Chapter 3: The Energetics of Life – Thermodynamics and Free Energy in Biochemistry

Chapter 3: The Energetics of Life

3.1 Free Energy

This section introduces the fundamental thermodynamic concepts that govern energy transformations in biological systems. Understanding these principles is essential for analyzing how cells extract, store, and utilize energy.

• Thermodynamic Systems: A system is the part of the universe chosen for study; everything else is the surroundings. Systems are characterized by their composition, temperature, pressure, and volume.

• Types of Systems:

  • Open system: Exchanges both matter and energy with surroundings (e.g., living cells).

  • Closed system: Exchanges energy but not matter with surroundings.

  • Isolated system: Exchanges neither matter nor energy with surroundings.

• First Law of Thermodynamics: Energy is conserved. In a closed system, energy can be exchanged as heat or work, but the total energy remains constant.

• Enthalpy (H): The heat exchanged at constant pressure, typical of biological systems.

• Reversible vs. Irreversible Processes:

  • Reversible process: Occurs near equilibrium; forward and reverse rates are equal (e.g., ice melting at 0°C).

  • Irreversible process: Proceeds far from equilibrium toward equilibrium (e.g., burning paper).

• Second Law of Thermodynamics: The entropy (S) of an isolated system tends to increase to a maximum value. Entropy measures the disorder or randomness of a system.

Example: Melting ice involves a transition from a low-entropy (ordered) solid to a higher-entropy (disordered) liquid.

Table: Examples of Lower-Entropy and Higher-Entropy States

System	Lower Entropy	Higher Entropy
Water	Ice (solid)	Liquid water
Gas	Compressed gas	Expanded gas
Solute	Crystalline salt	Dissolved ions

3.2 Free Energy: The Second Law in Open Systems

Biological systems are open, exchanging both matter and energy with their environment. The second law must be restated for such systems, incorporating both enthalpy and entropy.

• Gibbs Free Energy (G): The portion of total energy change available to do useful work at constant temperature and pressure.

• The change in free energy, ΔG, determines whether a process is spontaneous:

  • ΔG < 0: Exergonic (spontaneous, energy-releasing)

  • ΔG = 0: At equilibrium

  • ΔG > 0: Endergonic (non-spontaneous, energy-requiring)

• Equation for Free Energy Change:

$\Delta G = \Delta H - T\Delta S$

• Effect of Temperature: The sign and magnitude of ΔG depend on both ΔH (enthalpy change) and ΔS (entropy change), as well as temperature (T).

Example: Ice melting at temperatures above 0°C is favorable (ΔG < 0) because the increase in entropy outweighs the enthalpy input.

Table: Free Energy Rules

Process	ΔG	Spontaneity
Exergonic	< 0	Spontaneous
At Equilibrium	= 0	No net change
Endergonic	> 0	Non-spontaneous

3.3 The Relationships Between Free Energy, the Equilibrium State, and Nonequilibrium Concentrations of Reactants and Products

This section explores how free energy relates to chemical equilibrium and the concentrations of reactants and products in biological reactions.

• Chemical Equilibrium: For a general reaction, the equilibrium constant (K) is defined as:

$K = \frac{[products]}{[reactants]}$

• Mass Action Expression (Q): For reactions not at equilibrium, Q represents the ratio of product to reactant concentrations at any given moment.

• Free Energy Change at Any State:

$\Delta G = \Delta G^\circ + RT \ln Q$

• At equilibrium, Q = K and ΔG = 0, so:

$\Delta G^\circ = -RT \ln K$

• Homeostasis vs. Equilibrium:

  • Equilibrium: No net change; ΔG = 0; Q = K.

  • Homeostasis: Living systems maintain steady-state concentrations far from equilibrium (Q ≠ K), requiring energy input.

• Coupling Reactions: Unfavorable (endergonic) reactions can be driven by coupling them to favorable (exergonic) reactions, such as ATP hydrolysis.

Example: The hydrolysis of ATP (a highly exergonic reaction) is often coupled to biosynthetic reactions that are otherwise unfavorable.

Table: Relationships between K, Q, and ΔG

Condition	Q vs. K	ΔG
At equilibrium	Q = K	0
Spontaneous forward	Q < K	< 0
Spontaneous reverse	Q > K	> 0

The Biochemical Standard State

Biochemical reactions often involve protons (H+) and water, which are not at 1 M concentration in cells. The biochemical standard state (denoted by a prime, e.g., ΔG°′) is defined at pH 7, 25°C, and 1 M concentrations for solutes (except H+ and H2O).

• Standard Free Energy Change (ΔG°′): Used as a reference for comparing reactions under physiological conditions.

Example Calculation: For ATP hydrolysis at pH 7.4 and 25°C, with given concentrations of ATP, ADP, and Pi, ΔG can be calculated using the above equations.

3.4 Free Energy in Biological Systems

Cells use free energy to drive essential processes. ATP is the universal energy currency, and its hydrolysis is highly exergonic.

• ATP Hydrolysis: The breakdown of ATP to ADP and inorganic phosphate (Pi) releases free energy that can be harnessed for cellular work.

• Phosphoryl Group Transfer Potential: Some compounds (e.g., phosphoenolpyruvate, PEP) have even higher free energy of hydrolysis than ATP, allowing them to drive ATP synthesis.

Table: Standard Free Energy Changes for Hydrolysis of Phosphate Compounds

Compound	ΔG°′ (kJ/mol)
Phosphoenolpyruvate (PEP)	-61.9
1,3-Bisphosphoglycerate	-49.3
ATP (to ADP + Pi)	-30.5
Glucose-6-phosphate	-13.8

Additional info: Values are typical and may vary slightly by source.

• Concentration Gradients: The movement of molecules across membranes can be analyzed using free energy equations. The direction and favorability depend on the concentration ratio across the membrane.

$\Delta G = RT \ln \frac{[C]_2}{[C]_1}$

• If [C]2 < [C]1, ΔG is negative (favorable transfer from region 1 to 2).

• Redox Reactions and Reduction Potential: Oxidation–reduction (redox) reactions involve electron transfer. The standard reduction potential (E°′) measures a species' tendency to gain electrons under standard conditions.

$\Delta G^\circ' = -nF\Delta E^\circ'$

• n = number of electrons transferred

• F = Faraday's constant (96.5 kJ/mol·V)

• ΔE°′ = difference in standard reduction potentials between two redox couples

Example: The oxidation of ethanol by NAD+ can be analyzed using standard reduction potentials to calculate ΔG°′.

Summary

• Thermodynamic principles explain how cells extract and use energy.

• Spontaneous processes have negative ΔG (exergonic); non-spontaneous processes have positive ΔG (endergonic).

• Cells maintain homeostasis by keeping concentrations far from equilibrium, requiring energy input.

• Unfavorable reactions are driven by coupling to favorable ones (e.g., ATP hydrolysis).

• ΔG°′ can be calculated from equilibrium constants, reduction potentials, or by summing known ΔG°′ values for component reactions.