The Dissociation Constant Is a Measure of the Affinity of a Receptor for Its Ligand

Binding of a single ligand to a receptor can usually can be viewed as a simple reversible reaction, where the receptor is represented as R, the ligand as L, and the receptor-ligand complex as RL:

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where kon is the rate constant for formation of a receptor-ligand complex from free ligand and receptor and koff is the rate constant for dissociation of a ligand from its receptor. We define [R] and [L] as the concentrations of free receptor (that is, receptor without bound ligand) and ligand, respectively, and [RL] as the concentration of the receptor-ligand complex.

At equilibrium, the rate of formation of the receptor-ligand complex, [R] [L] kon, is equal to the rate of its dissociation, [RL] koff: thus at equilibrium, [R] [L] kon = [RL] koff. This situation can be described by the simple equilibrium-binding equation Kd = koff/kon, where Kd, the dissociation constant, is a measure of the affinity (or tightness of binding) of the receptor for its ligand (see Chapter 2).

Equivalently, we can write this equilibrium equation as

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The smaller the dissociation constant, the more stable the receptor-ligand complex. Another way of seeing this key point is that when the concentration of ligand equals Kd ([L] = Kd), then the concentration of free receptor [R] must equal the concentration of the receptor-ligand complex [RL]. That is, when the system is at equilibrium, half of the receptors have a ligand bound. The smaller the Kd, the lower the ligand concentration required to bind 50 percent of the cell-surface receptors. The Kd for a binding reaction here is similar to the Michaelis constant, Km, which reflects the affinity of an enzyme for its substrate (see Chapter 3).

Most hormone-receptor systems are finely balanced: too much or too little of a hormone can cause trouble. Consider, for example, the hormone tumor necrosis factor alpha (TNFα), which is secreted by a number of immune-system cells. TNFα induces inflammation by binding to TNFα receptors on several types of immune-system cells and recruiting them to a site of injury or infection; thus the body needs to make sufficient TNFα to protect against infections, but abnormally high levels of TNFα can cause the excessive inflammation seen in patients with autoimmune diseases such as the blistering skin disease psoriasis or the joint disease rheumatoid arthritis. These diseases are being treated by drugs that deplete the amount of TNFα in the joint or circulating in the body. One such drug is on the principle that hormone receptors are characterized by their high affinity and specificity for their ligands. This drug is a chimeric “fusion” protein, generated by recombinant DNA techniques, that contains the extracellular TNFα-binding domain of a TNFα receptor fused to the constant (Fc) region of a human immunoglobulin (see Figures 3-21 and 23-9). The water-soluble drug can be injected into the body, where it binds tightly to the potentially dangerous free TNFα and prevents it from binding to its cell-surface receptors and causing inflammation; the fused Fc domain causes the protein to be stable when injected into the body.