A Single and a Dual-Fractal Analysis of Analyte-Receptor Binding Kinetics for Surface Plasmon Resonance Biosensor Applications

The diffusion-limited binding kinetics of analyte in solution to either a receptor immobilized on a surface or to a receptorless surface is analyzed within a fractal framework for a surface plasmon resonance biosensor. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modeled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot (32) was used to determine if a single fractal analysis is sufficient or if 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 analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate, in general, the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and 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-115-21.BSA immobilized on a surface plasmon resonance (SPR) surface (33), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, is 6.4405. Similarly, for a dual-fractal analysis and for the binding of 10(-6) to 10(-4) M bSA in solution to a receptorless surface (direct binding to SPR surface) (41) the order of dependence of k1 and k2 on Df1 and Df2 were -2.356 and 6.241, respectively. Binding rate coefficient expressions are also developed as a function of the analyte 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 SPR biosensor performance by linking it to the degree of heterogeneity that exists on the SPR biosensor surface. Copyright 1999 Academic Press.     

A Predictive Approach Using Fractal Analysis for Analyte-Receptor Binding and Dissociation Kinetics for Surface Plasmon Resonance Biosensor Applications

A predictive approach using fractal analysis 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. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the binding and the affinity (k(diss)/k(bind)) as a function of the analyte concentration are of particular value since they provide a means by which the binding and the affinity rate coefficients may be manipulated. Relationships are also presented for the binding and the dissociation rate coefficients and for the affinity 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. 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. The binding and the dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f,bind) (or D(f1)) and D(f,diss), respectively, that exists on the biosensor surface. For example, the order of dependence on D(f,bind) (or D(f1)) and D(f2) is 6.69 and 6.96 for k(bind,1) (or k(1)) and k(2), respectively, for the binding of 0.085 to 0.339 μM Fab fragment 48G7(L)48G7(H) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue immobilized on a surface plasmon resonance (SPR) biosensor. The order of dependence on D(f,diss) (or D(f,d)) is 3.26 for the dissociation rate coefficient, k(diss), for the dissociation of the 48G7(L)48G7(H)-PNP complex from the SPR surface to the solution. The predictive relationships presented for the binding and the affinity as a function of the analyte concentration in solution provide further physical insights into the reactions on the surface and should assist in enhancing SPR biosensor performance. In general, the technique is applicable to other reactions occurring on different types of biosensor surfaces and other surfaces such as cell-surface reactions. Copyright 2000 Academic Press.     

Analyte-receptor binding kinetics for biosensor applications

The diffusion-limited binding kinetics of antigen (analyte), in solution with antibody (receptor) immobilized on a biosensor surface, is analyzed within a fractal framework. Most of the data presented is adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. A single example of a dual-fractal analysis is also presented. It is of interest to note that the binding-rate coefficient (k) and the fractal dimension (D_f) both exhibit changes in the same and in the reverse direction for the antigen-antibody systems analyzed. Binding-rate coefficient expressions, as a function of the D_f developed for the antigen-antibody binding systems, indicate the high sensitivity of thek on the D_f when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis, and for the binding of antibody Mab 0.5β in solution to gpl20 peptide immobilized on a BIAcore biosensor, the order of dependence on the D_f was 4.0926. For a dual-fractal analysis, and for the binding of 25-100 ng/mL TRITC-LPS (lipopolysaccharide) in solution with polymyxin B immobilized on a fiberoptic biosensor, the order of dependence of the binding-rate coefficients, k₁ and k₂ on the fractal dimensions, D_f1 and D_f2, were 7.6335 and-11.55, respectively. The fractional order of dependence of thek(s) on the D_f(s) further reinforces the fractal nature of the system. Thek(s) expressions developed as a function of the D_f(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 further emphasize, in a quantitative sense, the importance of the nature of the surface in biosensor performance.     

Analyte-receptor binding kinetics for different types of biosensors

A fractal analysis is presented for analyte-receptor binding kinetics for different types of biosensor applications. Data taken from the literature may be modeled using a single-fractal analysis, a single- and a dual-fractal analysis, or a dual-fractal analysis. The latter two methods represent a change in the binding mechanism as the reaction progresses on the surface. Predictive relationships developed for the binding rate coefficient as a function of the analyte concentration are of particular value since they provide a means by which the binding rate coefficients may be manipulated. Relationships are presented for the binding rate coefficients as a function of the fractal dimension D _f or the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity on the surface (increase in D _f ) leads to an increase in the binding 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 rate coefficient. The binding rate coefficient is rather sensitive to the degree of heterogeneity, D _f , that exists on the biosensor surface. For example, the order of dependence on D _f1 is 7.25 for the binding rate coefficient k ₁ for the binding of a Fab fragment of an antiparaquat monoclonal antibody in solution to an antigen in the form of a paraquat analog immobilized on a sensor surface. The predictive relationships presented for the binding rate coefficient and the fractal dimension as a function of the analyte concentration in solution provide further physical insights into the binding reactions on the surface, and should assist in enhancing biosensor performance. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.     

Antigen-antibody binding kinetics for 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 fit obtained by a dual-fractal analysis is compared with that obtained from a single-fractal analysis. In some cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (San Rafael, CA). These examples are presented. It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase (or decrease, a single example is presented for this case) as the reaction progresses on the biosensor surface. For example, for the binding of monoclonal antibody MAb 49 in solution to surface-immobilized antigen, a 90.4% increase in the fractal dimension (D_f1 toD _f2 ) from 1.327 to 2.527 leads to an increase in the binding rate coefficient (k₁ to k₂) by a factor of 9.4 from 11.74 to 110.3. The different examples analyzed and presented together provide a means by which the antigen-antibody reactions may be better controlled by noting the magnitude of the changes in the fractal dimension and in the binding rate coefficient as the reaction progresses on the biosensor surface.     

A Fractal Analysis Approach for the Evaluation of Hybridization Kinetics in Biosensors

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Sigmaplot, Scientific Graphing Software, User's Manual, Jandel Scientific, CA, 1993). It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes, in general, in the same direction for both the single-fractal and the dual-fractal analysis examples presented. The binding rate coefficient expression developed as a function of the analyte concentration in solution and the fractal dimension is of particular value since it provides a means to better control biosensor or immunosensor performance. Copyright 2001 Academic Press.     

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

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ER) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. Both cases are analyzed: unliganded as well as liganded. 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 signaling and signaling deleterious to health) may be better controlled. The fractal approach is applied to analyte-ER interaction data available in the literature. 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. For example, the binding rate coefficient, k, exhibits a 4.60 order of dependence on the fractal dimension, D(f), for the binding of unliganded and liganded VDR mixed with GST-RXR in solution to Spp-1 VDRE (1,25-dihydroxyvitamin D(3) receptor element) DNA immobilized on a sensor chip surface (Cheskis and Freedman, Biochemistry 35 (1996) 3300-3318). 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. A predictive relationship is also presented for the ratio K(A)(=k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). This has biomedical and environmental implications in that the dissociation and binding rate coefficients may be used to alleviate deleterious effects or enhance beneficial effects by selective modulation of the surface. The K(A) exhibits a 112-order dependence on the ratio of the fractal dimensions for the ligand effects on VDR-RXR interaction with specific DNA.     

Antigen-antibody diffusion-limited binding kinetics for biosensors

A fractal analysis is made for antigen-antibody binding kinetics for different biosensor applications available in the literature. Both types of examples are considered wherein: (1) the antigen is in solution and the antibody is immobilized on the fiberoptic surface, and (2) the antibody is in solution and the antigen is immobilized on the fiberoptic surface. For example, when the antibody is immobilized on the surface, an increase in the antigenClostridium botulinum toxin A concentration in solution leads to (1) a decrease in the fractal dimension value or state of disorder, and (2) a higher rate constant for binding on the fiberoptic surface. An analysis of the effect of the influence of different parameters on the fractal dimension values for a particular example, such as varying treatments or incubation procedures, helps provide insights into the conformational states and reactions occurring on the fiberoptic surface. The analysis of the different examples taken together provides novel physical insights into the state of “disorder” and reactions occurring on the surface. Such types of analysis should help contribute toward manipulating the reactions occurring on the fiberoptic surfaces in desired directions.     

Antigen-antibody binding kinetics for biosensors

The diffusion-limited binding kinetics of antigen in solution to antibody immobilized on a biosensor surface is analyzed within a fractal framework. Changes in the fractal dimension, D_f observed are in the same and in the reverse directions as the forward binding rate coefficientk. For example, an increase in the concentration of the isoenzyme human creatine kinase isoenzyme MB form (CK-MB) (antigen) solution from 0.1 to 50 ng/mL and bound to anti-CK-MB antibody immobilized on fused silica fiber rods leads to increases in the fractal dimension D_f from 0.294 to 0.5080, and in the forward binding rate coefficientk from 0.1194 to 9.716, respectively. The error in the fractal dimension D_f decreases with an increase in the CK-MB isoenzyme concentration in solution. An increase in the concentration of human chorionic gonadotrophin (hCG) in solution from 4000 to 6000 mIU/mL hCG and bound to anti-hCG antibody immobilized on a fluorescence capillary fill device leads to a decrease in the fractal dimension D_f from 2.6806 to 2.6164, and to an increase in the forward binding rate coefficientk from 3.571 to 4.033, respectively. The different examples analyzed and presented together indicate one means by which the forward binding rate coefficientk may be controlled, that is by changing the fractal dimension or the ‘disorder’ on the surface. The analysis should assist in helping to improve the stability, the sensitivity, and the response time of biosensors.     

Atomic force microscopy for the characterization of immobilized enzyme molecules on biosensor surfaces

The development of biosensors has been one of the key areas in biotechnology and biomedical studies. Often it is difficult to investigate the immobilized biomolecules on the surfaces for biosensor optimization. Atomic force microscopy (AFM) should provide an ideal means for the visualization of biosensor surface and for the investigation of biomolecule activities. Therefore, AFM has been employed to study the surface topography of immobilized glutamate dehydrogenase (GDH) on two-dimensional glutamate biosensor surfaces. Correlation between the surface topography and the activity of the biosensor was investigated. Surface analysis has revealed that the enzymatic activity of the immobilized GDH molecules on the biosensor surface is linked to surface roughness, as measured by the peak-to-valley distance. Fractal dimension of the immobilization sensor surface was found to be a good parameter for judging the quality of the immobilized biosensors. As enzyme immobilization time increases, the biosensor has its maximum activity with around 18 h of immobilization in 10^–6 M GDH solution. Various biosensors prepared under different experimental conditions have been studied by AFM. This technique is shown to be an effective tool to characterize biosensor surfaces.     

Atomic force microscopy for the characterization of immobilized enzyme molecules on biosensor surfaces

The development of biosensors has been one of the key areas in biotechnology and biomedical studies. Often it is difficult to investigate the immobilized biomolecules on the surfaces for biosensor optimization. Atomic force microscopy (AFM) should provide an ideal means for the visualization of biosensor surface and for the investigation of biomolecule activities. Therefore, AFM has been employed to study the surface topography of immobilized glutamate dehydrogenase (GDH) on two-dimensional glutamate biosensor surfaces. Correlation between the surface topography and the activity of the biosensor was investigated. Surface analysis has revealed that the enzymatic activity of the immobilized GDH molecules on the biosensor surface is linked to surface roughness, as measured by the peak-to-valley distance. Fractal dimension of the immobilization sensor surface was found to be a good parameter for judging the quality of the immobilized biosensors. As enzyme immobilization time increases, the biosensor has its maximum activity with around 18 h of immobilization in 10(-6) M GDH solution. Various biosensors prepared under different experimental conditions have been studied by AFM. This technique is shown to be an effective tool to characterize biosensor surfaces.     

A beta-cyclodextrin based fiber-optic chemical sensor: a fractal analysis

A fractal analysis is presented for the binding of pyrene in solution to beta-cyclodextrin attached to a fiber-optic chemical sensor. The specific (k(l)) and non-specific binding rate coefficients and the fractal dimension (D(f)) (specific binding case only) both tend to increase as the pyrene concentration in solution increases from 12.4 to 124 ng ml(-1). Predictive relations for the binding rate coefficient (specific as well as non-specific binding) and for D(f) (specific binding case only) as a function of pyrene concentration are provided. These relations fit the calculated k(l) and D(f) values in the pyrene concentration range reasonably well. Fractal analysis data seem to indicate that an increase in the pyrene concentration in solution increases the "ruggedness" or inhomogeneity on the fiber-optic biosensor surface. The fractal analysis provides novel physical insights into the reactions occuring on the fiber-optic chemical surface and should assist in the design of fiber-optic chemical sensors.     

Microscopic and voltammetric characterization of bioanalytical platforms based on lactate oxidase

A microscopic and voltammetric characterization of lactate oxidase- (LOx-) based bioanalytical platforms for biosensor applications is presented. In this context, emphasis is placed on amperometric biosensors based on LOx that have been immobilized by direct absorption on carbon surfaces, in particular, glassy carbon (GC) and highly ordered pyrolytic graphite (HOPG). The immobilized LOx layers have been characterized using atomic force microscopy (AFM) under liquid conditions and cyclic voltammetry. In addition, spatially resolved mapping of enzymatic activity has been carried out using scanning electrochemical microscopy (SECM). In the presence of lactate with hydroxymethylferrocene (HMF) as a redox mediator in solution, biosensors obtained by direct adsorption of LOx onto GC electrodes exhibited a clear electrocatalytic activity, and lactate could be determined amperometrically at 300 mV versus SSCE. The proposed biosensor also exhibits good operating performance in terms of linearity, detection limit, and lifetime.     

Comparative Assessment of Oriented Antibody Immobilization on Surface Plasmon Resonance Biosensing

Protein A and protein G are extremely useful molecules for the immobilization of antibodies. However, there are limited comparative reports available to evaluate their immobilization performance for use as biosensors. In this study, a comparative analysis was made of approaches that use protein A and protein G for avian leukosis virus detection. The antibody‐protein binding affinities were determined using surface plasmon resonance (SPR) analysis. The immobilization efficiency was obtained by calculating the number of the protein molecular binding sites. The positive influence of sensor response on antigen detection indicates that the amount of immobilized antibody plays a major role in the extent of immobilization. Moreover, the biosensors constructed using both proteins were found to be regenerative. The SPR results from this study suggest that the surfaces of protein G provide a better equilibrium constant and binding efficacy for immobilized antibodies, resulting in enhanced antigen detection.     

Electrochemical technique for the determination of fractal dimension of dental surfaces

Fractal dimension of a carious tooth surface was determined using an electrochemical method. The method was based on time-dependent diffusion towards electrode surfaces, which is one of the most useful and reliable methods for the determination of fractal dimension of electrode surfaces. For this purpose, the tooth was covered with a gold layer, which acted as an electrode in electrochemical experiments. It is suggested that the fractal dimension can be used as a quantitative measure of the state of dental surfaces. The method presented demonstrates the power of electrochemical techniques for the determination of fractal dimension of surface of non-conducting objects.     

Quartz crystal microbalance biosensor for recombinant human interferon-beta detection based on antisense peptide approach

Quartz crystal microbalance (QCM) biosensors for recombinant human interferon-β (rhIFN-β) were constructed by utilizing antisense peptides adhering to the QCM gold surfaces. Two antisense peptides, both corresponding to the N-terminal fragment 1-14 of rhIFN-β, were used in this study. Antisense peptide AS-1 was the original antisense peptide and AS-2 was the modified antisense peptide based on the antisense peptide degeneracy. Both antisense peptides were immobilized on the gold electrodes of piezoelectric crystals, respectively, via a self-assembling monolayer of 1,2-ethanedithiol. The binding affinity between rhIFN-β and each immobilized antisense peptide in solution was evaluated using a quartz crystal microbalance-flow injection analysis (QCM-FIA) system. The dissociation constant of rhIFN-β on the antisense peptide AS-1 and AS-2 biosensor was (1.89 ± 0.101) × 10⁻⁴ and (1.22 ± 0.0479) ×10⁻⁵ mol L⁻¹, respectively. The results suggested that AS-2 had a higher binding affinity to rhIFN-β than AS-1. The detection for rhIFN-β using each biosensor was precise and reproducible. The linear response ranges of rhIFN-β binding to both biosensors were same with a concentration range of 0.12-0.96 mg mL⁻¹. The results demonstrated the successful construction of highly selective QCM biosensors using antisense peptide approach, and also confirmed the feasibility of increasing antisense peptide binding affinity by appropriate sequence modification.     

Biosensors based on direct electron transfer in redox proteins

In biosensors based on direct electron transfer in redox proteins, efficient electron-transfer pathways between the immobilized redox protein and the electrode surface have to be established so to allow a fast electron transfer and concomitantly avoiding free-diffusing redox species. In this review, prerequisites for the direct electron transfer of redox proteins and immobilization of redox proteins on the electrode surfaces are addressed. Based on the specific nature of different proteins and non-manual immobilization procedures, possible biosensor designs are discussed, namely biosensors based on (1) ferritin; (2) cytochrome c; (3) myoglobin; (4) hemoglobin; (5) horseradish peroxidase; (6) catalase; (7) glucose oxidase; and (8) xanthine oxidase.     

Electrochemical glucose biosensor based on silver nanoparticles/multiwalled carbon nanotubes modified electrode

A novel glucose biosensor was fabricated by immobilizing glucose oxidase (GOx) on Ag nanoparticles-decorated multiwalled carbon nanotube (AgNP-MWNT) modified glass carbon electrode (GCE). The AgNP-MWNT composite membrane showed an improving biocompatibility for GOx immobilization and an enhancing electrocatalytic activity toward reduction of oxygen due to decoration of AgNPs on MWNT surfaces. The AgNPs also accelerated the direct electron transfer between redox-active site of GOx and GCE surface because of their excellent conductivity and large capacity for protein loading, leading to direct electrochemistry of GOx. The glucose biosensor of this work showed a lower limit of detection of 0.01 mM (S/N?=?3) and a wide linear range from 0.025 to 1.0 mM, indicating an excellent analytical performance of the obtained biosensor to glucose detection. The resulting biosensor exhibits good stability and excellent reproducibility. Such bionanocomposite provides us good candidate material for fabrication of biosensors based on direct electrochemistry of immobilized enzymes.     

Redesigning of Microbial Cell Surface and Its Application to Whole-Cell Biocatalysis and Biosensors

Microbial cell surface display technology can redesign cell surfaces with functional proteins and peptides to endow cells some unique features. Foreign peptides or proteins are transported out of cells and immobilized on cell surface by fusing with anchoring proteins, which is an effective solution to avoid substance transfer limitation, enzyme purification, and enzyme instability. As the most frequently used prokaryotic and eukaryotic protein surface display system, bacterial and yeast surface display systems have been widely applied in vaccine, biocatalysis, biosensor, bioadsorption, and polypeptide library screening. In this review of bacterial and yeast surface display systems, different cell surface display mechanisms and their applications in biocatalysis as well as biosensors are described with their strengths and shortcomings. In addition to single enzyme display systems, multi-enzyme co-display systems are presented here. Finally, future developments based on our and other previous reports are discussed.     

Steric crowding effects on target detection in an affinity biosensor

This work quantifies the impact of steric crowding on whole antibody (Ab) receptor immobilization and target Ab detection and also demonstrates how the versatile biotin/streptavidin receptor immobilization system must be tuned to optimize target detection in designing biosensors. Results are demonstrated on a label-free optical biosensor fabricated from n-type macroporous porous silicon (PSi) with approximately 88-107 nm diameter pores. We employ a sandwich assay scheme comprising a linking chemistry (biotin/streptavidin) to attach biotinylated anti-rabbit IgG (receptor) to detect rabbit IgG (target). A "bottom-up" approach was taken to investigate each layer of the sandwich assay to optimize target binding. Steric crowding was observed to hinder subsequent layer binding for each layer in the sandwich (biotin, streptavidin, and receptor). Our results give definitive evidence that the onset of steric crowding within the biotin layer occurs at a surface coverage of 57%, which is much higher compared to that from published work on well-ordered self-assembled biotin monolayers on planar gold surfaces. This difference is attributed to the topographical heterogeneity of the PSi substrate. Streptavidin (SA) binding to surface-linked biotin was altered by preblocking the streptavidin binding sites with biotin. Through consistent trends in data, preblocking SA was shown to reduce steric crowding within the SA layer, which translated into increased receptor immobilization. The final detection range of rabbit IgG was 0.07-3 mg mL(-1) (0.4-17 ng mm(-2)), and binding specificity was demonstrated by employing an anti-chicken IgG control receptor. This study underlines the importance of considering binding avidity and surface topography in optimizing chip-based biosensors.