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Example 1(cont.)

Answer To address this problem it is first necessary to calculate the specific binding of

the ligand to the receptor (Bs). The use of a large excess of unlabelled competitive

antagonist enables the non-specific binding to be measured. The difference between

this and the total binding gives the specific binding. Once this is known, various

graphical options are open to evaluate the data. The simplest is a plot of the specific

ligand binding as a function of the total ligand binding. More accurate methods are

those based on linear plots such as a Scatchard plot (equation 17.4) and a

Lineweaver–Burk plot (equation 17.7). In addition, it is possible to carry out a Hill

plot (equation 17.9) to obtain an estimate of the Hill constant,h. The derived data for

each of these three plots are shown in the following table:

[Ligand] (nM)

40 60 80 120 200 500 1000 2000

Total bound ligand

(pmol 10^6 cells)

0.284 0.365 0.421 0.547 0.756 1.269 2.147 2.190

Non-specific binding

(Bns) (pmol 10^6 cells)

0.054 0.068 0.084 0.142 0.243 0.621 1.447 1.460

Specific binding (Bs)

(pmol 10^6 cells)

0.230 0.297 0.337 0.405 0.513 0.648 0.700 0.730

Bs/[L] 103

(dm^310 ^6 cells)

5.75 4.95 4.21 3.37 2.56 1.30 0.70 0.43

1/[Bs] (pmol 10^6

cells)^1

4.35 3.37 2.97 2.47 1.95 1.54 1.43 1.37

1/[L] (nM)^1 0.0250 0.0170 0.0125 0.0083 0.0050 0.0020 0.0010 0.0005

(Bmax–Bs)

(pmol 10^6 cells)

0.52 0.45 0.413 0.345 0.237 0.102 0.050 0.020

Bs/(Bmax–Bs) 0.44 0.66 0.816 1.174 2.164 6.35 14.00 36.50

logBs/(Bmax–Bs) 0.356 0.180 0.088 0.070 0.335 0.803 1.146 1.562

log [L] 1.60 1.78 1.90 2.08 2.30 2.70 3.00 3.30

The hyperbolic plot allows an estimate to be made of the maximum ligand binding,

Bmax. It is approximately 0.75 pmoles 10^6 cells. An estimate can then be made ofKd

by reading the value of [L] that gives a ligand binding value of 0.5Bmax(0.375

pmoles 10^6 cells). It gives an approximate value forKdof 100 nM.

A Scatchard plot obtained by regression analysis gives a correlation coefficient,r,

of 0.996,Bmaxof 0.786 pmoles 10^6 cells andKdof 97.3 nM. A Lineweaver–Burk

plot gives a correlation coefficient,r,of 0.998,Bmaxof 0.746 pmoles 10^6 cells and

Kdof 90.5 nM. Note that there is some variation between these three sets of

calculated values and the ones given by the Lineweaver–Burk plot are more likely to

be correct since, as previously pointed out, the Scatchard plot overestimates both

values when the binding data are subjected to linear regression analysis.

The Hill plot based on a value ofBmaxof 0.75 pmoles 10^6 cells, gave a correlation

coefficient of 0.998 and a value for the slope of 1.13. This is equal to the Hill constant,h.

676 Cell membrane receptors and cell signalling