Free energy and chemical potential are key concepts in biological thermodynamics. They help us understand why reactions happen and how energy flows in living systems. These ideas explain everything from enzyme reactions to how cells maintain their structure.

Gibbs free energy determines if a process will happen on its own. Chemical potential drives the movement of substances in cells. Together, they're essential for predicting and explaining the complex chemical dance of life.

Gibbs free energy in biological systems

Definition and significance

• Gibbs free energy represents the maximum amount of work that can be extracted from a system at constant temperature and pressure
• The change in Gibbs free energy (ΔG) determines the spontaneity of a reaction or process
  • A negative ΔG indicates a spontaneous process
  • A positive ΔG indicates a non-spontaneous process
• Gibbs free energy is a crucial factor in determining the direction and feasibility of biochemical reactions in biological systems
  • Examples include metabolic pathways, protein folding, and ligand binding
• The change in Gibbs free energy is influenced by the change in enthalpy (ΔH), the change in entropy (ΔS) of the system, and the temperature (T) according to the equation: $ΔG = ΔH - TΔS$
• The standard Gibbs free energy change (ΔG°) is the change in free energy under standard conditions (1 atm pressure, 1 M concentration, and 298 K temperature) and serves as a reference point for comparing the spontaneity of different reactions

Factors influencing Gibbs free energy

• Temperature affects the change in Gibbs free energy by influencing the entropy term (TΔS) in the equation $ΔG = ΔH - TΔS$
  • Higher temperatures favor reactions with positive entropy changes (ΔS > 0)
  • Lower temperatures favor reactions with negative entropy changes (ΔS < 0)
• Pressure can impact the change in Gibbs free energy, particularly for reactions involving gases, by altering the enthalpy term (ΔH) in the equation $ΔG = ΔH - TΔS$
  • Increasing pressure favors reactions that result in a decrease in volume (fewer moles of gas)
  • Decreasing pressure favors reactions that result in an increase in volume (more moles of gas)
• Concentration of reactants and products affects the change in Gibbs free energy by influencing the reaction quotient (Q) in the equation $ΔG = ΔG° + RT \ln Q$
  • Higher concentrations of reactants relative to products drive the reaction forward (negative ΔG)
  • Higher concentrations of products relative to reactants drive the reaction backward (positive ΔG)

Calculating Gibbs free energy changes

Calculating ΔG using the reaction quotient

• The change in Gibbs free energy for a reaction can be calculated using the equation: $ΔG = ΔG° + RT \ln Q$
  • R is the gas constant (8.314 J/mol·K)
  • T is the temperature in Kelvin
  • Q is the reaction quotient
• The reaction quotient (Q) is the ratio of the product of the concentrations of the reaction products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients
• At equilibrium, ΔG = 0 and Q = K, where K is the equilibrium constant
  • The relationship between ΔG° and K is given by the equation: $ΔG° = -RT \ln K$

Calculating ΔG using standard Gibbs free energy of formation

• The change in Gibbs free energy can also be calculated using the standard Gibbs free energy of formation (ΔG°f) of the reactants and products according to the equation: $ΔG° = Σ(n × ΔG°f \text{ products}) - Σ(n × ΔG°f \text{ reactants})$
  • n is the stoichiometric coefficient
• Standard Gibbs free energy of formation values are tabulated for many compounds at standard conditions (1 atm pressure, 1 M concentration, and 298 K temperature)
• By using these tabulated values, the ΔG° for a reaction can be calculated without the need for experimental measurements

Coupling reactions to drive spontaneity

• Coupling reactions with favorable (negative) ΔG to reactions with unfavorable (positive) ΔG can drive the overall process in the direction of spontaneity
• This coupling is essential for many biological processes
  • ATP synthesis is driven by the coupling of the unfavorable reaction (positive ΔG) with the favorable oxidation of glucose (negative ΔG) during cellular respiration
  • Active transport of molecules across membranes against their concentration gradient (positive ΔG) is coupled with the favorable hydrolysis of ATP (negative ΔG)

Chemical potential and free energy

Definition and relationship to Gibbs free energy

• Chemical potential (μ) represents the change in Gibbs free energy of a system when one mole of a substance is added or removed at constant temperature, pressure, and composition of other components
• The chemical potential of a substance depends on its concentration and other factors such as temperature, pressure, and the presence of other substances in the system
• In a mixture of substances, the chemical potential of each component is related to its partial molar Gibbs free energy, which is the contribution of that component to the total Gibbs free energy of the system

Driving force for substance movement

• The difference in chemical potential between two states or locations is the driving force for the net movement of a substance
  • Examples include diffusion, osmosis, and active transport across biological membranes
• Substances tend to move from regions of higher chemical potential to regions of lower chemical potential, reducing the overall Gibbs free energy of the system
• At equilibrium, the chemical potentials of a substance in all phases or compartments of a system are equal, resulting in no net movement of the substance

Spontaneity of biological processes

Predicting spontaneity using ΔG

• The spontaneity of a biological process can be predicted by considering the change in Gibbs free energy (ΔG) of the system
  • Processes with a negative ΔG are spontaneous
  • Processes with a positive ΔG are non-spontaneous
• The direction of a biochemical reaction can be determined by comparing the chemical potentials of the reactants and products
  • Reactions proceed in the direction that reduces the overall Gibbs free energy of the system

Examples of spontaneity in biological systems

• Maintenance of concentration gradients across biological membranes
  • Requires the input of energy to overcome the natural tendency of substances to move down their concentration gradients (from high chemical potential to low chemical potential)
• Conformational changes in proteins (enzyme catalysis, signal transduction)
  • Driven by the minimization of Gibbs free energy, resulting in the most stable and thermodynamically favorable structures
• Binding of ligands to proteins (oxygen to hemoglobin, substrates to enzymes)
  • Governed by the change in Gibbs free energy of the system, with the most stable complexes having the lowest free energy
• Protein folding and stability
  • Native protein structures represent the lowest Gibbs free energy state under physiological conditions
  • Denaturation of proteins occurs when the Gibbs free energy of the unfolded state becomes lower than that of the native state (e.g., due to changes in temperature, pH, or presence of denaturants)