Anal. Chem. 2008, 80, 2365-2371
Method of Measuring Oligonucleotide-Metal Affinities: Interactions of the Thrombin Binding Aptamer with K+ and Sr2+ J. Micah Wilcox, Don L. Rempel, and Michael L. Gross*
Department of Chemistry, Washington University in St. Louis, 1 Brookings Drive, Saint Louis, Missouri 63130
We report a new, mass spectrometry-based method for measuring affinity constants for specific metal ion binding to DNA, particularly for quadruplex DNA. This method, which is applicable to other systems, utilizes the gas-phase signal fractions, as determined by mass spectrometry, from the bound and unbound species as input into a mathematical model that determines various parameters, one of which is the binding affinity constant. The system used to develop and test the model was the thrombinbinding aptamer, an appropriate quadruplex structure that binds both K+ and Sr2+ cations. Using this method, we measured the binding constants of potassium and strontium cations with the quadruplex structure to be 5000 and 240 nM, respectively. We then applied the method to measure the change in enthalpy of the binding of strontium cations to the thrombin binding aptamer. The ∆H for this interaction is -71 kJ/mol (-17 kcal/mol). The binding constant measurements are consistent with earlier measurements on the same system, and the measured change in enthalpy is in excellent agreement with previous work. Noncovalent interactions of DNA and metal cations mediate proper folding of DNA and influence its solution structure. Although the predominant interactions of metal cations with bulk, genomic DNA are nonspecific, specific interactions do occur. DNA aptamers, for example, are single-stranded molecules that bind specific targets and often require metal cations for proper functioning.1,2 Both DNA and RNA aptamers fold into unique structures in the presence of specific metal cations; these structures are called quadruplexes. Quadruplex structures are noncanonical forms of DNA or RNA that contain two or more guanine quartets (G-quartets) linked together by a series of loops so that the bases may stack. G-quartets are nearly coplanar associations of four guanine nucleotides in a cyclic, self-complementary, hydrogen-bonding pattern that uses both the Hoogstein and Watson-Crick faces of the nucleotide. Early gel work revealed that only certain metal ions stabilize quadruplex structures.3-5 Patel and co-workers6 * To whom correspondence should be addressed. (1) Ulrich, H.; Trujillo, C. A.; Nery, A. A.; Alves, J. M.; Majumder, P.; Resende, R. R.; Martins, A. H. Comb. Chem. High Throughput Screening 2006, 9, 619-632. (2) Rimmele, M. ChemBioChem 2003, 4, 963-971. (3) Sen, D.; Gilbert, W. Nature 1988, 334, 364-366. 10.1021/ac701903w CCC: $40.75 Published on Web 03/05/2008
© 2008 American Chemical Society
highlighted the crucial nature of the cation when they found that the same oligodeoxynucleotide (ODN) sequence adopts two different quadruplex structures depending on the cation present. Quadruplex structures display a wide range of topology, which is classified by the strand stoichiometry and polarity, loop orientation, and nucleotide conformation about the glycosidic bonds.7 Accurate and rapid analytical methods are needed to determine quadruplex-metal ion binding affinities. Traditionally, NMR spectroscopy, calorimetry, and optical spectroscopy have been used to determine affinity constants. Another powerful analytical technique for measuring binding constants, affinity capillary electrophoresis, has not been applied, to our knowledge, to quadruplex-cation interactions. For quadruplex structures, solution NMR techniques using surrogate spin 1/2 probes (e.g., ref 15, NH4+) can localize metal cations and measure their binding affinities.8-10 Recently, solid-state NMR has played a role in quadruplex structure determination and also in affinity measurements.11-13 Both solid and solution NMR require milligram to gram amounts of pure samples; as a result, these techniques suffer when measuring “tight” binding interactions (dissociation constants in the micro- and nanomolar range) that are characteristic of quadruplex-metal ion interactions. In general, solution NMR also requires special nuclear probes for binding affinity measurements, and solid-state NMR is limited to relative measurements only. To fill the need for metal ion-oligonucleotide affinity measurements, mass spectrometry (MS) based techniques offer four principal advantages: (1) fast data acquisition, (2) low sample consumption (as low as femtogram), (3) ability to handle mixtures of nonisomeric compounds, and (4) ability to make direct measurements of the mass-to-charge ratio (m/z) of the species in equilibrium. Consequently, several groups have used MS to (4) Williamson, J. R.; Raghuraman, M. K.; Cech, T. R. Cell 1989, 59, 871-880. (5) Raghuraman, M. K.; Cech, T. R. Nucleic Acids Res. 1990, 18, 4543-4552. (6) Bouaziz, S.; Kettani, A.; Patel, D. J. J. Mol. Biol. 1998, 282, 637-652. (7) Burge, S.; Parkinson, G. N.; Hazel, P.; Todd, A. K.; Neidle, S. Nucleic Acids Res. 2006, 34, 5402-5415. (8) Basu, S.; Szewczak, A. A.; Cocco, M.; Strobel, S. A. J. Am. Chem. Soc. 2000, 122, 3240-3241. (9) Hud, N. V.; Schultze, P.; Sklenar, V.; Feigon, J. J. Mol. Biol. 1999, 285, 233-243. (10) Schultze, P.; Hud, N. V.; Smith, F. W.; Feigon, J. Nucleic Acids Res. 1999, 27, 3018-3028. (11) Wong, A.; Ida, R.; Wu, G. Biochem. Biophys. Res. Commun. 2005, 337, 363366. (12) Wu, G.; Wong, A. Biochem. Biophys. Res. Commun. 2004, 323, 1139-1144. (13) Wu, G.; Wong, A. NMR Spectrosc. Biol. Solids 2006, 317-344.
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investigate equilibria involving peptides, proteins, and DNA molecules with a wide range of ligands (metal cations, small molecules, and other macromolecules).14-19 For biomolecules, the principal problems encountered in making direct measurements of equilibrium species concentrations by MS are electrospray ionization (ESI) discrimination and measurement of free ligand concentration at equilibrium for ligands that do not produce an MS signal. In comparison to other MS-based approaches, the approach described here addresses the problem of ESI discrimination directly by modeling the relative ESI efficiency of the bound species versus the unbound species. A recently developed method20 handles this problem by keeping the ligand/ODN mole ratio at unity throughout the titration while varying the absolute concentration of the two species. This method, however, is applicable only to ODN-ligand interactions with a 1:1 stoichiometry, whereas our method is extendable to other stoichiometries. A limitation of many MS-based methods is that weakly bound complexes dissociate in the gas-phase introduction processes. A recently developed MS-based approach21 considered such gasphase fragmentation and determined both a response factor and the binding affinity constant of a complex by using the mass spectral intensity of the bound complex. The use of absolute spectral intensities, however, may pose problems if the electrospray process has local variations in the spray or if the mass spectrometer itself becomes contaminated during analysis. Thus, we developed a new MS-based approach to overcome these limitations and to enable the direct determination of quadruplexmetal cation binding affinity constants. In this investigation, we focus on the interactions of the thrombin-binding aptamer (TBA) with alkali metal cations. This 15-mer DNA aptamer is composed of guanidine and thymidine nucletotides and was discovered using a combinatorial selection procedure; this aptamer was selected based upon its ability to bind R-thrombin and inhibit its coagulation role in the blood-clotting cascade.22-24 The system is an attractive model because its solution structure has been solved by NMR and X-ray crystallography,23-27 and the affinity constant of the TBA-K+ interaction is known.28 We show that the traditional problems of (14) Brodbelt, J. S. Int. J. Mass Spectrom. 2000, 200, 57-69. (15) Hagan, N.; Fabris, D. Biochemistry 2003, 42, 10736-10745. (16) Raji, M. A.; Frycak, P.; Beall, M.; Sakrout, M.; Ahn, J. M.; Bao, Y.; Armstrong, D. W.; Schug, K. A. Int. J. Mass Spectrom. 2007, 262, 232-240. (17) Rosu, F.; Gabelica, V.; Houssier, C.; De Pauw, E. Adv. Mass Spectrom. 2001, 15, 795-796. (18) Rosu, F.; Pirotte, S.; Pauw, E. D.; Gabelica, V. Int. J. Mass Spectrom. 2006, 253, 156-171. (19) Wortmann, A.; Rossi, F.; Lelais, G.; Zenobi, R. J. Mass Spectrom. 2005, 40, 777-784. (20) Gabelica, V.; Galic, N.; Rosu, F.; Houssier, C.; De Pauw, E. J. Mass Spectrom. 2003, 38, 491-501. (21) Tjernberg, A.; Carnoe, S.; Oliv, F.; Benkestock, K.; Edlund, P.-O.; Griffiths, W. J.; Hallen, D. Anal. Chem. 2004, 76, 4325-4331. (22) Bock, L. C.; Griffin, L. C.; Latham, J. A.; Vermaas, E. H.; Toole, J. J. Nature (London, U.K.) 1992, 355, 564-566. (23) Paborsky, L. R.; McCurdy, S. N.; Griffin, L. C.; Toole, J. J.; Leung, L. L. K. J. Biol. Chem. 1993, 268, 20808-20811. (24) Padmanabhan, K.; Padmanabhan, K. P.; Ferrara, J. D.; Sadler, J. E.; Tulinsky, A. J. Biol. Chem. 1993, 268, 17651-17654. (25) Macaya, R. F.; Schultze, P.; Smith, F. W.; Roe, J. A.; Feigon, J. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 3745-3749. (26) Schultze, P.; Macaya, R. F.; Feigon, J. J. Mol. Biol. 1994, 235, 1532-1547. (27) Wang, K. Y.; McCurdy, S.; Shea, R. G.; Swaminathan, S.; Bolton, P. H. Biochemistry 1993, 32, 1899-1904.
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direct MS measurements discussed above can be overcome by using appropriate MS measurement and a mathematical model to account for ESI discrimination, gas-phase dissociation of bound complexes, and by calculating the free ligand as a function of the total ligand. Here we present results to demonstrate the validity of this method, use it to measure the affinity constant of the TBASr2+ interaction, and apply it to measure the enthalpy of binding in the TBA-Sr2+ interaction. EXPERIMENTAL SECTION Reagents. Both the thrombin-binding aptamer (5′ GGT TGG TGT GGT TGG 3′) and the scrambled sequence oligodeoxynucleotide (5′ GGT GGT GGT TGT GGT 3′) were purchased from Integrated DNA Technologies, Inc. (Coralville, IA) as ammonium salts. The samples were purified using reversed-phase chromatography by the manufacturer to exclude salts as much as possible. Weighed amounts of solid samples were dissolved in water to prepare a master solution. Their concentrations were determined by UV absorption spectrophotometry whereby a calibration plot was prepared to give the molar absorptivity. That value agreed to within 1% with the value calculated by using the nearest neighbor method for the given sequences. These results also agreed with those reported by the manufacturer. Mass Spectrometry. The mass spectra were acquired using a ThermoFinnigan (now ThermoFisher) LCQ Classic (San Jose, CA) ion-trap mass spectrometer equipped with an electrospray ionization (ESI) source. The instrument was operated in the negative-ion mode, and the spectra were acquired from m/z 1502000 using an automatic gain control setting of 1 × 105 counts. The oligodeoxynucleotide (ODN) and quadruplex signal fractions were determined from mass spectra created by averaging 50 scans together with the Qual Browser (version 2.0) software that is packaged with ThermoFisher’s XCALIBUR (version 1.3) software. The spectra were acquired by using a spray voltage of -3 kV, a tube lens voltage of -10 V, a capillary temperature of 200 °C, a capillary voltage of -15 V, and sheath and auxiliary gas flows of 60 and 0 arbitrary units, respectively. The raw data mass spectrum generated by Qual Browser was input into the MagTran29 (version 1.03 b1) software to generate deconvoluted (or decharged) mass spectra. MagTran used the all charged species within the range of m/z 150-2000 having a signal-to-noise value greater than or equal to 2 to create the deconvolution mass spectra. From the deconvoluted mass spectra, the experimental signal fractions of the bound and unbound species were calculated. The output range of the deconvoluted spectra was 4500 to 5200 Da. Circular Dichroism. The circular dichroism spectra were acquired using a Jasco-100 spectropolarimeter (Easton, MD). The solutions were analyzed in a quartz cuvette with a 0.10 cm path length after incubation at 25 °C for 5 min. During spectral acquisition, the light was scanned from 220 to 360 nm at a rate of 50 nm/min. Titration Experiments. In the titration experiments, a series of aqueous solutions containing a fixed amount of the TBA and a variable amount of KCl or Sr(NO3)2 were prepared. For the titration of TBA with Sr(NO3)2 or KCl at 25 °C, the concentration (28) Kumar, N.; Maiti, S. Biochem. Biophys. Res. Commun. 2004, 319, 759767. (29) Zhang, Z.; Marshall, A. G. J. Am. Soc. Mass Spectrom. 1998, 9, 225-233.
of TBA in aqueous solution was fixed at 5 µM. Each solution was incubated at a fixed temperature for 5 min prior to dilution (1:1) with the ESI solvent. As a result, the final solutions that were infused into the mass spectrometer contained 2.5 µM TBA in 25% MeOH and 0.50% NH4OH (v/v). Each solution was infused at a rate of 5 µL/min. In a separate series of experiments, the thermodynamics of the interaction of the thrombin binding aptamer and Sr2+ was investigated by performing titration experiments at different temperatures (2 °C, 30 °C, and 40 °C). In these experiments, the aqueous solution contained a fixed concentration of TBA of 1 µM and was incubated at the appropriate temperature for 5 min with various amounts of Sr(NO3)2. The temperature of the infused solution was controlled through the use of an LC oven (Waters, model WAT038000, Milford, MA) or an ice bath for the 2 °C measurements. Following incubation, the aqueous solutions were again diluted (1:1) with ESI solvent that had been also incubated at the appropriate temperature for 5 min. As a result, the final solutions infused into the mass spectrometer contained 0.5 µM TBA in 25% MeOH and 0.5% NH4OH (v/v). In the temperature study experiments, the solutions were infused into the mass spectrometer at a rate of 10 µL/min. MATHEMATICAL MODELING We processed the titration data and performed the mathematical modeling with custom spreadsheets prepared in MathCAD Professional 2001i software (MathSoft Engineering and Education Inc., Cambridge, MA). The error values reported for the dissociation constants (Kd) are the standard errors (standard deviation of the mean) of the best-fit parameter values obtained by separately fitting each trial of titration data. To find the best dissociation constant values, a parametrized model was fit to the titration data. The model has four parameters: the affinity binding constant (Ka), the fraction of bound species that dissociates in the gas-phase (ff), the electrospray ionization (ESI) gain factor (yield) of the bound species relative to the unbound species (G), and the concentration of the free ligand in the titration experiment (lig0). The model is constructed using the nomenclature described in the Wyman and Gill textbook.30 In the model, the binding affinity constant parameters are handled as overall Adair constants (β), each β is the product of the appropriate, stepwise macroscopic equilibrium constants (K).
β0 ) 1 β1 ) K 1 β2 ) K1K2 β3 ) K1K2K3
(1)
The various macromolecular species are represented in the model by using the appropriate terms of the partition function; this function describes all solution species relative to the unbound species by using the free ligand concentrations and overall Adair constants (eq 2). The variable N is the total number of ligand (30) Wyman, J.; Gill, Stanley J. Binding and Linkage: Functional Chemistry of Biological Macromolecules; University Science Books: Mill Valley, CA, 1990.
binding sites on the macromolecule. N
P)
∑β [Lig] ) 1 + β [Lig] + β [Lig] i
i
1
2
2
+ β3[Lig]3 + ...
(2)
i)0
The model is constructed to be general and, therefore, to handle interactions of macromolecules with multiple ligands. In the system studied here, however, only a single binding site exists. Thus, only the first two terms of the partition function are needed to describe the quadruplex-metal cation interaction (see eqs 3-6 below). Nevertheless, we wish to present a general model. In titrating a macromolecule with a single binding site and one ligand, both bound and unbound forms of the macromolecule exist in solution. The species fractions are given below.
β1[Lig] 1 + β1[Lig]
bound
1 unbound 1 + β1[Lig]
(3)
(4)
The species fractions, however, were not directly measured in these experiments. Instead, the signal fractions were calculated from the mass spectra. The signal fractions are related to the species fractions but are not identical because there is not a oneto-one correspondence between solution concentrations and electrospray signals. The lack of equality occurs first because the electrospray ionization (ESI) method can be highly discriminatory; not all solution species are ionized with equal efficiency. Second, a fraction of the bound species may dissociate to an unbound species prior to detection. To solve these problems, the model uses the G and ff parameters, respectively (see above for definitions). The bound (S1) and unbound (S0) signal fractions are given below.
S1 )
(1 - ff)Gβ1[Lig]
S0 )
1 + Gβ1[Lig] 1 + ffGβ1[Lig] 1 + Gβ1[Lig]
(5)
(6)
These expressions indicate that the mass spectral signal observed for the bound species is weighted by the ESI efficiency of that species relative to that of the unbound species (G) and is diminished by some fraction of the bound complex that dissociates (ff) to an unbound species. By similar reasoning, the mass spectral signal observed for the unbound species has two components: (1) the species fraction of the unbound species and (2) the fraction of the bound complex (appropriately weighted) that undergoes dissociation. To calculate the signal fractions, the solution concentration of the free ligand must be known but determining this concentration is difficult. Although an expression of the free ligand concentration as a function of the total ligand concentration is needed, it is not possible to write such an expression in algebraic closed form. Only for certain numbers of ligands (N e 3) are such expressions possible. To make the model as robust as possible, we developed Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
2367
a different way to determine the free ligand concentration, a way that is applicable to any system regardless of the number of ligands that interact with the macromolecule. The intention is to create a table containing the free ligand concentrations indexed by the total ligand concentrations. To accomplish this goal, the model uses an apparent indirection and applies simple calculus and the inverse function theorem. The table is constructed by first writing the total ligand concentration as a function of the free ligand concentration, the apparent indirection. N
∑ iβ [Lig]
[Lig]Total ) [Lig] + [M]
i
(7)
i
i)0
In eq 7, the new term [M] represents the free macromolecule concentration in solution (note also that [M] is a function of the free ligand concentration). Taking the derivative with respect to the free ligand concentration of eq 7 gives eq 8.
d[Lig]Total d[Lig]
)1+
N
d[M]
∑ d[Lig]
N
iβi[Lig]i + [M]
i)0
∑(i β [Lig] 2
i
i)1
i-1
)
(8)
Equation 9 is the expression of the total macromolecule concentration, and eq 10 is the derivative of the free macromolecule concentration with respect to the free ligand concentration. N
[M]Total ) [M]
∑β [Lig]
i
(9)
i
( ) i)0
d[M] d[Lig]
) [M]Total
-1
N
∑iβ [Lig]
(
N
∑β [Lig] )
i 2
(
i-1
i
) (10)
i)1
i
i)0
Equation 11 is the complete expression of the derivative of eq 7 with respect to the free ligand concentration as obtained by the substitution of eq 10 into eq 8.
d[Lig]Total d[Lig]
)1+
( ) ( ) -1
[M]Total
N
∑β [Lig]
i
N
∑i β [Lig] 2
(
i-1
i
)+
i)1
i
i)0
-1
[M]Total
N
∑
(
N
∑(β [Liq] ) i
i)0
iβi[Lig]i-1)(
N
∑i β [Lig] ) 2
i
i
(11)
i)1
i
i)0
The ordinary differential equation31,32 shown in eq 11 was then inverted to give the derivative of the free ligand concentration (31) Press, W. H. T. S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992. (32) Gear, C. W. Numerical Initial Value Problems in Ordinary Differential Equations; Prentice Hall: Englewoods Cliffs, NJ, 1971.
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with respect to the total ligand concentration (i.e., d[Lig]/ d[Lig]Total) by using the inverse function theorem.33 The ordinary differential equation that results from the inversion was numerically integrated to give the free ligand concentration as a function of the total ligand concentration by integrating the differential eq 11.34 The numerical integration was done using the “Radau” function in MathCAD with the initial condition of zero free ligand concentration at zero total ligand concentration. The number of integration steps was 5000 to afford data for a table that can be used to “look up” the free ligand concentration as a function of the total ligand concentration. The model output is three signal functions, two signal fractions, and the total signal (STotal) function. The total signal predicted by the model up to a constant proportionality is shown in eq 12 and is the sum of the species ionization yields (the denominator of eqs 5 and 6 before the common term [M] is eliminated).
STotal ) [M] + Gβ1[M][Lig]
(12)
The best-fit parameter values of the final curve are determined by using a nonlinear least-squares (NLLS) regression analysis. The search for the model parameters starts at “good guess” parameter values that are input into the model each time a search is made. The best-fit parameter values are determined by using a quasi-Newtonian method to minimize the square root of the mean of the squares of the differences between the experimental data and the model output (i.e., the rms) over an appropriate range of total ligand concentration. All requirements35-37 for the correct use of NLLS algorithms are assumed to be satisfied in the application of this model. The search is implemented at four levels. Each level uses its own search process with a unique rms function for comparison of the model output with the experimental data and searches for the best-fit value of a single parameter. In the highest level of search, the parameter searched is the β parameter, and the rms is computed for the residuals between the model signal fractions (S1 and S0 in eqs 5 and 6) and the corresponding experimental signal fractions at all of the titration points. In the next highest search level, the parameter searched is the relative ESI efficiency parameter G, and the rms is computed for the residuals between the model total signal function (eq 12) and the normalized sum of relevant peak intensities from all experimental titration points. The relevant peak intensity sums are normalized to the relevant peak intensity sum of the first titration point. In the next highest search level, the ff parameter (the fraction of gas-phase dissociation) is searched, and the rms is computed for the residuals between the two model signal fractions and the corresponding experimental signal fractions at the last four titration points (see Figure 1). This region of the titration curve is chosen for comparison because the effect of the ff parameter is the most evident in this region. In the lowest level of search, the parameter lig0 is searched, and the rms is computed for the residuals (33) Weisstein, E. W. CRC Concise Encyclopedia of Mathematics, 2nd ed.; Chapman & Hall: Boca Raton, FL, 2003. (34) Williamson, R. E.; Crowell, R. H.; Trotter, H. F. Calculus of Vector Functions, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1962. (35) Johnson, M. L. Methods Enzymol. 2000, 321, 417-424. (36) Johnson, M. L. Methods Enzymol. 2000, 321, 424-446. (37) Johnson, M. L. Anal. Biochem. 1992, 206, 215-225.
Figure 1. Theoretical titration data showing the bound and unbound species signal fractions as a function of the ligand/ODN mole ratio. Highlighted with boxes are the regions of the titration curve that are used in the optimization of the lig0 and ff parameters, respectively.
Figure 3. van’t Hoff plot showing the linear correlation between the binding constants for strontium ligand to the thrombin binding aptamer as a function of temperature. From the slope of this line, the ∆H is -71 ( 4 kJ/mol (-17 kcal/mol).
Each trial in the search for the highest level parameter (e.g., the β parameter) triggers a new search at the next lower level (e.g., the G parameter) because the trial β parameter value of the higher level can affect the lower level search result for the G parameter. This fact is evidenced by the presence of the β, G, and ff parameters in the signal fractions (eqs 5 and 6). By analogy, each trial in the search at the G parameter level triggers a new search at the ff parameter level, and each trial in the search at the ff parameter level triggers a new search at the lig0 parameter level. Figure 2. Titration data and best-fit curves generated by the nonlinear least-square fitting algorithm and the experimentally determined dissociation constants for the strontium and potassium cations at 25 °C. In these experiments, the concentration of the thrombinbinding aptamer was fixed at 5 µM. The Kd for Sr2+ is 240 ( 50 nM while the Kd for K+ is 5000 ( 1000 nM.
between the two model signal fractions and the corresponding experimental signal fractions at the titration points with ligand concentrations less than the ligand concentration at which the two experimental signal fractions cross (see Figure 1). This region of the titration curve is chosen for comparison because the effect of the lig0 parameter is most evident in this region. The parameter lig0 is necessary because, for a titration of this nature, the adventitious presence of certain metal ions makes the desired measurement impossible without it. For example, we found that the lyophilized oligodeoxynucleotides received from the manufacturer contain a small (but significant) amount of potassium contamination; the potassium-bound form of the thrombin binding aptamer (TBA) accounts for approximately 5% of the total TBA signal in the mass spectra of TBA “alone” (i.e., without the deliberate addition of potassium chloride to the solution). The presence of potassium contamination represents a significant challenge that was overcome through inclusion of the lig0 parameter in the model.
RESULTS AND DISCUSSION Titration Experiment. To determine metal ion affinity, we titrated the TBA with K+ and Sr2+ and followed the extent of metal complexation by using an ion-trap mass spectrometer. Each titration point made use of a solution consisting of a constant amount of TBA with a variable amount of the metal ion (i.e., K+). We determined the signal fractions of both the bound and unbound species from the mass spectra generated by analysis of the titration-point solutions. The signal fraction of a given species is the peak area of that species divided by the sum of the peak areas from all species in the deconvoluted mass spectrum. Data analysis affords a plot of the ODN signal fraction vs the mole ratio of ligand to ODN. The binding affinity constant (Ka) is determined from this curve by using an adaptation of the PLIMSTEX and SIMSTEX models;38-40 that adaptation is described in the previous section of this paper. Measurement of TBA)Cation Interactions. Analysis of the results from the titration give an affinity constant for the binding of K+ to the TBA quadruplex structure at 25 °C in aqueous (38) Chitta, R. K.; Rempel, D. L.; Gross, M. L. J. Am. Soc. Mass Spectrom. 2005, 16, 1031-1038. (39) Zhu, M. M.; Rempel, D. L.; Du, Z.; Gross, M. L. J. Am. Chem. Soc. 2003, 125, 5252-5253. (40) Zhu, M. M.; Rempel, D. L.; Gross, M. L. J. Am. Soc. Mass Spectrom. 2004, 15, 388-397.
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solution. As shown in Figure 2, the Kd determined from the bestfit curve is 5000 ( 1000 nM for the interaction of TBA and K+. This measurement agrees within a factor of approximately six with the value previously determined (800 nM) by using fluorescence energy resonance transfer (FRET) spectroscopy.28 We also measured the binding constant of the interaction of TBA and Sr2+ at 25 °C by using our method. As shown in Figure 2, the Kd determined from the best-fit curve is 240 ( 50 nM for the interaction of TBA and Sr2+. The measurements indicate that the Sr2+-TBA interaction is greater, affording a “tighter” complex than that of the K+-TBA interaction. This observation is in agreement with the conclusions drawn from an earlier thermodynamic study of the TBA and Sr2+ interaction;41 that measurement was by traditional calorimetric methods. To continue the application of this method, we investigated the thermodynamics of Sr2+ binding to TBA. In these experiments, we titrated TBA with Sr(NO3)2 at different temperatures and followed the extent of metal-ion binding as before. To determine the enthalpy of Sr2+ binding to TBA, we used a traditional van’t Hoff analysis and assumed that the change in enthalpy is independent of temperature over the temperature range studied (2-40 °C). Data analysis affords a linear relation of the natural logarithm of the binding constants as a function of the reciprocal of absolute temperature (Figure 3). From the slope of the van’t Hoff plot, the change in enthalpy is determined to be -71 ( 4 kJ/mol (-17 kcal/mol). This value is in excellent agreement with the isothermal calorimeter titration value of -16.8 kcal/mol obtained previously.41 The presence of the potassium contamination in the TBA sample requires that our model handles a situation in which two different ligands compete for the same macromolecular binding site. The model outputs the signal fractions of two quadruplex species, one for the potassium-bound species and one for the strontium-bound species. If both ligands are present (as in the strontium titration), the model requires the binding affinity constant of the “contaminating” ligand. That binding-affinity value is used in the model and is not searched or optimized. In the case of the strontium titration of TBA, the adventitious K+ also binds to TBA. To determine ultimately the strontium-TBA Ka values at the various temperatures of interest, we first determined the potassium Ka values at each temperature by a single potassium titration of TBA at each temperature. We then used those potassium Ka values in determining the strontium Ka at the three temperatures of interest. Requirements for Method Validity. In our view, a sufficient demonstration of the method’s validity is to establish that four requirements are met. They are (1) the observed quadruplex signals reflect the extent of potassium adduct formation in solution and are not a result of the gas-phase binding that occurs in the ESI process, (2) the quadruplex signals reflect the equilibrium of the bound and unbound species in the aqueous solution and not in the final, ESI-suitable solution, (3) the quadruplex structure of TBA is not disrupted or altered upon dilution of the aqueous solution with the ESI solvent, and (4) the observed quadruplex signals do not reflect nonspecific affinity of the ODN for metal cations in solution. (41) Kankia, B. I.; Marky, L. A. J. Am. Chem. Soc. 2001, 123, 10799-10804.
2370 Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
Table 1. Theoretical Oligodeoxynucleotide Signal Fractions and the Experimentally Determined Signal Fractions concentration TBA and Sr2+ (µm)
theoretical ODN signal fractions
experimental ODN signal fractions
average error
1 5 10
0.59 0.40 0.37
0.57 0.40 0.35
0.04 0.04 0.02
To show that the first two requirements are met, we prepared three solutions that contained a 1:1 ratio of TBA and Sr(NO3)2 in each solution but a different absolute amount of TBA; the aqueous solutions contained 1, 5, and 10 µM TBA and Sr(NO3)2, respectively. After incubation for 5 min at 25 °C, the aqueous solutions were diluted with different volumes of ESI solvent so that the final solutions had the same concentration of TBA and Sr(NO3)2 (0.5 µM each). We analyzed the solutions by MS and determined the ratio of ODN signal fraction in each solution. If the measurement truly reflects the equilibrium position in the aqueous solution, then the three solutions will have decreasing amounts of signal for the free species as the concentration increases. The results (Table 1) clearly indicate that the concentration of the species in the initial, aqueous solution determines the ODN signal fraction measured by the instrument. This experiment also shows that the equilibrium under measurement is not a gas-phase phenomenon nor is it an artifact of the ESI process. Assuming the measured valued of Kd is correct, we are able to calculate the theoretical signal fractions at each concentration displayed in Table 1. This calculation reveals that the theoretical signal fractions of the unbound species at 1, 5, and 10 µM are 0.59, 0.40, and 0.37, respectively. These results clearly match the experimentally determined values of the deconvoluted signals within the reported error (Table 1) and show that the test is conducted over an appropriate concentration range where the ODN fraction is changing significantly. To demonstrate that the third requirement is satisfied, we used circular dichroism (CD) spectroscopy as a sensitive probe of the quadruplex structure.42-44 CD spectra of quadruplexes possessing an antiparallel, chair-type topology have a maximum at 295 nm and a minimum at 265 nm, whereas quadruplexes possessing a parallel-stranded topology have a maximum at 264 nm and a minimum at 240 nm. We obtained CD spectra of TBA in the presence of water/KCl and water/KCl/ESI solvent. In both spectra (data not shown), the maxima occur at 294 nm and the minima occur at 266 nm. As a negative control experiment, we measured the CD spectrum of the scrambled ODN in aqueous KCl solution. As expected, this spectrum has a maximum at 263 nm and a minimum at 248 nm. Together these spectra demonstrate that the quadruplex structure is preserved upon dilution in ESI solvent, satisfying the third requirement. To address the fourth requirement, we prepared and analyzed solutions of TBA and its scrambled analogue, each having the (42) Dapic, V.; Abdomerovic, V.; Marrington, R.; Peberdy, J.; Rodger, A.; Trent, J. O.; Bates, P. J. Nucleic Acids Res. 2003, 31, 2097-2107. (43) Olsen, C. M.; Gmeiner, W. H.; Marky, L. A. J. Biomed. Nanotechnol. 2006, 2, 62-70. (44) Rachwal, P. A.; Brown, T.; Fox, K. R. Biochemistry 2007, 46, 3036-3044.
Figure 4. Mass spectra showing the fraction of bound Sr2+ complex for both the thrombin binding aptamer (TBA) and its scrambled sequence when incubated with Sr(NO3)2 (1:1 mole ratio Sr(NO3)2/TBA) for 5 min at 25 °C. The ( indicate the signals from the strontium-bound complex, these ions contain a single strontium cation.
same mole ratio of Sr(NO3)2 to ODN. If the metal cations are nonspecifically associating with the ODN, then the two spectra will have the same bound species signal fractions. Given that the spectra have different signal fractions (Figure 4), the fourth requirement is also satisfied. In Figure 4, the peaks labeled with diamonds (() represent the strontium bound quadruplex and contain a single metal ion, the divalent strontium cation. CONCLUSION There is a need for accurate and rapid analytical methods to measure the binding affinities of large biomolecules and various ligands. A specific example (i.e., the constant for a metal cation and quadruplex DNA) motivates the development described in this paper. The MS method that we report is simple, sensitive, direct, and fast. It affords binding constants from the ratio of the
signals of the gas-phase species in equilibrium by using nonlinear mathematical modeling. We demonstrate its validity and use this method to measure the binding constants of the interactions of the thrombin-binding aptamer with both potassium and strontium cations. A study as a function of temperature gives the change in enthalpy of the binding interaction of strontium cations and TBA. ACKNOWLEDGMENT This research was supported by a grant from the National Centers for Research Resources of the NIH (Grant 2P41RR000954).
Received for review September 10, 2007. Accepted December 17, 2007. AC701903W
Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
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