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Center for Biomolecular Interaction Analysis, University of Utah, School of Medicine, Salt Lake City, Utah 84132, USA
Reprint requests to: David G. Myszka, Center for Biomolecular Interaction Analysis, University of Utah, 50 N. Medical Drive, School of Medicine, Room 4A417, Salt Lake City, UT 84132, USA; e-mail: david.myszka{at}cores.utah.edu; fax: (801) 585-2978.
(RECEIVED October 25, 2001; FINAL REVISION January 15, 2002; ACCEPTED January 15, 2002)
Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.4330102.
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Keywords: Isothermal titration calorimetry; kinetics; optical biosensor; stopped-flow fluorescence; surface plasmon resonance; thermodynamics
Abbreviations: CA II, carbonic anhydrase II • CBS, 4-carboxybenzenesulfonamide • DNSA, dansylamide • ITC, isothermal titration calorimetry • PBS, phosphate-buffered saline • SFF, stopped-flow fluorescence • SPR, surface plasmon resonance
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Introduction |
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TOPAbstractIntroductionResultsDiscussionMaterials and methodsReferences |
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With the goal of evaluating how well SPR measurements match those performed in solution, we compared the binding equilibrium constants, thermodynamics, and kinetics for a small-molecule system measured on Biacore with two solution-based biophysical methods: isothermal titration calorimetry (ITC) and stopped-flow fluorescence (SFF). We focused our investigation on the binding of the enzyme carbonic anhydrase isozyme II (CA II, EC 4.2.1.1) (Chegwidden and Carter 2000) with two arylsulfonamide compounds, 4-carboxybenzenesulfonamide (CBS) and the fluorescent 5-dimethyl-amino-1-naphthalenesulfonamide, commonly known as dansylamide (DNSA) (Fig. 1A,B
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). ITC was employed to directly measure the complete thermodynamic profiles for the CA II/inhibitor interactions in solution (Fig. 1D), and SFF was used to resolve the reaction kinetics for soluble CA II binding to DNSA (Fig. 1E). The data from our comparative study revealed that the binding constants determined from the biosensor were equivalent to those determined using solution-based methods. Our results demonstrate that, when properly applied, the biosensor is a reliable method for characterizing the kinetics and thermodynamics of binding interactions.
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Results |
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TOPAbstractIntroductionResultsDiscussionMaterials and methodsReferences |
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), demonstrating nonspecific binding was not an issue.
SPR kinetic analysis of the CA II/CBS interaction
The response data for the binding of CBS to both surface densities of CA II were fit simultaneously to a simple 1:1 interaction model, constraining the kinetic rate constants to a single value (Fig. 2B,C). Local Rmax values were floated for each surface. Global fitting results in a more robust evaluation of the shared parameter values, which should be independent of the concentration of the analyte and the surface density of the immobilized ligand. The statistical behavior of the parameter estimates is also improved (Morton and Myszka 1998). A simple 1:1 interaction model provided an excellent fit to the data, as shown by the overlay of the simulated binding responses (red lines in Fig. 2B,C) with the experimental data (black lines in Fig. 2B,C).
A total of 14 data sets were collected for the CA II/CBS interaction by replicating the CBS concentration series, typically 40 nM to 20 µM, six times across 11 different CA II surfaces, which ranged in density from 2000 to 8400 RU, and were distributed over five different sensor chips. The mean kinetic rate constants describing the CA II/CBS interaction were calculated to be ka = 4.8 ± 0.2 x 104 M-1s-1 and kd = 0.0365 ± 0.0006 s-1, which yielded an equilibrium dissociation constant of KD = 760 ± 30 nM at 25°C. These parameters are tabulated in Table 1.
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). The mass transport coefficient (kt), which describes the first step in the reaction, had a mean value of 2.65 ± 0.6 x 107 RU M-1s-1. This is very similar to the predicted transport coefficient of 2.16 x 107 RU M-1s-1 based on the molecular weight of the analyte, flow rate, and flow cell configuration (Myszka et al. 1998). The mean kinetic rate constants describing the CA II/DNSA interaction were calculated to be ka = 3.9 ± 0.5 x 105 M-1s-1 and kd = 0.13 ± 0.01 s-1, which yielded a KD = 340 ± 40 nM at 25°C (see Table 1). It is interesting to note that although CA II binds to DNSA with higher affinity than CBS, the DNSA actually forms a kinetically weaker complex, as shown by a faster dissocation rate.
ITC thermodynamic analysis of CA II interactions with CBS and DNSA
Interactions of CA II with both sulfonamides were assayed by isothermal titration calorimetry to determine solution-based equilibrium constants. ITC directly measures changes in heat that occur during complex formation. A typical calorimetric analysis of CBS binding to CA II is shown in Figure 3. Similar data were collected for the CA II/DNSA interaction; however, the orientation of the assay was reversed to account for low aqueous solubility of DNSA (data not shown). Importantly, all buffer and stock solutions were identical to those used in the biosensor assays (see Materials and Methods).
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). Within experimental error, these affinity values are identical to the values determined by SPR. The binding stoichiometries were calculated to be 0.97 ± 0.09 to 1 for CBS and 0.87 ± 0.08 to 1 for DNSA, indicating that each sulfonamide populated a single site per enzyme molecule, which was also consistent with the mechanism predicted by SPR analysis.
Although both compounds had favorable binding enthalpies, their values were significantly different, with 
H = -11.9 ± 0.4 kcal/mol and -4.8 ± 0.4 kcal/mol for CBS and DNSA, respectively. The two sulfonamides bound with opposite changes in entropy (S = -12 ± 1 and 13 ± 1 cal/mol K for CBS and DNSA, respectively), which led to similar overall changes in Gibbs free energy of -8.4 ± 0.2 kcal/mol and -8.8 ± 0.9 kcal/mol for CBS and DNSA, respectively.
Temperature dependence of CA II interactions with CBS and DNSA as determined by SPR
The ability to monitor binding reactions from 4 to 40°C using Biacore makes it possible to collect temperature-dependent binding constants on the biosensor (Roos et al. 1998; Myszka 2000). To compare surface-based thermodynamic parameters with the values determined in solution using titration calorimetery, binding data for the CA II/sulfonamide interactions were collected at 5, 15, 25, and 35°C on the biosensor, as shown in Figure 4. Excellent fits were obtained when the responses from each CA II reaction were fit to 1:1 binding models to extract temperature-dependent rate constants. A total of six replicate temperature-dependent data sets were collected for CBS. Similarly, a total of eight replicate data sets were collected for DNSA.
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van't Hoff analysis of SPR data
The equilibrium constants determined from the temperature-dependent SPR analyses were used to determine van't Hoff enthalpies by plotting ln(KD) versus 1/T. As shown in Figure 5, the van't Hoff plots are linear for both CBS and DNSA, which is consistent with an invariant binding mechanism across the temperature range studied. As shown in Table 1, the van't Hoff enthalpies and entropies determined for both compounds from SPR analysis were very similar to the thermodynamic constants measured by ITC.
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shows a kinetic analysis of the CA II/DNSA interaction at two different temperatures, 5 and 25°C. Quadruplicate reactions for each DNSA concentration yielded superimposable traces, demonstrating that the association SFF measurements were reproducible. Because the displacement assay requires a separate experiment, only a single DNSA concentration was monitored to collect dissociation data at both temperatures. The association and dissociation data were fit simultaneously to a simple 1:1 interaction model. The rate constants determined from the SFF study (ka5°C = 1.4 ± 0.2 x 105 M-1s-1, kd5°C = 0.022 ± 0.005 s-1; ka25°C = 3.8 ± 0.9 x 105 M-1s-1, kd25°C = 0.16 ± 0.03 s-1) were similar to the rate constants determined by SPR at these temperatures (Table 1). Demonstrating the rate constants obtained by SPR agreed well with those measured in solution confirms the dependability of the SPR data. Because the kinetic rate constants from SPR are temperature dependent, these data can be used to characterize the transition states involved in the CA II/sulfonamide interactions for both compounds.
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. The plots are linear, which is consistent with H
and S for both reactions exhibiting no temperature dependence across the range studied (5–35°C). The activation parameters obtained for the binding of CA II to the two sulfonamides are summarized in Table 2. The reaction coordinates tracing the lowest energy continuous pathway between reactants and product on the potential energy surface for CBS and DNSA are shown in Figure 8. The species of maximum energy is defined by the transition state. Although the free energy path for both compounds is similar, the enthalpic and entropic terms for the transition state and the product are different, demonstrating unique thermodynamic parameters drive complex formation for CBS and DNSA with CA II.
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Discussion |
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The fact that biosensors require the immobilization of one of the binding partners onto a surface has brought about speculation that the immobilization would perturb the binding constants. In these studies, the agreement between the solution- and surface-based interaction parameters likely stems from the fact that the protein was tethered to a noncrosslinked dextran layer instead of to a solid surface. The dextran layer, commonly employed in Biacore analysis, retains much of the rotational entropic properties of the immobilized macromolecule, along with providing some degree of diffusional freedom (Karlsson et al. 1994). The flow cell system used in Biacore is also essential for rapid delivery of a constant supply of analyte during the association phase, and for rapid washout of the surface during the dissociation phase. This helps to minimize or eliminate concentration gradients at the surface that would otherwise alter the apparent binding reactions.
By no means do we imply that all rate constants determined from biosensors will match those obtained from solution-based methods. To appropriately compare biosensor data with data from solution-based assays, it is critical that biosensor experiments be conducted with care to avoid potential artifacts such as mass transport, nonspecific binding, and avidity effects that could alter the apparent binding constants (Myszka 1997; Morton and Myszka 1998). Applying robust data processing methods is important for improving the quality of the binding data (Myszka 1999b). Additionally, employing global fitting techniques helps ensure that appropriate models are used to interpret the reaction constants (Morton et al. 1995).
We also stress that although the SPR data were collected and fit simultaneously from multiple capacity surfaces, this was done to demonstrate the exceptional quality of the binding data available from the biosensor. Although fitting data from multiple capacity surfaces provides more information about binding reactions, it is not a requirement to extract accurate binding constants for a given interaction. In most cases, enough binding information is available from a single surface.
Determining the kinetics of the CA II/sulfonamide interactions yielded information that was unavailable solely from equilibrium data. For example, CA II was found to have a higher affinity for DNSA than for CBS (340 nM versus 760 nM at 25°C), but analysis of the rate constants showed that the CA II/CBS complex was kinetically more stable, having a fourfold slower dissociation rate (Table 1). The reaction and transition-state thermodynamics also showed that although the overall Gibbs free energy for complex formation was similar between the two compounds, the entropic and enthalpic contributions were significantly different. This detailed kinetic and thermodynamic information will help in characterizing how drug candidates interact with their macromolecular targets.
The examples of small-molecule biosensor analysis provided by these carbonic anhydrase inhibitors do not represent the limits of rate constants available from the biosensor. With carefully designed experiments, association and dissociation rates in the ranges of 1 x 103 to 1 x 107 M-1s-1 and 1 to 1 x 10-6 s-1, respectively, are possible (Myszka 1997). Even these ranges may be expanded, depending on the system. Also, the ability to monitor small analytes binding to even larger immobilized targets is possible. With current biosensor technology, monitoring interactions between analytes and immobilized targets differing in molecular mass on the order of 1000-fold should be feasible.
Biosensor analysis affords several advantages over other biophysical techniques, including its high information content, real-time monitoring, and high sensitivity, as well as the use of label-free reactants and low sample consumption. The ability to collect reliable equilibrium, kinetic, and thermodynamic information for small molecules from a single platform will expand the role biosensors play in life science research and the pharmaceutical industry.
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Materials and methods |
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Surface plasmon resonance
Immobilization of CA II
Prior to use, biosensor chips were docked into the instrument and preconditioned in water at 100 µL/min by applying two consecutive 20-µL pulses of 50 mM NaOH, then 10 mM HCl, and finally 0.1% SDS. CA II surfaces were prepared by standard coupling via exposed primary amines on CA II (Johnsson et al. 1991). Immobilizations were conducted at 25°C in PBS running buffer (20 mM sodium phosphate, 150 mM sodium chloride, pH 7.4), flowed at a rate of 10 µL/min. Flow cells were activated for 7 min by injecting a 70-µL mixture of 50 mM NHS:200 mM EDC. To prepare a high-capacity surface, 100 µL of a 0.1-mg/mL solution of CA II was injected for 10 min, followed by a 70-µL injection of ethanolamine to block any remaining surface-activated groups. Typical immobilization levels ranged from 6000 to 8000 RU. Lower CA II surface densities were achieved by injecting a diluted CA II acetate solution (0.03 mg/mL) for 5 min. Nonderivatized flow cells served as reference surfaces.
High-resolution CA II/sulfonamide interaction studies
Interaction analyses of CBS and DNSA binding to CA II surfaces in a high-resolution mode were performed at 25°C. Prior to each binding study, the instrument was primed three times with PBS, which served as the running buffer. All assays were run at a flow rate of 100 µL/min and a data collection rate of 2.5 Hz. Both the CBS and DNSA binding assays were repeated 10–20 times on newly immobilized CA II surfaces.
For the CBS study, a 2.0-mM stock CBS solution was prepared directly in running buffer from which twofold serial dilutions were made, typically spanning 40 nM to 20 µM. CBS was tested for binding simultaneously to CA II immobilized at two different surface densities. Each CBS concentration was dispensed into triplicate aliquots, randomized in the sample block, and injected across the four flow cells for 1 min using the KINJECT command. To monitor the dissociation of the CBS/CA II complex, running buffer was made to flow over the surface for 3 min, after which the IFC (integrated fluidic cartridge) was washed using the EXTRACLEAN command. Five or more samples of PBS running buffer alone were injected at the start of the analysis to ensure the instrument was fully equilibrated and additional blanks were injected after every fifth sample injection for double referencing.
Unlike CBS, which was readily soluble in PBS, DNSA required initial dissolution in methanol. Methanol stocks of 2.0 mM DNSA were diluted to 10 µM, from which twofold serial dilutions were prepared, typically 5 µM to 2 nM. The DNSA assay was conducted similarly to that described above for CBS.
Temperature-dependent CA II/sulfonamide interaction studies
Temperature-dependent studies of CA II/CBS and DNSA interactions were conducted at 5, 15, 25, and 35°C. For each compound, the entire temperature range was analyzed in a single experiment using an automated method. All samples were prepared as threefold serial dilutions in running buffer. CBS (40 nM to 10 µM) and DNSA (7 nM to 5 µM) were injected in triplicate for 1 min at a flow rate of 100 µL/min. A blank injection was included between each concentration series. The entire experiment was replicated for each compound, using different chips and newly immobilized CA II surfaces.
Determining kinetic and thermodynamic parameters
All sensorgrams were processed using a double-referencing method (Myszka 2000). First, the responses from the reference surface were subtracted from the binding responses collected over the reaction surfaces to correct for bulk refractive index changes. Second, the response from an average of the blank injections was subtracted to remove any systematic artifacts observed between the reaction and reference flow cells. Corrected response data were then fit in CLAMP, a data analysis program designed to interpret the binding kinetics of interactions recorded on biosensors by combining numerical integration and nonlinear global curve fitting routines (Morton and Myszka 1998). A global analysis of the CBS/CA II interaction was obtained by fitting the kinetic response data from differing-capacity CA II surfaces simultaneously to a simple reversible bimolecular interaction model (A + B = AB), assuming one set of rate constants yet allowing each surface its own maximum capacity. Having resolved the kinetic rate constants, the equilibrium dissociation constant KD was determined by the quotient kd/ka.
Because a fast association rate constant was observed for the formation of the CA II/DNSA complex, DNSA binding responses were fit using the model, A0 = A, A + B = AB, to correct for the potential mass transport limitations imposed on this interaction (Myszka et al. 1998). This model accounts for the diffusion of the soluble analyte within the flow cell to the sensor surface and the reversible interaction with its immobilized binding partner. For consistency between the SPR and SFF analyses, the refractive index of each sensorgram was floated during the fitting routine for the DNSA binding data.
Thermodynamic and transition state analysis
van't Hoff analysis was performed by substituting KD = 1/KA and G = H-TS into the van't Hoff equation, G = -RT ln(KA), yielding ln(KD) = H/(RT)-S/R, which is of the linear form y = a + bx. Plotting y = ln(KD) versus x = 1/T gives a = -S/R and b = H/R, where R is the universal gas constant, 1.987 cal/(mol K).
Transition state analysis was carried out using the statistical mechanical Eyring equation, k = (kBT/h)exp(S/R)exp(-H/RT), which gives the specific reaction rate (k = ka or kd) for a chemical reaction in terms of the enthalpy and entropy of activation (H and S, respectively) and the temperature (in Kelvin). Recasting the Eyring equation into the linear form of y = a + bx, plotting y = Rln(hk/kBT) versus x = l/T, and applying the universal gas constant, Planck's constant (h = 1.584 x 10-34 cal sec), and the Boltzmann constant (kB = 3.30 x 10-24 cal K) yields a = S and b = -H.
van't Hoff and Eyring plots were constructed in TableCurve 2D Windows v2.00 (Jandel Scientific, AISN software), fitting replicate data sets to a robust straight line of the form y = a + bx using a Gaussian standard error.
Isothermal titration calorimetry
CA II/sulfonamide interaction studies
CA II was extensively dialyzed against PBS buffer at pH 7.4, the identical buffer in which CBS and DNSA were solubilized for the SPR assays. All solutions were degassed prior to use. Titrations were carried out using 10-µL injections applied 4 min apart. An initial injection of 2 µL was made before each titration to ensure that the titrant concentration was at its loading value. For the CBS binding assay, the concentration of sulfonamide in the syringe was 20 times the concentration of enzyme in the cell: 400 µM CBS was titrated into 20 µM CA II protein. The orientation of the titration was reversed for DNSA binding assays due to the low solubility of DNSA in the aqueous reaction buffer. In this case, 200 µM CA II protein was titrated into 10 µM DNSA, equivalent to a 20:1 molar ratio of enzyme:inhibitor. All titration data were collected at 25°C and replicated to determine the experimental standard deviations for each parameter.
Extracting thermodynamic parameters from ITC data
Binding isotherms were fit by nonlinear regression using the single-site model provided by Origin software (MicroCal, Inc.). The stoichiometry of the interaction (N), equilibrium association constant (KA), and change in enthalpy (H) were floated during the fitting of all titration data. Equilibrium dissociation constants (KD) were calculated as the reciprocal of KA.
Stopped-flow fluorescence
High-resolution CA II/DNSA interaction studies
The reaction kinetics of CA II with the fluorescent probe DNSA in PBS at 25°C were measured by monitoring the change in the fluorescence of DNSA as it was bound to and released from the active site of CA II. In PBS, the absorption and emission maxima of unbound DNSA are 340 and 578 nm, respectively. When bound to CA II, the emission of DNSA increases in intensity and undergoes a blueshift to a maximum at 450 nM. This emission maximum is sufficiently remote from the chosen excitation wavelength of DNSA to prevent significant interference from Raman and Rayleigh scattering. Using an excitation wavelength of 340 nm through 4 nm-wide slits, emission was collected with a pass filter set at a cut-on wavelength of 450 ± 5 nm.
A methanol stock solution of 2.0 mM DNSA was diluted to 10 µM in PBS, from which all serial dilutions were made. To directly measure the association rate constant, the two reactants were mixed to yield final concentrations of 5 nM CA II and 39 nM to 20 µM DNSA, prepared by twofold serial dilutions. Analysis of each concentration was replicated four times.
Experiments to measure the dissociation rate constant were performed by mixing 10 µM DNSA prebound to 10 nM CA II with 2 mM CBS, a nonfluorescent competitive inhibitor of the CA II/DNSA interaction. Upon mixing, the final concentrations of these species were halved. The decrease in fluorescence was recorded as the DNSA bound to CA II was replaced with CBS. Dissociation studies were replicated three times.
Temperature-dependent CA II/DNSA interaction studies
To observe the effect of temperature on the rate constants, the CA II/DNSA interaction was also monitored at 5°C. In this case, the two reactants were mixed to yield final concentrations of 5 nM CA II and 60 nM to 5 µM DNSA, prepared by threefold serial dilutions. The analysis of each concentration was replicated three times.
Determining kinetic parameters from SFF data
To approximate pseudofirst-order reaction conditions, DNSA was always at least eightfold in molar excess of CA II. Normalized fluorescence data, with the initial point of each trace set to t = 0 sec, were globally fit in CLAMP to a simple bimolecular interaction model, A + B = AB.
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Acknowledgments |
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The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.
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References |
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