Enzymes speed up the rate of chemical reactions, but the properties of the reaction—whether it can take place at all and the degree to which the enzyme accelerates the reaction—depend on energy differences between reactants and products. Gibbs free energy (G), which was touched on in Chapter 1, is a thermodynamic property that is a measure of useful energy, or the energy that is capable of doing work. To understand how enzymes operate, we need to consider only two thermodynamic properties of the reaction: (1) the free-energy difference (ΔG) between the products and reactants and (2) the energy required to initiate the conversion of reactants into products. The former determines whether the reaction will take place spontaneously, whereas the latter determines the rate of the reaction. Enzymes affect only the latter. Let us review some of the principles of thermodynamics as they apply to enzymes.

As discussed in Chapter 1, the free-energy change of a reaction (ΔG) tells us if the reaction can take place spontaneously:

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As for any reaction, we need to be able to determine ΔG for an enzyme-catalyzed reaction to know whether the reaction is spontaneous or requires an input of energy. To determine this important thermodynamic parameter, we need to take into account the nature of both the reactants and the products as well as their concentrations.

Consider the reaction

The ΔG of this reaction is given by

in which ΔG° is the standard free-energy change, R is the gas constant, T is the absolute temperature, and [A], [B], [C], and [D] are the molar concentrations (more precisely, the activities) of the reactants. ΔG° is the free-energy change for this reaction under standard conditions—that is, when each of the reactants A, B, C, and D is present at a concentration of 1.0 M (for a gas, the standard state is usually chosen to be 1 atmosphere). Thus, the ΔG of a reaction depends on the nature of the reactants (expressed in the ΔG° term of equation 1) and on their concentrations (expressed in the logarithmic term of equation 1).

A convention has been adopted to simplify free-energy calculations for biochemical reactions. The standard state is defined as having a pH of 7. Consequently, when H⁺ is a reactant, its activity has the value 1 (corresponding to a pH of 7) in equations 1 and 3 (below). The activity of water also is taken to be 1 in these equations. The standard free-energy change at pH 7, denoted by the symbol ΔG°′, will be used throughout this book. The kilojoule (abbreviated kJ) and the kilocalorie (kcal) will be used as the units of energy. One kilojoule is equivalent to 0.239 kilocalorie.

A simple way to determine ΔG°′ is to measure the concentrations of reactants and products when the reaction has reached equilibrium. At equilibrium, there is no net change in reactants and products; in essence, the reaction has stopped and ΔG = 0. At equilibrium, equation 1 then becomes

and so

The equilibrium constant under standard conditions, is defined as

Substituting equation 4 into equation 3 gives

which can be rearranged to give

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Substituting R = 8.315 × 10⁻³ kJ mol⁻¹ deg⁻¹ and T = 298 K (corresponding to 25° C) gives

where ΔG°′ is here expressed in kilojoules per mole because of the choice of the units for R in equation 7. Thus, the standard free energy and the equilibrium constant of a reaction are related by a simple expression. For example, an equilibrium constant of 10 gives a standard free-energy change of −5.69 kJ mol⁻¹ (−1.36 kcal mol⁻¹) at 25° C (Table 8.3). Note that, for each 10-fold change in the equilibrium constant, the ΔG°′ changes by 5.69 kJ mol⁻¹ (1.36 kcal mol⁻¹).

As an example, let us calculate ΔG°′ and ΔG for the isomerization of dihydroxyacetone phosphate (DHAP) to glyceraldehyde 3-phosphate (GAP). This reaction takes place in glycolysis (Chapter 16). At equilibrium, the ratio of GAP to DHAP is 0.0475 at 25°C (298 K) and pH 7. Hence, . The standard free-energy change for this reaction is then calculated from equation 5:

Under these conditions, the reaction is endergonic. DHAP will not spontaneously convert into GAP.

Now let us calculate ΔG for this reaction when the initial concentration of DHAP is 2 × 10⁻⁴ M and the initial concentration of GAP is 3 × 10⁻⁶ M. Substituting these values into equation 1 gives

This negative value for the ΔG indicates that the isomerization of DHAP to GAP is exergonic and can take place spontaneously when these species are present at the preceding concentrations. Note that ΔG for this reaction is negative, although ΔG°′ is positive. It is important to stress that whether the ΔG for a reaction is larger, smaller, or the same as ΔG°′ depends on the concentrations of the reactants and products. The criterion of spontaneity for a reaction is ΔG, not ΔG°′. This point is important because reactions that are not spontaneous based on ΔG°′ can be made spontaneous by adjusting the concentrations of reactants and products. This principle is the basis of the coupling of reactions to form metabolic pathways (Chapter 15).

Because enzymes are such superb catalysts, it is tempting to ascribe to them powers that they do not have. An enzyme cannot alter the laws of thermodynamics and consequently cannot alter the equilibrium of a chemical reaction. Consider an enzyme-catalyzed reaction, the conversion of substrate, S, into product, P. Figure 8.2 shows the rate of product formation with time in the presence and absence of enzyme. Note that the amount of product formed is the same whether or not the enzyme is present but, in the present example, the amount of product formed in seconds when the enzyme is present might take hours (or centuries, see Table 8.1) to form if the enzyme were absent.

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Why does the rate of product formation level off with time? The reaction has reached equilibrium. Substrate S is still being converted into product P, but P is being converted into S at a rate such that the amount of P present stays the same.

Let us examine the equilibrium in a more quantitative way. Suppose that, in the absence of enzyme, the forward rate constant (k_F) for the conversion of S into P is 10⁻⁴ s⁻¹ and the reverse rate constant (k_R) for the conversion of P into S is 10⁻⁶ s⁻¹. The equilibrium constant K is given by the ratio of these rate constants:

The equilibrium concentration of P is 100 times that of S, whether or not enzyme is present. However, it might take a very long time to approach this equilibrium without enzyme, whereas equilibrium would be attained rapidly in the presence of a suitable enzyme (Table 8.1). Enzymes accelerate the attainment of equilibria but do not shift their positions. The equilibrium position is a function only of the free-energy difference between reactants and products.