《生物化学原理》英文版 chapter 5 PROTEIN FUNCTION

8885ac05157-1898/12/038:55 AM Page157mac78mac78:385p chapter PROTEIN FUNCTION 5.1 Reversible Binding of a Protein to a Ligand: proteins interact with other molecules and how their in- Oxygen-Binding Proteins 158 teractions are related to dynamic protein structure. The 5.2 Complementary Interactions between Proteins importance of molecular interactions to a proteins func and Ligands: The Immune System and tion can hardly be overemphasized. In Chapter 4, we saw Immunoglobulins 174 that the function of fibrous proteins as structural ele- 5.3 Protein Interactions Modulated by Chemical Energy ments of cells and tissues depends on stable, long-term Actin, Myosin, and Molecular Motors 182 quaternary interactions between identical polypeptide chains. As we shall see in this chapter, the functions of many other proteins involve interactions with a variety have occasionally seen in almost dried blood, placed of different molecules. Most of these interactions are between glass plates in a desiccator, rectangula fleeting, though they may be the basis of complex phys- iological processes such as oxygen transport, immune crystalline structures, which under the microscope had function, and muscle contraction-the topics we exam- sharp edges and were bright red ine in detail in this chapter. The proteins that carry out -Friedrich Ludwig Hunefeld, Der Chemismus in these processes illustrate the following key principles of der thierischen Organisation, 1840 protein function, some of which will be familiar from the (one of the first observations of hemoglobin) chapte The functions of many proteins involve the Since the proteins participate in one way or another in all reversible binding of other molecules. A molecule chemical processes in the living organism, one may bound reversibly by a protein is called a ligand expect highly significant information for biological A ligand may be any kind of molecule, including chemistry from the elucidation of their structure and their another protein. The transient nature of protein- transformations ligand interactions is critical to life, allowing an -Emil Fischer article in berichte der deutschen organism to respond rapidly and reversibly to changing environmental and metabolic chemischen gesellschaft zu berlin, 1906 A ligand binds at a site on the protein called the binding site, which is complementary to the nowing the three-dimensional structure of a protein ligand in size, shape, charge, and hydrophobic or an important part of understanding how the pro- hydrophilic character. Furthermore, the interaction tein functions However the structure shown in two di is specific: the protein can discriminate among the mensions on a page is deceptively static. Proteins are thousands of different molecules in its environment dynamic molecules whose functions almost invariably and selectively bind only one or a few. a given depend on interactions with other molecules, and these protein may have separate binding sites for several interactions are affected in physiologically important different ligands. These specific molecular ways by sometimes subtle, sometimes striking changes interactions are crucial in maintaining the high in protein conformation. In this chapter, we explore how degree of order in a living system. (This discussion

chapter PROTEIN FUNCTION 5.1 Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins 158 5.2 Complementary Interactions between Proteins and Ligands: The Immune System and Immunoglobulins 174 5.3 Protein Interactions Modulated by Chemical Energy: Actin, Myosin, and Molecular Motors 182 I have occasionally seen in almost dried blood, placed between glass plates in a desiccator, rectangular crystalline structures, which under the microscope had sharp edges and were bright red. —Friedrich Ludwig Hünefeld, Der Chemismus in der thierischen Organisation, 1840 (one of the first observations of hemoglobin) Since the proteins participate in one way or another in all chemical processes in the living organism, one may expect highly significant information for biological chemistry from the elucidation of their structure and their transformations. —Emil Fischer, article in Berichte der deutschen chemischen Gesellschaft zu Berlin, 1906 5 Knowing the three-dimensional structure of a protein is an important part of understanding how the pro￾tein functions. However, the structure shown in two di￾mensions on a page is deceptively static. Proteins are dynamic molecules whose functions almost invariably depend on interactions with other molecules, and these interactions are affected in physiologically important ways by sometimes subtle, sometimes striking changes in protein conformation. In this chapter, we explore how proteins interact with other molecules and how their in￾teractions are related to dynamic protein structure. The importance of molecular interactions to a protein’s func￾tion can hardly be overemphasized. In Chapter 4, we saw that the function of fibrous proteins as structural ele￾ments of cells and tissues depends on stable, long-term quaternary interactions between identical polypeptide chains. As we shall see in this chapter, the functions of many other proteins involve interactions with a variety of different molecules. Most of these interactions are fleeting, though they may be the basis of complex phys￾iological processes such as oxygen transport, immune function, and muscle contraction—the topics we exam￾ine in detail in this chapter. The proteins that carry out these processes illustrate the following key principles of protein function, some of which will be familiar from the previous chapter: The functions of many proteins involve the reversible binding of other molecules. A molecule bound reversibly by a protein is called a ligand. A ligand may be any kind of molecule, including another protein. The transient nature of protein￾ligand interactions is critical to life, allowing an organism to respond rapidly and reversibly to changing environmental and metabolic circumstances. A ligand binds at a site on the protein called the binding site, which is complementary to the ligand in size, shape, charge, and hydrophobic or hydrophilic character. Furthermore, the interaction is specific: the protein can discriminate among the thousands of different molecules in its environment and selectively bind only one or a few. A given protein may have separate binding sites for several different ligands. These specific molecular interactions are crucial in maintaining the high degree of order in a living system. (This discussion 157 8885d_c05_157-189 8/12/03 8:55 AM Page 157 mac78 mac78:385_REB:

8885dc05157-1898/12/038:55 AM Page158mac78mac78:385 158 Part I Structure and Catalysis excludes the binding of water, which may interact molecules illustrate almost every aspect of that most weakly and nonspecifically with many parts of central of biochemical processes: the reversible binding protein. In Chapter 6, we consider water as a of a ligand to a protein. This classic model of protein specific ligand for many enzymes. function tells us a great deal about how proteins work Proteins are flexible. Changes in conformation 6 Oxygen-Binding Proteins--Myoglobin: Oxygen Storage may be subtle, reflecting molecular vibrations and Oxygen Can Be Bound to a Heme Prosthetic Group small movements of amino acid residues throughout the protein. a protein flexing in this Oxygen is poorly soluble in aqueous solutions (see Table way is sometimes said to"breathe. Changes in 2-3)and cannot be carried to tissues in sufficient quan conformation may also be quite dramatic, with tity if it is simply dissolved in blood serum. Diffusion of major segments of the protein structure moving oxygen through tissues is also ineffective over distances as much as several nanometers. Specific greater than a few millimeters. The evolution of larger onformational changes are frequently essential to multicellular animals depended on the evolution of pro- a proteins function. teins that could transport and store oxygen. However, The binding of a protein and ligand is often none of the amino acid side chains in proteins is suited for the reversible binding of oxygen molecules. This role coupled to a conformational change in the protein is filled by certain transition metals, among them iron that makes the binding site more complementary to the ligand, permitting tighter binding. The and copper, that have a strong tendency to bind oxy gen. Multicellular organisms exploit the properties of structural adaptation that occurs between proten metals, most commonly iron, for oxygen transport. How and ligand is called induced fit. ever, free iron promotes the formation of highly reac In a multisubunit protein, a conformational tive oxygen species such as hydroxyl radicals that can change in one subunit often affects the damage DNA and other macromolecules. Iron used in conformation of other subunits cells is therefore bound in forms that sequester it and/or Interactions between ligands and proteins may be make it less reactive In multicellular organisms--espe- regulated, usually through specific interactions cially those in which iron, in its oxygen-carrying capac with one or more additional ligands. These other ty, must be transported over large distances--iron is of- igands may cause conformational changes in the ten incorporated into a protein-bound prosthetic group protein that affect the binding of the first ligand called heme.(Recall from Chapter 3 that a prosthetic group is a compound permanently associated with a pro- Enzymes represent a special case of protein func tein that contributes to the proteins function.) Heme (or haen) consists of a complex organic ring tion. Enzymes bind and chemically transform other mol- structure, protoporphyrin, to which is bound a single ecules--they catalyze reactions. The molecules acted upon by enzymes are called reaction substrates rather iron atom in its ferrous(Fe-s) state(Fig 5-1). The iron than ligands, and the ligand-binding site is called the atom has six coordination bonds, four to nitrogen atoms that are part of the flat porphyrin ring system and catalytic site or active site. In this chapter we two perpendicular to the porphyrin. The coordinated emphasize the noncatalytic functions of proteins. In Chapter 6 we consider catalysis by enzymes, a central nitrogen atoms(which have an electron-donating char topic in biochemistry. You will see that the themes of acter) help prevent conversion of the heme iron to the this chapter--binding, specificity, and conformational ferric(Fe t )state. Iron in the Fet state binds oxygen change-are continued in the next chapter, with the reversibly; in the Fe state it does not bind oxygen. added element of proteins acting as reactants in chem- Heme is found in a number of oxygen-transporting ical transformations proteins, as well as in some proteins, such as the cytochromes, that participate in oxidation-reduction (electron-transfer) reactions(Chapter 19) In free heme molecules (heme not bound to pro- 5.1 Reversible Binding of a Protein tein), reaction of oxygen at one of the two"open"CO- to a Ligand: Oxygen-Binding Proteins ordination bonds of iron(perpendicular to the plane of the porphyrin molecule, above and below) can result Myoglobin and hemoglobin may be the most-studied and in irreversible conversion of Fe-t to Fe. In heme- best-understood proteins. They were the first proteins containing proteins, this reaction is prevented by se- for which three-dimensional structures were deter- questering of the heme deep within the protein struc mined, and our current understanding of myoglobin and ture where access to the two open coordination bonds hemoglobin is garnered from the work of thousands of is restricted. One of these two coordination bonds is oc- biochemists over several decades. Most important, these cupid by a side-chain nitrogen of a His residue. The

excludes the binding of water, which may interact weakly and nonspecifically with many parts of a protein. In Chapter 6, we consider water as a specific ligand for many enzymes.) Proteins are flexible. Changes in conformation may be subtle, reflecting molecular vibrations and small movements of amino acid residues throughout the protein. A protein flexing in this way is sometimes said to “breathe.” Changes in conformation may also be quite dramatic, with major segments of the protein structure moving as much as several nanometers. Specific conformational changes are frequently essential to a protein’s function. The binding of a protein and ligand is often coupled to a conformational change in the protein that makes the binding site more complementary to the ligand, permitting tighter binding. The structural adaptation that occurs between protein and ligand is called induced fit. In a multisubunit protein, a conformational change in one subunit often affects the conformation of other subunits. Interactions between ligands and proteins may be regulated, usually through specific interactions with one or more additional ligands. These other ligands may cause conformational changes in the protein that affect the binding of the first ligand. Enzymes represent a special case of protein func￾tion. Enzymes bind and chemically transform other mol￾ecules—they catalyze reactions. The molecules acted upon by enzymes are called reaction substrates rather than ligands, and the ligand-binding site is called the catalytic site or active site. In this chapter we emphasize the noncatalytic functions of proteins. In Chapter 6 we consider catalysis by enzymes, a central topic in biochemistry. You will see that the themes of this chapter—binding, specificity, and conformational change—are continued in the next chapter, with the added element of proteins acting as reactants in chem￾ical transformations. 5.1 Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins Myoglobin and hemoglobin may be the most-studied and best-understood proteins. They were the first proteins for which three-dimensional structures were deter￾mined, and our current understanding of myoglobin and hemoglobin is garnered from the work of thousands of biochemists over several decades. Most important, these molecules illustrate almost every aspect of that most central of biochemical processes: the reversible binding of a ligand to a protein. This classic model of protein function tells us a great deal about how proteins work. Oxygen-Binding Proteins—Myoglobin: Oxygen Storage Oxygen Can Be Bound to a Heme Prosthetic Group Oxygen is poorly soluble in aqueous solutions (see Table 2–3) and cannot be carried to tissues in sufficient quan￾tity if it is simply dissolved in blood serum. Diffusion of oxygen through tissues is also ineffective over distances greater than a few millimeters. The evolution of larger, multicellular animals depended on the evolution of pro￾teins that could transport and store oxygen. However, none of the amino acid side chains in proteins is suited for the reversible binding of oxygen molecules. This role is filled by certain transition metals, among them iron and copper, that have a strong tendency to bind oxy￾gen. Multicellular organisms exploit the properties of metals, most commonly iron, for oxygen transport. How￾ever, free iron promotes the formation of highly reac￾tive oxygen species such as hydroxyl radicals that can damage DNA and other macromolecules. Iron used in cells is therefore bound in forms that sequester it and/or make it less reactive. In multicellular organisms—espe￾cially those in which iron, in its oxygen-carrying capac￾ity, must be transported over large distances—iron is of￾ten incorporated into a protein-bound prosthetic group called heme. (Recall from Chapter 3 that a prosthetic group is a compound permanently associated with a pro￾tein that contributes to the protein’s function.) Heme (or haem) consists of a complex organic ring structure, protoporphyrin, to which is bound a single iron atom in its ferrous (Fe2
) state (Fig. 5–1). The iron atom has six coordination bonds, four to nitrogen atoms that are part of the flat porphyrin ring system and two perpendicular to the porphyrin. The coordinated nitrogen atoms (which have an electron-donating char￾acter) help prevent conversion of the heme iron to the ferric (Fe3
) state. Iron in the Fe2
state binds oxygen reversibly; in the Fe3
state it does not bind oxygen. Heme is found in a number of oxygen-transporting proteins, as well as in some proteins, such as the cytochromes, that participate in oxidation-reduction (electron-transfer) reactions (Chapter 19). In free heme molecules (heme not bound to pro￾tein), reaction of oxygen at one of the two “open” co￾ordination bonds of iron (perpendicular to the plane of the porphyrin molecule, above and below) can result in irreversible conversion of Fe2
to Fe3
. In heme￾containing proteins, this reaction is prevented by se￾questering of the heme deep within the protein struc￾ture where access to the two open coordination bonds is restricted. One of these two coordination bonds is oc￾cupied by a side-chain nitrogen of a His residue. The 158 Part I Structure and Catalysis 8885d_c05_157-189 8/12/03 8:55 AM Page 158 mac78 mac78:385_REB:

8885ac05157-1898/12/038:55 AM Page159mac78mac78:385 Protein Function CH CHI Fe- ch CH CH CH FIGURE 5-1 Heme. The heme group is present in myoglobin, hemo- role rings linked by methene bridges, with substitutions at one or more globin, and many other proteins, designated heme proteins. Heme of the positions denoted X. (b, c) Two representations of heme(De- onsists of a complex organic ring structure, protoporphyrin IX, to rived from PDB ID 1CCR The iron atom of heme has six coordina- hich is bound an iron atom in its ferrous(Fe2+)state. (a) Porphyrins tion bonds: four in the plane of, and bonded to, the flat porphyrin ring of which protoporphyrin IX is only one example, consist of four pyr- stem,and(d) two perpendicular to it. other is the binding site for molecular oxygen(O2)(Fig Myoglobin Has a Single Binding Site for Oxygen 5-2). When oxygen binds, the electronic properties of heme iron change; this accounts for the change in color Myoglobin(Mr 16, 700; abbreviated Mb) is a relatively from the dark purple of oxygen-depleted venous blood simple oxygen-binding protein found in almost all mam- to the bright red of oxygen-rich arterial blood. Some mals, primarily in muscle tissue. As a transport protein, it facilitates oxygen diffusion in muscle. Myoglobin is tric oxide (NO), coordinate to heme iron with greater particularly abundant in the muscles of diving mammals affinity than does O, When a molecule of co is bound such as seals and whales, where it also has an oxygen- to heme, O2 is excluded, which is why Co is highly toxic storage function for prolonged excursions undersea to aerobic organisms(a topic explored later, in Box Proteins very similar to myoglobin are widely distrib- 1). By surrounding and sequestering heme, oxygen uted, occurring even in some single-celled organisms binding proteins regulate the access of CO and other Myoglobin is a single polypeptide of 153 amino acid small molecules to the heme iron residues with one molecule of heme. It is typical of the family of proteins called globins, all of which have sim- ilar primary and tertiary structures. The polypeptide is made up of eight a-helical segments connected by bends Edge view (Fig. 5-3). About 78% of the amino acid residues in the protein are found in these a helices. Any detailed discussion of protein function in- evitably involves protein structure. To facilitate our treatment of myoglobin, we first introduce some struc tural conventions peculiar to globins. As seen in Figure 5-3, the helical segments are named A through H. An individual amino acid residue is designated either by its Histidine Plane of position in the amino acid sequence or by its location residue porphyrin within the sequence of a particular a-helical segment ring system For example, the His residue coordinated to the heme FIGURE 5-2 The heme group viewed from the side. This view shows in myoglobin, His(the 93rd amino acid residue from the two coordination bonds to Fe2+ perpendicular to the porphyri the amino-terminal end of the myoglobin polypeptide ring system. One of these two bonds is occupied by a His residu sequence), is also called His F8(the Sth residue in a sometimes called the proximal His. The other bond is the binding site helix F). The bends in the structure are designated AB for oxygen. The remaining four coordination bonds are in the plane CD, EF, FG, and so forth, reflecting the a-helical seg of, and bonded to, the flat porphyrin ring system ments they connect

other is the binding site for molecular oxygen (O2) (Fig. 5–2). When oxygen binds, the electronic properties of heme iron change; this accounts for the change in color from the dark purple of oxygen-depleted venous blood to the bright red of oxygen-rich arterial blood. Some small molecules, such as carbon monoxide (CO) and ni￾tric oxide (NO), coordinate to heme iron with greater affinity than does O2. When a molecule of CO is bound to heme, O2 is excluded, which is why CO is highly toxic to aerobic organisms (a topic explored later, in Box 5–1). By surrounding and sequestering heme, oxygen￾binding proteins regulate the access of CO and other small molecules to the heme iron. Myoglobin Has a Single Binding Site for Oxygen Myoglobin (Mr 16,700; abbreviated Mb) is a relatively simple oxygen-binding protein found in almost all mam￾mals, primarily in muscle tissue. As a transport protein, it facilitates oxygen diffusion in muscle. Myoglobin is particularly abundant in the muscles of diving mammals such as seals and whales, where it also has an oxygen￾storage function for prolonged excursions undersea. Proteins very similar to myoglobin are widely distrib￾uted, occurring even in some single-celled organisms. Myoglobin is a single polypeptide of 153 amino acid residues with one molecule of heme. It is typical of the family of proteins called globins, all of which have sim￾ilar primary and tertiary structures. The polypeptide is made up of eight
-helical segments connected by bends (Fig. 5–3). About 78% of the amino acid residues in the protein are found in these
helices. Any detailed discussion of protein function in￾evitably involves protein structure. To facilitate our treatment of myoglobin, we first introduce some struc￾tural conventions peculiar to globins. As seen in Figure 5–3, the helical segments are named A through H. An individual amino acid residue is designated either by its position in the amino acid sequence or by its location within the sequence of a particular
-helical segment. For example, the His residue coordinated to the heme in myoglobin, His93 (the 93rd amino acid residue from the amino-terminal end of the myoglobin polypeptide sequence), is also called His F8 (the 8th residue in
helix F). The bends in the structure are designated AB, CD, EF, FG, and so forth, reflecting the
-helical seg￾ments they connect. Chapter 5 Protein Function 159 O C O O Fe
CH3 CH N
CH2 CH2 CH2 CH2 CH2 C H3 C H3 CH3 CH CH CH CH CH O C C C C C C C C C C C C C C C N N N CH2 C (b) C (a) NH X N HN N X X X X X X X (c) (d) Fe FIGURE 5–1 Heme. The heme group is present in myoglobin, hemo￾globin, and many other proteins, designated heme proteins. Heme consists of a complex organic ring structure, protoporphyrin IX, to which is bound an iron atom in its ferrous (Fe2
) state. (a) Porphyrins, of which protoporphyrin IX is only one example, consist of four pyr￾role rings linked by methene bridges, with substitutions at one or more of the positions denoted X. (b, c) Two representations of heme. (De￾rived from PDB ID 1CCR.) The iron atom of heme has six coordina￾tion bonds: four in the plane of, and bonded to, the flat porphyrin ring system, and (d) two perpendicular to it. FIGURE 5–2 The heme group viewed from the side. This view shows the two coordination bonds to Fe2
perpendicular to the porphyrin ring system. One of these two bonds is occupied by a His residue, sometimes called the proximal His. The other bond is the binding site for oxygen. The remaining four coordination bonds are in the plane of, and bonded to, the flat porphyrin ring system. HN CH2 C CH Edge view ring system residue C N Fe O2 Histidine Plane of porphyrin H 8885d_c05_157-189 8/12/03 8:55 AM Page 159 mac78 mac78:385_REB:

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 that

Protein-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:

8885ac05157-1898/12/038:55 AM Page161mac78mac78:385p Protein function 161 1.0 1.0 00.5 0.5 (arbitrary units) (b) pO2(kPa) FIGURE 5-4 Graphical representations of ligand binding. The frac- or Kd. The curve has a horizontal asymptote at 0=1 and a vertical tion of ligand-binding sites occupied, e, is plotted against the con- asymptote (not shown)at [L]=-1/Ka (b)A curve describing the bind centration of free ligand. Both curves are rectangular hyperbolas. ing of oxygen to myoglobin. The partial pressure of O2 in the air above (a)A hypothetical binding curve for a ligand L. The [L] at which half the solution is expressed in kilopascals(kPa). Oxygen binds tightly to of the available ligand-binding sites are occupied is equivalent to 1/K. myoglobin, with a Pso of only 0.26 kPa a lower value of Kd corresponds to a higher affinity of As for any ligand, Ka is equal to the [oa] at which half igand for the protein. The mathematics can be reduced of the available ligand-binding sites are occupied, or to simple statements: Kd is equivalent to the molar con- [O.s. Equation 5-9 thus becomes centration of ligand at which half of the available ligand binding sites are occupied. At this point, the protein is (5-10) said to have reached half-saturation with respect to lig. nd binding. The more tightly a protein binds a ligand, In experiments using oxygen as a ligand, it is the par the lower the concentration of ligand required for half tial pressure of oxygen in the gas phase above the the binding sites to be occupied, and thus the lower the solution, pO,, that is varied, because this is easier to value of Kd. Some representative dissociation constants measure than the concentration of oxygen dissolved in are given in Table 5-1 the solution The concentration of a volatile substance The binding of oxygen to myoglobin follows the pat in solution is always proportional to the local partial terns discussed above. However, because oxygen is a pressure of the gas. So, if we define the partial pressure gas, we must make some minor adjustments to the equa- of oxygen at [ojO.s as Pso, substitution in Equation 5-10 tions so that laboratory experiments can be carried out gives more conveniently. We first substitute the concentration 02 of dissolved oxygen for L in Equation 5-8 to give (5-11) a binding curve for myoglobin that relates e to pOe is shown in Figure 5-4b TABLE 5-1 Some Protein Dissociation Constants Prote Ligand Kd(M) Avidin(egg white Biotin 1×10 Insulin receptor(human) Insulin 1×10 gp41(HIV-1 surface protein) 4 Nickel-binding protein(E. co) 1×10-7 3×10-6 rticular solution cond tions under which it was measured. Ke values for a protein-ligand interaction I be altered, sometimes by several orders of magnitude, by changes in the solutions salt concentration, pH, or other variables. ' interaction of avidin with biotin, an enzyme cofactor, is among the strongest noncovalent biochemical interactions known. "This immunoglobulin w and the K repo should not be considered characteristic of all immunoglobulins Calmodulin has four binding sites for calum. The values shown reflect the highest- and lowest-affinity bind ng sites observed in one set of measurements

a lower value of Kd corresponds to a higher affinity of ligand for the protein. The mathematics can be reduced to simple statements: Kd is equivalent to the molar con￾centration of ligand at which half of the available ligand￾binding sites are occupied. At this point, the protein is said to have reached half-saturation with respect to lig￾and binding. The more tightly a protein binds a ligand, the lower the concentration of ligand required for half the binding sites to be occupied, and thus the lower the value of Kd. Some representative dissociation constants are given in Table 5–1. The binding of oxygen to myoglobin follows the pat￾terns discussed above. However, because oxygen is a gas, we must make some minor adjustments to the equa￾tions so that laboratory experiments can be carried out more conveniently. We first substitute the concentration of dissolved oxygen for [L] in Equation 5–8 to give [O2 [ ] O
2] Kd (5–9) As for any ligand, Kd is equal to the [O2] at which half of the available ligand-binding sites are occupied, or [O2]0.5. Equation 5–9 thus becomes [O2]
[O [ 2 O ]  2]0.5 (5–10) In experiments using oxygen as a ligand, it is the par￾tial pressure of oxygen in the gas phase above the solution, pO2, that is varied, because this is easier to measure than the concentration of oxygen dissolved in the solution. The concentration of a volatile substance in solution is always proportional to the local partial pressure of the gas. So, if we define the partial pressure of oxygen at [O2]0.5 as P50, substitution in Equation 5–10 gives pO2 pO
2 P50 (5–11) A binding curve for myoglobin that relates to pO2 is shown in Figure 5–4b. Chapter 5 Protein Function 161 1.0 0.5 0 v P50 5 10 (b) pO2 (kPa) 1.0 0.5 0 v 5 (a) Kd 10 [L] (arbitrary units) FIGURE 5–4 Graphical representations of ligand binding. The frac￾tion of ligand-binding sites occupied, , is plotted against the con￾centration of free ligand. Both curves are rectangular hyperbolas. (a) A hypothetical binding curve for a ligand L. The [L] at which half of the available ligand-binding sites are occupied is equivalent to 1/Ka, or Kd. The curve has a horizontal asymptote at 1 and a vertical asymptote (not shown) at [L] 1/Ka. (b) A curve describing the bind￾ing of oxygen to myoglobin. The partial pressure of O2 in the air above the solution is expressed in kilopascals (kPa). Oxygen binds tightly to myoglobin, with a P50 of only 0.26 kPa. TABLE 5–1 Some Protein Dissociation Constants Protein Ligand Kd (M)* Avidin (egg white)† Biotin 1  1015 Insulin receptor (human) Insulin 1  1010 Anti-HIV immunoglobulin (human)‡ gp41 (HIV-1 surface protein) 4  1010 Nickel-binding protein (E. coli) Ni2
1  107 Calmodulin (rat)§ Ca2
3  106 2  105 *A reported dissociation constant is valid only for the particular solution conditions under which it was measured. Kd values for a protein-ligand interaction can be altered, sometimes by several orders of magnitude, by changes in the solution’s salt concentration, pH, or other variables. † Interaction of avidin with biotin, an enzyme cofactor, is among the strongest noncovalent biochemical interactions known. ‡ This immunoglobulin was isolated as part of an effort to develop a vaccine against HIV. Immunoglobulins (described later in the chapter) are highly variable, and the Kd reported here should not be considered characteristic of all immunoglobulins. § Calmodulin has four binding sites for calcium. The values shown reflect the highest- and lowest-affinity binding sites observed in one set of measurements. 8885d_c05_157-189 8/12/03 8:55 AM Page 161 mac78 mac78:385_REB: