Signaling systems have evolved such that a rise in the level of extracellular signaling molecules induces a proportional response in the responding cell. For this to happen, the binding affinity (K_d value) of a cell-surface receptor for a signaling molecule must be large compared with the signaling molecule’s normal unstimulated level in the extracellular fluid, or in blood. We can see this principle in practice by comparing the levels of insulin present in the body and the K_d for binding of insulin to its receptor on liver cells, 1.4 × 10⁻¹⁰ M (0.14 nM). Suppose, for instance, that the normal concentration of insulin in the blood is 5 × 10⁻¹² M. By substituting this value of L and the K_d into equation 15-2, we can calculate the fraction of insulin receptors with bound insulin, [RL]/[R_T], at equilibrium as 0.0344; that is, about 3 percent of the total insulin receptors will have insulin bound to them. If the insulin concentration rises fivefold to 2.5 × 10⁻¹¹ M, as it does after a meal, the number of receptor-hormone complexes will rise proportionately, almost fivefold, so that about 15 percent of the total receptors will have insulin bound to them. If the extent of the induced cellular response parallels the number of insulin-receptor complexes [RL], as is often the case, then the cellular response will also increase by about fivefold.

On the other hand, suppose that the normal concentration of insulin in the blood were the same as the K_d value of 1.4 × 10⁻¹⁰ M; in that case, 50 percent of the total receptors would have insulin bound to them. A fivefold increase in the insulin concentration to 7 × 10⁻¹⁰ M would result in 83 percent of all insulin receptors having insulin bound to them (only a 66 percent increase). Thus, in order for a rise in hormone concentration to cause a proportional increase in the fraction of receptors with bound ligand, the K_d value must be much larger than the normal concentration of the hormone.

In general, the maximal cellular response to a particular ligand is induced when much less than 100 percent of its receptors are bound to the ligand. This phenomenon can be revealed by comparing the extent of the response and of receptor-ligand binding at different concentrations of ligand (see Figure 15-8). For example, a cell in the bone marrow (called an erythroid progenitor cell) has 1000 surface receptors for erythropoietin, the protein hormone that induces these cells to proliferate and differentiate into red blood cells; the K_d for erythropoietin binding is 1 nM. But only 180 of these receptors (18 percent of them) need to bind Epo to induce 50 percent of the maximal cellular response. Thus the ligand concentration needed for a significant cellular response (i.e., the division of the progenitor cell in this case) is considerably lower than the K_d value. In such cases, a plot of the percentage of maximal binding versus ligand concentration is different from a plot of the percentage of maximal cellular response versus ligand concentration.