C hapter 3

Thermodynamics of Biological Systems

Sun emblem of Louis XIV on a gate at Versailles. The sun is the prime source of energy for life,
and thermodynamics is the gateway to understanding metabolism. (Giraudon/Art Research, New York)

The activities of living things require energy. Movement, growth, synthesis of biomolecules, and the transport of ions and molecules across membranes all demand energy input. All organisms must acquire energy from their surroundings and must utilize that energy efficiently to carry out life processes. To study such bioenergetic phenomena requires familiarity with thermodynamics, a collection of laws and principles describing the flows and interchanges of heat, energy, and matter in systems of interest. Thermodynamics also allows us to determine whether or not chemical processes and reactions occur spontaneously. The student should appreciate the power and practical value of thermodynamic reasoning and realize that this is well worth the effort needed to understand it.
Even the most complicated aspects of thermodynamics are based ultimately on three rather simple and straightforward laws. These laws and their extensions sometimes run counter to our intuition. However, once truly understood, the basic principles of thermodynamics become powerful devices for sorting out complicated chemical and biochemical problems. At this milestone in our scientific development, thermodynamic thinking becomes an enjoyable and satisfying activity.
            Several basic thermodynamic principles are presented in this chapter, including the analysis of heat flow, entropy production, and free energy functions and the relationship between entropy and information. In addition, some ancillary concepts are considered, including the concept of standard states, the effect of pH on standard-state free energies, the effect of concentration on the net free energy change of a reaction, and the importance of coupled processes in living things. The chapter concludes with a discussion of ATP and other energy-rich compounds.

3.1 · Basic Thermodynamic Concepts

In any consideration of thermodynamics, a distinction must be made between the system and the surroundings. The system is that portion of the universe with which we are concerned, whereas the surroundings include everything else in the universe (Figure 3.1).

Figure 3.1 • The characteristics of isolated, closed, and open systems. Isolated systems exchange neither matter nor energy with their surroundings. Closed systems may exchange energy, but not matter, with their surroundings. Open systems may exchange either matter or energy with the surroundings.

The nature of the system must also be specified. There are three basic systems: isolated, closed, and open. An isolated system cannot exchange matter or energy with its surroundings. A closed system may exchange energy, but not matter, with the surroundings. An open system may exchange matter, energy, or both with the surroundings. Living things are typically open systems that exchange matter (nutrients and waste products) and heat (from metabolism, for example) with their surroundings.

The First Law: Heat, Work, and Other Forms of Energy

It was realized early in the development of thermodynamics that heat could be converted into other forms of energy, and moreover that all forms of energy could ultimately be converted to some other form. The first law of thermodynamics states that the total energy of an isolated system is conserved. Thermo-dynamicists have formulated a mathematical function for keeping track of heat transfers and work expenditures in thermodynamic systems. This function is called the internal energy, commonly designated E or U. The internal energy depends only on the present state of a system and hence is referred to as a state function. The internal energy does not depend on how the system got there and is thus independent of path. An extension of this thinking is that we can manipulate the system through any possible pathway of changes, and as long as the system returns to the original state, the internal energy, E, will not have been changed by these manipulations.
            The internal energy, E, of any system can change only if energy flows in or out of the system in the form of heat or work. For any process that converts one state (state 1) into another (state 2), the change in internal energy, DE, is given as

                            (3.1)

where the quantity q is the heat absorbed by the system from the surroundings, and w is the work done on the system by the surroundings. Mechanical work is defined as movement through some distance caused by the application of a force. Both of these must occur for work to have occurred. For example, if a person strains to lift a heavy weight but fails to move the weight at all, then, in the thermodynamic sense, no work has been done. (The energy expended in the muscles of the would-be weight lifter is given off in the form of heat.) In chemical and biochemical systems, work is often concerned with the pressure and volume of the system under study. The mechanical work done on the system is defined as w = -P D V, where P is the pressure and D V is the volume change and is equal to V₂ - V₁. When work is defined in this way, the sign on the right side of Equation (3.1) is positive. (Sometimes w is defined as work done by the system; in this case, the equation is D E = q - w.) Work may occur in many forms, such as mechanical, electrical, magnetic, and chemical. D E, q, and w must all have the same units. The calorie, abbreviated cal, and kilocalorie (kcal), have been traditional choices of chemists and biochemists, but the SI unit, the joule, is now recommended.

Enthalpy: A More Useful Function for Biological Systems

If the definition of work is limited to mechanical work, an interesting simplification is possible. In this case, D E is merely the heat exchanged at constant volume. This is so because if the volume is constant, no mechanical work can be done on or by the system. Then D E = q. Thus D E is a very useful quantity in constant volume processes. However, chemical and especially biochemical processes and reactions are much more likely to be carried out at constant pressure. In constant pressure processes, D E is not necessarily equal to the heat transferred. For this reason, chemists and biochemists have defined a function that is especially suitable for constant pressure processes. It is called the enthalpy, H, and it is defined as

                             (3.2)

               (3.3)

Clearly, D H is equal to the heat transferred in a constant pressure process. Often, because biochemical reactions normally occur in liquids or solids rather than in gases, volume changes are small and enthalpy and internal energy are often essentially equal.
            In order to compare the thermodynamic parameters of different reactions, it is convenient to define a standard state. For solutes in a solution, the standard state is normally unit activity (often simplified to 1 M concentration). Enthalpy, internal energy, and other thermodynamic quantities are often given or determined for standard-state conditions and are then denoted by a superscript degree sign (“°”), as in D H°, D E°, and so on.

            Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2).

Figure 3.2 • Diagram of a calorimeter. The reaction vessel is completely submerged in a water bath. The heat evolved by a reaction is determined by measuring the rise in temperature of the water bath. 

 Alternatively, for any process A ⇌ B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant:

                             (3.4)

Here R is the gas constant, defined as R = 8.314 J/mol • K. A plot of R(ln K_eq) versus 1/T is called a van’t Hoff plot.

Example

In a study¹ of the temperature-induced reversible denaturation of the protein chymotrypsinogen,

Native state (N) ⇌ denatured state (D)

K _eq = [D]/[N]

T(K):    324.4   326.1   327.5   329.0   330.7   332.0   333.8

    K _eq :      0.041   0.12     0.27     0.68     1.9       5.0       21

A plot of R(ln K_eq) versus 1/T (a van’t Hoff plot) is shown in Figure 3.3.

Figure 3.3 • The enthalpy change, D H°, for a reaction can be determined from the slope of a plot of R ln K_eq versus 1/T. To illustrate the method, the values of the data points on either side of the 327.5 K (54.5°C) data point have been used to calculate D H° at 54.5°C. Regression analysis would normally be preferable. (Adapted from Brandts, J. F., 1964. The thermodynamics of protein denaturation. I. The denaturation of chymotrypsinogen. Journal of the American Chemical Society 86:4291–4301.) 

DH ° for the denaturation process at any temperature is the negative of the slope of the plot at that temperature. As shown, DH ° at 54.5°C (327.5 K) is

DH ° = -[-3.2 -(-17.6)]/[(3.04 - 3.067) x 10^-3] = +533 kJ/mol

What does this value of DH ° mean for the unfolding of the protein? Positive values of D H ° would be expected for the breaking of hydrogen bonds as well as for the exposure of hydrophobic groups from the interior of the native, folded protein during the unfolding process. Such events would raise the energy of the protein-water solution. The magnitude of this enthalpy change (533 kJ/mol) at 54.5°C is large, compared to similar values of DH ° for other proteins and for this same protein at 25°C (Table 3.1).

If we consider only this positive enthalpy change for the unfolding process, the native, folded state is strongly favored. As we shall see, however, other parameters must be taken into account.

The Second Law and Entropy: An Orderly Way of Thinking About Disorder

The second law of thermodynamics has been described and expressed in many different ways, including the following.

1.      Systems tend to proceed from ordered (low entropy or low probability) states to disordered (high entropy or high probability)          states.

2.       The entropy of the system plus surroundings is unchanged by reversible processes; the entropy of the system plus                       surroundings increases for irreversible processes.

3.       All naturally occurring processes proceed toward equilibrium, that is, to a state of minimum potential energy.

Several of these statements of the second law invoke the concept of entropy, which is a measure of disorder and randomness in the system (or the surroundings). An organized or ordered state is a low-entropy state, whereas a disordered state is a high-entropy state. All else being equal, reactions involving large, positive entropy changes, DS, are more likely to occur than reactions for which DS is not large and positive.
            Entropy can be defined in several quantitative ways. If W is the number of ways to arrange the components of a system without changing the internal energy or enthalpy (that is, the number of microscopic states at a given temperature, pressure, and amount of material), then the entropy is given by

S = k ln W            (3.5)

where k is Boltzmann’s constant (k = 1.38 x 10^-23 J/K). This definition is useful for statistical calculations (it is in fact a foundation of statistical thermodynamics), but a more common form relates entropy to the heat transferred in a process:

             (3.6)

where dS_reversible is the entropy change of the system in a reversible² process, q is the heat transferred, and T is the temperature at which the heat transfer occurs.

The Third Law: Why Is “Absolute Zero” So Important?

The third law of thermodynamics states that the entropy of any crystalline, perfectly ordered substance must approach zero as the temperature approaches 0 K, and at T = 0 K entropy is exactly zero. Based on this, it is possible to establish a quantitative, absolute entropy scale for any substance as

          (3.7)

          (3.8)

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known.

Free Energy: A Hypothetical but Useful Device

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

                               (3.9)

For any process at constant pressure and temperature, the free energy change is given by

                       (3.10)

If DG is equal to 0, the process is at equilibrium, and there is no net flow either in the forward or reverse direction. When DG = 0, DS = DH/T, and the enthalpic and entropic changes are exactly balanced. Any process with a nonzero DG proceeds spontaneously to a final state of lower free energy. If DG is negative, the process proceeds spontaneously in the direction written. If DG is positive, the reaction or process proceeds spontaneously in the reverse direction. (The sign and value of DG do not allow us to determine how fast the process will go.) If the process has a negative DG, it is said to be exergonic, whereas processes with positive DG values are endergonic.

The Standard-State Free Energy Change

The free energy change, DG, for any reaction 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 define 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.

           (3.11)

    (3.12)

                                  (3.13)

                               (3.14)

                                 (3.15)

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 importantly, it states that the equilibrium established for a reaction in solution is a function of the standard-state free energy change for the process. That is, DG° is another way of writing an equilibrium constant.

Example

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so

The positive sign of DG° 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 DG° means that the folded form is only slightly favored. Figure 3.4 shows the dependence of DG° on temperature for the denaturation data at pH 3 (from the data given in the Example on page 59).

Figure 3.4 • The dependence of DG° 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 American Chemical Society 86:4291–4301.)

Having calculated both DH ° and DG° for the denaturation of chymotrypsinogen, we can also calculate DS °, using Equation (3.10):

      (3.16)

Figure 3.5 • The dependence of D 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 American Chemical Society 86:4291–4301.)

Figure 3.5 presents the dependence of DS ° on temperature for chymotryp-sinogen denaturation at pH 3. A positive DS ° 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 DS ° in Table 3.1 shows that the present value (for chymotrypsinogen at 54.5°C) is quite large. The physical significance of the thermodynamic parameters for the unfolding of chymotryp-sinogen becomes clear in the next section.

3.2 ·  The Physical Significance of Thermodynamic Properties

What can thermodynamic parameters tell us about biochemical events? The best answer to this question is that a single parameter (DH or DS, for example) is not very meaningful. A positive DH ° for the unfolding of a protein might reflect either the breaking of hydrogen bonds within the protein or the exposure of hydrophobic groups to water (Figure 3.6).

Figure 3.6 • Unfolding of a soluble protein exposes significant numbers of nonpolar groups to water, forcing order on the solvent and resulting in a negative D S° for the unfolding process. Yellow spheres represent nonpolar groups; blue spheres are polar and/or charged groups.

 However, comparison of several thermodynamic parameters can provide meaningful insights about a process. For example, the transfer of Na⁺ and Cl^- ions from the gas phase to aqueous solution involves a very large negative DH ° (thus a very favorable stabilization of the ions) and a comparatively small DS ° (Table 3.2). The negative entropy term reflects the ordering of water molecules in the hydration shells of the Na⁺ and Cl^- ions. This unfavorable effect is more than offset by the large heat of hydration, which makes the hydration of ions a very favorable process overall. The negative entropy change for the dissociation 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, DG° for dissociation of acetic acid in water is positive, and acetic acid is thus a weak (largely undissociated) acid.

            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 involves a negative DS °, a positive DG°, and a DH ° that is small compared to DG° (a pattern similar to that observed for the dissociation of acetic acid). What distinguishes these two very different processes is the change in heat capacity (Table 3.2). A positive heat capacity change for a process indicates that the molecules have acquired new ways to move (and thus to store heat energy). A negative DC_P means that the process has resulted in less freedom of motion for the molecules involved. DC_P is 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 organization 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 water. 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 DC_P should be negative for the dissociation of ions in solution, as observed for acetic acid (Table 3.2).

*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.

3.3 · The Effect of pH on Standard-State Free Energies

For biochemical reactions in which hydrogen ions (H⁺) are consumed or produced, the usual definition of the standard state is awkward. Standard state for the H⁺ ion 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 DG°´ ,K ´ _eq , D H ° ´ , and so on. For values determined in this way, a standard state of 10^-7 M H⁺ and 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 assumed. The two standard states can be related easily. For a reaction in which H⁺ is produced,

    (3.17)

(3.18)

          (3.19)

                (3.20)

                (3.21)

  (3.22)

3.4 · The Important Effect of Concentration on Net Free Energy Changes

Equation (3.12) shows that the free energy change for a reaction can be very different from the standard-state value if the concentrations of reactants and products differ significantly from unit activity (1 M for solutions). The effects can often be dramatic. Consider the hydrolysis of phosphocreatine:

                         (3.23)

        (3.24)

                   (3.25)

At 37°C, the difference between standard-state and 1mM concentrations for such a reaction is thus approximately -17.7 kJ/mol.

3.5 ·  The Importance of Coupled Processes in Living Things

Many of the reactions necessary to keep cells and organisms alive must run against their thermodynamic potential, that is, in the direction of positive D G. Among these are the synthesis of adenosine triphosphate and other high-energy molecules and the creation of ion gradients in all mammalian cells. These processes are driven in the thermodynamically unfavorable direction via coupling with highly favorable processes. Many such coupled processes are discussed later in this text. They are crucially important in intermediary metabolism, oxidative phosphorylation, and membrane transport, as we shall see.

            We can predict whether pairs of coupled reactions will proceed spontaneously by simply summing the free energy changes for each reaction. For example, consider the reaction from glycolysis (discussed in Chapter 19) involving the conversion of phospho(enol)pyruvate (PEP) to pyruvate (Figure 3.7).

Figure 3.7 • The pyruvate kinase reaction.

         (3.26)

                    (3.27)

(3.28)

The net reaction catalyzed by this enzyme depends upon coupling between the two reactions shown in Equations (3.26) and (3.27) to produce the net reaction shown in Equation (3.28) with a net negative DG°´ . Many other examples of coupled reactions are considered in our discussions of intermediary metabolism (Part III). In addition, many of the complex biochemical systems discussed in the later chapters of this text involve reactions and processes with positive DG°´ values that are driven forward by coupling to reactions with a negative DG°´.

3.6 · The 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. Organisms that absorb light energy directly are called phototrophic organisms. 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 oxidative 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 controlled exergonic reactions to drive a variety of life processes (which require energy). A small family of universal biomolecules mediates the flow of energy from exergonic 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 DG°´ is more negative than -25 kJ/mol).

            Table 3.3 lists the most important members of the high-energy phosphate compounds. Such molecules include phosphoric anhydrides (ATP, ADP), an enol- phosphate (PEP), an acyl phosphate (acetyl phosphate), and a guanidino phosphate (creatine phosphate). Also included are thioesters, such as acetyl-CoA, which do not contain phosphorus, but which have a high free energy of hydrolysis. As noted earlier in this chapter, the exact amount of chemical free energy available from the hydrolysis of such compounds depends on concentration, pH, temperature, and so on, but the DG°´ values for hydrolysis of these substances are substantially more negative than for most other metabolic species. Two important points: first, high-energy phosphate compounds are not long-term 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 decompose unpredictably. ATP, for example, is quite a stable molecule. A substantial activation energy must be delivered to ATP to hydrolyze the terminal, or g , phosphate group. In fact, as shown in Figure 3.8, the activation energy that must be absorbed by the molecule to break the O-P _g bond is normally 200 to 400 kJ/mol, which is substantially larger than the net 30.5 kJ/mol released in the hydrolysis reaction.

Figure 3.8 • The activation energies for phosphoryl group-transfer reactions (200 to 400 kJ/mol) are substantially larger than the free energy of hydrolysis of ATP (-30.5 kJ/mol).

Biochemists 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 understanding 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, cyclic AMP, 1,3-BPG, phosphocreatine, acetyl phosphate, and pyrophosphate all exhibit higher values of DG°´. This is not a biological anomaly. ATP is uniquely situated between the very high energy phosphates synthesized in the breakdown of fuel molecules and the numerous lower-energy acceptor molecules that are phosphorylated 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 intermediate energy-shuttle device that interacts with many different energy-coupling enzymes of metabolism.

Table 3.3
Free Energies of Hydrolysis of Some High-Energy Compounds*
Compound (and Hydrolysis Product)	DG°' (kJ/mol)	Structure
	-62.2
	-50.4
	-49.6
	-43.3
	-43.3
	-35.7†
	-30.5
	-35.7
	-33.6
	-32.3	(See ATP structure above)
	-31.9
	-31.5
	-25.6‡
Lower-Energy Phosphate Compounds
	-21.0
	-16.0
	-13.9
	-9.2
	-9.2

 *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.

Group Transfer Potential

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 define the group transfer potential as the free energy change that occurs upon hydrolysis, 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 in terms of appropriate measures of transfer potential (pK_a and reduction potential, E_o, 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

(3.29a)

       (3.29b)

         (3.30)

                 (3.31a)

           (3.31b)

    (3.32)

where n is the number of equivalents of electrons transferred, and Á 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 transfer. It is common to write for the hydrolysis of ATP

                   (3.33)

       (3.34)

     (3.35)

Even this set of equations represents an approximation, because ATP, ADP, and P_i  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.

Table 3.4
Types of Transfer Potential
	Proton Transfer Potential (Acidity)	Standard Reduction Potential (Electron Transfer Potential)	Group Transfer Potential (High-Energy Bond)
Simple equation
Equation including acceptor
Measure of transfer potential
Free energy change of transfer is given by:	DG° per mole of H+ transferred	DG° per mole of e- transferred	DG° per mole of phosphate transferred

Adapted from: Klotz, I. M., 1986. Introduction to Biomolecular Energetics. New York: Academic Press.          

Phosphoric Acid Anhydrides

ATP contains two pyrophosphoryl or phosphoric acid anhydride linkages, as shown in Figure 3.9.  

Figure 3.9 • The triphosphate chain of ATP contains two pyrophosphate linkages, both of which release large amounts of energy upon hydrolysis.

 Other common biomolecules possessing phosphoric acid anhydride linkages include ADP, GTP, GDP and the other nucleoside triphosphates, sugar nucleotides such as UDP-glucose, and inorganic pyrophosphate itself. All exhibit large negative free energies of hydrolysis, as shown in Table 3.3. The chemical reasons for the large negative DG°´ values for the hydrolysis 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.

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 3.10a, the electronegative carbonyl oxygen atoms withdraw electrons from the C » O 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 nature. 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 PP_i with respect to its hydrolysis products. Furthermore, the reverse reaction, reformation of the anhydride bond from the two anionic products, requires that the electrostatic repulsion between these anions be overcome (see following).

(b) The competing resonances of acetic anhydride and the simultaneous resonance forms of the hydrolysis product, acetate.

Stabilization of Hydrolysis Products by Ionization and Resonance

The pyrophosphate moiety possesses three negative charges at pH values above 7.5 or so (note the pK_a values, Figure 3.10a). The hydrolysis products, two molecules of inorganic hosphate, both carry about two negative charges, at pH values above 7.2. The increased ionization of the hydrolysis products helps to stabilize the electrophilic phosphorus nuclei.

            Resonance stabilization in the products is best illustrated by the reactant anhydrides (Figure 3.10b). The unpaired electrons of the bridging oxygen atoms in acetic anhydride (and phosphoric anhydride) cannot participate in resonance structures with both electrophilic centers at once. This competing resonance situation is relieved 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 3.11, the hydrolysis of ATP (as pH values above 7) creates three species—ADP, inorganic phosphate (P_i), and a hydrogen ion—from only two reactants (ATP and H₂O). The entropy of the solution increases because the more particles, the more disordered the system.³ (This effect is ionization-dependent because, at low pH, the hydrogen ion created in many of these reactions simply protonates one of the phosphate oxygens, and one fewer “particle” results from the hydrolysis.)

A Comparison of the Free Energy of Hydrolysis of ATP, ADP, and AMP

The concepts of destabilization of reactants and stabilization of products described for pyrophosphate also apply for ATP and other phosphoric anhydrides (Figure 3.11).

Figure 3.11 • Hydrolysis of ATP to ADP (and/or of ADP to AMP) leads to relief of electrostatic repulsion.

  ATP and ADP are destabilized relative to the hydrolysis products by electrostatic 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 electrostatic repulsion and resonance stabilization. Thus, the DG°´ for hydrolysis of AMP is much smaller than the corresponding values for ATP and ADP.

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 (Figure 3.12).

Figure 3.12 • The hydrolysis reactions of acetyl phosphate and 1,3-bisphosphoglycerate.

Once again, the large DG°´ values indicate that the reactants are 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 reactants also contribute to the large negative DG°´ values. The value of DG°´ depends on the pK_a values of the starting anhydride and the product phosphoric and carboxylic acids, and of course also on the pH of the medium.

Enol Phosphates

The largest value of DG°´ in Table 3.3 belongs to phosphoenolpyruvate or PEP, an example of an enolic phosphate. This molecule is an important intermediate in carbohydrate metabolism and, due to its large negative DG°´, it is a potent phosphorylating agent. PEP is formed via dehydration of 2-phosphoglycerate by enolase during fermentation and glycolysis. PEP is subsequently transformed into pyruvate upon transfer of its phosphate to ADP by pyruvate kinase (Figure 3.13).

Figure 3.13 • Phosphoenolpyruvate (PEP) is produced by the enolase reaction (in glycolysis; see Chapter 19) and in turn drives the phosphorylation of ADP to form ATP in the pyruvate kinase reaction.  

  The very large negative value of DG° ´ for the latter reaction is to a large extent the result of a secondary reaction of the enol form of pyruvate. Upon hydrolysis, the unstable enolic form of pyruvate immediately converts to the keto form with a resulting large negative DG°´ (Figure 3.14). Together, the hydrolysis and subsequent tautomerization result in an overall DG°´ of -62.2 kJ/mol.

Figure 3.14 • Hydrolysis and the subsequent tautomerization account for the very large DG°´ of PEP.

  3.7 · Complex Equilibria Involved in ATP Hydrolysis

So far, as in Equation (3.33), the hydrolyses of ATP and other high-energy phosphates have been portrayed as simple processes. The situation in a real biological system is far more complex, owing to the operation of several ionic equilibria. First, ATP, ADP, and the other species in Table 3.3 can exist in several different ionization states that must be accounted for in any quantitative analysis. Second, phosphate compounds bind a variety of divalent and monovalent cations with substantial affinity, and the various metal complexes must also be considered in such analyses. Consideration of these special cases makes the quantitative analysis far more realistic. The importance of these multiple equilibria in group transfer reactions is illustrated for the hydrolysis of ATP, but the principles and methods presented are general and can be applied to any similar hydrolysis reaction.

The Multiple Ionization States of ATP and the pH Dependence of DG°´

Figure 3.15 • Adenosine 5 ´ -triphosphate (ATP).

   ATP has five dissociable protons, as indicated in Figure 3.15. Three of the protons on the triphosphate chain dissociate at very low pH. The adenine ring amino group exhibits a pK_a of 4.06, whereas the last proton to dissociate from the triphosphate chain possesses a pK_a of 6.95. At higher pH values, ATP is completely deprotonated. ADP and phosphoric acid also undergo multiple ionizations. These multiple ionizations make the equilibrium constant for ATP hydrolysis more complicated than the simple expression in Equation (3.35). Multiple ionizations must also be taken into account when the pH dependence of DG° is considered. The calculations are beyond the scope of this text, but Figure 3.16 shows the variation of DG° as a function of pH.

Figure 3.16 • The pH dependence of the free energy of hydrolysis of ATP. Because pH varies only slightly in biological environments, the effect on D G is usually small.

The free energy of hydrolysis is nearly constant from pH 4 to pH 6. At higher values of pH, DG° varies linearly with pH, becoming more negative by 5.7 kJ/mol for every pH unit of increase at 37°C. Because the pH of most biological tissues and fluids is near neutrality, the effect on DG ° is relatively small, but it must be taken into account in certain situations.

The Effect of Metal Ions on the Free Energy of Hydrolysis of ATP

Most biological environments contain substantial amounts of divalent and monovalent metal ions, including Mg²⁺, Ca²⁺, Na⁺, K⁺, and so on. What effect do metal ions have on the equilibrium constant for ATP hydrolysis and the associated free energy change? Figure 3.17 shows the change in DG°´ with pMg (that is, -log₁₀[Mg²⁺]) at pH 7.0 and 38°C.

Figure 3.17 • The free energy of hydrolysis of ATP as a function of total Mg²⁺ ion concentration at 38°C and pH 7.0. (Adapted 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.) 

The free energy of hydrolysis of ATP at zero Mg²⁺ is -35.7 kJ/mol, and at 5 mM free Mg²⁺ (the minimum in the plot) the DG _obs ° is approximately -31 kJ/mol. Thus, in most real biological environments (with pH near 7 and Mg²⁺concentrations of 5 mM or more) the free energy of hydrolysis of ATP is altered more by metal ions than by protons. A widely used “consensus value” for DG°´ of ATP in biological systems is -30.5 kJ/mol (Table 3.3). This value, cited in the 1976 Handbook of Biochemistry and Molecular Biology (3rd ed., Physical and Chemical Data, Vol. 1, pp. 296-304, Boca Raton, FL: CRC Press), was determined in the presence of “excess Mg²⁺.” This is the value we use for metabolic calculations in the balance of this text.

The Effect of Concentration on the Free Energy of Hydrolysis of ATP

Through all these calculations of the effect of pH and metal ions on the ATP hydrolysis equilibrium, we have assumed “standard conditions” with respect to concentrations of all species except for protons. The levels of ATP, ADP, and other high-energy metabolites never even begin to approach the standard state of 1 M. In most cells, the concentrations of these species are more typically 1 to 5 mM or even less. Earlier, we described the effect of concentration on equilibrium constants and free energies in the form of Equation (3.12). For the present case, we can rewrite this as

         (3.36)

where the terms in brackets represent the sum ( S ) of the concentrations of all the ionic forms of ATP, ADP, and P_i.

            It is clear that changes in the concentrations of these species can have large effects on D. The concentrations of ATP, ADP, and P_i may, of course, vary rather independently in real biological environments, but if, for the sake of some model calculations, we assume that all three concentrations are equal, then the effect of concentration on D is as shown in Figure 3.18. The free energy of hydrolysis of ATP, which is -35.7 kJ/mol at 1 M, becomes -49.4 kJ/mol at 5 mM (that is, the concentration for which pC = -2.3 in Figure 3.18). At 1 mM ATP, ADP, and P_i, the free energy change becomes even more negative at -53.6 kJ/mol. Clearly, the effects of concentration are much greater than the effects of protons or metal ions under physiological conditions.

Figure 3.18 • The free energy of hydrolysis of ATP as a function of concentration at 38°C, pH 7.0. The plot follows the relationship described in Equation (3.36), with the concentrations [C] of ATP, ADP, and P_i assumed to be equal.

               Does the “concentration effect” change ATP’s position in the energy hierarchy (in Table 3.3)? Not really. All the other high- and low-energy phosphates experience roughly similar changes in concentration under physiological conditions and thus similar changes in their free energies of hydrolysis. The roles of the very high-energy phosphates (PEP, 1,3-bisphosphoglycerate, and creatine phosphate) in the synthesis and maintenance of ATP in the cell are considered in our discussions of metabolic pathways. In the meantime, several of the problems at the end of this chapter address some of the more interesting cases.

3.8 · The Daily Human Requirement for ATP

We can end this discussion of ATP and the other important high-energy compounds in biology by discussing the daily metabolic consumption of ATP by humans. An approximate calculation gives a somewhat surprising and impressive result. Assume that the average adult human consumes approximately 11,700 kJ (2800 kcal, that is, 2,800 Calories) per day. Assume also that the metabolic pathways leading to ATP synthesis operate at a thermodynamic efficiency of approximately 50%. Thus, of the 11,700 kJ a person consumes as food, about 5,860 kJ end up in the form of synthesized ATP. As indicated earlier, the hydrolysis of 1 mole of ATP yields approximately 50 kJ of free energy under cellular conditions. This means that the body cycles through 5860/50 = 117 moles of ATP each day. The disodium salt of ATP has a molecular weight of 551 g/mol, so that an average person hydrolyzes about

The average adult human, with a typical weight of 70 kg or so, thus consumes approximately 65 kilograms of ATP per day, an amount nearly equal to his/her own body weight! Fortunately, we have a highly efficient recycling system for ATP/ADP utilization. The energy released from food is stored transiently in the form of ATP. Once ATP energy is used and ADP and phosphate are released, our bodies recycle it to ATP through intermediary metabolism, so that it may be reused. The typical 70-kg body contains only about 50 grams of ATP/ADP total. Therefore, each ATP molecule in our bodies must be recycled nearly 1300 times each day! Were it not for this fact, at current commercial prices of about $10 per gram, our ATP “habit” would cost approximately $650,000 per day! In these terms, the ability of biochemistry to sustain the marvelous activity and vigor of organisms gains our respect and fascination.