Bioenergetics.

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 (DG^o') 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 DG^o' 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 DG^o' is shown in the table below.

Keq	DGo' (kJ/mol)	Starting with 1 M reactants and products, the reaction:
104	– 23	proceeds forward (spontaneous)
102	– 11	proceeds forward (spontaneous)
100 = 1	0	is at equilibrium
10–2	+ 11	proceeds in reverse
10–4	+ 23	proceeds 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 + P_i .................. DG^o' = -31 kJoules/mol
• P_i + glucose « glucose-6-P + H₂O ... DG^o' = +14 kJoules/mol

Coupled reaction: ATP + glucose « ADP + glucose-6-P .. DG^o' = -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 be coupled by a common intermediate (reactant or product).
A hypothetical, but typical, example involving pyrophosphate:

• enzyme 1: A + ATP « B + AMP + PP_i ....DG^o' = +15 kJ/mol
• enzyme 2: PP_i + H₂O « 2 P_i ....................DG^o' = –33 kJ/mol

Overall: A + ATP + H₂O « B + AMP  +  2P_i ... DG^o' = –18 kJ/mol
Pyrophosphate (PP_i) is often the product of a reaction that needs a driving force. Its spontaneous hydrolysis, catalyzed by Pyrophosphatase enzyme, drives the reaction for which PP_i 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 (DG^o' is negative in the direction of ATP hydrolysis. The magnitude of DG depends also on concentrations of ATP, ADP, and P_i .)

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, P_i may be spontaneously removed from ATP for transfer to another compound (e.g., to a hydroxyl group on glucose).
Potentially two "high energy" bonds can be cleaved, as two phosphates are released by hydrolysis from ATP (adenosine triphosphate), yielding ADP (adenosine diphosphate), and ultimately AMP (adenosine monophosphate). This may be represented as follows (omitting waters of hydrolysis):

• AMP~P~P ® AMP~P + P_i   (ATP ® ADP + P_i)
• AMP~P ® AMP + P_i            (ADP  ® AMP + P_i)

Alternatively, as discussed above:

• AMP~P~P ® AMP + P~P_i    (ATP ® AMP + PP_i)
• P~P ® 2 P_i

ATP often serves as an energy source. Hydrolytic cleavage of one or both of the "high energy" bonds of ATP is coupled to an energy-requiring (non-spontaneous) reaction, as in the examples presented above.
AMP functions as an energy sensor and regulator of metabolism. When ATP production does not keep up with needs, a higher portion of a cell's adenine nucleotide pool is in the form of AMP. AMP then stimulatesmetabolic pathways that produce ATP.

• Some examples of this role involve direct allosteric activation of pathway enzymes by AMP. (E.g., activation of the Glycogen Phosphorylase enzyme by AMP will be discussed later.)
• Some regulatory effects of AMP are mediated by the enzyme AMP-Activated Protein Kinase. (For example the role of AMP-Activated Protein Kinase in stimulation of fatty acid catabolism by AMP will be discussed later.)

Artificial ATP analogs have been designed that are resistant to cleavage of the terminal phosphate by hydrolysis, e.g., AMPPNP, depicted at right.Such analogs have been used to study the dependence of coupled reactions on ATP hydrolysis. In addition, they have made it possible to crystallize an enzyme that catalyzes ATP hydrolysis with an ATP analog at the active site.

A reaction that is important for equilibrating ~P among adenine nucleotides within a cell is that catalyzed by Adenylate Kinase:

 ATP + AMP « 2 ADP

The Adenylate Kinase reaction is also important because the substrate for ATP synthesis, e.g., by the mitochondrial ATP Synthase, is ADP, while some cellular reactions dephosphorylate ATP all the way to AMP.
The enzyme Nucleoside Diphosphate Kinase (NuDiKi) equilibrates ~P among the various nucleotides that are needed, e.g., for synthesis of DNA and RNA. NuDiKi catalyzes reversible reactions such as:

ATP + GDP « ADP + GTP  ,   ATP + UDP « ADP + UTP  , etc.

Many organisms store energy as inorganic polyphosphate, a chain of many phosphate residues linked by phosphoanhydride bonds. It may be represented as: P~P~P~P~P... Hydrolysis of P_i residues from polyphosphate may be coupled to energy-dependent reactions. Depending on the organism or cell type, inorganic polyphosphate may have additional functions. For example, it may serve as a reservoir for P_i, a chelator of metal ions, a buffer, or a regulator.
Why do phosphoanhydride linkages have a high free energy of hydrolysis? Contributing factors for ATP and PP_i are thought to include:

• Resonance stabilization of the products of hydrolysis exceeds resonance stabilization of the compound itself. See Fig. 16-22 p. 568.
• Electrostatic repulsion between negatively charged phosphate oxygens favors separation of the phosphates.

Phosphocreatine (also called creatine phosphate), another compound with a "high energy" phosphate linkage, is used in nerve and muscle cells for storage of ~P bonds.Creatine Kinase catalyzes:   phosphocreatine + ADP « ATP + creatine This is a reversible reaction, though the equilibrium constant slightly favors phosphocreatine formation. Phosphocreatine is produced when ATP levels are high. When ATP is depleted during exercise in muscle, phosphate is transferred from phosphocreatine to ADP, to replenish ATP.

Phosphoenolpyruvate (PEP), involved in production of ATP in Glycolysis, has a larger negative DG of phosphate hydrolysis than ATP.Removal of phosphate from the ester linkage in PEP is spontaneous because the enol product spontaneously converts to a ketone.

The ester linkage in PEP is an exception. Generally phosphate esters, formed by splitting out water between a phosphoric acid and a hydroxyl group, have a low but negative DG of hydrolysis. Examples, shown below, include:

the linkage between the first phosphate and the ribose hydroxyl of ATP. the linkage between phosphate and a hydroxyl group in glucose-6-phosphate or glycerol-3-phosphate. the linkage between phosphate and the hydroxyl group of an amino acid residue in a protein (serine, threonine or tyrosine). Regulation of proteins by phosphorylation and dephosphorylation will be discussed later. An example mentioned above is AMP-Activated Protein Kinase.

ATP has special roles in energy coupling and phosphate transfer. The free energy of hydrolysis of phosphate from ATP is intermediate among the examples listed in the table below (more complete table p. 566). ATP can thus act as a phosphate donor, and ATP can be synthesized by transfer of phosphate from other compounds, such as phosphoenolpyruvate (PEP).