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CHAPTER 7 Enzymes II: Regulation The metabolic rate of key substances, which can proceed in multiple pathways, is regulated and integrated. A close interrelationship exists among products formed by different metabolic pathways from a common metabolite. For example, glucose can be consumed either by oxidation to CO2 or by conversion to glycogen, lipid, nonessential amino acids, or other sugar molecules. The glucose supply of the body can be derived either from the diet or from the breakdown of glycogen, a polymer of glucose (primarily from the liver and the kidney), or it can be synthesized from some amino acids or lactate (predominantly in the liver). These processes of glucose utilization and synthesis are under tight regulation. In fact, the plasma glucose level is maintained at the level at which tissues (e.g., brain, erythrocytes, kidney medulla, and the lens and cornea of the eye) that require glucose as a primary substrate are not deprived of this essential fuel. Each of these metabolic pathways is mediated by enzymes that are unique for a given pathway and that are under control. Metabolic pathways do not usually compete with each other for utilization of a substrate, and they operate only to serve a particular physiological need or function. 7.1 Types of Regulation A metabolic pathway involves many enzymes functioning in a sequential manner or in some unique arrangement to carry out a particular metabolic process. Control of a pathway is accomplished through modulation of the activity of only one or a few key enzymes. These regulatory enzymes usually catalyze the first or an early reaction in a metabolic sequence. A regulatory enzyme catalyzes a rate-limiting (or rate-determining) chemical reaction that controls the overall pathway. It may also catalyze a chemical reaction unique to that pathway, which is known as a committed step. In the metabolic pathway for the formation of E from A, A -~ B -~-~ C -~ D -~ E the conversion of A to B, catalyzed by the enzyme El, is the rate-limiting step and also a committed step. The ratelimiting step need not be the same as the committed step. In the branched metabolic pathway, E1 A E2 ~B E3 E4 ~ C ------* D E6 L *E E7 *M ~-N if the conversion of A to B is the rate-limiting step, the committed step in the pathway for the formation of N is the conversion of B to L (B --+ L), catalyzed by the enzyme E5. Those enzymes which catalyze the rate-limiting step or the committed step of a pathway are under regulation. When the end product exceeds the steady-state level concentration, it inhibits the regulatory enzyme in an 109 110 attempt to normalize the overall process. This type of control, known as feedback inhibition (see below), ensures a high degree of efficiency in the utilization of materials and of energy in living systems. Regulation may be achieved in other ways. The absolute amount of a regulatory enzyme may be altered through mechanisms that control gene expression (Chapter 26). This regulation at the genetic level occurs during various phases of reproduction, growth, and development, with different metabolic pathways being turned on or off in accordance with the special requirements of each phase. In eukaryotic cells, regulation at the genetic level is relatively a long-term process. Several short-term regulatory mechanisms control metabolic activity rapidly (see below). Both substrates and some hormones play significant roles in regulating the concentration of key enzymes at this level. Many drugs or other chemicals can increase levels of enzymes that affect their own metabolism. Thus, phenobarbital and polycyclic hydrocarbons increase the levels of microsomal enzyme systems involved in their metabolism. Regulation of metabolic processes can be accomplished by other methods. One is the use of a multienzyme complex (e.g., pyruvate dehydrogenase complex or fatty acid synthase complex) in which various enzymes are organized such that the product of one becomes the substrate for an adjacent enzyme. A single polypeptide chain may contain multiple catalytic centers that carry out a sequence of transformations (e.g., the mammalian fatty acid synthase; see Chapter 18). Such multifunctional polypeptides increase catalytic efficiency by abolishing the accumulation of free intermediates and by maintaining a stoichiometry of 1:1 between catalytic centers. Another type of regulation is accomplished by a series of proenzymes in which activation of the initial proenzyme by a biological signal activates the second proenzyme which, in turn, activates the third, and so on. Such an enzyme cascade process provides great amplification in terms of the amount of final product formed. Examples are blood coagulation, the dissolution of blood clots, complement activation, and glycogen breakdown. Regulation is also accomplished by compartmentalization of enzyme systems involved in anabolic and catabolic pathways into different cell organelles. For example, fatty acid synthesis occurs in the soluble fraction of the cytoplasm, whereas fatty acid oxidation takes place in mitochondria. Heme synthesis begins and is completed in mitochondria, but some of the intermediate reactions take place in the cytosol. Heme catabolism is initiated in the smooth endoplasmic reticulum. Transport of key metabolites across an organelle membrane system is also a form of regulation. CHAPTER7 Enzymes I1: Regulation Many enzymes occur in several molecular forms called isoenzymes (or isozymes), and those which are genetically determined may be called primary isoenzymes. The different primary isoenzymes catalyze the same chemical reaction but may differ in their primary structure and kinetic properties. The tissue distribution of isoenzymes imparts distinctive properties and specific patterns of metabolism to organs of the body. The presence of isoenzymes may reveal differences not only between organs but also between cells that make up an organ or between organelles of a cell. During different stages of differentiation and development from embryonic life to adulthood, the isoenzyme distribution in an organ undergoes characteristic changes. When an adult organ reverts to the embryonic or fetal state (e.g., in cancer), the isoenzyme distributions change to those characteristic of that developmental state. The existence of isoenzymes in human tissues has important implications in the study of human disease. Zymogen (e.g., trypsinogen and chymotrypsinogen) synthesis, secretion, transport, and activation and the rate of inactivation of the active enzyme by inhibitors may all be considered means of enzyme regulation. Enzyme activity can be regulated by covalent modification or by noncovalent (allosteric) modification. A few enzymes can undergo both forms of modification (e.g., glycogen phosphorylase and glutamine synthetase). Some covalent chemical modifications are phosphorylation and dephosphorylation, acetylation and deacetylation, adenylylation and deadenylylation, uridylylation and deuridylylation, and methylation and demethylation. In mammalian systems, phosphorylation and dephosphorylation are most commonly used as means of metabolic control. Phosphorylation is catalyzed by protein kinases and occurs at specific seryl (or threonyl) residues and occasionally at tyrosyl residues; these amino acid residues are not usually part of the catalytic site of the enzyme. Dephosphorylation is accomplished by phosphoprotein phosphatases: ATP ADP O Mg2+ Enzyme-Ser-OH ~,. f Phosphoprotein-"~ phosphatase O H20 II Enzyme-Ser-O--P--O- I O- II HO--P--O- I O- The overall process of phosphorylation and dephosphorylation is a cascade of reactions and consists of an extracellular signal, commonly referred to asfirst messenger (e.g., hormones, such as glucag0n); a specific receptor on the cell membrane of the target cell; a transducer coupled to the SECTION 7.2 AIIostericEnzymeRegulation receptor that produces an intracellular signal (i.e., a second messenger); one or more modifying enzymes whose activity is affected by the intracellular signal; a target enzyme, which is the substrate for the modifying enzyme and subjected to covalent modification with consequent metabolic alteration; and an enzyme that reverses the modification of the target enzyme. The transducer of the system is adenylate cyclase, and it catalyzes the cyclization of ATP to cyclic AMP (cAMP), the second messenger. The modifying enzyme is a protein kinase activated by cAME Other protein kinases are activated by non-cAMPdependent or CaZ+-dependent systems (Chapter 30). Phosphorylation of a target enzyme may be either stimulatory or inhibitory. For example, phosphorylation converts glycogen phosphorylase to an activated form and glycogen synthase to an inactivated form, thus preventing the simultaneous occurrence of glycogen breakdown and synthesis (Chapter 15). 7.2 AIIosteric Enzyme Regulation Those enzymes in metabolic pathways whose activities can be regulated by noncovalent interactions of certain compounds at sites other than the catalytic are known as allosteric enzymes. They are usually rate-determining enzymes and play a critical role in the control and integration of metabolic processes. The term "allosteric" is of Greek origin, the root word "allos" meaning "other." Thus, an allosteric site is a unique region of an enzyme other than the substrate binding site that leads to catalysis. At the allosteric site, the enzyme is regulated by noncovalent interaction with specific ligands known as effectors, modulators, or modifiers. The properties of allosteric enzymes differ significantly from those of nonregulatory enzymes. Ligands (in some instances even the substrate) can bind at such sites by a cooperative binding process. Cooperativity describes the process by which binding of a ligand to a regulatory site affects binding of the same or of another ligand to the enzyme. Allosteric enzymes have a more complex structure than nonallosteric enzymes and do not follow Michaelis-Menten kinetics. An allosteric site is specific for its ligand, just as the active site is specific for its substrate. Binding of an allosteric modulator causes a change in the conformation of the enzyme (see below) that leads to a change in the binding affinity of the enzyme for the substrate. The effect of a modulator may be positive (activatory) or negative (inhibitory). The former leads to increased affinity of the enzyme for its substrate, whereas the reverse is true for the latter. Activatory sites and inhibitory sites are separate and specific for their 111 respective modulators. Thus, if an end product of a metabolic pathway accumulates in excess of its steadystate level, it can slow down or turn off the metabolic pathway by binding to the inhibitory site of the regulatory enzyme of the pathway. As the concentration of the end product (inhibitor) decreases below the steady-state level, the number of enzymes having bound inhibitor decreases and they revert to their active form. In this instance, the substrate and the negative modulator bear no structural resemblance. An allosteric enzyme may be positively modulated by the substrate itself or by a metabolite of another pathway that depends on production of the end product in question for its eventual utilization (e.g., pathways of synthesis of purine and pyrimidine nucleotides in the formation of nucleic acids; see Chapter 27). Most allosteric enzymes are oligomers (i.e., they consist of two or more polypeptide chains or subunits). The subunits are known asprotomers. Two types of interaction occur in allosteric enzymes: homotropic and heterotropic. In a homotropic interaction, the same ligand influences positively the cooperativity between different modulator sites. An example is a regulatory enzyme modulated by its own substrate. Thus, this class of enzyme has at least two substrate binding sites which respond to situations that lead to substrate excess by increasing its rate of removal. Heterotropic interaction refers to the effect of one ligand on the binding of a different ligand. For example, a regulatory enzyme modulated by a ligand other than its substrate constitutes a heterotropic system, in which the cooperativity can be positive or negative. Some allosteric enzymes exhibit mixed homotropic and heterotropic interactions. Kinetics of Allosteric Proteins The kinetic properties of allosteric enzymes vary significantly from those of nonallosteric enzymes, exhibiting cooperative interactions between the substrate, the activator, and the inhibitor sites. These properties are responsible for deviations from the classic Michaelis-Menten kinetics that apply to nonallosteric enzymes. Nonallosteric enzymes yield a rectangular hyperbolic curve when the initial velocity (v) is plotted against the substrate concentration [S]. For allosteric enzymes, a plot of v versus [S] yields curves of different shapes, including sigmoidshaped curves in some cases. (A sigmoidal curve can result from other mechanisms.) The v versus [S] plot for a homotropic enzyme is shown in Figure 7-1. The following features should be noted: 1. The substrate functions as a positive modulator; i.e., there is positive cooperativity between the substrate binding sites so that binding of the substrate at one 112 CHAPTER7 Enzymes I1: Regulation FIGURE 7-1 Relationship between the initial velocity (v) and the substrate concentration [S] for an allosteric enzyme that shows a homotropic effect. The substrate functions as a positive modulator. The profile is sigmoidal, and during the steep part of the profile, small changes in [S] can cause large changes in v. K0.5 representsthe substrate concentration corresponding to half-maximalvelocity. FIGURE 7-2 Relationship between the initial velocity (v) and the substrate concentration [S] for an allosteric enzyme that shows a heterotropiceffect with constant Vmaxbut with varying K0.5. Curve a is obtained in the absence of any modulators,curve b in the presence of a positive modulator, and curve c in the presence of a negativemodulator. Regulation is achieved by modulation of K0.5 without change in Vmax. binding site greatly enhances binding of the substrate at the other sites. As the substrate concentration increases, there is a large increase in the velocity of the reaction. 2. Owing to the above effect, the shape of the curve is sigmoidal. 3. The value of the substrate concentration corresponding to half-maximal velocity is designated as K0.5 and not Km since the allosteric kinetics do not follow the hyperbolic M i c h a e l i s - M e n t e n relationship. 4. M a x i m u m velocity (Vmax) is attainable at a rather high substrate concentration, implying saturation of the catalytic site of the enzyme. can be turned on or off with appropriate modulators. Figure 7-3 shows v versus [S] plots for allosteric enzymes modulated by changes in Vmax but retaining an essentially constant K0.5. This type of modulation is less c o m m o n than the two previous cases considered. The positive modulator increases gmax(curve b), whereas the negative modulator decreases Vmax (curve c). We will consider two specific examples of allosteric p r o t e i n s m o n e an e n z y m e and the other an oxygen transport protein. The v versus [S] plot for heterotropic enzymes is more complex. The kinetic profiles can be divided into two classes, depending upon whether the allosteric effector alters K0.5 and maintains a constant Vmax or alters Vmax and maintains a nearly constant K0.5. The v versus [S] profile of an allosteric e n z y m e that follows the former set of properties is shown in Figure 7-2. In the absence of any modulators, the profile is sigmoidal (curve a). In the presence of a positive modulator (curve b), the value for K0.5 is decreased; i.e., a lower substrate concentration is required to attain half-maximal velocity. Curve b is more hyperbolic than sigmoidal. Curve c obtained with a negative modulator is more sigmoidal than curve a, and the K0.5 value is increased, reflecting a decreased affinity for the substrate, i.e., a higher substrate concentration is required to attain half-maximal velocity. Regulation of the e n z y m e is achieved through positive and negative modulators. Thus, at a given substrate concentration (e.g., steady-state level), the activity of the e n z y m e FIGURE 7-3 Relationship between the initial velocity (v) and the substrate concentration [S] for an allosteric enzyme that shows a heterotropiceffect with constant K0.5 but with varying Vmax.Curve a is obtained in the absence of any modulator, curve b in the presence of a positive modulator, and curve c in the presence of a negativemodulator. Regulationis achieved by modulation of Vmaxwithout change in K0.5. E x a m p l e s of A l l o s t e r i c P r o t e i n s SECTION7.2 AIIosteric Enzyme Regulation 113 1. Aspartate transcarbamoylase (ATCase) is an allosteric enzyme of the bacterium Escherichia coli, which has been extensively studied. This enzyme catalyzes the transfer of the carbamoyl group from carbamoyl phosphate to the u-amino group of aspartate: CO2 + Glutamine + ATP Carbamoyl phosphate Aspartate---~l N- Carbamoyl aspartate O O II II H + I 3 I E m. H2NmC--O--P~O- + H3N~C~COO- I O- CH2 I Uridine monophosphate (UMP) [ O ,4 COO Carbamoyl phosphate Aspartate Uddine triphosphate (UTP) o --4 "o O II HO~I~OOInorganic phosphate (P~ O H II I H2N--C--NmC--COO- + H + H I CH2 I COO N-Carbamoyl aspartate This committed reaction, catalyzed by a regulatory enzyme, is the second step (Figure 7-4) in the biosynthesis of pyrimidines. N-carbamoylaspartate ultimately is converted to the pyrimidine nucleotide cytidine triphosphate (CTP), which is the negative modulator of the enzyme. That is, as the CTP concentration increases, it inhibits the ATCase by decreasing its affinity for substrates. The preceding is an example of an allosteric feedback inhibition. ATCase has a molecular weight of 310,000 and consists of 12 polypeptide chains (subunits). The catalytic and the regulatory sites reside on two different sets of subunits: six larger subunits (M.W. 33,000) have catalytic sites, and six smaller subunits (M.W. 17,000) have regulatory sites. X-ray crystallographic studies of ATCase by Lipscomb showed that the molecule is roughly triangular. The six catalytic subunits (C) are present as two trimers (C3), one above the other (but not exactly parallel), with the dimeric regulatory subunits (R2) forming an equatorial belt around the edges of the trimers (Figure 7-5). In the center of the molecule, an aqueous cavity is accessible through several openings. ATCase can be dissociated into two unequal clusters with different subunit arrangements by treatment with mercurials (e.g., p-hydroxymercuribenzoate). The larger cluster containing three catalytic subunits (C3) Cytidine triphosphate (CTP) F I G U R E 7-4 Regulation of pyrimidine nucleotide biosynthesis in E. coli. is catalytically active. The v versus [S] plot exhibits a hyperbolic profile and is insensitive to CTE The smaller cluster is a dimer of regulatory subunits (R2) and, as expected, shows no catalytic activity but does bind to CTE The native enzyme can be reconstituted with return of the allosteric activity by removal of the mercurial compound and mixing of both catalytic and regulatory clusters: 2C3 -k3R2 --+ R6C6 Catalytic Regulatory Native cluster cluster enzyme Reconstitution also requires zinc ions (Zn2+), since the native enzyme contains six atoms of Zn 2+. C3 and R2 clusters can be dissociated further into their respective, inactive monomeric subunits by strong denaturing agents (Figure 7-5). ATCase can assume different conformations depending on whether it is active or inactive. In the presence of the substrate or positive modulator, it is in a catalytically more active conformation known as the relaxed state or R-state. In the presence of the negative modulator, the enzyme is in less active conformation known as the taut state or T-state. The allosteric kinetic effects of ATCase are shown in Figure 7-6. The interaction of substrates with the enzyme is cooperative (an example of homotropic cooperativity), as indicated by the sigmoidal shapes of the v versus [S] plots, CTP being an inhibitor and ATP an activator. These modulators compete for the same regulatory site and modulate the affinity of the enzyme for its 114 CHAPTER7 Enzymes I1: Regulation Hg 2+ ( +3 Native enzyme Active catalytic subunit Active regulatory su]~unit I SDS 0 Inactive catalytic subunit o Inactive regulatory subunit (a) Substrates ~ '""J ~ CTP R state T state (6) F I ( ; U R E 7-5 Schematic representation of the subunit structure of aspartate transcarbamoylase and its dissociation into catalytic and regulatory subunits by mercurials, which can be further converted to inactive monomeric subunits by strong denaturing agents (e.g., sodium dodecyl sulfate). The native enzyme consists of two catalytic trimers placed one above the other, along with three dimeric regulatory subunits surrounding the catalytic trimers in an equatorial plane (a). Substrate maintains the enzyme in the catalytically more active relaxed (R) conformation, while cytidine triphosphate maintains it in the catalytically less active taut (T) conformation (b). [Reproduced, with permission from E. L. Smith, R. L. Hill, I. R. Lehman, et al: Principles of Biochemistry: General A.wects, 7th ed. McGraw-Hill, New York, 1983]. substrates, without altering Vmax. The biological significance of the activation by the purine nucleotide ATP can be appreciated, since both ATP and CTP are eventually utilized in the biosynthesis of double-helical DNA, which contains equal amounts of purines and pyrimidines. Thus, modulation of ATCase activity equalizes the rates of formation of purine and pyrimidine nucleotides. Other regulatory and metabolic aspects of purines and pyrimidines are discussed in Chapter 27. 2. Hemoglobin binding of oxygen is a classic example of the homotropic effect. Hemoglobin also shows heterotropic effects with specific molecules in its environment. These effects are intimately related to the function of hemoglobin as a carrier not only of oxygen but of H + and CO2 (Chapters 1 and 28). The heterotropic modulators are H +, CO2, and F I G U R E 7-6 Relationship between the initial velocity (v) of aspartate transcarbamoylase and the substrate concentration. Note that ATP is a positive allosteric modulator, which causes decreased K0.5, whereas CTP is a negative allosteric modulator, which causes increased K0.5. SECTION7.2 Allosteric Enzyme Regulation FIGURE 7-7 Profiles of oxygenationof myoglobinand hemoglobinas a function of partial pressure of oxygen.Myoglobinshows a typicalMichaelis-Menten type of rectangularhyperbolicsaturationcurve, whereashemoglobin shows a sigmoidalsaturationcurve, consistentwith its allostericproperties. Myoglobinat any partial pressure of oxygenhas muchhigher affinityfor oxygen than does hemoglobin. [Reproducedwith permissionfrom A. Lehninger,Principles of Biochemistry. Worth,New York, 1982.] 2,3-bisphosphoglycerate (BPG or DPG). The cooperativity of oxygen binding to hemoglobin and the alterations of hemoglobin by various ligands provide the most extensively investigated molecular regulation of a biological process. Hemoglobin carries oxygen from the lungs to the tissues and carries CO2 and H + back from the tissues to the lungs (Chapter 1), whereas myoglobin functions as an oxygen store in muscle. Consistent with its function, myoglobin has a higher affinity for oxygen at any partial pressure of oxygen than does hemoglobin (Figure 7-7). Thus, oxygen can be transferred easily from hemoglobin to myoglobin. Hemoglobin is a tetramer consisting of two different subunit types (e.g., ot and/3 in hemoglobin A). Each polypeptide contains one heme group (an iron-porphyrin prosthetic group) that binds to one oxygen molecule by a cooperative process. Myoglobin, a monomeric protein with one heme group, remains monomeric under a wide range of concentrations and does not show cooperative binding with oxygen. The polypeptides of myoglobin and hemoglobin exhibit many differences with respect to their primary structures. For example, the many amino acid residues present on the surface of 115 myoglobin are polar, whereas many of those in the individual hemoglobin polypeptide chains are capable of participating in nonpolar interactions with other subunits. Despite these differences, critical regions are conserved in the polypeptide chains of myoglobin and hemoglobin, namely, the proximal and distal histidyl residues that interact with the heme iron, the hydrophobic amino acid residues that surround the heme group, and certain prolyl residues that interrupt the helical regions to allow the chain to fold back upon itself. The region of the polypeptide chain in contact with the heme group is known as the heme pocket. The amino acid residues in this pocket maintain the heme iron in the divalent state, which is the functional oxidation state of iron in both myoglobin and hemoglobin. Thus, the single polypeptide chain of myoglobin and the two different chains of hemoglobin are remarkably similar in secondary and tertiary structures (Figure 7-8). These similarities support the hypothesis that myoglobin and hemoglobin evolved by gene duplication and subsequent mutation from a common ancestral oxygen-binding heme protein. The binding of oxygen to myoglobin is not cooperative, but the binding of oxygen to hemoglobin is cooperative. This difference can be accounted for kinetically by considering the equilibrium for dissociation of oxymyoglobin (MbO2) to deoxymyoglobin (Mb) and oxygen (O2): MbO2 ~- Mb + 02 (7.1) The equilibrium constant, Kd -- [Mb][O2] [MbO2] (7.2) is expressed in moles per liter, and its value depends on pH, ionic strength, and temperature. Since myoglobin has a single oxygen binding site, a single equilibrium defines the dissociation of oxymyoglobin. So that we can deal with measurable parameters, Equation (7.2) needs to be modified by the introduction of two terms, Y and Ps0. Y is defined as the fractional saturation of myoglobin, e.g., when Y = 0.3, 30% of the available sites on the myoglobin are occupied by oxygen. Thus, Y number of binding sites occupied by 02 total number of binding sites available for binding 02 or Y= [MbO2] [Mb] + [MbO2] (7.3) 116 CHAPTER7 Enzymes I1 Regulation [F$ try{ NAI d 13-Chain of hemoglobin Myoglobin FIGURE 7-8 The remarkable similarity in the conformations of myoglobin and of the/3-chain of hemoglobin. [Reproduced with permission from A. Fersht, Enzyme Structure and Mechanism. (W. H. Freeman, New York, 1977.] Substituting Equation (7.2) into Equation (7.3), we obtain [02] Y = (7.4) Equation (7.8) is known as the Hill equation. A plot of l o g ( Y / 1 - Y) versus log Po2 yields a straight line with a slope of 1 (the Hill coefficient) (Figure 7-10). Thus, a value [02] -']- Kd Because 02 is a gas, it is convenient to express [02] in terms of its partial pressure in units of Torr (or m m Hg; multiply by 0.133 to obtain kilopascals). Therefore, y = Po2 Po2 + Kd (7.5) Now we can substitute for Kd the term Ps0, which is defined as the partial pressure of oxygen at which 50% of the sites are occupied (i.e., when Y -- 0.5), because this situation is analogous to the M i c h a e l i s - M e n t e n treatment of e n z y m e kinetics. y = Po2 (7.6) Po: +/'50 A plot of Y versus Po2 yields an oxygen saturation profile that is a rectangular hyperbola (Figure 7-9), indicating that the binding of oxygen to myoglobin is noncooperative. Equation (7.6) can be rearranged to yield a linear plot as follows: Y 1 - = Y Po2 Ps0 (7.7) Taking the logarithms of both sides of Equation (7.7) yields log 1 -Y Y ) -- log Po2 - l o g / 5 0 (7.8) FIGURE 7-9 Profiles of fractional saturation of myoglobin and of hemoglobin with oxygen as a function of partial pressure of oxygen. Under physiological conditions,/50 for myoglobin is only 1 or 2 torr, whereas for hemoglobin it is 26 torr, indicating that oxygen is bound much more tightly to myoglobin than to hemoglobin. The loading and unloading to oxygen are cooperative in the case of hemoglobin but not cooperative in the case of myoglobin. SECTION 7.2 AIIosteric EnzymeRegulation 117 Rearrangement of Equation (7.14) yields Y ~.(eo2~ n 1 -Y \-~5o/ The Hill equation is obtained by taking the logarithm of both sides: log FIGURE 7-10 Hill plots for myoglobin and hemoglobin. A slope of 1.0 for myoglobin is consistent with noncooperative oxygen binding, whereas a slope of 2.8 for hemoglobin is indicative of cooperative oxygen binding. of 1 for the Hill coefficient is indicative of noncooperativity; as we will see with hemoglobin, values greater than 1 indicate positive cooperativity, and values less than 1 indicate negative cooperativity. A molecule of hemoglobin (Hb) can bind four molecules of oxygen, and therefore four equilibrium expressions can be written to describe the dissociations of HbO2, Hb(O2)2, Hb(O2)3, and Hb(O2)4. For simplicity, we consider an equilibrium in which Hb(O2)4 dissociates into deoxyhemoglobin and four molecules of oxygen: Hb(O2)4 ~- Hb + 402 (7.9) The equilibrium constant for Reaction (7.9) is" K -- [Hb] [02] 4 [Hb (O2)4] (7.10) Based upon considerations similar to those for myoglobin dissociation, the value for Y is (Po2) 4 Y = (7.11) (P02)4 _Jr_(P50) 4 A plot of Y versus /~ yields a sigmoidal curve, indicating cooperative binding of oxygen to hemoglobin. A general expression for the dissociation of oxyhemoglobin to deoxyhemoglobin and oxygen may be written as Hb(O2)n ~-- Hb + nO2 (7.12) where n is the number of molecules of oxygen. The equilibrium constant for reaction (7.12) is K -- [Hb] [O21n [Hb (O2)n] (7.13) and Y = (/'02)" (P02) n --]--(P50) n (7.14) 1-Y --nlogPo2-nlogPs0 A plot of log ( Y / 1 - Y) versus log Po2 yields a straight line with a slope of n, the Hill coefficient. For hemoglobin, n = 2.8 (Figure 7-10), which signifies that the binding of oxygen to hemoglobin exhibits positive cooperativity. From a physiological point of view, the cooperative oxygen binding characteristics of hemoglobin are eminently suited for the transport of oxygen from the lungs to the tissues. In the alveolar spaces of the lungs, the partial pressure of oxygen is about 100 Torr, and about 97% of the hemoglobin is combined with oxygen (i.e., 97% saturation with 02). As the oxygenated blood passes through the tissue capillaries, where the partial pressure of oxygen often falls below 40 Torr (in actively exercising muscle, the Poe is about 20 Torr), about 30% of the oxygen is unloaded from oxyhemoglobin to tissue cells. This process is cooperative, so that as 02 is released from oxygen-saturated hemoglobin because of a drop in Po2, the loss of a single 02 molecule causes rapid release of the remaining ones. Similarly in the lungs, the affinity of hemoglobin for binding the first 02 molecule is low; however, once this molecule is bound, the affinity increases. Myoglobin, in conformity with its storage function, has higher affinity for oxygen than does hemoglobin at any partial pressure of oxygen (Figure 7-9). X-ray studies have shown that oxyhemoglobin (R form) and deoxyhemoglobin (T form) have different threedimensional conformations. However, no changes in the tertiary structure of the individual subunits have been observed. The molecular mechanisms of cooperative binding of oxygen are known, and the details of this process along with other ligand interactions with hemoglobin are discussed in Chapter 28. Theoretical Models for Allosteric Effect Two theoretical models for allosteric effects have been proposed to explain the mechanism for ligand-protein cooperative interactions: the concerted (or symmetry) model of Monod, Wyman, and Changeux and the sequentially inducedfit model of Koshland. The nomenclature associated with allosterism and cooperativity originated from the concerted model. Both models assume that 1. Each subunit of an oligomeric protein exists in two forms, T and R, which bind the ligand with low and high affinity, respectively; and 2. The T ~-- R transformations involve noncovalent bonds and result in changes in the quaternary structure of the enzyme. 118 CHAPTER 7 EnzymesI1 Regulation Catalyticsiteswith low affinityf.orsubstrate Catalytic sites with low affinity for substrate AIIosteric AIIosteric site site eAiiosteric..___.~~ t is ~ "~ ~,,_._.__ AIIosteric site TT state TTstate Positive modulator (or substrate in positive homotropic cooperativity)preferentially bindsto the R form and maintains the allosteric protein in the RR conformation. Catalytic sites with high affinity for substrate modulator preferentially binds to the T form and maintains the allosteric protein in the TT conformation, Negative Negative modulator Positive modulator Ne0atve cooperativity Postve coope rativity TR state Negative modulator Positive modulator RR state FIGURE 7-11 Schematic diagram of conformational changes of concerted model for a dimeric allosteric enzyme. All subunits are either in the T-form with low affinity for the substrate or in the R-form with high affinity for the substrate. The concerted model has the following features. The allosteric protein exists only in two states: T or R. If, for example, an allosteric protein contains two subunits, the sole permissible conformation states are TT and RR (RT is not allowed because R and T cannot form a stable pair). Thus, in this model (also called the "all or none" model), symmetry of the allosteric protein is preserved (Figure 7-11). It is assumed that the T and R forms are in equilibrium, that significant binding of ligand occurs only to the R form, and that this binding shifts the equilibrium strongly in favor of formation of the R form. Thus, a conformational change in one subunit that occurs after it binds to a ligand causes a corresponding change in all of the subunits without formation of hybrid species. The concerted model accounts for the kinetic behavior of many allosteric proteins, but it cannot account for negative cooperativity; i.e., the decrease in affinity for a ligand by the allosteric protein as the sites become occupied. The sequential model proposes that as the ligand binds to a subunit a conformational change is induced that stabilizes the ligand-allosteric protein complex such that a second ligand molecule is bound more readily than the first (Figure 7-12). This effect is of positive cooperativity. However, if the initial binding of the ligand results in a ligandprotein complex with decreased stability, the binding of additional ligand molecules, or ligand-induced substrate binding, becomes increasingly difficult. This effect is negative cooperativity. In this model, the notion of symmetry is discarded, since a conformational change induced by a ligand that binds to a subunit also induces a conformational change in an adjacent subunit. Figure 7-13 shows sequential transmission of conformational changes through contiguous subunits upon RR state FI(;URE 7-12 Schematic diagram of conformational changes of sequentially induced-fit model for a dimeric allosteric enzyme. The TT conformation is progressively converted to the RR conformation via the intermediateTR conformation through cooperative interaction in the presence of the positive modulator. In the presence of the negative modulator, the opposite conformational changes occur. In this model, the notion of symmetryis discarded and the concept of induced fit is emphasized. ligand binding. The behavior of some allosteric proteins is best explained by the concerted model, whereas for others the sequential model is more appropriate. For many proteins, neither model is satisfactory and a more complex model may be required. T form R form m=m=FF 88---88 FIGURE 7-13 Sequential transmission of conformational changes through contiguous subunits induced by a ligand (S). In idealized form, the conformational changes proceed diagonally as the protein progressivelybinds ligand. 119 Supplemental Readings and References Supplemental Readings and References Enzyme Regulation (General) Z. Dische: The discovery of feedback inhibition; Trends in Biochemical Sciences 1, 269 (1976). D. E. Koshland, G. Nemethy, and D. Filmer: Comparison of experimental binding data and theoretical models in proteins containing subunits; Biochemistry 5, 365 (1966). J. Monod, J.-E Changeux, and E Jacob: Allosteric proteins and cellular control systems. Journal of Molecular Biology 6, 306 (1963). J. Monod, J. Wyman, and J.-E Changeux: On the nature of allosteric transitions: A plausible model. Journal of Molecular Biology 12, 88 (1965). H. L. Segal: Enzymatic interconversions of active and inactive forms of enzymes. Science 180, 25 (1973). G. Weber, (Ed): Advances in Enzyme Regulation, Vols. 1-6. Pergamon Press, London, 1963-1979. Allosteric Properties of Aspartate Transcarbamoylase and Hemoglobin Aspartate Transcarbamoylase E Hensley and H. K. Schachman: Communication between dissimilar subunits in aspartate transcarbamoylase: Effect of inhibitor and activator on the conformation of the catalytic polypeptide chains. Proceedings of the National Academy of Sciences USA. 76, 3732 (1979). E. V. Kantrowitz, S. C. Pastra-Landis, and W. N. Lipscomb: E. coli aspartate transcarbamoylase. Part 2. Structure and allosteric interactions. Trends in Biochemical Sciences 5, 150 (1980). I. L. Monoco, J. L. Crawford, and W. N. Lipscomb: Three dimensional structures of aspartate transcarbamoylase from Escherichia coli and its complex with cytidine triphosphate. Proceedings of the National Academy of Sciences USA. 75, 5276 (1978). Hemoglobin J. Baldwin and C. Chothia: Hemoglobin: The structural changes related to ligand binding and its allosteric mechanism. Journal of Molecular Biology 129, 175 (1979). M. F. Perutz: Stereochemistry of cooperative effects of hemoglobin. Nature 228, 726 (1970). M. E Perutz: Hemoglobin structure and respiratory transport. Scientific American 239(6), 92 (1978). M. E Perutz: Regulation of oxygen affinity of hemoglobin: Influence of structure of the globin on the heme iron. Annual Review of Biochemistry 48, 327 (1979).