Theoretical assessments of errors in rapid immunoassays-how critical is the exact timing and reagent concentrations?

The reliability of rapid immunoassay is a concern due to an incomplete incubation to a non-equilibrium state and is susceptible to different error factors causing variance. The most critical point in the process should be found in order to improve the accuracy, and reproducibility of immunoassays, and enhance the system robustness. In this paper, the behavior of rapid assays is predicted by simulations using mechanistic assay model, based on antibody-analyte binding reaction kinetics. This antibody-analyte binding reaction kinetics model was constructed for a generic three-component (immunometric) assay and the parameters were chosen to be those of a known surface binding assay. The effects of the exact incubation timing and the initial reagent concentrations were studied focusing on the early phase of incubation, the non-equilibrium state. The magnitudes of errors in the input parameters were estimated using knowledge from practical immunoassays. According to simulations, inaccurate incubation timing adds error in the results at very short incubation times, especially in low analyte concentrations. The inaccurate reagent concentrations increase variance at short incubation times, as well. The error decreases rapidly after the first few minutes of incubation.     

Modelling of multi-component immunoassay kinetics — A new node-based method for simulation of complex assays

The behaviour of binding reactions in immunoassays can be predicted and studied by modelling methods. Simple antibody-analyte binding reaction kinetics can be simulated by e.g. a mechanistic assay model based on differential equations. However, the mathematical modelling becomes more complicated if multivalent-structured components are involved and the number of binding complexes increases.In this paper, a new node-based method to model complex binding reactions is introduced. The principle of this method is to construct a network of the initial components, reaction intermediates and end-products by forming a network of nodes. This network is then solved, node by node, breaking the initial problem into smaller partial problems, still obeying the laws of chemical reaction kinetics and without ignoring any parts of the problem.This method provides an easy and quick way to study complex binding reactions since simulation networks are simple to construct directly from the reaction scheme. This presented new “NODE”-method is compared with the well known mechanistic assay model.     

Calculating the probability of detection for inhibitors in enzymatic or binding reactions in high-throughput screening

In high-throughput screening (HTS) for drug candidates from a library containing tens of thousands to millions of chemical compounds, one problem is assessing the sensitivity of an assay for detecting compounds with a particular potency. For example, when looking for inhibitors of an enzyme, what is the potency of an inhibitor that will be readily detected by an enzyme inhibition assay? Similarly, when assessing compounds that inhibit binding between receptors and ligands or similar molecule-to-molecule interactions, what potency of an inhibitor will be readily detected? In this article, the well-established concepts of Michaelis-Menten kinetics and Langmuir binding isotherms are combined with fundamental statistical principles to yield a measure of assay sensitivity. The approach is general and can be modified to accommodate situations where the reaction kinetics is known to be more complicated than situations described by the Michaelis-Menten and Langmuir equations. The calculations presented take into account the concentration of inhibitor used, the variability of the assay, the relationship between the K(m) or K(d) of the reaction and the substrate or ligand concentration used, the threshold or cutoff value used for determining "hits," and the number of replicates used in screening.     

Factor Xa active site substrate specificity with substrate phage display and computational molecular modeling

Structural origin of substrate-enzyme recognition remains incompletely understood. In the model enzyme system of serine protease, canonical anti-parallel beta-structure substrate-enzyme complex is the predominant hypothesis for the substrate-enzyme interaction at the atomic level. We used factor Xa (fXa), a key serine protease of the coagulation system, as a model enzyme to test the canonical conformation hypothesis. More than 160 fXa-cleavable substrate phage variants were experimentally selected from three designed substrate phage display libraries. These substrate phage variants were sequenced and their specificities to the model enzyme were quantified with quantitative enzyme-linked immunosorbent assay for substrate phage-enzyme reaction kinetics. At least three substrate-enzyme recognition modes emerged from the experimental data as necessary to account for the sequence-dependent specificity of the model enzyme. Computational molecular models were constructed, with both energetics and pharmacophore criteria, for the substrate-enzyme complexes of several of the representative substrate peptide sequences. In contrast to the canonical conformation hypothesis, the binding modes of the substrates to the model enzyme varied according to the substrate peptide sequence, indicating that an ensemble of binding modes underlay the observed specificity of the model serine protease.     

Measurement of mass transport and reaction parameters in bulk solution using photobleaching. Reaction limited binding regime.

Fluorescence recovery after photobleaching (FRAP) has been used previously to investigate the kinetics of binding to biological surfaces. The present study adapts and further develops this technique for the quantification of mass transport and reaction parameters in bulk media. The technique's ability to obtain the bulk diffusion coefficient, concentration of binding sites, and equilibrium binding constant for ligand/receptor interactions in the reaction limited binding regime is assessed using the B72.3/TAG-72 monoclonal antibody/tumor associated antigen interaction as a model in vitro system. Measurements were independently verified using fluorometry. The bulk diffusion coefficient, concentration of binding sites and equilibrium binding constant for the system investigated were 6.1 +/- 1.1 x 10(-7) cm2/s, 4.4 +/- 0.6 x 10(-7) M, and 2.5 +/- 1.6 x 10(7) M-1, respectively. Model robustness and the applicability of the technique for in vivo quantification of mass transport and reaction parameters are addressed. With a suitable animal model, it is believed that this technique is capable of quantifying mass transport and reaction parameters in vivo.     

Investigation of the UDP-glucose dehydrogenase reaction for a coupled assay of UDP-glucose pyrophosphorylase activities.

An optimized coupled enzyme assay for UDP-glucose pyrophosphorylase (EC 2.7.7.9) using UDP-glucose dehydrogenase (EC 1.1.1.22) is presented. This optimized assay was developed by a detailed investigation of the kinetics of the UDP-glucose dehydrogenase reaction. In addition the data provide a basis for the enzymatic synthesis of UDP-glucuronic acid. The results demonstrate that the two binding sites of the dehydrogenase differ since a different modulation of the enzyme activity and stability is observed after preincubation with UDP-glucose or NAD+ at various pH values. This is of general interest for the preparation of assay mixtures where UDP-glucose dehydrogenase is used as an auxiliary enzyme.     

Adhesion frequency assay for in situ kinetics analysis of cross-junctional molecular interactions at the cell-cell interface

The micropipette adhesion assay was developed in 1998 to measure two-dimensional (2D) receptor-ligand binding kinetics. The assay uses a human red blood cell (RBC) as adhesion sensor and presenting cell for one of the interacting molecules. It employs micromanipulation to bring the RBC into contact with another cell that expresses the other interacting molecule with precisely controlled area and time to enable bond formation. The adhesion event is detected as RBC elongation upon pulling the two cells apart. By controlling the density of the ligands immobilized on the RBC surface, the probability of adhesion is kept in mid-range between 0 and 1. The adhesion probability is estimated from the frequency of adhesion events in a sequence of repeated contact cycles between the two cells for a given contact time. Varying the contact time generates a binding curve. Fitting a probabilistic model for receptor-ligand reaction kinetics to the binding curve returns the 2D affinity and off-rate. The assay has been validated using interactions of Fcγ receptors with IgG Fc, selectins with glycoconjugate ligands, integrins with ligands, homotypical cadherin binding, T cell receptor and coreceptor with peptide-major histocompatibility complexes. The method has been used to quantify regulations of 2D kinetics by biophysical factors, such as the membrane microtopology, membrane anchor, molecular orientation and length, carrier stiffness, curvature, and impingement force, as well as biochemical factors, such as modulators of the cytoskeleton and membrane microenvironment where the interacting molecules reside and the surface organization of these molecules. The method has also been used to study the concurrent binding of dual receptor-ligand species, and trimolecular interactions using a modified model. The major advantage of the method is that it allows study of receptors in their native membrane environment. The results could be very different from those obtained using purified receptors. It also allows study of the receptor-ligand interactions in a sub-second timescale with temporal resolution well beyond the typical biochemical methods. To illustrate the micropipette adhesion frequency method, we show kinetics measurement of intercellular adhesion molecule 1 (ICAM-1) functionalized on RBCs binding to integrin α(L)β(2) on neutrophils with dimeric E-selectin in the solution to activate α(L)β(2).     

Extracting kinetic rate constants from surface plasmon resonance array systems

Surface plasmon resonance imaging systems, such as Flexchip from Biacore, are capable of monitoring hundreds of reaction spots simultaneously within a single flow cell. Interpreting the binding kinetics in a large-format flow cell presents a number of potential challenges, including accounting for mass transport effects and spot-to-spot sample depletion. We employed a combination of computer simulations and experimentation to characterize these effects across the spotted array and established that a simple two-compartment model may be used to accurately extract intrinsic rate constants from the array under mass transport-limited conditions. Using antibody systems, we demonstrate that the spot-to-spot variability in the binding kinetics was <9%. We also illustrate the advantage of globally fitting binding data from multiple spots within an array for a system that is mass transport limited.     

Lipase kinetics: hydrolysis of triacetin by lipase from Candida cylindracea in a hollow-fiber membrane reactor

The aptitude of a hollow-fiber membrane reactor to determine lipase kinetics was investigated using the hydrolysis of triacetin catalyzed by lipase from Canadida cylindracea as a model system. The binding of the lipase to the membrane appears not to be very specific (surface adsorption), and probably its conformation is hardly altered by immobilization, resulting in an activity comparable to that of the enzyme in its native form. The reaction kinetics defined on the membrane surface area were found to obey Michaelis-Menten kinetics. The specific activity of the lipase in the membrane reactor was found to be significantly higher than in an emulsion reactor. The activity and stability of the enzyme immobilized on a hydrophilic membrane surface seem not to be influenced significantly by the choice of the membrane material. The hollow-fiber membrane reactor is a suitable tool to assess lipase kinetics in a fast and convenient way.     

Cytochrome c and c2 binding dynamics and electron transfer with photosynthetic reaction center protein and other integral membrane redox proteins

To further the understanding of the details of c-type cytochrome action as a redox carrier between major electron-transfer proteins, the single-turnover kinetics time course of cytochrome c and cytochrome c2 oxidation by flash-activated photosynthetic reaction center (purified from the bacterium Rhodobacter sphaeroides) has been examined under a wide variety of conditions of concentration, ionic strength, and viscosity with reaction center present in detergent dispersion and phosphatidylcholine proteoliposomes. We find that the three-state model proposed by Overfield and Wraight [Overfield, R. E., & Wraight, C. A. (1980) Biochemistry 19, 3322-3327] is generally sufficient to model the kinetics time course; many similarities are found with the cytochrome c-cytochrome c oxidase interaction in mitochondria. Further, we find the following: (1) Significant "product inhibition" by oxidized cytochrome c (c2) bound to the reaction center is apparent. (2) The viscosity sensitivity of the electron transfer into the reaction center from bound cytochrome c (c2) suggests a physical interpretation of the distal state. (3) The exchange dynamics of oxidized and reduced cytochrome c (c2) are similar regardless of the state of activation of the reaction center. (4) Preferential binding of the oxidized form of cytochrome c is revealed upon reconstitution of the reaction center into neutral lipid vesicles, permitting an independent confirmation of the binding suggested by the kinetics. (5) Flash-activated electron-transfer kinetics in reaction center hybrid protein systems have shown that diffusion and competitive binding characterize the behavior of cytochrome c as a redox carrier between the reaction center protein and either the cytochrome bc1 complex or the cytochrome c oxidase.     

The kinetics of E. coli RNA polymerase.

Using an assay specific for chain elongation of E. coli RNA polymerase the kinetics of this propagation reaction have been studied. The kinetic behaviour is consistent woth the mathematical model formulated for this multisubstrate enzyme. The effect of increasing salt concentration on the kinetics of the reaction indicated that DNA unwinding is probably a necessary step in the propagation step, although this may not be the rate limiting step under all conditions.     

Interaction of cisplatin and DNA-targeted 9-aminoacridine platinum complexes with DNA

Interaction of acridine- and 9-aminoacridinecarboxamide platinum complexes with DNA was investigated with respect to their DNA sequence specificity and kinetics of binding. The DNA sequence specificity of the compounds was quantitatively analyzed using a polymerase stop assay with the plasmid pUC19. The 9-aminoacridinecarboxamide platinum complexes exhibited a different sequence specificity to that of cisplatin, shifted away from runs of consecutive guanines (the main binding site for cisplatin). This alteration was dependent on chain length. Shorter chain length compounds (n = 2, 3) showed a greater difference in sequence specificity, while longer chain length compounds (n = 4, 5) more closely resembled cisplatin. An acridinecarboxamide platinum complex showed a similar sequence specificity to cisplatin, revealing that the major change of sequence specificity was due to the presence of the 9-amino substituent. A linear amplification system was used to investigate the time course of the reaction. The presence of an intercalating group (acridinecarboxamide or 9-aminoacridinecarboxamide) greatly increased the rate of reaction with DNA; this is proposed to be due to a different reaction mechanism with DNA (direct displacement by the N-7 of guanine).     

Modeling micropatterned antigen-antibody binding kinetics in a microfluidic chip

The reaction kinetics of antigen-antibody binding in the electrokinetically controlled microfluidic heterogeneous immunoassays has been investigated by numerical simulations. A two-dimensional computational model was employed to include the mass transport (convection and diffusion) and binding reaction between the antigen in the bulk flow and the immobilized antibody at the channel surface. The influence of the bulk velocity, the concentrations of the antibody and antigen, and the geometry of the microchips was studied for a variation of conditions and the guidance for designing of microfluidic immunoassay was provided. The model also shows that electrokinetically driven immunoassays have better reaction kinetics than pressure-driven ones, resulting from the plug-like velocity profile. Finally, a multi-patch immunoassay chip was analyzed and the reaction kinetics was optimized by rearranging the reaction patches at the channel surfaces.     

The kinetics of binding of serum lipoproteins by immobilized heparin.

A model arterial system of heparin immobilized on an agarose gel was used to study the amount and kinetics of binding of porcine serum lipoproteins to heparin. Binding occurred to lipoproteins in the density range 1.006 less than d less than 1.062, but there was no binding with high density lipoprotein. A theoretical model of the kinetic experiments was formulated and used to demonstrate that the rate of the binding reaction could be considered instantaneous relative to the rate of transport of lipoproteins. Extrapolation of these results to arterial levels of glycosaminoglycans and lipoprotein indicate that complexes of lipoprotein and the glycosaminoglycans could account for much of the cholesterol entrapment in atherosclerotic lesions.     

Mathematical modeling the kinetics of cell distribution in the process of ligand-receptor binding

A statistical approach is presented to model the kinetics of cell distribution in the process of ligand-receptor binding on cell surfaces. The approach takes into account the variation of the amount of receptors on cells assuming the homogeneity of monovalent binding sites and ligand molecules. The analytical expressions for the kinetics of cell distribution have been derived in the reaction-limited approximation. In order to demonstrate the applicability of the mathematical model, the kinetics of binding the rabbit, anti-mouse IgG with Ig-receptors of the murine hybridoma cells has been measured. Anti-mouse IgG was labeled with fluorescein isothiocyanate (FITC). The kinetics of cell distribution on ligand-receptor complexes was observed during the reaction process by real-time measuring of the fluorescence and light-scattering traces of individual cells with the scanning flow cytometer. The experimental data were fitted by the mathematical model in order to obtain the binding rate constant and the initial cell distribution on the amount of receptors.     

Kinetic study of a substrate cycle involving a chemical step: highly amplified determination of phenolic compounds

A kinetic analysis of a substrate cycle in which one of the two steps was substituted by a chemical reaction has been made. The model is illustrated by the amplified determination, in a continuous assay, of phenolic compounds at low concentrations using the enzyme tyrosinase and β-NADH to reduce the o-quinone product of catalytic activity. Progress curves corresponding to β-NADH disappearance were not linear and followed first-order kinetics. Knowledge of the kinetics of the reaction has allowed us to achieve detection limits as low as 50 nM in a simple 10-min assay. There is no analytical solution to the non-linear differential equation system that describes the kinetics of the reaction, therefore, computer simulations of its dynamic behaviour are also presented, good agreement with the experimental results being obtained. The method is applicable to the measurement of any other metabolite, and its amplification capacity as well as the simplicity of determining kinetic parameters enable it to be implemented in a bioreactor for automation purposes.     

Activation of D-tyrosine by Bacillus stearothermophilus tyrosyl-tRNA synthetase: 2. Cooperative binding of ATP is limited to the initial turnover of the enzyme

The activation of D-tyrosine by tyrosyl-tRNA synthetase has been investigated using single and multiple turnover kinetic methods. In the presence of saturating concentrations of D-tyrosine, the activation reaction displays sigmoidal kinetics with respect to ATP concentration under single turnover conditions. In contrast, when the kinetics for the activation reaction are monitored using a steady-state (multiple turnover) pyrophosphate exchange assay, Michaelis-Menten kinetics are observed. Previous investigations indicated that activation of l-tyrosine by the K233A variant of Bacillus stearothermophilus tyrosyl-tRNA synthetase displays sigmoidal kinetics similar to those observed for activation of d-tyrosine by the wild-type enzyme. Kinetic analyses indicate that the sigmoidal behavior of the d-tyrosine activation reaction is not enhanced when Lys-233 is replaced by alanine. This supports the hypothesis that the mechanistic basis for the sigmoidal behavior is the same for both d-tyrosine activation by wild-type tyrosyl-tRNA synthetase and activation of l-tyrosine by the K233A variant. The observed sigmoidal behavior presents a paradox, as tyrosyl-tRNA synthetase displays an extreme form of negative cooperativity, known as "half-of-the-sites reactivity," with respect to tyrosine binding and tyrosyl-adenylate formation. We propose that the binding of D-tyrosine weakens the affinity with which ATP binds to the functional subunit in tyrosyl-tRNA synthetase. This allows ATP to bind initially to the nonfunctional subunit, inducing a conformational change in the enzyme that enhances the affinity of the functional subunit for ATP. The observation that sigmoidal kinetics are observed only under single turnover conditions suggests that this conformational change is stable over multiple rounds of catalysis.     

Recognition Kinetics of Biomolecules at the Surface of Different-Sized Spheres

Bead-based assay is widely used in many bioanalytical applications involving the attachment of proteins and other biomolecules to the surface. For further understanding of the formation of a sphere-biomolecule complex and easily optimizing the use of spheres in targeted biological applications, it is necessary to know the kinetics of the binding reaction at sphere/solution interface. In our presented work, a simple fluorescence analysis method was employed to measure the kinetics for the binding of biotin to sphere surface-bound FITC-SA, based on the fact that the fluorescence intensity of FITC was proportionally enhanced by increasing the binding amount of biotin. By monitoring the time-dependent changes of FITC fluorescence, it was found that the binding rate constant of biotin to sphere surface-immobilized FITC-SA was much smaller than that of biotin to freely diffusing FITC-SA. This can be attributed to the decreased encounter frequency of the reaction pair, restricted motion of the attached biomolecule, and the weakened steric accessibility of the binding site. These factors would become more obvious when increasing the size of the sphere upon which the FITC-SA was immobilized. Additionally, the effect of nanoparticles on the diffusion-controlled bimolecular binding reaction was more evident than that on the chemical recognition-controlled binding reaction.     

Application of europium(III) chelate-dyed nanoparticle labels in a competitive atrazine fluoroimmunoassay on an ITO waveguide

We have demonstrated the use of an optical indium tin oxide (ITO) (quartz) waveguide as a new platform for immunosensors with fluorescent europium(III) chelate nanoparticle labels (Seradyn) in a competitive atrazine immunoassay. ITO as a solid surface facilitated the successful use of particulate labels in a competitive assay format. The limit of detection in the new nanoparticle assay was similar to a conventional ELISA. The effect of particle size on bioconjugate binding kinetics was studied using three sizes of bioconjugated particle labels (107, 304, and 396nm) and a rabbit IgG/anti-IgG system in a 96-well plate. A decrease in particle size resulted in faster binding but did not increase the assay sensitivity. Flux calculations based on the particle diffusivity prove that faster binding of the small particles in this study was primarily due to diffusion kinetics and not necessarily to a higher density of antibodies on the particle surface. The results suggest that ITO could make a good platform for an optical immunosensor using fluorescent nanoparticle labels in a competitive assay format for small molecule detection. However, when used in combination with fluorescent particulate labels, a highly sensitive excitation/detection system needs to be developed to fully utilize the kinetic advantage from small particle size. Different regeneration methods tested in this study showed that repeated washings with 0.1 M glycine-HCl facilitated the reuse of the ITO waveguide.