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The Energetics of Life: Thermodynamics and Free Energy in Biochemistry

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Chapter 3 – The Energetics of Life

Introduction to Thermodynamics in Biochemistry

Understanding the energetics of life is essential for biochemistry, as it explains how energy transformations govern biological processes. This chapter covers the laws of thermodynamics, enthalpy, entropy, Gibbs free energy, chemical equilibrium, and the coupling of reactions in living systems.

Thermodynamic Systems

Types of Systems

  • System: The part of the universe chosen for study; everything else is the surroundings.

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

  • Closed System: Exchanges energy (heat or work) but not matter with surroundings.

  • Open System: Exchanges both matter and energy with surroundings. Living systems are open systems, typically operating at constant temperature and pressure.

The First Law of Thermodynamics and Enthalpy

Energy Conservation

  • First Law: The total energy of an isolated system is constant; energy can be transferred or transformed but not created or destroyed.

  • Enthalpy (H): The heat exchanged between the system and surroundings at constant pressure, a common condition for biological systems.

Measuring the heat of a reaction with a piston system

State Functions

  • State functions depend only on the initial and final states, not the path taken (e.g., temperature, pressure, free energy, enthalpy, entropy).

  • Change in enthalpy:

The Second Law of Thermodynamics and Entropy

Entropy and Spontaneity

  • Second Law: The entropy (S) of an isolated system tends to increase; systems naturally progress toward greater disorder.

  • Entropy (S): A measure of randomness or disorder in a system.

  • Systems tend to maximize the number of possible arrangements (microstates).

  • Boltzmann equation: (where is Boltzmann's constant, is the number of microstates).

Diffusion as an example of entropy increaseDistribution of molecules in different statesProbability of molecular arrangementsComparison of an organized and messy room as an analogy for entropy

Gibbs Free Energy and Biological Systems

Gibbs Free Energy (G)

  • For open systems (like cells), the second law is expressed using Gibbs free energy:

  • ΔG represents the energy available to do work at constant temperature and pressure.

  • If , the process is exergonic (spontaneous/favorable).

  • If , the process is endergonic (non-spontaneous/unfavorable).

  • If , the system is at equilibrium.

Exergonic and endergonic processes

If ΔG is …

Free energy is …

The process is …

Negative

Available to do work

Thermodynamically favorable

Zero

Zero

Reversible; system at equilibrium

Positive

Required to do work

Thermodynamically unfavorable

Table of free energy rules

Effect of Temperature on ΔG

ΔH

ΔS

Low T

High T

+

+

ΔG positive; not favored

ΔG negative; favored

+

-

ΔG positive; not favored

ΔG positive; not favored

-

+

ΔG negative; favored

ΔG negative; favored

-

-

ΔG negative; favored

ΔG positive; not favored

Table of temperature effects on ΔG

Examples of Enthalpy and Entropy Interplay

  • Melting of ice at different temperatures demonstrates how ΔH and ΔS determine spontaneity.

  • At low T, ΔG is positive (unfavorable); at high T, ΔG is negative (favorable).

Examples of enthalpy and entropy contributions

Chemical Equilibrium and Free Energy

Equilibrium Constant (K) and Reaction Quotient (Q)

  • Equilibrium constant (K): Describes the ratio of product and reactant concentrations at equilibrium.

  • Reaction quotient (Q): Same form as K, but for any set of concentrations.

Equation for reaction quotient Q

Equation for equilibrium constant K

Relationship Between ΔG, ΔG°, and Concentrations

  • Standard free energy change () is measured under standard conditions (1 bar, 25°C, 1 M solute).

  • Actual free energy change () depends on concentrations:

Equation relating ΔG, ΔG°, and Q

  • At equilibrium, and :

Equation for ΔG at equilibrium

Value of Q

Value of ΔG

Favored Direction

< K

< 0

Forward reaction (formation of products)

= K

= 0

Neither (system at equilibrium)

> K

> 0

Reverse reaction (formation of reactants)

Table of relationships between K, Q, and ΔG

Coupled Reactions in Biochemistry

Driving Unfavorable Reactions

  • Cells couple unfavorable (endergonic) reactions with favorable (exergonic) ones to drive essential processes.

  • Examples: ATP hydrolysis drives muscle contraction, active transport, and biosynthesis.

Coupling of unfavorable and favorable reactions

Calculating ΔG for Coupled Reactions

  • Reverse the sign of ΔG when reversing a reaction.

  • Add ΔG values for the overall reaction.

Protocol for calculating ΔG for coupled reactionsExample of coupled reactions and ΔG calculation

ATP: The Energy Currency of the Cell

ATP Hydrolysis and Energy Release

  • ATP hydrolysis is highly exergonic and provides energy for cellular work.

  • Standard free energy change for ATP hydrolysis: kJ/mol.

  • Actual ΔG depends on cellular concentrations of ATP, ADP, and Pi.

Structure of ATPHydrolysis of ATP, ADP, and AMP

Why Are Some Compounds Energy-Rich?

  • Resonance stabilization of products

  • Electrostatic repulsion in reactants

  • Tautomerization of products

Reasons for high energy of phosphate compounds

Hydrolysis Reactions of Phosphate-Containing Metabolites

Hydrolysis Reaction

ΔG°' (kJ/mol)

Phosphoenolpyruvate + H2O → pyruvate + Pi

-61.9

1,3-Bisphosphoglycerate + H2O → 3-phosphoglycerate + Pi

-49.4

ATP + H2O → AMP + PPi + H+

-45.6

Acetyl phosphate + H2O → acetate + Pi

-43.1

Creatine phosphate + H2O → creatine + Pi

-43.1

ADP + H2O → AMP + Pi + H+

-32.4

ATP + H2O → ADP + Pi + H+

-32.2

PPi + H2O → 2 Pi

-19.2

Glucose-1-phosphate + H2O → glucose + Pi

-13.8

Table of ΔG°' for hydrolysis of phosphate compounds

Equilibration and Transport Across Membranes

Diffusion and Free Energy

  • Movement of solutes across membranes is driven by concentration gradients.

  • Free energy change for transport:

Equilibration of solute concentrations across a membraneEquation for ΔG in membrane transport

Oxidation-Reduction (Redox) Reactions

Redox Chemistry in Biochemistry

  • Redox reactions involve electron transfer between donor (reductant) and acceptor (oxidant).

  • Standard reduction potential () measures the tendency to gain electrons; higher means stronger oxidant.

  • Standard free energy change for redox reactions:

  • n = number of electrons transferred; F = Faraday's constant (96.5 kJ/mol·V).

Redox half-reactions and standard reduction potentialsMeasuring E° in a galvanic cell

Oxidant (e- acceptor)

Reductant (e- donor)

n

E°'(V)

H+ + e-

H2

2

-0.421

NAD+

NADH

2

-0.315

1,3-Bisphosphoglycerate

Glyceraldehyde-3-phosphate + Pi

2

-0.290

FAD

FADH2

2

-0.219

Acetoacetate

Ethanol

2

-0.185

Pyruvate

Lactate

2

-0.187

H2O2

H2O

2

+0.815

Table of standard reduction potentials

Example Calculation

  • For the oxidation of ethanol by NAD+, combine the half-reactions, reverse as needed, sum E°' values, and calculate ΔG°'.

Example calculation of ΔG°' for a redox reaction

Summary

  • Thermodynamics provides the framework for understanding energy flow in biological systems.

  • ΔG determines reaction spontaneity and direction.

  • Cells use coupling and redox reactions to drive essential processes far from equilibrium.

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