Combined affinity and rate constant distributions of ligand populations from experimental surface binding kinetics and equilibria

The present article considers the influence of heterogeneity in a mobile analyte or in an immobilized ligand population on the surface binding kinetics and equilibrium isotherms. We describe strategies for solving the inverse problem of calculating two-dimensional distributions of rate and affinity constants from experimental data on surface binding kinetics, such as obtained from optical biosensors. Although the characterization of a heterogeneous population of analytes binding to uniform surface sites may be possible under suitable experimental conditions, computational difficulties currently limit this approach. In contrast, the case of uniform analytes binding to heterogeneous populations of surface sites is computationally feasible, and can be combined with Tikhonov-Phillips and maximum entropy regularization techniques that provide the simplest distribution that is consistent with the data. The properties of this ligand distribution analysis are explored with several experimental and simulated data sets. The resulting two-dimensional rate and affinity constant distributions can describe well experimental kinetic traces measured with optical biosensors. The use of kinetic surface binding data can give significantly higher resolution than affinity distributions from the binding isotherms alone. The shape and the level of detail of the calculated distributions depend on the experimental conditions, such as contact times and the concentration range of the analyte. Despite the flexibility introduced by considering surface site distributions, the impostor application of this model to surface binding data from transport limited binding processes or from analyte distributions can be identified by large residuals, if a sufficient range of analyte concentrations and contact times are used. The distribution analysis can provide a rational interpretation of complex experimental surface binding kinetics, and provides an analytical tool for probing the homogeneity of the populations of immobilized protein.     

Control of kinetics by cooperative interactions

Cooperative effects in ligand binding and dissociation kinetics are much less investigated than steady state kinetics or equilibrium binding. Nevertheless, cooperativity in ligand binding leads necessarily to characteristic properties with respect to kinetic properties of the system. In case of positive cooperativity as found in oxygen binding proteins, a typical property is an autocatalytic ligand dissociation behavior leading to a time dependent, apparent ligand dissociation rate. To follow systematically the influence of the various potentially involved parameters on this characteristic property, simulations based on the simple MWC model were performed which should be relevant for all types of models based on the concept of an allosteric unit. In cases where the initial conformational distribution is very much dominated by the R-state, the intrinsic kinetic properties of the T-state are of minor influence for the observed ligand dissociation rate. Even for fast conformational transition rates, the R-state properties together with the size of the allosteric unit and the allosteric equilibrium constant define the shape of the curve. In such a case, a simplified model of the MWC-scheme (the irreversible n-chain model) is a good approximation of the full scheme. However, if in the starting conformational distribution some liganded T-molecules are present (a few percent is enough), the average off-rates can be significantly altered. Thus, the assignment of the initial rates to R-state properties has to be done with great care. However, if the R-state strongly dominates initially it is even possible to get an estimation of the lower limit for the number of interacting subunits from kinetic data: similar to the Hill-coefficient for equilibrium conditions, a measure for "kinetic cooperativity" can be derived by comparing initial and final ligand dissociation rates.     

The kinetics of analyte capture on nanoscale sensors

This article presents a number of kinetic analyses related to binding processes relevant to capture of target analyte species in nanoscale cantilever-type devices designed to detect small concentrations of biomolecules. The overall analyte capture efficiency is a crucial measure of the ultimate sensitivity of such devices, and a detailed kinetic analysis tells us how rapidly such measurements may be made. We have analyzed the capture kinetics under a variety of conditions, including the possibility of so-called surface-enhanced ligand capture. One of the modalities studied requires ligand capture through a cross-linking mechanism, and it was found that this mode may provide a robust and sensitive approach to biomolecular detection. For the two modalities studied, we find that detection of specific biomolecules down to concentration levels of 1 nM or less appear to be quite feasible for the device configurations studied.     

A single-fractal analysis of cellular analyte-receptor binding kinetics utilizing biosensors

A fractal analysis of a confirmative nature only is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using a single-fractal analysis. Relationships are presented for the binding rate coefficient as a function of the fractal dimension and for the analyte concentration in solution. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. It is of interest to note that examples are presented where the binding coefficient, k exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficient (or affinity). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensor or other surfaces.     

Experimental design for analysis of complex kinetics using surface plasmon resonance

Using BIAcore surface plasmon resonance technology, we found that the real-time association kinetics of Fabs specific for hen egg-white lysozyme did not conform to a 1:1 Langmuir association model. Heterogeneity of the components is not the source of the complex kinetics. Informed by independent structural data suggesting conformational flexibility differences among these antibodies, we chose global mathematical analysis based on a two-phase model, consistent with the encounter-docking view of protein-protein associations. Experimental association times (T(a)) from 2 to 250 min revealed that initial dissociation rates decreased with increasing T(a), confirming a multiphasic association. The relationship between observed dissociation rate and T(a) is characteristic of each antibody-antigen complex. We define a new parameter, T(50), the time at which the encounter and final complexes are of equimolar concentration. The observed T(50) is a function of analyte concentration and the encounter and docking rate constants. Simulations showed that when the ligand is saturated at high analyte concentrations, T(50) reaches a minimum value, T(50)(MIN), which can be used to compare antigen-antibody complexes. For high-affinity complexes with rapid rearrangement to a stable complex, T(50)(MIN) approaches T(1/2) of the rearrangement forward rate constant. We conclude that experiments with a range of T(a) are essential to assess the nature of the kinetics, regardless of whether a two-state or 1:1 model is applicable. We suggest this strategy because each T(a) potentially reveals a different distribution of molecular states; for two-step analysis, a range of T(a) that brackets T(50) is optimal.     

Reaction kinetics of a two-photon excitation microparticle based immunoassay--from modelling to practice

Real time observation of reaction kinetics is one of the key features of the newly developed microparticle based two-photon excitation fluorescence immunoassay system (TPX). By observing binding reactions at the surface of individual microparticles during the incubation of an assay, the binding constants of an assay become apparent. This paper describes the use of the new system in quantifying the reaction parameters of human thyroid stimulating hormone (hTSH) assay. A mechanistic reaction model for the assay is presented. The reaction model is further shown to precisely predict the behaviour of the assay kinetics over a wide range of analyte concentrations.     

Comparison between the kinetics of heterogeneous and sequentially co-operative binding systems

The kinetics of ligand binding to a dimer displaying anticooperative interactions is analysed and compared with the kinetics of binding to two classes of independent sites. Both systems are characterized by a bi-exponential kinetics. However, the relation between the coefficients of these exponentials and the concentration of ligand is linear in case of sites heterogeneity and hyperbolic (parabolic in some cases) for a co-operative dimer. The pre-exponential factors are always negative in case of sites heterogeneity and their modulus increases monotonically as a hyperbolic function of the ligand concentration. In cases of anticooperative interaction, one of the pre-exponential factors can be positive and the modulus can change biphasically as a function of the concentration of ligand. The detailed study of binding kinetics at different ligand concentrations provides a potential tool to discriminate between binding sites heterogeneity and negative co-operativity.     

Exploring "one-shot" kinetics and small molecule analysis using the ProteOn XPR36 array biosensor

A ProteOn XPR36 parallel array biosensor was used to characterize the binding kinetics of a set of small molecule/enzyme interactions. Using one injection with the ProteOn's crisscrossing flow path system, we collected response data for six different concentrations of each analyte over six different target protein surfaces. This "one-shot" approach to kinetic analysis significantly improves throughput while generating high-quality data even for low-molecular-mass analytes. We found that the affinities determined for nine sulfonamide-based inhibitors of the enzyme carbonic anhydrase II were highly correlated with the values determined using isothermal titration calorimetry. We also measured the temperature dependence (from 15 to 35 degrees C) of the kinetics for four of the inhibitor/enzyme interactions. Our results illustrate the potential of this new parallel-processing biosensor to increase the speed of kinetic analysis in drug discovery and expand the applications of real-time protein interaction arrays.     

Selected-fit versus induced-fit protein binding: kinetic differences and mutational analysis

The binding of a ligand molecule to a protein is often accompanied by conformational changes of the protein. A central question is whether the ligand induces the conformational change (induced-fit), or rather selects and stabilizes a complementary conformation from a pre-existing equilibrium of ground and excited states of the protein (selected-fit). We consider here the binding kinetics in a simple four-state model of ligand-protein binding. In this model, the protein has two conformations, which can both bind the ligand. The first conformation is the ground state of the protein when the ligand is off, and the second conformation is the ground state when the ligand is bound. The induced-fit mechanism corresponds to ligand binding in the unbound ground state, and the selected-fit mechanism to ligand binding in the excited state. We find a simple, characteristic difference between the on- and off-rates in the two mechanisms if the conformational relaxation into the ground states is fast. In the case of selected-fit binding, the on-rate depends on the conformational equilibrium constant, whereas the off-rate is independent. In the case of induced-fit binding, in contrast, the off-rate depends on the conformational equilibrium, while the on-rate is independent. Whether a protein binds a ligand via selected-fit or induced-fit thus may be revealed by mutations far from the protein's binding pocket, or other "perturbations" that only affect the conformational equilibrium. In the case of selected-fit, such mutations will only change the on-rate, and in the case of induced-fit, only the off-rate.     

Direct observation of protein-ligand interaction kinetics

Internal dynamics on the micro- to millisecond time scale have a strong influence on the affinity and specificity with which a protein binds ligands. This time scale is accessible through relaxation dispersion measurements using NMR. By studying the dynamics of a protein with different concentrations of a ligand, one can determine the dynamic effects induced by the ligand. Here we have studied slow internal dynamics of the N-terminal src homology 2 domain of phosphatidylinositide 3-kinase to probe the role of individual residues for the interaction with a tyrosine-phosphorylated binding sequence from polyoma middle T antigen. While slow dynamic motion was restricted to a few residues in the free SH2 and in the SH2 complex, motion was significantly enhanced by adding even small amounts of ligand. Kinetic rates induced by ligand binding varied between 300 and 2000 s(-1). High rates reflected direct interactions with the ligand or rearrangements caused by ligand binding. Large differences in rates were observed for residues adjacent in the primary sequence reflecting their individual roles in ligand interaction. However, rates were similar for residues involved in the same side chain interactions, reflecting concerted motions during ligand binding. For a subset of residues, exchange must involve structural intermediates which play a crucial role in high-affinity ligand binding. This analysis supports a new view of the dynamics of individual sites of a protein during ligand interaction.     

The effect of mitochondrial energization on cytochrome c oxidase kinetics as measured at low temperatures. I. The reaction with carbon monoxide.

The kinetics of CO binding by the cytochrome c oxidase of pigeon heart mitochondria were studied as a function of membrane energization at temperatures from 180 to 280 degrees K in an ethylene glycol/water medium. Samples energized by ATP showed acceleration of CO binding compared to those untreated or uncoupled by carbonylcyanide p-trifluoromethyoxyphenylhydrazone but only at relatively low temperatures and high CO concentrations. Experiments using samples in a "mixed valency" (partially oxidized) state showed that the acceleration of ligand binding is not due to the formation of a partially oxidized state via reverse electron transport. It is concluded that in the deenergized state one CO molecule can be closely associated with the cytochrome a3 heme site without actually being bound to the heme iron; in the energized state, two or more ligand molecules can occupy this intermediate position. The change in the apparent ligand capacity of a region near the heme iron in response to energization is evidence for an interaction between cytochrome oxidase and the ATPase system. Furthermore, these results suggest a control mechanism for O2 binding.     

A fractal analysis of analyte-estrogen receptor binding and dissociation kinetics using biosensors: environmental and biomedical effects

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ERs) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. The influence of different ligands is also analyzed. A better understanding of the kinetics provides physical insights into the interactions, and suggests means by which appropriate interactions (to promote correct signaling) and inappropriate interactions such as with xenoestrogens (to minimize inappropriate and deleterious to health signaling) may be better controlled. The fractal approach is applied to analyte–ER interaction data available in the literature. The units for the different parameters (rate coefficients and affinities) in fractal-type kinetics are different from those obtained in classical kinetics. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D_f) present on the biosensor chip surface. In general, the binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity on the surface. A single-fractal analysis is adequate in some cases. In others (that exhibit complexities in the binding or the dissociation curves) a dual-fractal analysis is required to obtain a better fit. This has biomedical and environmental implications in that the dissociation (and the binding) rate coefficient may be used to alleviate (deleterious effects) or enhance (beneficial effects) by selective modulation of the surface. The affinity values obtained in the analysis are consistent with the numbers required to (a) promote signaling between the correct analyte and the estrogen receptor, and (b) minimize the signaling between xenoestrogens and the estrogen receptor.     

Equilibrium and kinetics of the reaction of Aplysia myoglobin with azide.

The present paper reports a study on the equilibria and kinetics of the acid-alkaline transition and the azide binding reaction by ferric Aplysia myoglobin. A single completely reversible spectrophotometric titration curve is found over the pH range from similar to 5 to similar to 9, with an apparent pK equals to 7.5 for the acid-alkaline transition. The kinetics of the process, followed by the temperature-jump method, gives, at pH values close to the pK of the transition, one single, well-resolved, relaxation independent of protein concentration and of type of buffer used. The pattern accords to a simple pH dependent reaction, in buffered medium, between the two forms of the protein. The results of the azide binding reaction show that the process conforms to simple equilibrium as expected for a single site protein. The méasured association constant is reported as a function of pH. The kinetics of the reaction of Aplysia metMb with N3- minus shows, on the other hand, a complex behavior. The relaxation pattern is found to strongly depend on pH and ligand concentration in such a way to suggest a linkage between ligand binding and acid-alkaline transition. The system is discussed on the basis of two simplifying conditions, i.e., at low and higher pH with respect to the pK of the acid-alkaline transition. At acid pH the reaction corresponds to a single bimolecular process as expected for a simple binding reaction; at alkaline pH, the dependence of relaxation time on ligand concentration implies the existence of a rate-limiting monomolecular step. On the basis of a reaction scheme implying that binding of the ligand can only occur through the acid (aquomet) form of the protein via the displacement of the water molecule, the experimental data are quantitatively accounted for.     

Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry

BackgroundIsothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.Scope of reviewThis article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.Major conclusionsA complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.General significanceMethods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Investigations of photolysis and rebinding kinetics in myoglobin using proximal ligand replacements

We use laser flash photolysis and time-resolved Raman spectroscopy of CO-bound H93G myoglobin (Mb) mutants to study the influence of the proximal ligand on the CO rebinding kinetics. In H93G mutants, where the proximal linkage with the protein is eliminated and the heme can bind exogenous ligands (e.g., imidazole, 4-bromoimidazole, pyridine, or dibromopyridine), we observe significant effects on the CO rebinding kinetics in the 10 ns to 10 ms time window. Resonance Raman spectra of the various H93G Mb complexes are also presented to aid in the interpretation of the kinetic results. For CO-bound H93G(dibromopyridine), we observe a rapid large-amplitude geminate phase with a fundamental CO rebinding rate that is approximately 45 times faster than for wild-type MbCO at 293 K. The absence of an iron proximal ligand vibrational mode in the 10 ns photoproduct Raman spectrum of CO-bound H93G(dibromopyridine) supports the hypothesis that proximal ligation has a significant influence on the kinetics of diatomic ligand binding to the heme.     

Activation kinetics reveal the number of glutamate and glycine binding sites on the N-methyl-D-aspartate receptor.

The activation kinetics of N-methyl-D-aspartate (NMDA) channels in outside-out patches from cultured hippocampal neurons were analyzed to determine the number of glutamate and glycine binding sites per channel. Following rapid steps into high concentrations of glutamate, the activation time course was concentration-independent and limited by transitions between the shut, but fully liganded state and the open state. At lower concentrations, ligand binding was rate-limiting. The resulting sigmoidal activation time course was best fitted by a kinetic model with two glutamate binding sites. Glycine concentration jumps in the continuous presence of glutamate were also best fitted with a two-site model. Agonist and co-agonist binding were better described by an independent, rather than a sequential model. We suggest that the NMDA receptor is at least a tetramer containing four ligand binding subunits, assuming a single binding site per subunit.     

Insulin receptor binding kinetics: modeling and simulation studies

Biological actions of insulin regulate glucose metabolism and other essential physiological functions. Binding of insulin to its cell surface receptor initiates signal transduction pathways that mediate cellular responses. Thus, it is of great interest to understand the mechanisms underlying insulin receptor binding kinetics. Interestingly, negative cooperative interactions are observed at high insulin concentrations while positive cooperativity may be present at low insulin concentrations. Clearly, insulin receptor binding kinetics cannot be simply explained by a classical bimolecular reaction. Mature insulin receptors have a dimeric structure capable of binding two molecules of insulin. The binding affinity of the receptor for the second insulin molecule is significantly lower than for the first bound insulin molecule. In addition, insulin receptor aggregation occurs in response to ligand binding and aggregation may also influence binding kinetics. In this study, we develop a mathematical model for insulin receptor binding kinetics that explicitly represents the divalent nature of the insulin receptor and incorporates receptor aggregation into the kinetic model. Model parameters are based upon published data where available. Computer simulations with our model are capable of reproducing both negative and positive cooperativity at the appropriate insulin concentrations. This model may be a useful tool for helping to understand the mechanisms underlying insulin receptor binding and the coupling of receptor binding to downstream signaling events.