9780521516358book.pdf

In this case, a plot ofr/[L] againstrwill again be linear with a slope of1/Kdbut in

this case the intercept on thex-axis will be equal to the number of ligand-binding

sites,n, on the receptor.

Alternative linear plots to the Scatchard plot are:

Lineweaver–Burk plot

1

B¼

1

Bmaxþ

Kd

Bmax½LŠ ð^17 :^7 Þ

Hanes plot

½LŠ

B

¼ Kd

Bmax

þ ½LŠ

Bmax

ð 17 : 8 Þ

In practice, Scatchard plots are most commonly carried out although statistically

they are prone to error since the experimental variableBoccurs in both thexandy

terms so that linear regression of these plots overestimates bothKdandBmax. There is

a view that linear transformations of the three types above are all inferior to the non-

linear regression analysis of equation 17.2 since they all distort the experimental

error. For example, linear regression assumes that the scatter of experimental points

around the line obeys Gaussian distribution and that the standard deviation of the

points is the same. In practice this is rarely true and as a consequence values of the

slope and intercept are not the ‘best’ value. It can be seen from equation 17.2 that

when the receptor sites are half saturated, i.e.B¼Bmax/2, then [L]¼Kd. HenceKdwill

have units of molarity.

The derivation of equation 17.2 is based on the assumption that there is a single set

of homogeneous receptors and that there is no cooperativity between them in the

binding of the ligand molecules. In practice, two other possibilities arise namely that

there are two distinct populations of receptors each with different binding constants

(a)

(b)

(c)

(d)

r

__r

[L]

Fig. 17.4Scatchard plot for (a) a single set of sites with no cooperativity, (b) two sets of sites with no

cooperativity, (c) a single set of sites with positive cooperativity, and (d) a single set of sites with negative

cooperativity.

673 17.2 Quantitative aspects of receptor–ligand binding