🧪Biophysical Chemistry Unit 4 – Chemical Kinetics and Enzyme Catalysis

Key Concepts and Definitions

• Chemical kinetics studies the rates of chemical reactions and the factors that influence them
• Reaction rate measures the change in concentration of reactants or products per unit time, typically expressed in units of molarity per second (M/s)
• Rate law is a mathematical expression that relates the reaction rate to the concentrations of reactants, often written as $rate = k[A]^m[B]^n$ where $k$ is the rate constant and $m$ and $n$ are the reaction orders with respect to reactants A and B
• Reaction order describes the dependence of the reaction rate on the concentration of a particular reactant
  • Zero-order reactions have rates independent of reactant concentrations
  • First-order reactions have rates directly proportional to the concentration of one reactant
  • Second-order reactions have rates proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants
• Enzymes are biological catalysts that accelerate chemical reactions in living organisms by lowering the activation energy barrier
• Michaelis-Menten kinetics is a model that describes the kinetic behavior of many enzymes, relating reaction velocity to substrate concentration

Reaction Rates and Rate Laws

• Reaction rates can be determined experimentally by measuring the change in concentration of reactants or products over time using techniques such as spectrophotometry or titration
• Differential rate laws express the reaction rate as a function of reactant concentrations and can be derived from the balanced chemical equation and experimental data
• Integrated rate laws describe the concentration of reactants or products as a function of time and are obtained by integrating the differential rate law
  • For a first-order reaction, the integrated rate law is $ln[A]_t = -kt + ln[A]_0$, where $[A]_t$ is the concentration of reactant A at time $t$, $[A]_0$ is the initial concentration, and $k$ is the rate constant
• Half-life ($t_{1/2}$) is the time required for the concentration of a reactant to decrease by half and is related to the rate constant for first-order reactions by $t_{1/2} = ln(2)/k$
• Activation energy ($E_a$) is the minimum energy required for reactants to overcome and form products, and its relationship with the rate constant is described by the Arrhenius equation, $k = Ae^{-E_a/RT}$, where $A$ is the pre-exponential factor, $R$ is the gas constant, and $T$ is the absolute temperature

Factors Affecting Reaction Rates

• Temperature increases reaction rates by providing more energy for reactants to overcome the activation energy barrier, typically doubling the rate for every 10°C rise in temperature
• Concentration of reactants affects reaction rates, with higher concentrations leading to more frequent collisions and faster rates, as described by the rate law
• Pressure changes can affect the rates of gas-phase reactions by altering the frequency of collisions between reactant molecules
• Catalysts accelerate reactions by providing an alternative pathway with a lower activation energy barrier, increasing the rate without being consumed in the reaction
  • Homogeneous catalysts are in the same phase as the reactants (e.g., acids and bases in solution)
  • Heterogeneous catalysts are in a different phase from the reactants (e.g., solid metal surfaces catalyzing gas-phase reactions)
• Surface area of solid reactants influences reaction rates, with smaller particle sizes and larger surface areas leading to faster rates due to increased contact between reactants

Reaction Mechanisms and Order

• Reaction mechanisms describe the step-by-step sequence of elementary reactions that lead to the overall chemical change, including the formation and breakdown of reaction intermediates
• Elementary steps are the individual molecular events that make up a reaction mechanism, each with its own rate law and molecularity
• Molecularity refers to the number of reactant species that participate in an elementary step, classified as unimolecular (one reactant), bimolecular (two reactants), or termolecular (three reactants)
• Rate-determining step is the slowest elementary step in a reaction mechanism, controlling the overall rate of the reaction
• Steady-state approximation assumes that the concentration of reaction intermediates remains constant over time, simplifying the kinetic analysis of complex mechanisms
• Pre-equilibrium approximation assumes that certain elementary steps reach equilibrium much faster than others, allowing the use of equilibrium constants to relate the concentrations of reactants and intermediates

Enzyme Structure and Function

• Enzymes are globular proteins with specific three-dimensional structures that enable them to bind substrates and catalyze reactions
• Active site is the region of an enzyme where substrates bind and the catalytic reaction occurs, typically consisting of a cleft or pocket lined with specific amino acid residues
• Substrate specificity refers to an enzyme's ability to discriminate between potential substrates, binding only to those with complementary shape and chemical properties
  • Lock-and-key model suggests that the active site and substrate have rigid, complementary shapes that fit together precisely
  • Induced fit model proposes that the active site is flexible and undergoes conformational changes upon substrate binding to optimize the fit
• Cofactors are non-protein molecules that some enzymes require for catalytic activity, such as metal ions (e.g., Zn^2+, Mg^2+) or organic molecules (e.g., NAD^+, FAD)
• Enzyme-substrate complex is the temporary association between an enzyme and its substrate, formed through non-covalent interactions such as hydrogen bonds and van der Waals forces

Enzyme Kinetics and Michaelis-Menten Model

• Michaelis-Menten equation relates the initial reaction velocity ($v_0$) to the substrate concentration ($[S]$), maximum velocity ($V_{max}$), and Michaelis constant ($K_m$): $v_0 = V_{max}[S] / (K_m + [S])$
  • $V_{max}$ represents the maximum reaction rate achieved at saturating substrate concentrations and is proportional to the total enzyme concentration
  • $K_m$ is the substrate concentration at which the reaction velocity is half of $V_{max}$ and indicates the enzyme's affinity for the substrate
• Lineweaver-Burk plot (double-reciprocal plot) is a linear transformation of the Michaelis-Menten equation, used to determine $V_{max}$ and $K_m$ from experimental data: $1/v_0 = (K_m/V_{max})(1/[S]) + 1/V_{max}$
• Turnover number ($k_{cat}$) represents the maximum number of substrate molecules converted to product per enzyme molecule per unit time and is related to $V_{max}$ by $k_{cat} = V_{max}/[E]_t$, where $[E]_t$ is the total enzyme concentration
• Catalytic efficiency ($k_{cat}/K_m$) measures an enzyme's overall effectiveness in catalyzing a reaction, considering both substrate binding and turnover

Inhibition and Regulation of Enzymes

• Enzyme inhibitors are molecules that decrease the activity of enzymes by binding to them and interfering with their function
• Competitive inhibitors bind to the active site of an enzyme, competing with the substrate and increasing the apparent $K_m$ without affecting $V_{max}$
  • Competitive inhibition can be overcome by increasing the substrate concentration
• Non-competitive inhibitors bind to an allosteric site on the enzyme, distinct from the active site, and decrease the apparent $V_{max}$ without affecting $K_m$
  • Non-competitive inhibition cannot be overcome by increasing the substrate concentration
• Uncompetitive inhibitors bind only to the enzyme-substrate complex, decreasing both the apparent $V_{max}$ and $K_m$
• Allosteric regulation involves the binding of effector molecules to allosteric sites, inducing conformational changes that alter the enzyme's activity
  • Allosteric activators enhance enzyme activity, while allosteric inhibitors decrease it
• Feedback inhibition is a regulatory mechanism in which the end product of a metabolic pathway inhibits the activity of an earlier enzyme in the pathway, preventing the excessive accumulation of intermediates

Real-World Applications and Examples

• Pharmaceutical industry uses enzyme kinetics to design and develop drugs that target specific enzymes involved in disease processes
  • HIV protease inhibitors (e.g., saquinavir, ritonavir) are competitive inhibitors that block the viral enzyme responsible for maturation of new virus particles
  • Statins (e.g., atorvastatin, simvastatin) are competitive inhibitors of HMG-CoA reductase, an enzyme involved in cholesterol biosynthesis, and are used to treat hypercholesterolemia
• Bioremediation employs microorganisms and their enzymes to degrade environmental pollutants such as oil spills, pesticides, and industrial waste
  • Dehalogenases catalyze the removal of halogen atoms from organic compounds, enabling bacteria to break down chlorinated pollutants like PCBs (polychlorinated biphenyls)
• Biosensors are analytical devices that use enzymes to detect and quantify specific molecules in biological samples, environmental monitoring, and food safety testing
  • Glucose oxidase-based biosensors measure blood glucose levels in people with diabetes by detecting the oxidation of glucose to gluconic acid and hydrogen peroxide
• Enzyme engineering involves modifying the structure and function of enzymes through genetic manipulation or directed evolution to improve their stability, specificity, or catalytic efficiency for industrial applications
  • Thermostable DNA polymerases (e.g., Taq polymerase from Thermus aquaticus) have been engineered for use in polymerase chain reaction (PCR) to amplify DNA at high temperatures
  • Cellulases from fungi and bacteria have been optimized to break down cellulose more efficiently for biofuel production from plant biomass