Thermodynamics

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Cells need energy to
Laws of Thermodynamics
Biochemical Energy
Coupled Reactions

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.

ΔS_cell + ΔS_environment = ΔS_system

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=ΔG^o+RTln([Y]/[X])

at standard conditions: 1M substrate, 1M product, 25^oC, atmospheric pressure: ΔG=ΔG^o
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=ΔG^o+RTln([Y]/[X])
0=ΔG^o+RTlnK_eq
ΔG^o=-RTlnK_eq

At pH 7, ΔG^o=-RTlnK_eq 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
ΔG^o=ΔG^o₁+ΔG^o₂

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 + P_i ΔG=-78 kJ/mol (exergonic)
ADP + P_i → 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)