up of several different immunoglobulin domains, here shaded either blue or gray. The antigen-binding site is formed where a heavy-chain variable domain (VH) and a light-chain variable domain (VL) come close together. These are the domains that differ most in their sequence and structure in different antibodies. At the end of each of the two arms of the antibody molecule, these two domains form loops that bind to the antigen (see Movie 24.5).
the surfaces of molecules A and B, and A and C, are a poor match and are capable of forming only a few weak bonds; thermal motion rapidly breaks them apart molecule A randomly encounters other molecules (B, C, and D) the surfaces of molecules A and D match well and therefore can form enough weak bonds to withstand thermal jolting; they therefore
We can measure the strength with which any two molecules bind to each other. As an example, consider a population of identical antibody molecules that suddenly encounters a population of ligands diffusing in the fluid surrounding them. At frequent intervals, one of the ligand molecules will bump into the binding site of an antibody and form an antibody–ligand complex. The population of antibody–ligand complexes will therefore increase, but not without limit: over time, a second process, in which individual complexes break apart because of thermally induced motion, will become increasingly important. Eventually, any population of antibody molecules and ligands will reach a steady state, or equilibrium, in which the number of binding (association) events per second is precisely equal to the number of “unbinding” (dissociation) events (see Figure 2–30).
From the concentrations of the ligand, antibody, and antibody–ligand complex at equilibrium, we can calculate a convenient measure of the strength of bind-ing—the equilibrium constant (K)—(Figure 3–44A). This constant was described in detail in Chapter 2, where its connection to free energy differences was derived (see p. 62). The equilibrium constant for a reaction in which two molecules (A and
B) bind to each other to form a complex (AB) has units of liters/mole, and half of the binding sites will be occupied by ligand when that ligand’s concentration (in moles/liter) reaches a value that is equal to 1/K. This equilibrium constant is larger the greater the binding strength, and it is a direct measure of the free-energy difference between the bound and free states (Figure 3–44B). Even a change stay bound to each other
Figure 3–43 How noncovalent bonds mediate interactions between macromolecules (see Movie 2.1).
Figure 3–44 Relating standard free-energy difference (ΔG°) to the equilibrium constant (K). (A) The equilibrium between molecules A and B and the complex AB is maintained by a balance between the two opposing reactions shown in panels 1 and 2. Molecules A and B must collide if they are to react, and the association rate is therefore proportional to the product of their individual concentrations [A] × [B]. (Square brackets indicate concentration.) As shown in panel 3, the ratio of the rate constants for the association and the dissociation reactions is equal to the equilibrium constant (K) for the reaction (see also p. 63). (B) The equilibrium constant in panel 3 is that for the reaction A + B ↔ AB, and the larger its value, the stronger the binding between A and B. Note that for every 5.91 kJ/mole decrease in standard free energy, the equilibrium constant increases by a factor of 10 at 37°C.