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.     

A kinetic study of analyte-receptor binding and dissociation for biosensor applications: a fractal analysis for two different DNA systems

A fractal analysis of DNA binding and dissociation kinetics on biosensor surfaces is presented. The fractal approach provides an attractive, convenient method to model the kinetic data taking into account the effects of surface heterogeneity brought about by ligand immobilization. The fractal technique can be used in conjunction or as an alternate approach to conventional modeling techniques, such as the Langmuir model, saturation model, etc. Examples analyzed include a DNA molecular beacon biosensor and a plasmid DNA-(cationic polymer) interaction biosensor. The molecular beacon example provides some insights into the nature of the surface and how it influences the binding rate coefficients. The DNA-cationic polymer interaction example provides some quantitative results on the binding and dissociation rate coefficients. 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 results indicate 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 example presented. Relationships are presented for the binding rate coefficients as a function of their corresponding fractal dimension, D(f), which is an indication of the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity of the surface (increase in D(f)) leads to an increase in the binding rate coefficient.     

A single- and a dual-fractal analysis of antigen-antibody binding kinetics for different biosensor applications.

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modelled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot, 1993 (Scientific Graphing Software: User's Manual. Jandel Scientific, San Rafael, CA) was utilized to determine if a single-fractal analysis is sufficient, or a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the antigen-antibody systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the antigen-antibody binding systems indicate a high sensitivity of the binding rate coefficient on the fractal dimension when both a single -as well as a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-1(15-21) x BSA (bovine serum albumin) immobilised on a surface plasmon resonance surface, the order of dependence of the binding rate coefficient, k on the fractal dimension, Df is 7.0945. Similarly, for a dual-fractal analysis and for the binding of parasite L. donovani diluted pooled sera in solution to fluorescein isothiocyanate-labeled anti-human immunoglobulin IgG immobilized on an optical fibre, the order of dependence of k1 and k2 on Df1 and Df2 were 6.8018 and -4.393, respectively. Binding rate coefficient expressions are also developed as a function of the analyte (antigen or antibody) concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface, and emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.     

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.     

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.     

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.     

Analyte-receptor binding on surface plasmon resonance biosensors: a fractal analysis of Cre-loxP interactions and the influence of Cl, O, and S on drug-liposome interactions

A fractal analysis of the association and dissociation (whereever applicable) of Cre-loxP interactions and drug-liposome interactions on a sensor chip surface is presented. In both of these cases a dual-fractal analysis is required to adequately describe the association kinetics. The dissociation kinetics for Cre-loxP interactions is adequately described by a single-fractal analysis. The dual-fractal analysis used to describe the association kinetics of Cre-loxP interactions is consistent with the original two-step mechanism presented using a surface plasmon resonance biosensor. Our analysis includes both diffusion and surface effects by introducing the fractal dimension which makes quantitative the degree of heterogeneity on the sensor chip surface. Affinities are provided. Only the association kinetics were analysed for drug-liposome interactions since the initial sections of the dissociation curves were too steep to obtain reasonable drug-liposome complex concentration values on the sensor chip with time. Attempts made to relate the association rate coefficients with the molecular weight of the drug were unsuccessful. On using desipramine and imipramine as "arbitrarily selected standards" or "references" (only C, H, and N atoms present), it was noticed from the data analysed that the inclusion of the O and S atoms in the drug leads to a decrease in the association rate coefficients, ka1 (or k1) and ka2 (or k2) (compared with the arbitrarily selected standards or references). Similarly, the addition of the Cl atom in the drug leads to an increase in the association rate coefficient (compared with the arbitrarily selected standards or references). More data needs to be analysed to determine whether this is true for other drugs also.     

A fractal analysis of protein to DNA binding kinetics using biosensors

A fractal analysis of a confirmative nature only is presented for the binding of estrogen receptor (ER) in solution to its corresponding DNA (estrogen response element, ERE) immobilized on a sensor chip surface [J. Biol. Chem. 272 (1997) 11384], and for the cooperative binding of human 1,25-dihydroxyvitamin D(3) receptor (VDR) to DNA with the 9-cis-retinoic acid receptor (RXR) [Biochemistry 35 (1996) 3309]. Ligands were also used to modulate the first reaction. Data taken from the literature may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of either the analyte concentration in solution or the fractal dimension that exists on the biosensor surface. The binding rate expressions developed exhibit a wide range of dependence on the degree of heterogeneity that exists on the surface, ranging from sensitive (order of dependence equal to 1.202) to very sensitive (order of dependence equal to 12.239). In general, the binding rate coefficient increases as the degree of heterogeneity or the fractal dimension of the surface increases. The predictive relationships presented provide further physical insights into the reactions occurring on the biosensor surface. Even though these reactions are occurring on the biosensor surface, the relationships presented should assist in understanding and in possibly manipulating the reactions occurring on cellular surfaces.     

Use of a biosensor to determine the binding kinetics of five lectins for Galactosyl-N-acetylgalactosamine

The dietary lectins, edible mushroom (ABL) and Jacalin (JAC) inhibit the proliferation of colonic cancer cells, whereas Amaranth (ACL) and peanut (PNA) stimulate their proliferation. All these lectins share as their preferred ligand the Thomsen-Friedenreich (TF) antigen galactosyl 1,3 N-Acetylgalactosamine (Gal1,3GalNAc), but differ in their finer specificities for modifications of this determinant and in their specificities for cancerous epithelia. We have investigated, using a resonant mirror biosensor, the kinetics of binding of these lectins, and Maclura pomifera lectin (MPL), which is similar to JAC, to two different Gal-GalNac bearing glycoproteins, antarctic fish antifreeze glycoprotein (AFG) and asialofetuin. JAC had the highest affinity for AFG [K _d 0.027 M] due to a fast association rate constant [k _ass 610,000 (Ms)^–1]. The other lectins had considerably lower affinities, with K _d ranging from 0.16 M (ABL) to 5.7 M (PNA), largely due to slower k _ass [ABL 74,000 (Ms)^–1 to PNA 2700 (Ms)^–1]. Similarly, JAC had a much higher affinity for asialofetuin [K _d 0.083 M] than the other lectins [K _d 1.0 M–4.5 M]. Affinities were also calculated from the extent of binding at equlibrium and were generally similar to those calculated from the kinetic parameters indicating the true nature of these values.     

Binding and dissociation kinetics using fractals: an analysis of electrostatic effects and randomly coupled and oriented coupled receptors on biosensor surfaces

A fractal analysis is used to analyze the influence of: (a) electrostatic interactions on binding and dissociation rate coefficients for antibodies HH8, HH10, and HH26 in solution to hen egg-white lysozyme (HEL) immobilized on a sensor chip surface [Biophys. J. 83 (2002) 2946]; and (b) the binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip surface [Methods 20 (2000) 310]. Single- and dual-fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s) and the fractal dimensions were obtained from a regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited, Ottawa, Canada. 1997). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. It is of interest to compare the results obtained by the fractal analysis with that of the original analysis [Biophys. J. 83 (2002) 2946]. For example, as one goes from the binding of 21 nM HH10/HEL to the binding of 640 nM HH10/HEL(K97A), Sinha et al. [Biophys. J. 83 (2002) 29461 indicate that the enhancement of diffusional encounter rates may be due to 'electrostatic steering' (a long-range interaction). Our analysis indicates that there is an increase in the value of the fractal dimension, Df1 by a factor of 1.12 from a value of 2.133-2.385. This increase in the degree of heterogeneity on the surface leads to an increase in the binding rate coefficient, k1 by a factor of 1.59 from 12.92 to 20.57. The fractal analysis of binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip [Methods 20 (2000) 310] surface are consistent with the degree of heterogeneity present on the sensor chip surface for the random and the oriented case. As expected, the random case will exhibit a higher degree of heterogeneity than the oriented case, leading to subsequently a higher binding rate coefficient.     

Quantitative measurement of binding kinetics in sandwich assay using a fluorescence detection fiber-optic biosensor

Fiber-optic biosensors have been studied intensively because they are very useful and important tools for monitoring biomolecular interactions. Here we describe a fluorescence detection fiber-optic biosensor (FD-FOB) using a sandwich assay to detect antibody-antigen interaction. In addition, the quantitative measurement of binding kinetics, including the association and dissociation rate constants for immunoglobulin G (IgG)/anti-mouse IgG, is achieved, indicating 0.38 × 10⁶ M⁻¹ s⁻¹ for k_a and 3.15 × 10⁻³ s⁻¹ for k_d. These constants are calculated from the fluorescence signals detected on fiber surface only where the excited evanescent wave can be generated. Thus, a confined fluorescence-detecting region is achieved to specifically determine the binding kinetics at the vicinity of the interface between sensing materials and uncladded fiber surface. With this FD-FOB, the mathematical deduction and experimental verification of the binding kinetics in a sandwich immunoassay provide a theoretical basis for measuring rate constants and equilibrium dissociation constants. A further measurement to study the interaction between human heart-type fatty acid-binding protein and its antibody gave the calculated kinetic constants k_a, k_d, and K_D as 8.48 × 10⁵ M⁻¹ s⁻¹, 1.7 × 10⁻³ s⁻¹, and 2.0 nM, respectively. Our study is the first attempt to establish a theoretical basis for the florescence-sensitive immunoassay using a sandwich format. Moreover, we demonstrate that the FD-FOB as a high-throughput biosensor can provide an alternative to the chip-based biosensors to study real-time biomolecular interaction.     

Design of acetylcholinesterases for biosensor applications

In recent years, the use of acetylcholinesterases (AChEs) in biosensor technology has gained enormous attention, in particular with respect to insecticide detection. The principle of biosensors using AChE as a biological recognition element is based on the inhibition of the enzyme's natural catalytic activity by the agent that is to be detected. The advanced understanding of the structure-function-relationship of AChEs serves as the basis for developing enzyme variants, which, compared to the wild type, show an increased inhibition efficiency at low insecticide concentrations and thus a higher sensitivity. This review describes different expression systems that have been used for the production of recombinant AChE. In addition, approaches to purify recombinant AChEs to a degree that is suitable for analytical applications will be elucidated as well as the various attempts that have been undertaken to increase the sensitivity of AChE to specified organophosphates and carbamates using side-directed mutagenesis and employing the enzyme in different assay formats.     

Porous gold surfaces for biosensor applications

The sensitivity of optical biosensors where the detection takes place on a planar gold surface can be improved by making the surface porous. The porosity allows a larger number of ligands per surface area resulting in larger optical shifts when interacting with specifically binding analyte molecules. The porous gold was deposited as a thin layer on a planar gold surface by electrochemical deposition in a solution of tetrachloroaurate and lead acetate. A protein, streptavidin, was adsorbed into the formed porous layer and the time course of the adsorption was monitored by in-situ ellipsometry. When the porous layer was 500 nm in thickness a six-fold increase of the ellipsometric response was obtained compared with a planar gold surface. The dependency of porosity and layer thickness was explained with a mathematical model of the gold/porous gold/protein/solution system.     

Single molecule force spectroscopy on ligand-DNA complexes: from molecular binding mechanisms to biosensor applications

Recent developments in single molecule force spectroscopy (SMFS) allow direct observation and measurements of forces that hold protein-DNA complexes together. Furthermore, the mechanics of double-stranded (ds) DNA molecules in the presence of small binding ligands can be detected. The results elucidate molecular binding mechanisms and open the way for ultra sensitive and powerful biosensor applications.     

Self-assembled monolayers as a tunable platform for biosensor applications.

Considerable attention has been drawn during the last two decades to functionalize noble metal surfaces by forming ordered organic films of few nm to several hundred-nm thickness. Self-assembled monolayer (SAM) provides one simple route to functionalize electrode surfaces by organic molecules (both aliphatic and aromatic) containing free anchor groups such as thiols, disulphides, amines, silanes, or acids. The monolayer produced by self-assembly allows tremendous flexibility with respect to several applications depending upon their terminal functionality (hydrophilic or hydrophobic control) or by varying the chain length (distance control). For example, SAM of long chain alkane thiol produces a highly packed and ordered surface, which can provide a membrane like microenvironment, useful for immobilising biological molecules. The high selectivity of biological molecules integrated with an electrochemical, optical or piezoelectric transduction mode of analyte recognition offers great promise to exploit them as efficient and accurate biosensors. It is demonstrated with suitable examples that monolayer design plays a key role in controlling the performance of these SAM based biosensors, irrespective of the immobilisation strategy and sensing mechanism.     

Combinatorial augmentation for a multi-pathogen biosensor: signal analysis and design

Recent advances in combinatorial chemistries have revolutionized approaches to drug candidate synthesis and screening. Combinatorial approaches are also beginning to be used to increase the performance of diagnostic devices for both clinical and field uses. The use of combinatorial technologies is motivated by a general desire to detect as many different pathogens using the smallest, most inexpensive and fastest system possible. We examine the potential for rational design approaches to enhance the performance and miniaturization of biosensors. We describe novel combinatorial biosensor systems, in addition to mathematical frameworks for their optimization and performance prediction. The biosensors are assumed to be composed of multiple detection channels with the following characteristics. Each channel has a single output and can be dynamically set to respond to some or all of a set of pathogens. Regardless of the number of pathogens detected, however, there is a single numerical output from a channel. We evaluate the amount of ambiguity of positive signals produced as a result of increasing both the number of channels and the number of pathogens detected per channel and the effect this ambiguity has on system performance. We further discuss strategies for disambiguating positive signals. Finally we cite specific biosensor configurations that exploit the findings above and compare them to “brute force” approaches. Overall we suggest the approach we refer to as “n-squared” to simultaneously optimize device cost, speed and reagent usage.     

Comparison of biosensor platforms in the evaluation of high affinity antibody-antigen binding kinetics

The acquisition of reliable kinetic parameters for the characterization of biomolecular interactions is an important component of the drug discovery and development process. While several benchmark studies have explored the variability of kinetic rate constants obtained from multiple laboratories and biosensors, a direct comparison of these instruments' performance has not been undertaken, and systematic factors contributing to data variability from these systems have not been discussed. To address these questions, a panel of ten high-affinity monoclonal antibodies was simultaneously evaluated for their binding kinetics against the same antigen on four biosensor platforms: GE Healthcare's Biacore T100, Bio-Rad's ProteOn XPR36, ForteBio's Octet RED384, and Wasatch Microfluidics's IBIS MX96. We compared the strengths and weaknesses of these systems and found that despite certain inherent systematic limitations in instrumentation, the rank orders of both the association and dissociation rate constants were highly correlated between these instruments. Our results also revealed a trade-off between data reliability and sample throughput. Biacore T100, followed by ProteOn XPR36, exhibited excellent data quality and consistency, whereas Octet RED384 and IBIS MX96 demonstrated high flexibility and throughput with compromises in data accuracy and reproducibility. Our results support the need for a “fit-for-purpose” approach in instrument selection for biosensor studies.     

Heme orientation modulates histidine dissociation and ligand binding kinetics in the hexacoordinated human neuroglobin

Neuroglobin (Ngb) is a globin present in the brain and retina of mammals. This hexacoordinated hemoprotein binds small diatomic molecules, albeit with lower affinity compared with other globins. Another distinctive feature of most mammalian Ngb is their ability to form an internal disulfide bridge that increases ligand affinity. As often seen for prosthetic heme b containing proteins, human Ngb exhibits heme heterogeneity with two alternative heme orientations within the heme pocket. To date, no details are available on the impact of heme orientation on the binding properties of human Ngb and its interplay with the cysteine oxidation state. In this work, we used ¹H NMR spectroscopy to probe the cyanide binding properties of different Ngb species in solution, including wild-type Ngb and the single (C120S) and triple (C46G/C55S/C120S) mutants. We demonstrate that in the disulfide-containing wild-type protein cyanide ligation is fivefold faster for one of the two heme orientations (the A isomer) compared with the other isomer, which is attributed to the lower stability of the distal His64–iron bond and reduced steric hindrance at the bottom of the cavity for heme sliding in the A conformer. We also attribute the slower cyanide reactivity in the absence of a disulfide bridge to the tighter histidine–iron bond. More generally, enhanced internal mobility in the CD loop bearing the disulfide bridge hinders access of the ligand to heme iron by stabilizing the histidine–iron bond. The functional impact of heme disorder and cysteine oxidation state on the properties of the Ngb ligand is discussed.     

Basic principles and applications of fractal geometry in pathology: a review

The basic principles and prospects of fractal geometry in pathology are promising. All articles found with a PubMed search with the keywords fractal dimension (FD) and related to pathology were reviewed. All fractal objects have FDs, commonly calculated with box counting. Fractal geometry has been applied to measure the irregularities of nuclear and glandular margins to distinguish malignant lesions from benign ones, to measure the infiltrative margin of a malignant tumor, to assess tumor angiogenesis and to measure the distribution of collagen in tissue. Fractal geometry has also been applied to assess the irregular distribution of chromatin in malignant cells. Biologic model formation is possible with fractal geometry. In the future, fractal geometry may help with the diagnosis, understanding of pathogenesis and management of lesions. It may also provide new insights into disease processes.