8885dc05157-1898/12/038:55 AM Page160mac78mac78:385 160 Part I Structure and Catalysis a higher affinity of the ligand for the protein. a re- arrangement of Equation 5-2 shows that the ratio of bound to free protein is directly proportional to the con KaLLI When the concentration of the ligand is much greater than the concentration of ligand-binding sites, the binding of the ligand by the protein does not apprecia- bly change the concentration of free (unbound)li- gand-that is, L remains constant. This condition is broadly applicable to most ligands that bind to proteins in cells and simplifies our description of the binding equilibrium. We can now consider the binding equilibrium from the standpoint of the fraction, e(theta), of ligand binding sites on the protein that are occupied by ligand FIGURE 5-3 The structure of myoglobin (PDB ID 1MBO) The eight IPL (5-4) a-helical segments (shown here as cylinders) are labeled A through H. Nonhelical residues in the bends that connect them are labeled Substituting KalLJP for [PL(see Eqn 5-3)and re- AB,CD,EF, and so forth, indicating the segments they interconnect. arranging terms gives A few bends, including BC and DE, are abrupt and do not contain any residues; these are not normally labeled. (The short segment vis- KaLLJPI ble between D and E is an artifact of the computer representation The heme is bound in a pocket made up largely of the E and F he. although amino acid residues from other segments of the pro The value of Ka can be determined from a plot of e ver also participate. sus the concentration of free ligand, L(Fig. 5-4a). Any equation of the form =y/(y +2) describes a hyper bola, and 0 is thus found to be a hyperbolic function of Protein-Ligand Interactions Can Be L. The fraction of ligand-binding sites occupied ap- Described Quantitatively proaches saturation asymptotically as l increases. The L at which half of the available ligand-binding sites are The function of myoglobin depends on the proteins abil- occupied (at 0=0.5) corresponds to 1/K ity not only to bind oxygen but also to release it when It is more common (and intuitively simpler), how- and where it is needed. Function in biochemistry often ever, to consider the dissociation constant, Kd, which revolves around a reversible protein-ligand interaction is the reciprocal of Ka(Kd= 1/Ka) and is given in units of this type. A quantitative description of this interac- of molar concentration(M). Ka is the equilibrium con- tion is therefore a central part of many biochemical in- stant for the release of ligand. The relevant expressions vestigations change to In general, the reversible binding of a protein(P) to a ligand () can be described by a simple equilib- rium expression: P+L (5-1) The reaction is characterized by an equilibrium con- stant, K. such that (5-2) When L is equal to Kd, half of the ligand-binding sites are occupied. As falls below Kd, progressively less of The term Ka is an association constant (not to be the protein has ligand bound to it. In order for 90%of confused with the Ka that denotes an acid dissociation the available ligand-binding sites to be occupied, L onstant; p. 63). The association constant provides a must be nine times greater than Kd measure of the affinity of the ligand L for the protein. In practice, Kd is used much more often than Ka to Ka has units of M; a higher value of Ka corresponds to express the affinity of a protein for a ligand. Note thatProtein-Ligand Interactions Can Be Described Quantitatively The function of myoglobin depends on the protein’s abil￾ity not only to bind oxygen but also to release it when and where it is needed. Function in biochemistry often revolves around a reversible protein-ligand interaction of this type. A quantitative description of this interac￾tion is therefore a central part of many biochemical in￾vestigations. In general, the reversible binding of a protein (P) to a ligand (L) can be described by a simple equilib￾rium expression: P
L PL (5–1) The reaction is characterized by an equilibrium con￾stant, Ka, such that Ka [ [ P P ] L [L ] ] (5–2) The term Ka is an association constant (not to be confused with the Ka that denotes an acid dissociation constant; p. 63). The association constant provides a measure of the affinity of the ligand L for the protein. Ka has units of M1 ; a higher value of Ka corresponds to yz a higher affinity of the ligand for the protein. A re￾arrangement of Equation 5–2 shows that the ratio of bound to free protein is directly proportional to the con￾centration of free ligand: Ka[L]  [P [P L ] ]  (5–3) When the concentration of the ligand is much greater than the concentration of ligand-binding sites, the binding of the ligand by the protein does not apprecia￾bly change the concentration of free (unbound) li￾gand—that is, [L] remains constant. This condition is broadly applicable to most ligands that bind to proteins in cells and simplifies our description of the binding equilibrium. We can now consider the binding equilibrium from the standpoint of the fraction, (theta), of ligand￾binding sites on the protein that are occupied by ligand: [PL [P ]
L] [P] (5–4) Substituting Ka[L][P] for [PL] (see Eqn 5–3) and re￾arranging terms gives Ka[ K L a ][ [ P L ] ][
P] [P] Ka K [L a[ ] L
] 1 (5–5) The value of Ka can be determined from a plot of ver￾sus the concentration of free ligand, [L] (Fig. 5–4a). Any equation of the form x y/(y
z) describes a hyper￾bola, and is thus found to be a hyperbolic function of [L]. The fraction of ligand-binding sites occupied ap￾proaches saturation asymptotically as [L] increases. The [L] at which half of the available ligand-binding sites are occupied (at 0.5) corresponds to 1/Ka. It is more common (and intuitively simpler), how￾ever, to consider the dissociation constant, Kd, which is the reciprocal of Ka (Kd 1/Ka) and is given in units of molar concentration (M). Kd is the equilibrium con￾stant for the release of ligand. The relevant expressions change to Kd  [P [P ][ L L ] ]  (5–6) [PL]  [P K ][ d L]  (5–7) [L] [
L] Kd (5–8) When [L] is equal to Kd, half of the ligand-binding sites are occupied. As [L] falls below Kd, progressively less of the protein has ligand bound to it. In order for 90% of the available ligand-binding sites to be occupied, [L] must be nine times greater than Kd. In practice, Kd is used much more often than Ka to express the affinity of a protein for a ligand. Note that  [L] [L]
K 1 a   binding sites occupied total binding sites 160 Part I Structure and Catalysis A EF F H FG C CD D B G E GH AB FIGURE 5–3 The structure of myoglobin. (PDB ID 1MBO) The eight
-helical segments (shown here as cylinders) are labeled A through H. Nonhelical residues in the bends that connect them are labeled AB, CD, EF, and so forth, indicating the segments they interconnect. A few bends, including BC and DE, are abrupt and do not contain any residues; these are not normally labeled. (The short segment vis￾ible between D and E is an artifact of the computer representation.) The heme is bound in a pocket made up largely of the E and F he￾lices, although amino acid residues from other segments of the pro￾tein also participate. 8885d_c05_157-189 8/12/03 8:55 AM Page 160 mac78 mac78:385_REB: