Free energy and chemical equilibrium:

G < 0, spontaneous; G > 0, not spontaneous; G = 0, at equilibrium

A + B <==> C + D

Equilibrium exists when the rate of forward reaction equals that of the reverse reaction.

In isolated systems at equilibrium, concentrations do not change with time.

Caution: Biochemists, however, must distinguish between equilibrium and steady state because living systems are not isolated (or closed) systems

Example of steady state: A_o --> A + B <==> C + D --> D'

Ao is a nutrient entering the cell and D' is a waste product being released. In this case ABCD are not at equilibrium, even though their concentrations do not change with time, because they are part of an open system.

G = G^o + RT ln [C][D]/[A][B] for A + B <==> C + D

At equilibrium G = 0 therefore G^o = -RT ln [C][D]/[A][B]

but [C][D]/[A][B] = K_eq therefore G^o = -RT ln K_eq

So knowing the concentrations of substances at equilibrium (these are easy to measure, because concentrations are not changing) allows for the calculation of K_eq and the standard free energy change = G^o

If, however, we examine conditions in the cell at any one instant, we can determine how far away from equilibrium the system lies and in which direction it is likely to move. (The concentrations of reactants and products may or may not be changing, but they can not be equilibrium concentrations or the cell would be dead.)

Sample calculation:

glucose 1-phosphate   <==>   glucose 6-phosphate

                    phosphoglucomutase

This reaction is reversible:

If one starts with 0.02 M G-1-P and adds enzyme, the final concentrations (at equilibrium) will be 0.001 M G-1-P and 0.019 G-6-P; if one starts with 0.02 M G-6-P, the final concentrations will also be 0.001 M G-1-P and 0.019 G-6-P! (In fact, this is one way to determine whether a reaction is a equilibrium.)

K_eq = [G-6-P ]/[ G-1-P ] 0.019/0.001 = 19 at pH 7 and 25 C

G^o' = -RT ln K_eq from above

Substituting:
G^o' = -8.314 J/omol x 298 x ln 19 = -7,295 J/mol or -7.3 kJ/mol

Therefore conversion of glucose 1-phosphate to glucose 6-phosphate is exergonic. (Why is this reasonable from a chemical point of view?)

Coupled reactions:

The thermodynamic secret of living systems is chemically coupling spontaneous reactions to those that are not.

Individual reactions may have unfavorable free energy (i.e. won't go to completion), but combined reactions must have favorable free energies.

Can drive reactions in one direction by removing products and keeping them far from equilibrium (LeChatellier's principle).

Example:

ATP   <===>  ADP  +   Pi           DG  = -31 kJ/mol

glucose  +    Pi  <===>  glucose-6-phosphate   DG  = +14 kJ/mol
glucose  +   ATP    <===>  glucose-6-phosphate   +  ADP     DG  = -17 kJ/mol

In living systems, the driving reaction often involves the hydrolysis of high energy phosphates:

Compound Free energy change (hydrolysis)

1. phosphoenolpyruvate - 62 kJ/mol
2. 1,3 Bis-phosphoglycerate - 49
3. creatine phosphate - 43
4. pyrophosphate - 33 (acid anhydride)
5. ATP --> ADP --> AMP - 31 (acid anhydride)
6. AMP --> adenosine - 14 (ester)
7. glycerol phosphate - 10 (ester)

Why does ATP have so much free energy of hydrolysis?

1. phosphate has large number of resonance structures
2. hydration of products of hydrolysis (especially if both are charged)
3. electrostatic repulsion between products (charged)
4. enhanced resonance structures for other product

Metastability:

ATP is a metastable compound because it has a high free energy of hydrolysis, or is thermodynamically unstable, but is kinetically stable (only very slowly hydrolyzed in absence of catalyst)