On-line dynamic titration: determination of dissociation constants for noncovalent complexes using Gaussian concentration profiles by electrospray ionization mass spectrometry

A new method for determination of dissociation constants (Kd) using on-line titration by electrospray ionization mass spectrometry is presented. Unlike in common titration experiments, where a set of discrete solutions with a fixed concentration of host and increasing concentration of guest is measured, here a continuous Gaussian concentration profile of guest, formed by band-broadening dispersion during passage through a long tubing, is utilized. An equation allowing access to dissociation constant values from experimental data fit to a 1:1 binding model was derived and incorporated into an in-house-written computer program for automated data processing. The new method is demonstrated for noncovalent complexes of cinchona alkaloid carbamate chiral selectors with N-dinitrobenzoylleucine enantiomers and a series of cyclodextrins with sulfonated azo dyes.     

pK Determination of Sparingly Soluble Compounds by Difference Potentiometry

Abstract

A differential potentiometric titration technique is described which allows the determination of dissociation constants of sparingly soluble and/or labile compounds. The dissociation constants of a series of beta-blockers were determined by this technique. Dissociation constants determined by routine potentiometric titration techniques were found to be equivalent to those determined by the differential potentiometric titration method

By using a computer to accumulate the titration data, it is shown that the dissociation constants of compounds which degrade due to added titrant base can be accurately determined. This is accomplished by shortening the duration of the experiment (total time < 10 minutes) such that minimal degradation occurs during the course of the titration. By combining the computer technique with a differential potentiometric titration technique, it is possible to determine the dissociation constants of sparingly soluble compounds which are not stable in solution

In the determination of dissociation constants, if two pKs are separated by less than 4 pH units, then these constants are said to overlap. To accurately determine a pK, both dissociation constants must be solved for simultaneously. A method is described which corrects for overlapping pKs in a differential potentiometric titration, which then allows the unambiguous determination of the dissociation constants. Also described is a method to correct the differential titration when the amount of overlap is small and the pK of one of the overlapping constants is known     

Concentration jump experiments for the precise determination of rate constants of reverse reactions in the millisecond time range

Low dissociation or reverse rate constants of single-step or multistep complex formation equilibria are usually obtained with reduced precision from standard stopped-flow binding experiments by determination of the intercept of the concentration dependence of k(obs). Large and fast concentration jumps, based on two different step-motor-driven mixing setups, are performed with 60-300-fold dilutions that allow the precise, convenient, and independent determination of dissociation rate constants in the range of approximately 0.1-100 s(-1) in a single stopped-flow dissociation experiment. A theoretical basis is developed for the design and for the evaluation of such dilution experiments by considering the rebinding occurring during dissociation. The kinetics of three chemical systems are investigated, the binding of Mg2+ to 8-hydroxyquinoline as well as of Ca2+ and K+ to the cryptand [2.2.2], by carrying out standard stopped-flow binding as well as dissociation experiments employing various dilution factors. The advantage of the dilution method for investigating chemical and biological systems is emphasized.     

Syntheses of immobilized G protein-coupled receptor chromatographic stationary phases: characterization of immobilized mu and kappa opioid receptors

Opioid receptors are members of the superfamily of G protein-coupled receptors (GPCRs). Liquid chromatographic stationary phases containing either the human mu or kappa opioid receptor subtypes have been developed to study the binding between the opioid receptors and their ligands. The receptors were obtained from Chinese hamster ovary cells stably transfected with human mu or kappa receptor subtypes. The receptors were isolated through partial solubilization with sodium cholate detergent, and the partially purified receptor complex was immobilized in the phospholipid analogue monolayer of an immobilized artificial membrane liquid chromatographic stationary phase. The resulting phase was packed into a glass column (1.8 x 0.5 (i.d.) cm) and used in the on-line chromatographic determination of drug/ligand binding affinities to the immobilized opioid receptors. Preliminary on-line binding studies employing frontal chromatographic techniques were conducted with the known mu antagonist (naloxone) and a kappa agonist (U69593). The calculated dissociation constants (Kd) were 110 nM for naloxone and 84 nM for U69593. The results indicate that the immobilized receptors retained their ability to specifically bind ligands and were active for 1200 column volumes applied over two weeks. Zonal chromatographic experiments were also conducted, and competitive displacements of the marker ligands were observed. The results suggest that the immobilized opioid receptor stationary phases can be used to qualitatively assess the binding affinities of compounds to the immobilized receptors and represent the first example of the use of immobilized GPCRs in a chromatographic system.     

Desorption/ionization on porous silicon mass spectrometry studies on pentose-borate complexes

Desorption/ionization on porous silicon mass spectrometry (DIOS-MS) was used to investigate the binding affinities between aldopentose isomers and boron. Boron has been recognized for its importance in pentose synthesis and stabilization in prebiotic conditions. Boron may also account for the fact that ribose, among other aldopentoses, is the favored building block in RNA synthesis. This research started with the detection of aldopentoses in the positive mode through cationization and the aldopentose-borate complexes in the negative mode. Then two competition schemes, one using a pentose structure analogue and the other using 13C-labeled ribose, were designed to compare the relative binding affinities of four aldopentoses (xylose, lyxose, arabinose, and ribose) to boron. Both approaches determined the binding preference to be ribose > lyxose > arabinose > xylose. This work illustrates the potential of DIOS-MS in the analyses of nonvolatile, small molecules in delicate chemical equilibria. Without externally introduced matrices, background signals are not a limiting factor. Furthermore, the possible dramatic change of pH associated with the matrix introduction, which may disturb the equilibria of interest, is avoided.     

Measurement of solution-phase chiral molecular recognition in the gas phase using electrospray ionization-mass spectrometry

Development of chiral selectors (SOs) is important both for understanding chiral molecular recognition processes and for their use in the separation of chiral species (selectands). Their evaluation by chromatographic procedures (e.g., as chiral stationary phase) can, however, be time-consuming. In this respect, electrospray ionization-MS (ESI-MS) is tested here as a possible alternative for screening enantioselective binding by SOs. The set of well-characterized cinchona alkaloid SOs are investigated with respect to their enantioselective binding to a set of model enantiomers, dinitrobenzoyl-(R)- and dinitrobenzoyl-(S)-leucine. MS-based enantioselectivity values from normalized gas-phase ion abundances for the diastereomeric complexes are compared empirically to chromatographic (HPLC) enantioselectivity results and shown to be consistent. Investigations into the fundamentals of measuring unbiased enantioselectivity values in the limit of dilute solution by correlation between experimental and modeled theoretical data are shown. Titration experiments are used to extract binding constants and are compared with published calorimetric (ITC) data. Results show that while the magnitude of binding affinities determined for various diastereomeric complexes is attenuated, the relative ranking and stereochemical preference in binding are consistently reproduced. This work represents a fundamental study of solution- versus gas-phase correlation for enantioselective systems by ESI-MS and indicates that, although not all questions and assumptions can be clearly engaged, for these enthalpically driven binding systems, the relative degree of binding affinity and selectivity is preserved.     

Determination of binding constants on microarrays with confocal fluorescence detection

Confocal laser scanning microscopy was employed for the determination of binding constants of receptor-ligand interactions in a microarray format. Protocols for a localized immobilization of amine containing substances on glass via GOPTS (3-glycidyloxypropyl)trimethoxysilane) were optimized with respect to the detection of ligand binding by fluorescence. Compatibility with miniaturization by nanopipetting devices was ensured during all steps. The interaction of the tripeptide L-Lys-D-Ala-D-Ala with vancomycin immobilized on glass served as a model. To minimize consumption of ligand, binding constants were determined by stepwise titration of binding sites. The binding constant of the unlabeled ligand was determined by competitive titration with a fluorescently labeled analogue. The determined binding constants agreed well with those determined by other techniques, previously. Labeled ligand bound stronger than the unlabeled one. This difference was dye-dependent. Still, binding was specific for the tripeptide moiety confirming that ligand and fluorescent analogue competed for the same binding sites these results validate the determination of binding constants by competitive titration. The protocols established for confocal fluorescence detection are applicable to axially resolved detection modalities and screening for unlabeled ligands by competitive titration in general.     

Potentiometric Determination of Thermodynamic and Apparent Dissociation Constants by Nonlinear Least Squares Fitting

Abstract

Potentiometric titration curve models have been developed for mono-, di- and triprotic weak electrolytes. Apparent dissociation constants or thermodynamic dissociation constants, corrected for ionic strengths of up to O.5M, can be determined by nonlinear least squares fitting of potentiometric data to the models. A commercially available program, PCNONLIN (an IBM PC version of NONLlN84), was utilized for the fitting, allowing the models to be portable. The models have been tested with theoretical data containing random or systematic error, and data for several model compounds of various weak electrolyte class.

The method in this report has several advantages over traditional 'half neutralization' or graphical methods. First, the models are based on the analytic solution of the charge balance equation, with no simplifying approximations. Second, the method can determine dissociation constants in cases where no inflection point is present, such as for overlaping ionization processes or low concentration of compound. Finally, alterations in ionic strength during the titration were accounted for in the models.     

Quantitative determination of noncovalent binding interactions using automated nanoelectrospray mass spectrometry

Electrospray ionization mass spectrometry (ESI-MS) has proven to be an extremely powerful tool for studying biomolecular structures and noncovalent interactions. Here we report a method using a fully automated, chip-based nanoESI-MS system to determine the dissociation constants (Kd) for the complexes of two different proteins with their ligands. The automated nanoelectrospray system, consisting of the NanoMate and ESI chip, serves functionally as a combination of autosampler and nanoelectrospray ionization source. This system provides all the advantages of conventional nanoelectrospray plus automated, high-throughput analyses without carryover. The automated nanoESI system was used to investigate quantitative noncovalent interactions between ribonuclease A (RNase A) and cytidylic acid ligands (2'-CMP, CTP), a well-characterized model protein-ligand complex, and between an inactive endocellulase mutant (Thermobifida fusca Cel6A D117Acd) and four oligosaccharide ligands (cellotriose, cellotetraose, cellopentaose, cellohexaose). Both titration and competitive binding approaches were performed prior to automated nanoESI-MS analysis with a Q-TOF mass spectrometer. Dissociation constants for each complex were calculated from the sum of ion peak areas of free and complexed proteins during the titration and competition experiments. The measured Kd values for the RNase A-CMP and Cel6A D117Acd-G3 complexes were found to be in excellent agreement with the available published values obtained by standard spectroscopic titration techniques. To our knowledge, this is the first report of using an ESI-MS approach to study the interactions between a cellulase and oligosaccharides. The results provide new insights for understanding the nature of cellulase-cellulose interactions.     

Partitioning model for competitive host-guest complexation in ESI-MS

Mathematical models based on equilibrium partitioning theory were developed to relate ion abundances produced by electrospray ionization mass spectrometry with solution concentrations of complexes resulting from competitive host-guest binding. Through modeling the possible equilibria in the electrospray droplets, including the partitioning between the droplet surface and interior that dictate what ions are generated by an electrospray, the factors responsible for distorting the distribution of ions from their solution concentrations were evaluated. Experiments with crown ether-alkali metal complexes confirm the validity of the models and yield a greater understanding of the behavior of host-guest complexes in ESI-MS, allowing for more accurate and less trouble-prone measurements of solution binding interactions.     

Kinetics and thermodynamics of biotinylated oligonucleotide probe binding to particle-immobilized avidin and implications for multiplexing applications

In this work, the kinetics and dissociation constant for the binding of a biotin-modified oligonucleotide to microparticle-immobilized avidin were measured. Avidin has been immobilized by both covalent coupling and bioaffinity capture to a surface prefunctionalized with biotin. The measured rate and equilibrium dissociation constants of avidin immobilized by these different methods have been compared with those for nonimmobilized avidin. We found that immobilization resulted in both a decrease in the rate of binding and an increase in the rate of dissociation leading to immobilized complexes having equilibrium dissociation constants of 7 ± 3 × 10(-12) M, higher than the value measured for the complex between biotin-modified oligonucleotide and nonimmobilized avidin and approximately 4 orders of magnitude larger than values for the wild-type avidin-biotin complex. Immobilized complex half-lives were found to be reduced to 5 days, which resulted in biotin ligands migrating between protein attached to different particles. Different immobilization methods showed little variation in complex stability but differed in total binding and nonspecific biotin-modified oligonucleotide binding. These findings are critical for the design of multiplexed assays where probe molecules are immobilized to biosensors via the avidin-biotin interaction.     

A cluster expansion method for the complete resolution of microscopic ionization equilibria from NMR titrations

The NMR chemical shift of spin 1/2 nuclei in a polyprotic molecule represents a sensitive probe of microscopic protonation equilibria. However, these equilibria are commonly parametrized in terms of microscopic equilibrium constants, whose number increases very rapidly with the number of ionizable groups. For that reason their determination was considered to be basically impossible except for the cases of the simplest molecules. On the basis of a cluster expansion of the free energy of a microstate, we propose a novel parametrization of this problem that drastically reduces the number of necessary parameters needed to specify the microscopic equilibria. Such cluster parameters can be extracted from NMR titration data in a straightforward way. Once these parameters are known, all microscopic equilibrium constants can be obtained.     

Nonlinear analyte concentration gradients for one-step kinetic analysis employing optical microring resonators

Conventional methods to probe the binding kinetics of macromolecules at biosensor surfaces employ a stepwise titration of analyte concentrations and measure the association and dissociation to the immobilized ligand at each concentration level. It has previously been shown that kinetic rates can be measured in a single step by monitoring binding as the analyte concentration increases over time in a linear gradient. We report here the application of nonlinear analyte concentration gradients for determining kinetic rates and equilibrium binding affinities in a single experiment. A versatile nonlinear gradient maker is presented, which is easily applied to microfluidic systems. Simulations validate that accurate kinetic rates can be extracted for a wide range of association and dissociation rates, gradient slopes, and curvatures, and with models for mass transport. The nonlinear analyte gradient method is demonstrated with a silicon photonic microring resonator platform to measure prostate specific antigen-antibody binding kinetics.     

Determination of ligand-protein dissociation constants by electrospray mass spectrometry-based diffusion measurements

A novel approach for the quantification of ligand-protein interactions is presented. Electrospray ionization mass spectrometry (ESI-MS) is used to monitor the diffusion behavior of noncovalent ligands in the presence of their protein receptors. These data allow the fraction of free ligand in solution to be determined, such that the corresponding dissociation constants can be calculated. A set of conditions is developed that provides an "allowable range" of concentrations for this type of assay. The method is tested by applying it to two different inhibitor-enzyme systems. The dissociation constants measured for benzamidine-trypsin and for N,N',N' '-triacetylchitotriose-lysozyme are (50 +/- 10) and (6 +/- 1) mM, respectively. Both of these results are in good agreement with previous data from the literature. In contrast to traditional ESI-MS-based methods, the approach used in this work does not rely on the preservation of specific solution-type noncovalent interactions in the gas phase. It is shown that this method allows an accurate determination of dissociation constants, even in cases in which the ion abundance ratio of free to ligand-bound protein in ESI-MS does not reflect the corresponding concentration ratio in solution.     

An equilibrium partitioning model for predicting response to host-guest complexation in electrospray ionization mass spectrometry

While electrospray ionization mass spectrometry (ESI-MS) has become a powerful technique for analyzing many types of host-guest complexation, questions remain as to just how accurately ion abundances generated by ESI reflect the true distribution of species at equilibrium in solution. To better understand this relationship, an equilibrium partitioning model was developed to explain the various interactions that dictate how much of a particular host-guest complex is transferred from solution into the gas phase in the ESI process. By evaluating the simultaneous equilibria of the complexation reaction and the partitioning of species between the surface and interior of the ESI droplets, one can estimate the ion abundances generated. The predictions of this new model were evaluated and experimentally confirmed through the analysis of the complexes of 18-crown-6 with alkali metal cations in an ESI quadrupole ion trap mass spectrometer, and it was determined that binding constants alone may not give accurate predictions about the observed ESI-MS response to different host-guest complexes.     

Revealing the quaternary structure of a heterogeneous noncovalent protein complex through surface-induced dissociation

As scientists begin to appreciate the extent to which quaternary structure facilitates protein function, determination of the subunit arrangement within noncovalent protein complexes is increasingly important. While native mass spectrometry shows promise for the study of noncovalent complexes, few developments have been made toward the determination of subunit architecture, and no mass spectrometry activation method yields complete topology information. Here, we illustrate the surface-induced dissociation of a heterohexamer, toyocamycin nitrile hydratase, directly into its constituent trimers. We propose that the single-step nature of this activation in combination with high energy deposition allows for dissociation prior to significant unfolding or other large-scale rearrangement. This method can potentially allow for dissociation of a protein complex into subcomplexes, facilitating the mapping of subunit contacts and thus determination of quaternary structure of protein complexes.     

Understanding molecular association and isomers recognition in isomer-cyclodextrin multiple complex formation by improved liquid chromatographic studies

Equations are derived that allow the determination of guest-cyclodextrin primary (K(11)), secondary (K(12)), and higher order (K(1)(n)) binding constants as well as the degree of complexation n? (the percent of complexed guest), by monitoring the observed capacity factor k'(obs) for guests that can be structural, geometric, or optical isomers. The retention behavior (elution order) in a mixture of isomers is dependent on the cyclodextrin concentration in the mobile phase as well as on the stoichiometry and the binding constant of the guest-cyclodextrin (G-CD) complex. The simplification of higher order complexes (G-CD(n)) to that with 1:1 stoichiometry can lead to erroneous results; therefore, it is important for the stoichiometry to be determined accurately, prior to any binding constant calculations, following the continuous variation method. The proposed models are solved iteratively using nonlinear least-squares analysis and following specific algorithms.     

Determination of dissociation constants for protein-ligand complexes by electrospray ionization mass spectrometry

A fully automated biophysical assay based on electrospray ionization mass spectrometry (ESI-MS) for the determination of the dissociation constants (KD) between soluble proteins and low molecular mass ligands is presented. The method can be applied to systems where the relative MS response of the protein and the protein-ligand complexes do not reflect relative concentrations. Thus, the employed approach enables the use of both electrostatically and nonpolar bound complexes. The dynamic range is wider than for most biological assays, which facilitates the process of establishing a structure-activity relationship. This fully automated ESI-MS assay is now routinely used for ligand screening. The entire procedure is described in detail using hGHbp, a 25-kDa extracellular soluble domain of the human growth hormone receptor, as a model protein.     

Ion chromatographic separation of rare-Earth elements using a nitrilotriacetate-type chelating resin as the stationary phase

The chromatographic retention behavior of rare-earth elements (REEs) on a chelating resin having a nitrilotriacetate group (NTA gel) was evaluated. The capacity factors for a series of REEs on the NTA gel were in fairly good agreement (R(2) = 0.978) with the stability constants of the corresponding NTA complexes. The NTA gel was applied to the column stationary phase for the ion chromatographic separation of REE. A favorable separation of a series of REEs was achieved within 15 min using a gradient elution of nitric acid. The separated REE ions were detected using the postcolumn derivatization method with chlorophosphonazo III as a colorization reagent. The present chromatographic system, interfaced with inductively coupled plasma mass spectrometry, was applied for the simultaneous determination of 14 REEs.     

A capillary electrophoretic reactor with an electroosmosis control method for measurement of dissociation kinetics of metal complexes

The solvolytic dissociation rate constants of 1:2 complexes of Al3+ and Ga3+ with an azo dye ligand, 2,2'-dihydroxyazobenzene-5,5'-disulfonate (DHABS, H2L2-), have been evaluated with a capillary electrophoretic reactor (CER) system. This CER system is based on the fact that metal complexes encounter an overwhelming force to dissociate when apart from the ligand by CE resolution. Treatment of a capillary with a slightly acidic buffer solution, e.g., pH 5, reduces the double-layer potential (zeta) of the inner silica wall. Owing to slow relaxation of the deprotonation equilibria of superficial silanol groups known as the pH hysteresis, this zeta potential can be actually retained during the electrophoresis of the metal complexes in question with a neutral buffer at pH 7.0. This method enables one to manipulate migration times, namely, residence times in a capillary tube, from 5 to 90 min, depending on the prescribed conditioning pH, without changing any other operation conditions such as buffer composition and electric field strength. The excellent performance of the CER is exemplified by the accurate estimation of the dissociation degree of the complexes. The dissociation degree-time profiles for the complexes are quantitatively described using both internal and external standards; the very inert complex of [Co(III)L2]5- for the peak signal standardization and methyl orange for the injection volume correction. The solvolytic dissociation rate constants of the 1:2 complexes of Al3+ and Ga3+ ions with DHABS [AlL2]5- and [GaL2]5- into the 1:1 ones have been determined as (4.9+/-1.0) x 10(-4) and (3.7+/-0.3) x 10(-3) s(-1) at 303 K, respectively.