Competitive ELISA. In this technique, antibody is first incubated in solution with a sample containing antigen. The antigen-antibody mixture is then added to an antigen coated microtiter well.
The more antigen present in the sample, the less free antibody will be available to bind to the antigen-coated well. 
Addition of an enzyme-conjugated secondary antibody (Ab2) specific for the isotype of the primary antibody can be used to determine the amount of primary antibody bound to the well as in an indirect ELISA. 
In the competitive assay, however, the higher the concentration of antigen in the original sample, the lower the absorbance.

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#Unit 13. Methods in Biology

The total concentration of antibody in the equilibrium dialysis chamber is known, the equilibrium equation can be rewritten as:

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#Unit 13. Methods in Biology

Scatchard plots are based on repeated equilibrium dialyses with a constant concentration of antibody and varying concentration of ligand. 

If all antibodies have the same affinity, then a Scatchard plot yields a straight line with a slope of Ka. The x intercept is n, the valency of the antibody, which is 2 for IgG and other divalent Igs. For IgM, which is pentameric, n  10, and for dimeric IgA, n  4. In this graph, antibody #1 has a higher affinity than antibody #2. .  

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#Unit 13. Methods in Biology

If the antibody preparation is polyclonal and has a range of affinities, Scatchard plot yields a curved line whose slope is constantly changing. The average affinity constant K0 can be calculated by determining the value of Ka when half of the binding sites are occupied (i.e., when r  1 in this example). In this graph, antiserum #3 has a higher affinity (K0  2.4  108) than antiserum #4 (K0  1.25  108)

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#Unit 13. Methods in Biology

The bacterium Streptococcus pyogenes, for example, expresses cell-wall proteins called M antigens. Antibodies produced to streptococcal M antigens have been shown to cross-react with several myocardial and skeletal muscle proteins and have been implicated in heart and kidney damage following streptococcal infections. 

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#Unit 13. Methods in Biology

Glycosphingolipids as determinants of blood groups

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#Unit 13. Methods in Biology

Antibody and soluble antigen interacting in aqueous solution form a lattice that eventually develops into a visible precipitate. Antibodies that aggregate soluble antigens are called precipitins.