🧪Biophysical Chemistry Unit 2 – Biological Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the flow and transformation of energy in systems, including biological systems
• Enthalpy ($H$) represents the total heat content of a system
  • Includes both the internal energy ($U$) and the product of pressure and volume ($PV$)
• Entropy ($S$) measures the degree of disorder or randomness in a system
  • Higher entropy indicates greater disorder and lower available energy for work
• Gibbs free energy ($G$) predicts the spontaneity of a reaction or process
  • Defined as $G = H - TS$, where $T$ is the absolute temperature
• Chemical potential ($\mu$) describes the energy required to add or remove a particle from a system
• Equilibrium occurs when a system reaches a state of minimum free energy and maximum entropy
  • At equilibrium, the forward and reverse reaction rates are equal

Laws of Thermodynamics in Biology

• The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • In biological systems, energy is conserved through metabolic pathways and energy coupling
• The Second Law of Thermodynamics asserts that the total entropy of an isolated system always increases over time
  • Biological systems maintain order by consuming energy and exporting entropy to the environment
• The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero is zero
  • Provides a reference point for measuring entropy changes in biological systems
• Zeroth Law of Thermodynamics defines thermal equilibrium and allows for the measurement of temperature
• Biological systems operate far from equilibrium, requiring a constant input of energy to maintain their organized state

Energy and Entropy in Biological Systems

• Biological systems require a continuous supply of energy to maintain their structure and function
• Metabolism involves the breakdown of complex molecules (catabolism) to release energy and the synthesis of complex molecules (anabolism) using that energy
  • Catabolic pathways (glycolysis, citric acid cycle) release energy by oxidizing organic molecules
  • Anabolic pathways (photosynthesis, protein synthesis) consume energy to build complex molecules
• ATP (adenosine triphosphate) serves as the primary energy currency in cells
  • Hydrolysis of ATP to ADP (adenosine diphosphate) and inorganic phosphate releases energy for cellular processes
• Entropy drives the formation of more disordered states, such as the denaturation of proteins or the diffusion of molecules across membranes
• Cells maintain low entropy by coupling endergonic (energy-consuming) processes with exergonic (energy-releasing) processes
  • Example: ATP synthesis is coupled to the electron transport chain in oxidative phosphorylation

Free Energy and Spontaneous Processes

• Gibbs free energy ($G$) determines the spontaneity of a process at constant temperature and pressure
  • A negative change in free energy ($\Delta G < 0$) indicates a spontaneous process
  • A positive change in free energy ($\Delta G > 0$) indicates a non-spontaneous process
• The change in free energy is given by $\Delta G = \Delta H - T\Delta S$
  • $\Delta H$ is the change in enthalpy, $T$ is the absolute temperature, and $\Delta S$ is the change in entropy
• Exergonic reactions release energy ($\Delta G < 0$) and are spontaneous
  • Examples: ATP hydrolysis, glucose oxidation, and the formation of peptide bonds
• Endergonic reactions require an input of energy ($\Delta G > 0$) and are non-spontaneous
  • Examples: ATP synthesis, protein folding, and the formation of glycosidic bonds
• Coupled reactions can drive endergonic processes by linking them to exergonic processes
  • Example: ATP synthesis is coupled to the proton gradient generated by the electron transport chain

Equilibrium in Biochemical Reactions

• Chemical equilibrium occurs when the forward and reverse reaction rates are equal
  • At equilibrium, the concentrations of reactants and products remain constant
• The equilibrium constant ($K_{eq}$) is the ratio of the product concentrations to the reactant concentrations at equilibrium
  • $K_{eq} = \frac{[Products]}{[Reactants]}$, where brackets denote concentrations
• The standard free energy change ($\Delta G^{\circ}$) is related to the equilibrium constant by $\Delta G^{\circ} = -RT \ln K_{eq}$
  • $R$ is the gas constant, and $T$ is the absolute temperature
• Le Châtelier's principle states that a system at equilibrium will shift to counteract any disturbance
  • Example: Increasing the concentration of a reactant will shift the equilibrium towards the products
• Many biochemical reactions are reversible and can be driven in either direction by changing the concentrations of reactants or products
  • Example: The phosphorylation of glucose by hexokinase is reversible and can be driven towards glucose-6-phosphate by increasing the concentration of ATP

Thermodynamics of Protein Folding

• Protein folding is the process by which a polypeptide chain adopts its native three-dimensional structure
• The native state of a protein is the conformation with the lowest Gibbs free energy
  • The folding process is driven by a decrease in free energy ($\Delta G < 0$)
• Protein stability is determined by the balance between enthalpic and entropic contributions
  • Enthalpic contributions (hydrogen bonding, van der Waals interactions) favor the folded state
  • Entropic contributions (conformational entropy, hydrophobic effect) favor the unfolded state
• The hydrophobic effect is a major driving force for protein folding
  • Nonpolar amino acids are buried in the protein interior to minimize their contact with water
• Protein denaturation occurs when the native structure is disrupted by heat, pH, or chemical denaturants
  • Denaturation is an endothermic process ($\Delta H > 0$) driven by an increase in entropy ($\Delta S > 0$)
• Chaperones are proteins that assist in the folding of other proteins
  • Example: Hsp70 (heat shock protein 70) binds to unfolded proteins and prevents aggregation

Membrane Potentials and Ion Transport

• Biological membranes maintain concentration gradients of ions across their surface
  • The concentration gradient generates an electrochemical potential difference called the membrane potential
• The Nernst equation relates the membrane potential to the concentration gradient of an ion
  • $E = \frac{RT}{zF} \ln \frac{[Ion]_{out}}{[Ion]_{in}}$, where $E$ is the membrane potential, $R$ is the gas constant, $T$ is the absolute temperature, $z$ is the ion's charge, and $F$ is Faraday's constant
• Ion channels and transporters facilitate the movement of ions across membranes
  • Ion channels (voltage-gated, ligand-gated) allow passive diffusion down the electrochemical gradient
  • Transporters (pumps, exchangers) use energy to move ions against their electrochemical gradient
• The sodium-potassium pump (Na+/K+ ATPase) maintains the resting membrane potential in neurons
  • Pumps 3 Na+ out of the cell and 2 K+ into the cell for each ATP hydrolyzed
• The action potential is a rapid depolarization and repolarization of the membrane potential in neurons
  • Triggered by the opening of voltage-gated sodium channels and the influx of Na+
• Thermodynamics governs the direction and magnitude of ion fluxes across membranes
  • Ions move down their electrochemical gradient to minimize the system's free energy

Applications in Molecular Biology and Biotechnology

• Thermodynamic principles are used to design and optimize biochemical assays and processes
• Polymerase chain reaction (PCR) relies on temperature cycling to amplify DNA
  • Denaturation (94°C) separates DNA strands, annealing (50-60°C) allows primers to bind, and extension (72°C) synthesizes new DNA
• Isothermal titration calorimetry (ITC) measures the heat released or absorbed during a biomolecular interaction
  • Used to determine binding affinities, stoichiometry, and thermodynamic parameters ($\Delta H$, $\Delta S$, $\Delta G$)
• Differential scanning calorimetry (DSC) measures the heat capacity of a protein as a function of temperature
  • Used to study protein stability, folding, and ligand binding
• Thermodynamic analysis guides the design of metabolic pathways for the production of biofuels and chemicals
  • Example: The introduction of a non-native pathway for butanol synthesis in Escherichia coli
• Directed evolution uses iterative rounds of mutation and selection to improve enzyme stability and activity
  • Thermodynamic principles (free energy, entropy) guide the selection of stable and active variants
• Thermodynamics is essential for understanding and engineering biological systems for various applications
  • Examples: Drug design, protein engineering, metabolic engineering, and synthetic biology