New multi-step kinetics using common affinity biosensors saves time and sample at full access to kinetics and concentration

Today, affinity-based biosensorics is a standard technology in quantitative biomolecular interaction analysis, but suffers from low sample throughput and sometimes from inaccessible kinetics. A new methodology for such biosensors is introduced here that cuts down measurement time dramatically and increases confidentiality of results. In contrast to traditional applications, the ligand immobilized on the sensor chip is exposed to the binding analyte at a rapid stepwise change of the analyte concentration without the need for regenerations between analyte additions. In the application presented here, each addition of the analyte is succeeded by a buffer flow, yielding alternating association and dissociation phases in a "zigzag" style. This binding curve pattern is analyzed by means of novel fitting algorithms, which render detailed kinetics rate constants at a high level of self-consistency, and hence, validity due to multiple cross-checks. In comparison with traditional sequential kinetics analysis, this new multi-step kinetics approach returns practically identical (or improved) kinetics constants--at valuable savings in time/material since regeneration steps, ligand re-captures, or titration equilibrations are unnecessary.     

Surface plasmon resonance for probing quadruplex folding and interactions with proteins and small molecules

Surface plasmon resonance is a technique for detecting binding events at the surface of a thin metal film. Through the commercial availability of instrumentation and sensor chips, the technique has found widespread application for determining the affinity and kinetics of macromolecular interactions. A variety of quadruplex forming oligonucleotides have been immobilized to sensor chips to permit analysis of their binding interactions with both small molecule and protein analytes. The fold of the quadruplex must be maintained through an appropriate choice of buffer, and care must be taken to ensure that data interpretation is not hampered by non-specific binding and adsorption of the analyte to the sensor surface and instrument. Affinity constants determined by surface plasmon resonance for interactions with quadruplexes correlate meaningfully with other methods, such as UV-visible and fluorescence titrations, enzyme linked immunosorbent assay, thermal melting studies and telomerase inhibition. Kinetic measurements of the association and dissociation of duplexes of quadruplex forming oligonucleotides and their complementary strands have enabled calculation of the folding and unfolding rates of the quadruplex itself, and determination of its stability as a function of buffer composition.     

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.     

Determination of interaction kinetic constants for HIV-1 protease inhibitors using optical biosensor technology

The interaction between HIV-1 protease and inhibitors has been studied with optical biosensor technology. Optimized experimental procedures and mathematical analysis permitted determination of association and dissociation rate constants. A sensor surface with native enzyme was unstable and exhibited a drift that was influenced by the binding of inhibitor. This was hypothesized to be due to a specific mechanism involving autoproteolysis and/or dimer dissociation. The use of a mutant predicted to be less susceptible to autoproteolysis (Q7K) than wild-type enzyme resulted in a minor effect on surface stability, while a completely stable surface was obtained by treatment of the immobilized enzyme with N-ethyl-N'-(dimethylaminopropyl)-carbodiimide and N-hydroxysuccinimide; the most stable surface was achieved by chemically modifying the Q7K enzyme. The stabilized surface was enzymatically active and the interaction with inhibitors was similar to that for native enzyme. Several of the inhibitors had very high association rates, and estimation of kinetic constants was therefore performed with a binding equation accounting for limited mass transport. Of the clinical inhibitors studied, saquinavir had the highest affinity for the enzyme, a result of the lowest dissociation rate. Although the dissociation rate for ritonavir was sixfold faster, the affinity was only twofold lower than that for saquinavir since the association rate was threefold faster. Nelfinavir and indinavir exhibited lower affinities relative to the other inhibitors, a consequence of a slower association for nelfinavir and a relatively fast dissociation for indinavir. These results show that biosensor-based interaction studies can resolve affinity into association and dissociation rates, and that these are characteristic parameters for the interaction between enzymes and inhibitors.     

Compensation for loss of ligand activity in surface plasmon resonance experiments

The determination of equilibrium binding constants is an important aspect of the analysis of protein-protein interactions. In recent years surface plasmon resonance experiments (e.g., with a BIAcore instrument) have provided a valuable experimental approach to determining such constants. The standard method is based on measuring amounts of analyte bound at equilibrium for different analyte concentrations. During the course of a typical surface plasmon resonance experiment the measured equilibrium levels for a given analyte concentration often decrease. This appears to be due to a loss of activity of the protein coupled to the sensor chip or other phenomena. The loss in signal can lead to an erroneous determination of the equilibrium constant. A data analysis approach is introduced that aims to compensate for the loss of activity so that its influence on the results of the experiments is reduced.     

Kinetic analysis of the mass transport limited interaction between the tyrosine kinase lck SH2 domain and a phosphorylated peptide studied by a new cuvette-based surface plasmon resonance instrument

We explored the use of a newly developed cuvette-based surface plasmon resonance (SPR) instrument (IBIS) to study peptide-protein interactions. We studied the interaction between the SH2 domain of lck and a phosphotyrosine peptide EPQY*EEIPIYL which was immobilized on a sensor chip. No indications for mass transport limitation (MTL) were observed when standard kinetic approaches were used. However, addition of competing peptide during dissociation revealed a high extent of rebinding. A dissociation rate constant (k(d)) of 0.6+/-0.1 s(-1) was obtained in the presence of large amounts of peptide. A simple bimolecular binding model, applying second-order kinetics for the cuvette system, could not adequately describe the data. Fits were improved upon including a step in the model which describes diffusion of the SH2 domain from the bulk to the sensor, especially for a surface with high binding capacity. From experiments in glycerol-containing buffers, it appeared that the diffusion rate decreased with higher viscosity. It is demonstrated that MTL during association and dissociation can be described by the same diffusion rate. A binding constant (K(D)) of 5.9+/-0.8 nM was obtained from the SPR equilibrium signals by fitting to a Langmuir binding isotherm, with correction for loss of free analyte due to binding. An association rate constant k(a) of 1.1(+/-0.2)x10(8) M(-1) x s(-1) was obtained from k(d)/K(D). The values for k(a) and k(d) obtained in this way were 2-3 orders larger than that from standard kinetic analysis, ignoring MTL. We conclude that in a cuvette the extent of MTL is comparable to that in a flow system.     

Influence of various fluorescent and non-fluorescent labels on the kinetics of the complex formation of alpha-chymotrypsin with basic pancreatic trypsin inhibitor (Kunitz).

The association of alpha-chymotrypsin with basic pancreatic trypsin inhibitor was studied using extrinsic signals produced by fluorescent and nonfluorescent labels. The reactive dyes were covalently bound to the proteins in the complexed state, in which the binding region was protected. The signals were sufficiently large to measure the complex formation at protein concentrations of 10(-9)M by fluorescence and down to 10(-6)M by absorption. Therefore, the association and dissociation could be followed over a broad range of concentration. Good correspondence was observed between data which were obtained with different labels and with published values for the unlabeled proteins. Existing differences could be explained by different buffer conditions used by the different authors. Also the pH dependence of the dissociation rate constants was essentially unaltered by the introduction of the labels. The large signals allowed a direct measurement of the equilibrium constants of dissociation, even at high pH, at which they are in the range of 10(-8)M. The experimentally determined binding constants were in agreement with those calculated from the rate constants. The temperature dependence of the binding constants revealed a small positive and pH-dependent enthalpy change [deltaHo = 4.0 kcal/mol (16.7 kJ) at H 7.0[. The results prove that the labeling can be performed in such a way that the equilibrium and kinetic parameters of the system studied are not significantly influenced.     

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.     

A kinetic study of analyte-receptor binding and dissociation, and dissociation alone, for biosensor applications: a fractal analysis

A fractal analysis is presented for (a) analyte-receptor binding and dissociation kinetics and (b) dissociation kinetics alone for biosensor applications. Emphasis is placed on dissociation kinetics. Data taken from the literature may be modeled, in the case of binding, using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the dissociation rate coefficient(s) as a function of the analyte concentration are of particular value since they provide a means by which the dissociation rate coefficients may be manipulated. Relationships are also presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient.     

The binding of guanine-guanine mismatched DNA to naphthyridine dimer immobilized sensor surfaces: kinetic aspects

Naphthyridine dimer composed of two naphthyridine chromophores and a linker connecting them strongly, and selectively, binds to the guanine-guanine mismatch in duplex DNA. The kinetics for the binding of the G-G mismatch to the naphthyridine dimer was investigated by surface plasmon resonance assay. The sensor surface was prepared by immobilizing naphthyridine dimer through a long poly(ethylene oxide) linker with the ligand density of 9.1 x 10(-12) fmolnm(-2). The kinetic analyses revealed that the binding of the G-G mismatch was sequence dependent on the flanking base pairs, and the G-G mismatches flanking at least one G-C base pair bound to the surface via a two-step process with a 1:1 DNA-ligand stoichiometry. The first association rate constant for the binding of the G-G mismatch in the 5'-CGG-3'/3'-GGC-5' sequence to the naphthyridine dimer-immobilized sensor surface was 3.2 x 10(3)M(-1)s(-1) and the first dissociation rate constant was 1.4 x 10(-2)s(-1). The association and dissociation rate constants for the second step were insensitive to the flanking sequences, and were almost of the same order of magnitude as the first dissociation rate constant. This indicates that the second step had only a small energetic contribution to the binding. The association constant calculated from kinetic parameters was 2.7 x 10(5)M(-1), which is significantly smaller than the apparent association constants obtained from experiments in solution. Electrospray ionization time-of-flight (ESI-TOF) mass spectrometry on the complex produced from the G-G mismatch and naphthyridine dimer showed the formation of the 1:1 complex and a 1:2 DNA-ligand complex in solution. The latter complex became the dominant complex when a six-fold excess of naphthyridine dimer was added to DNA.     

The influence of signal noise on the accuracy of kinetic constants measured by surface plasmon resonance experiments.

An analysis is carried out to investigate the accuracy of kinetic parameters obtained using surface plasmon resonance methodology with a BIAcore instrument. The Cramer Rao lower bound for the least possible variance of an estimator of the kinetic parameters is determined. Using simulations it is shown that the standard least-squares estimation technique provides estimates that achieve this bound. The theoretical and simulation results are compared with experimental data obtained from an analysis of the interaction of the myc peptide with the anti-myc antibody, 9E10. This investigation indicates that the accuracy of the results depends on the signal level which has particular relevance to the design of experiments with low signal levels. It is shown how the accuracy of the estimates of the kinetic constants depends on the kinetic constants themselves and how the accuracy of the association constants depends on the concentration of the analyte that is used in the experiment. In addition, the effects of increasing the number of data points in the analysis of dissociation data on the accuracy of the estimates are quantitated. It is also demonstrated that signal averaging of data derived from repeat sensorgrams can result in a significant decrease in the standard deviation of the estimates.     

Bayesian Estimation of the Active Concentration and Affinity Constants Using Surface Plasmon Resonance Technology

Surface plasmon resonance (SPR) has previously been employed to measure the active concentration of analyte in addition to the kinetic rate constants in molecular binding reactions. Those approaches, however, have a few restrictions. In this work, a Bayesian approach is developed to determine both active concentration and affinity constants using SPR technology. With the appropriate prior probabilities on the parameters and a derived likelihood function, a Markov Chain Monte Carlo (MCMC) algorithm is applied to compute the posterior probability densities of both the active concentration and kinetic rate constants based on the collected SPR data. Compared with previous approaches, ours exploits information from the duration of the process in its entirety, including both association and dissociation phases, under partial mass transport conditions; do not depend on calibration data; multiple injections of analyte at varying flow rates are not necessary. Finally the method is validated by analyzing both simulated and experimental datasets. A software package implementing our approach is developed with a user-friendly interface and made freely available.     

Kinetic analysis of the binding of monomeric and dimeric ephrins to Eph receptors: correlation to function in a growth cone collapse assay

Eph receptors and ephrins play important roles in regulating cell migration and positioning during both normal and oncogenic tissue development. Using a surface plasma resonance (SPR) biosensor, we examined the binding kinetics of representative monomeric and dimeric ephrins to their corresponding Eph receptors and correlated the apparent binding affinity with their functional activity in a neuronal growth cone collapse assay. Our results indicate that the Eph receptor binding of dimeric ephrins, formed through fusion with disulfide-linked Fc fragments, is best described using a bivalent analyte model as a two-step process involving an initial monovalent 2:1 binding followed by a second bivalent 2:2 binding. The bivalent binding dramatically decreases the apparent dissociation rate constants with little effect on the initial association rate constants, resulting in a 30- to 6000-fold decrease in apparent equilibrium dissociation constants for the binding of dimeric ephrins to Eph receptors relative to their monomeric counterparts. Interestingly, the change was more prominent in the A-class ephrin/Eph interactions than in the B-class of ephrins to Eph receptors. The increase in apparent binding affinities correlated well with increased activation of Eph receptors and the resulting growth cone collapse. Our kinetic analysis and correlation of binding affinity with function helped us better understand the interactions between ephrins and Eph receptors and should be useful in the design of inhibitors that interfere with the interactions.     

Complete disulfide bond assignment of a recombinant immunoglobulin G4 monoclonal antibody

Surface plasmon resonance biosensor analysis was used to evaluate the thermodynamics and binding kinetics of naturally occurring and synthetic cobalamins interacting with vitamin B(12) binding proteins. Cyanocobalamin-b-(5-aminopentylamide) was immobilized on a biosensor chip surface to determine the affinity of different cobalamins for transcobalamin, intrinsic factor, and nonintrinsic factor. A solution competition binding assay, in which a surface immobilized cobalamin analog competes with analyte cobalamin for B(12) protein binding, shows that only recombinant human transcobalamin is sensitive to modification of the corrin ring b-propionamide of cyanocobalamin. A direct binding assay, where recombinant human transcobalamin is conjugated to a biosensor chip, allows kinetic analysis of cobalamin binding. Response data for cyanocobalamin binding to the transcobalamin protein surface were globally fitted to a bimolecular interaction model that includes a term for mass transport. This model yields association and dissociation rate constants of k(a) = 3 x 10(7) M(-1) s(-1) and k(d) = 6 x 10(-4) s(-1), respectively, with an overall dissociation constant of K(D) = 20 pM at 30 degrees C. Transcobalamin binds cyanocobalamin-b-(5-aminopentylamide) with association and dissociation rates that are twofold slower and threefold faster, respectively, than transcobalamin binding to cyanocobalamin. The affinities determined for protein-ligand interaction, using the solution competition and direct binding assays, are comparable, demonstrating that surface plasmon resonance provides a versatile way to study the molecular recognition properties of vitamin B(12) binding proteins.     

Kinetics of the reaction between testosterone and antitestosterone antiserum

In order to characterize from a kinetic viewpoint the antibody population mainly involved in the binding of testosterone by its homologous antiserum, the kinetics of the association reaction between [1,2,6,7-3H]-testosterone and rabbit antiserum anti-testosterone-3-(O-carboxymethyl)oxime-bovine serum albumin (Ab R2603-1) was followed at pH 7.4 and at constant ionic strength, at temperatures ranging from 2 degrees C to 37 degrees C and at concentration near to work conditions for testosterone radioimmunoassay; dextran coated charcoal suspension was used for the bound/free separation. In the examined concentration range, the observed kinetics trends can be explained by assuming the existence of two classes of antibody binding sites, Ab1 and Ab2. The kinetics of the dissociation reaction of the testosterone-antibody complex was also followed after the addition of a large excess of unlabeled testosterone. At 22.0 degrees C, association and dissociation rate constants are 2.1.10(7) s-1M-1 and 3.7.10(-3) s-1, respectively, for the Ab1 class of antibody binding sites, and 3.6.10(6) s-1M-1 and 7.0.10(-4) s-1 for the Ab2 class. Equilibrium constants obtained from kinetic data were very similar for both classes of antibody binding sites and in good agreement with the equilibrium values obtained from linear Scatchard plot. The order of magnitude of the second order rate constants and the high activation enthalpy for the forward and reverse reaction suggest a mechanism more complex than a simple second order.     

Fractal Binding and Dissociation Kinetics of Heart-Related Compounds on Biosensor Surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (), and TRITC-labeled HDL in solution to a bare optical fiber surface (). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.     

Kinetic analysis of binding between Shiga toxin and receptor glycolipid Gb3Cer by surface plasmon resonance

Shiga toxin (Stx) binds to the receptor glycolipid Gb3Cer on the cell surface and is responsible for hemolytic uremic syndrome. Stx has two isoforms, Stx1 and Stx2, and in clinical settings Stx2 is known to cause more severe symptoms, although the differences between the mechanisms of action of Stx1 and Stx2 are as yet unknown. In this study, the binding modes of these two isoforms to the receptor were investigated with a surface plasmon resonance analyzer to compare differences by real time receptor binding analysis. A sensor chip having a lipophilically modified dextran matrix or quasicrystalline hydrophobic layer was used to immobilize an amphipathic lipid layer that mimics the plasma membrane surface. Dose responsiveness was observed with both isoforms when either the toxin concentration or the Gb3Cer concentration was increased. In addition, this assay was shown to be specific, because neither Stx1 nor Stx2 bound to GM3, but both bound weakly to Gb4Cer. It was also shown that a number of fitting models can be used to analyze the sensorgrams obtained with different concentrations of the toxins, and the "bivalent analyte" model was found to best fit the interaction between Stxs and Gb3Cer. This shows that the interaction between Stxs and Gb3Cer in the lipid bilayer has a multivalent effect. The presence of cholesterol in the lipid bilayer significantly enhanced the binding of Stxs to Gb3Cer, although kinetics were unaffected. The association and dissociation rate constants of Stx1 were larger than those of Stx2: Stx2 binds to the receptor more slowly than Stx1 but, once bound, is difficult to dissociate. The data described herein clearly demonstrate differences between the binding properties of Stx1 and Stx2 and may facilitate understanding of the differences in clinical manifestations caused by these toxins.     

Equilibrium and kinetic studies of oxygen binding to the haemocyanin from the freshwater snail Lymnaea stagnalis.

The binding of oxygen by the haemocyanin of the gastropod Lymnaea stagnalis was studied by equilibrium and kinetic methods. The studies were performed under conditions in which the haemocyanin molecule was in the native state. Over the pH range 6.8-7.6, in the presence of 10mM-CaCl2 the haemocyanin bound O2 cooperatively. Over this pH range the haemocyanin molecule displayed a normal Bohr effect whereby the O2 affinity of the molecule decreased with a fall in the pH of the solution. The maximum slope of the Hill plot (hmax.) was 3.5, obtained at pH 7.5. An increase in the CaCl2 concentration from 5 to 20 mM at pH 6.8 resulted in a slight increase in the oxygen affinity, with hmax. remaining virtually unchanged. At constant pH and CaCl2 concentration, an increase in NaCl concentration from 0 to 50 mM resulted in a small decrease in O2 affinity, but a significant increase in the value of hmax. from 3.5 to 8.6. Temperature-jump relaxation experiments over a range of O2 concentrations produced single relaxation times. The dependence of the relaxation time on the reactant concentrations indicated a simple bimolecular binding process. The calculated association and dissociation rate constants for this process at pH 7.5 are 29.5 X 10(6) M-1 X S-1 and 49 S-1 respectively. The association rate constant kon was found to be essentially independent of pH and CaCl2 concentration. The dissociation rate constant, koff, however, increased with a decrease in the pH, but was also independent of CaCl2 concentration. These results indicate that the stability of the haemocyanin-O2 complex is determined by the dissociation rate constant.     

Determination of the equilibrium association constant between Tet repressor and tetracycline at limiting Mg2+ concentrations: a generally applicable method for effector-dependent high-affinity complexes.

An analytical method for determining very high binding constants at equilibrium for reactions requiring an effector is proposed and applied to study the interaction of tetracycline with the repressor of the tetracycline resistance gene from Tn10. In this method complex formation is limited by low concentrations of the effector, which is Mg2+ for the interaction of tetracycline and Tet repressor. The binding of Mg2+ to tetracycline and subsequent formation of the ternary repressor-Mg(2+)-tetracycline complex are coupled reactions yielding a dependence of repressor-tetracycline-Mg2+ complex formation on the concentration of free Mg2+. The binding constants can be determined from the quantitative analysis of ternary complex formation with increasing Mg2+ concentrations. This method allows the determination of very high association constants at equilibrium in a large range of protein concentrations. In the case of repressor and tetracycline, the same affinity constant of 3 +/- 2 x 10(9) M-1 was found in the range of 0.1 to 5 microM of repressor. This result indicates that no association or dissociation of the repressor subunits occurs upon binding of tetracycline. Furthermore, the results show that a repressor dimer binds two effector molecules without significant cooperativity.     

Fractal binding and dissociation kinetics of heart-related compounds on biosensor surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (1), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (2), and TRITC-labeled HDL in solution to a bare optical fiber surface (3). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (4). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.