-
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