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

A predictive approach using fractal analysis is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the binding and the affinity (k(diss)/k(bind)) as a function of the analyte concentration are of particular value since they provide a means by which the binding and the affinity rate coefficients may be manipulated. Relationships are also presented for the binding and the dissociation rate coefficients and for the affinity as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient. The binding and the dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f,bind) (or D(f1)) and D(f,diss), respectively, that exists on the biosensor surface. For example, the order of dependence on D(f,bind) (or D(f1)) and D(f2) is 6.69 and 6.96 for k(bind,1) (or k(1)) and k(2), respectively, for the binding of 0.085 to 0.339 μM Fab fragment 48G7(L)48G7(H) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue immobilized on a surface plasmon resonance (SPR) biosensor. The order of dependence on D(f,diss) (or D(f,d)) is 3.26 for the dissociation rate coefficient, k(diss), for the dissociation of the 48G7(L)48G7(H)-PNP complex from the SPR surface to the solution. The predictive relationships presented for the binding and the affinity as a function of the analyte concentration in solution provide further physical insights into the reactions on the surface and should assist in enhancing SPR biosensor performance. In general, the technique is applicable to other reactions occurring on different types of biosensor surfaces and other surfaces such as cell-surface reactions. Copyright 2000 Academic Press.     

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, D(f), 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 (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 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. Copyright 2000 Academic Press.     

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

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

Analyte-receptor binding kinetics for biosensor applications

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

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

The diffusion-limited binding kinetics of analyte in solution to either a receptor immobilized on a surface or to a receptorless surface is analyzed within a fractal framework for a surface plasmon resonance biosensor. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modeled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot (32) was used to determine if a single fractal analysis is sufficient or if a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate, in general, the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-115-21.BSA immobilized on a surface plasmon resonance (SPR) surface (33), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, is 6.4405. Similarly, for a dual-fractal analysis and for the binding of 10(-6) to 10(-4) M bSA in solution to a receptorless surface (direct binding to SPR surface) (41) the order of dependence of k1 and k2 on Df1 and Df2 were -2.356 and 6.241, respectively. Binding rate coefficient expressions are also developed as a function of the analyte concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control SPR biosensor performance by linking it to the degree of heterogeneity that exists on the SPR biosensor surface. Copyright 1999 Academic Press.     

Analyte-receptor binding kinetics for different types of biosensors

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

Antigen-antibody binding kinetics for biosensor applications

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

Cooperative motions of protein and hydration water molecules: molecular dynamics study of scytalone dehydratase

Two molecular dynamics (MD) simulations totaling 25 ns of simulation time of monomeric scytalone dehydratase (SD) were performed. The enzyme has a ligand-binding pocket containing a cone-shaped alpha+beta barrel, and the C-terminal region covers the binding pocket. Our simulations clarified the difference in protein dynamics and conformation between the liganded protein and the unliganded protein. The liganded protein held the ligand molecule tightly and the initial structure was maintained during the simulation. The unliganded protein, on the other hand, fluctuated dynamically and its structure changed largely from the initial structure. In the equilibrium state, the binding pocket was fully solvated by opening of the C-terminal region, and the protein dynamics was connected with hydration water molecules entry into and release from the binding pocket. In addition, the cooperative motions of the unliganded protein and the hydration water molecules produced the path through the protein interior for ligand binding.     

Antigen-antibody binding kinetics for biosensors

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

Oxygen equilibrium properties of myoglobin locked in the liganded and unliganded conformations

A comparison of the O(2) equilibrium curves of sperm-whale myoglobin locked in the liganded (CO-bound) and unliganded (deoxy) conformations by encapsulation in a wet porous sol-gel silica reveals a marked difference between them. The CO-bound state-locked myoglobin showed a nearly monophasic (hyperbolic) O(2) equilibrium curve with a dissociation constant of 0.2 Torr, which is smaller than that of myoglobin in solution (0.5 Torr). On the other hand, the deoxy state-locked myoglobin exhibited a multiphasic O(2) equilibrium curve that can be represented by a sum of three independent components with dissociation constants of 0.19, 0.90, and 44 Torr, respectively, indicating that deoxymyoglobin exists in multiple conformations. These results show that myoglobin can be frozen into ligand-dependent conformational populations at room temperature in the wet sol-gel and suggest that the overall O(2) equilibrium properties of myoglobin in solution are generated by a redistribution of protein conformational populations in response to ligand binding.     

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.     

Reversible immobilization of proteins with streptavidin affinity tags on a surface plasmon resonance biosensor chip

Dissociation of biotin from streptavidin is very difficult due to their high binding affinity. The re-use of streptavidin-modified surfaces is therefore almost impossible, making devices containing them (e.g. surface plasmon resonance (SPR) sensor chips) expensive. This paper describes a new protocol for reversible and site-directed immobilization of proteins with streptavidin affinity tags on the streptavidin-coated SPR biosensor chip (SA chip). Two streptavidin affinity tags, nano-tag and streptavidin-binding peptide (SBP tag), were applied. They both can specifically interact with streptavidin but have weaker binding force compared to the biotin–streptavidin system, thus allowing association and dissociation under controlled conditions. The SA chip surface could be regenerated repeatedly without loss of activity by injection of 50 mM NaOH solution. The fusion construct of a SBP tag and a single-chain antibody to mature bovine prion protein (scFv-Z186-SBP) interacts with the SA chip, resulting in a single-chain-antibody-modified surface. The chip showed kinetic response to the prion antigen with equilibrium dissociation constant K _D≈4.01×10⁻⁷. All results indicated that the capture activity of the SA chip has no irreversible loss after repeated immobilization and regeneration cycles. The method should be of great benefit to various biosensors, biochips and immunoassay applications based on the streptavidin capture surface.     

A comparative analysis of localized and propagating surface plasmon resonance sensors: the binding of concanavalin a to a monosaccharide functionalized self-assembled monolayer

A comparative analysis of the properties of two optical biosensor platforms: (1) the propagating surface plasmon resonance (SPR) sensor based on a planar, thin film gold surface and (2) the localized surface plasmon resonance (LSPR) sensor based on surface confined Ag nanoparticles fabricated by nanosphere lithography (NSL) are presented. The binding of Concanavalin A (ConA) to mannose-functionalized self-assembled monolayers (SAMs) was chosen to highlight the similarities and differences between the responses of the real-time angle shift SPR and wavelength shift LSPR biosensors. During the association phase in the real-time binding studies, both SPR and LSPR sensors exhibited qualitatively similar signal vs time curves. However, in the dissociation phase, the SPR sensor showed an approximately 5 times greater loss of signal than the LSPR sensor. A comprehensive set of nonspecific binding studies demonstrated that this signal difference was not the consequence of greater nonspecific binding to the LSPR sensor but rather a systematic function of the Ag nanoparticle's nanoscale structure. Ag nanoparticles with larger aspect ratios showed larger dissociation phase responses than those with smaller aspect ratios. A theoretical analysis based on finite element electrodynamics demonstrates that this results from the characteristic decay length of the electromagnetic fields surrounding Ag nanoparticles being of comparable dimensions to the ConA molecules. Finally, an elementary (2 x 1) multiplexed version of an LSPR carbohydrate sensing chip to probe the simultaneous binding of ConA to mannose and galactose-functionalized SAMs has been demonstrated.     

Antigen-antibody diffusion-limited binding kinetics for biosensors

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

一种糖生物传感芯片制备的新方法

建立了一种用于SPR生物传感器分析的糖生物传感芯片制备新方法。在已二胺大量过量的情况下，海洋硫酸多糖911还原末端的半缩醛基与已二胺的一个氨基进行还原胺化反应，引入一个伯氨基，该伯氨基进一步与sulfo-NHS-biotin反应，使911的还原末端生物素化，通过预偶联到GM5芯片上的链酶抗生素抗体，以俘获法将生物素化的911固定到芯片表面。该方法避免已有固定方法对糖内部结构的破坏，减少了非特异性耦联，能更好地反映糖类与其它分子的相互作用特性，且操作简单，适应于多数具有还原末端的糖类。911经该方法固定后，利用SPR生物传感器，研究了其与HIV gp120蛋白V3区的相互作用动力学，初步证明两者之间存在强烈的相互作用，KA与KD分别为：2.25e5与4.44e-6。     

Estrogen receptor microarrays: subtype-selective ligand binding

We present the first example of a nuclear hormone receptor microarray, using for illustration the ligand-binding domains of the two estrogen receptors, ERalpha-LBD and ERbeta-LBD. The proteins are printed and allowed to attach to aldehyde slides; the efficiency of attachment depends on whether the LBD is liganded with agonists (low attachment) versus liganded with antagonists or unliganded (high attachment). This suggests that attachment is orientation specific and involves principally a single lysine residue. The attached ERs retain good ligand-binding activity that can be assessed using an estradiol-fluorophore conjugate, and specific and ER subtype-selective binding of ligands can be determined conveniently in competitive binding assays. This powerful new, high-throughput technique to study ligand binding to ER-LBDs can be extended to other nuclear hormone receptors and adapted to assay the recruitment of coregulator proteins.     

Facile fabrication of branched-chain carbohydrate chips for studying carbohydrate-protein interactions by QCM biosensor

A novel approach for fabricating branched-chain (BC) carbohydrate chips to study carbohydrate-protein interactions using quantz crystal microbalance (QCM) biosensor was developed. This approach utilizes functional alkynyl-branch molecule modified chip surfaces, which is functionalized with terminal alkynyl group for covalent linking of unprotected azide-carbohydrates via click chemistry.     

Quantitative estimation of interaction between carbohydrates and concanavalin A by surface plasmon resonance biosensor

We measured the affinity of more than 20 sugars with concanavalin A (ConA) by an optical biosensor (surface plasmon resonance sensor) using asialofetuin (ASF) as an immobilized binding partner of ConA. We determined kinetic parameters of the effects of sugars on the dissociation of ConA from ASF quantitatively, and the structural requirements of the functional groups of sugars for binding with ConA. We found that the affinity of ConA for sugars is dependent on its conformation induced by interaction with the binding partner. In addition, the results showed that optical biosensor system is well mimics the interaction of ConA with sugars in biomembrane.     

Enantioselective analysis of melagatran via an LSPR biosensor integrated with a microfluidic chip

The impact of chiral compounds on pharmacological and biological processes is well known. With the increasing need for enantiomerically pure compounds, effective strategies for enantioseparation and chiral discrimination are in great demand. Herein we report a simple but efficient approach for the enantioselective determination of chiral compounds based on a localized surface plasmon resonance (LSPR) biosensor integrated with a microfluidic chip. A glass microfluidic chip with an effective volume of ～0.75 μL was fabricated for this application. Gold nanorods (AuNRs) with an aspect ratio of ～2.6 were self-assembled onto the surface of the inner wall of the chip to serve as LSPR transducers, which would translate the analyte binding events into quantitative concentration information. Human α-thrombin was immobilized onto the AuNR surface for enantioselective sensing of the enantiomers of melagatran. The proposed sensor was found to be highly selective for RS-melagatran, while the binding of its enantiomer, SR-melagatran, to the sensor was inactive. Under optimal conditions, the limit of detection of this sensor for RS-melagatran was found to be 0.9 nM, whereas the presence of 10?000-fold amounts of SR-melagatran did not interfere with the detection. To the best of our knowledge, this is the first demonstration of an LSPR-based enantioselective biosensor.