Free energy is the driving force behind chemical reactions. It determines whether a process will occur spontaneously or not. In biological systems, understanding free energy changes helps explain how cells harness energy from nutrients to power vital functions.

Gibbs free energy combines enthalpy and entropy to predict reaction spontaneity. Negative ΔG values indicate spontaneous reactions, while positive values show non-spontaneous ones. This concept is crucial for grasping metabolic pathways and cellular energetics in biochemistry.

Gibbs Free Energy and Spontaneity

Thermodynamic Potential and Reaction Direction

• Gibbs free energy (G) measures maximum reversible work performed by thermodynamic system at constant temperature and pressure
• Change in Gibbs free energy (ΔG) determines direction and extent of chemical reaction
• Gibbs free energy expressed as $G = H - TS$ (H enthalpy, T temperature, S entropy)
• Negative ΔG indicates spontaneous reaction
• Positive ΔG indicates non-spontaneous reaction
• Zero ΔG (ΔG = 0) signifies reaction at equilibrium

Applications in Biochemical Systems

• Gibbs free energy crucial for understanding energetics of biochemical reactions and cellular processes
• Standard Gibbs free energy change (ΔG°) calculated using standard enthalpies of formation and standard entropies
• Relationship between ΔG and ΔG° given by $ΔG = ΔG° + RT ln Q$ (R gas constant, T temperature, Q reaction quotient)
• In biochemical systems, standard state typically defined at pH 7.0 (resulting standard free energy change denoted as ΔG°')
• Magnitude of ΔG provides information about driving force of reaction
  • Larger negative values indicate greater tendency for reaction to proceed forward
• Many biological processes utilize coupled reactions
  • Overall ΔG sum of individual ΔG values for each reaction in series

Calculating Gibbs Free Energy Change

Fundamental Equations and Standard Conditions

• Change in Gibbs free energy (ΔG) calculated using equation $ΔG = ΔH - TΔS$ (ΔH change in enthalpy, T temperature, ΔS change in entropy)
• Standard Gibbs free energy change (ΔG°) calculated under standard conditions
  • Standard conditions temperature 25°C, pressure 1 atm, concentrations 1 M
• Relationship between ΔG and equilibrium constant (K) given by $ΔG° = -RT ln K$ (R gas constant, T temperature)
• Spontaneity of reaction can change with temperature due to $ΔG = ΔH - TΔS$ relationship
  • Reactions may become spontaneous or non-spontaneous at different temperatures

Practical Applications and Examples

• ΔG calculations essential for predicting feasibility of chemical reactions (industrial processes, drug design)
• Example: Combustion of methane
  • $CH_4 + 2O_2 → CO_2 + 2H_2O$
  • ΔG° = -818 kJ/mol (highly spontaneous reaction)
• Example: Synthesis of ammonia
  • $N_2 + 3H_2 → 2NH_3$
  • ΔG° = -33.3 kJ/mol (spontaneous but less so than methane combustion)
• In biochemistry, ΔG calculations help understand metabolic pathways (glycolysis, citric acid cycle)
  • Example: Glucose breakdown in glycolysis
    • $C_6H_{12}O_6 + 2NAD^+ + 2ADP + 2Pi → 2C_3H_4O_3 + 2NADH + 2H^+ + 2ATP + 2H_2O$
    • ΔG°' = -74 kJ/mol (spontaneous under cellular conditions)

Predicting Reaction Spontaneity

Criteria for Spontaneity and Equilibrium

• Reaction spontaneous when ΔG < 0 (products have lower free energy than reactants)
• Reaction non-spontaneous when ΔG > 0 (products have higher free energy than reactants)
• Reaction at equilibrium when ΔG = 0 (no net change in concentrations of reactants and products)
• Larger magnitude of negative ΔG indicates greater driving force for reaction
• Spontaneity does not necessarily imply fast reaction rate
  • Kinetically unfavorable reactions may still be thermodynamically spontaneous

Biological Systems and Coupled Reactions

• Many thermodynamically unfavorable reactions (positive ΔG) coupled with favorable reactions (negative ΔG) in biological systems
• ATP hydrolysis often drives unfavorable reactions in cells
  • Example: Glucose phosphorylation in glycolysis
    • $Glucose + ATP → Glucose-6-phosphate + ADP$ (ΔG°' = +13.8 kJ/mol)
    • Coupled with ATP hydrolysis (ΔG°' = -30.5 kJ/mol)
    • Overall reaction becomes spontaneous
• Redox reactions in electron transport chain drive ATP synthesis
  • Example: NADH oxidation coupled to ATP synthesis in mitochondria
    • $NADH + H^+ + 1/2O_2 → NAD^+ + H_2O$ (ΔG°' = -220 kJ/mol)
    • Drives ATP synthesis (ΔG°' = +30.5 kJ/mol)

Enzyme Impact on Activation Energy

Enzyme Mechanism and Catalysis

• Enzymes biological catalysts lowering activation energy (Ea) of reaction without being consumed
• Enzymes increase rate of both forward and reverse reactions allowing faster equilibrium
• Enzyme-substrate complex formation stabilizes transition state providing alternative reaction pathway with lower activation energy
• Active site of enzyme specifically shaped to bind substrate(s) and facilitate reaction through various mechanisms
  • Proximity effects bring reactants closer together
  • Orientation effects align substrates in optimal position for reaction
  • Transition state stabilization lowers energy barrier

Enzyme Kinetics and Regulation

• Enzymes do not change overall ΔG of reaction only affect kinetics by lowering activation energy barrier
• Michaelis-Menten equation describes kinetics of enzyme-catalyzed reactions
  • $v = \frac{V_{max}[S]}{K_m + [S]}$ (v reaction rate, Vmax maximum rate, [S] substrate concentration, Km Michaelis constant)
• Enzyme activity regulated through various mechanisms
  • Allosteric regulation involves binding of effector molecules to site other than active site
  • Covalent modification alters enzyme structure and activity (phosphorylation, acetylation)
  • Competitive inhibition involves inhibitor binding to active site
  • Non-competitive inhibition involves inhibitor binding to allosteric site
• Example: Catalase enzyme decomposition of hydrogen peroxide
  • $2H_2O_2 → 2H_2O + O_2$
  • Catalase lowers activation energy from 75 kJ/mol to 8 kJ/mol
  • Reaction rate increases by factor of 10^7