Enzyme kinetics is the study of the rates at which enzymes catalyze biochemical reactions. By measuring how reaction velocity changes with substrate concentration, scientists can determine key parameters that describe an enzyme’s activity and efficiency.
Key Concepts in Enzyme Kinetics
Reaction Velocity
The velocity of an enzyme-catalyzed reaction is measured as the amount of product formed per unit time. Initial velocity (V0) is measured at the beginning of the reaction when substrate concentration is much higher than product concentration.
Michaelis-Menten Equation
The Michaelis-Menten model describes the relationship between substrate concentration [S] and reaction velocity V:
V = Vmax × [S] / (Km + [S])
Vmax is the maximum velocity when the enzyme is saturated with substrate. Km (the Michaelis constant) is the substrate concentration at which the reaction rate is half of Vmax. It reflects the enzyme’s affinity for its substrate: a low Km means high affinity.
Michaelis-Menten Plot
When velocity is plotted against substrate concentration, the resulting curve is a hyperbola. At low substrate concentrations, velocity increases linearly. As substrate concentration increases, the curve approaches Vmax asymptotically.
Lineweaver-Burk Plot
The Lineweaver-Burk plot linearizes the Michaelis-Menten equation by taking the reciprocal of both sides:
1/V = (Km/Vmax) × 1/[S] + 1/Vmax
The x-intercept is -1/Km, and the y-intercept is 1/Vmax. This plot is useful for determining kinetic parameters and identifying types of enzyme inhibition.
Turnover Number (kcat)
The turnover number kcat represents the number of substrate molecules converted to product per enzyme molecule per second. It is calculated as kcat = Vmax / [E]total. The ratio kcat/Km measures catalytic efficiency.
Practical Michaelis-Menten Assay Protocol
Purify the enzyme of interest to homogeneity and determine its concentration by BCA assay. Prepare a 10× stock of substrate in the assay buffer. In a 96-well plate, set up 12 substrate concentrations spanning a range of 0.2× to 10× the estimated Km — use serial 2-fold dilutions (e.g., 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500 µM). Add 20 µL of substrate, 160 µL of assay buffer, and start the reaction with 20 µL of enzyme solution (final concentration adjusted to give a measurable rate). Measure product formation continuously for 5–10 minutes using a spectrophotometer or fluorometer at the appropriate wavelength (e.g., NADH absorbance at 340 nm for dehydrogenase reactions). Calculate initial velocity (V0) from the linear portion of the progress curve (typically the first 1–3 minutes) in units of µM product/min. Plot V0 vs. [S] and fit the Michaelis-Menten equation using nonlinear regression in GraphPad Prism or similar software. Extract Vmax and Km from the fit. For a Lineweaver-Burk plot, calculate 1/V0 and 1/[S], then plot 1/V0 on the y-axis vs. 1/[S] on the x-axis. The x-intercept = −1/Km, the y-intercept = 1/Vmax. For inhibitor characterization, repeat the assay at 2–3 inhibitor concentrations. Competitive inhibition shows a common y-intercept with increasing slopes (Km increases, Vmax unchanged); noncompetitive inhibition shows a common x-intercept with decreasing y-intercept (Vmax decreases, Km unchanged). Calculate Ki by replotting slopes vs. inhibitor concentration.
Real-World Application
The enzyme acetylcholinesterase (AChE) is assayed using acetylthiocholine as substrate, with DTNB (Ellman’s reagent) detecting the thiocholine product at 412 nm. Km for the reaction is 50 µM and Vmax is 150 µmol/min/mg. The inhibitor donepezil (an Alzheimer’s drug) shows competitive inhibition with a Ki of 2 nM. This characterization validates donepezil as a potent, reversible AChE inhibitor and supports its clinical dosing regimen.
