Biochemical Energetics

The free energy change (DG) of a reaction determines its spontaneity. The free energy change (DG), and its relation to equilibrium constant, are discussed on p. 57-59 of Biochemistry 3rd Edition by Voet & Voet. A reaction is spontaneous if DG is negative (if the free energy of the products is less than the free energy of the reactants).

DG = change in free energy,
DGo' = standard free energy change (with 1 M reactants and products, at pH 7),
R = gas constant, T = absolute temperature.
Note that the standard free energy change (DGo') of a reaction may be positive, for example, and the actual free energy change (DG) negative, depending on cellular concentrations of reactants and products. Many reactions for which DGo' is positive are spontaneous because other reactions cause depletion of products or maintenance of high substrate concentrations.
At equilibrium, DG equals zero. Solving for DGo' yields the relationship at left.K'eq, the ratio [C][D]/[A][B] at equilibrium, is called the equilibrium constant.
An equilibrium constant greater than one (more products than reactants at equilibrium) indicates a spontaneous reaction (negative DG�').
The variation of equilibrium constant with DGo' is shown in the table below.

KeqDGo' (kJ/mol)
Starting with 1 M reactants and products, the reaction:
104– 23proceeds forward (spontaneous)
102– 11proceeds forward (spontaneous)
100 = 10is at equilibrium
10–2+ 11proceeds in reverse
10–4+ 23proceeds in reverse
Energy coupling is discussed on p. 59-60 & 566-567.
  • A spontaneous reaction may drive a non-spontaneous reaction.
  • Free energy changes of coupled reactions are additive.
Examples of different types of coupling:
A. Some enzyme-catalyzed reactions are interpretable as two coupled half-reactions, one spontaneous and the other non-spontaneous. At the enzyme active site, the coupled reaction is kinetically facilitated, while the individual half-reactions are prevented. The free energy changes of the half-reactions may be summed, to yield the free energy of the coupled reaction.
For example, in the reaction catalyzed by the Glycolysis enzyme Hexokinase, the two half-reactions are:
  • ATP + H2O � ADP + Pi .................. DGo' = -31 kJoules/mol
  • Pi + glucose � glucose-6-P + H2O ... DGo' = +14 kJoules/mol
Coupled reaction: ATP + glucose � ADP + glucose-6-P .. DGo' = -17 kJoules/mol
The structure of the enzyme active site, from which water is excluded, prevents the individual hydrolytic reactions, while favoring the coupled reaction. 
B. Two separate enzyme-catalyzed reactions occurring in the same cellular compartment, one spontaneous and the other non-spontaneous, may becoupled by a common intermediate (reactant or product).
A hypothetical, but typical, example involving pyrophosphate:
  • enzyme 1: A + ATP � B + AMP + PPi ....DGo' = +15 kJ/mol
  • enzyme 2: PPi + H2O � 2 Pi ....................DGo' = –33 kJ/mol
Overall: A + ATP + H2O � B + AMP  +  2Pi ... DGo' = –18 kJ/mol
Pyrophosphate (PPi) is often the product of a reaction that needs a driving force. Its spontaneous hydrolysis, catalyzed by Pyrophosphatase enzyme, drives the reaction for which PPi is a product. For an example of such a reaction, see the discussion of cAMP formation below.
C. Ion transport may be coupled to a chemical reaction, e.g., hydrolysis or synthesis of ATP.In the diagram at right and below, water is not shown. It should be recalled that the ATP hydrolysis/synthesis reaction is ATP + H2O � ADP + Pi.
Equivalent to equation 20-3 on p. 727, the free energy change (electrochemical potential difference) associated with transport of an ion S across a membrane from side 1 to side 2 is represented below.
R = gas constant, T = temperature, Z = charge on the ion, F = Faraday constant, and DY = voltage across the membrane.
Since free energy changes are additive, the spontaneous direction for the coupled reaction will depend on the relative magnitudes of:
  • DG for the ion flux (DG varies with the ion gradient and voltage.)
  • DG for the chemical reaction (DGo' is negative in the direction of ATP hydrolysis. The magnitude of DG depends also on concentrations of ATP, ADP, and Pi .)
Two examples of such coupling are:1. Active transport. Spontaneous ATP hydrolysis (negative DG) is coupled to (drives) ion flux against a gradient (positive DG). For an example, see the discussion of SERCA.
2. ATP synthesis in mitochondria. Spontaneous H+ flux across a membrane (negative DG) is coupled to (drives) ATP synthesis (positive DG). See the discussion of the ATP Synthase.
"High Energy" Bonds
The structure of ATP is shown below at right (see also p. 566). Anhydride bonds (in red) link the terminal phosphates.
Phosphoanhydride bonds (formed by splitting out water between two phosphoric acids or between a carboxylic acid and a phosphoric acid) tend to have a large negative DG of hydrolysis, and are thus said to be "high energy" bonds. It is important to realize that the bond energy is not necessarily high, just the free energy of hydrolysis.
"High energy" bonds are often represented by the "~" symbol (squiggle), with ~P representing a phosphate group with a high free energy of hydrolysis.
Compounds with "high energy" bonds are said to have high group transfer potential. For example, Pi may be spontaneously removed from ATP for transfer to another compound (e.g., to a hydroxyl group on glucose).
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