Ammonium sulphate precipitation (Farr assay)

3.1.3 Ammonium sulphate precipitation (Farr assay)

Determination of antibody affinity can be simplified and speeded up by using precipitation. Tests based on secondary mechanisms, such as precipitation, do not necessarily measure the degree of primary binding of antigen to antibody, as although antigen–antibody interactions occur for all proportions of antigen and antibody, in the region of antibody excess there is very little precip- itate; the complexes form but remain soluble. Techniques such as the Farr assay were designed to overcome these problems and so are more direct measures of the primary binding reaction.

The basis of Farr assay is as follows: ammonium sulphate is added to diluted serum to 50% saturation, and most of the immunoglobulin is precipitated, while other serum proteins such as albumin, remain in solution. Antigen, e.g. albumin, is radiolabelled and allowed to react with antibody, generally in antigen excess, so that soluble complexes are formed. An equal volume of saturated ammonium sulphate is added and all the immunoglobulin is precipitated. Only anti- gen complexed with antibody is precipitated under these conditions. The precipitates are washed with 50% saturated ammonium sulphate solution to remove any free antigen and their radio- active content determined. The amount of radioactivity in the precipitate is proportional to the amount of antigen bound by the antibody, and so results are expressed in terms of the antigen- binding capacity per ml of serum.

For accurate determinations, the results need to be calculated to the same degree of antigen excess for each antiserum. Therefore, in the original form of the assay, constant amounts of anti- gen are added to a series of dilutions of serum and the antigen-binding capacity determined at each dilution. By convention, all results are calculated on the 33% end-point, i.e. the dilution of serum that binds 33% of the added antigen. For many purposes a simpler assay can be used at a single antiserum dilution.

Determination of antigen-binding capacity

MATERIALS AND EQUIPMENT Radiolabelled 125 I-albumin (2 mg/ml), specific activity 5–30 × 10 5 Bq/mg protein Test anti-albumin sera, diluted 1 : 10 with phosphate-buffered saline (PBS) Control serum diluted 1 : 10, to determine background binding Saturated ammonium sulphate solution (Section 1.1.2) Gamma spectrometer

3.1DETERMINATION OF ANTIBODY AFFINITY

Protocol. Tube number (in duplicate) Solution to be added

1 2.................... n

Serum diluted 1 : 10 with PBS

0 20 µl⎯⎯⎯⎯⎯⎯⎯⎯⎯→ 125 I-albumin, 2 mg/ml

100 µl⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ Incubate and then add:

PBS

0 400 µl⎯⎯⎯⎯⎯⎯⎯⎯⎯ → Saturated ammonium sulphate

0 520 µl⎯⎯⎯⎯⎯⎯⎯⎯⎯ →

Repeat for each test antiserum and normal serum control. PBS, phosphate-buffered saline.

METHOD

1 Add 20 µl of each diluted serum to tubes, preferably in duplicate (see Protocol).

2 Add 100 µl of 125 I-albumin to each tube. Cap the duplicate tubes labelled number 1; these are for determining the c.p.m. in the original aliquot.

3 Incubate with occasional shaking at 37°C for 2 h, then 2 h in the cold at 4°C.

4 Add 400 µl PBS to each test tube.

5 Add an equal volume (520 µl) of saturated ammonium sulphate solution to each tube, mix rapidly and thoroughly. Allow to stand for 15 min.

6 Spin at 3000 g for 10 min.

7 Remove and discard the supernatant.

8 Wash precipitate twice with 50% saturated ammonium sulphate solution by centrifugation.

9 After removing final wash supernatant, count the precipitate and the tubes labelled 1 (containing 125 I-albumin alone) in a g spectrometer.

Calculation of results

no. c.p.m. in 100 µ l × 10

Specific activity of albumin c.p.m./µg =

protein concentration ( g/ml) µ

Antigen content of precipitate no. c.p.m. of antiserum precipitate no. c.p.m. of normal serum precipitate −

= specific activity of the albumin

Antigen-binding capacity/ml of serum = antigen content of precipitate × 50 × original serum dilution.

The antigen-binding capacity is expressed as µg albumin bound/ml original serum. TECHNICAL NOTES

• Specific activity is quoted in Bq rather than c.p.m./mg as this enables standardization. Determination of c.p.m. depends upon the efficiency of the counting equipment and so would vary from laboratory to laboratory.

78 C H A P T E R 3: Antibody interactions with antigens

• For demonstration purposes, the incubation times in step 3 above may be reduced to 15 min at 37°C and 30 min on ice, and still yield useful data. • With some antigens it is necessary to use precipitating agents other than ammonium sulphate

to ensure that the antigen remains in solution unless bound to antibody. A mixture of ethanol and ammonium acetate has been found useful for several assays of antibody binding to hormones, and polyethylene glycol (PEG) for peptide and immunoglobulin antigens. A neat adaptation utilizes PEG, in which labelled C1q is soluble, to precipitate and detect immune complexes binding to the labelled C1q (see also June et al. 1979).

• The technique can be modified to yield qualitative as well as quantitative information. With

ammonium sulphate each immunoglobulin isotype is precipitated; however, it is possible to induce selective precipitation by adding an excess of anti-isotype serum. For example, anti-IgG precipitation of IgG antibodies would allow the determination of the antigen-binding capacity of this isotype in a polyclonal serum. This can be repeated with specific antisera for each class and subclass. The response in the different classes is found to differ markedly with different immunization schedules.

Ammonium sulphate precipitation for determining antibody affinity

Determination of antibody affinity can be simplified by using a variation of the Farr assay. A con- stant amount of antibody is reacted with increasing concentrations of antigen and left to equi- librate. The concentration of bound antigen is detected in the complex after ammonium sulphate precipitation and the concentration of free antigen determined in the supernatant. If the recip- rocal of bound antigen is plotted against the reciprocal of the free antigen concentration and the line extrapolated to 1/[Ag] = 0, the reciprocal of the bound antigen will equal the reciprocal of the total antibody-combining sites.

MATERIALS AND EQUIPMENT Radiolabelled antigen, e.g. 125

I human serum albumin (HSA)

Antiserum, e.g. anti-HSA Normal serum, as control Saturated ammonium sulphate solution Conical centrifuge tubes, 0.4 ml capacity Beckman 152 microfuge (or equivalent) Gamma spectrometer

Protocol.

Tube number

Antiserum or control serum

50 µl ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ PBS

3.1DETERMINATION OF ANTIBODY AFFINITY

METHOD

1 Set up 16 tubes (eight each for antiserum and normal control serum) as shown in the Protocol.

2 Mix the contents of the tubes thoroughly and incubate for 1 h at room temperature.

3 Add 0.2 ml saturated ammonium sulphate solution and mix immediately.

4 Incubate for 1 h at room temperature.

5 Spin the tubes at 10 000 g for 5 min.

6 Remove and keep 0.1 ml of supernatant.

7 Wash each precipitate twice with 50% saturated ammonium sulphate.

8 Determine the c.p.m. of radioactivity in the supernatant samples and precipitates using a g spectrometer.

Data required Free antigen concentration = total radioactivity (c.p.m.) in the supernatant, i.e. radioactivity

in 100 µl sample from step 6 multiplied by 4. Bound antigen concentration = (c.p.m. antiserum precipitate – c.p.m. control precipitate), for each antigen concentration.

Calculation of results All the values should be expressed as molar concentrations; 1 pmol HSA = 0.068 µg.

1 Record and calculate the results as in Table 3.1(a,b).

2 Plot 1/b (column 9) against 1/[Ag] (column 10). Extrapolate the graph line to 1/[Ag] = 0, i.e. the intercept on the 1/b axis: this is the value of 1/[Ab t ].

3 Use the value for [Ab t ] to calculate the values shown in Table 3.1(b).

4 From Table 3.1(b) plot: log b

(column 3) against log[Ag] (column 4). Ab t − b The intercept on the log[Ag] axis, i.e. when

log b = 0 [ Ab t ] − b equals 1/K, therefore:

1 K= [ Ag ]

The units of K are litres per mole. Low-affinity antibodies have K values around 10 5 l/mol, whereas high-affinity antibodies

often have K values of 10 12 l/mol or more.

TECHNICAL NOTES • Errors always occur during the washing of precipitates, particularly as dissociation may take

place on removal of the free antibody and free antigen. A procedure to avoid this has been introduced using radioactive sodium as a buffer tracer. This is described below.

• There has been discussion as to how quickly the addition of ammonium sulphate freezes the equilibrium. Most authors assume that this is immediate and so calculate the concentrations,

80 C H A P T E R 3: Antibody interactions with antigens

Table 3.1(a) Table for calculation of Ab t

Column number

1 2 3 4 5 6 7 8 9 10 µg

c.p.m. in

c.p.m.

c.p.m.

Tube albumin pmoles of

Moles of Ag

Moles of

no. per tube albumin

free [Ag]

bound ( b)

free Ag

1/ b 1/[Ag]

1 2.5 1 pmole =

c.p.m. col. 4 –

c.p.m. col. 6

c.p.m. col. 3

Reciprocal Reciprocal

2 5 0.068 µg

c.p.m. col. 5

÷ SA

÷ SA

of col. 7 of col. 8

8 320 * Specific activity (SA) of antigen =

c.p.m. molar concentration of antigen .

Table 3.1(b) Table for calculation of K Column number

1 2 3 4 pmoles of

b Log

Tube no. antigen [ Ab t ] − b [ Ab t ] − b Log[ Ag]

Log 10 col. 2

Log 10 free antigen

2 concentration, i.e.

3 log col. 8, Fig. 3.1a.

at equilibrium, on the volumes prior to adding ammonium sulphate, but it has been suggested that calculating the concentration on the basis of the volume after adding the precipitating agent is more accurate.

• It must be recognized that the high salt concentrations used to precipitate the immunoglobulin may also dissociate some of the complexes, particularly those involving low-affinity antibodies. The use of polyethylene glycol as a precipitating agent avoids this problem.