Rucete ✏ Lehninger Principles of Biochemistry In a Nutshell
6.3 Enzyme Kinetics as an Approach to Understanding Mechanism
This chapter explains how enzyme kinetics—the study of reaction rates—provides critical insights into enzyme mechanisms, using the Michaelis-Menten equation and inhibition analysis as core tools. It covers the effects of substrate concentration, reaction conditions, and inhibitors, as well as the interpretation and comparison of kinetic parameters.
Principles of Enzyme Kinetics and Mechanistic Analysis
• Enzyme mechanisms can be explored by studying the 3D structure, mutagenesis, protein chemistry, and most fundamentally, by measuring how reaction rates change under varying experimental conditions (enzyme kinetics).
• The most widely used approach is steady-state kinetics: measuring how the reaction rate (velocity) changes as a function of substrate concentration, under initial conditions where enzyme-substrate complex concentration is nearly constant.
• In an enzyme-catalyzed reaction, the enzyme cycles between free (E) and substrate-bound (ES) forms; after a brief pre–steady state, the ES complex concentration reaches a steady state for much of the reaction course.
Dependence of Reaction Rate on Substrate Concentration
• The initial velocity (v₀) is measured before significant substrate is converted to product, allowing [S] to be treated as constant.
• At low [S], v₀ increases almost linearly with [S]; at higher [S], increases in [S] have diminishing effect, and v₀ approaches a maximum velocity (Vmax), characteristic of saturation kinetics.
• This saturation effect reflects that, at high [S], essentially all enzyme is in ES form and further increases in substrate cannot increase the rate.
The Michaelis-Menten Equation and Its Derivation
• The Michaelis-Menten equation quantitatively relates initial velocity (v₀), substrate concentration ([S]), maximum velocity (Vmax), and the Michaelis constant (Km):
v₀ = (Vmax × [S]) / (Km + [S])
• Km is the substrate concentration at which the reaction rate is half-maximal.
• The equation is derived by assuming a rapid equilibrium of E and S forming ES, with breakdown of ES to product as the rate-limiting step; the steady-state assumption equates the rate of ES formation to its breakdown.
• At low [S], the equation simplifies to first-order kinetics (v₀ ∝ [S]); at high [S], to zero-order (v₀ ≈ Vmax).
• Parameters can be determined by nonlinear regression or, classically, using linear transformations such as the Lineweaver-Burk (double-reciprocal) plot.
Interpretation of Kinetic Parameters (Km, Vmax, kcat)
• Km varies with enzyme and substrate and is sometimes, but not always, a measure of ES complex affinity; its precise meaning depends on the reaction mechanism.
• Vmax reflects the turnover limit of the enzyme at saturating substrate. kcat (turnover number) is the number of substrate molecules converted to product per enzyme molecule per unit time at saturation (kcat = Vmax/[E]total).
• The specificity constant (kcat/Km) measures catalytic efficiency; the theoretical upper limit is set by substrate diffusion (about 10⁸–10⁹ M⁻¹s⁻¹). Enzymes with kcat/Km near this limit are considered "catalytically perfect."
Kinetics of Multisubstrate Reactions
• Many enzymes catalyze reactions with two or more substrates (bisubstrate reactions), proceeding via ternary complex formation (random or ordered) or via a Ping-Pong (double displacement) mechanism.
• The Michaelis-Menten approach and Lineweaver-Burk analysis can distinguish these mechanisms; e.g., intersecting lines indicate a ternary complex, parallel lines indicate a Ping-Pong pathway.
• Cleland nomenclature provides a standardized shorthand for describing multisubstrate mechanisms.
Effects of pH on Enzyme Activity
• Enzymes exhibit optimal activity at a specific pH or pH range; activity decreases outside this optimum due to effects on ionizable groups in the active site or on the substrate.
• pH-rate profiles can suggest the involvement of specific amino acid residues, but interpretation must consider protein microenvironments that may alter apparent pKa values.
Pre–Steady State Kinetics
• Pre–steady state kinetics (transient phase) allows measurement of individual reaction steps and identification of the rate-limiting step, often using rapid-mixing or stopped-flow techniques.
• Observation of a "burst" of product formation can indicate which step is limiting (e.g., product release).
Enzyme Inhibition: Reversible and Irreversible
• Enzyme inhibitors are classified as reversible (competitive, uncompetitive, mixed) or irreversible.
• Competitive inhibitors bind the active site, increasing apparent Km without affecting Vmax; uncompetitive inhibitors bind only to ES complex, decreasing both apparent Km and Vmax; mixed inhibitors bind either E or ES, affecting both parameters to varying degrees.
• Lineweaver-Burk plots help distinguish these inhibition types: competitive (lines intersect on y-axis), uncompetitive (parallel lines), mixed (intersecting off axes).
• Irreversible inhibitors covalently modify the enzyme or bind so tightly as to permanently inactivate it; suicide inactivators and transition-state analogs are key tools in drug design and mechanistic analysis.
Worked Examples and Medical Relevance
• Calculations demonstrate how to use the Michaelis-Menten equation to determine kinetic parameters and the effects of inhibitors.
• Clinical examples: competitive inhibition in methanol poisoning treatment with ethanol; suicide inactivators in treatment of African sleeping sickness; transition-state analogs in modern drug design.
In a Nutshell
• Enzyme kinetics—especially analysis using the Michaelis-Menten equation—remains the foundation for understanding how enzymes work, how their activity is regulated, and how they are inhibited.
• Key parameters (Km, Vmax, kcat, kcat/Km) provide quantitative measures of catalytic efficiency and allow mechanistic comparison between enzymes and reaction conditions.
• Analysis of kinetic data, effects of pH, and inhibitor types supports not only mechanistic understanding but also rational drug discovery and the design of enzyme-targeted therapies.