Reading:

a) W.B. Wood, J.H. Wilson, R.M. Benbow & L.W. Hood, Biochemistry: A Problems Approach - pages 175-191.

b) D. White, The Physiology & Biochemistry of Prokaryotes, Ch. 7, pp 141-154.

Free Energy and the Laws of Thermodynamics

The synthesis of macromolecules, the transport of solutes across membranes, flagellar motion, etc., all require an input of energy. Energy is released by the breakdown of food molecules such as glucose. Since energy can neither be created nor destroyed, the energy consumed in synthesizing a complex molecule must be released by its breakdown.

FIRST LAW OF THERMODYNAMICS

Energy is neither created nor destroyed. (It may be interconverted with mass, though not in bacteria!)

SECOND LAW OF THERMODYNAMICS

Entropy always increases in a closed system.

Free energy, DeltaG, is the energy available to do useful work (at constant temperature and pressure). However, not all the released energy can be used to perform useful work (whether for chemical synthesis or mechanical motion). Of the total energy (=DeltaH), some of the energy (= TDeltaS) is always lost.

DeltaG = DeltaH - T DeltaS

DeltaG = free energy change

DeltaH = change in enthalpy, or heat content, in calories/mole

T = temp in K° (= C° + 273)

DeltaS = entropy in cal deg-1 (or entropy unit)

T DeltaS is therefore the energy lost as entropy. Entropy is a measure of randomness, and the universe tends to disorder. To reverse disorder, energy must come in from some outside source.

Reactions for which DeltaG is negative release energy and therefore tend to proceed. If DeltaG is positive reactions do not occur unless they are driven by an input of energy. If DeltaG = 0 the system is at equilibrium.

DG Is Related To The Equilibrium Constant

Consider the reaction: A + B = C + D

At any point in time we can measure the amount of each molecule and calculate the ratio, K:

K = [C] [D] = Products

[A] [B] Reactants

Delta G = Delta G° + RT ln K (at constant temperature and pressure)

Delta G° = Standard free energy change - for unit molarity, and standard temperature (25°C = 298°K) and pressure (1 atm).

1n x = 2.303 log x

R = gas constant (1.987 cal K-1 mole-1) and RT = approximately 0.6 kcal K-1 mole-1 at 25°C

When equilibrium has been reached, K becomes Keq, the equilibrium constant, which is the final ratio of products to reactants. At equilibrium, energy is neither released or consumed, so DeltaG = 0. Therefore:

DeltaG° = -RT 1n Keq

Note that if DeltaG° is positive a reaction can still proceed provided that temperature, pressure or concentration are altered so that DeltaG is negative. Thus DeltaG determines what actually happens, DeltaG° refers to a standard state. For example consider the hydrolysis of ATP = ADP + Pi

DeltaG° (at pH 7.5) = -7 kcal/mole (this refers to 1.0 Molar ATP)

DeltaG for 10mM ATP = -10 kcal/mole (10mM is more physiological)

If a reaction has DeltaG° = -1.2 kcal then Keq = 8.7

If a reaction has DeltaG° = -5.5 kcal then Keq = 10,000

Thus a relatively small negative DeltaG° gives a reasonable Keq in the forward direction. If DeltaG° is more negative than approximately 5.5 kcal, the reaction is essentially irreversible (i.e. Keq greater than 104). Note that the concentration of H2O in all reactions is omitted by convention, or formally we set [H2O] = 1. (H2O is actually 55Molar).

Compound	—DeltaG°´ (pH 7)
Valyl-tRNA (30°)	8,400
p-Nitrophenyl acetate	13,010
S-Acetylmercaptoacetate	7,200
Acetyl Coenzyme A	7,520
Acetoacetyl Coenzyme A	10,500
Acetyl phosphate	10,300
Phosphoenolpyruvate	14,800
Carbamyl phosphate (pH 9.5)	12,300
Creatine phosphate (37°)	10,300
Phosphoarginine (pH 8)	7,700
Adenosine triphosphate (to AMP & PPi)	7,700
Adenosine triphosphate (to ADP & Pi)	7,300
Pyrophosphate	8,000
Glucose-1-phosphate	5,000
Glucose-6-phosphate	3,300
Uridine diphosphate glucose (pH 7.5)	7,300
Acetyl adenylate	13,300
Peptides	ca 500
Glutamine	3,400
Acetylimidazole	12,970
Maltose	4,000
Sucrose (dihemiacetal)	7,000
Glycogen	4,000

DeltaG° itself is pH independent even if the reaction depends on pH. What this means is that if H+ or OH- are involved in the reaction, their concentrations must be included as part of Keq. Normally, data are standardized to neutrality for biochemistry:

DeltaG°´ = DeltaG° at pH 7.0 K´eq = Keq at pH 7.0

One confusing point is that chemists standardize to pH 7.0 whereas biochemists often standardize to pH 7.5 because this is approximately the pH inside a typical living cell. In practice, for most reactions, it makes little difference.

Coupled Reactions

DeltaG is additive for a series of reactions:

Then for A ==> D the total DeltaG = DeltaG1 + DeltaG2 + DeltaG3.

e.g. ATP + Glucose = Glucose-6P + ADP DeltaG°´ = -4.0 kcal

Glucose-6P + H2O = Glucose + Pi DeltaG°´ = -3.3 kcal

adding these two reactions:

ATP + H2O = ADP + Pi DeltaG°´ = -7.3 kcal

or consider:

ATP + H2O = ADP + Pi DeltaG°´ = -7.3 kcal

Acetyl-P + H2O = Acetate + Pi DeltaG°´ = -10.3 kcal

This allows us to predict that acetyl-P will tend to donate its phosphate to ADP since this reaction has an overall negative DeltaG°´.

High Energy Compounds

ATP is used by cells to drive many energy consuming reactions. It is a high energy compound, because it has a large negative free energy of hydrolysis under physiological conditions. Compounds with DeltaG more negative than 7 kcal/mole may be regarded as high energy compounds.

ATP is present in cells at 1 to 10mM, it is anionic, carrying four negative charges at pH 7.0, and is neutralized by complexing with Mg2+. ATP is sometimes described as the universal energy currency of living cells - an exaggeration. In bacteria such as E. coli, energy is provided by:

ATP - most biosynthetic reactions, some transport systems

GTP - e.g. protein synthesis

Thioesters - e.g. fatty acid synthesis

PEP - e.g. phosphotransferase system

Proton Motive Force - e.g. flagella, some transport systems

These other energy sources do not necessarily depend on ATP for their production. In fact, ATP may be generated from these other forms of energy.

Chemical Types Of High Energy Compound

1) Acid Anhydride Structures

Both X atoms may be carbon or both may be phosphorus or we may have one of each. Competing resonance applies to all three possibilities and can be illustrated using acetic anhydride. Although this molecule is not found in biology it is a high energy compound and releases about 7 kcal upon hydrolysis, like ATP.

In competing resonance both of the carbonyl groups are competing for the electrons on the single central oxygen. Obviously they cannot both win and only one resonance structure is possible. Suppose we hydrolyse acetic anhydride into two molecules of acetate then we get:

Now each carbonyl can resonate and we have four total resonance structures. This is more stable and so energy is released upon hydrolysis.

Phosphoric anhydrides (e.g. ATP, pyrophosphate) have two phosphorus atoms, and these are pentavalent so they have an extra oxygen attached to each of them. However, the same principle of competing resonance applies. Note that the first phosphate of ATP is an ester bonded phosphate and this is NOT a high energy bond. The outer two phosphates are linked by high energy phosphoric anhydride linkages.

Carboxylic-phosphoric mixed anhydrides have one X = phosphorus and one X = carbon and include acyl phosphates such as acetyl phosphate and acyl adenylates, such as the amino acid adenylates made as precursors for protein synthesis.

Another factor is electrostatic repulsion. This applies to ATP and other multiple anions, but not to acyl phosphates and adenylates where there is only a single negatively charged group. Splitting apart multiple phosphates relieves the strain due to repulsion of several negative charges.

2) Enol Phosphates Phosphenol pyruvate (PEP) is a high energy phosphate, but for a completely different reason than ATP. PEP is formed in the glycolytic pathway and is used to synthesize ATP from ADP. It has a DeltaG° = -15 kcal (approximately twice that of ATP) and its reaction with ADP to form ATP is therefore essentially irreversible.

Two factors are important. Firstly the enol form of pyruvic acid is less stable than the keto form by approximately 10-12 kcal/mole. The phosphate can only exist as the high energy enol form. Thus when the phosphate group is removed, the pyruvate can revert back to the stable, low-energy keto form and the surplus energy is released.

Secondly, sp2 bonds are inherently less stable than sp3 bonds, i.e. an enol phosphate is less stable than an ordinary phosphate ester would be by about 3 kcal/mole.

3) Thiol Esters (thioesters). Especially thioesters of coenzyme A e.g. acetyl-CoA. The important factor is the diminished resonance interaction between the pi electrons of the sulfur atom and the carbonyl group (relative to the resonance in an oxygen ester). In other words, the sulfur will not form a double bond anywhere near as readily as an oxygen will.

4) Reduced Pyridine Nucleotides. Transfer of 2 electrons from NAD(P)H2 to O2 yields 40 kcal/mole and this is employed for the synthesis of 3 moles of ATP via the electron transport chain (to be discussed later).

Activation Energy

Even if DeltaG is negative and a reaction can in theory proceed, it may not actually do so. Although DeltaG predicts the final equilibrium, it does not reveal the rate of reaction. Reactions usually go via transition states. The pathway for a simple reaction with only one transition state is as shown:

The energy of reaction, DeltaG, is the difference in free energy between the products and reactants. The transition state energy, DeltaG*, is the difference in free energy between the transition state and reactants. It is the energy needed to prime the reaction and is released once the reaction is over. If DeltaG* is zero (or negative) the reaction is spontaneous and fast. If DeltaG* is positive (as shown), the reaction is slow.

The energy of individual molecules of reactant varies according to the normal distribution (Boltzmann's distribution). Molecules with energy greater than G* (* refers to transition state) can proceed over the energy barrier and react. The rate of reaction is proportional to the concentration of the transition state intermediate and hence to the number of molecules with energy greater than G*.

There are two ways to increase the rate of a reaction: 1) The input of energy, usually as heat, increases the proportion of reactive molecules. 2) Catalysis which operates by lowering the transition state energy.

Catalysts may provide alternative reaction pathways of lower energy or stabilize (i.e. reduce the energy) of the original transition state intermediate. Enzymes are sophisticated catalysts designed to speed up biologically important reactions at physiological temperatures.

Oxidation-Reduction Reactions

Apart from photosynthesis, all organisms derive their energy by means of oxidation-reduction (redox) reactions. Remember:

Oxidation = loss of electrons or hydrogen

Reduction = gain of electrons or hydrogen

The redox potential (E) measures the tendency of a substance to donate or accept electrons. E is measured in volts. The standard redox potential Eo´ refers to standard conditions (all reactants at 1.0 Molar; 1 atm pressure; pH 7.0; 25°C or 298°K - as for DeltaG°´). Redox potentials are given for half reactions, written by convention in the order:

electron acceptor + e- = electron donor
(oxidized) (reduced)

Values are given relative to the standard electrode which is 1.0 molar H+ ions in equilibrium with H2 gas at 1 atm pressure and by definition has Eo = 0. Note that the pH is NOT 7, but pH 0 due to the 1.0 molar acid. At pH 7, Eo becomes Eo´ and for H2/H+ this is -420mV, no longer zero.

Energetics of Redox Reactions

A complete redox reaction consists of two half reactions. The difference in the two Eo' values (the DeltaE) tells whether or not the reaction will go in the direction written. The greater the DeltaE between two pairs, the greater the release of free energy which the cell may use (e.g. to synthesize ATP). The half reaction with the more negative Eo´ will donate electrons (i.e. act as the reducing agent) and should be written in reverse to pair it with its partner. For example:

NAD+ + 2H+ + 2e- = NADH + H+ Eo´ = -320mV

Pyruvate + 2H+ + 2e- = Lactate Eo´ = -190mV

a) Reverse the NAD+/NADH half reaction as it has the more negative Eo´

NADH + H+ = NAD+ + 2H+ + 2e-

b) Now add in the pyruvate/lactate half reaction:

NADH + H+ + Pyruvate + 2H+ + 2e- = NAD+ + 2H+ + 2e- + Lactate

c) Cancel out those items on both sides:

NADH + H+ + Pyruvate = NAD+ + Lactate

d) Compute the DeltaE:

DeltaEo´ = Eo´ (Acceptor half reaction) – Eo´ (Donor half reaction)

DeltaEo´ = Eo´ (pyruvate/lactate) – Eo´ (NAD+/NADH)

DeltaEo´ = (-190) - (-320) = 130 millivolts or 0.13 volts

If DeltaE is positive the reaction will go forward. A positive DeltaE corresponds to a negative DeltaG and the two may be interconverted by:

DeltaG°´ = –nFDeltaEo´

F = Faradays constant = 23 kcal/volt.

n = number of electrons transferred; n = 2 for the reaction above as in most biological reactions.

Thus DeltaG°´ = –2(23)(0.13) = –5.98 kcal/mole

However, DeltaG°´ and DeltaEo´ are for standard conditions but for an actual reaction, what matters is DeltaG and DeltaE. The actual redox potential is given by the Nernst equation:

E = Eo´ + 2.303RT log [electron acceptor]

nF [electron donor]

To decide which direction an actual redox reaction will go:

1) look up the two Eo´ values in the table

2) convert each to E by Nernst equation

[at 298°K (i.e. 25°C) and for n = 2 then 2.303RT/nF = approximately 0.3]

3) subtract E1 from E2 to give DeltaE

4) convert to DeltaG = –nFDeltaE as for DeltaG°´ and DeltaEo´

 

Standard reduction potentials for systems of biochemical importance

	Eo´ (pH7) volts
Oxygen/water	0.816
Ferric/ferrous	0.77
Nitrate/nitrite	0.42
Ferricyanide/ferrocyanide	0.36
Oxygen/hydrogen peroxide	0.30
Cytochrome a; ferric/ferrous	0.29
Cytochrome c; ferric/ferrous	0.25
Cytochrome b2; ferric/ferrous	0.12
Ubiquinone; ox/red	0.10
Dehydroascorbic acid/ascorbic acid	0.06
Fumarate/succinate	0.03
Methylene blue, ox/red	0.01
Pyruvate + ammonium/alanine	-0.13
alpha-Oxoglutarate + ammonium/glutamate	-0.14
Oxalacetate/malate	-0.17
Pyruvate/lactate	-0.19
Acetaldehyde/ethanol	-0.20
Riboflavin, ox/red	-0.21
Glutathione, ox/red	-0.23
Acetoacetate/beta-hydroxybutyrate	-0.27
Lipoic acid, ox/red	-0.29
NAD+/NADH	-0.32
Pyruvate/malate	-0.33
Cystine/cysteine	-0.34
Ferredoxin; ox/red	-0.41
Carbon dioxide/formate	-0.42
H+/H2	-0.42
Acetate/acetaldehyde	-0.60
succinate/alpha-oxoglutarate	-0.67
Acetate + carbon dioxide/pyruvate	-0.70