Free Energy and Thermodynamics in Biological Systems

Thermodynamic Systems

Thermodynamics studies the flow and transformation of energy in the universe. In chemistry, we define a system as the part of the universe we are interested in, while everything else is the surroundings. Systems are characterized by their composition, temperature, pressure, and volume.

• Open systems: Exchange both matter and energy with their surroundings. Example: a living cell.

• Closed systems: Exchange energy (as heat or work) but not matter with their surroundings. Example: a sealed, heated container.

• Isolated systems: Exchange neither matter nor energy with their surroundings. Example: an insulated thermos bottle.

Most chemical and biological systems operate at constant temperature and pressure.

The First Law of Thermodynamics and Enthalpy

The first law of thermodynamics states that energy is conserved: it cannot be created or destroyed, only transformed. In a closed system, energy can be exchanged with the surroundings as work or heat.

• Enthalpy (H): The heat exchanged between the system and surroundings at constant pressure. It is a state function, meaning its value depends only on the current state of the system, not the path taken to reach it.

Equation:

Reversible and Irreversible Processes

Processes in thermodynamics can be classified as reversible or irreversible:

• Reversible process: Occurs near equilibrium, where the system is in its lowest energy state and the forward and reverse rates are equal. Example: Ice melting at 0°C.

• Irreversible process: Occurs far from equilibrium and proceeds spontaneously toward equilibrium. Example: Burning paper.

The Second Law of Thermodynamics and Entropy

The second law of thermodynamics states that the entropy of an isolated system will tend to increase to a maximum value. Entropy (S) is a measure of the degree of randomness or disorder in a system.

• As a system becomes more disordered, its entropy increases.

• At equilibrium, entropy is maximized for an isolated system.

Equation:

Free Energy in Open Systems: Gibbs Free Energy

Biological systems are open, exchanging both energy and matter with their surroundings. The second law for open systems is expressed in terms of Gibbs free energy (G):

• Gibbs free energy (G): The portion of a system's energy that is available to do work at constant temperature and pressure.

• Equation:

• Change in free energy:

• If , the process is spontaneous (exergonic).

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

• If , the system is at equilibrium.

Free Energy, Equilibrium, and Reaction Direction

The direction of a chemical reaction and its equilibrium position are determined by changes in free energy.

• Exergonic process: ; spontaneous, releases energy.

• Endergonic process: ; non-spontaneous, requires energy input.

Equilibrium Constant and Reaction Quotient

For a general reaction :

• Equilibrium constant (K):

• Reaction quotient (Q): Same form as K, but for any set of concentrations, not just at equilibrium.

• If , the reaction proceeds forward (toward products).

• If , the reaction proceeds in reverse (toward reactants).

• If , the system is at equilibrium.

Relationship Between Free Energy and Equilibrium

The free energy change for a reaction under non-standard conditions is given by:

• At equilibrium, and , so

• Where is the gas constant and is the temperature in Kelvin.

Homeostasis vs. Equilibrium in Biological Systems

Homeostasis refers to the maintenance of constant internal conditions (such as temperature, pH, and concentrations of ions and metabolites) in living organisms. While both equilibrium and homeostasis involve constant concentrations, homeostasis is maintained far from equilibrium and requires energy input.

• At equilibrium, no net change occurs; in homeostasis, steady-state concentrations are maintained by continuous energy expenditure.

• Equilibrium is reached only at death in living systems.

Coupling Favorable and Unfavorable Reactions

Cells often couple energetically unfavorable (endergonic) reactions with favorable (exergonic) ones to drive necessary processes forward. This is essential for chemical reactions, active transport, nerve impulses, and muscle contraction.

• Example: ATP hydrolysis (favorable) is coupled to biosynthetic reactions (unfavorable).

ATP as the Common Energy Currency

Adenosine triphosphate (ATP) is the primary energy carrier in cells. Its hydrolysis releases energy that can be used to drive other reactions.

• Hydrolysis of ATP:

• Standard free energy change: for ATP hydrolysis is highly negative, making it a favorable reaction.

Phosphoryl Group Transfer Potential

Some phosphate compounds have a higher phosphoryl group transfer potential than ATP, allowing them to donate phosphate groups to ADP to form ATP in coupled reactions.

• Example: Phosphoenolpyruvate (PEP) has a higher transfer potential than ATP due to resonance stabilization, charge repulsion, and product tautomerization.

Free Energy and Concentration Gradients Across Membranes

The movement of molecules across membranes is governed by free energy changes related to concentration gradients.

• Equation:

• If , is negative and transfer from region 1 to 2 is favorable.

• If , is positive and transfer is unfavorable.

• If , and the system is at equilibrium.

Free Energy and Reduction Potentials

Oxidation-reduction (redox) reactions involve the transfer of electrons. The standard reduction potential (E°) measures a species' tendency to gain electrons under standard conditions.

• The greater the E°, the greater the tendency to be reduced.

• Redox reactions are fundamental to energy generation in biological systems, such as ATP synthesis.

Summary Table: Types of Thermodynamic Systems

Summary Table: Relationships Between K, Q, and ΔG

Additional info: Some explanations and equations have been expanded for clarity and completeness, as is standard in academic study guides.