Thermodynamics of Biological Systems

Thermodynamics and Metabolism

• Thermodynamics is crucial in understanding metabolism because it deals with the relationships between heat, work, and energy.
• It involves the transfer of energy between a system and its surroundings, or the conversion of energy from one form to another.
• The laws of thermodynamics govern the behavior of all systems, including biological ones, helping to explain why certain reactions occur spontaneously while others do not.

Gibbs Free Energy (G)

• The spontaneity of a reaction is determined by both enthalpy (H) and entropy (S).
• Gibbs free energy (G) is expressed as: $G = H - TS$

Internal Energy (E) and Enthalpy (H)

• Internal energy (E) is the sum of all energies within a system, measured in Joules.
• For closed systems, internal energy relates to the total energy of the molecules within the system.
• Enthalpy (H) is defined as: $H = E + PV$ where P is pressure and V is volume.
• Change in enthalpy is given by: $\Delta H = \Delta E + P\Delta V$
• In biochemical processes occurring in liquids, the change in volume ($\Delta V$) is often negligible, thus: $\Delta H \approx \Delta E$

Enthalpy (H) and Bond Energies

• Atoms in a bond are in a lower energy state compared to unbound atoms.
• Energy is released when bonds form (heat).
• Energy is required to break bonds.
• Each molecule has characteristic bond energies. For example:
  • C-C bond: $347 \text{ kJ/mol}$
  • C=C bond: $614 \text{ kJ/mol}$

Enthalpy Change in Reactions

• For reactions, the enthalpy change ($\Delta H$) relates to energy changes due to bond breaking and formation:
  $\Delta E \approx \Delta H$
• $\Delta E$ is the energy used to break bonds plus the energy released when bonds form.
• If energy used to break bonds > energy released when bonds form: $\Delta E \approx \Delta H$ is positive, indicating an endothermic reaction.
• If energy used to break bonds < energy released when bonds form: $\Delta E \approx \Delta H$ is negative, indicating an exothermic reaction.

Second Law of Thermodynamics and Entropy (S)

• Systems tend to move from ordered (low entropy) to disordered states (high entropy).
• The entropy of the universe (system and surroundings) is unchanged in reversible processes and increases in irreversible processes.
• $\Delta S<em>{\text{universe}} = \Delta S</em>{\text{system}} + \Delta S_{\text{surroundings}} \geq 0$
• Entropy (S) represents energy unavailable to do work and measures the disorder of a system.

Gibbs Free Energy (G) and Spontaneity

• For any reaction at constant temperature (T) and pressure:
  $\Delta G = \Delta H - T\Delta S$
• Based on the second law of thermodynamics:
  • If $\Delta G$ is negative, the reaction is spontaneous.
  • If $\Delta G$ is positive, the reaction is non-spontaneous.

Standard State Reactions

• A standard state is defined to compare thermodynamic parameters of different reactions.
• For a reaction $A + B \leftrightarrow C + D$, the standard state is when the concentration of reactants and products are at 1M.
• Thermodynamic parameters in the standard state are indicated by "$\circ$ ", e.g., $H^\circ, S^\circ, G^\circ$
• The standard state for $H^+$ ions corresponds to pH ~ 0.
• For biological systems, a modified standard state (designated by "$\circ'$ ") is used at pH 7.

Spontaneous Reactions and Concentration

• If $\Delta G$ is negative, the reaction is spontaneous at a given temperature T.
• If $\Delta G$ is positive, the reaction is non-spontaneous at a given temperature T.
• The influence of concentration on spontaneity is given by: $\Delta G = \Delta G^\circ + RT \ln \frac{[C][D]}{[A][B]}$
  • T = temperature in Kelvin (K)
  • R = gas constant (8.314 J/mol·K)

Calculating $\Delta G$

• For the reaction $[A] \leftrightarrow [B] + [C]$ with $\Delta G^\circ = 0.0 \text{ kJ/mol}$
• $\Delta G = \Delta G^\circ + RT \ln \frac{[B][C]}{[A]}$
• Given conditions at 310K:
  • Condition 1: [A] = $1 \times 10^{-3}$ M, [B] = $1 \times 10^{-6}$ M, [C] = $1 \times 10^{-2}$ M
  • Condition 2: [A] = $1 \times 10^{-6}$ M, [B] = $1 \times 10^{-3}$ M, [C] = $1 \times 10^{-2}$ M

Spontaneity and $\Delta G$

• If $\Delta G$ is negative, the reaction is spontaneous at a given temperature T.
• If $\Delta G$ is positive, the reaction is non-spontaneous at a given temperature T.
• For the reaction $A + B \leftrightarrow C + D$, the spontaneity depends on the concentrations: $\Delta G = \Delta G^\circ + RT \ln \frac{[C][D]}{[A][B]}$
  • T = temperature in Kelvin (K)
  • R = gas constant (8.314 J/mol·K)
• $\Delta G$ is negative when \Delta G^\circ + RT \ln \frac{[C][D]}{[A][B]} < 0
• Since R and T are constant, $RT \ln \frac{[C][D]}{[A][B]}$ depends on the concentration of reactants and products.

High Energy Compounds

• These compounds have large negative free energies of hydrolysis.
• Example: ATP hydrolysis: $ATP + H<em>2O \rightarrow ADP + P</em>i$ with \Delta G^\circ' = -30.5 \text{ kJ/mol}
• These compounds are transient forms of stored energy, carrying energy from one reaction to another.
• High energy does not equate to instability; the activation energy needed to break the O-P bond in ATP is between 200 - 400 kJ/mol.

ATP Hydrolysis

• The hydrolysis of ATP involves a phosphoryl group transfer potential of approximately $-30.5 \text{ kJ/mol}$.

Coupled Reactions

• A coupled reaction involves the product of one reaction serving as the substrate for another, or sharing a common intermediate.
• This allows reactions to proceed against their thermodynamic potential (i.e., in the direction of a positive $\Delta G$).
• The energy released from a thermodynamically favorable reaction can drive a thermodynamically unfavorable reaction, as long as the overall $\Delta G$ is negative.
• Example:
  • $Glucose + P<em>i \rightarrow Glucose \text{ 6-P} + H</em>2O$ \Delta G^\circ' = 13.8 \text{ kJ/mol}
  • $ATP + H<em>2O \rightarrow ADP + P</em>i$ \Delta G^\circ' = -30.5 \text{ kJ/mol}
  • Coupled reaction: $Glucose + ATP \rightarrow Glucose \text{ 6P} + ADP$ \Delta G^\circ' = -16.7 \text{ kJ/mol}