSD was determined to be 13.2%; for other systems, it is assumed to be similar). In the literature, a considerable range of values has been reported using different methods by different researchers (see references in Table 1). The best agreement is observed for NPX, where the Kd values from solubility studies are in good agreement both to one another and to the results obtained from dynamic and static titrations in this study. For IBP and FBP, the results from our titration measurements fall within the “brackets” given by the literature values. It should be noted that while all referenced data were obtained in aqueous environment, the pH and ionic strength differed or unbuffered solutions were used. Dissociation
Figure 5. Fitting a curve into the data obtained from static titration of β-CD (50 µM) with NPX in aqueous environment.
constants of the β-CD•IBP complex measured by Manzoori and Amjadi by spectrofluorometry separately for deprotonated and neutral IBP show, however, that deprotonation increases the Kd only by a factor of 2 (ref 47)stoo small a difference to explain the wide variation seen among the literature data. The fact that the possible inequality of response factors of the free host and the corresponding complexes could not be accounted for (because the response factors of the complexes were not known) may also have some influence on the measured dissociation constants. In summary, the ESI-MS-based titration methods can be considered a viable alternative to solution-phase methods for studying this class of host-guest binding systems. Following initial experiments, titrations based on reversedphase chromatographic separations were performed. To demonstrate the applicability of dynamic titration in situations when guests coelute, a 25:75 aqueous ACN mobile phase was used. Under these conditions, peaks of both NPX and IBP overlap with FBP and, to some extent, with each other (see Figure 6). Spectra of the guest mixtures with β-CD look qualitatively the same as those taken in purely aqueous environment. Mixtures of γ-CD with the guests yield a little bit more complicated spectra. The ions observed in the spectrum taken for the γ-CD + NPX mixture (see Figure 7) are: [γ-CD + 2Cl]2-, [γ-CD + Na + 3Cl]2-, [γ-CD - H + 2Na + 3Cl]2-, [γ-CD•NPX - H + Cl]2-, [γ-CD•NPX + 2Cl]2-, [γ-CD - H]-, [γ-CD + Cl]-, [γ-CD + Na + 2Cl]-, and [γ-CD + 2Na + 3Cl]-. Peaks of the same ionic species were observed in the spectrum of the γ-CD + FBP mixture. In contrast, binding of IBP to γ-CD was very weak and dissociation constants were not determined for this host-guest combination. The guests were injected both in mixture and separately evaluated by dynamic titration. Static titrations were also performed for comparison in this solvent system. The results can be found in Table 1, sections II (β-CD) and III (γ-CD). Generally good agreement is shown both between the two approaches for Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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Table 1. Dissociation Constants for Complexes of βand γ-CD with IBP, NPX and FBP I. Host: β-CD Solvent: H2O, 10 mM HCl Kd/µM (RSD%, n ) 6)a complex
dynamic one-on-onec
static
literature
β-CD•IBP
1170 (4.7)
1010
590045; 94.346; 52.647 68048; 59049 22450; 59051; 16751
β-CD•NPX β-CD•FBP
475 (15.4) 455 (13.9)
428 489
II. Host: β-CD Solvent: H2O/ACN 50/50, 10 mM HCl Kd/µM (RSD%, n ) 36)b complex
dynamic one-on-onec
dynamic competitived
static
β-CD•IBP β-CD•NPX β-CD•FBP
1220 (21.8) 312 (14.1) 303 (14.8)
1260 (21.4) 328 (11.3) 393 (15.8)
1740 334 (13.2)e 372
Figure 6. Peaks of IBP, NPX, and FBP detected after chromatographic separation as their complexes with β-CD. Traces from top: β-CD, β-CD•IBP complex, β-BCD•NPX complex, and β-CD•FBP complex.
III. Host: γ-CD Solvent: H2O/ACN 50/50, 10 mM HCl Kd/µM (RSD%, n ) 6)a complex
dynamic one-on-onec
dynamic competitived
static
γ-CD•NPX γ-CD•FBP
290 (5.2) 1110 (5.8)
322 (4.8) 1240 (5.7)
364 1810
IV. Hosts: γ-CD + β-CD Solvent: H2O/ACN 50/50, 10 mM HCl Kd/µM (RSD%, n ) 6)a
Figure 7. Spectrum of 50 µM γ-CD with 50 µM NPX in water/ACN 50:50 with 10 mM HCl.
complex
dynamic one-on-onec
dynamic competitived
static
β-CD•NPX β-CD•FBP γ-CD•NPX γ-CD•FBP
349 (8.2) 344 (2.9) 440 (2.1) 1440 (5.8)
347 (8.9) 372 (6.9) 468 (5.1) 1690 (6.0)
334 (13.2)e 372 364 1810
a Averages of six repetitions done immediately one after another, so the RSD reflects repeatability of the measurements. b Averages of 36 values measured in groups of six and repeated in six consecutive days to assess day-to-day reproducibility. c “One-on-one” means that at any time point during the experiment, a single guest binds to a single host. d In competitive format, up to three guests at a time compete for one or two hosts (see Figures 6 and 8). e Average and RSD for the static titration repeated six times in different days.
dynamic titration (single host with single guest versus single host with more guests) and between dynamic and static titration. The slight discrepancies for relatively weaker complexes β-CD•IBP and γ-CD•FBP can be explained; e.g., by the greater contribution of noise to the signal of complex, which is lower in systems exhibiting a higher Kd (weaker binding affinity). Using higher concentration of guests to increase the signal of its complex was avoided, however, since it can undesirably influence response of other analytes by competing at the surface of the droplets (which is a different kind of competition than is accounted for in the derived model). Under the conditions used, no signal suppression (decrease of the total ion current) was observed even when the guests coeluted. Ultimately, dynamic titrations of both hosts simultaneously were carried out. Figure 8 shows the corresponding chromato1392 Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
graphic traces of both hosts and their complexes with NPX and FBP that were injected either together (to coelute) or separately. The resulting Kd values are summarized in Table 1 (section IV). Again, a reasonable level of agreement is observed in the data, demonstrating the potential of the developed method for highthroughput determination of dissociation constants in a multiplexed format. From the standpoint of general usage of the method, some requirements must be met regardless of the host-guest system examined. The concentrations of both host and guest should be in the region where they afford sufficient intensity of the complex and the free host. Since it may not be viable to adjust independently the concentrations of guests in their mixture, the extent of complex formation can be adjusted by setting different concentration of host(s) in different time segments of the separation corresponding to elution of different guests. This would be technically realized by premixing the host solution from two syringe pumps, one containing stock solution of the host and the other one only pure solvent. By changing the flow rates from the two pumps, while keeping the total flow rate constant, the desired concentration of the host would be conveniently achieved. Next, the width of the guest distributions must be compatible with the scanning speed of the mass spectrometric detector. The concept of dynamic titration is theoretically applicable to any type of liquid chromatography separation (e.g., UPLC, capillary LCMS) provided that the mass spectrometer can sample sufficient
Figure 8. Peaks of NPX and FBP detected after chromatographic separation as their complexes with β-CD and γ-CD. Traces from top: β-CD, β-CD•NPX complex, β-CD•FBP complex, γ-CD, γ-CD•NPX complex, and γ-CD•FBP complex.
number of points over the guest peaks (for quantitation purposes, the recommended minimum number of points per peak is usually 10). CONCLUSIONS A theoretical model allowing measurement of dissociation constants for noncovalent complexes from titration of fixed host concentration with time-varying concentration of guest formed by flow injection or column separation (dynamic titration) was developed. Unlike its previous version,43 this model accounts for possible competition; i.e., more than one host can be used in the experiments and the concentration distributions of guests after their chromatographic separation can overlap to any extent. The model can also deal with any type of distribution, not just Gaussian, enabling titration from asymmetric chromatographic peaks.
The method was used to determine dissociation constants for complexes of β- and γ-CD with nonsteroidal anti-inflammatory drugs IBP, NPX, and FBP. The first set of experiments was carried out in an aqueous environment by flow injection, and the resulting dissociation constants were found to compare well to literature values measured by independent methods. Next, the guests were separated on a chromatographic column using a mixture of water and ACN as the mobile phase. The composition of mobile phase was chosen to yield overlapping peaks of guests (unresolved peaks). Guests were injected both separately and in mixture. Traditional static titration experiments were performed for comparison under identical solution and instrumental conditions. The dissociation constants in all cases agreed reasonably well, validating the new method. The advantages of the presented method are its speed, ability to operate in a highly automated fashion, and low consumption of hosts and guests (nanomoles of host and guest were consumed in one titration). A limitation is, on the other hand, that the solvent and additives used must be compatible with electrospray ionization. Further research is needed particularly in the areas of the fundamental factors that determine how well solution-phase equilibrium concentrations are reflected by gas-phase ion abundances observed in a mass spectrum. This includes the investigation of response factor disparities, the effects of competition by analytes at the droplet surface, and whether it is possible to extend the linear dynamic range to be able to better study weakly bound systems at higher concentrations (where a greater fraction of host is bound in the complex). Thorough understanding of these key facets of the ionization process would allow the technique to be used as a mature alternative to solution-phase methods on a routine basis. ACKNOWLEDGMENT The authors thank U.T.-Arlington and the Office of the Provost for start-up funds used to perform these investigations. P.F. thanks the Ministry of Education of the Czech Republic (MSM6198959216).
Received for review November 22, 2007. Accepted January 15, 2008. AC7024078
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