Michaelis-Menten Calculator

Calculate enzyme reaction velocity using the Michaelis-Menten equation for enzyme kinetics

Km = substrate concentration at ½Vmax

Understanding Michaelis-Menten Kinetics

The Michaelis-Menten equation is fundamental to enzyme kinetics, describing how the rate of an enzyme-catalyzed reaction depends on substrate concentration. It provides crucial parameters that characterize enzyme efficiency and affinity for substrates.

The Michaelis-Menten Equation

v = (Vmax × [S]) / (Km + [S])

Enzyme reaction velocity equation

v = Reaction velocity

The rate at which product is formed (units: M/s, µM/min, etc.)

Vmax = Maximum velocity

The maximum rate when enzyme is saturated with substrate

[S] = Substrate concentration

The concentration of the substrate (units: M, mM, µM)

Km = Michaelis constant

The substrate concentration at which v = ½Vmax (same units as [S])

Understanding Km

The Michaelis constant (Km) is a key parameter that indicates:

  • Low Km (e.g., 10 µM): High enzyme-substrate affinity, enzyme binds substrate tightly
  • High Km (e.g., 10 mM): Low enzyme-substrate affinity, weak binding
  • Practical meaning: Km represents the substrate concentration needed to reach half-maximum velocity

Practical Example

Hexokinase Enzyme

  • Vmax = 100 µM/min
  • Km = 0.1 mM (100 µM)
  • [Glucose] = 0.2 mM (200 µM)

v = (100 × 200) / (100 + 200)
v = 20,000 / 300
v = 66.67 µM/min

This is 66.67% of Vmax, showing the enzyme is working efficiently at this substrate concentration

Key Concepts

🧬 Enzyme-Substrate Complex

E + S ⇌ ES → E + P (Formation of ES complex is key)

📊 Saturation Kinetics

At high [S], all enzyme active sites are occupied

⚡ Catalytic Efficiency

kcat/Km ratio measures enzyme efficiency

🎯 Steady State

[ES] remains constant during the reaction

Experimental Determination

Lineweaver-Burk Plot

A double reciprocal plot (1/v vs 1/[S]) linearizes the Michaelis-Menten equation:

1/v = (Km/Vmax) × (1/[S]) + 1/Vmax

  • • y-intercept = 1/Vmax
  • • x-intercept = -1/Km
  • • slope = Km/Vmax

Applications

  • 💊
    Drug Development: Understanding enzyme inhibition for designing pharmaceuticals
  • 🧬
    Metabolic Studies: Analyzing metabolic pathways and enzyme deficiencies
  • 🔬
    Diagnostic Assays: Clinical enzyme assays for disease detection
  • 🏭
    Industrial Biotechnology: Optimizing enzyme-based production processes
  • 🧪
    Research: Characterizing new enzymes and understanding catalytic mechanisms
  • 🌱
    Agriculture: Studying plant enzymes for crop improvement

🧬Quick Reference

Units:

M/s, µM/min, mM/s

Formula:

v = (Vmax × [S]) / (Km + [S])

At Km:

v = ½Vmax

Applications:

Enzyme kinetics, drug design

Level:

College Biochemistry

🔗Related Calculators

📐Related Formulas

🎯Where It's Used

  • 💊

    Pharmaceutical Industry

    Drug design and testing

  • 🏥

    Clinical Diagnostics

    Enzyme activity assays

  • 🔬

    Research

    Enzyme characterization

  • 🏭

    Biotechnology

    Industrial enzyme optimization