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The association rate constant,kþ 1 (units: M^1 time^1 ), is best estimated by the

approach to equilibrium methodby which the extent of agonist binding is monitored

continuously until equilibrium is reached under conditions that are such that [L]>>

[Rt] (this gives pseudo first-order conditions rather than second order; under these

conditions [Rt] decreases with time but [L] remains constant.) Ligand binding increases

asymptotically such that:

log

Beq

BeqBt



¼ 2 : 303 ðkþ 1 ½LŠþk 1 Þt ð 17 : 11 Þ

Thus a plot of logBeq/(Beq–Bt) against time will be linear with a slope of 2.303(kþ 1 [L]þ

k 1 ) whereBeqandBtare the ligand binding at equilibrium and timetrespectively.

From knowledge ofk 1 (obtained by the method discussed above) and [L], the value of

kþ 1 can be calculated from the slope.

TheKdvalues observed for a range of receptors binding to their physiological

agonist are in the range 10^6  10 ^11 M, which is indicative of a higher affinity than

is typical of enzymes for their substrates. The correspondingkþ 1 rate constants are in

the range 10^5  108 M^1 min^1 andk 1 in the range 0.0010.5 min^1. Studies with

G-protein-coupled receptors that form a tertiary complex (AR*G) have shown that the

tertiary complex has a higher affinity for the agonist than has the binary complex

(AR*). Receptor affinity for its agonist is also influenced by receptor interaction with

various adaptor protein molecules present in the intracellular cell membrane. This is

discussed more fully later.

It is relatively easy to calculate the number of receptors on cell membranes from

binding data. The number is in the range 10^3 –10^6 per cell. Although this may appear

Example 1ANALYSIS OF LIGAND-BINDING DATA

Question The extent of the binding of an agonist to its membrane-bound receptor on intact
cells was studied as a function of ligand concentration in the absence and presence
of a large excess of unlabelled competitive antagonist. In all cases the extent of total
ligand binding was such that there was no significant change in the total ligand
concentration. What quantitative information about the binding of the ligand to the
receptor can be deduced from this data?

[Ligand] (nM)

40 60 80 120 200 500 1000 2000

Total ligand bound

(pmoles 10^6 cells)

0.284 0.365 0.421 0.547 0.756 1.269 2.147 2.190

Ligand binding in presence

of competitive antagonist

(pmoles 10^6 cells)

0.054 0.068 0.084 0.142 0.243 0.621 1.447 1.460

675 17.2 Quantitative aspects of receptor–ligand binding