The Standard-State Free Energy Change The free energy change, G, for any re-action depends upon the nature of the reactants and products, but it is also affected by the conditions of th
Trang 1Free Energy Provides a Simple Criterion for Equilibrium
An important question for chemists, and particularly for biochemists, is, “Will the
reaction proceed in the direction written?” J Willard Gibbs, one of the founders of
thermodynamics, realized that the answer to this question lay in a comparison of
the enthalpy change and the entropy change for a reaction at a given temperature
The Gibbs free energy, G, is defined as
For any process A34 B at constant pressure and temperature, the free energy change
is given by
IfG is equal to 0, the process is at equilibrium and there is no net flow either in the
en-tropic changes are exactly balanced Any process with a nonzero G proceeds
spon-taneously to a final state of lower free energy If G is negative, the process proceeds
spontaneously in the direction written If G is positive, the reaction or process
pro-ceeds spontaneously in the reverse direction (The sign and value of G do not
al-low us to determine how fast the process will go.) If the process has a negative G, it
is said to be exergonic, whereas processes with positive G values are endergonic.
The Standard-State Free Energy Change The free energy change, G, for any
re-action depends upon the nature of the reactants and products, but it is also affected
by the conditions of the reaction, including temperature, pressure, pH, and the
concentrations of the reactants and products As explained earlier, it is useful to
de-fine a standard state for such processes If the free energy change for a reaction is
sensitive to solution conditions, what is the particular significance of the
standard-state free energy change? To answer this question, consider a reaction between two
reactants A and B to produce the products C and D
The free energy change for non–standard-state concentrations is given by
or, in base 10 logarithms,
This can be rearranged to
Keq 10G °/2.3RT (3.16)
In any of these forms, this relationship allows the standard-state free energy change
for any process to be determined if the equilibrium constant is known More
im-portant, it states that the point of equilibrium for a reaction in solution is a function of the
standard-state free energy change for the process That is, G° is another way of writing an
equilibrium constant
The equilibrium constants determined by Brandts at several
temper-atures for the denaturation of chymotrypsinogen (see previous example) can be
used to calculate the free energy changes for the denaturation process For
exam-ple, the equilibrium constant at 54.5°C is 0.27, so
G° (8.314 J/mol K)(327.5 K) ln (0.27)
G° (2.72 kJ/mol) ln (0.27)
G° 3.56 kJ/mol
[C][D]
[A][B]
Trang 254 Chapter 3 Thermodynamics of Biological Systems
The positive sign of G° means that the unfolding process is unfavorable; that is,
the stable form of the protein at 54.5°C is the folded form On the other hand, the relatively small magnitude of G° means that the folded form is only slightly
denatura-tion data at pH 3 (from the data given in the example on page 50)
we can also calculate S°, using Equation 3.11:
At 54.5°C (327.5 K),
S° (3560 533,000 J/mol)/327.5 K
S° 1620 J/mol K
denaturation at pH 3 A positive S° indicates that the protein solution has become
more disordered as the protein unfolds Comparison of the value of 1.62 kJ/mol K with the values of S° in Table 3.1 shows that the present value (for
chymotrypsino-gen at 54.5°C) is quite large The physical significance of the thermodynamic param-eters for the unfolding of chymotrypsinogen becomes clear later in this chapter
3.2 What Is the Effect of Concentration on Net Free Energy Changes?
Equation 3.13 shows that the free energy change for a reaction can be very differ-ent from the standard-state value if the concdiffer-entrations of reactants and products
differ significantly from unit activity (1 M for solutions) The effects can often be
dramatic Consider the hydrolysis of phosphocreatine:
This reaction is strongly exergonic, and G° at 37°C is 42.8 kJ/mol Physiological
concentrations of phosphocreatine, creatine, and inorganic phosphate are
nor-mally between 1 and 10 mM Assuming 1 mM concentrations and using Equation
3.13, the G for the hydrolysis of phosphocreatine is
At 37°C, the difference between standard-state and 1 mM concentrations for such a
reaction is thus approximately 17.7 kJ/mol
3.3 What Is the Effect of pH on Standard-State Free Energies?
pro-duced, the usual definition of the standard state is awkward Standard state for the
Hion is 1 M, which corresponds to pH 0 At this pH, nearly all enzymes would be
denatured and biological reactions could not occur It makes more sense to use free energies and equilibrium constants determined at pH 7 Biochemists have thus adopted a modified standard state, designated with prime () symbols, as in G°,
Keq, H°, and so on For values determined in this way, a standard state of 107M
Hand unit activity (1 M for solutions, 1 atm for gases and pure solids defined as
unit activity) for all other components (in the ionic forms that exist at pH 7) is
as-[0.001][0.001]
[0.001]
( G H°) T
10
Temperature (°C)
8
6
4
2
0
–2
–4
–6
–8
–10
FIGURE 3.3 The dependence of G° on temperature for
the denaturation of chymotrypsinogen (Adapted from
Brandts, J F., 1964 The thermodynamics of protein denaturation.
I The denaturation of chymotrypsinogen Journal of the
Ameri-can Chemical Society 86:4291–4301.)
2.4
52
Temperature (°C)
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
54 56 58 60
FIGURE 3.4 The dependence of S° on temperature for
the denaturation of chymotrypsinogen (Adapted from
Brandts, J F., 1964 The thermodynamics of protein denaturation.
I The denaturation of chymotrypsinogen Journal of the
Ameri-can Chemical Society 86:4291–4301.)
Go to CengageNOW at www
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to see the relationships between free energies and
the following: changes to temperature, equilibrium
constants, and concentrations of reactants and
products.
Trang 3sumed The two standard states can be related easily For a reaction in which His
produced,
the relation of the equilibrium constants for the two standard states is
andG° is given by
For a reaction in which His consumed,
the equilibrium constants are related by
andG° is given by
3.4 What Can Thermodynamic Parameters Tell Us
About Biochemical Events?
The best answer to this question is that a single parameter (H or S, for example)
is not very meaningful A positive H° for the unfolding of a protein might reflect
either the breaking of hydrogen bonds within the protein or the exposure of
hy-drophobic groups to water (Figure 3.5) However, comparison of several thermodynamic
parameters can provide meaningful insights about a process For example, the transfer of
Naand Clions from the gas phase to aqueous solution involves a very large
neg-ativeH° (thus a very favorable stabilization of the ions) and a comparatively small
S° (Table 3.2) The negative entropy term reflects the ordering of water molecules
contribu-tion is more than offset by the large heat of hydracontribu-tion, which makes the hydracontribu-tion
of ions a very favorable process overall The negative entropy change for the
disso-ciation of acetic acid in water also reflects the ordering of water molecules in the
ion hydration shells In this case, however, the enthalpy change is much smaller in
magnitude As a result, G° for dissociation of acetic acid in water is positive, and
acetic acid is thus a weak (largely undissociated) acid
1 [H]
Keq [H]
Folded
Unfolded
ANIMATED FIGURE 3.5 Unfolding of a soluble protein exposes significant numbers of nonpo-lar groups to water, forcing order on the solvent and resulting in a negative S° for the unfolding process.
Orange spheres represent nonpolar groups; blue
spheres are polar and/or charged groups See this
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Trang 456 Chapter 3 Thermodynamics of Biological Systems
The transfer of a nonpolar hydrocarbon molecule from its pure liquid to water
is an appropriate model for the exposure of protein hydrophobic groups to solvent when a protein unfolds The transfer of toluene from liquid toluene to water in-volves a negative S°, a positive G°, and a H° that is small compared to G° (a pattern similar to that observed for the dissociation of acetic acid) What distin-guishes these two very different processes is the change in heat capacity (Table 3.2) A
posi-tive heat capacity change for a process indicates that the molecules have acquired
process has resulted in less freedom of motion for the molecules involved CPis negative for the dissociation of acetic acid and positive for the transfer of toluene
to water The explanation is that polar and nonpolar molecules both induce organi-zation of nearby water molecules, but in different ways The water molecules near a nonpolar solute are organized but labile Hydrogen bonds formed by water molecules
near nonpolar solutes rearrange more rapidly than the hydrogen bonds of pure wa-ter On the other hand, the hydrogen bonds formed between water molecules near
an ion are less labile (rearrange more slowly) than they would be in pure water This means that CPshould be negative for the dissociation of ions in solution, as ob-served for acetic acid (Table 3.2)
3.5 What Are the Characteristics of High-Energy Biomolecules?
Virtually all life on earth depends on energy from the sun Among life forms, there
is a hierarchy of energetics: Certain organisms capture solar energy directly, whereas others derive their energy from this group in subsequent processes
Or-ganisms that absorb light energy directly are called phototrophic orOr-ganisms These
organisms store solar energy in the form of various organic molecules Organisms that feed on these latter molecules, releasing the stored energy in a series of
oxida-tive reactions, are called chemotrophic organisms Despite these differences, both
types of organisms share common mechanisms for generating a useful form of chemical energy Once captured in chemical form, energy can be released in con-trolled exergonic reactions to drive a variety of life processes (which require en-ergy) A small family of universal biomolecules mediates the flow of energy from ex-ergonic reactions to the energy-requiring processes of life These molecules are the
reduced coenzymes and the high-energy phosphate compounds Phosphate compounds are
considered high energy if they exhibit large negative free energies of hydrolysis (that is, if G° is more negative than 25 kJ/mol).
Table 3.3 lists the most important members of the high-energy phosphate
com-pounds Such molecules include phosphoric anhydrides (ATP, ADP), an enol phosphate (PEP), acyl phosphates (such as acetyl phosphate), and guanidino phosphates (such as
creatine phosphate) Also included are thioesters, such as acetyl-CoA, which do not contain phosphorus, but which have a large negative free energy of hydrolysis As
Hydration of ions†
Na(g) Cl(g)⎯⎯→ Na(aq) Cl(aq) 760.0 0.185 705.0 Dissociation of ions in solution‡
Transfer of hydrocarbon from pure liquid to water‡
*All data collected for 25°C.
†Berry, R S., Rice, S A., and Ross, J., 1980 Physical Chemistry New York: John Wiley.
‡Tanford, C., 1980 The Hydrophobic Effect New York: John Wiley.
Trang 5noted earlier, the exact amount of chemical free energy available from the
hydrol-ysis of such compounds depends on concentration, pH, temperature, and so on,
but the G° values for hydrolysis of these substances are substantially more
nega-tive than those for most other metabolic species Two important points: First,
high-energy phosphate compounds are not long-term high-energy storage substances They
are transient forms of stored energy, meant to carry energy from point to point,
from one enzyme system to another, in the minute-to-minute existence of the cell
(As we shall see in subsequent chapters, other molecules bear the responsibility for
long-term storage of energy supplies.) Second, the term high-energy compound should
not be construed to imply that these molecules are unstable and hydrolyze or
de-compose unpredictably ATP, for example, is quite a stable molecule A substantial
activation energy must be delivered to ATP to hydrolyze the terminal, or , phosphate
group In fact, as shown in Figure 3.6, the activation energy that must be absorbed
substantially larger than the net 30.5 kJ/mol released in the hydrolysis reaction
Bio-chemists are much more concerned with the net release of 30.5 kJ/mol than with the
activation energy for the reaction (because suitable enzymes cope with the latter)
The net release of large quantities of free energy distinguishes the high-energy
phosphoric anhydrides from their “low-energy” ester cousins, such as
glycerol-3-phosphate (Table 3.3) The next section provides a quantitative framework for
un-derstanding these comparisons
ATP Is an Intermediate Energy-Shuttle Molecule
One last point about Table 3.3 deserves mention Given the central importance of
ATP as a high-energy phosphate in biology, students are sometimes surprised to find
that ATP holds an intermediate place in the rank of high-energy phosphates PEP,
1,3-BPG, creatine phosphate, acetyl phosphate, and pyrophosphate all exhibit
higher values of G° This is not a biological anomaly ATP is uniquely situated
be-tween the very-high-energy phosphates synthesized in the breakdown of fuel
mole-cules and the numerous lower-energy acceptor molemole-cules that are phosphorylated
1,3-Bisphosphoglycerate⎯⎯→ 3-phosphoglycerate Pi 49.6 Figure 3.12
Adenosine-5-triphosphate ⎯⎯→ ADP Pi 35.7† Figure 3.9
(with excess Mg2)
Pyrophosphate⎯⎯→ Pi Pi(in 5 mM Mg2) 33.6 Figure 3.10
Adenosine-5-triphosphate ⎯⎯→ AMP PPi(excess Mg2) 32.3 Figure 10.11
Uridine diphosphoglucose⎯⎯→ UDP glucose 31.9 Figure 22.10
S-adenosylmethionine⎯⎯→ methionine adenosine 25.6‡ Figure 25.28
Adenosine-5-monophosphate ⎯⎯→ adenosine Pi 9.2 Figure 10.11
*Adapted primarily from Handbook of Biochemistry and Molecular Biology, 1976, 3rd ed In Physical and Chemical Data,
G Fasman, ed., Vol 1, pp 296–304 Boca Raton, FL: CRC Press.
† From Gwynn, R W., and Veech, R L., 1973 The equilibrium constants of the adenosine triphosphate hydrolysis and the
adenosine triphosphate-citrate lyase reactions Journal of Biological Chemistry 248:6966–6972.
‡From Mudd, H., and Mann, J., 1963 Activation of methionine for transmethylation Journal of Biological Chemistry
238:2164–2170.
Trang 658 Chapter 3 Thermodynamics of Biological Systems
in the course of further metabolic reactions ADP can accept both phosphates and energy from the higher-energy phosphates, and the ATP thus formed can donate both phosphates and energy to the lower-energy molecules of metabolism The ATP/ADP pair is an intermediately placed acceptor/donor system among high-energy phosphates In this context, ATP functions as a very versatile but intermedi-ate energy-shuttle device that interacts with many different energy-coupling en-zymes of metabolism
Group Transfer Potentials Quantify the Reactivity
of Functional Groups
Many reactions in biochemistry involve the transfer of a functional group from a
donor molecule to a specific receptor molecule or to water The concept of group
transfer potential explains the tendency for such reactions to occur Biochemists de-fine the group transfer potential as the free energy change that occurs upon hy-drolysis, that is, upon transfer of the particular group to water This concept and its
terminology are preferable to the more qualitative notion of high-energy bonds.
The concept of group transfer potential is not particularly novel Other kinds of transfer (of hydrogen ions and electrons, for example) are commonly characterized
poten-tial,Ᏹo, respectively) As shown in Table 3.4, the notion of group transfer is fully analogous to those of ionization potential and reduction potential The similarity is anything but coincidental, because all of these are really specific instances of free energy changes If we write
we really don’t mean that a proton has literally been removed from the acid AH In the gas phase at least, this would require the input of approximately 1200 kJ/mol!
What we really mean is that the proton has been transferred to a suitable acceptor
molecule, usually water:
The appropriate free energy relationship is of course
2.303 RT
Activation energy
艑 200–400 molkJ
Reactants
Products
Transition state
Phosphoryl group transfer potential
艑 –30.5 kJ/mol
ADP+ Pi
ATP
FIGURE 3.6 The activation energies for phosphoryl
group transfer reactions (200 to 400 kJ/mol) are
sub-stantially larger than the free energy of hydrolysis of ATP
( 30.5 kJ/mol).
Trang 7Similarly, in the case of an oxidation-reduction reaction
we don’t really mean that A oxidizes independently What we really mean (and what
is much more likely in biochemical systems) is that the electron is transferred to a
suitable acceptor:
A H⎯⎯→ A 1
and the relevant free energy relationship is
where n is the number of equivalents of electrons transferred and Ᏺ is Faraday’s
constant.
Similarly, the release of free energy that occurs upon the hydrolysis of ATP and
other “high-energy phosphates” can be treated quantitatively in terms of group
trans-fer It is common to write for the hydrolysis of ATP
The free energy change, which we henceforth call the group transfer potential, is
given by
written as
all exist in solutions as a mixture of ionic species This problem is discussed in a
later section For now, it is enough to note that the free energy changes listed in
Table 3.3 are the group transfer potentials observed for transfers to water
The Hydrolysis of Phosphoric Acid Anhydrides Is Highly Favorable
ATP contains two pyrophosphoryl or phosphoric acid anhydride linkages, as shown in
Figure 3.7 Other common biomolecules possessing phosphoric acid anhydride
linkages include ADP, GTP, GDP and the other nucleoside diphosphates and
triphosphates, sugar nucleotides such as UDP–glucose, and inorganic
pyrophos-phate itself All exhibit large negative free energies of hydrolysis, as shown in
Table 3.3 The chemical reasons for the large negative G° values for the
hydrol-ysis reactions include destabilization of the reactant due to bond strain caused by
electrostatic repulsion, stabilization of the products by ionization and resonance,
and entropy factors due to hydrolysis and subsequent ionization
[ADP][Pi]
G°
nᏲ
Proton Transfer Potential Standard Reduction Potential Group Transfer Potential
G°
RT
G°
nᏲ
G°
2.303 RT
Adapted from: Klotz, I M., 1986 Introduction to Biomolecular Energetics New York: Academic Press.
Trang 860 Chapter 3 Thermodynamics of Biological Systems
Destabilization Due to Electrostatic Repulsion Electrostatic repulsion in the reactants is best understood by comparing these phosphoric anhydrides with other reactive anhydrides, such as acetic anhydride As shown in Figure 3.8a, the electronegative carbonyl oxygen atoms withdraw electrons from the CPO bonds, producing partial negative charges on the oxygens and partial positive charges on the carbonyl carbons Each of these electrophilic carbonyl carbons is further destabilized by the other acetyl group, which is also electron-withdrawing in na-ture As a result, acetic anhydride is unstable with respect to the products of hydrolysis
The situation with phosphoric anhydrides is similar The phosphorus atoms of the pyrophosphate anion are electron-withdrawing and destabilize PPiwith respect
to its hydrolysis products Furthermore, the reverse reaction, reformation of the an-hydride bond from the two anionic products, requires that the electrostatic repul-sion between these anions be overcome (see following)
Stabilization of Hydrolysis Products by Ionization and Resonance The pyro-phosphoryl moiety possesses two negative charges at pH values above 7.5 or so (Figure 3.8a) The hydrolysis products, two phosphate esters, each carry about two negative charges at pH values above 7.2 The increased ionization of the hydrolysis products helps stabilize the electrophilic phosphorus nuclei
Resonance stabilization in the products is best illustrated by the reactant anhy-drides (Figure 3.8b) The unpaired electrons of the bridging oxygen atom in acetic anhydride (and phosphoric anhydride) cannot participate in resonance structures
with both electrophilic centers at once This competing resonance situation is
re-lieved in the product acetate or phosphate molecules
Entropy Factors Arising from Hydrolysis and Ionization For the phosphoric anhydrides, and for most of the high-energy compounds discussed here, there is
an additional “entropic” contribution to the free energy of hydrolysis Most of the hydrolysis reactions of Table 3.3 result in an increase in the number of molecules
in solution As shown in Figure 3.9, the hydrolysis of ATP (at pH values above 7)
ionization-dependent because, at low pH, the hydrogen ion created in many of these reac-tions simply protonates one of the phosphate oxygens, and one fewer “particle” re-sults from the hydrolysis.)
OH
NH2
P O
O–
P O
O–
P O
O–
O CH2
OH O
N N
Phosphoric anhydride linkages
–O
ATP
(adenosine-5'-triphosphate)
O O
ACTIVE FIGURE 3.7 The triphosphate
chain of ATP contains two pyrophosphate linkages, both
of which release large amounts of energy upon
hydroly-sis Test yourself on the concepts in this figure at
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3 Imagine the “disorder” created by hitting a crystal with a hammer and breaking it into many small pieces.
Trang 9The Hydrolysis G° of ATP and ADP Is Greater Than That of AMP
The concepts of destabilization of reactants and stabilization of products described
for pyrophosphate also apply for ATP and other phosphoric anhydrides (Figure
3.9) ATP and ADP are destabilized relative to the hydrolysis products by
electro-static repulsion, competing resonance, and entropy AMP, on the other hand, is a
phosphate ester (not an anhydride) possessing only a single phosphoryl group and
is not markedly different from the product inorganic phosphate in terms of
elec-trostatic repulsion and resonance stabilization Thus, the G° for hydrolysis of
AMP is much smaller than the corresponding values for ATP and ADP
Acetyl Phosphate and 1,3-Bisphosphoglycerate Are
Phosphoric-Carboxylic Anhydrides
The mixed anhydrides of phosphoric and carboxylic acids, frequently called acyl
phosphates, are also energy-rich Two biologically important acyl phosphates are
acetyl phosphate and 1,3-bisphosphoglycerate Hydrolysis of these species yields
acetate and 3-phosphoglycerate, respectively, in addition to inorganic phosphate
destabilized relative to products This arises from bond strain, which can be
traced to the partial positive charges on the carbonyl carbon and phosphorus
atoms of these structures The energy stored in the mixed anhydride bond
(which is required to overcome the charge–charge repulsion) is released upon
hydrolysis Increased resonance possibilities in the products relative to the
2 CH3C O–
O
H2O
H2O
CH3
2 H+
+
H2O
(a)
(b)
Competing resonance in acetic anhydride:
O These can only occur alternately
Simultaneous resonance in the hydrolysis products:
These resonances can occur simultaneously
O
O–
P O
O–
O
O–
O
O–
C
O
C
O–
O
H3C
C
O–
C O
O
C O
C –O
C
O
C O–
H3C C
O C O
CH3
H3C
ACTIVE FIGURE 3.8 (a) Electrostatic repulsion between adjacent partial positive charges (on
carbon and phosphorus, respectively) is relieved upon hydrolysis of the anhydride bonds of acetic anhydride
and phosphoric anhydrides (b) The competing resonances of acetic anhydride and the simultaneous
reso-nance forms of the hydrolysis product, acetate Test yourself on the concepts in this figure at www
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Trang 1062 Chapter 3 Thermodynamics of Biological Systems
O–
O –O
OH
P
O–
O
OH
NH2
N N
OH
O
OH
NH2
N N
OH
O
OH
NH2
N N
ATP
ADP
AMP
O–
O
O–
O
+
O–
O
O–
O
O–
O
+
O–
O
H2O
H2O
ANIMATED FIGURE 3.9 Hydrolysis of
ATP to ADP (and/or of ADP to AMP) leads to relief of
electrostatic repulsion See this figure animated at
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1,3-Bisphosphoglycerate 3-Phosphoglycerate
Acetyl phosphate
CH3
O
O
O–
O
O–
CH3
O
O C HCOH
O
O
O–
O
O–
O
CH2
C HCOH
O
O–
O
CH2
HO O
O–
O
G°' = –49.6 kJ/mol
G°' = –43.3 kJ/mol
ACTIVE FIGURE 3.10The hydrolysis reactions of acetyl phosphate and 1,3-bisphosphoglycerate.
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