explain that the maximum rate of reaction (Vmax) is used to derive the Michaelis–Menten constant (Km), which is used to compare the affinity of different enzymes for their substrates

Factors that Affect Enzyme Action

Learning Objective

Explain that the maximum rate of reaction (V_max) is used to derive the Michaelis–Menten constant (K_m), which is then used to compare the affinity of different enzymes for their substrates.

1. Introduction to Enzyme Kinetics

Enzymes are biological catalysts that accelerate chemical reactions by lowering the activation energy. The rate at which an enzyme catalyses a reaction depends on several factors, the most important of which are substrate concentration, temperature, pH, and the presence of inhibitors or activators.

2. Key Factors Influencing Enzyme Activity

• Substrate concentration: At low concentrations the reaction rate increases proportionally with substrate; at high concentrations the rate approaches a maximum (V_max).
• Temperature: Reaction rates rise with temperature up to an optimum; beyond this, denaturation reduces activity.
• pH: Each enzyme has an optimum pH; deviations alter ionisation of active‑site residues.
• Inhibitors:

  • Competitive – bind to the active site, increasing apparent K_m but not affecting V_max.
  • Non‑competitive – bind elsewhere, decreasing V_max without changing K_m.

• Co‑factors and co‑enzymes: Required for activity of many enzymes; their absence lowers the observed rate.

3. Michaelis–Menten Kinetics

The relationship between reaction velocity (v) and substrate concentration ([S]) for many enzymes is described by the Michaelis–Menten equation:

\$\$

v = \frac{V{\text{max}}[S]}{Km + [S]}

\$\$

Where:

• V_max = maximum velocity when all enzyme molecules are saturated with substrate.
• K_m = substrate concentration at which the reaction proceeds at half of V_max (i.e., \$v = \tfrac{1}{2}V_{\text{max}}\$).

4. Determining V_max and K_m

1. Measure initial reaction rates (v) at a series of substrate concentrations.
2. Plot the data on a Michaelis–Menten curve (v vs. [S]). The asymptote of the curve gives V_max.
3. Alternatively, transform the data using a Lineweaver–Burk plot (double reciprocal):

   \$\$

   \frac{1}{v} = \frac{Km}{V{\text{max}}}\frac{1}{[S]} + \frac{1}{V_{\text{max}}}

   \$\$

   The y‑intercept equals \$1/V{\text{max}}\$ and the slope equals \$Km/V_{\text{max}}\$, from which both constants can be calculated.

5. Using K_m to Compare Enzyme Affinity

A lower K_m indicates that the enzyme reaches half‑maximal velocity at a lower substrate concentration, reflecting a higher affinity for that substrate. Conversely, a higher K_m denotes lower affinity.

6. Summary

• The maximum rate (V_max) reflects the catalytic capacity of an enzyme when fully saturated with substrate.
• The Michaelis constant (K_m) is derived from V_max and provides a quantitative measure of substrate affinity.
• Comparing K_m values across enzymes allows us to predict which enzyme will be more effective at low substrate concentrations.
• Understanding how temperature, pH, and inhibitors affect V_max and K_m helps explain enzyme behaviour in physiological and experimental contexts.