Bioenergetics, free energy, ATP and redox in biology

Principles of bioenergetics

Bioenergetics and thermodynamics

Bioenergetics concerns the flow and transformation of energy in biochemical systems. Thermodynamics underpins this study, describing how enthalpy ( $H$ ), entropy ( $S$ ), and free energy ( $G$ ) interact to determine whether and how a reaction proceeds.

Free energy, equilibrium, and $K_{e q}$

Free energy ( $G$ ) measures the amount of energy available in a system to do work. For a reaction, the change in free energy ( $G$ ) is given by the equation:

$Δ$ $G$ = $Δ$ $H$ − T $Δ$ $S$

where $Δ$ $H$ is enthalpy change, $T$ is absolute temperature (in Kelvin), and $Δ$ $S$ is entropy change.

A negative $Δ$ $G$ indicates a spontaneous reaction (favorable), whereas a positive $Δ$ $G$ signifies nonspontaneous behavior under given conditions. However, spontaneity does not speak to reaction speed—that depends on kinetics.
The equilibrium constant ( $K_{e q}$ ) reflects the ratio of products to reactants at equilibrium. Under standard conditions, the relationship between $K_{e q}$ and $Δ$ $G^{\circ}$ is: $Δ$ $G^{\circ}$ = − $RTl n K_{e q}$

Concentration and Le Châtelier’s Principle
Changing reactant or product concentrations can push the reaction in one direction or another. According to Le Châtelier’s Principle, a system will shift its equilibrium to counteract any imposed change, restoring balance.

Endothermic and Exothermic Reactions

Enthalpy ( $H$ ) represents the heat content of a reaction. By convention,

Endothermic processes absorb heat ( $Δ$ $H > 0$ ).
Exothermic processes release heat ( $Δ$ $H < 0$ ).

Standard heats of reaction ( $Δ$ $H_{r x n}$ ) or formation ( $Δ$ $H_{f}$ ) describe enthalpy changes under standard conditions (1 bar pressure, specified temperature).

$Δ$ $H$ represents the change in heat content during a reaction, with a positive value indicating that heat is absorbed and a negative value indicating that heat is released.

The standard heat of reaction ( $Δ$ $H_{r x n}$ ) measures this change in heat content for a specific chemical reaction under standard conditions.

Similarly, the standard heat of formation ( $Δ$ $H_{f}$ ) quantifies the change in heat when a compound is formed from its elements in their most stable forms.

These elements are in their standard state (the lowest energy configuration found naturally); for example, oxygen exists as $O_{2}$ (a diatomic gas) and carbon as solid graphite.

In a formation reaction, a substance is generated from its elements in their standard states (e.g., diatomic $O_{2}$ , graphite carbon).

Enthalpy is typically measured in joules ( $J$ ) or, more commonly in chemistry, in joules per mole ( $J / m o l$ ).

Hess’ Law allows enthalpy changes to be summed: $Δ$ $H_{r x n}$ = $Σ$ $Δ$ $H_{f}$ ,products − $Σ$ $Δ$ $H_{f}$ ,reactants

Spontaneous reactions and standard free energy change

Spontaneous reactions occur without the need for continuous external energy input (in fact, spontaneously), a fact indicated by a negative change in free energy (ΔG).

Although a negative $Δ$ $G$ shows that a reaction is thermodynamically favorable, the rate at which it proceeds is governed by kinetic factors; thus, even spontaneous reactions can be slow.

Notably, the relationship between heat exchange and spontaneity is complex:

an exothermic reaction ( $Δ$ $H < 0$ ) might not be spontaneous if it is accompanied by a significant decrease in entropy ( $Δ$ $S$ )
an endothermic reaction ( $Δ$ $H > 0$ ) can be spontaneous if it involves a large increase in entropy.

Phosphoryl group transfers and ATP

In biological systems, energy transfer is often driven by the hydrolysis of ATP, a reaction with a very negative $Δ$ $G$ ( $Δ$ $G << 0$ ) that releases ample energy to fuel processes such as phosphoryl group transfers.

ATP hydrolyzes into ADP in the following reaction:

$A TP + H_{2} O \to A D P + P i +$ free energy

ATP molecule structure showing adenosine and three phosphate groups

Biological oxidation-reduction
Cellular energy production relies on oxidation-reduction (redox) reactions, which involve the transfer of electrons through half-reactions. These redox processes are mediated by soluble electron carriers and enzymes like flavoproteins, which facilitate the flow of electrons and play critical roles in the cell’s bioenergetic pathways.

Principles of bioenergetics

Free energy, equilibrium, and Keq​

Endothermic and Exothermic Reactions

Spontaneous reactions and standard free energy change

Phosphoryl group transfers and ATP

Free energy, equilibrium, and $K_{e q}$