A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.     

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.     

Fractal analysis of binding and dissociation kinetics and interactions of cancer markers on biosensor surfaces

A fractal analysis is presented for the binding and dissociation of different cancer markers on biosensor surfaces. The data analyzed include putrescine in solution to PDDA/APTES/MWCNT/Puo-modified GCE (glassy carbon electrode) (8) and vascular endothelial growth factor (VEGF) in solution to the soluble form of the VEGF receptor (SFlt-1 or VEGF-1) immobilized on a sensor chip (1). Single- and dual-fractal models were used to fit the data. Values of the binding and dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (13). The binding rate coefficients and the affinity values are 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 heterogeneity present on the biosensor chip surface. The analysis presented provides physical insights into these cancer biomarker-receptor reactions occurring on the different biosensor surfaces.     

Analyte-receptor binding and dissociation kinetics for biosensor applications: a fractal analysis

A fractal analysis of confirmative nature only is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. 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. Relationships are presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, Df 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 Df) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient (Martin S.J., Granstaff, V.E., Frye, G.C., Anal. Chem., 65, (1991) 2910). The binding and the dissociation rate coefficient are rather sensitive to the degree of heterogeneity, Df,bind and Df,diss respectively, that exists on the biosensor surface. For example, the order of dependence on Df,bind is 19.2 for the binding rate coefficient, kbind for the binding of 0.03-1.0 microM SH-2Ld in solution to 2C TCR immobilized on a surface plasmon resonance (SPR) biosensor (Corr, M., Salnetz, A.E., Boyd, L.F., Jelonek, M.T., Khilko, S., Al-Ramadi, B.K., Kim, Y.S., Maher, S.E., Bothwell, A.L.M., Margulies, D.H., Science, 265, (1994) 946). The order of dependence on Df,diss is -6.22 for the dissociation rate coefficient, kdiss for the dissociation of 250-1000 nM Sophora japonica agglutinin (SJA)-lactose complex from the SPR surface. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.     

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.     

Binding kinetics of soluble ligands to transmembrane proteins: comparing an optical biosensor and dynamic flow cytometry

BACKGROUND: The kinetics of protein-protein interactions can be monitored with optical biosensors based on the principles of either surface plasmon resonance or mirror resonance. These methods are straightforward for soluble proteins, but not for proteins inserted in the plasma membrane. METHODS: We monitored with an IASys biosensor system, based on a resonant mirror: (1) the binding of cells to an immobilized ligand, (2) the binding of a soluble ligand to immobilized cells, and (3) the binding of a soluble ligand to immobilized plasma membrane vesicles. For comparison, the kinetics of fluorescent antibody binding to intact cells were measured by dynamic flow cytometry. RESULTS: With an optical biosensor, the useful configuration is the one based on immobilized plasma membrane vesicles. However, signals can be detected only for very abundant binding sites (>10(6) per cell). Dynamic flow cytometry allows the accurate determination of the k(on) and k(off) of antibody binding. The sensitivity of the method is two orders of magnitude better than with an optical biosensor. CONCLUSIONS: Although biosensors constitute a method of choice for measuring the interactions between soluble proteins, they are not well suited for measuring the interaction between soluble proteins and membrane-embedded proteins. On the contrary, flow cytometry is well suited for such an application, when it is used in a dynamic mode.     

Real-time analysis of the carbohydrates on cell surfaces using a QCM biosensor: a lectin-based approach

A novel approach to the study of molecular interactions on the surface of mammalian cells using a QCM biosensor was developed. For this study, an epidermoid carcinoma cell line (A-431) and a breast adenocarcinoma cell line (MDA-MB-468) were immobilized onto polystyrene-coated quartz crystals. The binding and dissociation between the lectin Con A and the cells as well as the inhibition of the binding by monosaccharides were monitored in real time and provided an insight into the complex avidic recognition of cell glycoconjugates. The real-time lectin screening of a range of lectins, including Con A, DBA, PNA and UEA-I, enabled the accurate study of the glycosylation changes between cells, such as changes associated with cancer progression and development. Furthermore, the kinetic parameters of the interaction of Con A with MDA-MB-468 cells were studied. This application provides investigators in the field of glycobiology with a novel tool to study cell surface glycosylation and may also have impacts on drug discovery.     

A living cell-based biosensor utilizing G-protein coupled receptors: principles and detection methods

This study explores the feasibility of using a bullfrog fibroblast cell line (FT cells) expressing G protein coupled receptors (GPCRs) as the basis for a living cell-based biosensor. We have fabricated gold microelectrode arrays on a silicon dioxide substrate that supports long term, robust growth of the cells at room temperature and under ambient atmospheric conditions. Activation of an endogenous GPCR to ATP was monitored with an optical method that detects rises in intracellular calcium and with an electrochemical method that monitors the increased secretion of pre-loaded norepinephrine on a MEMS device. FT cells were also transfected to express reporter genes driven by several different promoters, raising the possibility that they could be modified genetically to express novel GPCRs as well. The ability to harness GPCRs for BioMEMS applications by using cells that are easy to grow on MEMS devices and to modify genetically opens the way for a new generation of devices based on these naturally selective and highly sensitive chemoreceptors.     

The effects of sloped surfaces on locomotion: an electromyographic analysis

Investigations using quadrupeds have suggested that the motor programs used for slope walking differ from that used for level walking. This idea has not yet been explored in humans. The aim of this study was to use electromyographic (EMG) signals obtained during level and slope walking to complement previously published joint angle and joint moment data in elucidating such control strategies. Nine healthy volunteers walked on an instrumented ramp at each of five grades (-39%, -15%, 0%, +15%, +39%). EMG activity was recorded unilaterally from eight lower limb muscles (gluteus maximus (GM), rectus femoris (RF), vastus medialis (VM), biceps femoris (BF), semimembranosus (SM), soleus (Sol), medial gastrocnemius (MG), and tibialis anterior (TA)). The burst onset, duration, and mean activity were calculated for each burst in every trial. The burst characteristics were then averaged within each grade and subject and submitted to repeated measures ANOVAs to assess the effect of grade (alpha=0.05, a priori). Power production increased during upslope walking, as did the mean activity and burst durations of most muscles. In this case, the changes in muscle activity patterns were not predictable based on the changes in joint moments because of the activation of biarticular muscles as antagonists. During downslope walking power absorption increased, as did knee extensor activity (mean and duration) and the duration of the ankle plantarflexor activity. The changes in muscle activity during this task were directly related to the changes in joint moments. Collectively these data suggest that the nervous system uses different control strategies to successfully locomote on slopes, and that joint power requirements are an important factor in determining these control strategies.     

In situ phosphorylation of immobilized receptors on biosensor surfaces: application to E-cadherin/beta-catenin interactions

Phosphorylation is a key posttranslational modification for modulating biological interactions. Biosensor technology is ideally suited for examining in real time the role of phosphorylation on protein-protein interactions in signaling pathways. We have developed processes for on-chip phosphorylation of immobilized receptors on biosensor surfaces. These processes have been used to analyze E-cadherin/beta-catenin interactions. Phosphorylation of the intracellular domain (ICD) of E-cadherin modulates its affinity to beta-catenin and consequently the strength of cell-cell adhesion. We have phosphorylated immobilized E-cadherin ICD in situ using casein kinase 1 (CK1), casein kinase 2 (CK2), and src. On-chip phosphorylation of E-cadherin was confirmed using anti-phosphoserine and anti-phosphotyrosine antibodies. The binding of beta-catenin to E-cadherin was analyzed quantitatively. CK1 phosphorylation of E-cadherin increased the binding affinity to beta-catenin from approximately 230 to 4 nM. A similar increase in affinity, from 260 to 4 nM, was obtained with CK2 phosphorylation of E-cadherin. However, phosphorylation by src kinase decreased the affinity constant from approximately 260 nM to 4 microM. Interestingly, phosphorylation of E-cadherin by CK1 or CK2 prevented the inhibition of beta-catenin binding by src phosphorylation.     

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.     

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.     

Binding kinetics and multi-bond: Finding correlations by synthesizing interactions between ligand-coated bionanoparticles and receptor surfaces

The number of bonds formed between one single bionanoparticle and many surface receptors is an important subject to be studied but is seldom quantitatively investigated. A new evaluation of the correlation between binding kinetics and number of bonds is presented by varying ligand density and receptor density. An experimental system was developed using measurements with surface plasmon resonance spectroscopy. A corresponding multi-site adsorption model elucidated the correlation. The results show that with the increase of the receptor density, the adsorption rate first decreased when the number of bonds was below a maximum value and then increased when the number of bonds stayed at this maximum value. The investigation on ligand density variation suggests that the coating density on top of the bionanoparticle surface may have a particular value below which more ligand will accelerate the adsorption rate. The ratio of ligand amount bound by the receptors to the total ligand amount associated with a single bionanoparticle will remain constant even if one attaches more ligands to a bionanoparticle. We envision that the bionanoparticle desorption will not depend on density changes from either ligand or receptor when the number of bonds reaches a specific efficient value.     

Binding kinetics and footprinting of TaqI endonuclease: effects of metal cofactors on sequence-specific interactions.

Restriction endonucleases achieve sequence-specific recognition and strand cleavage through the interplay of base, phosphate backbone, and metal cofactor interactions. In this study, we investigate the binding kinetics of TaqI endonuclease using the wild-type enzyme and a binding proficient, catalysis deficient mutant TaqI-D137A both in the absence of a metal cofactor and in the presence of Mg2+ or Ca2+. As demonstrated by gel mobility shift analyses, TaqI endonuclease requires a metal cofactor for achieving high-affinity specific binding to its cognate sequence, TCGA. In the absence of a metal cofactor, the enzyme binds all DNA sequences (TaqI cognate site, star site, and nonspecific site) with essentially equal affinity, thereby exhibiting little discrimination. The dissociation constant of the cognate sequence in the presence of Mg2+ at 60 degrees C is 0. 26 nM, a value comparable to our previously reported Km of 0.5 nM measured under steady-state conditions. The TaqI-TCGA-Mg2+ complex is stable, with a half-life of 21 min at 60 degrees C. The boundary of the protein-DNA interface is approximated to be about 18 bp as determined by DNase I footprinting. Data from this study support the notion that a metal cofactor plays a critical role for achieving sequence-specific discrimination in a subset of nucleases, including TaqI, EcoRV, and others.     

Solubilization, stabilization, and purification of chemokine receptors using biosensor technology

Establishing solubilization conditions for membrane-associated receptors is often a tedious empirical process. Here we describe a novel application of SPR biosensor technology to screen solubilization conditions automatically and to assess receptor activity directly. We focus on two chemokine receptors, CXCR4 and CCR5, which are important in HIV cell invasion. The autosampler in Biacore 3000 permitted whole cells expressing C-terminally tagged receptors to be automatically lysed under a given solubilization condition and the lysates to be injected over an antibody surface. The total amount of solubilized receptor could be quantitated from the antibody capture level, whereas the amount of active receptor could be quantitated using a subsequent injection of conformationally sensitive antibody or protein. Using this approach, we identified detergent/lipid/buffer combinations that enhanced and maintained receptor activity. We also used the biosensor to demonstrate CD4-dependent binding of gp120 to solubilized CCR5 and to develop affinity chromatography-based purification methods that increased receptor activity more than 300%. Together, these results illustrate the benefits of using the biosensor as a tool for isolating functional membrane receptors and for analyzing ligand/receptor interactions.     

Effects of receptor clustering on ligand dissociation kinetics: theory and simulations

Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans (HSPGs), co-receptors for FGF-2. In this article, we develop a continuum stochastic formalism to address how receptor clustering might influence ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows nonmonotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with FGF-2-HSPG experimental results is made and suggests that the theory could be used to analyze similar biological systems. We further present an analysis of an additional cooperative internal-diffusion model that might be used by other systems to increase ligand retention when simple rebinding is insufficient.     

Kinetic analysis of enzymatic hydrolysis of crystalline cellulose by cellobiohydrolase using an amperometric biosensor

An amperometric biosensor for the detection of cellobiose has been introduced to study the kinetics of enzymatic hydrolysis of crystalline cellulose by cellobiohydrolase. By use of a sensor in which pyrroloquinoline quinone-dependent glucose dehydrogenase was immobilized on the surface of electrode, direct and continuous observation of the hydrolysis can be achieved even in a thick cellulose suspension. The steady-state rate of the hydrolysis increased with increasing concentrations of the enzyme to approach a saturation value and was proportional to the amount of the substrate. The experimental results can be explained well by the rate equations derived from a three-step mechanism consisting of the adsorption of the free enzyme onto the surface of the substrate, the reaction of the adsorbed enzyme with the substrate, and the liberation of the product. The catalytic constant of the adsorbed enzyme was determined to be 0.044+/-0.011s(-1).     

Rat brain TRH receptors: kinetics, pharmacology, distribution and ionic effects

Optimal conditions for measuring receptor binding for thyrotropin-releasing hormone (TRH) in the rat central nervous system (CNS) have been determined using 3H-labelled [3-Me-His2]TRH [( 3H]MeTRH). Binding assays conducted at 0 degree C for 5-6 h using sodium phosphate- and/or Hepes-buffered tissue resuspensions, with subsequent filtration through Whatman GF/B filters, yielded the best results. Association and dissociation of [3H]MeTRH binding to amygdala membranes were time and temperature dependent. Dissociation kinetics appeared biphasic. Progressive reduction in receptor affinity and capacity and increased radioligand breakdown were observed at elevated temperatures. Bacitracin (25-1000 microM) prevented peptide degradation but inhibited receptor binding (8-37%). Detailed competition experiments using MeTRH and other drugs yielded a pharmacological profile similar to that observed previously in other tissues indicating TRH receptor identification. Highest density of TRH receptors was observed in the retina and numerous limbic areas. Monovalent and divalent cations modulated [3H]MeTRH binding by reducing apparent receptor number.     

Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies

We describe a procedure for performing quantitative analyses of fields f(r) on molecular surfaces, including statistical quantities and locating and evaluating their local extrema. Our approach avoids the need for explicit mathematical representation of the surface and can be implemented easily in existing graphical software, as it is based on the very popular representation of a surface as collection of polygons. We discuss applications involving the volumes, surface areas and molecular surface electrostatic potentials, and local ionization energies of a group of 11 molecules.