Bioenergetics and Thermodynamics

Bioenergetics is the quantitative study of the energy transductions that occur in living cells and of the nature and function of the chemical processes underlying these transductions. Although many of the principles of thermodynamics have been introduced in earlier chapters and may be familiar to you, a review of the quantitative aspects of these principles is useful here.

Biological Energy Transformations Obey the Laws of Thermodynamics

Many quantitative observations made by physicists and chemists on the interconversion of different forms of energy led, in the nineteenth century, to the formulation of two fundamental laws of thermodynamics. The first law is the principle of the conservation of energy: for any physical or chemical change, the total amount of energy in the universe remains constant; energy may change form or it may be transported from one region to another, but it cannot be created or destroyed. The second law of thermodynamics, which can be stated in several forms, says that the universe always tends toward increasing disorder: in all natural processes, the entropy of the universe increases.

Living organisms consist of collections of molecules much more highly organized than the surrounding materials from which they are constructed, and organisms maintain and produce order, seemingly oblivious to the second law of thermodynamics. But living organisms do

"Now, in the second law of thermodynamics

not violate the second law; they operate strictly within it. To discuss the application of the second law to biological systems, we must first define those systems and their surroundings.

The reacting system is the collection of matter that is undergoing a particular chemical or physical process; it may be an organism, a cell, or two reacting compounds. The reacting system and its surroundings together constitute the universe. In the laboratory, some chemical or physical processes can be carried out in isolated or closed systems, in which no material or energy is exchanged with the surroundings. Living cells and organisms, however, are open systems, exchanging both material and energy with their surroundings; living systems are never at equilibrium with their surroundings, and the constant transactions between system and surroundings explain how organisms can create order within themselves while operating within the second law of thermodynamics.

In Chapter 1 (p. 23) we defined three thermody-namic quantities that describe the energy changes occurring in a chemical reaction:

Gibbs free energy, G, expresses the amount of energy capable of doing work during a reaction at constant temperature and pressure. When a reaction proceeds with the release of free energy (that is, when the system changes so as to possess less free energy), the free-energy change, AG, has a negative value and the reaction is said to be exergonic. In endergonic reactions, the system gains free energy and AG is positive.

Enthalpy, H, is the heat content of the reacting system. It reflects the number and kinds of chemical bonds in the reactants and products. When a chemical reaction releases heat, it is said to be exothermic; the heat content of the products is less than that of the reactants and AH has, by convention, a negative value. Reacting systems that take up heat from their surroundings are endothermic and have positive values of A H.

Entropy, S, is a quantitative expression for the randomness or disorder in 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 a gain in entropy.

The units of AG and AH are joules/mole or calories/mole (recall that 1 cal = 4.184 J); units of entropy are joules/mole • Kelvin (J/mol • K) (Table 13-1).

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

TABLE 13-1 Some Physical Constants and Units Used in Thermodynamics

Boltzmann constant, k = Avogadro's number, N = Faraday constant, = Gas constant, R = (=

1.381 X 10~23 J/K 6.0 2 2 X 1023 moP1 96,480 J/V • mol 8.315 J/mol • K 1.987 cal/mol • K)

Units of AG and AH are J/mol (or cal/mol) Units of AS are J/mol • K (or cal/mol • K) 1 cal = 4.184 J

Units of absolute temperature, T, are Kelvin, K 25 °C = 298 K At 25 °C, RT = 2.479 kJ/mol (= 0.592 kcal/mol)

in which AG is the change in Gibbs free energy of the reacting system, AH is the change in enthalpy of the system, T is the absolute temperature, and AS is the change in entropy of the system. By convention, A 5 has a positive sign when entropy increases and AH, as noted above, has a negative sign when heat is released by the system to its surroundings. Either of these conditions, which are typical of favorable processes, tend to make AG negative. In fact, AG of a spontaneously reacting system is always negative.

The second law of thermodynamics states that the entropy of the universe increases during all chemical and physical processes, but it does not require that the entropy increase take place in the reacting system itself. The order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division (see Box 1-3, case 2). In short, living organisms preserve their internal order by taking from the surroundings free energy in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy.

Cells Require Sources of Free Energy

Cells are isothermal systems—they function at essentially constant temperature (they also function at constant pressure). Heat flow is not a source of energy for cells, because heat can do work only as it passes to a zone or object at a lower temperature. The energy that cells can and must use is free energy, described by the Gibbs free-energy function G, which allows prediction of the direction of chemical reactions, their exact equilibrium position, and the amount of work they can in theory perform at constant temperature and pressure. Heterotrophic cells acquire free energy from nutrient molecules, and photosynthetic cells acquire it from absorbed solar radiation. Both kinds of cells transform this free energy into ATP and other energy-rich compounds capable of providing energy for biological work at constant temperature.

The Standard Free-Energy Change Is Directly Related to the Equilibrium Constant

The composition of a reacting system (a mixture of chemical reactants and products) tends to continue changing until equilibrium is reached. At the equilibrium concentration of reactants and products, the rates of the forward and reverse reactions are exactly equal and no further net change occurs in the system. The concentrations of reactants and products at equilibrium define the equilibrium constant, Keq (p. 26). In the general reaction aA + bB y cC + dD, where a, b, c, and d are the number of molecules of A, B, C, and D participating, the equilibrium constant is given by

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

When a reacting system is not at equilibrium, the tendency to move toward equilibrium represents a driving force, the magnitude of which can be expressed as the free-energy change for the reaction, AG. Under standard conditions (298 K = 25 °C), when reactants and products are initially present at 1 m concentrations or, for gases, at partial pressures of 101.3 kilopascals (kPa), or 1 atm, the force driving the system toward equilibrium is defined as the standard free-energy change, AG°. By this definition, the standard state for reactions that involve hydrogen ions is [H+] = 1 m, or pH 0. Most biochemical reactions, however, occur in well-buffered aqueous solutions near pH 7; both the pH and the concentration of water (55.5 m) are essentially constant. For convenience of calculations, biochemists therefore define a different standard state, in which the concentration of H+ is 10~7m (pH 7) and that of water is 55.5 m; for reactions that involve Mg2+ (including most in which ATP is a reactant), its concentration in solution is commonly taken to be constant at 1 mm. Physical constants based on this biochemical standard state are called standard transformed constants and are written with a prime (such as AG'° and Keq) to distinguish them from the untransformed constants used by chemists and physicists. (Notice that most other textbooks use the symbol AG°' rather than AG'°. Our use of AG'°, recommended by an international committee of chemists and biochemists, is intended to emphasize that the transformed free energy G' is the criterion for equilibrium.) By convention, when H2O, H+, and/or Mg2 + are reactants or products, their concentrations are not included in equations such as Equation 13-2 but are instead incorporated into the constants Keq and AG'°.

Just as Keq is a physical constant characteristic for each reaction, so too is AG'° a constant. As we noted in Chapter 6, there is a simple relationship between Keq and AG'°:

The standard free-energy change of a chemical reaction is simply an alternative mathematical way of expressing its equilibrium constant. Table 13-2 shows the relationship between AG'° and Keq. If the equilibrium constant for a given chemical reaction is 1.0, the standard free-energy change of that reaction is 0.0 (the natural logarithm of 1.0 is zero). If Keq of a reaction is greater than 1.0, its AG'° is negative. If Keq is less than 1.0, AG'° is positive. Because the relationship between AG'° and Keq is exponential, relatively small changes in AG'° correspond to large changes in Keq.

It may be helpful to think of the standard free-energy change in another way. AG'° is the difference between the free-energy content of the products and the free-energy content of the reactants, under standard conditions. When AG'° is negative, the products contain less free energy than the reactants and the reaction will proceed spontaneously under standard conditions; all chemical reactions tend to go in the direction that results in a decrease in the free energy of the system. A positive value of AG'° means that the products of the reaction contain more free energy than the reactants, and this reaction will tend to go in the reverse direction if we start with 1.0 m concentrations of all components (standard conditions). Table 13-3 summarizes these points.

*Although joules and kilojoules are the standard units of energy and are used throughout this text, biochemists sometimes express AG'° values in kilocalories per mole. We have therefore included values in both kilojoules and kilocalories in this table and in Tables 13-4 and 13-6. To convert kilojoules to kilocalories, divide the number of kilojoules by 4.184.

TABLE 13-3 Relationships among K'eq, AG'0, and the Direction of Chemical Reactions under Standard Conditions

When K'eq is ... AG'° is . .

Starting with all components at 1 m, the reaction . . .

>1.0 negative

1.0 zero <1.0 positive

proceeds forward is at equilibrium proceeds in reverse

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