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

Kinetic titration method in flow cytometry for quantification of cell receptors

For the quantitative determination of cell receptors by fluorescence flow cytometry, we proposed a new method, which takes into account the reaction kinetics. The binding reaction of the ligand with receptors begins after placing the cells in the ligand solution. In the proposed method, there are several samples with the same concentration of cells and different initial concentrations of fluorescently labeled ligand, and each sample is measured by a flow cytometer once at the time when the following condition is met: the product of the incubation time (cells with ligand) and the initial concentration of ligand is the same for all samples. The proposed approach eliminates disadvantages and combines advantages of both kinetic and titration methods for quantification of receptors on single cells without the use of traditional calibration fluorescent beads. Practical application of the method was demonstrated in quantification of CD8 and CD14 on peripheral blood human leukocytes. Particularly, we found decreased (by a factor of two) mean number of CD14 on monocytes and granulocytes in patients with atherosclerosis (treated in the hospital) compared to conditionally healthy donors, whereas no difference was found in the mean CD8 expression on leukocytes between the same patient and donor groups.

Calibration-free quantitative immunoassay by flow cytometry: Theoretical consideration and practical implementation for IgG antibody binding to CD14 receptors on human leukocytes

We propose a calibration-free method to determine the number of receptors per cell, as well as the direct and the reverse reaction rate constants for a single receptor. The method is based on the analysis of the temporal evolution of the cells mean fluorescent intensity measured by a flow cytometer during the ligand-receptor (antigen-antibody) binding under the conditions of their comparable concentrations. We developed the kinetic approach accounting both for the delay between the dilution and the measurement and for the practical duration of the measurement itself. The method was applied to determine thenumber of CD14 receptors on human blood mononuclear (granulocytes, monocytes, lymphocytes) cells of several donors. We also obtained the direct ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math> (5.6 ± 0.2) × 10⁷ M^-1 min^-1 ) and reverse ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mo>-</mml:mo></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math> (1.3 ± 0.2) × 10^-2 min^-1 ) rate constants of ligand-receptor interaction, and estimated the size of the binding site as b = 0.5 nm. The latter allows one to recalculate the rate constants for a different ligand, fluorescent label, medium viscosity, and/or temperature. The knowledge of the rate constants is essential for the calibration-free determination of the number of receptors per cell from a single kinetic curve of the cells mean fluorescence intensity.

Dynamic quantification of antigen molecules with flow cytometry

Traditional methods for estimating the number of expressed molecules, based on the detection of target antigens bound with fluorescently labeled antibodies, assume that the antigen-antibody reaction reaches equilibrium. A calibration procedure is used to convert the intensity of the fluorescence signal to the number of target molecules. Along with the different limitations of every calibration system, this substantially limits the applicability of the traditional approaches especially in the case of low affinity antibodies. We address this problem here with studies in which we demonstrate a new approach to the antigen molecule quantification problem. Instead of using a static calibration system, we analyzed mean fluorescence values over time by flow cytometry during antibody-antigen binding. Experimental data obtained with an LSRII cytometer were fitted by a diffusion-reaction mathematical model using the Levenberg-Marquardt nonlinear least squares curve-fitting algorithm in order to obtain the number of target antigen molecules per cell. Results were compared with the Quanti-BRITE calibration system. We conclude that, instead of using experiment-specific calibration, the value of the binding rate constant for each particular antibody-antigen reaction can be used to quantify antigen molecules with flow cytometry. The radius of CD8 antibody molecule binding site was found, that allows recalculating the binding rate constant for other conditions (different sizes of reagent molecules, fluorescent label, medium viscosity and temperature). This approach is independent of specially prepared calibration beads, antibody reagents and the specific dye and can be applied to both low and high affinity antibodies, under both saturating and non-saturating binding conditions. The method was demonstrated on a human blood sample dataset investigating CD8α antigen on T cells in stable binding conditions.

Characterization and Optimization of Gold Nanoparticle-Based Silver-Enhanced Immunoassays

Silver-enhanced nanoparticle-labeled immunoassays provide a simple, low-cost, and effective way of detecting antigens in dilute solutions. The physical mechanisms behind their operation, however, have not been fully investigated. We present a semiquantitative approach for optimizing sandwich nanoparticle immunoassays using an adsorption-controlled kinetic model. Primary antibodies were immobilized on a solid substrate to bind the target antigens in solution. An optical signal was measured by secondary labeling of antigens with gold nanoparticles and their enhancement by silver nucleation. The opacity of the silver-enhanced spots was quantified by densitometry. The selectivity of the sandwich immunoassays was adequately high, and antigen concentrations as low as 0.1 microg cm(-3) (4 ng total) were detected reproducibly. The role of mass transfer was investigated, and a model was developed to optimize the performance of immunoassays by correlating the opacities of silver spots to the concentration and incubation times of antigens and gold nanoparticles. The results could allow the development of more rapid and reliable nanoparticle immunoassays.