Solid-phase Displacement Research Articles

Dissociation Rate Kinetics in a Solid-Phase Flow Immunoassay

Solid-phase displacement assays allow extremely fast analyses when performed under continuous flow conditions. Continuous dissociation of labeled antigen from the immobilized saturated antibodies occurs even in the absence of competing unlabeled antigen. This spontaneous dissociation creates more unoccupied antibody binding sites which affect the magnitude of the signal generated. In order to evaluate the impact of this phenomenon in more detail, we extended the law of mass action to solid-phase binding assays and analyzed the dissociation kinetics of labeled antigen under continuous flow conditions. The effect of the flow on the dissociation kinetics was determined by calculation of the apparent dissociation rate constants (kd) which increase with an increase in the flow rate. These dissociation rate constants are approximately 20- to 30-fold lower than those obtained from displacement studies (i.e., in the presence of competing unlabeled antigen). The difference in the dissociation rate constants obtained in the two studies is most likely a function of the degree of reassociation. The results of this study provide a basis for better understanding antibody kinetics at solid-liquid interfaces under flow conditions.

Assessment of heterogeneity in antibody-antigen displacement reactions.

The intrinsic binding characteristics of monoclonal antibodies are modified upon immobilization onto a solid-phase matrix. Factors such as the distribution in affinity must therefore be taken into consideration in order to predict the kinetics of antibody binding at solid-liquid interfaces. A mathematical analysis is presented herein that allows the assessment of heterogeneity in the affinity of monoclonal antibodies immobilized onto a solid support. This model is based on a modified version of the Sips distribution function adapted to the conditions of a solid-phase displacement assay in flow. An assay for trinitrotoluene (TNT) provides the data to evaluate the extent of heterogeneity introduced by immobilization of antibodies in a flow immunoassay. We determined the index of antibody heterogeneity on two solid supports, controlled-pore glass beads and agarose beads, coated with a monoclonal anti-TNT antibody at varying densities. The data confirm that the threshold for crossover from homogeneous to heterogeneous forms of the reaction isotherm is different in displacement reactions than in association-dissociation reactions. Our analysis shows that the measured displacement isotherm is consistent with a homogeneous or only moderately heterogenous distribution of relative affinities.

Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer

A closed-form analytic solution for the motion of axisymmetric rigid pellets suspended in a Newtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. The analysis is motivated by its possible relevance to the rheology of blood in the microcirculation wherein the endothelial-cell glycocalyx – a carbohydrate-rich coat of macromolecules consisting of proteoglycans and glycoproteins expressed on the luminal surface of the capillary wall – might exhibit similar behaviour to the wall layer modelled here. Estimates of the permeability of the glycocalyx are taken from experimental data for fibrinogen gels formed in vitro. In a tube without pellets lined with a porous wall layer having a thickness which is 15% of the tube radius and having a permeability in the range of fibrinogen gels, approximately a 70% greater pressure drop is required to achieve the same volume flow as would occur in an equivalent smooth-walled tube without a wall layer. If, in the presence of this same wall layer, a rigid spherical pellet is introduced which is 99.5% of the free-lumen radius, the apparent viscosity increases by as much as a factor of four with a concomitant reduction in tube hematocrit of about 10% relative to the corresponding values in an equivalent smooth-walled tube having the same sphere-to-tube diameter ratio without a wall layer.

Binding kinetics of immobilized antibodies in a flow immunosensor

Abstract This study investigates the binding kinetics of immobilized antibody in a solid-phase displacement immunosensor conducted in flow under nonequuilibrium conditions. The experimental system studied employs a monoclonal antibody, specific for cocaine and its metabolite, benzoylecgonine, immobilized onto agarose beads. After saturation of antibody binding sites with the fluorophore-induced antigen, fluorescein-cadaverine-benzoylecgonine, the system is placed in a buffer flow. Injection of unlabeled antigen caused displacement of proportional amounts of antibody-bound labelled antigen, which is detected downstream. Using a repetitive displacement technique, we have characterized the kinetics by determining the displacement efficiency and apparent dissociation constant at various flow rates and different antibody surface densities. The experiments were performed with several antigen concentrations to evaluate the reliability of the repetitive displacement technique. The amount of displaced labeled antigen was found to be a function of both the density of antibody-bound labeled antigen and the amount of injected unlabeled antigen. Upon repetitive sample injections, as exponential decrease of displaced labeled antigen is observed, corresponding to a similar decrease in the undissociated fraction. Further kinetics analysis reveals that the displacement efficiency is dependent on the flow rate and the antibody surfacedensity. The antibody immobilized at low density is much more sensitive to changes in the flow rate than the antibody immobilized at high density, as indicated by the decrease in the displacement efficiency and increase in the apparent dissociation constant ( k d ) with the increase in flow rate.

Effect of antibody density on the displacement kinetics of a flow immunoassay

This study investigates the effect of antibody density on the kinetics of a solid-phase displacement immunoassay. Conducted in flow under nonequilibrium conditions, the assay utilizes a monoclonal antibody to the cocaine metabolite benzoylecgonine, which has been immobilized onto Sepharose beads and saturated with fluorophorelabeled antigen. Displacement of antibody-bound labeled antigen by non-labeled antigen occurs when sample is introduced in the buffer flow. Comparison of matrices coated with two different antibody densities revealed that the displacement efficiency is a function of the density of antibody-bound labeled antigen. A higher density of antibody provides a higher amount of displaced labeled antigen, but the displacement efficiency of the assay is decreased. The effect of antibody density on the immunoassay kinetics was analyzed using a mathematical formulation developed to characterize antibody-antigen interactions at solid-liquid interfaces. Higher antibody density proved to be associated with a lower apparent dissociation rate constant. The implications of these results on the design of immunassays in flow are discussed.

A mixed‐penalty finite element formulation of the linear biphasic theory for soft tissues

AbstractHydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed‐penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six‐node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six‐node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six‐node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed‐penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.

Effects of Friction on the Unconfined Compressive Response of Articular Cartilage: A Finite Element Analysis

A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.

Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissues

A finite element formulation of the linear biphasic model for articular cartilage and other hydrated soft tissues consisting of an incompressible, inviscid fluid phase and an incompressible solid phase is presented. The Galerkin weighted residual method is applied to the momentum equation and mechanical boundary conditions of both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via penalty method. The resulting weak form is expressed in terms of the solid phase displacements and fluid phase velocities, which are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. In the limiting case of steady permeation (no solid displacement) the penalty method is shown to produce L 2 convergence of both the pressure field and the fluid velocity field. In contrast, it is known that the limiting case of an incompressible solid (no fluid flow) yields H 1 convergence of the solid phase displacement. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problems of a cylindrical specimen of soft tissue in confined and perfectly lubricated unconfined compression, for which independent analytical solutions are available. The effects of mesh size and mesh distortion, solution parameters such as penalty number and time step size, and platen-specimen friction for the unconfined compression problem are evaluated.

Axial displacement of solid phase in a contained fluidized bed

Thermal labeling has been used to examine axial heat transport (solid-phase transport) in a fluidized bed with low-volume packing for columns of diameters 15, 30, and 70 cm.