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Michaelis-Menten Kinetics

How enzymes accelerate reactions: v = Vmax·[S] / (Km + [S])

Biochemistry Enzymology Kinetics Inhibition
Inhibitor:
Vmax = 10 µM/s Km = 5 µM Km(app) = 5 µM Vmax(app) = 10 µM/s kcat/Km = —

🧬 Michaelis-Menten Enzyme Kinetics

Enzymes bind substrate S into an active site, forming an enzyme–substrate complex ES, then release product P: E + S ⇌ ES → E + P

Under steady-state (d[ES]/dt ≈ 0), the reaction velocity follows the hyperbolic Michaelis-Menten equation: v = Vmax · [S] / (Km + [S])

Km (Michaelis constant) is the substrate concentration at which v = Vmax/2. A low Km means high affinity. Vmax = kcat · [E]total.

Inhibition types:

  • Competitive: Km(app) = Km(1 + [I]/Ki); Vmax unchanged. Inhibitor competes for active site.
  • Uncompetitive: Km(app) = Km/α'; Vmax(app) = Vmax/α'. Binds only ES complex.
  • Non-competitive: Km unchanged; Vmax(app) = Vmax/α'. Binds E and ES equally.

The Lineweaver-Burk double-reciprocal plot (1/v vs 1/[S]) linearises the hyperbola: x-intercept = −1/Km, y-intercept = 1/Vmax. Each inhibitor pattern shifts the line in a characteristic way.

About this simulation

This simulator plots enzyme reaction velocity against substrate concentration using the classic Michaelis-Menten equation, v = Vmax·[S] / (Km + [S]). The left canvas shows the hyperbolic v versus [S] curve; the right canvas shows the matching Lineweaver-Burk double-reciprocal plot. By adjusting Vmax, Km, the inhibitor concentration [I] and its dissociation constant Ki, you can watch how competitive, uncompetitive and non-competitive inhibition reshape the curve and its apparent parameters in real time.

🔬 What it shows

The steady-state Michaelis-Menten model of a single enzyme acting on one substrate. The hyperbola approaches Vmax at saturation, with Km marking the [S] where v equals Vmax/2. The Lineweaver-Burk plot linearises this hyperbola so the y-intercept reads 1/Vmax and the x-intercept reads −1/Km, making each inhibition pattern visually distinct.

🎮 How to use

Pick an inhibitor mode with the four buttons (None, Competitive, Uncompetitive, Non-competitive). Use the sliders to set Vmax (2–20 µM/s), Km (1–20 µM), inhibitor concentration [I] (0–10 µM) and Ki (0.5–10 µM). The stats bar updates Vmax, Km, the apparent Km(app) and Vmax(app), and a kcat/Km efficiency figure as you drag.

💡 Did you know?

Leonor Michaelis and Maud Menten published their equation in 1913 working on invertase. The specificity constant kcat/Km has an upper ceiling near 10⁸–10⁹ M⁻¹s⁻¹, set by the rate at which substrate can diffuse into the active site, and enzymes near this limit are called catalytically perfect.

Frequently asked questions

What is the Michaelis-Menten equation?

It is the rate law v = Vmax·[S] / (Km + [S]), describing how an enzyme's reaction velocity depends on substrate concentration [S]. It is derived under the steady-state assumption that the enzyme-substrate complex ES forms and breaks down at a constant rate, giving a hyperbolic relationship that levels off at the maximum velocity Vmax.

What do Km and Vmax actually mean?

Vmax is the maximum velocity reached when the enzyme is saturated with substrate, and it equals kcat times the total enzyme concentration. Km, the Michaelis constant, is the substrate concentration at which the velocity is exactly half of Vmax. A low Km signals high apparent affinity, since little substrate is needed to half-saturate the enzyme.

How do the three inhibition modes differ?

Competitive inhibitors raise the apparent Km to Km(1 + [I]/Ki) but leave Vmax unchanged, because high substrate can out-compete them. Uncompetitive inhibitors bind only the ES complex and divide both Km and Vmax by the same factor. Non-competitive inhibitors bind enzyme and complex equally, lowering Vmax while leaving Km unchanged.

Why use a Lineweaver-Burk plot?

Taking reciprocals turns the Michaelis-Menten hyperbola into a straight line of 1/v against 1/[S], where the y-intercept is 1/Vmax, the x-intercept is −1/Km and the slope is Km/Vmax. This makes the kinetic constants easy to read off and, crucially, gives each inhibition type a characteristic signature in how the intercepts shift.

Is this simulation physically accurate?

The curves use the exact textbook equations for Michaelis-Menten kinetics and the standard apparent-parameter formulas for the three inhibition types, so the shapes and intercepts are correct. It models an idealised single-substrate enzyme at steady state and does not capture cooperativity, multi-substrate mechanisms or product inhibition, which is appropriate for a teaching tool.