I believe that as the methods of structural chemistry are further appliedto physio logical problems, i t wi l l be found that the s igni f icance of thehydrogen bond for physiology is greater than that of any other singlestructural feature.

-Linus Pauling, The Nature of the Chemic al Bond, 1939

2.12.22.32.42.5

water molecules provide thewater a liouid at room tem-

perature and favor the extreme ordering of moleculesthat is tS,pical of crystalline water (ice). Polar biomole-cules dissolve readily in water because they can replacewater-water interactions with more energetically favor-able water-solute interactions. In contrast, nonpolarbiomolecules interfere with water-water interactionsbut are unable to form water-solute interactions-consequently, nonpolar molecules are poorly soluble inwater. In aqueous solutions, nonpolar molecules tend tocluster together. Hydrogen bonds and ionic, hydropho-bic (Greek, "water-fearing"), and van der Waals interac-tions are individually weak, but collectively they have avery significant influence on the three-dimensionalstructures of proteins, nucleic acids, polysaccharides,and membrane lipids.

Hydrogen Bonding Gives Water lts Unusual PropertiesWater has a higher melting point, boiling point, andheat of vaporization than most other common solvents(Table 2-1). These unusual properties are a conse-quence of attractions between adjacent water moleculesthat give liquid water great internal cohesion. A look atthe electron structure of the H2O molecule reveals thecause of these intermolecular attractions.

Each hydrogen atom of a water molecule shares anelectron pair with the central oxygen atom. The geome-try of the molecule is dictated by the shapes of the outerelectron orbitals of the oxygen atom, which are similarto the sp3 bonding orbitals of carbon (see Fig. I-I4).These orbitals describe a rough tetrahedron, with a hy-drogen atom at each of two corners and unshared elec-tron pairs at the other two corners (Fig. 2-la). TheH-O-H bond angle is 104.5', slightly less than the109.5'of a perfect tetrahedron because of crowding bythe nonbonding orbitals of the oxygen atom.

The oxygen nucleus attracts electrons more stronglythan does the hydrogen nucleus (a proton); that is, oxy-gen is more electronegative. This means that the shared

43

2.1 Weak Interactions in Aqueous SystemsHydrogen bonds betweencohesive forces that make

Water

Weak Interactions in Aqueous Systems 43lonization of Water,Weak Acids, and Weak Bases 54Buffering against pH Changes in BiologicalSystems 59Water as a Reactant 65The Fitness of the Aqueous Environment for Living0rganisms 65

ater is the most abundant substance in livingsystems, making tp 700/o or more of the weightof most organisms. The flrst IMng organisms on

Earth doubtless arose in an aqueous environment, andthe course of evolution has been shaped by the proper-ties of the aqueous medium in which life began.

This chapter begins with descriptions of the physicaland chemical properties of water, to which all aspects ofcell structure and function are adapted. The attractiveforces between water molecules and the slight tendency ofwater to ionize are of crucial importance to the structureand ftnction of biomolecules. We review the topic of ion-zation in terms of equiJibrium constants, pH, and titrationcurves, and consider how aqueous solutions of weak acidsor bases and their salts act as buffers against pH changes urbiologtcal systems. The water molecule and its ioruzationproducts, H* and OH-, profoundly influence the structure,self-assembly, and properties of all cellular components, in-cluding proteins, nucleic acids, and lipids. The noncovalentinteractions responsible for the strength and specificrty of"recognition" among biomolecules are decisively influ-enced by the solvent properties of water, includng its abil-ity to form hydrogen bonds with itself and with solutes.

Melting point ("C) Boiling point ('C) Ileat of vaporization (J/g) *WaterMethanol (CH3OH)Ethanol (CH3CH2OH)Propanol (CH3CH2CH2OH)Butanol (CH3(CH2)2CH2OH)Acetone (CH3COCHB)Hexane (CH3(CH2)4CH3)Benzene (CoHo)Butane (CH3(CH2)2CHB)Chloroform (CHCI3)

0-98

- . i - 1 /

- t L t

-90- vD

-98

o

- 135-63

100OD

7897

1 1 na l l

566980-U .D

61

2,2601 ,100

854687590523423394381247

*The heat energy required to convert 1.0 g of a liquid at its boiling point and at atmospheric pressure into its gaseous state at the same temperarure.It is a direct measure of the energy required to overcome attractive forces between molecules in the liquid Dhase.

electrons are more often in the vicinity of the oxygenatom than of the hydrogen. The result of this unequalelectron sharing is two electric dipoles in the water mol-ecule, one along each of the H-O bonds; each hydrogenbears a partial positive charge (6*), and the oxygenatom bears a partial negative charge equal in magnitudeto the sum of the two partial positives (2S-). As a result,there is an electrostatic attraction between the oxygenatom of one water molecule and the hydrogen of another(Fig. 2-1b), called a hydrogen bond. Throughout thisbook, we represent hydrogen bonds with three parallelblue lines, as in Figure 2-1b.

Hydrogen bonds are relatively weak. Those in liquidwater have a bond dissociation energy (the energy re-

quired to break a bond) of about 23 kJ/mol, comparedwith 470 kJ/mol for the covalent O-H bond in water or348 kJ/mol for a covalent C-C bond. The hydrogen bondis about 10% covalent, due to overlaps in the bonding or-bitals, and about 90% electrostatic. At room tempera-ture, the thermal energy of an aqueous solution (thekinetic energy of motion of the individual atoms andmolecules) is of the same order of magnitude as that re-quired to break hydrogen bonds. When water is heated,the increase in temperature reflects the faster motion ofindividual water molecules. At any given time, most ofthe molecules in liquid water are hydrogen bonded, butthe lifetime of each hydrogen bond is just I to 20 pi-coseconds (1 ps : 10-12 s); when one hydrogen bondbreaks, another hydrogen bond forms, with the samepartner or a new one, within 0.1 ps. The apt phrase "flick-ering clusters" has been applied to the short-lived groupsof water molecules interlinked by hydrogen bonds inliquid water. The sum of all the hydrogen bonds betweenH2O molecules confers great internal cohesion on liquidwater. Extended networks of hydrogen-bonded watermolecules also form bridges between solutes (proteinsand nucleic acids, for example) that allow the largermolecules to interact with each other over distances ofseveral nanometers without physically touching.

The nearly tetrahedral arrangement of the orbitalsabout the oxygen atom (Fig. 2-1a) allows each watermolecule to form hydrogen bonds with as many as fourneighboring water molecules. In liqurd water at roomtemperature and atmospheric pressure, however, watermolecules are disorganized and in continuous motion, sothat each molecule forms hydrogen bonds with an aver-age of only 3.4 other molecules. In ice, on the other hand,each water molecule is fixed in space and forms hydro-gen bonds with a full complement of four other watermolecules to fleld a regular lattice structure (Fig. 2-2)Breaking a sufficient proportion of hydrogen bonds todestabilize the crystal lattice of ice requires much thermalenergy, which accounts for the relatively high melting

6+

6+

(a)

6

FIGURE 2-l Structure of the water molecule. (a) The dipolar nature ofthe H2O molecule is shown in a bal l-and-st ick model; the dashed l inesrepresent the nonbonding orbitals. There is a nearly tetrahedralarrangement of the outer-shell electron pairs around the oxygen atom;the two hydrogen atoms have localized partial positive charges (6*)and the oxygen atom has a partial negative charge (6-). (b) Two HzOmolecules joined by a hydrogen bond (designated here, and through-outthis book, by three blue lines) between the oxygen atom ofthe up-per molecule and a hydrogen atom of the lower one. Hydrogen bondsare longer and weaker than covalent O-H bonds.

W

d

Hydrogen bond0.177 nm

Covalent bond0.0965 nm

(b)

Hydrogenacceptor

Hydrogendonor

\ . / \ , / - C \N O ' O: : :

H H Ht t l? ? zN.'

FIGURE 2-3 Common hydrogen bonds in biological systems. The hy-drogen acceptor is usually oxygen or nitrogen; the hydrogen donor isanother electronegative atom.

to carbon atoms do not participate in hydrogen bond-ing, because carbon is only slightly more electronega-tive than hydrogen and thus the C-H bond is only veryweakly polar. The distinction explains why butanol(CHB(CH2)2CH2OH) has a relatively high boiling pointof 1.17 oC, whereas butane (CH3(CH2)2CH3) has a boil-ing point of only -0.5 'C. Butanol has a polar hydroxylgroup and thus can form intermolecular hydrogenbonds. Uncharged but polar biomolecules such as sug-ars dissolve readily in water because of the stabilizingeffect of hydrogen bonds between the hydroxyl groupsor carbonyl oxygen of the sugar and the polar watermolecules. Alcohols, aldehydes, ketones, and com-pounds containing N-H bonds all form hydrogenbonds with water molecules (FiS. 2-4) and tend to besoluble in water.

Between the Between the Between peptidehydroxyl group carbonyl group groups inofan alcohol ofa ketone polypeptidesand water and water

\ , / \ , /O N

H H

N N, / \ , / \

Ia./\

o

HIoI

FIGURE 2-2 Hydrogen bonding in ice. In ice, each water moleculeforms four hydrogen bonds, the maximum possible for a water mole-cule, creating a regular crystal latt ice By contrast, in l iquid water atroom temperature and atmospheric pressure, each water moleculehydrogen-bonds with an average of 3.4 other water molecules. Thiscrystal latt ice structure makes ice less dense than l iquid water, and thusice f loats on l iouid water.

point of water (Table 2-l). When ice melts or waterevaporates, heat is taken up by the system:

H2O (solid) -+ H2O (liquid)H2O (liquid) --+ H2O (gas)

AFI : +5.9 kJ/mol

LH: +44.0 kJ/mol

During melting or evaporation, the entropy of theaqueous system increases as more highly ordered arraysof water molecules relax into the less orderly hydrogen-bonded arrays in liquid water or into the wholly disor-dered gaseous state. At room temperature, both themelting of ice and the evaporation of water occur spon-taneously; the tendency of the water molecules to asso-ciate through hydrogen bonds is outweighed by theenergetic push toward randomness. Recall that the free-energy change (AG) must have a negative value for aprocess to occur spontaneously: AG : LH - 7 AS,where AG represents the driving force, AF1 the enthalpychange from making and breaking bonds, and AS thechange in randomness. Because A11 is positive for melt-ing and evaporation, it is clearly the increase in entropy(AS) that makes AG negative and drives these changes.Water Forms Hydrogen Bonds with Polar SolutesHydrogen bonds are not unique to water. They readilyform between an electronegative atom (the hydrogenacceptor, usually oxygen or nitrogen) and a hydrogenatom covalently bonded to another electronegativeatom (the hydrogen donor) in the same or another mol-ecule (Fig. 2-3). Hydrogen atoms covalently bonded

R2IC

Rl- \o

HI

,.oH

R'.oIH

-o-rH H

)..-tiH

t t lR O

,^P*-a

Betweencomplementarybases ofDNA

HI

R -C_\

--CH3-N- --C-

c, I ThYmine

OZ-\N'--\Ot :

H H; l

O..N-CH

FIGURE 2-4 Some biologically important hydrogen bonds.

FIGURE 2-5 Directionality of the hydrogen bond. The attraction be-wveen the partial electric charges (see Fig 2-1 ) is greatest when the threeatoms involved in the bond (in this case o, H, and O) lie in a straight line.When the hydrogen-bonded moieties are structurally constrained (whenthey are parts of a single protein molecule, for example), this ideal geom-etry may not be possible and the resulting hydrogen bond is weaker.

Hydrogen bonds are strongest when the bondedmolecules are oriented to maximize electrostatic inter-action, which occurs when the hydrogen atom and thetwo atoms that share it are in a straight line-that is,when the acceptor atom is in line with the covalent bondbetween the donor atom and H (Fig. 2-b), putting thepositive charge of the hydrogen ion directly between thetwo partial negative charges. Hydrogen bonds are thushighly directional and capable of holding two hydrogen-bonded molecules or groups in a specific geometricarrangement. As we shall see later, this property ofhydrogen bonds confers very precise three-dimensionalstructures on protein and nucleic acid molecules, whichhave many intramolecular hydrogen bonds.

Water lnteracts Electrostatically with (harged SolutesWater 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 inwater are hydrophilic (Greek, "water-loving"). In con-

trast, nonpolar solvents such as chloroform and benzeneare poor solvents for polar biomolecules but easily dis-solve those that are hydrophobic-nonpolar moleculessuch as lipids and waxes.

Water dissolves salts such as NaCl by hydrating andstabilizing the Na+ and Cl- ions, weakening the electro-static interactions between them and thus counteract-ing their tendency to associate in a crystalline lattice(Fig. 2-ti). The same factors apply to charged biomole-cules, compounds with functional groups such asionized carboxylic acids (-COO-), protonated amines(-NHi), and phosphate esters or anhydrides. Waterreadily dissolves such compounds by replacing solute-solute hydrogen bonds with solute-water hydrogenbonds, thus screening the electrostatic interactions be-tween solute molecules.

Water is effective in screening the electrostatic in-teractions between dissolved ions because it has a highdielectric constant, a physical property that reflects thenumber of dipoles in a solvent. The strength, or force(F), of ionic interactions in a solution depends on themagnitude of the charges (8), the distance between thecharged groups (r), and the dielectric constant (e,which is dimensionless) of the solvent in which the in-teractions occur:

F:a*er-

For water at 25 oC, e is 78.5, and for the very nonpolarsolvent benzene, e is 4.6. Thus, ionic interactions be-tween dissolved ions are much stronger in less polar en-vironments. The dependence on rz is such that ionicattractions or repulsions operate only over shortdistances-in the range of 10 to 40 nm (depending onthe electrolyte concentration) when the solvent is water.

NonpolarTlrpical wax

AmphipathicPhenylalanine

oCHa(CHz)z -CH:CH- (CHr)6 - CH2 - C\

oCHs(CH2)z -CH:CH-(CHz, - 3",

Glycine

Aspartate

Lactate

Glycerol

+NH3-CH2-COO-

*NHsI

-ooc-cH2-cH-coo-

cH3-cH-COO-IOH

OHI

HOCH2-CH-CH2OH

Phosphatidylcholine OCHa(CHz)rsCHz-C-O-CH2cHg(cHz)rscH,-fr_o_?r

? +T(cH3)3

o 61r,-o-f-o-cH2-cH2o-

Entropy Increases as (rystalline 5ubstances DissolveAs a salt such as NaCl dissolves, the Na+ and CI- ionsleaving the crystal lattice acquire far greater freedom ofmotion (Fig. 2-6). The resulting increase in entropy(randomness) of the system is largely responsible forthe ease of dissolving salts such as NaCl in water. Inthermodynamic terms, formation of the solution occurswith a favorable free-energy change: LG : LH - 7 AS,where A11 has a small positive value and 7 AS a largepositive value; thus AG is negative.

Nonpolar Gases Are Poorly 5oluble in WaterThe molecules of the biologically important gases CO2,O2, znd N2 are nonpolar. In 02 and N2, electrons areshared equally by both atoms. In CO2, each C:O bondis polar, but the two dipoles are oppositely directed andcancel 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 watermolecules and therefore represents a decrease in en-tropy. The nonpolar nature of these gases and the de-

FIGURE 2-6 Water as solvent. Water dissolves manycrystalline salts by hydrating their component ions. TheNaCl crystal lattice is disrupted as water moleculescluster about the Cl- and Na* ions. The ionic chargesare partially neutralized, and the electrostatic attrac-tions necessary for lattice formation are weakened.

HydratedNa'ion

crease in entropy when they enter solution combine tomake them very poorly soluble in water (Table 2-3).Some organisms have water-soluble "carrier proteins"(hemoglobin and myoglobin, for example) that facili-tate the transport of 02. Carbon dioxide forms carbonicacid (H2CO3) in aqueous solution and is transported asthe HCO3 (bicarbonate) ion, either free-bicarbonateis very soluble in water (-100 glL at 25 oC)-or boundto hemoglobin. Three other gases, NH3, NO, and H2S,also have biological roles in some organisms; thesegases are polar, dissolve readily in water, and ionize inaqueous solution.

Nonpolar (ompounds Force Energetically Unfavorable(hanges in the Structure of WaterWhen water is mixed with benzene or hexane, twophases form; neither liquid is soluble in the other. Non-polar compounds such as benzene and hexane arehydrophobic-they are unable to undergo energeti-cally favorable interactions with water molecules, andthey interfere with the hydrogen bonding among water

Gas Strueturex PolaritySolubilityin water (g/[)r

NitrogenOxygenCarbon dioxide

Ammonia

Hydrogen sulflde

N:No:o6 - 6

NonpolarNonpolarNonpolar

Polar

Polar

0.018 (40'c)0.035 (50 "c)0.97 (45'C)

900 (10 "c)

1,860 (40'C)

O:C:O

s S nr\ l / / |

N l r -

H H I\ . / I

S + s -

*Thearrowsrepresentelectr icdipoles; thereisapart ia l negat ivecharge(6 )at theheadofthearrowapart ia l posi t ivecharge(6-; notshown here) at the tail.tNote that oolar molecules dissolve far better even at low temperatures than do nonpolar molecules at relatively high temperatures.

molecules. All molecules or ions in aqueous solution in-terfere with the hydrogen bonding of some water mole-cules in their immediate vicinity, but polar or chargedsolutes (such as NaCl) compensate for lost water-waterhydrogen bonds by forming new solute-water interac-tions. The net change in enthalpy (AIf for dissolvingthese solutes is generally small. Hydrophobic solutes,however, offer no such compensation, and their additionto water may therefore result h a small gain of enthalpy;the breaking of hydrogen bonds between water mole-cules takes up energy from the system, requiring theinput of energy from the surroundings. In addition torequiring this input of energy, dissolving hydrophobiccompounds in water produces a measurable decrease inentropy. Water molecules in the immediate vicinity of anonpolar solute are constrained in their possible orien-tations as they form a highly ordered cagelike shellaround each solute molecule. These water moleculesare not as highly oriented as those in clathrates, crys-talline compounds of nonpolar solutes and water, butthe effect is the same in both cases: the ordering of watermolecules reduces entropy. The number of orderedwater molecules, and therefore the magnitude of the en-tropy decrease, is proportional to the surface area of thehydrophobic solute enclosed within the cage of watermolecules. The free-energy change for dissolving a non-polar solute in water is thus unfavorable: A,G : L,H -7 AS, where All has a positive value, AS has a negativevalue, and AG is positive.

Hydrophilic'tread group"

Hydrophobicalkyl group

Highly ordered H2O molecules form"cages" around the hydrophobic alkyl chains

(a)FIGURE 2-7 Amphipathic compounds in aqueous solution. (a) Long-chain fatty acids have very hydrophobic alkyl chains, each ofwhich issurrounded by a layer of highly ordered water molecules. (b) By clus_tering together in micel les, the fatty acid molecules expose the small-est possible hydrophobic surface area to the water, and fewer watermolecules are required in the shell of ordered water. The energy gainedby freeing immobil ized water molecules stabi l izes the micel le.

Amphipathic compounds contain regions that arepolar (or charged) and regions that are nonpolar(Table 2-2). When an amphipathic compound is mixedwith water, the polar, hydrophiJic region interacts favor-ably with the solvent and tends to dissolve, but the non-polar, hydrophobic region tends to avoid contact withthe water (Fig. 2-7a). The nonpolar regions of themolecules cluster together to present the smallesthydrophobic area to the aqueous solvent, and the polarregions are arranged to maximize their interaction withthe solvent (Fig. 2-7b). These stable structures of arn-phipathic compounds in water, called mieelles, maycontain hundreds or thousands of molecules. The forces

F AllhydrophobicgToups aresequestered fromwater; orderedshell of H2Omolecules is

e{t4

(b)

Each lipidmolecule forcessurrounding H,

Enzyme-substrate interactionstabilized by hydrogen-bonding,ronic, and hydrophobic interactions

FIGURE 2-8 Release of ordered water favors formation of an enzyme-substrate complex. While separate, both enzyme and substrate forceneighboring water molecules into an ordered shel l Binding of sub-strate to enzyme releases some of the ordered water, and the resultingincrease in entropy provides a thermodynamic push toward formationof the enzyme-substrate complex (see p 'l 92).

poftant determinants of structure in biological mem-branes. Hydrophobic interactions between nonpolaramino acids also stabilize the three-dimensional struc-tures ofproteins.

Hydrogen bonding between water and polar solutesalso causes an ordering of water molecules, but the en-ergetic effect is Iess significant than with nonpolarsolutes. Part of the driving force for binding of a polarsubstrate (reactant) to the complementary polar sur-face of an enzlrne is the entropy increase as the enzlrnedisplaces ordered water from the substrate, and as thesubstrate displaces ordered water from the enz;.'rne sur-face (Fig. 2-8).

van der Waals Interactions Are WeakI nteratomic AttractionsWhen two uncharged atoms are brought very close to-gether, their surrounding electron clouds influence eachother. Random variations in the positions of the elec-trons around one nucleus may create a transient electricdipole, which induces a transient, opposite electric di-pole in the nearby atom. The two dipoles weakly attracteach other, bringing the two nuclei closer. These weakattractions are called van der Waals interactions(also known as London forces). As the two nucleidraw closer together, their electron clouds begin torepel each other. At the point where the net attraction ismaximal, the nuclei are said to be in van der Waals con-tact. Each atom has a characteristic van der Waalsradius, a measure of how close that atom will allowanother to approach (Table 24).In the "space-fllling"molecular models shown throughout this book, theatoms are depicted in sizes proportional to their van derWaals radii.

Covalent radius forsingle bond (nm)

that hold the nonpolar regions of the molecules togetherare called hydrophobie interactions. The strength ofhydrophobic interactions is not due to any intrinsic at-traction between nonpolar moieties. Rather, it resultsfrom the system's achieving greatest thermodynamicstability by minimizing the number of ordered watermolecules required to surround hydrophobic portions ofthe solute molecules.

Many biomolecules are amphipathic; proteins, pig-ments, certain vitamins, and the sterols and phospho-lipids of membranes all have both polar and nonpolarsurface regions. Structures composed of these mole-cules are stabilized by hydrophobic interactions amongthe nonpolar regions. Hydrophobic interactions amonglipids, and between lipids and proteins, are the most im-

Ordered waterinteracting with

substrate and enzyme

Disordered waterdisplaced by

enzyme-substrateinteraction Element

van derWaalsradius (nm)

HoN

SPI

Sources: Forvan derWaals radii, Chauvin, R. (1992) Explicit periodic trend ofvan derWaals radii. J. Phys. Chen.96,9194-9197. For covalent radii, Pauling, L. (1960)Nature of the Chenical Bond,3rd edn, Cornell University Press, lthaca, NY.Note: van derWaals radii describe the spaceJilling dimensions of atoms. When twoatoms are joined covalently, the atomic radii at the point of bonding are less than thevan der Waals radii, because the joined atoms are pulled together by the shared elec-tron pair.The distance between nuclei in a van derWaals interaction or a covalent bondis about equal to the sum of the van der Waals or covalent radii, respectively, for the twoatoms.lhus the length of a carbon-carbon single bond is about 0.077 nm * 0.077 nm :0 154 nm.

0 . 1 10 .150 .150 .170.180. i90.21

0.0300.0660.0700.0770.1040.1100.133

Weak lnteractions Are (rucial to MacromolecularStrurture and FunctionThe noncovalent interactions we have described-hydrogen bonds and ionic, hydrophobic, and van der Waalsinteractions (Table 2-5)-are much weaker than covalentbonds. An input of about 350 kJ of energy is required tobreak a mole (6 x 1023) of C-C single bonds, and about410 kJ to break a mole of C-H bonds, but as little as 4 kJis sufflcient to disrupt a mole of typical van der Waals in-teractions. Hydrophobic interactions are also much weakerthan covalent bonds, although they are substantiallystrengthened by a highly polar solvent (a concentrated saltsolution, for exampie). Ionic interactions and hydrogenbonds are variable in strength, dependrrg on the polanty ofthe solvent and the alignment of the hydrogen-bondedatoms, but they are always signiflcar-rtly weaker than cova-Ient bonds. In aqueous solvent at 25 "C, the available ther-mal energr can be of the same order of magnitude as thestrength of these weak interactions, and the interaction be-tween solute and solvent (water) molecules is nearlyas favorable as solute-solute interactions. Consequently,hydrogen bonds and ionic, hydrophobic, and van der Waalsinteractions are continually forming and breaking.

Although these four types of interactions are rndi-vidually weak relative to covalent bonds, the cumulativeeffect of many such interactions can be very significant.For example, the noncovalent binding of an enz;'rne toits substrate may involve several hydrogen bonds and

Hydrogen bondsBetween neutral groups

Between peptide bonds

lonic interactionsAttraction

Repulsion-*NHs

-HsN* -

Hydrophobicinteractions

Any two atoms inclose proximity

_*NHa _+ _O_C_

one or more ionic interactions, as well as hydrophobicand van der Waals interactions. The formation of each ofthese weak bonds contributes to a net decrease in thefree energy of the system. We can calculate the stabilityof a noncovalent interaction, such as that of a small mol-ecule hydrogen-bonded to its macromolecular partner,from the binding energy. Stability, as measured by theequilibrium constant (see below) of the binding reac-tion, varies erponentialfu vnthbinding energy. The dis-sociation of two biomolecules (such as an enzlnne andits bound substrate) that are associated noncovalentlythrough multiple weak interactions requires all these in-teractions to be disrupted at the same time. Because theinteractions fluctuate randomly, such simultaneous dis-ruptions are very unlikely. The molecular stability be-stowed by 5 or 20 weak interactions is therefore muchgreater than would be expected intuitively from asimple summation of small binding energies.

Macromolecules such as proteins, DNA, and RNAcontain so many sites of potential hydrogen bonding orionic, van der Waals, or hydrophobic interactions that thecumulative effect of the many small binding forces canbe enormous. For macromolecules, the most stable (thatis, the native) structure is usually that in which weakinteractions are maximized. The folding of a singlepolypeptide or polynucleotide chain into its three-dimensional shape is determined by this principle. Thebinding of an antigen to a specific antibody depends onthe cumulative effects of many weak interactions. Asnoted earlier, the energy released when an enz)..rne bindsnoncovalently to its substrate is the main source of theenz).rne's catalytic power. The binding of a hormone or aneurotransmitter to its cellular receptor protein is theresult of multiple weak interactions. One consequence ofthe large size of enz),rnes and receptors (relative to theirsubstrates or ligands) is that their extensive surfacesprovide many opportunities for weak interactions. At themolecular level, the complementarity between interact-ing biomolecules reflects the complementarity and weakinteractions between polar, charged, and hydrophobicgroups 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 Box 4-5,p.132), water molecules are often foundto be bound so tightly that they are part of the crystalstructure; the same is true for water in crystals of RNAor DNA. These bound water molecules, which can alsobe detected in aqueous solutions by nuclear magneticresonance, have distinctly different properties fromthose ofthe "bulk" water ofthe solvent. They are, for ex-ample, not osmotically active (see below). For manyproteins, tightly bound water molecules are essential totheir function. In a reaction central to the process ofphotosynthesis, for example, light drives protons acrossa biological membrane as electrons flowthrough a seriesof electron-carrying proteins (see Fig. 19-60). One ofthese proteins, cytochromeJ has a chain of five boundwater molecules (Fig. 2-f0) that may provide a pathfor protons to move through the membrane by a process

van der Waals interactions

(a) (b)FIGURE2-9Water binding in hemoglobin. (PDB lD 1A3N)The crystalstructure of hemoglobin, shown (a) with bound water molecules (redspheres) and (b) without the water molecules. The water molecules areso firmly bound to the protein that they affect the x-ray diffraction pat-tern as though they were fixed parts of the crystal. The two a subunitsof hemoglobin are shown in gray, the two p subunits in blue. Each sub-unit has a bound heme group (red st ick structure), vrsible only in theB subunits in this view. The structure and function of hemoglobin arediscussed in detai l in Chaoter 5.

known as "proton hopping" (described below). Anothersuch light-driven proton pump, bacteriorhodopsin, al-most certainly uses a chain of precisely oriented boundwater moiecules in the transmembrane movement ofprotons (see Fig. 19-67).

Solutes Affect the (olligative Properties ofAqueous SolutionsSolutes of all kinds alter certain physical propertiesof the solvent, water: its vapor pressure, boilingpoint, melting point (freezing point), and osmoticpressure. These are called colligative properties(colligative meaning "tied together"), because the ef-fect of solutes on all four properties has the same ba-sis: the concentration of water is lower in solutionsthan in pure water. The effect of solute concentrationon the colligative properties of water is independentof the chemical properties of the solute; it dependsonly on f"he number of solute particles (molecules,ions) in a given amount of water. A compound suchas NaCl, which dissociates in solution, has an effecton osmotic pressure, for example, that is twice thatof an equal number of moles of a nondissociatingsolute such as glucose. RoshanKetab 021-66950639

Water molecules tend to move from a region ofhigher water concentration to one of lower water con-centration, in accordance with the tendency in naturefor a system to become disordered. When two differentaqueous solutions are separated by a semipermeablemembrane (one that allows the passage of water but notsolute molecules), water molecules diffusing from theregion of higher water concentration to the region oflower water concentration produce osmotic pressure(FiS. 2-f f ). This pressure, fl, measured as the force

Force (II)resists osmosis

IY

Purewater

Nonpermeantsolute dissolvedin water

ib='.-a*"*

HN

H

H>N

5 2 ) Water

necessary to resist water movement (Fig. 2-11c), is ap-proximated by the van't Hoff equation:

fI - icRT

in which /? is the gas constant and 7 is the absolute tem-perature. The term ec is the osmolarity of the solution,the product of the van't Hoff factor i which is a measureof the extent to which the solute dissociates into two ormore ionic species, and the solute's molar concentra-tion c. In dilute NaCl solutions, the solute completelydissociates into Na+ and CI , doubling the number ofsolute particles, and thus i : 2 For all nonionizingsolutes, z : 1. For solutions of severai (n) solutes, [I isthe sum of the contributions of each species:

tI : RT (ip1 -r i2c2 + + i,cn)Osmosis, water movement across a semiperme-

able membrane driven by differences in osmotic pres-sure, is an important factor in the life of most cells.Plasma membranes are more permeable to water thanto most other small molecules, ions, and macromole-cules. This permeabil ity is due largely to protein chan-nels (aquaporins; see Fig. 11-46) in the membranethat selectively permit the passage of water. Solutionsof osmolarity equal to that of a cell's cytosol are said tobe isotonic relative to that celi. Surrounded by an iso-tonic solution, a cell neither gains nor loses water( I . ' ig . 2-12) . In a hypertonic soiut ion, one wi thhigher osmolarity than that of the cytosol, the cellshrinks as water moves out. In a hypotonic solution,one with a lower osmolarity than the cytosol, the cellswells as water enters. In their natural environments,cells generally contain higher concentrations of bio-molecules and ions than their surroundings, so os-motic pressure tends to drive water into cells. If notsomehow counterbaianced, this inward movement ofwater would distend the plasma membrane and even-tuaily cause bursting of the cell (osmotic lysis).

Several mechanisms have evolved to prevent thiscatastrophe. In bacteria and plants, the plasma mem-brane is surrounded by a nonexpandable cell wall ofsufficient rigidity and strength to resist osmotic pres-sure and prevent osmotic lysis. Certain freshwaterprotists that live in a highly hypotonic medium have anorganelle (contractile vacuole) that pumps water outof the cell. In multicellular animals, blood plasma andinterstitial fluid (the extracellular fluid of tissues) aremaintained at an osmolarity close to that of the cy-tosol. The high concentration of albumin and otherproteins in biood plasma contributes to its osmolarity.Cells also actively pump out Na+ and other ions intothe interstitial fluid to stay in osmotic balance withtheir surroundings.

Because the effect of soiutes on osmolarity dependson the number of dissolved particles, not their mosgmacromolecules (proteins, nucleic acids, polysaccha-rides) have far less effect on the osmolarity of a solutionthan would an equai mass of their monomeric compo-

FIGURE 2-12 Effect of extracellular osmolarity on water movementacross a plasma membrane. When a cel l in osmotic balance with i tssurrounding medium-that is, a cel l in (a) an isotonic medium-is trans-ferred into (b) a hypertonic solut ion or (c) a hypotonic solut ion, watermoves across the plasma membrane in the direct ion that tends toequalize osmolari ty outside and inside the cel l

nents. For example, a gram of a poiysaccharide com-posed of 1,000 glucose units has the same effect on os-molarity as a mzllzgram of glucose. Storing fuel aspolysaccharides (starch or glycogen) rather than as glu-cose or other simple sugars avoids an enormous in-crease in osmotic pressure in the storage cell.

Plants use osmotic pressure to achieve mechanicalrigidity The very high solute concentration in the plantcell vacuole draws water into the cell (Fig. 2-12),butthe nonexpandable cell wall prevents swelling; instead,the pressure exerted against the cell wall (turgor pres-sure) increases, stiffening the cell, the tissue, and theplant body. When the lettuce in your salad wilts, it is be-cause loss of water has reduced turgor pressure. Osmo-sis also has consequences for laboratory protocols.Mitochondria, chloroplasts, and lysosomes, for exam-ple, are enclosed by semipermeable membranes. In iso-Iating these organelles from broken cells, biochemistsmust perform the fractionations in isotonic solutions(see Fig. 1-8) to prevent excessive entry of water intothe organelles and the swelling and bursting that wouldfollow Buffers used in celiular fractionations commonlycontain sufficient concentrations of sucrose or someother inert solute to protect the organelles from os-motic lvsis.

Extracellularsolutes

a a

a aa a

a aa

a aa

_ a

a

a

a

t a '

a a

a a

a

a a

a a

(b) CelI in hypertonicsolution; water moves outand cell shrinks.

Intracellularsolutes

(a) Cell in isotonic' solution; no net water

movement.

(c) CelI in hypotonicsolution; water moves in,creating outward pressure;cell swells, may eventuallyburst.

oa

o a

a

a

o o

a

a

a

a

a

aa

aa

aa

at a '

a

. { '

a

a

I W0RKED EXAMPTE 2-1 Osmotic Strength of an 0rganelle ISuppose the major solutes in intact lysosomes are KCI (-0.1 tu) and NaCI (-0.03 u).When isolating lysosomes, what concentration of sucrose is required in the extract-ing solution at room temperature (25 'C) to prevent swelling and lysis?Solution: We want to find a concentration of sucrose that gives an osmotic strengthequal to that produced by the KCI and NaCl in the lysosomes. The equation for cal-culating osmotic strength (the van't Hoff equation) is

t I : RT( ip1 * i2c2* i scs* + incn)where r? is the gas constant 8.315 J/mol . K, 7 is the absolute temperature (KelvinJ,c1, c2, 3.r1d ca are the molar concentrations of each solute, and 41, i2, and a3 are thenumbers of particles each solute yields in solution (i, : 2 for KCI and NaCI).

The osmotic strength of the lysosomal contents isnt""o"o^" : RT(iKglcKgt * lN.g1cl.{sg1)

: nr[(2)(0.03 moVL) + (2)(0.1moVL)] : RT(0.26 moUL)Because the solute concentrations are only accurate to one signiflcant flgure, thisbecomes ilru"o"o-" : n7(0.3 mol,/L).

The osmotic strength of a sucrose solution is given by["r".o". : R?(i"r""o". c"r""o"")

In this case, ?sucrose : 1, because sucrose does not ionize. Thus,

i l"r".o". : R?(c"r""o".)The osmotic strength of the lysosomal contents equals that of the sucrose solutionwhen

n"r".o".: nly"o"o-"

R?(c",",o".) : R?(0.3 moVL)c"r."o"" : 0.3 moVL

So the required concentration of sucrose (FW 342) is (0.3 moVL)(342 g/mol) : 102.6gll,. Or, when signiflcant figures are taken into account, crr".o"e : 0.1 kg/L.

I WORKED EXAMPIE 2-2 0smoticStrength of an 0rganelle llSuppose we decided to use a solution of a polysaccharide, say glycogen (see p. 246),to balance the osmotic strength of the lysosomes (described in Worked Example 2-1).Assuming a linear pol}.'rner of 100 glucose units, calculate the amount of this pol)rynerneeded to achieve the same osmotic strength as the sucrose solution in WorkedExample 2-1. The M, of the glucose polyrner is -18,000, and, like sucrose, it doesnot ionize in solution.

Solution: As derived in Worked Example 2-1,[",""o"" : RT(03 moVL)

Similarly,ngly"og.. : R?(igty"og". cgly"og.r) : .B?(cg1y"og..)

For a glycogen solution with the same osmotic strength as the sucrose solution,[g ly"og.. : [" t" .o".

R7(cg1y"og.') : nT(0.3 moVL)cglycogen : 0.3 moVL : (O.3moVL)(18,000 g/mol) -- 5.4kg/L

Or, when signiflcant flgures are taken into account, cgrycogen : 5 kgy'L, an absurdlyhigh concentration.

As we'II see later (p. 246) , cells of liver and muscle store carbohydrate not as lowmolecular weight sugars such as glucose or sucrose but as the high molecular weightpolymer glycogen. This allows the cell to contain a Iarge mass of glycogen with aminimal effect on the osmolaritv of the cltosol.

SUMMARY 2.1 Weak Interact ions inAqueous Systems

r The very different electronegativities ofH and Omake water a highly polar molecule, capable offorming hydrogen bonds with itsel-f and with solutes.Hydrogen bonds are fleeting, primarily electrostatic,and weaker than covalent bonds. Water is a goodsolvent for polar (hydrophilic) solutes, with which itforms hydrogen bonds, and for charged solutes,with which it interacts electrostatically.

r Nonpolar (hydrophobic) compounds dissolvepoorly in water; they cannot hydrogen-bond withthe solvent, and their presence forces anenergetically unfavorable ordering of watermolecules at their hydrophobic surfaces. Tominimize the surface exposed to water, nonpolarcompounds such as lipids form aggregates(micelles) in which the hydrophobic moieties aresequestered in the interior, associating throughhydrophobic interactions, and only the more polarmoieties interact with water.

r Weak, noncovalent interactions, rn large numbers,decisively influence the folding of macromoleculessuch as proteins and nucleic acids. The most stablemacromolecular conformations are those in whichhydrogen bonding is maxirnized within the moleculeand between the molecule and the solvent, and inwhich hydrophobic moieties cluster in the interiorof the molecule away from the aqueous solvent.

r The physical properties of aqueous solutions arestrongly influenced by the concentrations ofsolutes. When two aqueous compartments areseparated by a semipermeable membrane (such asthe plasma membrane separating a cell from itssurroundings), water moves across that membraneto equalize the osmolarity in the two compart-ments. This tendency for water to move across asemipermeable membrane is the osmotic pressure.

2.2 lonization of Water, Weak Acids, andWeak BasesAlthough many of the solvent properties of water can beexplained in terms of the uncharged H2O molecule, thesmall degree of ionization of water to hydrogen ions(H+) and hydroxide ions (OH-) must also be taken intoaccount. Like all reversible reactions, the ionization ofwater can be described by an equilibrium constant.When weak acids are dissolved in water, they contributeH* by ionizing; weak bases consume H* by becomingprotonated. These processes are also governed by equi-Iibrium constants. The total hydrogen ion concentrationfrom all sources is experimentally measurable and is ex-pressed as the pH ofthe solution. To predict the state ofionization of solutes in water, we must take into accountthe relevant equilibrium constants for each ionization

reaction. We therefore turn now to a brief discussion ofthe ionization of water and of weak acids and bases dis-solved in water.

Pure Water ls Slightly lonizedWater molecules have a slight tendency to undergo re-versible ionization to yield a hydrogen ion (a proton)and a hydroxide ion, gMng the equilibrium

H 2 O : H * + O H - e-DAlthough we corrunonly show the dissociation productof water as H+, free protons do not exist in solution; hy-drogen ions formed in water are immediately hydratedto hydronium ions (HsO*). Hydrogen bonding be-tween water molecules makes the hydration of dissoci-ating protons virtually instantaneous:

H_O O i-----^ H_Ot_H + OH_H H

The ionization of water can be measured by its elec-trical conductivity; pure water carries electrical currentas H3O* migrates toward the cathode and OH- towardthe anode. The movement of hydronium and hydroxideions in the electric field is extremely fast compared withthat of other ions such as Na-, K-, and Cl-. This highionic mobility results from the kind of "proton hopping"shown in Figure 2-13. No individual proton moves veryfar through the bulk solution, but a series ofproton hops

Hydronium ion gives up a protonH H

g.- O.

- H

nWater accepts proton andbecomes a hydronium ion

FIGURE 2-13 Proton hopping. Short "hops" of protons between a seriesof hydrogen-bonded water molecules result in an extremely rapid netmovement of a proton over a long distance. As a hydronium ion (upperleft) gives up a proton, a water molecule some distance away (lower right)acquires one, becoming a hydronium ion. Proton hopping is much fasterthan true diffusion and explains the remarkably high ionic mobility of H+ions compared with other monovalent cations such as Na* and K*.

between hydrogen-bonded water molecules causes thenet 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+ (and of OH-, which also moves rapidly byproton hopping, but in the opposite direction), acid-base reactions in aqueous solutions are exceptionallyfast. As noted above, proton hopping very likely alsoplays a role in biological proton-transfer reactions(Fig. 2-10; see also Fig. 19-67).

Because reversible ionization is crucial to the role ofwater in cellular function, we must have a means of ex-pressing the extent of ionization of water in quantitativeterms. A brief review of some properties of reversiblechemical reactions shows how this can be done.

The position of equilibrium of any chemical reactionis given by its equilibrium constant, K"n (sometimesexpressed simply as K). For the generalized reaction

A + B . ' C + D (2-2)an equilibrium constant can be defined in terms of theconcentrations of reactants (A and B) and products (Cand D) at equilibrium:

K, [c]"qlDl.o

,O: tALJBhStrictly speaking, the concentration terms should be theactiui,tzes, or effective concentrations in nonideal solu-tions, of each species. Except in very accurate work,however, the equilibrium constant may be approximatedby measuring the concentrati,ons at equilibrium. For rea-sons beyond the scope of this discussion, equilibriun con-stants are dimensionless. Nonetheless, we have generallyretained the concentration units (v) in the equilibrium ex-pressions used in this book to remind you that molarity isthe unit of concentration used in calculating K"o.

The equilibrium constant is fixed and characteristicfor any given chemical reaction at a specified tempera-ture. It defines the composition of the final equilibriummixture, regardless of the starting amounts of reactantsand products. Conversely, we can calculate the equilib-rium constant for a given reaction at a given tempera-ture if the equilibrium concentrations of all its reactantsand products are known. As we showed in Chapter 1(p. 24), the standard free-energy change (AG") is di-rectly related to In K"o.

The lonization 0f Water ls [xpressed byan Equil ibriurn fonstantThe degree of ionization of water at equilibrium (Eqn 2-1)is small; at25"C only about two of every 10e molecules inpure water are ionized at any instant. The equrltbriumconstant for the reversible ionization of water is

tH* l toH- l^ 'o: [Ho]

(2-3)

In pure water at 25 oC, the concentration of water is55.5 u-grams of H2O in I L divided by its gram molecular

weight: (1,000 g/L)/(18.015 g/mol)-and is essentiallyconstant in relation to the very low concentrations of H-and OH-, namely, 1 x 10-7 u. Accordingly, we can sub-stitute 55.5 u in the equilibrium constant expression(Eqn 2-3) to yield

K _ t H ' l t o H - l'-ee [55'5 ru]

On rearranging, this becomes

(55.5 M)(K.q) : [H*]tOH-l : K* (2-4)

where K* designates the product (55.5 vt) (K"q), the ionproduct of water at 25'C.

The value for K.o, determined by electrical-conductivity measurements of pure water, is 1.8 X10-16 r,t at 25 "C. Substituting this value for K"o inEquation 2-4 gives the value of the ion product of water:

K*: [H+]IOH-] : (55.5 ru)(1.8 x 10-16u): 1.0 x 10-14 M2

Thus the product [H-][OH-] in aqueous solutions at25 "C always equals 1 x 10-14 ltz. When there are ex-actly equal concentrations of H- and OH , as in purewater, the solution is said to be at neutral pH. At thispH, the concentration of H* and OH- can be calculatedfrom the ion product of water as follows:

K*: tH*l tOH-l : [H*]2: tOH-12Solving for [H+] gives

lH*l : {K-: v1tlo=rzrr,I'lH ' l : toH- l : 10 7u

As the ion product of w_ater is constant, whenever [H*]is greater than 1 x l0-/ u, [OH-]must be less than 1 X10 7 n, and vice versa. When [H+] is very high, as in asolution of hydrochloric acid, [OH-] must be very lowFrom the ion product of water we can calculate [H+] ifwe know [OH-], and vice versa.

I W0RKED EXAMPTE 2-3 (alculationof [H+]What is the concentration of H+ in a solution of 0.1 nrNaOH?Solution: We begin with the equation for the ion productof water:

K*: tH*l toH-l

With [OH-] : 0.1 u, solving for [H*] gives

K* 1 x 10 lattt2 10 ralt2t ' l = t o H _ ] : o J , ' r : 1 0 " M

: 1 0 - 1 3 M

I W0RKED EXAMPIE 2-4 Catcutationof [0H-]What is the concentration of OH- in a solution with anH+ concentration of 1.3 x 10 4 n?Solution: We begin with the equation for the ion productof water:

K*: tH*l foH-lWith [H+] : 1.3 x 10-a lt, solving for [OH-] gives

K* 1 X 10 -14M2 10 14M2

lH*l 0.00013 u 1.3 x 10 4rvr

: 7 .7 x 10 -11n r

In all calculations be sure to round your answer to thecorrect number of significant flgures, as here.

The pH Scale Designates the H* and 0H- ConcentrationsThe ion product of water, K-, is the basis for the pHscale (Table 2-6).It is a convenient means of designat-ing the concentration of H* (and thus of OH-) in anyaqueous solution in the range between 1.0 u H+ and1.0 u OH . The term pH is defined by the expression

P H : l o g - : = - l o g [ H + ]- tH- lThe symbol p denotes "negative logarithm of." Fora precisely neutral solution at 25 "C, in which the

t0H- l (u ) poH*

1M NaOH

Household bleach

Household ammonia

Solution ofbakingsoda (NaHCOa)Seawater, egg whiteHuman blood, tears

Milk, saliva

Black coffee

BeerRed wine

Cola, vinegar

Lemon juiceGastric juice

1 M H C l

FIGURE 2-14 The pH of some aqueous fluids.

concentration ofhydrogen ions is 1.0 x l0-' lr, the pHcan be calculated as follows:

p H : l o g , 1 . , ; : 7 . 0- 1 . 0 x 1 0 - '

Note that the concentration of H+ must be expressed inmolar (vt) terms.

The value of 7 for the pH of a precisely neutral solu-tion is not an arbitrarily chosen flgure; it is derived fromthe absolute value of the ion product of water at 25 oC,which by convenient coincidence is a round number. So-Iutions having a pH greater than 7 are alkaline or basic;the concentration of OH- is greater than that of H+.Conversely, solutions having a pH less than 7 are acidic.

Keep in mind that the pH scale is logarithmic, notarithmetic. To say that two solutions differ in pH by I pHunit means that one solution has ten times the H* con-centration of the other, but it does not tell us the absolutemagnitude of the difference. Figure 2-14 gives the pHvalues of some conunon aqueous fluids. A cola drink (pH3.0) or red wine fuH 3.7) has an H+ concentration ap-proximately 10,000 times that of blood (pH 7.4).

The pH of an aqueous solution can be approxi-mately measured with various indicator dyes, includinglitmus, phenolphthalein, and phenol red, which undergocolor changes as a proton dissociates from the dye mol-ecule. Accurate determinations of pH in the chemical or

t4

t2

l 1

10

pH100 (1)10- 1

r0-210-31 0-41 0-510-61 0 * 710-810-e10- 10

1 0 - 1 110-1210- 13

10- 14

01234tr

o

78q

101 11213T4

I413I21 11 0

q

87o

A

210

10- 14

10- 13

10- 12

1 0 - 1 110- 10

10-e10-81 0 - 710-610-510-410-3l0 -21 0 - 1loo (1 )

+The expression poH is sometimes used to describe the basicity, or 0H concentra-tion, 0f a solution; poH is defined by the expression poH : -log [0H-], which isanalogous t0 the expression for pH. Note that in all cases, pH + poH : 14.

^lr

Neutral

\ 7V

lH*l (M)

clinical laboratory are made with a glass electrode that isselectively sensitive to H+ concentration but insensitiveto Na+, K*, and other cations. In a pH meter, the signalfrom the glass electrode placed in a test solution is am-plified and compared with the signal generated by a so-lution of accurately known pH.f, Measurement of pH is one of the most importantE and frequently used procedures in biochemistry.The pH affects the structure and activity of biologicalmacromolecules; for example, the catalytic activity ofenzymes is strongly dependent on pH (see Fig. 2-2I).Measurements of the pH of blood and urine are com-monly used in medical diagnoses. The pH of the bloodplasma of people with severe, uncontrolled diabetes, forexample, is often below the normal value of 7.4; thiscondition is called aeidosis (described in more detailbelow). In certain other diseases the pH of the blood ishigher than normal, a condition known as alkalosis.Extreme acidosis or alkalosis can be life-threatening. r

Weak Acids and Bases Have Characteristic AcidDissociation (onstantsHydrochloric, sulfuric, and nitric acids, commonly calledstrong acids, are completely ionized in dilute aqueoussolutions; the strong bases NaOH and KOH are also

Monoprotic acidsAcetic acid(K"= 1.74 x 10-5tvt)

Ammonium ion(K"=5.62 x 10-10M)

Diprotic acidsCarbonic acid(K"= 1.79 x 10-4 u);Bicarbonate(K" = 6.31 x 10-11 u)

Glycine, carboxyl(K"= 4.57 x 10-sM);Glycine, amino(K"= 2.51 x 10-10 na)

Triprotic acidsPhosphoric acid(K"= 7.25 x 10-s M);Dihydrogen phosphate16" = 1.38 x 10-7 u);Monohydrogen phosphate(K" = 3.98 x 10-rs m)

FIGURE 2-15 Conjugate acid-base pairs consist of a proton donor and aproton acceptor. Some compounds, such as acetic acid and ammoniumion, are monoprotic; they can give up only one proton. Others are diprotic(carbonic acid and glycine) or triprotic (phosphoric acid). The dissociation

completely ionized. Of more interest to biochemists isthe behavior of weak acids and bases-those not com-pletely ionized when dissolved in water. These are ubiq-uitous in biological systems and play important roles inmetabolism and its regulation. The behavior of aqueoussolutions of weak acids and bases is best understood ifwe flrst deflne some terms.

Acids may be defined as proton donors and bases asproton acceptors. A proton donor and its correspondingproton acceptor make up a coqiryate acid-base pair(Fig. 2-15). Acetic acid (CH3COOH), a proton donor,and the acetate anion (CH3COO-), the correspondingproton acceptor, constitute a conjugate acid-base pair,related by the reversible reaction

CHBCOOH i-----^ CH3COO- + H-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 tendencyof any acid (HA) to lose a proton and form its conjugatebase (A-) is defined by the equilibrium constant (Keq)for the reversible reaction

for whichIIA i- H" + A-

lH*l lA- l("o: [ I rU :( '

pH

reactions for each pair are shown where they occur along a pH gradient.The equilibrium or dissociation constant (K") and its negative logarithm, thepK", are shown for each reaction. +For an explanation of apparent discrep-ancies in pK" values for carbonic acid (HrCO3), see p. 63.

Yi ,,cH2c

H3PO4

cH,c(o : cHscOH

H2CO': IHCOI + H*pKu=,3 .77*

l'i 'o: C H 2 C \ i * H *

o-

H2PO; + l[*= 2 .14 i

; .- HPO*2-PK" = 6'86

NHi : N

co3- + H= 10.2

PO!- + H*

5{t Water

Equilibrium constants for ionization reactions are usuallycalled ionization constants or acid dissociation con-stants, often designated K.. The dissociation constantsof some acids are given in Figure 2-15. Stronger acids,such as phosphoric and carbonic acids, have larger ion-ization constants; weaker acids, such as monohydrogenphosphate (HPO!-), have smaller ionization constants.

Also included in Figure 2-I5 are values of p1{,,which is analogous to pH and is deflned by the equation

p K ^ : l o g ] - = - b g r c ^l la

The stronger the tendency to dissociate a proton, thestronger is the acid and the lower its pK". As we shallnow see, the pK" of any weak acid can be determinedquite easrly.

Titnation {urves Revealthe pfi of Weak AcidsTitration is used to determine the amount of an acid in agiven solution. A measured volume of the acid is titratedwith a solution of a strong base, usually sodium hydrox-ide (NaOH), of known concentration. The NaOH isadded in small increments until the acid is consumed(neutralized), as determined with an indicator dye or apH meter. The concentration of the acid in the originalsolution can be calculated from the volume and concen-tration of NaOH added

A plot of pH against the amount of NaOH added (atitration curve) reveals the pK. of the weak acid. Con-sider the titration of a 0.1 u solution of acetic acid with0.1 u NaOH at25"C (Fig. 2*l{i). T\.vo reversible equi-Iibria are involved in the process (here, for simplicity,acetic acid is denoted HAc):

cHscoo-

pH = pKa:4 .76

ICHsCOOHI = ICHBCOO-]

0.1 0.2 0.3 0.4 0.5 06 0.7 0.8 0,9 1.0OH- added (equivalents)

' l0 50 I00Vo

Percent titrated

FIGURE 2-16 The titration curve of acetic acid. After addition of each in-crement of NaOH to the acetic acid solution. the pH of the mixture ismeasured This value is plotted against the amount of NaOH added, ex-pressed as a fraction of the total NaOH required to convert all the aceticacid (CH3COOH) to its deprotonated form, acetate (CH:COO ) Thepoints so obtained yield the t i trat ion curve Shown in the boxes are thepredominant ionic forms at the points designated. At the midpoint ofthe titration, the concentrations of the proton donor and proton accep-tor are equal, and the pH is numerical ly equal to the pK". The shadedzone is the useful region of buffering power, generally between 10%and 90% ti trat ion of the weak acid

original acetic acid has undergone dissociation, so thatthe concentration of the proton donor, [HAc], nowequals that of the proton acceptor, [Ac-]. At this mid-point a very important relationship holds: the pH of theequimolar solution of acetic acid and acetate is exactlyequal to the pK. of acetic acid (pK" : 4.76; Figs 2-15,2-16). The basis for this relationship, which holds for allweak acids, will soon become clear.

As the titration is continued by adding further in-crements of NaOH, the remaining nondissociated aceticacid is gradually converted into acetate. The end pointofthe titration occurs at about pH 7.0: all the acetic acidhas lost its protons to OH-, to form H2O and acetate.Throughout the titration the two equilibria (Eqns 2-5,2-6) coexist, each always conforming to its equilibriumconstant.

Figure 2-17 compares the titration curves of threeweak acids with very different ionization constants:acetic acid (pK": 4.76); dihydrogen phosphate, H2PO,(pK^: 6.86); and ammonium ion, NHf, (pK^: 9.25).Although the titration curves of these acids have thesame shape, they are displaced along the pH axis be-cause the three acids have different strengths. Aceticacid, with the highest K" (lowest pK") of the three, is the

pH

1nH 5 .76

Bufferingreglon

J pH 3.76

H2O : H*+ OH-

IIAc -.. H* + Ac-

(2-5)(2-6)

(2-7)

(2-8)

The equilibria must simultaneously conform to their char-acteristic equilibrium constants, which are, respectively,

K*: tH* l toH I : 1 x 1o 1ana2

lH' l lAc- l" ,= f f i= r .?4x1o5M

At the beginning of the titration, before any NaOH isadded, the acetic acid is already slightly ionized, to anextent that can be calculated from its ionization con-stant (Eqn 2-8).

As NaOH is gradually introduced, the added OH-combines with the free H+ in the solution to form H2O,to an extent that satisfies the equilibrium relationship inEquation 2-T. As free H* is removed, HAc dissociatesfurther to satisfy its own equilibrium constant (Eqn 2-8).The net result as the titration proceeds is that more andmore HAc ionizes, forming Ac-, as the NaOH isadded. At the midpoint of the titration, at which exactly0.5 equivalent of NaOH has been added, one-haif of the

The Henderson-Hasselbalch equation also allows us to(1) calculate pKu, given pH and the molar ratio of protondonor and acceptor; (2) calculate pH, given pK, and themolar ratio ofproton donor and acceptor; and (3) calcu-late the molar ratio of proton donor and acceptor, givenpH and pK..

Weak Acids or Bases Buffer Cells and Tissuesagainst pH ChangesThe intracellular and extracellular fluids of multicellularorganisms have a characteristic and nearly constant pH.The organism's first line of defense agarnst changes rninternal pH is provided by buffer systems. The cfio-plasm of most cells contains high concentrations of pro-teins, which contain many amino acids with functionalgroups that are weak acids or weak bases. For example,the side charn of histidine (Fig. 2-19) has a pKu of 6.0;proteins containing histidine residues therefore buffereffectively near neutral pH, and histidine side chains ex-ist in either the protonated or unprotonated form nearneutral pH.

I W0RKED EXAMPTE 2-5 lonization of HistidineCalculate the fraction of histidine that has its imidazoleside chain protonated at pH 7.3. The pK" values forhistidine are pK1 : 1.82, pK2 Qrnidazole) : 6.00, andpKs: 9.17 (see Fig. 3-12b).Solution: The three ionizable groups in histidine havesufficiently different pK" values that the first acid(-COOH) is completely ionized before the second(protonated imidazole) begins to dissociate a proton, andthe second ionizes completely before the third (-NHf)begins to dissociate its proton. (With the Henderson-Hasselbalch equation, we can easily show that a weakacid goes from 1% ionized at 2 pH units below its pK, to99% ionized at 2 pH units above its pK,; see alsoFig. 3-12b.) At pH 7.3, the carboxyl group of histidine isentirely deprotonated (-COO-) and the a-aminogroup is fully protonated (-NHJ). We can therefore as-sume that at pH 7.3, the only group that is partially dis-sociated is the imidazole group, which can beprotonated (we'll abbreviate as HisH+) or not (His).

We use the Henderson-Hasselbalch equation:

pH: pK, * l"cftiSubstituting DKz: 6.0 and PH : 7.3:

z.B :6.0 * ton-El" [HisH*]

1.8 = loe [His]- [HisH*]

antilog 1.t : -!It4- = 2.0 x 10rlHisH*l

So the fraction of total histidine that is in the protonatedform HisH+ at pH 7.3 is 1l2l (1 part HisH+ in a total of21 parts histidine in either form), or about 4.8%.

Nucleotides such as ATP, as well as many low mo-lecular weight metabolites, contain ionizable groupsthat can contribute buffering power to the cytoplasm.Some highly specialized organelles and extracellularcompartments have high concentrations of compoundsthat contribute buffering capacity: organic acids bufferthe vacuoles of plant cells; ammonia buffers urine.

TWo especially important biological buffers are thephosphate and bicarbonate systems. The phosphatebuffer system, which acts in the cytoplasm of allcells, consists of H2POJ as proton donor and HPOa2- asproton acceptor:

H2PO| i- H* + HPO?-The phosphate buffer system is maximally effective at apH close to its pK, of 6.86 (Figs 2-15, 2-17) and thustends to resist pH changes in the range between about5.9 and 7.9. It is therefore an effective buffer in biologi-cal fluids; in mammals, for example, extracellular fluidsand most cy'toplasmic compartments have a pH in therange of 6.9 to 7.4 (see Worked Example 2-6).

Blood plasma is buffered in part by the bicarbonatesystem, consisting of carbonic acid (H2CO3) as protondonor and bicarbonate (HCOj) as proton acceptor (K1is the first of several equilibrium constants in the bicar-bonate buffering system) :

H2CO3 i- H* + HCO'

r.- _ [H.][HCO']'^r [H2co3]This buffer system is more complex than other conju-gate acid-base pairs because one of its components, car-bonic acid (H2CO3), is formed from dissolved (d) carbondioxide and water, in a reversible reaction:

COz(d) + H2O =+ H2COB

lH2co3lFIGURE 2-19 lonization of hist idine. The amino acid hist idine, a com-ponent of proteins, is a weak acid The pK" of the protonated nitrogenof the s ide cha in i s 6 .0 .

K z :lCOr1a11P1r61

Bufferingreglons:-Tr0.25NH,

-L r.ruT7.86Phosphate

-L u.ruT 5.76Acetate

rrru

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0OH added (equivalents)

I50

Percent titratedFI6URE 2-17 Comparison of the titration curves of three weak acids.Shown here are the t i trat ion curves for CH3COOH, H2POt, and NHfThe predominant ionic forms at designated points in the t i trat ion aregiven in boxes. The regions of buffering capacity are indicated at theright. Con.iugate acid-base pairs are effective buffers between approxi-mately 1 0% and 90% neutralization of the proton-donor species.

strongest of the three weak acids (loses its proton mostreadily); it is already half dissociated at pH 4.76.Dihy-drogen phosphate loses a proton less readily, being halfdissociated at pH 6.86. Ammonium ion is the weakestacid of the three and does not become half dissociateduntil pH 9.25.

The titration curve of a weak acid shows graphicallythat a weak acid and its anion-a conjugate acid-basepair-can act as a buffer, which we describe in the nextsectron.

SUMMARY 2.2 lon izat ion of Water , WeakAcids, and Weak Bases

r Pure water ionizes slightly, forming equal numbersof hydrogen ions (hydronium ions, H3O*) andhydroxide ions. The extent of ionization is described

lH+ l loH lby an equilibrium constant, K"q : ---l-Ltlzo]

from which the ion product of water, K-, is derived.At25"C,K*: [H*][OH-] : (55.5vr)Gf"") :l 0 - r 4 M 2 .

The pH of an aqueous solution reflects, on alogarithmic scale, the concentration of hydrogen ions:

1pH : Iog: i ; : -1og [H+].' .- [H*]The greater the acidity of a solution, the lower itspH. Weak acids partially ionize to release a hydro-gen ion, thus lowering the pH of the aqueous solu-tion. Weak bases accept a hydrogen ion, increasingthe pH. The extent of these processes is character-istic of each particular weak acid or base and isexpressed as an acid dissociation constant:

I H + I I A _ IK " o = # : K n .' tnAlThe pK, expresses, on a logarithmic scale, therelative strength of a weak acid or base:

1pK^: log

-

: - logKu.l\a

The stronger the acid, the lower its pKu; thestronger the base, the higher its pK,. The pK" canbe determined experimentally; it is the pH at themidpoint of the titration curve for the acid or base.

2.3 Buffering against pH Changes inBiological SystemsAlmost every biological process is pH-dependent; a smallchange in pH produces a large change in the rate of theprocess. This is true not only for the many reactions inwhich the H+ ion is a direct participant, but also forthose in which there is no apparent role for H+ ions. Theenzlrrnes that catalyze cellular reactions, and many ofthe molecules on which they act, contain ionizablegroups with characteristic pKu values. The protonatedamino and carboxyl groups of amino acids and the phos-phate groups of nucleotides, for example, function asweak acids; their ionic state is determined by the pH ofthe surrounding medium. (\Vhen an ionizable group issequestered in the middle of a protein, away from theaqueous solvent, its pKu, or apparent pKu, can be signif-icantly different from its pK. in water.) As we notedabove, ionic interactions are among the forces that sta-blbze a protein molecule and allow an enzyrne to recog-nize and bind its substrate.

Cells and organisms maintain a speci-flc and constantcytosolic pH, usually near pH 7, keeping biomolecules intheir optimal ionic state. In multicellular organisms, thepH of extracellular fluids is also tightly regulated. Con-stancy of pH is achieved primarily by biological buffers:mixtures of weak acids and their conjugate bases.

Buffen Are Mixtures of Weak Acids and Their(onjugate BasesBuffers are aqueous systems that tend to resistchanges in pH when small amounts of acid (H+) or base

Acetic acid(cH3cooH) Acetate(cH3coo-)

" t H ' l t A c - l

lHAcl

FIGURE 2-18 The acetic acid-acetate pair as a buffer system. The sys-tem is capable of absorbing either H* or OH- through the reversibi l-ity of the dissociation of acetic acid. The proton donor, acetic acid(HAc), contains a reserve of bound H*, which can be released to neu-tral ize an addit ion of OH- to the system, forming H2O. This happensbecause the product tH+ltOH-l transiently exceeds K- (1 x 10 r4 M2).The equil ibr ium quickly adjusts to restore the product to 1 x 10-14 ,ra2(at 25 "C), thus transiently reducing the concentrat ion of H*. But nowthe quotient IH-l tAc-l / tHAcl is less than K", so HAc dissociatesfurther to restore equi l ibr ium. Similarly, the conjugate base, Ac-, canreact with H- ions added to the system; again, the two ionization re-actions simultaneously come to equi l ibr ium. Thus a conjugate acid-base pair, such as acetic acid and acetate ion, tends to resist a changein pH when small amounts of acid or base are added. Buffering actionis simply the consequence of two reversible reactions taking place si-multaneously and reaching their points of equi l ibr ium as governed bytheir equi l ibr ium constants, K* and K".

(OH-) are added. A buffer system consists of a weakacid (the proton donor) and its conjugate base (the pro-ton acceptor). As an example, a mixture of equal con-centrations of acetic acid and acetate ion, found at themidpoint of the titration curve in Figure 2-16, is a buffersystem. Notice that the titration curve of acetic acid hasa relatively flat zone extendmg about 1 pH unit on eitherside of its midpoint pH of 4.76. In this zone, a givenamount of H+ or OH- added to the system has muchless effect on pH than the same aJnount added outsidethe zone. This relatively flat zone is the buffering re-gion of the acetic acid-acetate buffer pair. At the mid-point of the buffering region, where the concentration ofthe proton donor (acetic acid) exactly equals that oftheproton acceptor (acetate), the buffering power of thesystem is maximal; that is, its pH changes least on addi-tion of H+ or OH-. The pH at this point in the titrationcurve of acetic acid is equal to its pK,. The pH of the ac-etate buffer system does change slightly when a smallamount of H+ or OH- is added, but this change is verysmall compared with the pH change that would result ifthe same amount of H+ or OH- were added to pure wa-ter or to a solution ofthe salt ofa strong acid and strongbase, 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-ltl explains how a buffer system works.

, , +Whenever H- or OH- is added to a buffer, the result is asmall change in the ratio of the relative concentrationsof the weak acid and its anion and thus a small change inpH. The decrease in concentration of one component ofthe system is balanced exactly by an increase in theother. The sum of the buffer components does notchange, only their ratio.

Each conjugate acid-base pair has a characteristicpH zone in which it is an effective buffer (Fig. 2-17).The H2POa /HPOa2- pair has a pKu of 6.86 and thus canserve as an effective buffer system between approxi-mately pH 5.9 and pH 7.9; the NHiA{Hs pair, with a pKuof 9.25, can act as a buffer between approximately pH8.3 and pH 10.3.

The Henderson-llasselbalch [quation Relates pH, pl(*,and Buffer (oncentrationThe titration curves of acetic acid, H2POa , and NHi (Fig.2-I7) have nearly identical shapes, suggesting that thesecurves reflect a fundamental law or relationship. This isindeed the case. The shape of the titration curve of anyweak acid is described by the Henderson-Hasselbalchequation, which is important for understanding bufferaction and acid-base balance in the blood and tissues ofvertebrates. This equation is simply a useful way of re-stating the expression for the ionization constant of anacid. For the ionization of a weak acid HA, the Hender-son-Hasselbalch equation can be derived as follows:

tH*l tA-1^" : [{A]

First solve for [H*]:

tF-*. -- tllAlr t : ^ " [ A _ ]

Then take the negative logarithm of both sides:

-loe tH-l : -logK, - "*ffi

Substitute pH for -log [H*] and pK" for -log Ku:

pH: pK" - "r-[H

Now invert -log [HA]/[A-], which involves changing itssign, to obtain the Henderson-Hasselbalch equation:

pH: pK" * l"gffi (2-9)This equation flts the titration curve of all weak acidsand enables us to deduce some important quantitativerelationships. For example, it shows why the pKu of. aweak acid is equal to the pH of the solution at the mid-point of its titration. At that point, [HA] : [A-], and

pH : pK" + log 1 : pKu i 0 : pK"

62 ',,

Water

W0RKED EXAMPLE 2-5 Phosphate Buffers(a) What is the pH of a mixture of 0.042 n NaH2POa and 0.058 n Na2HPOa?Solution: We use the Henderson-Hasselbalch eouation. which we'll exoress here as

p H = p K " + l o g lconjugate basellacidl

In this case, the acid (the species that gives up a-proton) is H2POJ, and the conju-gate base (the species that loses a proton) is HPOa'-. Substituting the given concen-trations ofacid and conjugate base and the pK, (6.86),

pH : 6.86 . .* (t#) = 6.86 + log 1.88 : 6.86 + o.r4 : 7.0

We can roughly check this answer. When more conjugate base than acid ispresent, the acid is more than 50% titrated and thus the pH is above the pK. (6.86),where the acid is exactly 50% titrated.(b) If 1.0 mL of 10.0 N NaOH is added to a Iiter of the buffer prepared in (a), howmuch will the pH change?Solution: A liter of the buffer contains 0.042 mol of NaH2POa. Adding 1.0 mL of 10.0 NNaOH (0.010 mol) would titrate an equivalent amount (0.010 mol) of NaH2POa toNa2HPOa, resulting in 0.032 mol of NaH2POa and 0.068 mol of Na2HPOa. The new pH is

. IHPO?PH : Pf" * log lHfoo-l

0.068= 6.86 + tog OOS2

: 6.86 t 0.33 = 7.2

(c) If 1.0 mL of 10.0 N NaOH is added to a liter of pure water at pH 7.0, what is thefinal pH? Compare this with the answer in (b).Solution: The NaOH dissociates completely into Na+ and OH-, giving [OH-] : 0.010mol./L : 1.0 x 10-2 lr. The pOH is the negative logarithm of [OH-], so pOH : 2.0.Given that in all solutions, pH + pOH : 14, the pH of the solution is 12.

So, an amount of NaOH that increases the pH of water from 7 to 12 increases thepH of a buffered solution, as in (b), from 7.0 to just 7.2. Such is the power of buffering!

Carbon dioxide is a gas under normal conditions, andthe concentration of dissolved CO2 is the result of equi-libration with CO2 of the gas (g) phase:

COz(s) : CO2(d)

,, _ [co2(d)l" ' : t co le ) l

The pH of a bicarbonate buffer system depends on the con-centration of H2CO3 and HCO3, the proton donor and ac-ceptor components. The concentration of H2CO3 in turndepends on the concentration of dissolved CO2, which inturn depends on the concentration of CO2 in the gas phase,or the partial pressnre of CO2, denoted pCO2. Thus thepH of a bicarbonate buffer exposed to a gas phase is ulti-mately determined by the concentration of HCO3 in theaqueous phase and by pCO2 in the gas phase.S The bicarbonate buffer system is an effectiveE physiological buffer near pH 7.4, because theH2CO3 of blood plasma is in equilibrium with a largereserve capacity of CO2(g) in the air space of the lungs.As noted above, this buffer system involves three re-

versible equilibria, in this case between gaseous CO2 inthe lungs and bicarbonate (HCOs ) in the blood plasma( F i s . 2 - : 1 0 ) .

Aqueous phase(blood in capillaries)

H" + HCO;

I | ."u.tto. rI tH2C03

reaction 2

HrO HrO

d)reaction 3

Gas phase(Iung air space) COr(s)

FIGLIRE 2-?0 The bicarbonate buffer system. CO2 in the air space ofthe lungs is in equi l ibr ium with the bicarbonate buffer in the bloodplasma passing through the lung capi l lar ies. Because the concentra-t ion of dissolved CO2 can be adjusted rapidly through changes in therate of breathing, the bicarbonate buffer system of the blood is in near-equil ibr ium with a large potential reservoir of CO2.

When H+ (from the lactic acid produced in muscletissue during vigorous exercise, for example) is addedto blood as it passes through the tissues, reaction 1 inFigure 2-20 proceeds toward a new equilibrium, inwhich [H2CO3] is increased. This in turn increases[COz(d)] in the blood (reaction 2) and thus increasesthe partial pressure of CO2(g) in the air space of thelungs (reaction 3); the extra CO2 is exhaled Con-versely, when the pH of blood is raised (by the NH3produced during protein catabolism, for example), theopposite events occur: [H*] of blood plasma is lowered,causing more H2CO3 to dissociate into H+ and HCO3and thus more CO2(g) from the lungs to dissolve inblood plasma. The rate of respiration, or breathing-that is, the rate of inhaling and exhaling-can quicklyadjust these equil ibria to keep the blood pH nearlyconstant. The rate of respiration is controlled by thebrain stem, where detection of an increased bloodpCO2 or decreased blood pH triggers deeper and morefrequent breathing.

At the pH of blood plasma (7 .4) very little H2CO3 ispresent in comparison with HCOt, and the addition of asmall amount of base (NH3 or OH ) would titrate thisH2CO3, exhausting the buffering capacity. The impor-tant role for carbonic acid (pK" : 3.57 at 37 'C) inbuffering blood plasma (-pH 7.4) seems inconsistentwith our earlier statement that a buffer is most effectivein the range of 1 pH unit above and below its pK". Theexplanation for this paradox is the large reservoir ofCOz(d) in blood and its rapid equilibration with H2CO3:

c o z ( d ) + H 2 o + H 2 c o 3We can define a constant, KL, which is the equilibriumconstant for the hydration of CO2:

z-. - [H2CO3]

n - tcor(d)lThen, to take the COz(d) reservoir into account, we canexpress [H2CO3] as KL[CO2(d)], and substitute this ex-pression for [H2CO3] in the equation for the acid dissoci-ation of H2CO3:

- t H ' I [ H C O 3 | l H - l I H C O 3 ]

^" - lHrcor] - -r,.1cortorl

Noq the overall equilibrium for dissociation of H2CO:3can be expressed in these terms:

K 6 K u : K " ' ' - [ H - ] t H c o t lombined - tcor(dxWe can calculate the value of the new constant, Kcombi'ecl,and the corresponding apparent pK, or pKcombined,from the experimentally determined values of KL (3.0 x10-r nr) and K, (2.7 x 10-a u) at 37 oC:

Kcombined : (3.0 x 10 3 u) Q.7 x t0-4 trt)

: 8 . 1 x 1 0 7 u 2

PK"o-uir"a = 6.1

2.3 Buf fer ing against pH Changes in Bio logical Systems 63

In clinical medicine, it is common to refer to CO2(d)as the conjugate acid and to use the apparent, or com-bined, pKu of 6.1 to simplify calculation of pH fromtCO2(d)1. In this convention,

pH :6.1 * ro* ^ Jlto'^l^- - ' (0 .29 x pCo2)where pCO2 is expressed in kilopascals (kPa; typically,pCO2 is 4.6 to 6.7 kPa) and 0.23 is the correspondingsolubility coefficient for CO2 in water; thus the term0.23 x PCOz : 1.2 kPa. Plasma tHCOtl is normallyabout24 mM. I

U ntreated Diabetes Produces Life-ThreateningAcidosis

Human blood plasma normally has a pH between7.35 and 7.45, and many of the enzymes that

function in the blood have evolved to have maximal ac-tivity in that pH range. Although many aspects of cellstructure and function are influenced by pH, thecatalytic activity of enzymes is especially sensitive.Enz;.'rnes typically show maximal cataly'tic activity at acharacteristic pH, called the pH optimum (Fig. 2-Zf ).On either side of this optimum pH, catalytic activity of-ten declines sharply. Thus, a small change in pH canmake a large difference in the rate of some crucialenzyrne-catalyzed reactions. Biological control of the pHof cells and body fluids is therefore of central impor-tance in all aspects of metabolism and cellular activities,and changes in blood pH have marked physiological con-sequences (described with gusto in Box 2-1 !).

In individuals with untreated diabetes, the lack ofinsulin, or insensitivity to insulin (depending on the type

pH

FIGURE 2-21 The pH optima of some enzymes. Pepsin is a digestiveenzyme secreted into gastr ic juice, which has a pH ol -1 .5, al lowingpepsin to act optimally. Trypsin, a digestive enzyme that acts in thesmall intest ine, has a pH optimum that matches the neutral pH in thelumen of the small intest ine. Alkal ine phosphatase of bone t issue is ahydrolyt ic enzyme thought to aid in bone mineral izat ion

: 5 0X

F

h

This is an account by J.B.S. Haldane of physiologicalexperiments on controlling blood pH, from his bookPos-sCble Worlds (Harper and Brothers, 1928).

"l wanted to find out what happened to a man whenone made him more acid or more alkaline . . . One might, ofcourse, have tried experiments on a rabbit first, and somework had been done along these lines; but it is difflcult tobe sure how a rabbit feels at any time. Indeed, some rab-bits make no serious attempt to cooperate with one.

". . . A human colleague and I therefore began ex-periments on one another . . . My colleague Dr. H.W.Davies and I made ourselves alkaline by over-breathingand by eating an;,thing up to three ounces of bicarbon-ate of soda. We made ourselves acid by sitting in an air-tight room with between six and seven per cent ofcarbon dioxide in the air. This makes one breathe as ifone had just completed a boat-race, and also gives one arather violent headache . . . TWo hours was as long as anyone wanted to stay in the carbon dioxide, even if the gaschamber at our disposal had not retained an ineradica-ble odour of 'yellow cross gas' from some wartime ex-periments, which made one weep gently every time oneentered it. The most obvious thing to try was drinkinghydrochloric acid. If one takes it strong it dissolves one'steeth and burns one's throat, whereas I wanted to let itdiffuse gently all through my body. The strongest I evercared to drink was about one part of the commercialstrong acid in a hundred of water, but a pint of that wasenough for me, as it irritated my throat and stomach,while my calculations showed that I needed a gallon anda half to get the effect I wanted . . . I argued that if oneate ammonium chloride, it would partly break up in thebody, liberating hydrochloric acid. This proved to becorrect . . . the liver turns ammonia into a harrnless sub-stance called urea before it reaches the heart and brainon absorption from the gut. The hydrochloric acid is left

behind and combines with sodium bicarbonate, whichexists in all the tissues, producing sodium chloride andcarbon dioxide. I have had this gas produced in me inthis way at the rate of six quarts an hour (though not foran hour on end at that rate) . . .

"I was quite satisfied to have reproduced in myselfthe type of shortness ofbreath which occurs in the ter-minal stages of kidney disease and diabetes. This hadlong been knorlm to be due to acid poisoning, but in eachcase the acid poisoning is complicated by other chemi-cal abnormalities, and it had been rather uncertainwhich of the syrnptoms were due to the acid as such.

"The scene now shifts to Heidelberg, whereFreudenberg and Gy0rgy were studying tetany inbabies . . . it occurred to them that it would be wellworth trying the effect of making the body unusuallyacid. For tetany had occasionally been observed in pa-tients who had been treated for other complaints byvery large doses of sodium bicarbonate, or had lost largeamounts of hydrochloric acid by constant vomiting; andif alkalinity of the tissues will produce tetany, aciditymay be expected to cure it. Unfortunately, one couldhardly try to cure a dying baby by shutting it up in aroom full of carbonic acid, and still less would one give ithydrochloric acid to drink; so nothing had come of theiridea, and they were using lime salts, which are not veryeasily absorbed, and which upset the digestion, but cer-tainly beneflt many cases of tetany.

"However, the moment they read my paper on theeffects of ammonium cNoride, they began giving it tobabies, and were delighted to find that the tetanycleared up in a few hours. Since then it has been usedwith effect both in England and America, both on chil-dren and adults. It does not remove the cause, but itbrings the patient into a condition from which he has avery fair chance of recovering."

of diabetes), disrupts the uptake of glucose from bloodinto the tissues and forces the tissues to use stored fattyacids as their primary fuel. For reasons we will describein detail later (p. 914), this dependence on fatty acidsresults in the accumulation of high concentrations oftwo carboxylic acids, B-hydroxybutyric acid and ace-toacetic acid (blood plasma level of 90 mg/100 mL,compared with

I W0RKED EXAMPTE 2-7 Treatmentof AcidosiswithBicarbonate

Why does intravenous administration of a bicarbonatesolution raise the plasma pH?Solution: The ratio of [HCO3 ] to [COz(d)] determines thepH of the bicarbonate buffer, according to the equation

P H : 6 ' 1 t H c o t l* tog (o-23 x pcor)If IHCOt] is increased with no change in pCO2, the pHwill rise.

5 U M M A RY 2.3 Buffering against pH (hangesin Bio logical Systems

r A mixture of a weak acid (or base) and its saltresists changes in pH caused by the addition of H+or OH-. The mixture thus functions as a buffer.

r The pH of a solution of a weak acid (or base) andits salt is given by the Henderson-Hasselbalch

fA- lequation: pH : pK" + to8ffi.

r In cells and tissues, phosphate and bicarbonatebuffer systems maintain intracellular andextracellular fluids at their optimum (physiological)pH, which is usually close to pH 7. Enzyrnesgenerally work optimally at this pH.

r Medicai conditions that lower the pH of blood,causing acidosis, or raise it, causing alkalosis, canbe life threatening.

2.4 Water as a ReactantWater is not just the solvent in which the chemical reac-tions of living cells occur; it is very often a direct partic-ipant in those reactions. The formation of ATP fromADP and inorganic phosphate is an example of a con-densation reaetion in which the elements of water areeliminated (Fig. 2-22). The reverse of this reaction-cleavage accompanied by the addition of the elements of

oR-O-P-OH

Io

(ADP)

ooil tl.- R-O-P-O-P-O + H2O

oo-(ATP)Phosphoanhydride

FIGURE 2-22 Participation of water in biological reactions. ATP is aphosphoanhydride formed by a condensation reaction ( loss of the ele-ments of water) between ADP and phosphate. R represents adenosinemonophosphate (AMP). This condensation reaction requires energyThe hydrolysis of (addition of the elements of water to) ATP to formADP and phosphate releases an equivalent amount of energy. Thesecondensation and hydrolysis reactions of ATP are just one example ofthe role of water as a reactant in biological processes.

water-is a hydrolysis reaction. Hydrolysis reactionsare also responsible for the enz;.'rnatic depolymerizationof proteins, carbohydrates, and nucleic acids. Hydrolysisreactions, catalyzed by enz5rmes called hydrolases, arealmost invariably exergonic; by producing two mole-cules from one, they lead to an increase in the random-ness of the system. The formation of cellular polSrmersfrom their subunits by simple reversal of hydrolysis(that is, by condensation reactions) would be endergonicand therefore does not occur. As we shall see, cells cir-cumvent this thermodynamic obstacle by coupling en-dergonic condensation reactions 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 theoxidation of fuels such as Alucose. The overall reactioncan be summarized as

c6H12o6 + 602 -----+ 6co2 + 6H2oGlucose

The "metabolic water" formed by oxidation of foods andstored fats is actually enough to allow some animals invery dry habitats (gerbils, kangaroo rats, camels) to sur-vive for extended periods without drinking water.

The CO2 produced by glucose oxidation is con-verted in erythrocytes to the more soluble HCO3, in areaction catalyzed by