Binding Rate Coefficient Research Articles

A kinetic analysis using fractals of cellular analyte-receptor binding and dissociation.

A fractal analysis is presented for cellular analyte-receptor binding and dissociation kinetics using a biosensor. Data taken from the literature may be modelled, 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. The predictive relationship developed for the equilibrium constant, K (affinity which is equal to k(d)/k(1or2)), as a function of the analyte concentration is of particular value since it provides a means by which the affinity may be manipulated. This should be of assistance in cell-surface reactions, drug-candidate optimization and for the design of immunodiagnostic devices. 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, and the analyte concentration in solution. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f) or D(fd) as the case may be) leads to an increase in the binding and the dissociation rate coefficients. 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 the dissociation rate coefficients. The binding and dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f) and D(fd), respectively, that exists on the biosensor surface. The heterogeneity on the surface in general affects the binding and dissociation rate coefficients differently. In general, the analyte concentration in solution has a mild affect on the fractal dimension for binding or the fractal dimension for dissociation. This is indicated by the low values of the exponent in the predictive relationships developed.

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.

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.

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

A fractal analysis of confirmative nature only is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. Relationships are presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, 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 (Martin S.J., Granstaff, V.E., Frye, G.C., Anal. Chem., 65, (1991) 2910). The binding and the dissociation rate coefficient are rather sensitive to the degree of heterogeneity, D f,bind and D f,diss, respectively, that exists on the biosensor surface. For example, the order of dependence on D f,bind is 19.2 for the binding rate coefficient, k bind for the binding of 0.03–1.0 μM SH-2L d in solution to 2C TCR immobilized on a surface plasmon resonance (SPR) biosensor (Corr, M., Salnetz, A.E., Boyd, L.F., Jelonek, M.T., Khilko, S., Al-Ramadi, B.K., Kim, Y.S., Maher, S.E., Bothwell, A.L.M., Margulies, D.H., Science, 265, (1994) 946). The order of dependence on D f,diss is −6.22 for the dissociation rate coefficient, k diss for the dissociation of 250–1000 nM Sophora japonica agglutinin (SJA)-lactose complex from the SPR surface. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.

An Evaluation of Cellular Analyte–Receptor Binding Kinetics Utilizing Biosensors: A Fractal Analysis

A fractal analysis is presented for cellular analyte–receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using (a) a single-fractal analysis and (b) a single- and a dual-fractal analysis. Case (b) represents a change in the binding mechanism as the reaction progresses on the biosensor surface. Relationships are presented for the binding rate coefficient(s) as a function of the fractal dimension for the single-fractal analysis examples. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. For example, for the binding of mutagenized and back-mutagenized forms of peptide E1037 in solution to salivary agglutinin immobilized on a sensor chip, the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, is 13.2. It is of interest to note that examples are presented where the binding coefficient (k) exhibits an increase as the fractal dimension (Df) 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 us 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 coefficients (or affinities). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensors or other surfaces.

An evaluation of hybridization kinetics in biosensors using a single-fractal analysis.

The diffusion-limited hybridization kinetics of analyte in solution to receptor immobilized on a biosensor or immunosensor surface is analysed within a fractal framework. The data may be analysed by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot [Sigmaplot Users Manual (1993) Jandel Scientific, San Rafael, CA]. It is of interest to note that the binding-rate coefficient and the fractal dimension both exhibit changes in the same and in the opposite directions for the single example presented in each case. The binding-rate coefficient(s) expressions developed as a function of the analyte (DNA) concentration in solution and the fractal dimension are of particular value, since they provide a means to better control biosensor or immunosensor performance and provide physical insights into the hybridization process.

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·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, D f 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 k 1 and k 2 on D f1 and D f2 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.

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 10−6to 10−4M bSA in solution to a receptorless surface (direct binding to SPR surface) (41) the order of dependence ofk1andk2onDf1andDf2were −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.

Analysis of analyte-receptor binding kinetics for biosensor applications: an overview of the influence of the fractal dimension on the surface on the binding rate coefficient.

An overview of fractal analysis is presented for analyte-receptor binding kinetics for different types of biosensor application. Data taken from the literature can be modelled by using (1) a single-fractal analysis, (2) a single- and a dual-fractal analysis, and (3) a dual-fractal analysis. Cases (2) and (3) 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 because they provide a means by which the binding rate coefficients can be manipulated. Relationships are presented for the binding rate coefficients as a function of the fractal dimension, Df, or the degree of heterogeneity that exists on the surface. The binding rate coefficient is rather sensitive to the degree of heterogeneity, Df, that exists on the biosensor surface. For the examples analysed, the order of dependence of the binding rate coefficient on Df ranges from 1.4770 (k1), for the binding of intercalators and metabolites in solution to DNA immobilized at a positively charged surface, to 4.9434 for the binding of 5 nM nucleotide+GroEL in solution to GroES immobilized on a Ni2+-nitriloacetic acid sensor chip [Nieba, Nieba-Axmann, Persson, Hamalainen, Edebratt, Hansson, Lidholm, Magnusson, Karlsson and Pluckhun (1997) Anal. Biochem. 252, 217-228]. GroEl and GroES are two proteins (chaperones) which facilitate protein folding in the cell in an ATP-dependent manner [Hemmingson, Woolford, van der Vies, Tilly, Dennis, Georgopoulos, Henfrix and Ellis (1988) Nature (London) 333, 330-334]. The overview provides an overall analysis of the reaction parameters of importance observed and how they are influenced in antigen-antibody-binding kinetics for different biosensor applications. The predictive relationships presented provide further physical insights into the binding reactions on the surface, and should assist in enhancing biosensor performance. In general, the technique and the overview presented are applicable for the most part to other reactions occurring on different types of surface, for example cell-surface reactions.

Analyte-receptor binding kinetics for different types of biosensors. A fractal analysis.

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 Df 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 Df) 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, Df, that exists on the biosensor surface. For example, the order of dependence on Df1 is 7.25 for the binding rate coefficient k1 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.

Analyte–Receptor Binding Kinetics for Biosensor Applications: A Single-Fractal and a Dual-Fractal Analysis of the Influence of the Fractal Dimension on the Binding Rate Coefficient

The diffusion-limited binding kinetics of antigen (analyte) in solution to antibody (receptor) immobilized on a biosensor surface is analyzed within a fractal framework. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (“Scientific Graphing Procedure, User's Manual,” Jandel Scientific, San Rafael, CA, 1993). A couple of examples of a dual-fractal analysis are also presented. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction 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 the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis and for the binding of cell surface proteins fromHelicobacter pyloristrain in solution to sialyl-(α-2,3)-lactose-conjugated (20 mol%) polyacrylamide immobilized on a resonant mirror biosensor (S. Hirmoet al., Anal. Biochem.257, 63, 1998), the order of dependence of the binding rate coefficient,k,on the fractal dimension,Df, was 14.15. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient(s) 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 further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.

An analysis of analyte–receptor binding kinetics for biosensor applications: influence of the fractal dimension on the binding rate coefficient

The diffusion-limited binding kinetics of analyte in solution to receptor immobilized on a biosensor surface is analysed within a fractal framework. Both a single- as well as a dual-fractal analysis are utilized. Antigen–antibody and analyte–receptor systems are analysed. For the antigen–antibody and analyte–receptor systems where a single- or a dual-fractal analysis was used, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction. The binding rate coefficient expressions obtained as a function of the fractal dimension indicate the high sensitivity of the binding rate coefficient with respect to the fractal dimension. For example, for a single-fractal analysis and for the binding of (a) 1 μM BSA in solution to the anti-BSA-protein fused to a biosensor surface, and for (b) the binding of m-xylene-saturated STE buffer solution to the microorganism immobilized to the fiber-optic end and covered with a polycarbonate membrane, the orders of dependence of the binding rate coefficient on the fractal dimension were 5.535 and 3.314, respectively. This emphasizes the importance of the degree of heterogeneity on the biosensor surface and its impact on the binding rate coefficient, k. This high sensitivity is also indicated for a dual-fractal analysis, at least for the binding rate coefficient, k 2. For example, during regeneration runs and for the binding of polymerase chain-reaction amplified DNA in solution to DNA capture protein immobilized on a fiber-optic biosensor, the order of dependence of k 2 on D f2 was 3.399. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient expressions developed as a function of the fractal dimension for both single-fractal analysis and dual-fractal analysis systems are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface. Also, the importance of the nature of the surface on biosensor performance is emphasized in a quantitative sense.

Single- and Dual-Fractal Analysis of Hybridization Binding Kinetics: Biosensor Applications

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. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for both the single-fractal and the dual-fractal analysis examples presented. For example, for a single-fractal analysis and for the hybridization of 10 nM 16CFl (oligonucleotide) to 16B immobilized via sulfosuccinimidyl-6-(biotinamido)hexanoate and streptavidin using chemical and thermal regeneration (Abel, A. P.; Weller, M. G.; Duveneck, G. L.; Ehrat, M. Widmer, H. M. Anal. Chem. 1996, 68, 2905-2912), an increase in the fractal dimension, Df from 1.211 (chemical regeneration) to 1.394 (thermal regeneration), leads to an increase in the binding rate coefficient, k, from 86.53 (chemical regeneration) to 100.0 (thermal regeneration). An increase in the degree of heterogeneity on the biosensor surface leads to an increase in the binding rate coefficient. When a dual-fractal analysis was utilized, an increase in the fractal dimension value from Df1 to Df2 leads to an increase in the binding rate coefficient value from k1 to k2. The fractional order of dependence of the binding rate coefficient, k1, on (a) the analyte (rRNA) concentration in solution and (b) on the fractal dimension, Df1, for the hybridization kinetics to detect Listeria species (Fliss, R.; St-Laurent, M.; Emond, E.; Simard, R. E.; Lemieux, R.; Ettriki, A.; Pandian, S. Appl. Microbiol. Biotechnol. 1995, 43, 717-724.) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the analyte concentration in solution and the fractal dimension are of particular value since they provide a means to better control of biosensor or immunosensor performance.

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 (Df) 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 Df developed for the antigen-antibody binding systems, indicate the high sensitivity of the k on the Df 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 0.5 beta in solution to gp120 peptide immobilized on a BIAcore biosensor, the order of dependence on the Df 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, Df1 and Df2, were 7.6335 and -11.55, respectively. The fractional order of dependence of the k(s) on the Df(s) further reinforces the fractal nature of the system. The k(s) expressions developed as a function of the Df(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.

An Analysis of Analyte–Receptor Binding Kinetics for Biosensor Applications: Influence of the Fractal Dimension on the Binding Rate Coefficient

The diffusion-limited kinetics of binding of an analyte in solution to a receptor immobilized on a biosensor surface is analyzed within a fractal framework. Antigen–antibody, analyte–receptor, and analyte–receptorless systems are analyzed. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Jandel Scientific, San Rafael, CA, 1993). It is of interest to note that the binding rate coefficient,k, and the fractal dimension,Df, both exhibit changes in the same direction for the antigen–antibody and analyte–receptor systems analyzed. The binding rate coefficient,k, expressed as a function of the fractal dimension,Df, developed for the three types of binding systems indicates the sensitivity ofktoDf. For example, for the antigen–antibody binding of mAb 447/D-II to rgp 120(MN) immobilized on a biosensor surface and for mAb 9205 to rgp (IIIB) (37), the order of dependence onDfwas 10.221 and 9.668, respectively. The fractional order of dependence ofkonDffurther reinforces the fractal nature of the system. For the single example of an analyte–receptorless system (LDL protein adsorption) presented, a more organized biosensor surface (lowerDfvalue) leads to an increased value ofk. Expressions ofkas a function of the fractal dimension,Df, 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.

Influence of Different Parameters on a Dual-Fractal Analysis for 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 (46). It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase as the reaction progresses on the biosensor surface. For example, for the binding of HIV-1 p24 in solution to monoclonal antibody (MAb) 18 covalently attached to a biosensor surface (49), an increase in the fractal dimension by 59% from a value ofDf1equal to 1.91 toDf2equal to 2.95 leads to an increase in the binding rate coefficient by a factor of 15 fromk1equal to 21.1 tok2equal to 339. Also, the binding of MAb 6301 and 6303 in solution to insulin growth factor binding protein-1 (IGFBP-1) covalently attached to the sensor surface is adequately described by a single-fractal analysis (48). The binding of MAb 6302 to IGFBP-1, however, requires dual fractals. This indicates a difference in the binding mechanisms of these MAbs. 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. Also, the magnitude of the changes in the binding rate coefficients (k1andk2) and in the fractal dimensions (Df1andDf2) as different parameters are changed for the different biosensor applications are of particular value.

Influence of diffusion to fractal surfaces on the binding kinetics for antibody-antigen, analyte-receptor, and analyte-receptorless (protein) systems

The diffusion-limited binding kinetics of antigen-antibody, ligand-receptorless systems for biosensor applications is analyzed within a fractal framework. The analysis presented applies equally well to these types of systems. For example, for the binding of 2-( p-toluidinyl)-naphthalene-6-sulfonic acid (2,6-TNS) to β-cyclodextrin (ligand-receptor system) immobilized on a fiber-optic base inclusate biosensor, an increase in temperature from 4 to 30°C leads to an increase in the fractal dimension, D f and to a decrease in the binding rate coefficient, k l. For the binding of TRITC-labeled low-density proteins (LDL) directly to an optical fiber-based sensor (analyte-receptorless system), an increase in the LDL concentration from 5 to 50 μg ml −1 in solution leads to a decrease in the fractal dimension, D f and to an increase in the binding rate coefficient, k l. Also, during the binding of human chorionic gonadotropin (hCG) to anti-hCG antibody immobilized on a HPLC column (antigen-antibody system), an increase in temperature from 4 to 50°C leads to an increase in the fractal dimension, D f and in the binding rate coefficient, k l. The different examples analyzed and presented together for the three different types of systems provide one means of a ‘unified analysis,’ and a method by which the forward binding rate coefficient, k l may be controlled, that is, by changing the fractal dimension or ‘disorder’ on the surface. The analysis should assist in improving the stability, sensitivity, and response time of biosensors wherein different types of binding systems are utilized in the analysis method. More-or-less all of the treatment presented should be applicable to the above types of binding systems occurring in non-biosensor applications also. However, the single-fractal analysis is unable to describe the data over the full time course of some of the experiments.

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 (Df1 to Df2) 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.

Dual-fractal analysis for 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 and other surfaces is analyzed within a fractal framework. Often, the binding kinetics may be described by a single-fractal analysis. In some cases, the binding curve exhibits complexities. Then, for these cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This indicates a change in the reaction mechanism on the surface. It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase as the reaction progresses on the biosensor surface. For example, for the binding of 10 nM insulin growth factor-1 in solution to insulin growth factor binding protein-1 immobilized on a biosensor surface, a 64% increase in the fractal dimension from 1.73 (Df1) to 2.85 (Df2) leads to an increase in the binding rate coefficient by a factor of 31.8 from 3.92 (k1) to 125 (k2). Furthermore, as the IGF-1 concentration in solution increases from 10 to 80 nM in solution, k2 and Df2 exhibit a linear increase. k1 and Df1 exhibit a linear increase with the reciprocal of the IGF-1 concentration in solution. 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. Also, the magnitude of the changes in the binding rate coefficients (k1 and k2) and in the fractal dimensions (Df1 and Df2) as different parameters are changed for the different biosensor applications are of particular value, since they provide us with a measure or extent of changes in the binding rate coefficient on changing different experimental parameter values. It is of interest to note the effect of different parameters on the extent or heterogeneity that exists on the surface and how this influences the binding rate coefficients. This may be one method to help manipulate or control the binding rate coefficients on the reaction surface.

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, Df observed are in the same and in the reverse directions as the forward binding rate coefficient k. 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 Df from 0.294 to 0.5080, and in the forward binding rate coefficient k from 0.1194 to 9.716, respectively. The error in the fractal dimension Df 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 Df from 2.6806 to 2.6164, and to an increase in the forward binding rate coefficient k from 3.571 to 4.033, respectively. The different examples analyzed and presented together indicate one means by which the forward binding rate coefficient k 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.