《生物化学原理》（英文版）BIOENERGETICS AND METABOLISM

13.1 Bioenergetics and Thermodynamics 491 TABLE 13-1 Some Physical Constants and Units Used in Thermodynamics stant temperature. Boltzmann constant k= 1.381 x 10<3J/K Avogadro's number, N=6.022 X 1023mol-1 The Standard Free-Energy Change Is Directly Related Faraday constant, J=96, 480 J/. mol to the equilibrium Constant Gas constant, R=8.315 J/mol- K (=1.987ca/mol·8 The composition of a reacting system (a mixture of chemical reactants and products) tends to continue Units of△Gand△ H are j/mol(ca/mo changing until equilibrium is reached. At the equilibrium Units of△ S are j/mol·k(rca/mol·K) concentration of reactants and products, the rates of the 1ca=4.184」 forward and reverse reactions are exactly equal and no Units of absolute temperature, I, are Kelvin, K further net change occurs in the system. The concen- 25° trations of reactants and products at equilibrium A25°CRT=2.479k/mol define the equilibrium constant, Keg(p. 26). In the (0.592 kcal/mon) general reaction aA+ bB=c+ dD, where a, b, c, and d are the number of molecules of A, B. C, and D par ticipating, the equilibrium constant is given by in which AG is the change in Gibbs free energy of the ing system, AH is the change in enthalpy of th system, T is the absolute temperature, and AS is the change in entropy of the system. By convention, A Shas where [Al. [B. Cl and [D] are the molar concentrations a positive sign when entropy increases and A H, as noted of the reaction components at the point of equilibrium. above, has a negative sign when heat is released by the When a reacting system is not at equilibrium, the system to its surroundings. Either of these conditions tendency to move toward equilibrium rep which are typical of favorable processes, tend to make ing force, the magnitude of which can be expressed as AGnegative. In fact, AGof a spontaneously reacting sys. the ree-energy change for the reaction, AG. Under stan ons tem is always negative The second law of thermodynamics states that the products are initially present at 1 M concentrations or. entropy of the universe increases during all chemical and physical processes, but it does not require that the or I atm, the force driving the system toward equilib entropy increase take place in the reacting system it rium is defined as the standard free-energy change, AGo self. The order produced within cells as they grow ar By this definition, the standard state for reactions that divide is more than compensated for by the disorder involve hydrogen ions is[H]=l M, or pH 0. Most bio- chemical reactions however. occur in well-buffered they create in their surroundings in the course of growth aqueous solutions near pH 7: both the ph an and division(see Box 1-3, case 2). In short, living id the con- centration of water(55.5 M) essentially constant ganisms preserve their internal order by taking from the For convenience of calculations, biochemists therefore light, and returning to their surroundings an equal define a different standard state, in which the concen- amount of energy as heat and entropy tration of H is 10-M(pH 7)and that of water is 55.5 M; for reactions that involve Mgt(including n Cells Require Sources of Free Energy in which ATP is a reactant), its concentration in solu tion is commonly taken to be constant at 1 mM. phy Cells are isothermal systems-they function at essen- cal constants based on this biochemical standard stat tially constant temperature(they also function at con- are called standard transformed constants and e). Heat flow is not a of (such as AG and Keg) to dist cells, because heat can do work only as it passes to a guish them from the untransformed constants used by zone or object at a lower temperature. The energy that chemists and physicists. (Notice that most other text cells can and must use is free energy, described by the books use the symbol AG rather than AGo. Our use of Gibbs free-energy function G, which allows prediction AG, recommended by an international committee of of the direction of chemical reactions, their exact equi- chemists and biochemists, is intended to emphasize that librium position, and the amount of work they can in the transformed free energy G is the criterion for equi theory perform at constant temperature and pressure. librium )By convention, when H20, H*, and/or Mg2 Heterotrophic cells acquire free energy from nutrient are reactants or products, their concentrations are not molecules, and photosynthetic cells acquire it from ab- included in equations such as Equation 13-2 but are in- sorbed solar radiation. Both kinds of cells transform this stead incorporated into the constants Keg and AG

in which G is the change in Gibbs free energy of the reacting system, H is the change in enthalpy of the system, T is the absolute temperature, and S is the change in entropy of the system. By convention, S has a positive sign when entropy increases and H, 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 G negative. In fact, G of a spontaneously reacting sys￾tem 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 it￾self. 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 or￾ganisms preserve their internal order by taking from the surroundings free energy in the form of nutrients or sun￾light, 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 essen￾tially constant temperature (they also function at con￾stant 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 equi￾librium 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 ab￾sorbed 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 con￾stant 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 concen￾trations of reactants and products at equilibrium define the equilibrium constant, Keq (p. 26). In the general reaction aA bB cC dD, where a, b, c, and d are the number of molecules of A, B, C, and D par￾ticipating, the equilibrium constant is given by Keq   [ [ C A ] ] c a [ [ D B ] ] d b (13–2) 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 driv￾ing force, the magnitude of which can be expressed as the free-energy change for the reaction, G. Under stan￾dard 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 equilib￾rium is defined as the standard free-energy change, G . By this definition, the standard state for reactions that involve hydrogen ions is [H]  1 M, or pH 0. Most bio￾chemical reactions, however, occur in well-buffered aqueous solutions near pH 7; both the pH and the con￾centration of water (55.5 M) are essentially constant. For convenience of calculations, biochemists therefore define a different standard state, in which the concen￾tration of H is 107 M (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 solu￾tion is commonly taken to be constant at 1 mM. Physi￾cal constants based on this biochemical standard state are called standard transformed constants and are written with a prime (such as G and K eq) to distin￾guish them from the untransformed constants used by chemists and physicists. (Notice that most other text￾books use the symbol G rather than G . Our use of G , recommended by an international committee of chemists and biochemists, is intended to emphasize that the transformed free energy G is the criterion for equi￾librium.) 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 in￾stead incorporated into the constants K eq and G . yz 13.1 Bioenergetics and Thermodynamics 491 Boltzmann constant, k  1.381 1023 J/K Avogadro’s number, N  6.022 1023 mol1 Faraday constant,  96,480 J/V  mol Gas constant, R  8.315 J/mol  K ( 1.987 cal/mol  K) Units of G and H are J/mol (or cal/mol) Units of S 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) TABLE 13–1 Some Physical Constants and Units Used in Thermodynamics

492 Chapter 13 Principles of Bioenergetics Chapter 6, there is a simple relationship between Keg and the Direction of chemical reactions under and△G Standard Conditions △G°=- RTIn K Starting with all The standard free-energy change of a chemical re components at 1 action is simply an alternative mathematical way of When Keq is expressing its equilibrium constant. Table 13-2 >1.0 gative proceeds forward shows the relationship between AG and Keg. If the is at equilibrium equilibrium constant for a given chemical reaction is 1.0, <1.000 proceeds in reverse the standard free-energy change of that reaction is 0.0 ( the natural logarithm of 1.0 is zero). If Keg of a reac- tion is greater than 1.0, its AG" is negative. If Keg is less than 1.0, AG is positive. Because the relationship be- As an example, let's make a simple calculation of tween AG and Keg is exponential, relatively small the standard free-energy change of the reaction cat- changes in AG" correspond to large changes in Ke It may be helpful to think of the standard fre Glucose 1-phosphate e glucose 6-phosphate energy change in another way. AG is the difference be tween the free-energy content of the products and the Chemical analysis shows that whether we start with, say. free-energy content of the reactants, under standard 20 mM glucose 1-phosphate(but no glucose 6-phosphate) conditions. When AG is negative, the products contain with 20 mm glucose 6-phosphate (but no glucose less free energy than the reactants and the reaction will l-phosphate), the final equilibrium mixture at 25C and proceed spontaneously under standard conditions: all pH 7.0 will be the same: 1 mM glucose 1-phosphate and chemical reactions tend to go in the direction that re 19 mM glucose 6-phosphate.(Remember that sults in a decrease in the free energy of the system. a not affect the point of equilibrium of a reaction; they positive value of AG means that the products of the merely hasten its attainment. )From these data we can reaction contain more free energy than the reactants, calculate the equilibrium constant: and this reaction will tend to go in the reverse direction if we start with 1.0 M concentrations of all components K{-1m=19 (standard conditions). Table 13-3 summarizes these From this value of k we can calculate the standard free-energy change TABLE 13-2 Relationship between the AG°=- RTIn k quilibrium Constants and Standard Free-Energy =-(8315 J/mol.K(298Kn19) Changes of Chemical Reactions 7.3 kJ/mol Because the standard free-energy change is when the reaction starts with 1.0 M glucose 1-ph (kcal/mol) and 1.0 M glucose 6-phosphate, the conversion of gl cose 1-phosphate to glucose 6-phosphate proceeds with a loss (release)of free energy. For the reverse reaction (the conversion of glucose 6-phosphate to glucose l-phosphate), AG has the same magnitude but the op- 5.7 Table 13-4 gives the standard free-energy changes 000000 11.4 for some representative chemical reactions. Note that hydrolysis of simple esters, amides, peptides, and gly 22.8 cosides, as well as rearrangements and eliminations, proceed with relatively small standard free-energy 34.2 changes, whereas hydrolysis of acid anhydrides is ac- companied by relatively large decreases in standard free energy and are used energy. The complete oxidation of organic compounds throughout this text, biochemists sometimes epress 4Gvalues i kiloca ories mole. We have therefore included values in both kilojoules and kilocalories in this table such as glucose or palmitate to CO2 and H2O, which in and in Tables 13-4 and 13-6. To convert kilojoules to kilocalories diide the number cells requires many steps, results in very large decreases of kilojoules by 4.184 in standard free energy. However, standard free-energy

Just as K eq is a physical constant characteristic for each reaction, so too is G a constant. As we noted in Chapter 6, there is a simple relationship between K eq and G : G  RT ln K eq The standard free-energy change of a chemical re￾action is simply an alternative mathematical way of expressing its equilibrium constant. Table 13–2 shows the relationship between G and K eq. 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 K eq of a reac￾tion is greater than 1.0, its G is negative. If K eq is less than 1.0, G is positive. Because the relationship be￾tween G and K eq is exponential, relatively small changes in G correspond to large changes in K eq. It may be helpful to think of the standard free￾energy change in another way. G is the difference be￾tween the free-energy content of the products and the free-energy content of the reactants, under standard conditions. When G 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 re￾sults in a decrease in the free energy of the system. A positive value of G 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. As an example, let’s make a simple calculation of the standard free-energy change of the reaction cat￾alyzed by the enzyme phosphoglucomutase: Glucose 1-phosphate 34 glucose 6-phosphate Chemical analysis shows that whether we start with, say, 20 mM glucose 1-phosphate (but no glucose 6-phosphate) or with 20 mM glucose 6-phosphate (but no glucose 1-phosphate), the final equilibrium mixture at 25 C and pH 7.0 will be the same: 1 mM glucose 1-phosphate and 19 mM glucose 6-phosphate. (Remember that enzymes do not affect the point of equilibrium of a reaction; they merely hasten its attainment.) From these data we can calculate the equilibrium constant: K eq    1 1 9 m m M M 19 From this value of K eq we can calculate the standard free-energy change: G  RT ln K eq  (8.315 J/mol
K)(298 K)(ln 19)  7.3 kJ/mol Because the standard free-energy change is negative, when the reaction starts with 1.0 M glucose 1-phosphate and 1.0 M glucose 6-phosphate, the conversion of glu￾cose 1-phosphate to glucose 6-phosphate proceeds with a loss (release) of free energy. For the reverse reaction (the conversion of glucose 6-phosphate to glucose 1-phosphate), G has the same magnitude but the op￾posite sign. Table 13–4 gives the standard free-energy changes for some representative chemical reactions. Note that hydrolysis of simple esters, amides, peptides, and gly￾cosides, as well as rearrangements and eliminations, proceed with relatively small standard free-energy changes, whereas hydrolysis of acid anhydrides is ac￾companied by relatively large decreases in standard free energy. The complete oxidation of organic compounds such as glucose or palmitate to CO2 and H2O, which in cells requires many steps, results in very large decreases in standard free energy. However, standard free-energy  [glucose 6-phosphate] [glucose 1-phosphate] 492 Chapter 13 Principles of Bioenergetics G K eq (kJ/mol) (kcal/mol)* 103 17.1 4.1 102 11.4 2.7 101 5.7 1.4 1 0.0 0.0 101 5.7 1.4 102 11.4 2.7 103 17.1 4.1 104 22.8 5.5 105 28.5 6.8 106 34.2 8.2 Relationship between the Equilibrium Constants and Standard Free-Energy Changes of Chemical Reactions TABLE 13–2 Starting with all components at 1 M, When K eq is . . . G is . . . the reaction . . . 1.0 negative proceeds forward 1.0 zero is at equilibrium
1.0 positive proceeds in reverse Relationships among K eq, G, and the Direction of Chemical Reactions under Standard Conditions TABLE 13–3 *Although joules and kilojoules are the standard units of energy and are used throughout this text, biochemists sometimes express G 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.

13.1 Bioenergetics and Thermodynamics TABLE 13-4 Standard Free-Energy Changes of Some Chemical Reactions atpH7.0and25°c(2988 △G° (//mol) (kcal/mol) Hydrolysis reactions Acid anhydrides Acetic anhydride H20- 2 acetate 1.8 AIP+H0→→ADP AIP+H20→→AMP+PP -456 P+H20→→2 UDP-glucose+H20→→UMP+ glucose 1- phosphate 430 Ethyl acetate+ H20- ethanol t acetate -196 -4.7 Glucose 6-phosphate H glucose t Pi 13.8 Amides and peptides Glutamine H20- glutamate + NE -142 Glycylglycine+H20→→2 glycine Maltose+H0→2 glucose 155 3.7 Rear Glucose 1-phosphate→→ glucose6; phosphate Fructose6; phosphate→→ glucose6 - phosphate 1.7 -0.4 Maae→→ fumarate+H20 08 Oxidations with molecular oxygen Glucose 602-6C02+ 6H20 Palmitate+2302→→16002+16H20 9.770 -2338 changes such as those in Table 13-4 indicate how much energy change tells us in which direction and how far a free energy is available from a reaction under standard given reaction must go to reach equilibrium when the conditions. To describe the energy released under the initial concentration of each component is 1.0 M, the conditions existing in cells, an expression for the actual pH is 7.0, the temperature is 25.C, and the pressure is free-energy change is essential. 101.3 kPa. Thus ago is a constant: it has a character tic, unchanging value for a given reaction. But the ac- Actual Free-Energy Changes Depend on Reactant tual free-energy change, AG, is a function of reactant and product concentrations and product concentrations and of the temperature pre- vailing during the reaction, which will not necessarily We must be careful to distinguish between two differ- match the standard conditions as defined above. More- ent quantities: the free-energy change, AG, and the stan- over, the AG of any reaction proceeding spontaneously dard free-energy change, AG. Each chemical reaction toward its equilibrium is always negative, becomes less has a characteristic standard free-energy change, which negative as the reaction proceeds, and is zero at the may be positive, negative, or zero, depending on the point of equilibrium, indicating that no more work can equilibrium constant of the reaction. The standard free- be done by the reaction

changes such as those in Table 13–4 indicate how much free energy is available from a reaction under standard conditions. To describe the energy released under the conditions existing in cells, an expression for the actual free-energy change is essential. Actual Free-Energy Changes Depend on Reactant and Product Concentrations We must be careful to distinguish between two differ￾ent quantities: the free-energy change, G, and the stan￾dard free-energy change, G . Each chemical reaction has a characteristic standard free-energy change, which may be positive, negative, or zero, depending on the equilibrium constant of the reaction. The standard free￾energy change tells us in which direction and how far a given reaction must go to reach equilibrium when the initial concentration of each component is 1.0 M, the pH is 7.0, the temperature is 25 C, and the pressure is 101.3 kPa. Thus G is a constant: it has a character￾istic, unchanging value for a given reaction. But the ac￾tual free-energy change, G, is a function of reactant and product concentrations and of the temperature pre￾vailing during the reaction, which will not necessarily match the standard conditions as defined above. More￾over, the G of any reaction proceeding spontaneously toward its equilibrium is always negative, becomes less negative as the reaction proceeds, and is zero at the point of equilibrium, indicating that no more work can be done by the reaction. 13.1 Bioenergetics and Thermodynamics 493 G Reaction type (kJ/mol) (kcal/mol) Hydrolysis reactions Acid anhydrides Acetic anhydride H2O On 2 acetate 91.1 21.8 ATP H2O 88n ADP Pi 30.5 7.3 ATP H2O 88n AMP PPi 45.6 10.9 PPi H2O 88n 2Pi 19.2 4.6 UDP-glucose H2O 88n UMP glucose 1-phosphate 43.0 10.3 Esters Ethyl acetate H2O 88n ethanol acetate 19.6 4.7 Glucose 6-phosphate H2O 88n glucose Pi 13.8 3.3 Amides and peptides Glutamine H2O 88n glutamate NH4 14.2 3.4 Glycylglycine H2O 88n 2 glycine 9.2 2.2 Glycosides Maltose H2O 88n 2 glucose 15.5 3.7 Lactose H2O 88n glucose galactose 15.9 3.8 Rearrangements Glucose 1-phosphate 88n glucose 6-phosphate 7.3 1.7 Fructose 6-phosphate 88n glucose 6-phosphate 1.7 0.4 Elimination of water Malate 88n fumarate H2O 3.1 0.8 Oxidations with molecular oxygen Glucose 6O2 88n 6CO2 6H2O 2,840 686 Palmitate 23O2 88n 16CO2 16H2O 9,770 2,338 Standard Free-Energy Changes of Some Chemical Reactions at pH 7.0 and 25 C (298 K) TABLE 13–4

AG and AG for any reaction A+B=C+ D are urable rates. For example, combustion of firewood to related by the equation CO2 and H20 is very favorable thermodynamically, but firewood remains stable for years because the activation △G=△G°+RTl (13-3) energy(see Figs 6-2 and 6-3)for the combustion re- action is higher than the energy available at room tem- in which the terms in red are those actually prevail- perature. If the necessary activation energy is provided ing in the system under observation. The concentration (with a lighted match, for example), combustion will be terms in this equation express the effects commonly gin, converting the wood to the more stable products called mass action, and the term (CIDVAJB is called CO2 and H20 and releasing energy as heat and light.The the mass-action ratio, Q. As an example, let us sup- heat released by this exothermic reaction provides the pose that the reaction A+B=C+D is taking place activation energy for combustion of neighboring regions at the standard conditions of temperature(25 C)and of the firewood; the process is self-perpetuating pressure(101.3 kPa)but that the concentrations of A In living cells, reactions that would be extremely B, C, and D are not equal and none of the components slow if uncatalyzed are caused to proceed, not by sup is present at the standard concentration of 1.0 M. To de- plying additional heat but by lowering the activation er termine the actual free-energy change, AG, under these ergy with an enzyme. An enzyme provides an alternative nonstandard conditions of concentration as the reaction reaction pathway with a lower activation energy than the proceeds from left to right, we simply enter the actual uncatalyzed reaction, so that at room temperature a large oncentrations of A, B, C, and D in Equation 13-3: the fraction of the substrate molecules have enough thermal alues of R, T, and AG are the standard values. AG is energy to overcome the activation barrier, and the re- negative and approaches zero as the reaction proceeds action rate increases dramatically. The free-energy because the actual concentrations of a and b decrease change for a reaction is independent of the pathway and the concentrations of C and D increase. Notice that by which the reaction occurs; it depends only on the when a reaction is at equilibrium-when there is no nature and concentration of the initial reactants and the force driving the reaction in either direction and AG is final products. Enzymes cannot, therefore, change equi zero-Equation 13-3 reduces to librium constants; but they can and do increase the rate at which a reaction proceeds in the direction dictated by 0=△G=AG°+RTln thermodynamics Standard Free-Energy Changes Are Additive △G°=-RTln In the case of two sequential chemical reactions, A= B and B= C, each reaction has its own equilibrium which is the equation relating the standard free-energy constant and each has its characteristic standard free. change and equilibrium constant given earlier The criterion for spontaneity of a reaction is the energy change, AGi@ and AG2. As the two reactions value of△Gnot△c° A reaction with a positive△° sequential, B cancels out to give the overall reaction <s n go in the forward direction ifAG is negative. This A=C, which has its own equilibrium constant and thus its own standard free-energy change,△Gtoa.he△G is possible if the term RT In(products()n values of sequential chemical reactions are additive Equation 13-3 is negative and has a larger absolute For the overall reaction A= C, AGtotal is the sum of value than AG. For example, the immediate removal of the products of a reaction can keep the ratio pro the individual standard free-energy changes, AGi and ucts/ reactants] well below 1, such that the term RTIn △G2, of the two reactions:△ctoa=△G1°+△G2 (products)reactants) has a large, negative value. (1)A→B△G △G°and△ G are expressions of the maximun (2)B-C△G8 amount of free energy that a given reaction can theo- Sum:A-C△a+△G2 retically deliver-an amount of energy that could realized only if a perfectly efficient device were avail- This principle of bioenergetics explains how a ther modynamically unfavorable(endergonic)reaction can able to trap or harness it. Given that no such device is be driven in the forward direction by coupling it to possible(some free energy is always lost to entropy aur a highly exergonic reaction through a common inter- ing any process), the amount of work done by the re- action at constant temperature and pressure is always mediate. For example, the synthesis of glucose 6- less than the theoretical amount phosphate is the first step in the utilization of glucose Another important point is that some thermody namically favorable reactions(that is, reactions for Glucose + Pi- glucose 6-phosphate H2O which AG is large and negative) do not occur at meas- △G°=138kJ/mol

DG and DG for any reaction A B 34 C D are related by the equation G  G RT ln  [ [ C A ] ] [ [ D B] ]  (13–3) in which the terms in red are those actually prevail￾ing in the system under observation. The concentration terms in this equation express the effects commonly called mass action, and the term [C][D]/[A][B] is called the mass-action ratio, Q. As an example, let us sup￾pose that the reaction A B 34 C D is taking place at the standard conditions of temperature (25 C) and pressure (101.3 kPa) but that the concentrations of A, B, C, and D are not equal and none of the components is present at the standard concentration of 1.0 M. To de￾termine the actual free-energy change, G, under these nonstandard conditions of concentration as the reaction proceeds from left to right, we simply enter the actual concentrations of A, B, C, and D in Equation 13–3; the values of R, T, and G are the standard values. G is negative and approaches zero as the reaction proceeds because the actual concentrations of A and B decrease and the concentrations of C and D increase. Notice that when a reaction is at equilibrium—when there is no force driving the reaction in either direction and G is zero—Equation 13–3 reduces to 0  G  G RT ln [ [ C A ] ] e e q q [ [ D B] ] e e q q or G  RT ln K eq which is the equation relating the standard free-energy change and equilibrium constant given earlier. The criterion for spontaneity of a reaction is the value of G, not G . A reaction with a positive G can go in the forward direction if G is negative. This is possible if the term RT ln ([products]/[reactants]) in Equation 13–3 is negative and has a larger absolute value than G . For example, the immediate removal of the products of a reaction can keep the ratio [prod￾ucts]/[reactants] well below 1, such that the term RT ln ([products]/[reactants]) has a large, negative value. G and G are expressions of the maximum amount of free energy that a given reaction can theo￾retically deliver—an amount of energy that could be realized only if a perfectly efficient device were avail￾able to trap or harness it. Given that no such device is possible (some free energy is always lost to entropy dur￾ing any process), the amount of work done by the re￾action at constant temperature and pressure is always less than the theoretical amount. Another important point is that some thermody￾namically favorable reactions (that is, reactions for which G is large and negative) do not occur at meas￾urable rates. For example, combustion of firewood to CO2 and H2O is very favorable thermodynamically, but firewood remains stable for years because the activation energy (see Figs 6–2 and 6–3) for the combustion re￾action is higher than the energy available at room tem￾perature. If the necessary activation energy is provided (with a lighted match, for example), combustion will be￾gin, converting the wood to the more stable products CO2 and H2O and releasing energy as heat and light. The heat released by this exothermic reaction provides the activation energy for combustion of neighboring regions of the firewood; the process is self-perpetuating. In living cells, reactions that would be extremely slow if uncatalyzed are caused to proceed, not by sup￾plying additional heat but by lowering the activation en￾ergy with an enzyme. An enzyme provides an alternative reaction pathway with a lower activation energy than the uncatalyzed reaction, so that at room temperature a large fraction of the substrate molecules have enough thermal energy to overcome the activation barrier, and the re￾action rate increases dramatically. The free-energy change for a reaction is independent of the pathway by which the reaction occurs; it depends only on the nature and concentration of the initial reactants and the final products. Enzymes cannot, therefore, change equi￾librium constants; but they can and do increase the rate at which a reaction proceeds in the direction dictated by thermodynamics. Standard Free-Energy Changes Are Additive In the case of two sequential chemical reactions, A 34 B and B 34 C, each reaction has its own equilibrium constant and each has its characteristic standard free￾energy change, G1 and G2 . As the two reactions are sequential, B cancels out to give the overall reaction A 34 C, which has its own equilibrium constant and thus its own standard free-energy change, G total. The G values of sequential chemical reactions are additive. For the overall reaction A 34 C, G total is the sum of the individual standard free-energy changes, G1 and G2 , of the two reactions: G total  G1 G2 . (1) A88nB G1 (2) B88nC G2 Sum: A88nC G1 G2 This principle of bioenergetics explains how a ther￾modynamically unfavorable (endergonic) reaction can be driven in the forward direction by coupling it to a highly exergonic reaction through a common inter￾mediate. For example, the synthesis of glucose 6- phosphate is the first step in the utilization of glucose by many organisms: Glucose Pi 88n glucose 6-phosphate H2O G  13.8 kJ/mol 494 Chapter 13 Principles of Bioenergetics

13.1 Bioenergetics and Thermodynamics 495 The positive value of AG predicts that under standard cose 6-phosphate synthesis, the Keg for formation of conditions the reaction will tend not to proceed spon- glucose 6-phosphate has been raised by a factor of about taneously in the direction written. Another cellular re- 2 X 105 action, the hydrolysis of ATP to ADP and Pi, is very This common-intermediate strategy is employed by exergonIc all living cells in the synthesis of metabolic intermediates ATP+H2O→ADP+P1△G°=-30.5 kJ/mol and cellular components. Obviously, the strategy works only if compounds such as ATP are continuously avail These two reactions share the common intermediates able In the following chapters we consider several of the Pi and H20 and may be expressed as sequential reac- most important cellular pathways for producing ATP. tions. (1) Glucose+P→→ glucose6; phosphate+H2O SUMMARY 13. 1 Bioenergetics and Thermodynamics (2)ATP+H2O→ADP+P Sum: ATP glucose- ADP glucose 6-phosphate a Living cells constantly perform work. They require energy for maintaining their highly The overall standard free-energy change is obtained by organized structures, synthesizing cellular adding the△。 values for individual reactions components, generating electric currents, and △G°=13.8 kJ/mol+(-30.5kJmo=-167 kJ/mol other The overall reaction is exergonic. In this case, energy a Bioenergetics is the quantitative study of stored in ATP is used to drive the synthesis of glucose energy relationships and energy conversions in 6-phosphate, even though its formation from glucose biological systems. Biological energy and inorganic phosphate(P) is endergonic. The path transformations obey the laws of way of glucose 6-phosphate formation by phosphory transfer from ATP is different from reactions(1)and I All chemical reactions are influenced by two (2)above, but the net result is the same as the sum of forces: the tendency to achieve the most stable the two reactions. In thermodynamic calculations, all bonding state(for which enthalpy, H, is a that matters is the state of the system at the beginning useful expression) and the tendency to achieve of the process and its state at the end; the route be- the highest degree of randomness, expressed tween the initial and final states is immaterial entropy, S. The net driving force in We have said that△c° is a way of expressing the reaction is AG, the free-energy change, which equilibrium constant for a reaction. For reaction(1) represents the net effect of these two factors △G=△H-T△S Kn=厘g9=39×10x a The standard transformed free-energy change AG is a physical constant that is Notice that H20 is not included in this expression, as its haracteristic for a given reaction and can be concentration(55.5 M)is assumed to remain unchanged calculated from the equilibrium constant for the reaction:△G°=- RTIn ke by the reaction. The equilibrium constant for the hy drolysis of ATP is ■ The actual free-energy change.,△G,is variable that depends on△C° and on the =20×105M concentrations of reactants and products ATP △G=△G°+RTin( products reactants The equilibrium constant for the two coupled reactions ■When△ G is large and negative, the reaction tends to go in the forward direction; when AG Glucose 6-phosphate ADPIIPi is large and positive, the reaction tends to go in the reverse direction and when Ag=0. the system is at equilibrium =(Kn)(K)=(39×10-3M-)(20×10°M0 a The free-energy change for a reaction is his calculation illustrates an important point about reaction occurs. Free-energy changes are equilibrium constants: although the AG values for two additive: the net chemical reaction that results reactions that sum to a third are additive, the Keg for from successive reactions sharing a common a reaction that is the sum of two reactions is the prod intermediate has an overall free-energy change uctof their individual Kea values. Equilibrium constant that is the sum of the ag values for the are multiplicative. By coupling ATP hydrolysis to glu individual reactions

The positive value of G predicts that under standard conditions the reaction will tend not to proceed spon￾taneously in the direction written. Another cellular re￾action, the hydrolysis of ATP to ADP and Pi , is very exergonic: ATP H2O 88n ADP Pi G  30.5 kJ/mol These two reactions share the common intermediates Pi and H2O and may be expressed as sequential reac￾tions: (1) Glucose Pi 88n glucose 6-phosphate H2O (2) ATP H2O 88n ADP Pi Sum: ATP glucose 88n ADP glucose 6-phosphate The overall standard free-energy change is obtained by adding the G values for individual reactions: G  13.8 kJ/mol (30.5 kJ/mol)  16.7 kJ/mol The overall reaction is exergonic. In this case, energy stored in ATP is used to drive the synthesis of glucose 6-phosphate, even though its formation from glucose and inorganic phosphate (Pi ) is endergonic. The path￾way of glucose 6-phosphate formation by phosphoryl transfer from ATP is different from reactions (1) and (2) above, but the net result is the same as the sum of the two reactions. In thermodynamic calculations, all that matters is the state of the system at the beginning of the process and its state at the end; the route be￾tween the initial and final states is immaterial. We have said that G is a way of expressing the equilibrium constant for a reaction. For reaction (1) above, K eq1   3.9 103 M1 Notice that H2O is not included in this expression, as its concentration (55.5 M) is assumed to remain unchanged by the reaction. The equilibrium constant for the hy￾drolysis of ATP is K eq2  [A [ D A P T ] P [P ] i ]  2.0 105 M The equilibrium constant for the two coupled reactions is K eq3   (K eq1 )(K eq2 )  (3.9 103 M1 ) (2.0 105 M)  7.8 102 This calculation illustrates an important point about equilibrium constants: although the G values for two reactions that sum to a third are additive, the K eq for a reaction that is the sum of two reactions is the prod￾uct of their individual K eq values. Equilibrium constants are multiplicative. By coupling ATP hydrolysis to glu- [glucose 6-phosphate][ADP][Pi ] [glucose][Pi][ATP]  [glucose 6-phosphate] [glucose][Pi] cose 6-phosphate synthesis, the K eq for formation of glucose 6-phosphate has been raised by a factor of about 2 105 . This common-intermediate strategy is employed by all living cells in the synthesis of metabolic intermediates and cellular components. Obviously, the strategy works only if compounds such as ATP are continuously avail￾able. In the following chapters we consider several of the most important cellular pathways for producing ATP. SUMMARY 13.1 Bioenergetics and Thermodynamics ■ Living cells constantly perform work. They require energy for maintaining their highly organized structures, synthesizing cellular components, generating electric currents, and many other processes. ■ Bioenergetics is the quantitative study of energy relationships and energy conversions in biological systems. Biological energy transformations obey the laws of thermodynamics. ■ All chemical reactions are influenced by two forces: the tendency to achieve the most stable bonding state (for which enthalpy, H, is a useful expression) and the tendency to achieve the highest degree of randomness, expressed as entropy, S. The net driving force in a reaction is G, the free-energy change, which represents the net effect of these two factors: G  H  T S. ■ The standard transformed free-energy change, G , is a physical constant that is characteristic for a given reaction and can be calculated from the equilibrium constant for the reaction: G  RT ln K eq. ■ The actual free-energy change, G, is a variable that depends on G and on the concentrations of reactants and products: G  G RT ln ([products]/[reactants]). ■ When G is large and negative, the reaction tends to go in the forward direction; when G is large and positive, the reaction tends to go in the reverse direction; and when G  0, the system is at equilibrium. ■ The free-energy change for a reaction is independent of the pathway by which the reaction occurs. Free-energy changes are additive; the net chemical reaction that results from successive reactions sharing a common intermediate has an overall free-energy change that is the sum of the G values for the individual reactions. 13.1 Bioenergetics and Thermodynamics 495