Chemical equilibria

Considering the reaction:

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if solutions of A and B are mixed and an appropriate enzyme is added C and D will be formed. Once this happens the back reaction will also take place with the re-conversion of C + D to A + B. Net production of C and D proceeds until the concentrations of substrates and products have adjusted to values where the rate of the back reaction is equal to the rate of the forward reaction. At this point, there will be no further net formation of products and the reaction is said to have attained equilibrium.

The relative concentrations of reactants and products for a particular reaction at equilibrium is characteristic of that reaction and is defined by the equilibrium constant (K_eq). This is the product of the concentrations of products formed at equilibrium divided by the concentration of reactants remaining. Thus for the reaction given above:

Keq=[C]×[D][A]×[B]

Reactions have widely differing values of K_eq. Where K_eq is very large, the reaction proceeds until virtually all the initial reactants have been converted to products. Such reactions are described as irreversible or effectively irreversible. Where K_eq is very small, equilibrium is reached when only a small proportion of the initial reactants have been converted to products. Finally, for reactants with a value of K_eq near to 1, the reactants and products are present in nearly equal proportions at equilibrium and the reaction will proceed in either direction depending on the initial concentration of products and reactants.

Biochemists find it useful to employ a thermodynamic function termed Gibbs free energy (abbreviated to free energy or the symbol G) in the consideration of enzyme reactions. For present purposes, the free energy of a system may be described as the potential of that system for doing work at constant temperature and pressure. The free energy of a system is not measurable, but the free energy change (ΔG) which occurs during the conversion of substrate to products in an enzyme reaction can be quantified. The free energy change which occurs during a reaction is characteristic of that reaction if the reactants and products are initially present at standard concentrations. This standard free energy change (ΔG⁰) is defined as the free energy change which occurs when both substrate(s) and products(s) are initially present at a concentration of 1 M, and 1 mol of reactant is converted to 1 mol of product.

The standard free energy change of a reaction is related to the equilibrium constant as follows:

ΔG°=−RTlnKeq

where R is the gas constant and T is the absolute temperature.

Many reactions involve the production or removal of hydrogen ions. For this reason it is convenient to redefine the standard state to be at pH 7 rather than at pH 0 (i.e. 1 M H⁺). The standard free energy change at pH 7 is written ΔG⁰ and is related to the equilibrium constant at pH 7 (K_eq’) by the equation:

ΔG°′=−RTlnKeq’

Thus reactions with a high value of K_eq’ have a large negative standard free energy change, while reactions with a low K_eq’ have a large positive ΔG⁰’ For reactions with K_eq’ near 1, the standard free energy change is near zero. Values of K_eq’ together with the corresponding values of ΔG^0′ are given in Table 16.1.

Table 16.1

The numerical relationship between K_eq and ΔG⁰ at 25 °C

0·001 0·01 0·1

ATP (adenosine triphosphate)

ATP occurs in all cells and is a universal intermediate in cell energy metabolism. The structure of ATP is shown below. The base adenine is joined to C-1′ of ribose, the 5′ position of which is linked to a phosphate residue to form adenosine monophosphate (AMP). Addition of a second

ΔG=ΔG°′+RTln[C]×[D][A]×[B]

phosphate group to the first via an anhydride bond gives the compound adenosine diphosphate (ADP) while ATP is derived by the addition of a further phosphate again via an anhydride linkage. At pH 7·4 ATP bears four negative charges and forms a stable complex with Mg²⁺ ions.

ATP can be hydrolysed enzymically to ADP and inorganic phosphate:

ATP4−+H2O⇌ADP3−+phosphate2−+H+

The standard free energy change (ΔG⁰’) of this reaction is approximately −30 kJ mol⁻¹ and this is high relative to many other hydrolysis reactions (Table 16.2). The high standard free energy of hydrolysis of ATP arises in part from the fact that the products of the reaction, ADP and phosphate, both carry negative charges and hence tend to repel each other. Hydrolysis of the terminal phosphate–phosphate bond of ATP can be regarded as relieving some of the intramolecular strain caused by the presence of neighbouring negatively charged groups in the molecule.

Table 16.2

The standard free energy change (ΔG⁰’) of hydrolysis of some phosphate-containing compounds

Compound
Phosphoenolpyruvate	−53·5
1,3-Diphosphoglycerate	−49·5
Phosphocreatine	−44·0
ATP	−29·4
Glucose 1-phosphate	−21·0
Fructose 6-phosphate	−16·0
Glucose 6-phosphate	−13·8
3-Phosphoglycerate	−13·0
Glycerol 1-phosphate	−9·6

ATP can also undergo hydrolysis as follows:

ATP⇌AMP+pyrophosphate

The value of ΔG^0′ for this reaction is also −30 kJ mol⁻¹ Where this reaction occurs, the pyrophosphate is rapidly hydrolysed to phosphate by the enzyme pyrophosphatase:

Pyrophosphate + H₂O → 2 phosphate ΔG°’ = −30 kJ mol⁻¹

The overall effect of the combined reactions is the hydrolysis of the two terminal phosphate–phosphate bonds of ATP with the formation of AMP and two phosphate molecules. The value of ΔG^0′ for the overall reaction is then −60 kJ mol⁻¹.

The other nucleoside triphosphates UTP, CTP and GTP are also involved in certain biosynthetic reactions. These triphosphates are regenerated by transfer of the terminal phosphate group from ATP by the following transferase reactions:

ATP+GDP⇌ADP+GTPATP+UDP⇌ADP+UTPATP+CDP⇌ADP+CTP

The value of ΔG^0′ is approximately zero, i.e. the values of ΔG^0′ for hydrolysis for all the nucleoside triphosphates are similar so that the direction of the reaction depends on the relative concentrations of the reactants.

Since the hydrolysis of the terminal phosphate bond of ATP proceeds with a large negative standard free energy change, ATP is sometimes referred to as a high-energy compound, or, in older texts, as possessing high-energy bonds. It is important to realize that the function of ATP as an intermediate in energy metabolism depends on the fact that the value of ΔG for ATP hydrolysis at the concentrations of ATP, ADP and phosphate present in the cell, is large and negative, and this is the only sense in which the ‘high energy’ terminology should be understood. For example consider conditions under which ATP, ADP and phosphate are mixed at their equilibrium concentrations. Then the value of ΔG is zero and no energy could be obtained from the system, although ATP is still present.

Utilization of ATP

Biosynthetic reactions

Degradative and hydrolytic reactions in general have a large negative value of ΔG^0′. Consider for example the hydrolysis of the amino acid glutamine to glutamate and ammonium ions which is catalysed by the enzyme glutaminase:

Glutamine⇌gluamate+NH4+

ΔG^0′ for this reaction is −14·3 kJ mol⁻¹, i.e. the equilibrium position of the reaction lies far to the right. From the previous discussion, the value of AG for this reaction will be negative at physiological concentrations of glutamine and glutamate and the reaction will proceed in the direction of glutamine hydrolysis.

Under certain conditions it is necessary to synthesize glutamine from glutamate and ammonia. Free energy changes are additive, and glutamine is synthesized by using the free energy of ATP hydrolysis to reverse the glutamine hydrolysis reaction:

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