8885ac05157-1898/12/038:55 AM Page167mac78mac78:385 Chapter 5 Protein Function entire binding site were highly stable, then few struc practice, and the measured value of nH is always less tural changes could occur in this site or be propagated than the actual number of ligand-binding sites in the to other parts of the protein when a ligand binds tein As is the case with myoglobin, ligands other than An H of less than I indicates negative cooperativ oxygen can bind to hemoglobin. An important example in which the binding of one molecule of ligand im- is carbon monoxide, which binds to hemoglobin about pedes the binding of others. Well-documented cases of 250 times better than does oxygen. Human exposure to negative cooperativity are rare CO can have tragic consequences(Box 5-1) To adapt the hill equation to the binding of oxygen hemoglobin we must again substitute pO for L and Cooperative Ligand Binding Can Be Described P5o for Kd Quantitatively n log pO2-n log P5o (5-17) Cooperative binding of oxygen by hemoglobin was first analyzed by Archibald Hill in 1910. From this work came Hill plots for myoglobin and hemoglobin are given in Fig- a general approach to the study of cooperative ligand ure 5-14 binding to multisubunit proteins For a protein with n binding sites, the equilibrium Two Models Suggest Mechani of Equation 5-1 becomes for Cooperative Binding P+nL (5-12) Biochemists now know a great deal about the T and R and the expression for the association constant becomes states of hemoglobin, but much remains to be learned about how the t-R transition occurs Two models for the cooperative binding of ligands to proteins with mul- tiple binding sites have greatly influenced thinking The expression for g(see Egn 5-8)is about this problem The first model was proposed by Jacques Monod 6 Jeffries Wyman, and Jean-Pierre Changeux in 1965, and is called the mwc model or the concerted model (Fig. 5-15a). The concerted model assumes that the Rearranging, then taking the log of both sides, yields subunits of a cooperatively binding protein are func identical, that each subunit can exist in (at 65- where Kd=Lo. Hemoglobin Equation 5-16 is the Hill equation, and a plot of high-affinity log [e/(1-0] versus log L is called a Hill plot. Based on the equation, the Hill plot should have a slope of n. However, the experimentally determined slope actually reflects not the number of binding sites but the degree eD of interaction between them. The slope of a Hill plot is Myoglobin therefore denoted by nH, the Hill coefficient, which is a measure of the degree of cooperativity. If nH equals state 1, ligand binding is not cooperative, a situation that can arise even in a multisubunit protein if the subunits do not communicate. An nH of greater than I indicates positive cooperativity in ligand binding. This is the situation observed in hemoglobin, in which the binding of one molecule of ligand facilitates the binding of FIGURE 5-14 Hill plots for the binding of oxygen to myoglobin and others. The theoretical upper limit for nH is reached hemoglobin. When nH=1, there is no evident cooperativity. The max- when nH=n. In this case the binding would be com- imum degree of cooperativity observed for hemoglobin corresponds pletely cooperative: all binding sites on the protein approximately to nH=3. Note that while this indicates a high level would bind ligand simultaneously, and no protein mol- of cooperativity, nH is less than n, the number of O2-binding sites ecules partially saturated with ligand would be present hemoglobin. This is normal for a protein that exhibits allosteric bind- under any conditions. This limit is never reached inentire binding site were highly stable, then few struc￾tural changes could occur in this site or be propagated to other parts of the protein when a ligand binds. As is the case with myoglobin, ligands other than oxygen can bind to hemoglobin. An important example is carbon monoxide, which binds to hemoglobin about 250 times better than does oxygen. Human exposure to CO can have tragic consequences (Box 5–1). Cooperative Ligand Binding Can Be Described Quantitatively Cooperative binding of oxygen by hemoglobin was first analyzed by Archibald Hill in 1910. From this work came a general approach to the study of cooperative ligand binding to multisubunit proteins. For a protein with n binding sites, the equilibrium of Equation 5–1 becomes P
nL PLn (5–12) and the expression for the association constant becomes Ka [ [ P P ] L [L n ] ] n (5–13) The expression for (see Eqn 5–8) is [L] [ n L
] n Kd (5–14) Rearranging, then taking the log of both sides, yields 1   [ K L] d n  (5–15) log
1  n log [L] log Kd (5–16) where Kd [L]n 0.5. Equation 5–16 is the Hill equation, and a plot of log [/(1 )] versus log [L] is called a Hill plot. Based on the equation, the Hill plot should have a slope of n. However, the experimentally determined slope actually reflects not the number of binding sites but the degree of interaction between them. The slope of a Hill plot is therefore denoted by nH, the Hill coefficient, which is a measure of the degree of cooperativity. If nH equals 1, ligand binding is not cooperative, a situation that can arise even in a multisubunit protein if the subunits do not communicate. An nH of greater than 1 indicates positive cooperativity in ligand binding. This is the situation observed in hemoglobin, in which the binding of one molecule of ligand facilitates the binding of others. The theoretical upper limit for nH is reached when nH n. In this case the binding would be com￾pletely cooperative: all binding sites on the protein would bind ligand simultaneously, and no protein mol￾ecules partially saturated with ligand would be present under any conditions. This limit is never reached in yz Chapter 5 Protein Function 167 practice, and the measured value of nH is always less than the actual number of ligand-binding sites in the protein. An nH of less than 1 indicates negative cooperativ￾ity, in which the binding of one molecule of ligand im￾pedes the binding of others. Well-documented cases of negative cooperativity are rare. To adapt the Hill equation to the binding of oxygen to hemoglobin we must again substitute pO2 for [L] and P50 n for Kd: log
1  n log pO2 n log P50 n (5–17) Hill plots for myoglobin and hemoglobin are given in Fig￾ure 5–14. Two Models Suggest Mechanisms for Cooperative Binding Biochemists now know a great deal about the T and R states of hemoglobin, but much remains to be learned about how the T n R transition occurs. Two models for the cooperative binding of ligands to proteins with mul￾tiple binding sites have greatly influenced thinking about this problem. The first model was proposed by Jacques Monod, Jeffries Wyman, and Jean-Pierre Changeux in 1965, and is called the MWC model or the concerted model (Fig. 5–15a). The concerted model assumes that the subunits of a cooperatively binding protein are func￾tionally identical, that each subunit can exist in (at 3 log pO2 3 1 1 1 0 3 0 1 2 2 2 2 1 log   ) ( Hemoglobin nH 3 Hemoglobin high-affinity state nH 1 Myoglobin nH 1 Hemoglobin low-affinity state nH 1 FIGURE 5–14 Hill plots for the binding of oxygen to myoglobin and hemoglobin. When nH 1, there is no evident cooperativity. The max￾imum degree of cooperativity observed for hemoglobin corresponds approximately to nH 3. Note that while this indicates a high level of cooperativity, nH is less than n, the number of O2-binding sites in hemoglobin. This is normal for a protein that exhibits allosteric bind￾ing behavior. 8885d_c05_157-189 8/12/03 8:55 AM Page 167 mac78 mac78:385_REB: