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Biology LibreTexts

Thermodynamics

Cells need energy to

At the cellular level At the molecular level
move ion transport, reversible bond formation
grow synthesis and polymerization
maintain homeostasis heat production, entropy reduction

Laws of Thermodynamics

0) All closed systems move towards equilibrium.
1) Energy (work, heat, etc.) of a closed system is conserved.
2) Entropy of a closed system increases.
3) It is impossible to reach absolute zero (0K)
  • However, the second law poses a problem: How can cells reproduce to make more cells by using disordered raw materials, and thus create order? Cells are not closed systems, they interact with their environment.

ΔScell + ΔSenvironment = ΔSsystem

Biochemical Energy

In order to apply thermodynamics to biological reactions, we need a measure of energy that applies to living conditions.
  •  Consider the reaction X↔Y:
    • States X and Y have internal energy (E), pressure (P), volume (V), temperature (T), and entropy (S).
    • G(Gibb's free energy)=E+PV-TS
    • ΔG represents changes in internal energy and entropy for any reaction at constant temperature and pressure
    • For reaction X↔Y, G depends on concentrations of reactants and products as well as state variables E, P, V, T, S:

ΔG=ΔGo+RTln([Y]/[X])

  • at standard conditions: 1M substrate, 1M product, 25oC, atmospheric pressure: ΔG=ΔGo
  • If X→Y is spontaneous, G decreases and the reaction is considered to be exergonic:ΔG=G(products)-G(reactants)<0
    • [chart] when G is at a minimum, assume the reaction is at equilibrium and ΔG=0.
  • Let K=[Y]/[X], and assume that the reaction is at equilibrium (ΔG=0):

ΔG=ΔGo+RTln([Y]/[X])
0=ΔGo+RTlnKeq
ΔGo=-RTlnKeq

  • At pH 7, ΔGo=-RTlnKeq where [H+]=10-7M. This makes a difference when H+ is a reactant or a product.

Coupled Reactions

  • For two reactions: X↔Y    ΔG1
                               A↔B    ΔG2
    • If they are coupled (occur together), then X+A↔Y+B and:

ΔG=ΔG1+ΔG2
ΔGo=ΔGo1+ΔGo2

  • The coupled reaction proceeds (is spontaneous) if ΔG<0.
  • This means that conditions leading to exergonic (ΔG<0) reactions can be used to power endergonic (ΔG>0) reactions:
    • Exergonic reactions:
      • light absorption
      • redox disequilibrium relaxation
      • bond breaking/degradation
    • Endergonic reactions:
      • synthesis
      • polymerization
      • homeostasis
  • Example:

PEP + H2O → pyruvate + Pi    ΔG=-78 kJ/mol (exergonic)
ADP + Pi → ATP + H2O           ΔG=55 kJ/mol (endergonic)

  • combine the two reactions, and add their ΔG values:

PEP + ADP → pyruvate + ATP  ΔG=-23 kJ/mol (exergonic)