Free Energy Is a Useful Thermodynamic Function for Understanding Enzymes

I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
8.2. Free Energy Is a Useful Thermodynamic Function for Understanding Enzymes
Some of the principles of thermodynamics were introduced in Chapter 1 notably the idea of free energy (G). To fully
understand how enzymes operate, we need to consider two thermodynamic properties of the reaction: (1) the free-energy
difference (∆ G) between the products and reactants and (2) the energy required to initiate the conversion of reactants to
products. The former determines whether the reaction will be spontaneous, whereas the later determines the rate of the
reaction. Enzymes affect only the latter. First, we will consider the thermodynamics of reactions and then, in Section 8.3,
the rates of reactions.
8.2.1. The Free-Energy Change Provides Information About the Spontaneity but Not
the Rate of a Reaction
As stated in Section 1.3.3, the free-energy change of a reaction (∆ G) tells us if the reaction can occur spontaneously:
1. A reaction can occur spontaneously only if ∆ G is negative. Such reactions are said to be exergonic.
2. A system is at equilibrium and no net change can take place if ∆ G is zero.
3. A reaction cannot occur spontaneously if ∆ G is positive. An input of free energy is required to drive such a reaction.
These reactions are termed endergonic.
Two additional points need to be emphasized. The ∆ G of a reaction depends only on the free energy of the products (the
final state) minus the free energy of the reactants (the initial state). The ∆G of a reaction is independent of the path (or
molecular mechanism) of the transformation. The mechanism of a reaction has no effect on ∆ G. For example, the ∆ G
for the oxidation of glucose to CO2 and H2O is the same whether it occurs by combustion in vitro or by a series of
enzyme-catalyzed steps in a cell. The ∆ G provides no information about the rate of a reaction. A negative ∆ G indicates
that a reaction can occur spontaneously, but it does not signify whether it will proceed at a perceptible rate. As will be
discussed shortly (Section 8.3), the rate of a reaction depends on the free energy of activation (∆ G ), which is largely
unrelated to the ∆ G of the reaction.
8.2.2. The Standard Free-Energy Change of a Reaction Is Related to the Equilibrium
Constant
As for any reaction, we need to be able to determine ∆ G for an enzymecatalyzed reaction in order to know whether the
reaction is spontaneous or an input of energy is required. 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 ∆ G of this reaction is given by
in which ∆ G° 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. ∆ G° is the freeenergy 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 ∆ G of a reaction depends on the
nature of the reactants (expressed in the ∆ G° term of equation 1) and on their concentrations (expressed in the
logarithmic term of equation 1).
Units of energyA calorie (cal) is equivalent to the amount of heat required to raise
the temperature of 1 gram of water from 14.5°C to 15.5°C.
A kilocalorie (kcal) is equal to 1000 cal.
A joule (J) is the amount of energy needed to apply a 1-newton force
over a distance of 1 meter.
A kilojoule (kJ) is equal to 1000 J.
1 kcal = 4.184 kJ
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 4 (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 ∆ G° will be used throughout this book. The kilocalorie (abbreviated kcal) and
the kilojoule (kJ) will be used as the units of energy. One kilocalorie is equivalent to 4.184 kilojoules.
The relation between the standard free energy and the equilibrium constant of a reaction can be readily derived. This
equation is important because it displays the energetic relation between products and reactants in terms of their
concentrations. At equilibrium, ∆ G = 0. Equation 1 then becomes
and so
The equilibrium constant under standard conditions, K eq, is defined as
Substituting equation 4 into equation 3 gives
which can be rearranged to give
Substituting R = 1.987 × 10-3 kcal mol-1 deg-1 and T = 298 K (corresponding to 25°C) gives
where ∆ G° is here expressed in kilocalories 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 -1.36 kcal mol-1 (-5.69 kJ mol-1) at 25°C (Table 8.4).
Note that, for each 10-fold change in the equilibrium constant, the ∆ G° changes by 1.36 kcal mol-1 (5.69 kJ mol-1).
As an example, let us calculate ∆ G° and ∆ G for the isomerization of dihydroxyacetone phosphate (DHAP) to
glyceraldehyde 3-phosphate (GAP). This reaction takes place in glycolysis (Section 16.1.4). At equilibrium, the ratio of
GAP to DHAP is 0.0475 at 25°C (298 K) and pH 7. Hence, K eq = 0.0475. The standard free-energy change for this
reaction is then calculated from equation 6:
Under these conditions, the reaction is endergonic. DHAP will not spontaneously convert to GAP.
Now let us calculate ∆ G 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 ∆ G indicates that the isomerization of DHAP to GAP is exergonic and can occur
spontaneously when these species are present at the aforestated concentrations. Note that ∆ G for this reaction is
negative, although ∆ G ° is positive. It is important to stress that whether the ∆ G for a reaction is larger, smaller, or the
same as ∆ G° depends on the concentrations of the reactants and products. The criterion of spontaneity for a reaction is
∆ G, not ∆ G ° . This point is important because reactions that are not spontaneous based on ∆ G ° 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 14).
8.2.3. Enzymes Alter Only the Reaction Rate and Not the Reaction Equilibrium
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. This
inability means that an enzyme accelerates the forward and reverse reactions by precisely the same factor. Consider the
interconversion of A and B. Suppose that, in the absence of enzyme, the forward rate constant (k F) is 10-4 s-1 and the
reverse rate constant (k R) is 10-6 s-1. The equilibrium constant K is given by the ratio of these rate constants:
The equilibrium concentration of B is 100 times that of A, whether or not enzyme is present. However, it might take
considerable time to approach this equilibrium without enzyme, whereas equilibrium would be attained rapidly in the
presence of a suitable enzyme. 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.
I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
8.2. Free Energy Is a Useful Thermodynamic Function for Understanding Enzymes
Table 8.4. Relation between ∆ G° and K
DG°
K
kcal mol- kJ/mol1
1
6.82
28.53
5.46
22.84
4.09
17.11
2.73
11.42
1.36
5.69
102
0
-1.36
-2.73
0
-5.69
-11.42
103
-4.09
-17.11
104
-5.46
-22.84
105
-6.82
-28.53
eq
105
104
103
102
101
1
10
eq
(at 25°C)