9780521516358book.pdf

and secondly that there is cooperativity in binding within a single population. In both

cases the Scatchard plot will be curvilinear (Fig. 17.4). If cooperativity is suspected, it

should be confirmed by aHill plotwhich, in its non-kinetic form, is:

log Y

1 Y



¼hlog½LŠlogKd ð 17 : 9 Þ

or

log

B

BmaxB



¼hlog½LŠlogKd

whereYis the fractional saturation of the binding sites (from 01) andhis theHill

constant.For a receptor with multiple binding sites that function independently

h¼1, whereas for a receptor with multiple sites which are interdependent,his either

greater than 1 (positive cooperativity) or less than 1 (negative cooperativity).

Scatchard plots that are biphasic due to ligandmultivalence(i.e. multiple binding

sites) rather than receptor cooperativity, are sometimes taken to indicate that the two

extreme, and approximately linear, sections of the curvilinear plots represent high

affinity (high bound/free ratio at low bound values) and low affinity (low bound/free

ratio at high bound values) sites and that tangents drawn to these two sections of the

curve can be used to calculate the associatedKdandBmaxvalues. This is incorrect, and

the correct values can only be obtained from the binding data by means of careful

mathematical analysis generally undertaken by the use of special computer programs

many of which are commercially available.

Determination of rate constants

To determine the dissociation rate constant,k 1 (units: time^1 ) of any ligand for the

receptor, some of the receptor–ligand complex (B 0 ) is allowed to form usually using

the ligand labelled with a radioactive isotope. The availability of the remaining

unoccupied receptors to the labelled ligand is then blocked by the addition of at least

100-fold excess of the unlabelled ligand or competitive antagonist and the rate of

release (Bt) of the radiolabelled ligand from its binding site monitored as a function of

time. This generally necessitates the separation of the bound and unbound fractions.

The rate is given by the expression:

dB 0

dt

¼k 1 B 0

and the equation governing the release by the expression:

Bt¼B 0 ek^1 t

hence:

logBt¼logB 0  2 : 303 k 1 t ð 17 : 10 Þ

Thus a plot of logBtagainst time will give a straight line with a slope of –2.303k 1

allowingk 1 to be estimated.

674 Cell membrane receptors and cell signalling