《生物化学原理》英文版（一）：2

Chymotrypsin 8885d_c01_044 1/16/04 12:35 PM Page 44 mac76 mac76:385_reb: 2 Water 47 3 Amino Acids, Peptides, and Proteins 75 4 The Three-Dimensional Structure of Proteins 116 5 Protein Function 157 6 Enzymes 190 7 Carbohydrates and Glycobiology 238 8 Nucleotides and Nucleic Acids 273 9 DNA-Based Information Technologies 306 10 Lipids 343 11 Biological Membranes and Transport 369 12 Biosignaling 421 In 1897 Eduard Buchner, the German research worker, discovered that sugar can be made to ferment, not only with ordinary yeast, but also with the help of the expressed juices of yeast which contain none of the cells of the Saccharomyces ...Why was this apparently somewhat trivial experiment considered to be of such significance? The answer to this question is self-evident, if the development within the research work directed on the elucidation of the chemical nature of (life) is followed . . . there, more than in most fields, a tendency has showed itself to consider the unexplained as inexplicable . . . Thus ordinary yeast consists of living cells, and fermentation was considered by the majority of research workers—among them Pasteur—to be a manifestation of life, i.e. to be inextricably associated with the vital processes in these cells. Buchner’s discovery showed that this was not the case. It may be said that thereby, at a blow, an important class of vital processes was removed from the cells into the chemists’ laboratories, to be studied there by the chemists’ methods. It proved, too, that, apart from fermentation, combustion and respiration, the splitting up of protein substances, fats and carbohydrates, and many other similar reactions which characterise the living cell, could be imitated in the test tube without any cooperation at all from the cells, and that on the whole the same laws held for these reactions as for ordinary chemical processes. —A. Tiselius, in presentation speech for the award of the Nobel Prize in Chemistry to James B. Sumner, John H. Northrop, and Wendell M. Stanley, 1946 T he science of biochemistry can be dated to Eduard Buchner’s pioneering discovery. His finding opened a world of chemistry that has inspired researchers for well over a century. Biochemistry is nothing less than the chemistry of life, and, yes, life can be investigated, an- alyzed, and understood. To begin, every student of bio- chemistry needs both a language and some fundamen- tals; these are provided in Part I. The chapters of Part I are devoted to the structure and function of the major classes of cellular con- stituents: water (Chapter 2), amino acids and proteins (Chapters 3 through 6), sugars and polysaccharides (Chapter 7), nucleotides and nucleic acids (Chapter 8), fatty acids and lipids (Chapter 10), and, finally, mem- branes and membrane signaling proteins (Chapters 11 and 12). We supplement this discourse on molecules with information about the technologies used to study them. Some of the techniques sections are woven throughout the molecular descriptions, although one en- tire chapter (Chapter 9) is devoted to an integrated 45 STRUCTURE AND CATALYSIS PART I 8885d_c01_045 12/30/03 6:35 AM Page 45 mac76 mac76:385_reb: suite of modern advances in biotechnology that have greatly accelerated the pace of discovery. The molecules found in a cell are a major part of the language of biochemistry; familiarity with them is a prerequisite for understanding more advanced topics covered in this book and for appreciating the rapidly growing and exciting literature of biochemistry. We be- gin with water because its properties affect the struc- ture and function of all other cellular constituents. For each class of organic molecules, we first consider the covalent chemistry of the monomeric units (amino acids, monosaccharides, nucleotides, and fatty acids) and then describe the structure of the macromolecules and supramolecular complexes derived from them. An overriding theme is that the polymeric macromolecules in living systems, though large, are highly ordered chem- ical entities, with specific sequences of monomeric sub- units giving rise to discrete structures and functions. This fundamental theme can be broken down into three interrelated principles: (1) the unique structure of each macromolecule determines its function; (2) noncovalent interactions play a critical role in the structure and thus the function of macromolecules; and (3) the monomeric subunits in polymeric macromolecules occur in specific sequences, representing a form of information upon which the ordered living state depends. The relationship between structure and function is especially evident in proteins, which exhibit an extraor- dinary diversity of functions. One particular polymeric sequence of amino acids produces a strong, fibrous struc- ture found in hair and wool; another produces a protein that transports oxygen in the blood; a third binds other proteins and catalyzes the cleavage of the bonds between their amino acids. Similarly, the special functions of poly- saccharides, nucleic acids, and lipids can be understood as a direct manifestation of their chemical structure, with their characteristic monomeric subunits linked in pre- cise functional polymers. Sugars linked together become energy stores, structural fibers, and points of specific molecular recognition; nucleotides strung together in DNA or RNA provide the blueprint for an entire organ- ism; and aggregated lipids form membranes. Chapter 12 unifies the discussion of biomolecule function, describ- ing how specific signaling systems regulate the activities of biomolecules—within a cell, within an organ, and among organs—to keep an organism in homeostasis. As we move from monomeric units to larger and larger polymers, the chemical focus shifts from covalent bonds to noncovalent interactions. The properties of co- valent bonds, both in the monomeric subunits and in the bonds that connect them in polymers, place constraints on the shapes assumed by large molecules. It is the nu- merous noncovalent interactions, however, that dictate the stable native conformations of large molecules while permitting the flexibility necessary for their biological function. As we shall see, noncovalent interactions are essential to the catalytic power of enzymes, the critical interaction of complementary base pairs in nucleic acids, the arrangement and properties of lipids in mem- branes, and the interaction of a hormone or growth fac- tor with its membrane receptor. The principle that sequences of monomeric sub- units are rich in information emerges most fully in the discussion of nucleic acids (Chapter 8). However, pro- teins and some short polymers of sugars (oligosaccha- rides) are also information-rich molecules. The amino acid sequence is a form of information that directs the folding of the protein into its unique three-dimensional structure, and ultimately determines the function of the protein. Some oligosaccharides also have unique se- quences and three-dimensional structures that are rec- ognized by other macromolecules. Each class of molecules has a similar structural hierarchy: subunits of fixed structure are connected by bonds of limited flexibility to form macromolecules with three-dimensional structures determined by noncova- lent interactions. These macromolecules then interact to form the supramolecular structures and organelles that allow a cell to carry out its many metabolic func- tions. Together, the molecules described in Part I are the stuff of life. We begin with water. Part I Structure and Catalysis46 8885d_c01_046 12/30/03 6:35 AM Page 46 mac76 mac76:385_reb: chapter WATER 2.1 Weak Interactions in Aqueous Systems 47 2.2 Ionization of Water, Weak Acids, and Weak Bases 60 2.3 Buffering against pH Changes in Biological Systems 65 2.4 Water as a Reactant 69 2.5 The Fitness of the Aqueous Environment for Living Organisms 70 I believe that as the methods of structural chemistry are further applied to physiological problems, it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature. —Linus Pauling, The Nature of the Chemical Bond, 1939 What in water did Bloom, water lover, drawer of water, water carrier returning to the range, admire? Its universality, its democratic quality. —James Joyce, Ulysses, 1922 O O C C H H – 2 47 W ater is the most abundant substance in living sys- tems, making up 70% or more of the weight of most organisms. The first living organisms doubtless arose in an aqueous environment, and the course of evolution has been shaped by the properties of the aqueous medium in which life began. This chapter begins with descriptions of the physical and chemical properties of water, to which all aspects of cell structure and function are adapted. The attrac- tive forces between water molecules and the slight ten- dency of water to ionize are of crucial importance to the structure and function of biomolecules. We review the topic of ionization in terms of equilibrium constants, pH, and titration curves, and consider how aqueous solu- tions of weak acids or bases and their salts act as buffers against pH changes in biological systems. The water molecule and its ionization products, H H11001 and OH H11002 , pro- foundly influence the structure, self-assembly, and prop- erties of all cellular components, including proteins, nucleic acids, and lipids. The noncovalent interactions responsible for the strength and specificity of “recogni- tion” among biomolecules are decisively influenced by the solvent properties of water, including its ability to form hydrogen bonds with itself and with solutes. 2.1 Weak Interactions in Aqueous Systems Hydrogen bonds between water molecules provide the cohesive forces that make water a liquid at room tem- perature and that favor the extreme ordering of mole- cules that is typical of crystalline water (ice). Polar bio- molecules dissolve readily in water because they can replace water-water interactions with more energetically favorable water-solute interactions. In contrast, nonpo- lar biomolecules interfere with water-water interactions but are unable to form water-solute interactions— consequently, nonpolar molecules are poorly soluble in water. In aqueous solutions, nonpolar molecules tend to cluster together. Hydrogen bonds and ionic, hydrophobic (Greek, “water-fearing”), and van der Waals interactions are in- dividually weak, but collectively they have a very sig- nificant influence on the three-dimensional structures of proteins, nucleic acids, polysaccharides, and mem- brane lipids. Hydrogen Bonding Gives Water Its Unusual Properties Water has a higher melting point, boiling point, and heat of vaporization than most other common solvents (Table 2–1). These unusual properties are a consequence of 8885d_c02_47-74 7/25/03 10:05 AM Page 47 mac76 mac76:385_reb: attractions between adjacent water molecules that give liquid water great internal cohesion. A look at the elec- tron structure of the H 2 O molecule reveals the cause of these intermolecular attractions. Each hydrogen atom of a water molecule shares an electron pair with the central oxygen atom. The geom- etry of the molecule is dictated by the shapes of the outer electron orbitals of the oxygen atom, which are similar to the sp 3 bonding orbitals of carbon (see Fig. 1–14). These orbitals describe a rough tetrahedron, with a hydrogen atom at each of two corners and unshared electron pairs at the other two corners (Fig. 2–1a). The HOOOH bond angle is 104.5H11034, slightly less than the 109.5H11034 of a perfect tetrahedron because of crowding by the nonbonding orbitals of the oxygen atom. The oxygen nucleus attracts electrons more strongly than does the hydrogen nucleus (a proton); that is, oxygen is more electronegative. The sharing of electrons between H and O is therefore unequal; the electrons are more often in the vicinity of the oxygen atom than of the hydrogen. The result of this unequal electron sharing is two electric dipoles in the water mol- ecule, one along each of the HOO bonds; each hydro- gen bears a partial positive charge (H9254 H11001 ) and the oxygen atom bears a partial negative charge equal to the sum of the two partial positives (2H9254 H11002 ). As a result, there is an electrostatic attraction between the oxygen atom of one water molecule and the hydrogen of another (Fig. 2–1c), called a hydrogen bond. Throughout this book, we represent hydrogen bonds with three parallel blue lines, as in Figure 2–1c. Hydrogen bonds are relatively weak. Those in liq- uid water have a bond dissociation energy (the en- ergy required to break a bond) of about 23 kJ/mol, com- pared with 470 kJ/mol for the covalent OOH bond in Part I Structure and Catalysis48 TABLE 2–1 Melting Point, Boiling Point, and Heat of Vaporization of Some Common Solvents Melting point (°C) Boiling point (°C) Heat of vaporization (J/g)* Water 0 100 2,260 Methanol (CH 3 OH) H1100298 65 1,100 Ethanol (CH 3 CH 2 OH) H11002117 78 854 Propanol (CH 3 CH 2 CH 2 OH) H11002127 97 687 Butanol (CH 3 (CH 2 ) 2 CH 2 OH) H1100290 117 590 Acetone (CH 3 COCH 3 ) H1100295 56 523 Hexane (CH 3 (CH 2 ) 4 CH 3 ) H1100298 69 423 Benzene (C 6 H 6 ) 6 80 394 Butane (CH 3 (CH 2 ) 2 CH 3 ) H11002135 H110020.5 381 Chloroform (CHCl 3 ) H1100263 61 247 *The heat energy required to convert 1.0 g of a liquid at its boiling point, at atmospheric pressure, into its gaseous state at the same temperature. It is a direct measure of the energy required to overcome attractive forces between molecules in the liquid phase. 104.5H11034 Hydrogen bond 0.177 nm Covalent bond 0.0965 nm H H9254 H11001 H9254 H11002 H9254 H11002 H9254 H11001 H9254 H11001 H9254 H11001 (a) (b) (c) 2H9254 H11002 H O FIGURE 2–1 Structure of the water molecule. The dipolar nature of the H 2 O molecule is shown by (a) ball-and-stick and (b) space-filling models. The dashed lines in (a) represent the nonbonding orbitals. There is a nearly tetrahedral arrangement of the outer-shell electron pairs around the oxygen atom; the two hydrogen atoms have local- ized partial positive charges (H9254 H11001 ) and the oxygen atom has a partial negative charge (2H9254 H11002 ). (c) Two H 2 O molecules joined by a hydrogen bond (designated here, and throughout this book, by three blue lines) between the oxygen atom of the upper molecule and a hydrogen atom of the lower one. Hydrogen bonds are longer and weaker than cova- lent OOH bonds. 8885d_c02_47-74 7/25/03 10:05 AM Page 48 mac76 mac76:385_reb: water or 348 kJ/mol for a covalent COC bond. The hy- drogen bond is about 10% covalent, due to overlaps in the bonding orbitals, and about 90% electrostatic. At room temperature, the thermal energy of an aqueous solution (the kinetic energy of motion of the individual atoms and molecules) is of the same order of magnitude as that required to break hydrogen bonds. When water is heated, the increase in temperature reflects the faster motion of individual water molecules. At any given time, most of the molecules in liquid water are engaged in hy- drogen bonding, but the lifetime of each hydrogen bond is just 1 to 20 picoseconds (1 ps H11005 10 H1100212 s); upon break- age of one hydrogen bond, another hydrogen bond forms, with the same partner or a new one, within 0.1 ps. The apt phrase “flickering clusters” has been applied to the short-lived groups of water molecules interlinked by hydrogen bonds in liquid water. The sum of all the hy- drogen bonds between H 2 O molecules confers great in- ternal cohesion on liquid water. Extended networks of hydrogen-bonded water molecules also form bridges be- tween solutes (proteins and nucleic acids, for example) that allow the larger molecules to interact with each other over distances of several nanometers without physically touching. The nearly tetrahedral arrangement of the orbitals about the oxygen atom (Fig. 2–1a) allows each water molecule to form hydrogen bonds with as many as four neighboring water molecules. In liquid water at room temperature and atmospheric pressure, however, water molecules are disorganized and in continuous motion, so that each molecule forms hydrogen bonds with an av- erage of only 3.4 other molecules. In ice, on the other hand, each water molecule is fixed in space and forms hydrogen bonds with a full complement of four other water molecules to yield a regular lattice structure (Fig. 2–2). Breaking a sufficient proportion of hydrogen bonds to destabilize the crystal lattice of ice requires much thermal energy, which accounts for the relatively high melting point of water (Table 2–1). When ice melts or water evaporates, heat is taken up by the system: H 2 O(solid) 88n H 2 O(liquid) H9004H H11005H110015.9 kJ/mol H 2 O(liquid) 88n H 2 O(gas) H9004H H11005H1100144.0 kJ/mol During melting or evaporation, the entropy of the aqueous system increases as more highly ordered arrays of water molecules relax into the less orderly hydrogen- bonded arrays in liquid water or the wholly disordered gaseous state. At room temperature, both the melting of ice and the evaporation of water occur spontaneously; the tendency of the water molecules to associate through hydrogen bonds is outweighed by the energetic push toward randomness. Recall that the free-energy change (H9004G) must have a negative value for a process to occur spontaneously: H9004G H11005H9004H H11002 T H9004S, where H9004G represents the driving force, H9004H the enthalpy change from making and breaking bonds, and H9004S the change in randomness. Because H9004H is positive for melting and evaporation, it is clearly the increase in entropy (H9004S) that makes H9004G negative and drives these transformations. Water Forms Hydrogen Bonds with Polar Solutes Hydrogen bonds are not unique to water. They readily form between an electronegative atom (the hydrogen acceptor, usually oxygen or nitrogen with a lone pair of electrons) and a hydrogen atom covalently bonded to another electronegative atom (the hydrogen donor) in the same or another molecule (Fig. 2–3). Hydrogen atoms covalently bonded to carbon atoms do not par- ticipate in hydrogen bonding, because carbon is only Chapter 2 Water 49 FIGURE 2–2 Hydrogen bonding in ice. In ice, each water molecule forms the maximum of four hydrogen bonds, creating a regular crys- tal lattice. By contrast, in liquid water at room temperature and at- mospheric pressure, each water molecule hydrogen-bonds with an av- erage of 3.4 other water molecules. This crystal lattice of ice makes it less dense than liquid water, and thus ice floats on liquid water. Hydrogen Hydrogen donor acceptor H O O P C D DG OO J H N O OO DJ H N N OO DD H O O OO H O N P C DG OO DD H N O OO FIGURE 2–3 Common hydrogen bonds in biological systems. The hydrogen acceptor is usually oxygen or nitrogen; the hydrogen donor is another electronegative atom. 8885d_c02_47-74 7/25/03 10:05 AM Page 49 mac76 mac76:385_reb: slightly more electronegative than hydrogen and thus the COH bond is only very weakly polar. The distinc- tion explains why butanol (CH 3 (CH 2 ) 2 CH 2 OH) has a rel- atively high boiling point of 117 H11034C, whereas butane (CH 3 (CH 2 ) 2 CH 3 ) has a boiling point of only H110020.5 H11034C. Bu- tanol has a polar hydroxyl group and thus can form in- termolecular hydrogen bonds. Uncharged but polar bio- molecules such as sugars dissolve readily in water because of the stabilizing effect of hydrogen bonds be- tween the hydroxyl groups or carbonyl oxygen of the sugar and the polar water molecules. Alcohols, alde- hydes, ketones, and compounds containing NOH bonds all form hydrogen bonds with water molecules (Fig. 2–4) and tend to be soluble in water. Hydrogen bonds are strongest when the bonded molecules are oriented to maximize electrostatic inter- action, which occurs when the hydrogen atom and the two atoms that share it are in a straight line—that is, when the acceptor atom is in line with the covalent bond between the donor atom and H (Fig. 2–5). Hydrogen bonds are thus highly directional and capable of hold- ing two hydrogen-bonded molecules or groups in a spe- cific geometric arrangement. As we shall see later, this property of hydrogen bonds confers very precise three- dimensional structures on protein and nucleic acid molecules, which have many intramolecular hydrogen bonds. Water Interacts Electrostatically with Charged Solutes Water is a polar solvent. It readily dissolves most bio- molecules, which are generally charged or polar com- pounds (Table 2–2); compounds that dissolve easily in water are hydrophilic (Greek, “water-loving”). In con- trast, nonpolar solvents such as chloroform and benzene are poor solvents for polar biomolecules but easily dis- solve those that are hydrophobic—nonpolar molecules such as lipids and waxes. Water dissolves salts such as NaCl by hydrating and stabilizing the Na H11001 and Cl H11002 ions, weakening the elec- trostatic interactions between them and thus counter- acting their tendency to associate in a crystalline lattice (Fig. 2–6). The same factors apply to charged biomole- cules, compounds with functional groups such as ion- ized carboxylic acids (OCOO H11002 ), protonated amines (ONH 3 H11001 ), and phosphate esters or anhydrides. Water readily dissolves such compounds by replacing solute- solute hydrogen bonds with solute-water hydrogen bonds, thus screening the electrostatic interactions be- tween solute molecules. Water is especially effective in screening the elec- trostatic interactions between dissolved ions because it has a high dielectric constant, a physical property re- flecting the number of dipoles in a solvent. The strength, or force (F), of ionic interactions in a solution depends upon the magnitude of the charges (Q), the distance between the charged groups (r), and the dielectric con- stant (H9255) of the solvent in which the interactions occur: F H11005 H5007 Q H9255 1 r Q 2 2 H5007 Part I Structure and Catalysis50 Between the hydroxyl group of an alcohol and water Between the carbonyl group of a ketone and water Between peptide groups in polypeptides Between complementary bases of DNA O H A O G R HH H O G R 1 O OR E A H O B H N A H H B H N C C E C A R H C H N A H E C A N O H A A N H R E C H N C E CH 3 H C KH N H E N NE NH N E R OCH D R 2 A C K O N B C C A C l A Thymine Adenine B C i A H H H E H FIGURE 2–4 Some biologically important hydrogen bonds. Strong hydrogen bond Weaker hydrogen bond P K O H A O A R P K O H A O A R G D O G D O FIGURE 2–5 Directionality of the hydrogen bond. The attraction be- tween the partial electric charges (see Fig. 2–1) is greatest when the three atoms involved (in this case O, H, and O) lie in a straight line. When the hydrogen-bonded moieties are structurally constrained (as when they are parts of a single protein molecule, for example), this ideal geometry may not be possible and the resulting hydrogen bond is weaker. 8885d_c02_47-74 7/25/03 10:05 AM Page 50 mac76 mac76:385_reb: For water at 25 H11034C, H9255 (which is dimensionless) is 78.5, and for the very nonpolar solvent benzene, H9255 is 4.6. Thus, ionic interactions are much stronger in less polar envi- ronments. The dependence on r 2 is such that ionic at- tractions or repulsions operate only over short dis- tances—in the range of 10 to 40 nm (depending on the electrolyte concentration) when the solvent is water. Entropy Increases as Crystalline Substances Dissolve As a salt such as NaCl dissolves, the Na H11001 and Cl H11002 ions leaving the crystal lattice acquire far greater freedom of motion (Fig. 2–6). The resulting increase in entropy (randomness) of the system is largely responsible for the ease of dissolving salts such as NaCl in water. In Chapter 2 Water 51 Some Examples of Polar, Nonpolar, and Amphipathic Biomolecules (Shown as Ionic Forms at pH 7)TABLE 2–2 + Hydrated Na + ion Note the orientation of the water molecules Hydrated Cl – ion H 2 O Na + Cl – + – + – + – – – – + ++ + – – – – – – – – – + – – FIGURE 2–6 Water as solvent. Water dissolves many crystalline salts by hydrating their component ions. The NaCl crystal lattice is disrupted as water molecules cluster about the Cl H11002 and Na H11001 ions. The ionic charges are partially neutralized, and the electrostatic attractions nec- essary for lattice formation are weakened. H HO CH 2 OH O OH OH OH CH 2 H11001 NH 3 COO H11002 CH 2 H11002 OOC COO H11002 H H H H H11001 NH 3 CH CH OH OH CH 3 COO H11002 CH CH 2 OHHOCH 2 CH CHCH 3 (CH 2 ) 7 (CH 2 ) 6 CH 2 C CH CH(CH 2 ) 7 (CH 2 ) 7 CH 2 CH 3 CH 2 CH GNH 3 GN(CH 3 ) 3 O O COOJ CH 3 (CH 2 ) 15 CH 2 CH 2 CH 2 CH 2 O O OJ C CH 3 (CH 2 ) 15 CH 2 CHO O CH 2 O P C O O Polar groups Nonpolar groups Polar Glucose Glycine Aspartate Lactate Glycerol Nonpolar Typical wax Amphipathic Phenylalanine Phosphatidylcholine 8885d_c02_051 7/25/03 11:52 AM Page 51 mac76 mac76:385_reb: thermodynamic terms, formation of the solution occurs with a favorable free-energy change: H9004G H11005H9004H H11002 T H9004S, where H9004H has a small positive value and T H9004S a large positive value; thus H9004G is negative. Nonpolar Gases Are Poorly Soluble in Water The molecules of the biologically important gases CO 2 , O 2 , and N 2 are nonpolar. In O 2 and N 2 , electrons are shared equally by both atoms. In CO 2 , each CUO bond is polar, but the two dipoles are oppositely directed and cancel each other (Table 2–3). The movement of mole- cules from the disordered gas phase into aqueous solu- tion constrains their motion and the motion of water molecules and therefore represents a decrease in en- tropy. The nonpolar nature of these gases and the de- crease in entropy when they enter solution combine to make them very poorly soluble in water (Table 2–3). Some organisms have water-soluble carrier proteins (hemoglobin and myoglobin, for example) that facilitate the transport of O 2 . Carbon dioxide forms carbonic acid (H 2 CO 3 ) in aqueous solution and is transported as the HCO 3 H11002 (bicarbonate) ion, either free—bicarbonate is very soluble in water (~100 g/L at 25 H11034C)—or bound to hemoglobin. Two other gases, NH 3 and H 2 S, also have biological roles in some organisms; these gases are po- lar and dissolve readily in water. Nonpolar Compounds Force Energetically Unfavorable Changes in the Structure of Water When water is mixed with benzene or hexane, two phases form; neither liquid is soluble in the other. Non- polar compounds such as benzene and hexane are hydrophobic—they are unable to undergo energetically favorable interactions with water molecules, and they interfere with the hydrogen bonding among water mol- ecules. All molecules or ions in aqueous solution inter- fere with the hydrogen bonding of some water mole- cules in their immediate vicinity, but polar or charged solutes (such as NaCl) compensate for lost water-water hydrogen bonds by forming new solute-water interac- tions. The net change in enthalpy (H9004H) for dissolving these solutes is generally small. Hydrophobic solutes, however, offer no such compensation, and their addi- tion to water may therefore result in a small gain of en- thalpy; the breaking of hydrogen bonds between water molecules takes up energy from the system. Further- more, dissolving hydrophobic compounds in water pro- duces a measurable decrease in entropy. Water mole- cules in the immediate vicinity of a nonpolar solute are constrained in their possible orientations as they form a highly ordered cagelike shell around each solute mol- ecule. These water molecules are not as highly oriented as those in clathrates, crystalline compounds of non- polar solutes and water, but the effect is the same in both cases: the ordering of water molecules reduces en- tropy. The number of ordered water molecules, and therefore the magnitude of the entropy decrease, is pro- portional to the surface area of the hydrophobic solute enclosed within the cage of water molecules. The free- energy change for dissolving a nonpolar solute in water is thus unfavorable: H9004G H11005H9004H H11002 T H9004S, where H9004H has a positive value, H9004S has a negative value, and H9004G is positive. Amphipathic compounds contain regions that are polar (or charged) and regions that are nonpolar (Table 2–2). When an amphipathic compound is mixed with Part I Structure and Catalysis52 TABLE 2–3 Solubilities of Some Gases in Water Solubility Gas Structure* Polarity in water (g/L) ? Nitrogen NmN Nonpolar 0.018 (40 °C) Oxygen OPO Nonpolar 0.035 (50 °C) Carbon dioxide Nonpolar 0.97 (45 °C) Ammonia Polar 900 (10 °C) Hydrogen sulfide Polar 1,860 (40 °C)H G S D H H9254 H11002 H G N A H D H H9254 H11002 OPCPO H9254 H11002 H9254 H11002 *The arrows represent electric dipoles; there is a partial negative charge (H9254 H11002 ) at the head of the arrow, a partial positive charge (H9254 H11001 ; not shown here) at the tail. ? Note that polar molecules dissolve far better even at low temperatures than do nonpolar molecules at relatively high temperatures. 8885d_c02_47-74 7/25/03 10:05 AM Page 52 mac76 mac76:385_reb: Dispersion of lipids in H 2 O Clusters of lipid molecules Micelles (b) (a) “Flickering clusters” of H 2 O molecules in bulk phase Highly ordered H 2 O molecules form “cages” around the hydrophobic alkyl chains Hydrophilic “head group” O O C C H H H H O Each lipid molecule forces surrounding H 2 O molecules to become highly ordered. Only lipid portions at the edge of the cluster force the ordering of water. Fewer H 2 O molecules are ordered, and entropy is increased. All hydrophobic groups are sequestered from water; ordered shell of H 2 O molecules is minimized, and entropy is further increased. – Hydrophobic alkyl group water, the polar, hydrophilic region interacts favorably with the solvent and tends to dissolve, but the nonpo- lar, hydrophobic region tends to avoid contact with the water (Fig. 2–7a). The nonpolar regions of the mole- cules cluster together to present the smallest hy- drophobic area to the aqueous solvent, and the polar re- gions are arranged to maximize their interaction with the solvent (Fig. 2–7b). These stable structures of am- phipathic compounds in water, called micelles, may contain hundreds or thousands of molecules. The forces that hold the nonpolar regions of the molecules together are called hydrophobic interactions. The strength of hydrophobic interactions is not due to any intrinsic at- traction between nonpolar moieties. Rather, it results from the system’s achieving greatest thermodynamic stability by minimizing the number of ordered water molecules required to surround hydrophobic portions of the solute molecules. Many biomolecules are amphipathic; proteins, pig- ments, certain vitamins, and the sterols and phospho- lipids of membranes all have polar and nonpolar surface regions. Structures composed of these molecules are stabilized by hydrophobic interactions among the non- polar regions. Hydrophobic interactions among lipids, and between lipids and proteins, are the most impor- tant determinants of structure in biological membranes. Hydrophobic interactions between nonpolar amino acids also stabilize the three-dimensional structures of proteins. Hydrogen bonding between water and polar solutes also causes some ordering of water molecules, but the effect is less significant than with nonpolar solutes. Part Chapter 2 Water 53 FIGURE 2–7 Amphipathic compounds in aqueous solution. (a) Long- chain fatty acids have very hydrophobic alkyl chains, each of which is surrounded by a layer of highly ordered water molecules. (b) By clustering together in micelles, the fatty acid molecules expose the smallest possible hydrophobic surface area to the water, and fewer water molecules are required in the shell of ordered water. The energy gained by freeing immobilized water molecules stabilizes the micelle. 8885d_c02_47-74 7/25/03 10:05 AM Page 53 mac76 mac76:385_reb: of the driving force for binding of a polar substrate (re- actant) to the complementary polar surface of an en- zyme is the entropy increase as the enzyme displaces ordered water from the substrate (Fig. 2–8). van der Waals Interactions Are Weak Interatomic Attractions When two uncharged atoms are brought very close to- gether, their surrounding electron clouds influence each other. Random variations in the positions of the electrons around one nucleus may create a transient electric di- pole, which induces a transient, opposite electric dipole in the nearby atom. The two dipoles weakly attract each other, bringing the two nuclei closer. These weak at- tractions are called van der Waals interactions. As the two nuclei draw closer together, their electron clouds begin to repel each other. At the point where the van der Waals attraction exactly balances this repulsive force, the nuclei are said to be in van der Waals contact. Each atom has a characteristic van der Waals radius, a measure of how close that atom will allow another to approach (Table 2–4). In the “space-filling” molecular models shown throughout this book, the atoms are de- picted in sizes proportional to their van der Waals radii. Weak Interactions Are Crucial to Macromolecular Structure and Function The noncovalent interactions we have described (hy- drogen bonds and ionic, hydrophobic, and van der Waals interactions) (Table 2–5) are much weaker than cova- lent bonds. An input of about 350 kJ of energy is re- quired to break a mole of (6 H11003 10 23 ) COC single bonds, and about 410 kJ to break a mole of COH bonds, but as little as 4 kJ is sufficient to disrupt a mole of typical van der Waals interactions. Hydrophobic interactions are also much weaker than covalent bonds, although they are substantially strengthened by a highly polar sol- vent (a concentrated salt solution, for example). Ionic interactions and hydrogen bonds are variable in strength, depending on the polarity of the solvent and Part I Structure and Catalysis54 Substrate Enzyme Disordered water displaced by enzyme-substrate interaction Enzyme-substrate interaction stabilized by hydrogen-bonding, ionic, and hydrophobic interactions Ordered water interacting with substrate and enzyme FIGURE 2–8 Release of ordered water favors formation of an enzyme-substrate complex. While separate, both enzyme and sub- strate force neighboring water molecules into an ordered shell. Bind- ing of substrate to enzyme releases some of the ordered water, and the resulting increase in entropy provides a thermodynamic push to- ward formation of the enzyme-substrate complex. Sources: For van der Waals radii, Chauvin, R. (1992) Explicit periodic trend of van der Waals radii. J. Phys. Chem. 96, 9194–9197. For covalent radii, Pauling, L. (1960) Nature of the Chemical Bond, 3rd edn, Cornell University Press, Ithaca, NY. Note: van der Waals radii describe the space-filling dimensions of atoms. When two atoms are joined covalently, the atomic radii at the point of bonding are less than the van der Waals radii, because the joined atoms are pulled together by the shared electron pair. The distance between nuclei in a van der Waals interaction or a covalent bond is about equal to the sum of the van der Waals or covalent radii, respectively, for the two atoms. Thus the length of a carbon-carbon single bond is about 0.077 nm H11001 0.077 nm H11005 0.154 nm. van der Waals Covalent radius for Element radius (nm) single bond (nm) H 0.11 0.030 O 0.15 0.066 N 0.15 0.070 C 0.17 0.077 S 0.18 0.104 P 0.19 0.110 I 0.21 0.133 van der Waals Radii and Covalent (Single-Bond) Radii of Some Elements TABLE 2–4 8885d_c02_47-74 7/25/03 10:05 AM Page 54 mac76 mac76:385_reb: the alignment of the hydrogen-bonded atoms, but they are always significantly weaker than covalent bonds. In aqueous solvent at 25 H11034C, the available thermal energy can be of the same order of magnitude as the strength of these weak interactions, and the interaction between solute and solvent (water) molecules is nearly as favor- able as solute-solute interactions. Consequently, hydro- gen bonds and ionic, hydrophobic, and van der Waals interactions are continually formed and broken. Although these four types of interactions are indi- vidually weak relative to covalent bonds, the cumulative effect of many such interactions can be very significant. For example, the noncovalent binding of an enzyme to its substrate may involve several hydrogen bonds and one or more ionic interactions, as well as hydrophobic and van der Waals interactions. The formation of each of these weak bonds contributes to a net decrease in the free energy of the system. We can calculate the sta- bility of a noncovalent interaction, such as that of a small molecule hydrogen-bonded to its macromolecular part- ner, from the binding energy. Stability, as measured by the equilibrium constant (see below) of the binding re- action, varies exponentially with binding energy. The dissociation of two biomolecules (such as an enzyme and its bound substrate) associated noncovalently through multiple weak interactions requires all these in- teractions to be disrupted at the same time. Because the interactions fluctuate randomly, such simultaneous disruptions are very unlikely. The molecular stability be- stowed by 5 or 20 weak interactions is therefore much greater than would be expected intuitively from a sim- ple summation of small binding energies. Macromolecules such as proteins, DNA, and RNA contain so many sites of potential hydrogen bonding or ionic, van der Waals, or hydrophobic interactions that the cumulative effect of the many small binding forces can be enormous. For macromolecules, the most stable (that is, the native) structure is usually that in which weak-bonding possibilities are maximized. The folding of a single polypeptide or polynucleotide chain into its three-dimensional shape is determined by this princi- ple. The binding of an antigen to a specific antibody de- pends on the cumulative effects of many weak interac- tions. As noted earlier, the energy released when an enzyme binds noncovalently to its substrate is the main source of the enzyme’s catalytic power. The binding of a hormone or a neurotransmitter to its cellular recep- tor protein is the result of weak interactions. One con- sequence of the large size of enzymes and receptors is that their extensive surfaces provide many opportuni- ties for weak interactions. At the molecular level, the complementarity between interacting biomolecules re- flects the complementarity and weak interactions be- tween polar, charged, and hydrophobic groups on the surfaces of the molecules. When the structure of a protein such as hemoglobin (Fig. 2–9) is determined by x-ray crystallography (see Chapter 2 Water 55 Hydrogen bonds Between neutral groups Between peptide bonds Ionic interactions Attraction Repulsion Hydrophobic interactions van der Waals interactions Any two atoms in close proximity Four Types of Noncovalent (“Weak”) Interactions among Biomolecules in Aqueous Solvent TABLE 2–5 G C D POHOOO G C D G D POHON B H11001 NH 3 O H11002 OOO C H11001 NH 3 H 3 N H11001 O O A O CH 3 CH 3 CH 2 CH 2 A A G CH D water (a) (b) FIGURE 2–9 Water binding in hemoglobin. The crystal structure of hemoglobin, shown (a) with bound water molecules (red spheres) and (b) without the water molecules. These water molecules are so firmly bound to the protein that they affect the x-ray diffraction pattern as though they were fixed parts of the crystal. The gray structures with red and orange atoms are the four hemes of hemoglobin, discussed in detail in Chapter 5. 8885d_c02_47-74 7/25/03 10:05 AM Page 55 mac76 mac76:385_reb: Box 4–4, p. XX), water molecules are often found to be bound so tightly as to be part of the crystal structure; the same is true for water in crystals of RNA or DNA. These bound water molecules, which can also be de- tected in aqueous solutions by nuclear magnetic reso- nance, have distinctly different properties from those of the “bulk” water of the solvent. They are, for example, not osmotically active (see below). For many proteins, tightly bound water molecules are essential to their func- tion. In a reaction central to the process of photosyn- thesis, for example, light drives protons across a biolog- ical membrane as electrons flow through a series of electron-carrying proteins (see Fig. 19–XX). One of these proteins, cytochrome f, has a chain of five bound water molecules (Fig. 2–10) that may provide a path for pro- tons to move through the membrane by a process known as “proton hopping” (described below). Another such light-driven proton pump, bacteriorhodopsin, almost cer- tainly uses a chain of precisely oriented bound water molecules in the transmembrane movement of protons (see Fig. 19–XX). Solutes Affect the Colligative Properties of Aqueous Solutions Solutes of all kinds alter certain physical properties of the solvent, water: its vapor pressure, boiling point, melting point (freezing point), and osmotic pressure. These are called colligative (“tied together”) proper- ties, because the effect of solutes on all four properties has the same basis: the concentration of water is lower in solutions than in pure water. The effect of solute con- centration on the colligative properties of water is in- dependent of the chemical properties of the solute; it depends only on the number of solute particles (mole- cules, ions) in a given amount of water. A compound such as NaCl, which dissociates in solution, has twice the effect on osmotic pressure, for example, as does an equal number of moles of a nondissociating solute such as glucose. Solutes alter the colligative properties of aqueous solutions by lowering the effective concentration of wa- ter. For example, when a significant fraction of the mol- ecules at the surface of an aqueous solution are not wa- ter but solute, the tendency of water molecules to escape into the vapor phase—that is, the vapor pres- sure—is lowered (Fig. 2–11). Similarly, the tendency of water molecules to move from the aqueous phase to the surface of a forming ice crystal is reduced when some of the molecules that collide with the crystal are solute, not water. In that case, the solution will freeze more slowly than pure water and at a lower temperature. For a 1.00 molal aqueous solution (1.00 mol of solute per 1,000 g of water) of an ideal, nonvolatile, and nondis- sociating solute at 101 kPa (1 atm) of pressure, the freezing point is 1.86 H11034C lower and the boiling point is 0.543 H11034C higher than for pure water. For a 0.100 molal solution of the same solute, the changes are one-tenth as large. Water molecules tend to move from a region of higher water concentration to one of lower water con- centration. When two different aqueous solutions are separated by a semipermeable membrane (one that al- lows the passage of water but not solute molecules), wa- ter molecules diffusing from the region of higher water concentration to that of lower water concentration pro- duce osmotic pressure (Fig. 2–12). This pressure, H9016, measured as the force necessary to resist water move- ment (Fig. 2–12c), is approximated by the van’t Hoff equation: H9016H11005icRT in which R is the gas constant and T is the absolute tem- perature. The term ic is the osmolarity of the solution, the product of the solute’s molar concentration c and the van’t Hoff factor i, which is a measure of the extent to which the solute dissociates into two or more ionic species. In dilute NaCl solutions, the solute completely Part I Structure and Catalysis56 Asn 232 Arg 156 Asn 168 Asn 153 Heme propionate NH 2 Gln 158 Gln 59 Val 60 water H H H H H H H H N H O O – O O O O O O O O N N N N HN HN Fe HH HO CC H H N Ala 27 Pro 231 FIGURE 2–10 Water chain in cytochrome f. Water is bound in a pro- ton channel of the membrane protein cytochrome f, which is part of the energy-trapping machinery of photosynthesis in chloroplasts (see Fig. 19–XX). Five water molecules are hydrogen-bonded to each other and to functional groups of the protein, which include the side chains of valine, proline, arginine, alanine, two asparagine, and two gluta- mine residues. The protein has a bound heme (see Fig. 5–1), its iron ion facilitating electron flow during photosynthesis. Electron flow is coupled to the movement of protons across the membrane, which probably involves “electron hopping” (see Fig. 2–14) through this chain of bound water molecules. 8885d_c02_47-74 7/25/03 10:05 AM Page 56 mac76 mac76:385_reb: dissociates into Na H11001 and Cl H11002 , doubling the number of solute particles, and thus i H11005 2. For nonionizing solutes, i is always 1. For solutions of several (n) solutes, H9016 is the sum of the contributions of each species: H9016H11005RT(i 1 c 1 H11001 i 2 c 2 H11001 … H11001 i n c n ) Osmosis, water movement across a semipermeable membrane driven by differences in osmotic pressure, is an important factor in the life of most cells. Plasma membranes are more permeable to water than to most other small molecules, ions, and macromolecules. This permeability is due partly to simple diffusion of water through the lipid bilayer and partly to protein channels (aquaporins; see Fig. 11–XX) in the membrane that se- lectively permit the passage of water. Solutions of equal osmolarity are said to be isotonic. Surrounded by an isotonic solution, a cell neither gains nor loses water (Fig. 2–13). In a hypertonic solution, one with higher osmolarity than the cytosol, the cell shrinks as water flows out. In a hypotonic solution, with lower osmo- larity than the cytosol, the cell swells as water enters. In their natural environments, cells generally contain higher concentrations of biomolecules and ions than their surroundings, so osmotic pressure tends to drive water into cells. If not somehow counterbalanced, this inward movement of water would distend the plasma membrane and eventually cause bursting of the cell (osmotic lysis). Several mechanisms have evolved to prevent this catastrophe. In bacteria and plants, the plasma mem- brane is surrounded by a nonexpandable cell wall of suf- ficient rigidity and strength to resist osmotic pressure and prevent osmotic lysis. Certain freshwater protists that live in a highly hypotonic medium have an organelle (contractile vacuole) that pumps water out of the cell. In multicellular animals, blood plasma and interstitial fluid (the extracellular fluid of tissues) are maintained at an osmolarity close to that of the cytosol. The high concentration of albumin and other proteins in blood plasma contributes to its osmolarity. Cells also actively pump out ions such as Na H11001 into the interstitial fluid to stay in osmotic balance with their surroundings. Chapter 2 Water 57 Forming ice crystal (a) (b) In pure water, every molecule at the surface is H 2 O, and all contribute to the vapor pressure. Every molecule in the bulk solution is H 2 O, and can contribute to formation of ice crystals. In this solution, the effective concentration of H 2 O is reduced; only 3 of every 4 molecules at the surface and in the bulk phase are H 2 O. The vapor pressure of water and the tendency of liquid water to enter a crystal are reduced proportionately. = = H 2 O Solute FIGURE 2–11 Solutes alter the colligative properties of aqueous so- lutions. (a) At 101 kPa (1 atm) pressure, pure water boils at 100 H11034C and freezes at 0 H11034C. (b) The presence of solute molecules reduces the probability of a water molecule leaving the solution and entering the gas phase, thereby reducing the vapor pressure of the solution and in- creasing the boiling point. Similarly, the probability of a water mole- cule colliding with and joining a forming ice crystal is reduced when some of the molecules colliding with the crystal are solute, not wa- ter, molecules. The effect is depression of the freezing point. h Nonpermeant solute dissolved in water Pure water Piston Semipermeable membrane (a) (b) (c) FIGURE 2–12 Osmosis and the measurement of osmotic pressure. (a) The initial state. The tube contains an aqueous solution, the beaker contains pure water, and the semipermeable membrane allows the passage of water but not solute. Water flows from the beaker into the tube to equalize its concentration across the membrane. (b) The final state. Water has moved into the solution of the nonpermeant com- pound, diluting it and raising the column of water within the tube. At equilibrium, the force of gravity operating on the solution in the tube exactly balances the tendency of water to move into the tube, where its concentration is lower. (c) Osmotic pressure (H9016) is measured as the force that must be applied to return the solution in the tube to the level of that in the beaker. This force is proportional to the height, h, of the column in (b). 8885d_c02_47-74 7/25/03 10:05 AM Page 57 mac76 mac76:385_reb: Because the effect of solutes on osmolarity depends on the number of dissolved particles, not their mass, macromolecules (proteins, nucleic acids, polysaccha- rides) have far less effect on the osmolarity of a solu- tion than would an equal mass of their monomeric com- ponents. For example, a gram of a polysaccharide composed of 1,000 glucose units has the same effect on osmolarity as a milligram of glucose. One effect of stor- ing fuel as polysaccharides (starch or glycogen) rather than as glucose or other simple sugars is prevention of an enormous increase in osmotic pressure within the storage cell. Plants use osmotic pressure to achieve mechanical rigidity. The very high solute concentration in the plant cell vacuole draws water into the cell (Fig. 2–13). The resulting osmotic pressure against the cell wall (turgor pressure) stiffens the cell, the tissue, and the plant body. When the lettuce in your salad wilts, it is because loss of water has reduced turgor pressure. Sudden alter- ations in turgor pressure produce the movement of plant parts seen in touch-sensitive plants such as the Venus flytrap and mimosa (Box 2–1). Osmosis also has consequences for laboratory pro- tocols. Mitochondria, chloroplasts, and lysosomes, for ex- ample, are bounded by semipermeable membranes. In isolating these organelles from broken cells, biochemists must perform the fractionations in isotonic solutions (see Fig. 1–8). Buffers used in cellular fractionations commonly contain sufficient concentrations (about 0.2 M) of sucrose or some other inert solute to protect the organelles from osmotic lysis. SUMMARY 2.1 Weak Interactions in Aqueous Systems ■ The very different electronegativities of H and O make water a highly polar molecule, capable of forming hydrogen bonds with itself and with solutes. Hydrogen bonds are fleeting, primarily electrostatic, and weaker than covalent bonds. Water is a good solvent for polar (hydrophilic) solutes, with which it forms hydrogen bonds, and for charged solutes, with which it interacts electrostatically. ■ Nonpolar (hydrophobic) compounds dissolve poorly in water; they cannot hydrogen-bond with the solvent, and their presence forces an energetically unfavorable ordering of water molecules at their hydrophobic surfaces. To minimize the surface exposed to water, nonpolar compounds such as lipids form aggregates (micelles) in which the hydrophobic moieties are sequestered in the interior, associating through hydrophobic interactions, and only the more polar moieties interact with water. ■ Numerous weak, noncovalent interactions deci- sively influence the folding of macromolecules such as proteins and nucleic acids. The most stable macromolecular conformations are those in which hydrogen bonding is maximized within the molecule and between the molecule and the solvent, and in which hydrophobic moieties cluster in the interior of the molecule away from the aqueous solvent. ■ The physical properties of aqueous solutions are strongly influenced by the concentrations of solutes. When two aqueous compartments are separated by a semipermeable membrane (such as the plasma membrane separating a cell from its surroundings), water moves across that membrane to equalize the osmolarity in the two compartments. This tendency for water to move across a semipermeable membrane is the osmotic pressure. Part I Structure and Catalysis58 (b) Cell in hypertonic solution; water moves out and cell shrinks. (c) Cell in hypotonic solution; water moves in, creating outward pressure; cell swells, may eventually burst. (a) Cell in isotonic solution; no net water movement. Extracellular solutes Intracellular solutes FIGURE 2–13 Effect of extracellular osmolarity on water movement across a plasma membrane. When a cell in osmotic balance with its surrounding medium (that is, in an isotonic medium) (a) is transferred into a hypertonic solution (b) or hypotonic solution (c), water moves across the plasma membrane in the direction that tends to equalize osmolarity outside and inside the cell. 8885d_c02_47-74 7/25/03 10:05 AM Page 58 mac76 mac76:385_reb: Chapter 2 Water 59 BOX 2–1 THE WORLD OF BIOCHEMISTRY (b)(a) (a) (b) FIGURE 1 Touch response in the Venus flytrap. A fly approaching an open leaf (a) is trapped for digestion by the plant (b). FIGURE 2 The feathery leaflets of the sensitive plant (a) close and drop (b) to protect the plant from structural damage by wind. Touch Response in Plants: An Osmotic Event The highly specialized leaves of the Venus flytrap (Dionaea muscipula) rapidly fold together in re- sponse to a light touch by an unsuspecting insect, en- trapping the insect for later digestion. Attracted by nectar on the leaf surface, the insect touches three mechanically sensitive hairs, triggering the traplike closing of the leaf (Fig. 1). This leaf movement is pro- duced by sudden (within 0.5 s) changes of turgor pres- sure in mesophyll cells (the inner cells of the leaf), probably achieved by the release of K H11001 ions from the cells and the resulting efflux, by osmosis, of water. Di- gestive glands in the leaf’s surface release enzymes that extract nutrients from the insect. The sensitive plant (Mimosa pudica) also un- dergoes a remarkable change in leaf shape triggered by mechanical touch (Fig. 2). A light touch or vibra- tion produces a sudden drooping of the leaves, the re- sult of a dramatic reduction in turgor pressure in cells at the base of each leaflet and leaf. As in the Venus flytrap, the drop in turgor pressure results from K H11001 release followed by the efflux of water. 8885d_c02_47-74 7/25/03 10:05 AM Page 59 mac76 mac76:385_reb: 2.2 Ionization of Water, Weak Acids, and Weak Bases Although many of the solvent properties of water can be explained in terms of the uncharged H 2 O molecule, the small degree of ionization of water to hydrogen ions (H H11001 ) and hydroxide ions (OH H11002 ) must also be taken into account. Like all reversible reactions, the ionization of water can be described by an equilibrium constant. When weak acids are dissolved in water, they contribute H H11001 by ionizing; weak bases consume H H11001 by becoming protonated. These processes are also governed by equi- librium constants. The total hydrogen ion concentration from all sources is experimentally measurable and is ex- pressed as the pH of the solution. To predict the state of ionization of solutes in water, we must take into ac- count the relevant equilibrium constants for each ion- ization reaction. We therefore turn now to a brief dis- cussion of the ionization of water and of weak acids and bases dissolved in water. Pure Water Is Slightly Ionized Water molecules have a slight tendency to undergo re- versible ionization to yield a hydrogen ion (a proton) and a hydroxide ion, giving the equilibrium H 2 OH H11001 H11001 OH H11002 (2–1) Although we commonly show the dissociation product of water as H H11001 , free protons do not exist in solution; hy- drogen ions formed in water are immediately hydrated to hydronium ions (H 3 O H11001 ). Hydrogen bonding be- tween water molecules makes the hydration of dissoci- ating protons virtually instantaneous: The ionization of water can be measured by its elec- trical conductivity; pure water carries electrical current as H H11001 migrates toward the cathode and OH H11002 toward the anode. The movement of hydronium and hydroxide ions in the electric field is anomalously fast compared with that of other ions such as Na H11001 , K H11001 , and Cl H11002 . This high ionic mobility results from the kind of “proton hopping” shown in Figure 2–14. No individual proton moves very far through the bulk solution, but a series of proton hops between hydrogen-bonded water molecules causes the net movement of a proton over a long distance in a re- markably short time. As a result of the high ionic mo- bility of H H11001 (and of OH H11002 , which also moves rapidly by proton hopping, but in the opposite direction), acid-base reactions in aqueous solutions are generally exception- ally fast. As noted above, proton hopping very likely also plays a role in biological proton-transfer reactions (Fig. 2–10; see also Fig. 19–XX). Because reversible ionization is crucial to the role of water in cellular function, we must have a means of O H H H11001 OH H11002 O H H O H11001 HH H z y expressing the extent of ionization of water in quanti- tative terms. A brief review of some properties of re- versible chemical reactions shows how this can be done. The position of equilibrium of any chemical reac- tion is given by its equilibrium constant, K eq (some- times expressed simply as K ). For the generalized reaction A H11001 B C H11001 D (2–2) an equilibrium constant can be defined in terms of the concentrations of reactants (A and B) and products (C and D) at equilibrium: K eq H11005 H5007 [ [ C A ] ] [ [ D B] ] H5007 Strictly speaking, the concentration terms should be the activities, or effective concentrations in nonideal solutions, of each species. Except in very accurate work, however, the equilibrium constant may be approxi- z y Part I Structure and Catalysis60 O + O O O O O O H H Proton hop Hydronium ion gives up a proton Water accepts proton and becomes a hydronium ion H H H H H H H H H H H H H H H O O O H H H H FIGURE 2–14 Proton hopping. Short “hops” of protons between a se- ries of hydrogen-bonded water molecules effect an extremely rapid net movement of a proton over a long distance. As a hydronium ion (upper left) gives up a proton, a water molecule some distance away (lower right) acquires one, becoming a hydronium ion. Proton hop- ping is much faster than true diffusion and explains the remarkably high ionic mobility of H H11001 ions compared with other monovalent cations such as Na H11001 or K H11001 . 8885d_c02_47-74 7/25/03 10:05 AM Page 60 mac76 mac76:385_reb: mated by measuring the concentrations at equilibrium. For reasons beyond the scope of this discussion, equi- librium constants are dimensionless. Nonetheless, we have generally retained the concentration units (M) in the equilibrium expressions used in this book to remind you that molarity is the unit of concentration used in calculating K eq . The equilibrium constant is fixed and characteris- tic for any given chemical reaction at a specified tem- perature. It defines the composition of the final equi- librium mixture, regardless of the starting amounts of reactants and products. Conversely, we can calculate the equilibrium constant for a given reaction at a given temperature if the equilibrium concentrations of all its reactants and products are known. As we will show in Chapter 13, the standard free-energy change (H9004GH11034) is directly related to K eq . The Ionization of Water Is Expressed by an Equilibrium Constant The degree of ionization of water at equilibrium (Eqn 2–1) is small; at 25 °C only about two of every 10 9 mol- ecules in pure water are ionized at any instant. The equi- librium constant for the reversible ionization of water (Eqn 2–1) is K eq H11005 H5007 [H [ H11001 H ][ 2 O O H ] H11002 ] H5007 (2–3) In pure water at 25 H11034C, the concentration of water is 55.5 M (grams of H 2 O in 1 L divided by its gram molec- ular weight: (1,000 g/L)/(18.015 g/mol)) and is essen- tially constant in relation to the very low concentrations of H H11001 and OH H11002 , namely, 1 H11003 10 H110027 M. Accordingly, we can substitute 55.5 M in the equilibrium constant ex- pression (Eqn 2–3) to yield K eq H11005 H5007 [H 5 H11001 5 ][ .5 OH M H11002 ] H5007, which, on rearranging, becomes (55.5 M)(K eq ) H11005 [H H11001 ][OH H11002 ] H11005 K w (2–4) where K w designates the product (55.5 M)(K eq ), the ion product of water at 25 °C. The value for K eq , determined by electrical-con- ductivity measurements of pure water, is 1.8 H11003 10 H1100216 M at 25 H11034C. Substituting this value for K eq in Equation 2–4 gives the value of the ion product of water: K w H11005 [H H11001 ][OH H11002 ] H11005 (55.5 M)(1.8 H11003 10 H1100216 M) H11005 1.0 H11003 10 H1100214 M 2 Thus the product [H H11001 ][OH H11002 ] in aqueous solutions at 25 H11034C always equals 1 H11003 10 H1100214 M 2 . When there are ex- actly equal concentrations of H H11001 and OH H11002 , as in pure water, the solution is said to be at neutral pH. At this pH, the concentration of H H11001 and OH H11002 can be calculated from the ion product of water as follows: K w H11005 [H H11001 ][OH H11002 ] H11005 [H H11001 ] 2 Solving for [H H11001 ] gives [H H11001 ] H11005 H20857K w H33526 H11005 H208571 H11003 10H33526 H1100214 M 2 H33526 [H H11001 ] H11005 [OH H11002 ] H11005 10 H110027 M As the ion product of water is constant, whenever [H H11001 ] is greater than 1 H11003 10 H110027 M, [OH H11002 ] must become less than 1 H11003 10 H110027 M, and vice versa. When [H H11001 ] is very high, as in a solution of hydrochloric acid, [OH H11002 ] must be very low. From the ion product of water we can calculate [H H11001 ] if we know [OH H11002 ], and vice versa (Box 2–2). The pH Scale Designates the H H11545 and OH H11546 Concentrations The ion product of water, K w , is the basis for the pH scale (Table 2–6). It is a convenient means of desig- nating the concentration of H H11001 (and thus of OH H11002 ) in any aqueous solution in the range between 1.0 M H H11001 and 1.0 M OH H11002 . The term pH is defined by the expression pH H11005 log H5007 [H 1 H11001 ] H5007 H11005H11002log [H H11001 ] The symbol p denotes “negative logarithm of.” For a pre- cisely neutral solution at 25 H11034C, in which the concen- tration of hydrogen ions is 1.0 H11003 10 H110027 M, the pH can be calculated as follows: pH H11005 log H5007 1.0 H11003 1 10 H110027 H5007 H11005 log (1.0 H11003 10 7 ) H11005 log 1.0 H11001 log 10 7 H11005 0 H11001 7 H11005 7 Chapter 2 Water 61 TABLE 2–6 The pH Scale [H H11001 ] (M) pH [OH H11002 ] (M) pOH* 10 0 (1) 0 10 H1100214 14 10 H110021 11 H1100213 13 10 H110022 21 H1100212 12 10 H110023 310 H1100211 11 10 H110024 41 H1100210 10 10 H110025 51 H110029 9 10 H110026 610 H110028 8 10 H110027 71 H110027 7 10 H110028 81 H110026 6 10 H110029 910 H110025 5 10 H1100210 10 10 H110024 4 10 H1100211 11 10 H110023 3 10 H1100212 12 10 H110022 2 10 H1100213 13 10 H110021 1 10 H1100214 14 10 0 (1) 0 *The expression pOH is sometimes used to describe the basicity, or OH H11002 concentration, of a solution; pOH is defined by the expression pOH H11005H11002log [OH H11002 ], which is analogous to the expression for pH. Note that in all cases, pH H11001 pOH H11005 14. 8885d_c02_47-74 7/25/03 10:05 AM Page 61 mac76 mac76:385_reb: The value of 7 for the pH of a precisely neutral so- lution is not an arbitrarily chosen figure; it is derived from the absolute value of the ion product of water at 25 H11034C, which by convenient coincidence is a round num- ber. Solutions having a pH greater than 7 are alkaline or basic; the concentration of OH H11002 is greater than that of H H11001 . Conversely, solutions having a pH less than 7 are acidic. Note that the pH scale is logarithmic, not arithmetic. To say that two solutions differ in pH by 1 pH unit means that one solution has ten times the H H11001 concentration of the other, but it does not tell us the absolute magnitude of the difference. Figure 2–15 gives the pH of some com- mon aqueous fluids. A cola drink (pH 3.0) or red wine (pH 3.7) has an H H11001 concentration approximately 10,000 times that of blood (pH 7.4). The pH of an aqueous solution can be approximately measured using various indicator dyes, including litmus, phenolphthalein, and phenol red, which undergo color changes as a proton dissociates from the dye molecule. Accurate determinations of pH in the chemical or clin- ical laboratory are made with a glass electrode that is se- lectively sensitive to H H11001 concentration but insensitive to Na H11001 , K H11001 , and other cations. In a pH meter the signal from such an electrode is amplified and compared with the sig- nal generated by a solution of accurately known pH. Measurement of pH is one of the most important and frequently used procedures in biochemistry. The pH af- fects the structure and activity of biological macromol- ecules; for example, the catalytic activity of enzymes is strongly dependent on pH (see Fig. 2–21). Measurements of the pH of blood and urine are commonly used in med- ical diagnoses. The pH of the blood plasma of people Part I Structure and Catalysis62 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Household bleach Household ammonia Solution of baking soda (NaHCO 3 ) Seawater, egg white Human blood, tears Milk, saliva Black coffee Beer Tomato juice Red wine Cola, vinegar Lemon juice Gastric juice 1 M HCl 14 1 M NaOH Neutral Increasingly basic Increasingly acidic FIGURE 2–15 The pH of some aqueous fluids. BOX 2–2 WORKING IN BIOCHEMISTRY The Ion Product of Water: Two Illustrative Problems The ion product of water makes it possible to calcu- late the concentration of H H11001 , given the concentration of OH H11002 , and vice versa; the following problems demon- strate this. 1. What is the concentration of H H11001 in a solution of 0.1 M NaOH? K w H11005 [H H11001 ][OH H11002 ] Solving for [H H11001 ] gives [H H11001 ] H11005 H5007 [O K H w H11002 ] H5007 H11005 H5007 1 H11003 0 1 . 0 1 H11002 M 14 M 2 H5007 H11005 H5007 1 1 0 0 H11002 H11002 14 1 M M 2 H5007 H11005 10 H1100213 M (answer) 2. What is the concentration of OH H11002 in a solution with an H H11001 concentration of 1.3 H11003 10 H110024 M? K w H11005 [H H11001 ][OH H11002 ] Solving for [OH H11002 ] gives [OH H11002 ] H11005 H5007 [H K w H11001 ] H5007 H11005 H5007 1 1 .0 .3 H11003 H11003 1 1 0 0 H11002 H11002 14 4 M M 2 H5007 H11005 7.7 H11003 10 H1100211 M (answer) When doing these or any other calculations, be sure to round your answers to the correct number of significant figures. 8885d_c02_47-74 7/25/03 10:05 AM Page 62 mac76 mac76:385_reb: with severe, uncontrolled diabetes, for example, is of- ten below the normal value of 7.4; this condition is called acidosis. In certain other disease states the pH of the blood is higher than normal, the condition of alkalosis. Weak Acids and Bases Have Characteristic Dissociation Constants Hydrochloric, sulfuric, and nitric acids, commonly called strong acids, are completely ionized in dilute aqueous solutions; the strong bases NaOH and KOH are also com- pletely ionized. Of more interest to biochemists is the behavior of weak acids and bases—those not completely ionized when dissolved in water. These are common in biological systems and play important roles in metabo- lism and its regulation. The behavior of aqueous solu- tions of weak acids and bases is best understood if we first define some terms. Acids may be defined as proton donors and bases as proton acceptors. A proton donor and its correspon- ding proton acceptor make up a conjugate acid-base pair (Fig. 2–16). Acetic acid (CH 3 COOH), a proton donor, and the acetate anion (CH 3 COO H11002 ), the corre- sponding proton acceptor, constitute a conjugate acid- base pair, related by the reversible reaction CH 3 COOH H H11001 H11001 CH 3 COO H11002 Each acid has a characteristic tendency to lose its proton in an aqueous solution. The stronger the acid, the greater its tendency to lose its proton. The tendency of any acid (HA) to lose a proton and form its conju- gate base (A H11002 ) is defined by the equilibrium constant (K eq ) for the reversible reaction HA H H11001 H11001 A H11002 , which is K eq H11005 H5007 [H [ H11001 H ][ A A ] H11002 ] H5007 H11005 K a Equilibrium constants for ionization reactions are usu- ally called ionization or dissociation constants, often designated K a . The dissociation constants of some acids are given in Figure 2–16. Stronger acids, such as phos- phoric and carbonic acids, have larger dissociation con- stants; weaker acids, such as monohydrogen phosphate (HPO 4 2H11002 ), have smaller dissociation constants. z y z y Chapter 2 Water 63 Monoprotic acids Acetic acid (K a = 1.74 H11003 10 H110025 M) Diprotic acids Carbonic acid (K a = 1.70 H11003 10 H110024 M); Bicarbonate (K a = 6.31 H11003 10 H1100211 M) Triprotic acids Phosphoric acid (K a = 7.25 H11003 10 H110023 M); Dihydrogen phosphate (K a = 1.38 H11003 10 H110027 M); Monohydrogen phosphate (K a = 3.98 H11003 10 H1100213 M) Glycine, carboxyl (K a = 4.57 H11003 10 H110023 M); Glycine, amino (K a = 2.51 H11003 10 H1100210 M) Ammonium ion (K a = 5.62 H11003 10 H1100210 M) CH 3 C OH O CH 3 C H11001 O H11002 H H11001 O pK a = 4.76 H 2 CO 3 HCO 3 H11002 H11001 H H11001 pK a = 3.77 HCO 3 H11002 CO 3 2H11002 H11001 H H11001 pK a = 10.2 NH 4 H11001 NH 3 H11001 H H11001 pK a = 9.25 H 3 PO 4 H 2 PO 4 H11002 H11001 H H11001 pK a = 2.14 H 2 PO 4 H11002 HPO 4 2H11002 H11001 H H11001 pK a = 6.86 HPO 4 2H11002 PO 4 3H11002 H11001 H H11001 pK a = 12.4 CH 2 C OH O CH 2 C H11001 O H11002 H H11001 O pK a = 2.34 NH 3 H11001 NH 3 H11001 CH 2 C O H11002 O CH 2 C H11001 O H11002 H H11001 O pK a = 9.60 NH 3 H11001 NH 2 21 34567891011213 pH FIGURE 2–16 Conjugate acid-base pairs consist of a proton donor and a proton acceptor. Some compounds, such as acetic acid and ammonium ion, are monoprotic; they can give up only one proton. Others are diprotic (H 2 CO 3 (carbonic acid) and glycine) or triprotic (H 3 PO 4 (phosphoric acid)). The dissociation reactions for each pair are shown where they occur along a pH gradient. The equilibrium or dis- sociation constant (K a ) and its negative logarithm, the pK a , are shown for each reaction. 8885d_c02_47-74 7/25/03 10:05 AM Page 63 mac76 mac76:385_reb: Also included in Figure 2–16 are values of pK a , which is analogous to pH and is defined by the equation pK a H11005 log H5007 K 1 a H5007 H11005H11002log K a The stronger the tendency to dissociate a proton, the stronger is the acid and the lower its pK a . As we shall now see, the pK a of any weak acid can be determined quite easily. Titration Curves Reveal the pK a of Weak Acids Titration is used to determine the amount of an acid in a given solution. A measured volume of the acid is titrated with a solution of a strong base, usually sodium hydroxide (NaOH), of known concentration. The NaOH is added in small increments until the acid is consumed (neutralized), as determined with an indicator dye or a pH meter. The concentration of the acid in the original solution can be calculated from the volume and con- centration of NaOH added. A plot of pH against the amount of NaOH added (a titration curve) reveals the pK a of the weak acid. Con- sider the titration of a 0.1 M solution of acetic acid (for simplicity denoted as HAc) with 0.1 M NaOH at 25 H11034C (Fig. 2–17). Two reversible equilibria are involved in the process: H 2 O H H11001 H11001 OH H11002 (2–5) HAc H H11001 H11001 Ac H11002 (2–6) The equilibria must simultaneously conform to their characteristic equilibrium constants, which are, respec- tively, K w H11005 [H H11001 ][OH H11002 ] H11005 1 H11003 10 H1100214 M 2 (2–7) K a H11005 H5007 [H [ H11001 H ][ A A c c ] H11002 ] H5007 H11005 1.74 H11003 10 5 M (2–8) At the beginning of the titration, before any NaOH is added, the acetic acid is already slightly ionized, to an extent that can be calculated from its dissociation con- stant (Eqn 2–8). As NaOH is gradually introduced, the added OH H11002 combines with the free H H11001 in the solution to form H 2 O, to an extent that satisfies the equilibrium relationship in Equation 2–7. As free H H11001 is removed, HAc dissoci- ates further to satisfy its own equilibrium constant (Eqn 2–8). The net result as the titration proceeds is that more and more HAc ionizes, forming Ac H11002 , as the NaOH is added. At the midpoint of the titration, at which ex- actly 0.5 equivalent of NaOH has been added, one-half of the original acetic acid has undergone dissociation, so that the concentration of the proton donor, [HAc], now equals that of the proton acceptor, [Ac H11002 ]. At this midpoint a very important relationship holds: the pH of the equimolar solution of acetic acid and acetate is ex- z y z y actly equal to the pK a of acetic acid (pK a H11005 4.76; Figs 2–16, 2–17). The basis for this relationship, which holds for all weak acids, will soon become clear. As the titration is continued by adding further in- crements of NaOH, the remaining nondissociated acetic acid is gradually converted into acetate. The end point of the titration occurs at about pH 7.0: all the acetic acid has lost its protons to OH H11002 , to form H 2 O and acetate. Throughout the titration the two equilibria (Eqns 2–5, 2–6) coexist, each always conforming to its equilibrium constant. Figure 2–18 compares the titration curves of three weak acids with very different dissociation constants: acetic acid (pK a H11005 4.76); dihydrogen phosphate, H 2 PO 4 H11002 (pK a H11005 6.86); and ammonium ion, NH 4 H11001 (pK a H11005 9.25). Although the titration curves of these acids have the same shape, they are displaced along the pH axis be- cause the three acids have different strengths. Acetic acid, with the highest K a (lowest pK a ) of the three, is the strongest (loses its proton most readily); it is al- Part I Structure and Catalysis64 1.0 CH 3 COO H11002 CH 3 COOH pH H11005 pK a H11005 4.76 pH Buffering region OH H11002 added (equivalents) 0 100%50 Percent titrated 9 8 7 3 2 1 0 0 0.5 0.6 0.7 0.8 0.90.40.30.20.1 [CH 3 COOH] H11005 [CH 3 COO H11002 ] pH 5.76 pH 3.76 6 5 4 FIGURE 2–17 The titration curve of acetic acid. After addition of each increment of NaOH to the acetic acid solution, the pH of the mixture is measured. This value is plotted against the amount of NaOH expressed as a fraction of the total NaOH required to convert all the acetic acid to its deprotonated form, acetate. The points so obtained yield the titration curve. Shown in the boxes are the predominant ionic forms at the points designated. At the midpoint of the titration, the concentrations of the proton donor and proton acceptor are equal, and the pH is numerically equal to the pK a . The shaded zone is the useful region of buffering power, generally between 10% and 90% titration of the weak acid. 8885d_c02_064 7/25/03 10:16 AM Page 64 mac76 mac76:385_reb: ready half dissociated at pH 4.76. Dihydrogen phosphate loses a proton less readily, being half dissociated at pH 6.86. Ammonium ion is the weakest acid of the three and does not become half dissociated until pH 9.25. The most important point about the titration curve of a weak acid is that it shows graphically that a weak acid and its anion—a conjugate acid-base pair—can act as a buffer. SUMMARY 2.2 Ionization of Water, Weak Acids, and Weak Bases ■ Pure water ionizes slightly, forming equal num- bers of hydrogen ions (hydronium ions, H 3 O H11001 ) and hydroxide ions. The extent of ionization is described by an equilibrium constant, K eq H11005 H5007 [H H11001 [H ][ 2 O O H ] H11002 ] H5007, from which the ion product of water, K w , is derived. At 25 H11034C, K w H11005 [H H11001 ][OH H11002 ] H11005 (55.5 M)(K eq ) = 10 H1100214 M 2 . ■ The pH of an aqueous solution reflects, on a logarithmic scale, the concentration of hydrogen ions: pH H11005 log H5007 [H 1 H11001 ] H5007 H11005H11002log [H H11001 ]. ■ The greater the acidity of a solution, the lower its pH. Weak acids partially ionize to release a hydrogen ion, thus lowering the pH of the aqueous solution. Weak bases accept a hydro- gen ion, increasing the pH. The extent of these processes is characteristic of each particular weak acid or base and is expressed as a disso- ciation constant, K a : K eq H11005 H5007 [H [ H11001 H ][ A A ] H11002 ] H5007 H11005 K a . ■ The pK a expresses, on a logarithmic scale, the relative strength of a weak acid or base: pK a H11005 log H5007 K 1 a H5007 H11005H11002log K a . ■ The stronger the acid, the lower its pK a ; the stronger the base, the higher its pK a . The pK a can be determined experimentally; it is the pH at the midpoint of the titration curve for the acid or base. 2.3 Buffering against pH Changes in Biological Systems Almost every biological process is pH dependent; a small change in pH produces a large change in the rate of the process. This is true not only for the many reactions in which the H H11001 ion is a direct participant, but also for those in which there is no apparent role for H H11001 ions. The en- zymes that catalyze cellular reactions, and many of the molecules on which they act, contain ionizable groups with characteristic pK a values. The protonated amino and carboxyl groups of amino acids and the phosphate groups of nucleotides, for example, function as weak acids; their ionic state depends on the pH of the sur- rounding medium. As we noted above, ionic interactions are among the forces that stabilize a protein molecule and allow an enzyme to recognize and bind its substrate. Cells and organisms maintain a specific and con- stant cytosolic pH, keeping biomolecules in their opti- mal ionic state, usually near pH 7. In multicellular or- ganisms, the pH of extracellular fluids is also tightly regulated. Constancy of pH is achieved primarily by bi- ological buffers: mixtures of weak acids and their con- jugate bases. We describe here the ionization equilibria that ac- count for buffering, and we show the quantitative rela- tionship between the pH of a buffered solution and the pK a of the buffer. Biological buffering is illustrated by the phosphate and carbonate buffering systems of humans. Chapter 2 Water 65 1.0 NH 3 Midpoint of titration Buffering regions: pK a H11005 9.25 NH 3 [NH H11001 4 ]H11005[NH 3 ] CH 3 COO H11002 pK a H11005 6.86 pK a H11005 4.76 [CH 3 COOH] H11005 [CH 3 COO H11002 ] CH 3 COOH pH 10.25 5.76 3.76 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 0.50.40.30.20.1 0.6 0.7 0.8 0.9 [H 2 PO 4 H11002 ] H11005 [HPO 2 4 H11002 ] Phosphate Acetate NH 4 H11001 H 2 PO 4 H11002 8.25 7.86 5.86 HPO 4 2H11002 OH H11002 added (equivalents) 0 100%50 Percent titrated FIGURE 2–18 Comparison of the titration curves of three weak acids. Shown here are the titration curves for CH 3 COOH, H 2 PO 4 H11002 , and NH 4 H11001 . The predominant ionic forms at designated points in the titration are given in boxes. The regions of buffering capacity are indicated at the right. Conjugate acid-base pairs are effective buffers between ap- proximately 10% and 90% neutralization of the proton-donor species. 8885d_c02_47-74 7/25/03 10:05 AM Page 65 mac76 mac76:385_reb: Buffers Are Mixtures of Weak Acids and Their Conjugate Bases Buffers are aqueous systems that tend to resist changes in pH when small amounts of acid (H H11001 ) or base (OH H11002 ) are added. A buffer system consists of a weak acid (the proton donor) and its conjugate base (the proton ac- ceptor). As an example, a mixture of equal concentra- tions of acetic acid and acetate ion, found at the mid- point of the titration curve in Figure 2–17, is a buffer system. The titration curve of acetic acid has a relatively flat zone extending about 1 pH unit on either side of its midpoint pH of 4.76. In this zone, an amount of H H11001 or OH H11002 added to the system has much less effect on pH than the same amount added outside the buffer range. This relatively flat zone is the buffering region of the acetic acid–acetate buffer pair. At the midpoint of the buffering region, where the concentration of the proton donor (acetic acid) exactly equals that of the proton ac- ceptor (acetate), the buffering power of the system is maximal; that is, its pH changes least on addition of H H11001 or OH H11002 . The pH at this point in the titration curve of acetic acid is equal to its pK a . The pH of the acetate buffer system does change slightly when a small amount of H H11001 or OH H11002 is added, but this change is very small compared with the pH change that would result if the same amount of H H11001 or OH H11002 were added to pure water or to a solution of the salt of a strong acid and strong base, such as NaCl, which has no buffering power. Buffering results from two reversible reaction equi- libria occurring in a solution of nearly equal concentra- tions of a proton donor and its conjugate proton accep- tor. Figure 2–19 explains how a buffer system works. Whenever H H11001 or OH H11002 is added to a buffer, the result is a small change in the ratio of the relative concentrations of the weak acid and its anion and thus a small change in pH. The decrease in concentration of one component of the system is balanced exactly by an increase in the other. The sum of the buffer components does not change, only their ratio. Each conjugate acid-base pair has a characteristic pH zone in which it is an effective buffer (Fig. 2–18). The H 2 PO 4 H11002 /HPO 4 2H11002 pair has a pK a of 6.86 and thus can serve as an effective buffer system between approxi- mately pH 5.9 and pH 7.9; the NH 4 H11001 /NH 3 pair, with a pK a of 9.25, can act as a buffer between approximately pH 8.3 and pH 10.3. A Simple Expression Relates pH, pK a , and Buffer Concentration The titration curves of acetic acid, H 2 PO 4 H11002 , and NH 4 H11001 (Fig. 2–18) have nearly identical shapes, suggesting that these curves reflect a fundamental law or relationship. This is indeed the case. The shape of the titration curve of any weak acid is described by the Henderson- Hasselbalch equation, which is important for under- standing buffer action and acid-base balance in the blood and tissues of vertebrates. This equation is sim- ply a useful way of restating the expression for the dissociation constant of an acid. For the dissociation of a weak acid HA into H H11001 and A H11002 , the Henderson- Hasselbalch equation can be derived as follows: K a H11005 H5007 [H [ H11001 H ][ A A ] H11002 ] H5007 First solve for [H H11001 ]: [H H11001 ] H11005 K a H5007 [ [ H A H11002 A ] ] H5007 Then take the negative logarithm of both sides: H11002log [H H11001 ] H11005H11002log K a H11002 log H5007 [ [ H A H11002 A ] ] H5007 Substitute pH for H11002log [H H11001 ] and pK a for H11002log K a : pH H11005 pK a H11002 log H5007 [ [ H A H11002 A ] ] H5007 Part I Structure and Catalysis66 K w H11005 [H H11001 ][OH H11002 ] Acetic acid (CH 3 COOH) HAc Ac H11002 H H11001 OH H11002 H 2 O Acetate (CH 3 COO H11002 ) [H H11001 ][Ac H11002 ] [HAc] K a H11005 FIGURE 2–19 The acetic acid–acetate pair as a buffer system. The system is capable of absorbing either H H11001 or OH H11002 through the re- versibility of the dissociation of acetic acid. The proton donor, acetic acid (HAc), contains a reserve of bound H H11001 , which can be released to neutralize an addition of OH H11002 to the system, forming H 2 O. This happens because the product [H H11001 ][OH H11002 ] transiently exceeds K w (1 H11003 10 H1100214 M 2 ). The equilibrium quickly adjusts so that this product equals 1 H11003 10 H1100214 M 2 (at 25 H11034C), thus transiently reducing the concentration of H H11001 . But now the quotient [H H11001 ][Ac H11002 ] / [HAc] is less than K a , so HAc dissociates further to restore equilibrium. Similarly, the conjugate base, Ac H11002 , can react with H H11001 ions added to the system; again, the two ion- ization reactions simultaneously come to equilibrium. Thus a conju- gate acid-base pair, such as acetic acid and acetate ion, tends to re- sist a change in pH when small amounts of acid or base are added. Buffering action is simply the consequence of two reversible reactions taking place simultaneously and reaching their points of equilibrium as governed by their equilibrium constants, K W and K a . 8885d_c02_47-74 7/25/03 10:05 AM Page 66 mac76 mac76:385_reb: Now invert H11002log [HA]/[A H11002 ], which involves changing its sign, to obtain the Henderson-Hasselbalch equation: pH H11005 pK a H11001 log H5007 [ [ H A H11002 A ] ] H5007 (2–9) Stated more generally, pH H11005 pK a H11001 log This equation fits the titration curve of all weak acids and enables us to deduce a number of important quan- titative relationships. For example, it shows why the pK a of a weak acid is equal to the pH of the solution at the midpoint of its titration. At that point, [HA] equals [A H11002 ], and pH H11005 pK a H11001 log 1 H11005 pK a H11001 0 H11005 pK a As shown in Box 2–3, the Henderson-Hasselbalch equa- tion also allows us to (1) calculate pK a , given pH and the molar ratio of proton donor and acceptor; (2) cal- culate pH, given pK a and the molar ratio of proton donor and acceptor; and (3) calculate the molar ratio of pro- ton donor and acceptor, given pH and pK a . Weak Acids or Bases Buffer Cells and Tissues against pH Changes The intracellular and extracellular fluids of multicellu- lar organisms have a characteristic and nearly constant [proton acceptor] H5007H5007H5007 [proton donor] pH. The organism’s first line of defense against changes in internal pH is provided by buffer systems. The cyto- plasm of most cells contains high concentrations of pro- teins, which contain many amino acids with functional groups that are weak acids or weak bases. For example, the side chain of histidine (Fig. 2–20) has a pK a of 6.0; proteins containing histidine residues therefore buffer effectively near neutral pH. Nucleotides such as ATP, as well as many low molecular weight metabolites, contain ionizable groups that can contribute buffering power to the cytoplasm. Some highly specialized organelles and extracellular compartments have high concentrations of compounds that contribute buffering capacity: organic acids buffer the vacuoles of plant cells; ammonia buffers urine. Chapter 2 Water 67 BOX 2–3 WORKING IN BIOCHEMISTRY Solving Problems Using the Henderson- Hasselbalch Equation 1. Calculate the pK a of lactic acid, given that when the concentration of lactic acid is 0.010 M and the concentration of lactate is 0.087 M, the pH is 4.80. pH H11005 pK a H11001 log H5007 [la [l c a t c ic ta a t c e i ] d] H5007 pK a H11005 pH H11002 log H5007 [la [l c a t c ic ta a t c e i ] d] H5007 H11005 4.80 H11002 log H5007 0 0 . . 0 0 8 1 7 0 H5007 H11005 4.80 H11002 log 8.7 H11005 4.80 H11002 0.94 H11005 3.9 (answer) 2. Calculate the pH of a mixture of 0.10 M acetic acid and 0.20 M sodium acetate. The pK a of acetic acid is 4.76. pH H11005 pK a H11001 log H5007 [a [ c a e c t e ic ta a t c e i ] d] H5007 H11005 4.76 H11001 log H5007 0 0 . . 2 1 0 0 H5007 H11005 4.76 H11001 0.30 H11005 5.1 (answer) 3. Calculate the ratio of the concentrations of acetate and acetic acid required in a buffer system of pH 5.30. pH H11005 pK a H11001 log H5007 [a [ c a e c t e ic ta a t c e i ] d] H5007 log H5007 [a [ c a e c t e ic ta a t c e i ] d] H5007 H11005 pH H11002 pK a H11005 5.30 H11002 4.76 H11005 0.54 H5007 [a [ c a e c t e ic ta a t c e i ] d] H5007 H11005 antilog 0.54 H11005 3.5 (answer) To see the effect of pH on the degree of ionization of a weak acid, see the Living Graph for Equation 2–9. A G J A CH 2 C H CH H11001 H H11001 HC A G J A CH 2 C H CH H11001 HC Protein Protein 3::4 NN NN H FIGURE 2–20 The amino acid histidine, a component of proteins, is a weak acid. The pK a of the protonated nitrogen of the side chain is 6.0. 8885d_c02_067 9/10/03 10:37 AM Page 67 mac76 mac76:385_reb: Two especially important biological buffers are the phosphate and bicarbonate systems. The phosphate buffer system, which acts in the cytoplasm of all cells, consists of H 2 PO 4 H11002 as proton donor and HPO 4 2H11002 as pro- ton acceptor: H 2 PO 4 H11002 H H11001 H11001 HPO 4 2H11002 The phosphate buffer system is maximally effective at a pH close to its pK a of 6.86 (Figs 2–16, 2–18) and thus tends to resist pH changes in the range between about 5.9 and 7.9. It is therefore an effective buffer in biolog- ical fluids; in mammals, for example, extracellular flu- ids and most cytoplasmic compartments have a pH in the range of 6.9 to 7.4. Blood plasma is buffered in part by the bicarbonate system, consisting of carbonic acid (H 2 CO 3 ) as proton donor and bicarbonate (HCO 3 H11002 ) as proton acceptor: H 2 CO 3 H H11001 H11001 HCO 3 H11002 K 1 H11005 H5007 [H [ H11001 H ][ 2 H CO CO 3 ] 3 H11002 ] H5007 This buffer system is more complex than other conju- gate acid-base pairs because one of its components, car- bonic acid (H 2 CO 3 ), is formed from dissolved (d) car- bon dioxide and water, in a reversible reaction: CO 2 (d) H11001 H 2 O H 2 CO 3 K 2 H11005 H5007 [CO [H 2 ( 2 d C )] O [H 3 ] 2 O] H5007 Carbon dioxide is a gas under normal conditions, and the concentration of dissolved CO 2 is the result of equi- libration with CO 2 of the gas (g) phase: CO 2 (g) CO 2 (d) K 3 H11005 H5007 [ [ C C O O 2 2 ( ( d g) ) ] ] H5007 The pH of a bicarbonate buffer system depends on the concentration of H 2 CO 3 and HCO 3 H11002 , the proton donor and acceptor components. The concentration of H 2 CO 3 in turn depends on the concentration of dissolved CO 2 , which in turn depends on the concentration of CO 2 in the gas phase, called the partial pressure of CO 2 . Thus the pH of a bicarbonate buffer exposed to a gas phase is ultimately determined by the concentration of HCO 3 H11002 in the aqueous phase and the partial pressure of CO 2 in the gas phase (Box 2–4). Human blood plasma normally has a pH close to 7.4. Should the pH-regulating mechanisms fail or be over- whelmed, as may happen in severe uncontrolled dia- betes when an overproduction of metabolic acids causes acidosis, the pH of the blood can fall to 6.8 or below, leading to irreparable cell damage and death. In other diseases the pH may rise to lethal levels. z y z y z y z y Although many aspects of cell structure and func- tion are influenced by pH, it is the catalytic activity of enzymes that is especially sensitive. Enzymes typically show maximal catalytic activity at a characteristic pH, called the pH optimum (Fig. 2–21). On either side of the optimum pH their catalytic activity often declines sharply. Thus, a small change in pH can make a large difference in the rate of some crucial enzyme-catalyzed reactions. Biological control of the pH of cells and body fluids is therefore of central importance in all aspects of metabolism and cellular activities. SUMMARY 2.3 Buffering against pH Changes in Biological Systems ■ A mixture of a weak acid (or base) and its salt resists changes in pH caused by the addition of H H11001 or OH H11002 . The mixture thus functions as a buffer. ■ The pH of a solution of a weak acid (or base) and its salt is given by the Henderson- Hasselbalch equation: pH H11005 pK a H11002 log H5007 [ [ H A A H11002 ] ] H5007. ■ In cells and tissues, phosphate and bicarbonate buffer systems maintain intracellular and extra- cellular fluids at their optimum (physiological) pH, which is usually close to pH 7. Enzymes generally work optimally at this pH. Part I Structure and Catalysis68 100 7 pH Percent maximum activity Alkaline phosphatase 50 0 123456 8910 Pepsin Trypsin FIGURE 2–21 The pH optima of some enzymes. Pepsin is a digestive enzyme secreted into gastric juice; trypsin, a digestive enzyme that acts in the small intestine; alkaline phosphatase of bone tissue, a hy- drolytic enzyme thought to aid in bone mineralization. 8885d_c02_47-74 7/25/03 10:05 AM Page 68 mac76 mac76:385_reb: 2.4 Water as a Reactant Water is not just the solvent in which the chemical re- actions of living cells occur; it is very often a direct par- ticipant in those reactions. The formation of ATP from ADP and inorganic phosphate is an example of a con- densation reaction in which the elements of water are eliminated (Fig. 2–22a). The reverse of this reaction— cleavage accompanied by the addition of the elements of water—is a hydrolysis reaction. Hydrolysis reac- tions are also responsible for the enzymatic depolymer- ization of proteins, carbohydrates, and nucleic acids. Hydrolysis reactions, catalyzed by enzymes called Chapter 2 Water 69 BOX 2–4 BIOCHEMISTRY IN MEDICINE Blood, Lungs, and Buffer: The Bicarbonate Buffer System In animals with lungs, the bicarbonate buffer system is an effective physiological buffer near pH 7.4, be- cause the H 2 CO 3 of blood plasma is in equilibrium with a large reserve capacity of CO 2 (g) in the air space of the lungs. This buffer system involves three reversible equilibria between gaseous CO 2 in the lungs and bi- carbonate (HCO 3 H11002 ) in the blood plasma (Fig. 1). When H H11001 (from lactic acid produced in muscle tis- sue during vigorous exercise, for example) is added to blood as it passes through the tissues, reaction 1 proceeds toward a new equilibrium, in which the con- centration of H 2 CO 3 is increased. This increases the concentration of CO 2 (d) in the blood plasma (reac- tion 2) and thus increases the pressure of CO 2 (g) in the air space of the lungs (reaction 3); the extra CO 2 is exhaled. Conversely, when the pH of blood plasma is raised (by NH 3 production during protein catabo- lism, for example), the opposite events occur: the H H11001 concentration of blood plasma is lowered, causing more H 2 CO 3 to dissociate into H H11001 and HCO 3 H11002 . This in turn causes more CO 2 (g) from the lungs to dissolve in the blood plasma. The rate of breathing—that is, the rate of inhaling and exhaling CO 2 —can quickly adjust these equilibria to keep the blood pH nearly constant. (a) ROOOP B O A O H11002 OOOP B O A O H11002 OO H11002 H11001 H 2 O ROOP B O A O H11002 O H H11001 HOOP B O A O H11002 O (ATP) (ADP) (b) ROOOP B O A O H11002 OO H11002 H11001 H 2 O ROOH H11001 HOOP B O A O H11002 OO H11002 (c) R 1 OC J O G OR 2 H11001 H 2 R 1 OC J O G OH H11001 HOOR 2 (d) ROCOOOP B O A O H11002 OO H11002 H11001 H 2 ROC J O G OH H11001 HOOP B O A O H11002 OO H11002 O O B O O O O H11002 Acyl phosphate Carboxylate ester Phosphate ester Phosphoanhydride FIGURE 2–22 Participation of water in biological reactions. (a) ATP is a phosphoanhydride formed by a condensation reaction (loss of the elements of water) between ADP and phosphate. R represents adeno- sine monophosphate (AMP). This condensation reaction requires en- ergy. The hydrolysis of (addition of the elements of water to) ATP to form ADP and phosphate releases an equivalent amount of energy. Also shown are some other condensation and hydrolysis reactions common in biological systems (b), (c), (d). H H11001 H11001 HCO H11002 3 Aqueous phase (blood in capillaries) H 2 CO 3 H 2 OH 2 O reaction 2 CO 2 (g) reaction 3 Gas phase (lung air space) reaction 1 CO 2 (d) FIGURE 1 The CO 2 in the air space of the lungs is in equilibrium with the bicarbonate buffer in the blood plasma passing through the lung capillaries. Because the concentration of dissolved CO 2 can be adjusted rapidly through changes in the rate of breathing, the bi- carbonate buffer system of the blood is in near-equilibrium with a large potential reservoir of CO 2 . 8885d_c02_47-74 7/25/03 10:05 AM Page 69 mac76 mac76:385_reb: hydrolases, are almost invariably exergonic. The for- mation of cellular polymers from their subunits by sim- ple reversal of hydrolysis (that is, by condensation re- actions) would be endergonic and therefore does not occur. As we shall see, cells circumvent this thermody- namic obstacle by coupling endergonic condensation re- actions to exergonic processes, such as breakage of the anhydride bond in ATP. You are (we hope!) consuming oxygen as you read. Water and carbon dioxide are the end products of the oxidation of fuels such as glucose. The overall reaction can be summarized as C 6 H 12 O 6 H11001 6O 2 8n 6CO 2 H11001 6H 2 O Glucose The “metabolic water” formed by oxidation of foods and stored fats is actually enough to allow some animals in very dry habitats (gerbils, kangaroo rats, camels) to sur- vive for extended periods without drinking water. The CO 2 produced by glucose oxidation is con- verted in erythrocytes to the more soluble HCO 3 H11002 , in a reaction catalyzed by the enzyme carbonic anhydrase: CO 2 H11001 H 2 O HCO 3 H11002 H11001 H H11001 In this reaction, water not only is a substrate but also functions in proton transfer by forming a network of hydrogen-bonded water molecules through which pro- ton hopping occurs (Fig. 2–14). Green plants and algae use the energy of sunlight to split water in the process of photosynthesis: light 2H 2 O H11001 2A 88n O 2 H11001 2AH 2 In this reaction, A is an electron-accepting species, which varies with the type of photosynthetic organism, and water serves as the electron donor in an oxidation- reduction sequence (see Fig. 19–XX) that is fundamen- tal to all life. SUMMARY 2.4 Water as a Reactant ■ Water is both the solvent in which metabolic reactions occur and a reactant in many bio- chemical processes, including hydrolysis, con- densation, and oxidation-reduction reactions. 2.5 The Fitness of the Aqueous Environment for Living Organisms Organisms have effectively adapted to their aqueous en- vironment and have evolved means of exploiting the unusual properties of water. The high specific heat of water (the heat energy required to raise the tempera- ture of 1 g of water by 1 H11034C) is useful to cells and or- z y ganisms because it allows water to act as a “heat buffer,” keeping the temperature of an organism relatively con- stant as the temperature of the surroundings fluctuates and as heat is generated as a byproduct of metabolism. Furthermore, some vertebrates exploit the high heat of vaporization of water (Table 2–1) by using (thus losing) excess body heat to evaporate sweat. The high degree of internal cohesion of liquid water, due to hydrogen bonding, is exploited by plants as a means of trans- porting dissolved nutrients from the roots to the leaves during the process of transpiration. Even the density of ice, lower than that of liquid water, has important bio- logical consequences in the life cycles of aquatic or- ganisms. Ponds freeze from the top down, and the layer of ice at the top insulates the water below from frigid air, preventing the pond (and the organisms in it) from freezing solid. Most fundamental to all living organisms is the fact that many physical and biological properties of cell macromolecules, particularly the proteins and nu- cleic acids, derive from their interactions with water molecules of the surrounding medium. The influence of water on the course of biological evolution has been pro- found and determinative. If life forms have evolved else- where in the universe, they are unlikely to resemble those of Earth unless their extraterrestrial origin is also a place in which plentiful liquid water is available. Part I Structure and Catalysis70 Aqueous environments support countless species. Soft corals, sponges, bryozoans, and algae compete for space on this reef substrate off the Philippine Islands. 8885d_c02_47-74 7/25/03 10:05 AM Page 70 mac76 mac76:385_reb: Chapter 2 Water 71 Key Terms Further Reading hydrogen bond 48 bond energy 48 hydrophilic 50 hydrophobic 50 amphipathic 52 micelle 53 hydrophobic interactions 53 van der Waals interactions 54 osmolarity 56 osmosis 57 isotonic 57 hypertonic 57 hypotonic 57 equilibrium constant (K eq ) 60 ion product of water (K w ) 61 pH 61 conjugate acid-base pair 63 dissociation constant (K a ) 63 pK a 64 titration curve 64 buffer 66 Henderson-Hasselbalch equation 66 condensation 69 hydrolysis 69 Terms in bold are defined in the glossary. General Belton, P.S. (2000) Nuclear magnetic resonance studies of the hydration of proteins and DNA. Cell. Mol. Life Sci. 57, 993–998. Denny, M.W. (1993) Air and Water: The Biology and Physics of Life’s Media, Princeton University Press, Princeton, NJ. A wonderful investigation of the biological relevance of the properties of water. Eisenberg, D. & Kauzmann, W. (1969) The Structure and Properties of Water, Oxford University Press, New York. An advanced, classic treatment of the physical chemistry of wa- ter and hydrophobic interactions. Franks, F. & Mathias, S.F. (eds) (1982) Biophysics of Water, John Wiley & Sons, Inc., New York. A large collection of papers on the structure of pure water and of the cytoplasm. Gerstein, M. & Levitt, M. (1998) Simulating water and the mol- ecules of life. Sci. Am. 279 (November), 100–105. A well-illustrated description of the use of computer simulation to study the biologically important association of water with proteins and nucleic acids. Gronenborn, A. & Clore, M. (1997) Water in and around pro- teins. The Biochemist 19 (3), 18–21. A brief discussion of protein-bound water as detected by crys- tallography and NMR. Kandori, H. (2000) Role of internal water molecules in bacterio- rhodopsin. Biochim. Biophys. Acta 1460, 177–191. Intermediate-level review of the role of an internal chain of wa- ter molecules in proton movement through this protein. Kornblatt, J. & Kornblatt, J. (1997) The role of water in recog- nition and catalysis by enzymes. The Biochemist 19 (3), 14–17. A short, useful summary of the ways in which bound water in- fluences the structure and activity of proteins. Kuntz, I.D. & Zipp, A. (1977) Water in biological systems. N. Engl. J. Med. 297, 262–266. A brief review of the physical state of cytosolic water and its in- teractions with dissolved biomolecules. Ladbury, J. (1996) Just add water! The effect of water on the specificity of protein-ligand binding sites and its potential applica- tion to drug design. Chem. Biol. 3, 973–980. Luecke, H. (2000) Atomic resolution structures of bacterio- rhodopsin photocycle intermediates: the role of discrete water molecules in the function of this light-driven ion pump. Biochim. Biophys. Acta 1460, 133–156. Advanced review of a proton pump that employs an internal chain of water molecules. Nicolls, P. (2000) Introduction: the biology of the water molecule. Cell. Mol. Life Sci. 57, 987–992. A short review of the properties of water, introducing several excellent advanced reviews published in the same issue (see especially Pocker and Rand et al., listed below). Pocker, Y. (2000) Water in enzyme reactions: biophysical aspects of hydration-dehydration processes. Cell. Mol. Life Sci. 57, 1008–1017. Review of the role of water in enzyme catalysis, with carbonic anhydrase as the featured example. Rand, R.P., Parsegian, V.A., & Rau, D.C. (2000) Intracellular osmotic action. Cell. Mol. Life Sci. 57, 1018–1032. Review of the roles of water in enzyme catalysis as revealed by studies in water-poor solutes. Record, M.T., Jr., Courtenay, E.S., Cayley, D.S., & Guttman, H.J. (1998) Responses of E. coli to osmotic stress: large changes in amounts of cytoplasmic solutes and water. Trends Biochem. Sci. 23, 143–148. Intermediate-level review of the ways in which a bacterial cell counters changes in the osmolarity of its surroundings. Stillinger, F.H. (1980) Water revisited. Science 209, 451–457. A short review of the physical structure of water, including the importance of hydrogen bonding and the nature of hydrophobic interactions. Symons, M.C. (2000) Spectroscopy of aqueous solutions: protein and DNA interactions with water. Cell. Mol. Life Sci. 57, 999–1007. Westhof, E. (ed.) (1993) Water and Biological Macromolecules, CRC Press, Inc., Boca Raton, FL. Fourteen chapters, each by a different author, cover (at an ad- vanced level) the structure of water and its interactions with proteins, nucleic acids, polysaccharides, and lipids. 8885d_c02_47-74 7/25/03 10:05 AM Page 71 mac76 mac76:385_reb: Part I Structure and Catalysis72 Wiggins, P.M. (1990) Role of water in some biological processes. Microbiol. Rev. 54, 432–449. A review of water in biology, including discussion of the physi- cal structure of liquid water, its interaction with biomolecules, and the state of water in living cells. Weak Interactions in Aqueous Systems Fersht, A.R. (1987) The hydrogen bond in molecular recognition. Trends Biochem. Sci. 12, 301–304. A clear, brief, quantitative discussion of the contribution of hy- drogen bonding to molecular recognition and enzyme catalysis. Frieden, E. (1975) Non-covalent interactions: key to biological flexibility and specificity. J. Chem. Educ. 52, 754–761. Review of the four kinds of weak interactions that stabilize macromolecules and confer biological specificity, with clear examples. Jeffrey, G.A. (1997) An Introduction to Hydrogen Bonding, Oxford University Press, New York. A detailed, advanced discussion of the structure and properties of hydrogen bonds, including those in water and biomolecules. Martin, T.W. & Derewenda, Z.S. (1999) The name is bondOH bond. Nat. Struct. Biol. 6, 403–406. Brief review of the evidence that hydrogen bonds have some covalent character. Schwabe, J.W.R. (1997) The role of water in protein-DNA inter- actions. Curr. Opin. Struct. Biol. 7, 126–134. An examination of the important role of water in both the specificity and the affinity of protein-DNA interactions. Tanford, C. (1978) The hydrophobic effect and the organization of living matter. Science 200, 1012–1018. A review of the chemical and energetic bases for hydrophobic interactions between biomolecules in aqueous solutions. Weak Acids, Weak Bases, and Buffers: Problems for Practice Segel, I.H. (1976) Biochemical Calculations, 2nd edn, John Wi- ley & Sons, Inc., New York. 1. Simulated Vinegar One way to make vinegar (not the preferred way) is to prepare a solution of acetic acid, the sole acid component of vinegar, at the proper pH (see Fig. 2–15) and add appropriate flavoring agents. Acetic acid (M r 60) is a liquid at 25 H11034C, with a density of 1.049 g/mL. Calculate the volume that must be added to distilled water to make 1 L of simulated vinegar (see Fig. 2–16). 2. Acidity of Gastric HCl In a hospital laboratory, a 10.0 mL sample of gastric juice, obtained several hours after a meal, was titrated with 0.1 M NaOH to neutral- ity; 7.2 mL of NaOH was required. The patient’s stomach con- tained no ingested food or drink, thus assume that no buffers were present. What was the pH of the gastric juice? 3. Measurement of Acetylcholine Levels by pH Changes The concentration of acetylcholine (a neuro- transmitter) in a sample can be determined from the pH changes that accompany its hydrolysis. When the sample is incubated with the enzyme acetylcholinesterase, acetyl- choline is quantitatively converted into choline and acetic acid, which dissociates to yield acetate and a hydrogen ion: In a typical analysis, 15 mL of an aqueous solution contain- ing an unknown amount of acetylcholine had a pH of 7.65. When incubated with acetylcholinesterase, the pH of the so- lution decreased to 6.87. Assuming that there was no buffer in the assay mixture, determine the number of moles of acetylcholine in the 15 mL sample. 4. Osmotic Balance in a Marine Frog The crab-eating frog of Southeast Asia, Rana cancrivora, develops and ma- tures in fresh water but searches for its food in coastal man- grove swamps (composed of 80% to full-strength seawater). When the frog moves from its freshwater home to seawater it experiences a large change in the osmolarity of its envi- ronment (from hypotonic to hypertonic). (a) Eighty percent seawater contains 460 mM NaCl, 10 mM KCl, 10 mM CaCl 2 , and 50 mM MgCl 2 . What are the con- centrations of the various ionic species in this seawater? As- suming that these salts account for nearly all the solutes in seawater, calculate the osmolarity of the seawater. (b) The chart below lists the cytoplasmic concentrations of ions in R. cancrivora. Ignoring dissolved proteins, amino acids, nucleic acids, and other small metabolites, calculate the osmolarity of the frog’s cells based solely on the ionic con- centrations given below. (c) Like all frogs, the crab-eating frog can exchange gases through its permeable skin, allowing it to stay under- water for long periods of time without breathing. How does the high permeability of frog skin affect the frog’s cells when it moves from fresh water to seawater? Na H11545 K H11545 Cl H11546 Ca 2H11545 Mg 2H11545 (mM)(mM)(mM)(mM)(mM) R. cancrivora 122 10 100 2 1 O H11002 H11001 N Acetylcholine Choline Acetate H 2 O CH 3 CH 2 CO O CH 2 CH 3 CH 3 CH 3 H11001 NH H11001 C O CH 3 HO H11001H11001 CH 3 CH 3 CH 3 CH 2 CH 2 Problems 8885d_c02_47-74 7/25/03 10:05 AM Page 72 mac76 mac76:385_reb: Chapter 2 Water 73 (d) The crab-eating frog uses two mechanisms to main- tain its cells in osmotic balance with its environment. First, it allows the Na H11001 and Cl H11002 concentrations in its cells to in- crease slowly as the ions diffuse down their concentration gradients. Second, like many elasmobranchs (sharks), it re- tains the waste product urea in its cells. The addition of both NaCl and urea increases the osmolarity of the cytosol to a level nearly equal to that of the surrounding environment. Assuming the volume of water in a typical frog is 100 mL, cal- culate how many grams of NaCl (formula weight (FW) 58.44) the frog must take up to make its tissues isotonic with sea- water. (e) How many grams of urea (FW 60) must it retain to accomplish the same thing? 5. Properties of a Buffer The amino acid glycine is of- ten used as the main ingredient of a buffer in biochemical ex- periments. The amino group of glycine, which has a pK a of 9.6, can exist either in the protonated form (ONH 3 H11001 ) or as the free base (ONH 2 ), because of the reversible equilibrium (a) In what pH range can glycine be used as an effec- tive buffer due to its amino group? (b) In a 0.1 M solution of glycine at pH 9.0, what frac- tion of glycine has its amino group in the ONH 3 H11001 form? (c) How much 5 M KOH must be added to 1.0 L of 0.1 M glycine at pH 9.0 to bring its pH to exactly 10.0? (d) When 99% of the glycine is in its ONH 3 H11001 form, what is the numerical relation between the pH of the solution and the pK a of the amino group? 6. The Effect of pH on Solubility The strongly polar, hydrogen-bonding properties of water make it an excellent solvent for ionic (charged) species. By contrast, nonionized, nonpolar organic molecules, such as benzene, are relatively insoluble in water. In principle, the aqueous solubility of any organic acid or base can be increased by converting the mol- ecules to charged species. For example, the solubility of ben- zoic acid in water is low. The addition of sodium bicarbonate to a mixture of water and benzoic acid raises the pH and de- protonates the benzoic acid to form benzoate ion, which is quite soluble in water. Are the following compounds more soluble in an aqueous solution of 0.1 M NaOH or 0.1 M HCl? (The dissociable pro- tons are shown in red.) 7. Treatment of Poison Ivy Rash The compo- nents of poison ivy and poison oak that produce the characteristic itchy rash are catechols substituted with long- chain alkyl groups. If you were exposed to poison ivy, which of the treatments below would you apply to the affected area? Justify your choice. (a) Wash the area with cold water. (b) Wash the area with dilute vinegar or lemon juice. (c) Wash the area with soap and water. (d) Wash the area with soap, water, and baking soda (sodium bicarbonate). 8. pH and Drug Absorption Aspirin is a weak acid with a pK a of 3.5. It is absorbed into the blood through the cells lining the stom- ach and the small intestine. Absorption requires passage through the plasma membrane, the rate of which is deter- mined by the polarity of the molecule: charged and highly po- lar molecules pass slowly, whereas neutral hydrophobic ones pass rapidly. The pH of the stomach contents is about 1.5, and the pH of the contents of the small intestine is about 6. Is more aspirin absorbed into the bloodstream from the stom- ach or from the small intestine? Clearly justify your choice. C B O G O C B O G OH CH 3 D OH (CH 2 ) n OCH 3 pK a ≈ 8 OH NI A H Pyridine ion pK a ≈ 5 (b) (c) (a) H9252-Naphthol pK a ≈ 10 C B H G N D H OC A H A C J O G OOCH 3 OCH 2 N-Acetyltyrosine methyl ester pK a ≈ 10 CH 3 D OH O O C B O OOH COO H11002 Benzoic acid Benzoate ion pK a ≈ 5 B O R H11001 H H11001H11001 NH 3 RNH 2 Urea (CH 4 N 2 O) NH 2 H 2 N C O 8885d_c02_47-74 7/25/03 10:05 AM Page 73 mac76 mac76:385_reb: Part I Structure and Catalysis74 9. Preparation of Standard Buffer for Calibration of a pH Meter The glass electrode used in commercial pH meters gives an electrical response proportional to the con- centration of hydrogen ion. To convert these responses into pH, glass electrodes must be calibrated against standard so- lutions of known H H11001 concentration. Determine the weight in grams of sodium dihydrogen phosphate (NaH 2 PO 4 H11554 H 2 O; FW 138.01) and disodium hydrogen phosphate (Na 2 HPO 4 ; FW 141.98) needed to prepare 1 L of a standard buffer at pH 7.00 with a total phosphate concentration of 0.100 M (see Fig. 2–16). 10. Calculating pH from Hydrogen Ion Concentration What is the pH of a solution that has an H H11001 concentration of (a) 1.75 H11003 10 H110025 mol/L; (b) 6.50 H11003 10 H1100210 mol/L; (c) 1.0 H11003 10 H110024 mol/L; (d) 1.50 H11003 10 H110025 mol/L? 11. Calculating Hydrogen Ion Concentration from pH What is the H H11001 concentration of a solution with pH of (a) 3.82; (b) 6.52; (c) 11.11? 12. Calculating pH from Molar Ratios Calculate the pH of a dilute solution that contains a molar ratio of potassium acetate to acetic acid (pK a H11005 4.76) of (a) 2:1; (b) 1:3; (c) 5:1; (d) 1:1; (e) 1:10. 13. Working with Buffers A buffer contains 0.010 mol of lactic acid (pK a H11005 3.86) and 0.050 mol of sodium lactate per liter. (a) Calculate the pH of the buffer. (b) Calculate the change in pH when 5 mL of 0.5 M HCl is added to 1 L of the buffer. (c) What pH change would you expect if you added the same quantity of HCl to 1 L of pure water? 14. Calculating pH from Concentrations What is the pH of a solution containing 0.12 mol/L of NH 4 Cl and 0.03 mol/L of NaOH (pK a of NH 4 H11001 /NH 3 is 9.25)? 15. Calculating pK a An unknown compound, X, is thought to have a carboxyl group with a pK a of 2.0 and another ionizable group with a pK a between 5 and 8. When 75 mL of 0.1 M NaOH was added to 100 mL of a 0.1 M solution of X at pH 2.0, the pH increased to 6.72. Calculate the pK a of the second ionizable group of X. 16. Control of Blood pH by Respiration Rate (a) The partial pressure of CO 2 in the lungs can be var- ied rapidly by the rate and depth of breathing. For example, a common remedy to alleviate hiccups is to increase the con- centration of CO 2 in the lungs. This can be achieved by hold- ing one’s breath, by very slow and shallow breathing (hy- poventilation), or by breathing in and out of a paper bag. Under such conditions, the partial pressure of CO 2 in the air space of the lungs rises above normal. Qualitatively explain the effect of these procedures on the blood pH. (b) A common practice of competitive short-distance runners is to breathe rapidly and deeply (hyperventilate) for about half a minute to remove CO 2 from their lungs just be- fore running in, say, a 100 m dash. Blood pH may rise to 7.60. Explain why the blood pH increases. (c) During a short-distance run the muscles produce a large amount of lactic acid (CH 3 CH(OH)COOH, K a H11005 1.38 H11003 10 H110024 ) from their glucose stores. In view of this fact, why might hyperventilation before a dash be useful? 8885d_c02_47-74 7/25/03 10:05 AM Page 74 mac76 mac76:385_reb: