Detection of glucose and related analytes by biosensors: a fractal analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness (fractal dimension, Df) present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from Df1 equal to 0.6827 to Df2 equal to 1.6852, the binding rate coefficient increases by a factor of 4.92 from k1 equal to 1.0232 to k2 equal to 5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose such as uric acid and ascorbic acid were also detected using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (29) (Lin, Y.; Lu, F.; Tu, Y.; Ren, Z. Nano Lett. 2004, 4 (2), 191-195). Attempts are made to standardize biosensor properties in terms of diffusion characteristics on in vivo responsiveness.     

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.     

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.     

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.     

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.     

Detection of glucose and related analytes by biosensors: a fractal analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness [fractal dimension (D(f))] present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from D(f1)=0.6827 to D(f2)=1.6852, the binding rate coefficient increases by a factor of 4.92 from k(1)=1.0232 to k(2)=5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose, such as uric acid and ascorbic acid, were also detected by using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (Lin Y, Lu F, Tu Y, Ren Z).     

Detection of Glucose and Related Analytes by Biosensors: A Fractal Analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness [fractal dimension (D_f)] present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from D_f1 = 0.6827 to D_f2 = 1.6852, the binding rate coefficient increases by a factor of 4.92 from k₁ = 1.0232 to k₂ = 5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose, such as uric acid and ascorbic acid, were also detected by using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (Lin Y, Lu F, Tu Y, Ren Z. Nano Lett 2004, 4, 191–195).     

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 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) () 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 (). 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 (). 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.     

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.     

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

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

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.     

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 surface plasmon resonance biosensor for the determination of binding constants of transiently expressed recombinant antibody to its antigen

Summary By using a commercially available surface plasmon resonance (SPR) biosensor, the values of the association rate constant (kass), dissociation rate constant (kdiss), and association constant (KA = kass / kdiss) for binding to the antigens were determined. They were almost the same for the recombinant antibody expressed in COS cells, CHO cells, and mouse hybridoma cells. The system of transient expression of the recombinant antibody (Ab) in COS cells and SPR analysis of the supernatant should be useful for rapid expression and evaluation of the binding ability of large numbers of engineered Abs.     

Kinetic modeling and determination of reaction constants of Alzheimer's beta-amyloid fibril extension and dissociation using surface plasmon resonance

To establish the kinetic model of the extension and dissociation of beta-amyloid fibrils (f(A)beta) in vitro, we analyzed these reactions using a surface plasmon resonance (SPR) biosensor. Sonicated f(A)beta were immobilized on the surface of the SPR sensor chip as seeds. The SPR signal increased linearly as a function of time after amyloid beta-peptides (Abeta) were injected into the f(A)beta-immobilized chips. The extension of f(A)beta was confirmed by atomic force microscopy. When flow cells were washed with running buffer, the SPR signal decreased with time after the extension reaction. The curve fitting resolved the dissociation reaction into the fast exponential and slow linear decay phases. Kinetic analysis of the effect of Abeta/f(A)beta concentrations on the reaction rate indicated that both the extension reaction and the slow linear phase of the dissociation were consistent with a first-order kinetic model; i.e., the extension/dissociation reactions proceed via consecutive association/dissociation of Abeta onto/from the end of existing fibrils. On the basis of this model, the critical monomer concentration ([M](e)) and the equilibrium association constant (K) were calculated, for the first time, to be 20 nM and 5 x 10(7) M(-1), respectively. Alternatively, [M](e) was directly measured as 200 nM, which may represent the equilibrium between the extension reaction and the fast phase of the dissociation. The SPR biosensor is a useful quantitative tool for the kinetic and thermodynamic study of the molecular mechanisms of f9A)beta formation in vitro.     

Ligand rebinding: self-consistent mean-field theory and numerical simulations applied to surface plasmon resonance studies

Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligands as a function of time. We show that, except for very low association rate and surface coverage, this function is nonexponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I–IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.