LEHNINGER PRINCIPLES OF BIOCHEMISTRY - VOL. 2. BIOENERGETICS AND METABOLISM - 2014

PART II. BIOENERGETICS AND METABOLISM

Class="center">By virtue of the isomorphism between Entropy and information, relationships can be established between two forms of energy: the energy to perform an action, and the energy to direct the action being performed.

François Jacob, La logique du vivant: une histoire de l'hérédité, 1970

13. BIOENERGETICS AND BIOCHEMICAL REACTION TYPES

Living Cells and organisms must carry out processes of self-maintenance, growth, and reproduction. The ability to extract and transform energy to drive biological work is a fundamental property of all living things, acquired early in cellular evolution. Modern organisms engage in a vast array of energy transformations, converting one form of energy into another. Living organisms use the chemical energy of cellular fuel molecules to synthesize complex, highly ordered macromolecules from simple precursor molecules. They also convert the chemical energy of cellular fuels into concentration gradients and electrical potential gradients, as well as motion and heat. A few organisms, such as fireflies and certain deep-sea fish, can emit light. Photosynthetic organisms convert light energy into Other forms of energy.

Antoine Lavoisier, 1743–1794

The chemical mechanisms underlying biological energy transformations have fascinated and challenged biologists for centuries. The French chemist Antoine Lavoisier observed that animals somehow convert chemical fuel—that is, substances from food—into heat, leading him to conclude that Respiration is a vital process.

...respiration is, in general, nothing more than a slow combustion of carbon and hydrogen, which is very similar to the process taking place in an oil lamp or candle. From this perspective, breathing animals are true fuel-burning boilers that consume and devour themselves. It can be said that this analogy between combustion and respiration did not escape the notice of poets—or rather, philosophers of antiquity. This fire stolen from the heavens, this torch of Prometheus, is not merely an idea born in the minds of engineers and poets; it is a faithful Description of the processes occurring in nature, at least in the case of breathing animals. Therefore, following ancient works, we too can philosophize and say that the torch of life is ignited the very moment an infant begins to breathe, and it is not extinguished until death occurs*

* From memoirs by Armand Séguin and Antoine Lavoisier, dated 1789; cited from [Lavoisier A. (1862) Oeuvres de Lavoisier, Imprimerie Impériale, Paris].

In the twentieth century, humanity achieved a preliminary understanding of most of the chemical processes of the "torch of life." Energy transformations in biological systems obey the same physical laws that govern all other natural processes. Therefore, it is essential for biochemistry students to understand these laws and how they apply to the flow of energy in the biosphere.

In this chapter, we first discuss the Laws of Thermodynamics and the quantitative relationships among Free energy, enthalpy, and entropy. Next, we examine the types of major biochemical reactions occurring in living cells that are necessary for the utilization, storage, transfer, and release of energy acquired by the Organism from its environment. Then, we look more closely at those reactions that play a special role in biological METABOLISM/26.html">Energy Metabolism, particularly ATP-driven reactions. Finally, we turn to important oxidation-reduction reactions in living cells, the energetic principles of electron transfer in biological systems, and the electron carriers that most frequently function as Cofactors in these processes.

13.1. Bioenergetics and Thermodynamics

Bioenergetics is the quantitative study of energy transformations—The conversion of one form of energy to another—that occur in living cells, as well as the chemical processes underlying these transformations. Although the laws of thermodynamics have been discussed in previous chapters, and you may have studied them previously, it is very useful here to review some of the quantitative aspects in general terms.

Energy Transformations in Biological Systems Obey the Laws of Thermodynamics

Numerous quantitative studies on the interconversion of Various Forms of energy, conducted by physicists and chemists, led to the formulation of the two fundamental laws of thermodynamics in the nineteenth century. The First Law is THE PRINCIPLE OF conservation of energy: in any physical or chemical change, the total amount of energy in the universe remains constant; energy may change form or be redistributed, but it cannot be created or destroyed. The Second Law states that all processes in the universe tend toward increased disorder (disorganization): the entropy of the universe increases during any spontaneous process.

Living organisms are assemblages of molecules, yet they are far more highly organized than their surroundings. Organisms are capable of creating and maintaining their characteristic internal order, which would seem to contradict the second law of thermodynamics. In reality, however, living organisms obey this law and operate strictly within its framework. Before discussing the second law of thermodynamics as applied to biological systems, we must define these systems and introduce THE CONCEPT OF the surroundings.

A reacting system is defined as all the constituents of a particular chemical or physical process. Such a system can be an organism, a Cell, or two reacting compounds. The reacting System and Its surroundings together constitute the universe. In the laboratory, certain chemical or physical processes can take place in isolated or closed systems, which are incapable of exchanging matter or energy with their surroundings. Living cells and organisms, however, are open systems that exchange both matter and energy with their surroundings. Living systems never reach equilibrium with their surroundings. The constant interactions between the system and its surroundings explain how organisms can maintain internal order while operating fully within the bounds of the second law of thermodynamics.

In Chapter 1 (Vol. 1, p. 22), we defined three quantitative thermodynamic Functions that can be used to express the energy changes taking place in a chemical reaction:

Gibbs free energy, G, is the portion of the total energy of a system that is available for doing work at constant Temperature and pressure. When a reaction proceeds with the release of free energy (i.e., the system undergoes a decrease in free energy), The change in free energy, ΔG, is negative, and the reaction is called exergonic. In endergonic reactions, the system gains (increases) Free Energy and ΔG > 0.

Enthalpy, H, is the heat content of the reacting system. It reflects the number and kinds of chemical bonds in the reactants and products. A chemical reaction that releases heat is called exothermic. If the enthalpy of formation, H_обр, of the products is less than that of the reactants, ΔH < 0. Reaction systems that absorb heat from their surroundings are called endothermic: for them, ΔH is a positive quantity.

Entropy, S, is a quantitative expression for the randomness or disorder of a system (see Box 1–3). When the products of a reaction are less complex and more disordered than the reactants, the reaction is said to proceed with an increase in entropy.

The units of ΔG and ΔH are J/mol (joules per mole) and cal/mol (calories per mole). Recall that 1 cal = 4.184 J. The units of entropy, S, are J/(mol·K) (joules per mole per kelvin) (Table 13–1).

Table 13-1. Some physical constants and dimensions of certain thermodynamic parameters

Boltzmann constant, k = 1,381 • 10^-23 J/K

Avogadro number, N = 6,022 • 10²³ mol^-1

Faraday constant, J = 96,480 J/(V • mol)

Gas constant, R = 8.315 J/(mol • K) (= 1.987 cal/(mol • K))

Dimension of ∆G and ∆H — J/mol (or cal/mol)

Dimension of ∆S — J/(mol • K) (or cal/(mol • K)) 1 cal = 4.184 J

Dimension of absolute temperature T — K (kelvins) 25 °C = 298 K

At 25 °C RT = 2.479 kJ/mol (= 0.592 kcal/mol)

Under conditions typical of biological systems (constant temperature and pressure), the changes in free energy, enthalpy, and entropy are quantitatively related to each other by the following equation:

∆G = ∆H — T∆S (13-1)

where ∆G is the free energy change of the reaction system, ∆H is the enthalpy change of the reaction system, T is the temperature (in kelvins, K), and ∆S is the entropy change of the system. By convention, ∆S > 0 when entropy increases, and, as noted above, ∆H < 0 when the reaction system releases heat to the surroundings. For spontaneous reactions and natural processes, ∆G is always < 0.

According to the second law of thermodynamics, the entropy of the universe increases during Chemical Reactions or physical processes. This law, however, does not imply that the increase in entropy must necessarily occur within the reaction system itself. The intracellular order created during Cell Growth and Division is more than compensated for by the resulting disorder in the environment. In short, living organisms maintain their internal order by acquiring free energy from the environment in the form of nutrients or sunlight and returning an equivalent amount of energy to it as heat and entropy.

Cells require sources of free energy

Cells are isothermal systems; they function at a constant temperature (as well as constant pressure). Heat cannot serve as an energy source for cells because heat can perform work only when it flows from a warmer body to a cooler one, or from a region of higher temperature to a region of lower temperature. Cells can and must utilize the Gibbs free energy G, which is related to the strength of chemical bonds between atoms, determines the state of equilibrium and the direction of chemical reactions; this is the theoretically possible chemical energy of the system that can be converted into work, i.e., released into the universe as heat and entropy during a chemical reaction proceeding at constant

temperature and constant pressure. Heterotrophic cells derive the necessary free energy from nutrient molecules, whereas photosynthetic cells absorb sunlight energy. Both convert free energy into ATP and other "high-energy" compounds capable of storing energy to perform work (biological processes) under conditions of constant temperature.

Standard Free Energy change is directly related to the Equilibrium Constant

The composition of a reaction system (a mixture of reactants and products) changes until equilibrium is established. Upon reaching equilibrium, the concentrations of reactants and products no longer change, the rates of the forward and reverse reactions become equal, and further Changes in the system cease. The equilibrium concentrations of reactants and products determine the equilibrium constant K_eq (v. 1, p. 24). Let us write for a generalized reaction

aA + bB ⇄ cC + dD

where a, b, c, and d are the numbers of molecules of A, B, C, and D, the equilibrium constant

(13-2)

where [A], [B], [C], and [D] are the molar concentrations of substances at equilibrium.

A nonequilibrium reaction system always spontaneously tends toward an equilibrium state under given conditions (concentration, temperature, pressure), accompanied by A change in the Free energy of the reaction, ∆G. Under standard conditions—i.e., at a temperature T = 298 K = 25 °C, initial concentrations of all reaction components of 1 mol/L (or M), or, for gaseous substances, a partial pressure of 101.3 kPa (kilopascals) = 1 atm—the driving force of the system toward The equilibrium state is determined by the standard free energy change ∆G°. Standard conditions for reactions involving hydrogen ions are [H⁺] = 1 M, or pH 0.

Most biochemical reactions occur in dilute Buffer solutions at pH ≈ 7. Under these conditions, both pH and the concentration of Water (for pure water, [H₂O] = 55.5 M) can be considered constant. For computational convenience, the following standard conditions are adopted for biochemical processes: a hydrogen ion concentration of 10^-7 M (pH 7), a water concentration of 55.5 M, and a Mg²⁺ concentration of 1 mM (for reactions involving Mg²⁺ ions, including most reactions in which ATP interacts).

Key Conventions

For convenience, the standard state (standard conditions) for biochemical systems is chosen to differ from the conventions used in chemistry and physics. Specifically, in biochemistry, the standard state corresponds to [Н⁺] = 10^-7 M (pH 7) and [Н₂О] = 55.5 M. For reactions involving Mg²⁺ ions (which include many ATP-dependent reactions), the concentration of Mg²⁺ in solution is typically assumed to be constant at 1 mM. ■

Physical parameters pertaining to the biochemical standard state are termed standard transformed parameters and are designated with a prime (e.g., ∆G'° and K′_eq) to distinguish them from untransformed parameters used by chemists and physicists. Note that other biochemistry textbooks more frequently use the notation ∆G°' (rather than ∆G'°, as introduced above). The parameter ∆G'° is recommended by the International Union of Pure and Applied Chemistry and the International Union of Biochemistry and Molecular Biology to emphasize that the transformed parameter G' serves as a criterion for equilibrium. For simplicity, here and henceforth these transformed parameters will be referred to as standard free-energy changes.

Key Conventions

According to another convention, when Н₂O, Н⁺, and/or Mg²⁺ participate as reactants or products, their concentrations are omitted from equilibrium equations such as (13-2) and are instead incorporated into the constants K'_eq and ∆G'°. ■

Thus, a given reaction is characterized by an equilibrium constant K'_еq, and consequently ∆G'° functions as a characteristic reaction parameter. As noted in Chapter 6, K'_eq and ∆G'° are related by the simple equation:

∆G'° = -RT In K'_eq (13-3)

This simply represents one of the Methods available for calculating a reaction's equilibrium constant from the standard free-energy change. Table 13-2 lists values of ∆G'° and K'_eq. If K'_еq = 1.0, then ∆G'° = 0.0 (since ln 1.0 = 0). If K'_eq > 1.0, then ∆G'° < 0. Conversely, if K'_еq < 1.0, then ∆G'° > 0. Because the dependence of ∆G'° on K'_eq is logarithmic, relatively small variations in ∆G'° result in substantial changes in K'_eq.

Table 13-2. Equilibrium Constants and Standard Free-Energy Changes of Reactions

* In SI units, energy is expressed in joules (and kilojoules), abbreviated as J (and kJ). However, biochemists most commonly report ∆G'° in kcal/mol (kilocalories per mole). 1 kJ = 4.184 kcal.

It is also useful to define the free-energy change from another perspective. ∆G'° represents the difference between the free energy of the products and that of the reactants. When ∆G'° < 0, the free energy of formation $G_{f}$ (products) < $G_{f}$ (reactants); such a reaction proceeds spontaneously under standard conditions, since all chemical processes tend to move in the direction that minimizes the free energy of the system. If ∆G'° > 0, then $G_{f}$ (products) > $G_{f}$ (reactants). At initial reactant concentrations of 1.0 M (standard conditions), such a reaction proceeds in the reverse direction. Table 13-3 summarizes these relationships.

Table 13-3. K'_eq, ∆G'°, and the Direction of Chemical Reactions Under Standard Conditions

Example 13-1. Calculation of ∆G'°

Determine the free-energy change for the reaction catalyzed by the enzyme phosphoglucomutase:

Glucose-1-phosphate ⇄ glucose-6-phosphate

At THE START OF the reaction, the concentration of glucose-1-phosphate was 20 mM, with no glucose-6-phosphate present in the reaction mixture. At equilibrium at 25 °C and pH 7.0, the mixture contains 1.0 mM glucose-1-phosphate and 19 mM glucose-6-phosphate. Does the reaction proceeding toward The formation of glucose-6-phosphate involve a loss or a gain of free energy?

Solution. First, calculate the equilibrium constant:

Now, the standard free-energy change can be determined:

∆G'° = -RT ln K'_eq = - (8.315 J/(mol·K)) (298 K) (ln 19) = -7.3 kJ/mol

Since ∆G'° < 0, the conversion of glucose-1-phosphate to glucose-6-phosphate is accompanied by a decrease (release/loss) of free energy. For the reverse reaction, the free-energy change is equal in magnitude but opposite in sign, meaning ∆G'° > 0.

Table 13-4 lists numerical values of standard free-energy changes for several important chemical reactions. Note that the Hydrolysis of simple esters, peptide amides, and Glycosides, as well as intramolecular rearrangements and eliminations, are accompanied by relatively small standard free-energy changes, whereas the hydrolysis of acid anhydrides results in a substantial decrease in standard free energy. Complete multi-step oxidation of organic molecules such as glucose or palmitic acid to CO₂ and H₂O yields a very large decrease in standard free energy. The data in Table 13-4 correspond to standard conditions. Parameters for reactions occurring within a living cell can be obtained by adjusting these standard-state values to actual intracellular conditions.

Table 13-4. Standard Free-Energy Changes of Selected Chemical Reactions at pH 7.0 and 25 °C (298 K)

Free-energy changes in real systems depend on the concentrations of reactants and products

We must clearly understand that the free-energy change ∆G and the standard free-energy change ∆G′° are numerically different. Every chemical reaction is characterized by a specific standard free-energy change, which can be positive, negative, or zero depending on the equilibrium constant of that reaction. The standard free-energy change indicates the direction in which a given reaction proceeds and how far it is from equilibrium under standard conditions: initial concentrations of all components at 1.0 M, pH 7.0, temperature 25 °C, and pressure 101.3 kPa. Thus, ∆G′° is a characteristic parameter (constant) for a given reaction. However, under real conditions, the actual free-energy change ∆G depends on the concentrations of reactants and products, as well as on temperature fluctuations as the reaction proceeds. Real conditions may deviate significantly from standard ones. Moreover, ∆G for any reaction spontaneously approaching equilibrium is always negative, and as the reaction proceeds, ∆G increases, ultimately approaching zero. At equilibrium, ∆G = 0, meaning no further work can be performed by the system.

For any reaction aA + bB ⇄ cC + dD, ∆G and ∆G′° are related by the equation

(13-4)

in which the parameters highlighted in red predominate in the system. The concentrations in equation 13-4 are commonly referred to as active masses, and the ratio [С]^с[D]d^|/[А]^а[В]^b expresses the mass action ratio Q. As an example, let us assume that the reaction A + B ⇄ C + D occurs under standard conditions of temperature (25 °C) and pressure (101.3 kPa), but that the concentrations of [A], [B], [C], and [D] are not equal to one another, nor is any of them equal to the standard concentration of 1.0 M. To find the free-energy change ∆G for the forward reaction under these non-standard conditions, we substitute the numerical values of the component concentrations A, B, C, and D into equation 13-3. The parameters R, T, and ∆G′° pertain to standard conditions. ∆G < 0, and as the reaction proceeds, this parameter approaches zero because substances A and B are consumed ([A] and [B] decrease) while substances C and D are formed ([C] and [D] increase). Note that at equilibrium, ∆G = 0, and equation 13-4 simplifies to:

∆G′° = -RT In K'_eq

i.e., we recover equation 13-3, which relates the standard free-energy change to the equilibrium constant.

The criterion for reaction spontaneity is determined by ∆G rather than ∆G′°. When ∆G° > 0, the reaction proceeds only if ∆G < 0. This is possible when, in equation 13-4, 0 < RT In([products]/[reactants]) > ∆G′. For example, upon the immediate removal of reaction products, the ratio [products]/[reactants] « 1, so that RT In [products]/[reactants] < 0 (a large negative number). The values of ∆G and ∆G′° represent the maximum amount of free energy that a reaction can theoretically deliver—that is, the energy that could be harnessed if a highly efficient conversion mechanism were available. Because no such mechanism exists (some free energy is always lost as entropy during any process), the actual work performed by a reaction at constant temperature and pressure is always less than theoretically expected.

Another important consideration is that some thermodynamically favorable reactions (specifically those for which ∆G'° « 0) proceed at an insufficiently rapid rate. For instance, the combustion (oxidation) of wood to CO₂ and H₂O is thermodynamically very favorable. Yet, wood can be stored for years—combustion does not start spontaneously because the activation energy (see Figs. 6-2 and 6-3) for combustion is higher than the thermal energy available at room temperature. Supplying the necessary activation energy (such as striking a match) initiates the combustion process, converting the wood into more stable products, CO₂ and H₂O, while releasing energy as heat and light. The heat evolved in this exothermic reaction provides the activation energy for burning adjacent portions of wood, allowing the process to continue continuously.

In living cells, chemical reactions would occur at extremely slow rates in the absence of efficient catalysts—Enzymes. Enzymes do not supply the reaction system with additional heat (energy); rather, they lower the activation energy. An enzyme provides an alternative reaction pathway with a lower activation energy than that of the uncatalyzed reaction, ensuring that a sufficient fraction of substrate molecules possess enough energy at room temperature to overcome the energy barrier (activation energy). Enzymatic Catalysis accelerates reaction rates by many orders of magnitude. The overall free-energy change of a reaction is independent of the pathway it follows, depending only on The Nature and concentrations of the initial reactants and final products. Enzymatic catalysis does not alter the equilibrium constant of a reaction; however, enzymes can increase—and

do indeed increase—the rates of both the forward and reverse reactions, driving the process in the thermodynamically permitted direction (determined by the sign of the free-energy change).

Standard free-energy changes are additive

Consider the sequential reactions A ⇄ B and B ⇄ C. Each reaction has its own equilibrium constant and is characterized by a specific standard free-energy change, ∆G₁'° and ∆G₂'°. Because these two reactions occur in sequence, component B can be eliminated from consideration. We can then examine the overall reaction A ⇄ C, which is characterized by an overall equilibrium constant and, consequently, an overall standard free-energy change, ∆G'°_total. For sequential chemical reactions, ∆G'° values are additive. For the overall reaction A ⇄ C, the total standard free-energy change ∆G'°_total equals the sum of the standard free-energy changes ∆G₁'° and ∆G₂'° of the individual reactions: ∆G'°_total ⇄ ∆G₁'° + ∆G₂'°

(1) A —> B ∆G₁'°

(2) B —> C ∆G₂'°

Total: A —> C ∆G₁'° + ∆G₂'°

This principle of bioenergetics explains how a thermodynamically unfavorable reaction (an endergonic reaction) can be driven forward by coupling it to a highly exergonic reaction via a shared intermediate. For example, in many organisms, the Synthesis of glucose-6-phosphate is the initial step in glucose utilization:

Glucose + P_i —> glucose-6-phosphate + H₂O

∆G'° = 13.8 kJ/mol

For this reaction, ∆G'° > 0, and under standard conditions, it does not proceed spontaneously in the forward direction. Another cellular process—the hydrolysis of ATP to ADP and P_i—is, by contrast, highly exergonic:

ATP + H₂O —> ADP + P_i

∆G'° = -30.5 kJ/mol

These two reactions share the common intermediates P_i and H₂O and can be treated as sequential reactions:

(1) Glucose + P_i —> glucose-6-phosphate + H₂O

(2) ATP + H₂O —> ADP + P_i

Overall: ATP + glucose —> ADP + glucose-6-phosphate

The overall standard free-energy change can be obtained as the sum of ∆G'° for the individual reactions:

∆G'° = 13.8 kJ/mol + (-30.5 kJ/mol) = -16.7 kJ/mol

The overall reaction is exergonic, and the energy trapped in ATP is used to drive the synthesis of glucose-6-phosphate, even though the formation of this compound from glucose and inorganic phosphate P_i is an endergonic process. The actual pathway of glucose-6-phosphate synthesis in The Cell via phosphoryl group transfer from ATP differs from reactions (1) and (2) given above, but the net result is identical to that obtained by summing these two reactions. In thermodynamic calculations, the initial and final states of the system are represented by these substances, whereas the pathway between the initial and final states is irrelevant.

We have already mentioned that ∆G'° is a way of expressing the reaction equilibrium constant. For reaction (1)

Note that H₂O is omitted from this expression because the concentration of water (55.5 M) remains essentially constant during the reaction. The equilibrium constant for the ATP hydrolysis reaction is

and the equilibrium constant for the two coupled reactions is

An important point regarding equilibrium constants should be noted here. Although the ∆G'° values of the two reactions that comprise the third are additive, the K'_eq of the overall reaction is equal to the product of the K’_eq values of the individual reactions. In other words, equilibrium constants are multiplicative. By coupling ATP hydrolysis with the synthesis of glucose-6-phosphate, K’_eq is increased by a factor of 2.0 • 10⁵.

This strategy, in which a common intermediate is shared in the Synthesis of Secondary metabolites and cellular components, is found in all living cells. Obviously, it only works if compounds such as ATP are continually available. In the following chapters, we will discuss some of the most important pathways of ATP synthesis.

Summary of Section 13.1. Bioenergetics and Thermodynamics

■ Living cells constantly perform work. Energy is required for cells to maintain their highly organized structures, synthesize cellular components, and drive many other processes.

■ Bioenergetics is the quantitative study of energy transductions in biological systems. Biological energy transformations are governed by the laws of thermodynamics.

■ The course of any chemical reaction is determined by two factors: the tendency to achieve a state with maximum bond stability (characterized by enthalpy H) and the tendency to achieve maximum system disorder (characterized by entropy S). The overall driving force of a reaction is the free-energy change ∆G, a thermodynamic parameter that accounts for the combined effect of these two factors: ∆G = ∆H — T∆S.

■ The standard free-energy change is a characteristic physicochemical parameter for a given reaction and can be calculated from its equilibrium constant: ∆G’° = - RTln K’_eq.

■ In a real system, the free-energy change ∆G is not a constant; it depends on ∆G’° as well as the actual concentrations of reactants and products:

■ When ∆G < 0, the reaction proceeds spontaneously from left to right (i.e., in the forward direction); when ∆G > 0, the reaction tends to proceed in the reverse direction; and when ∆G = 0, the system is at equilibrium.

■ The free-energy change of a reaction is independent of the reaction pathway. The free-energy changes of a series of sequential reactions (steps) are additive; the overall free-energy change of a net chemical reaction resulting from a sequence of reactions sharing a common intermediate is equal to the sum of the ∆G values of the individual reactions.