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 fractal analysis of pathogen detection by biosensors.

A fractal analysis is presented for the detection of pathogens such as Franscisela tularensis, Yersinia pestis (the bacterium that causes plague), Bacillus anthracis, Venezuelan equine encephalitis (VEE) virus, Vavcinia virus, and Escherichia coli using a cellular analysis and notification of antigens risks and yields (CANARY) biosensor [T.H. Rider, M.S. Petrovic, F.E. Nargi, J.D Harper, E.D. Schwoebel, R.H. Mathews, D.J. Blanchard, L.T Bortolin, A.M. Young, J. Chen, M.A. Hollis, A cell-based sensor for rapid identification of pathogens, Science 301 (2003, 11 July) 213-215, T.H. Rider, M.S. Petrovic, F.E. Nargi, J.D. Harper, E.D. Schwoebel, R.H. Mathews, D.J. Blanchard, L.T. Bortolin, A.M. Young, J. Chen, M.A. Hollis, A cell-based sensor for rapid identification of pathogens, Science 301 (2003, 11 July) 213-215. Science Online, www.sciencemag.org/cgi/content/full/031/5630/213/DC1]. In general, the binding and dissociation rate coefficients may be adequately described by either a single- or a dual-fractal analysis. An attempt is made to relate the binding rate coefficient to the degree of heterogeneity (fractal dimension value) present on the biosensor surface. Binding and dissociation rate coefficient values obtained are presented. Due to the dilute nature of the analyte(s) present, in some cases, a triple-fractal analysis is required to adequately describe the binding kinetics. It should be noted, and this is not entirely unexpected, that there is a lot of variation in the original experimental data when dilute concentrations of the analyte were analyzed by the CANARY biosensor [T.H. Rider, M.S. Petrovic, F.E. Nargi, J.D Harper, E.D. Schwoebel, R.H. Mathews, D.J. Blanchard, L.T Bortolin, A.M. Young, J. Chen, M.A. Hollis, A cell-based sensor for rapid identification of pathogens, Science 301 (2003, 11 July) 213-215, Science Online, www.sciencemag.org/cgi/content/full/031/5630/213/DC1]. The data analyzed in this manuscript appears smoother since only discrete points at different time intervals were analyzed. The kinetics aspects along with the affinity values presented are of interest and should along with the rate coefficients presented for the binding and the dissociation phase be of significant interest in help designing better biosensors for an application area that is bound to gain increasing importance in the future.

Protein amyloidose misfolding: mechanisms, detection, and pathological implications.

A variety of diseases result because of misfolded protein that deposits in extracellular space in the body. These deposits can be amorphous (disordered) or fibrillar (ordered). Inclusion bodies are an example of amorphous aggregates, and amyloid fibril is an example of fibrillar or ordered aggregates. In this chapter, we discuss a class of diseases caused by fibrillar aggregate deposits or amyloid fibrils called amyloidosis. We also review mechanisms by which different proteins misfold to form amyloid fibrils. Each amyloid fibril formed from a different protein causes a different disease by affecting a different organ in the body. However, the characteristics of different amyloid fibrils, namely structure and morphology, observed by electron microscopy and X-ray fiber diffraction appear to be quite similar in nature. We present therapeutic strategies developed to eliminate amyloid fibril formation. These strategies could possibly avert a whole class of fatal diseases caused by amyloid fibril deposition owing to similar characteristics of the amyloid fibrils.

Finding differentially expressed genes in high dimensional data: Rank based test statistic via a distance measure.

We present a rank-based test statistic for the identification of differentially expressed genes using a distance measure. The proposed test statistic is highly robust against extreme values and does not assume the distribution of parent population. Simulation studies show that the proposed test is more powerful than some of the commonly used methods, such as paired t-test, Wilcoxon signed rank test, and significance analysis of microarray (SAM) under certain non-normal distributions. The asymptotic distribution of the test statistic, and the p-value function are discussed. The application of proposed method is shown using a real-life data set.

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.

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 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 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 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.

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.

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).

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.

Identification of hair cycle-associated genes from time-course gene expression profile using fractal analysis.

Microarray technology permits one to monitor thousands of processes going on inside the cell. This tool has been used to study gene expression profiles associated with the hair-growth cycle. We provide a novel method called the fractal analysis method to identify hair-growth cycle associated genes from time course gene expression profiles. Fractal analysis is a much better method than the computational method used by Lin et al. (2004). The fractal dimension obtained by fractal analysis process also indicates the irregularity in hair-growth pattern. The computational method used by Lin et al. (2004) was unable to make any inference about the hair-growth pattern.

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.

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.

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.