Oncogenes, Tumor Suppressor Genes, and Programmed Cell Death:-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↔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
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, ΔG. 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, ΔG. 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 concentration of H+ is 10-7 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 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 ΔG0 and Keq) to distinguish them from the untransformed constants used by chemists and physicists. (Notice that most other text books use the symbol ΔG0 rather than ΔG0. Our use of ΔG0, 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 ΔG0.
Just as Keq 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 Keq and ΔG0:
ΔG0-=RT ln Keq
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 ΔG0 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 ΔG0 is negative. If Keq is less than 1.0, ΔG0 is positive. Because the relationship between ΔG0 and Keq is exponential, relatively small changes in ΔG0 correspond to large changes in Keq.
It may be helpful to think of the standard free energy change in another way. ΔG0 is the difference between the free-energy content of the products and the free-energy content of the reactants, under standard conditions. When ΔG0 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 ΔG0 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 ⇌ glucose 6-phosphate Chemical analysis shows that whether we start with, say, 20 mMglucose 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 mMglucose 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:
From this value of Keq we can calculate the standard free-energy change:
ΔG0=- RT ln Keq
=- (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 glucose 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), ΔG0 has the same magnitude but the opposite sign.
Table 13–4 gives the standard free-energy changes for some representative chemical reactions. Note that hydrolysis of simple esters, amides, peptides, and glycosides, 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
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.
