Physicists use ergs or Joules as units.

10⁷ ergs = 1 Joule

Some biochemists still use calories. 1 calorie is the amount of energy necessary to raise 1.00 g of water at 1 atm pressure from 15° to 16°C. Do not confuse calories with Calories (nutritional).

 1 calorie = 4.184 Joules

1 Calorie = 10³ calories = 1 kcal = 4.184 kJ

The laws governing the formation and utilization of energy for biological systems is the same as for the physical universe. They are called the first and second laws of thermodynamics. 

First Law.

In any physical or chemical change, the total amount of energy in the universe remains constant.

"Universe" is the system being studied plus its surroundings. For practical purposes, we can limit our definition to the planet earth when discussing bioenergetics. In simple terms, the first law states that energy can't be created or destroyed. It can be transformed, concentrated, diffused and used. 

At each step, the energy is converted to a different form of energy and some of the energy is lost as heat. As a consequence, biochemical efficiency is less than 100%.

Mechanical engines also convert energy from one form to another, thereby producing work. However they utilize a temperature or pressure gradient within the system as part of the mechanism. Biological systems are isothermal and isobaric.

What drives biochemical reactions?

Second Law.

All physical or chemical changes tend to proceed in such a direction that useful energy undergoes irreversible degradation into a random, disordered form called entropy. They come to a stop at an equilibrium point, at which the entropy formed is the maximum possible under the existing conditions.

This is usually defined by the equation: ΔG = ΔH - TΔS

ΔG is the Gibbs Free Energy, the energy that can do work at constant temperature and pressure.

ΔH is enthalpy, the change in heat content of the system.

T is absolute temperature measured in Kelvins.

ΔS is entropy, the change in the order of the system.

The natural tendency is for compounds to be broken down to products with less free energy, thereby diffusing the energy throughout the universe. The amount of free energy should tend to decrease.

If ΔG is positive, energy must be put into the system to force the reaction to go forward.  It naturally goes backwards.

If ΔG is negative, a reaction is spontaneous.

If ΔG is zero, the system is already at equilibrium; there is no net flux forward or backward.

Living organisms extract the free energy from reduced organic nutrients taken in from the surroundings, producing oxidized, less ordered, less energetic, compounds (which are dumped back into the environment). Heat is lost back into the surroundings as a byproduct.

• The total amount of energy taken in and given off is equal.
• Local order is maintained or increased, but the total order of the universe is decreased (ΔS increases).
• The increase in entropy or decrease in order is the driving force for biochemical reactions, making them unidirectional. The only way to reverse entropy -- taking simple molecules and making higher energy molecules--is to put energy into the system.

Free energy can produce biochemical "work" and is the source of energy for biochemical reactions and phenomena. The free energy of a reaction is related to the equilibrium constant of the reaction.

The Law of Mass Action:

The equilibrium constant of a reaction equals the product of the concentration of the products divided by the product of the reactants, each raised to a power equal to the number of times they occur in the reaction.

Note that Chemists use the term K_eq, but Biochemists use K_eq', which specifies a pH equal to 7.  Biochemists need to specify pH as well as temperature and pressure since many reactions in biochemistry involve H⁺. Biochemists use the symbol ΔG°' to indicate standard free energy changes at pH 7. Do not confuse with the chemists' ΔG° which is at pH 0. 

Free Energy (Theoretical)

Each reaction has a characteristic ΔG°' which is calculated for standard conditions (1 atm, 298 K, pH 7 and 1 M starting concentration of all reactants).

T is absolute temperature (298 K = 25°C)

R is the universal gas constant. (8.315 J mol^-1 K^-1)

If K_eq' is known, then ΔG°' can be calculated:

Free Energy (Real)

ΔG°' represents calculation based on concentrations starting at 1 M and finishing at equilibrium, when they are unchanging. What's important in biochemistry is the actual free energy (ΔG) based on the actual concentration of all reactants in the cell. This is based on Q, the instantaneous ratio of actual or steady-state concentrations of all the reactants (i.e. not the equilibrium concentrations).

If Q is equal to K_eq', the reaction is at equilibrium and the ΔG will be 0.

If Q < K_eq' (less than it would be at equilibrium because of higher [substrates] or lower [products]) then the reaction will tend to proceed and ΔG will be negative.

If Q > K_eq' (greater than it would be at equilibrium because [products] is already relatively high) then the reaction will proceed in the reverse and ΔG will be positive.

As the reaction proceeds, ΔG decreases in magnitude. When Q finally equals K_eq', then ΔG is 0 and the reaction stops.

Thus a cell can make a reaction with a positive ΔG°' proceed if [S] is large or [P] is small.

Important concept:

Standard free energies of sequential reactions are additive.

A ------> B     ΔG°'1
B ------> C     ΔG°'2
C ------> D     ΔG°'3
----------------------------------
A ------> D     ΔG°'total = ΔG°'1 + ΔG°'2 + ΔG°'3

The overall equilibrium for a series of reactions can be determined by the total change in free energy between the initial reactant and the final product. This is irrespective of the pathway of the reaction. The final equilibrium between A and D will be the same using either pathway.

A reaction with a positive ΔG°' will proceed if it is followed by a reaction with a strongly negative ΔG°'.

ΔG°' for A-->B is positive; ΔG°' for A-->C is negative  

Reactions with strongly negative ΔG are good control points because a modulation of the rate will control the flux of metabolites through the following steps in the pathway. Enzymatic reactions near equilibrium (ΔG near zero) are not good control points.  

The ΔG°' value is important for understanding whether biochemical reactions will "go".  

We assess the amount of potential energy in chemical bonds by measuring their ΔG°' for hydrolysis. This permits us to predict equilibria and overall directions for any combination of reactions. 

Chemically correct format:

ATP^4- + H₂O ---> ADP^3- + HPO₄^2- + H⁺

ΔG°'= -30.5 kJ/mol

Biochemical format:

ATP (gamma-P)

ΔG°'_hydrolysis = -30.5 kJ/mol

Much of this energy is derived from electrostatic repulsion of the phosphoanhydrides. These phosphates are usually complexed with Mg²⁺ ions, which decreases the ΔG°' of hydrolysis, but also decreases electrostatic repulsion between ATP^4- and enzyme active sites.

List of Free Energies for Hydrolysis of Favorite Metabolites

Molecule	ΔG°' hydrolysis (kJ/mol)
Phosphoenolpyruvate	-62.2
1,3-Bisphosphoglycerate	-49.6
Phosphocreatine	-43.3
Pyrophosphate	-33.6
ATP (gamma-P)	-30.5
ATP (beta-P)	-32.3
Glucose 1-phosphate	-21.0
Fructose 6-phosphate	-15.9
Glucose 6-phosphate	-13.9
Glycerol 3-phosphate	-9.2
Glycosides	approx. -12.5
Dihemiacetals (sucrose)	-27.6
Peptide bonds	approx. -4.1

These values can be combined to calculate ΔG°' values for enzyme catalyzed phosphotransfer reactions.  

Case #1.

     ΔG°' = +13.9 kJ/mol

The reaction does not proceed significantly because of the large positive ΔG°'. An enzyme can make a reaction go more rapidly by changing the required activation energy, but it does not alter the ΔG°' or Keq. 

Case #2.

An enzyme that transfers a PO₄ from ATP is called a kinase. The enzyme (either glucokinase or hexokinase) uses the excess free energy in the gamma-phosphodiester bond of ATP to make the phosphorylation of glucose practical. The ΔG°' for the overall reaction is negative and the Keq for the overall reaction is now large. Phosphate is readily transferred to form molecules with lower free energies for hydrolysis. 

Another example:

By knowing the ΔG°' for each hydrolysis reaction, we know the ΔG°' (and Keq) for the above reaction catalyzed by phosphoglucomutase.

Read the portion of this site on bioenergetics. [local]

Redox Reactions

Reduction/Oxidation [local] reactions also have free energy changes. In biochemistry, we normally view reduction/oxidation in terms of a transfer of electrons. The standard reaction is arbitrarily written as a reduction just as the standard for determining phosphate bond energy is written as a hydrolysis. The tendency to take up electron(s) and become reduced is expressed by the standard reduction potential (E°'). When two molecules with different E°' are mixed, electrons will flow from the molecule with the more negative E°' to the molecule with the more positive E°', releasing free energy (ΔG is negative). There is a course in this series on oxidation-reduction (CHEM 869U). Use it as a reference to refresh your knowledge or to look up specific points.

Hint: Draw a vertical axis for standard reduction potential and label it with the most negative at the top and the most positive at the bottom. When you place two molecules on this axis in their appropriate location with regard to E°', the electrons will flow 'downhill [local]' in a spontaneous fashion, releasing energy.

NAD and NADP are the primary redox intermediates of cellular metabolism.  

Redox Review [local]