v vs [S] — Michaelis-Menten curve & Lineweaver-Burk (inset)
[S] depletion & [P] formation over time
This simulation models how an enzyme converts substrate into product under the Michaelis-Menten framework. The initial reaction rate follows v = Vmax·[S] / (Km + [S]), a rectangular hyperbola that rises steeply at low substrate and plateaus at Vmax when active sites become saturated. It draws this v–[S] curve, an inset Lineweaver-Burk (double-reciprocal) plot, and a time course of substrate depletion and product formation.
Sliders set Vmax (1–30 μmol/min), Km (0.1–20 mM), initial substrate [S]₀, inhibitor concentration [I], and the inhibition constant Ki, while a menu chooses competitive, non-competitive or uncompetitive inhibition. Presets load real enzymes such as hexokinase, chymotrypsin and carbonic anhydrase. These ideas underpin drug design, where many medicines act as enzyme inhibitors.
What is the Michaelis-Menten equation?
It relates the initial reaction velocity to substrate concentration: v = Vmax·[S] / (Km + [S]). Vmax is the maximum rate at saturating substrate, and Km is the substrate concentration giving half of Vmax. The curve is a rectangular hyperbola.
What does Km tell you about an enzyme?
Km is the substrate concentration at which the rate reaches half of Vmax, expressed here in mM. A low Km means the enzyme reaches half-maximal speed at low substrate, which is often read as high apparent affinity for the substrate.
What is the Lineweaver-Burk plot in the inset?
It is the double-reciprocal plot of 1/v against 1/[S], which turns the hyperbola into a straight line. The y-intercept is 1/Vmax and the x-intercept is -1/Km, making it a classic way to read off kinetic parameters and identify inhibition types.
The Vmax and Km sliders set the shape of the grey reference curve, [S]₀ sets the starting substrate for the time course, and [I] plus Ki together with the inhibition menu define the inhibited indigo curve. The yellow dot marks the current substrate level as the reaction runs.
A competitive inhibitor binds the active site and competes with substrate, so it raises the apparent Km while leaving Vmax unchanged. In the model the apparent Km becomes Km·α with α = 1 + [I]/Ki, so high substrate can still out-compete the inhibitor.
A non-competitive inhibitor binds away from the active site and lowers the effective amount of working enzyme, reducing the apparent Vmax to Vmax/α while Km stays roughly the same. Adding more substrate cannot overcome it, because the inhibitor does not compete for the binding pocket.
An uncompetitive inhibitor binds only the enzyme-substrate complex, so it lowers both the apparent Vmax and the apparent Km by the same factor. On the Lineweaver-Burk plot this produces parallel lines rather than lines that share an intercept.
The panel reports Vmax/Km as a practical efficiency measure in μmol/(min·mM). In formal biochemistry the specificity constant kcat/Km compares how well enzymes process substrates at low concentration; a higher value indicates a more efficient catalyst under those conditions.
As the reaction proceeds the substrate is consumed and product accumulates, so [S] falls and the rate v drops along the Michaelis-Menten curve. The time-course panel shows substrate declining and product rising, and the run slows and stops once almost all substrate is used up.
It captures the standard initial-rate Michaelis-Menten model and idealised reversible inhibition, which match introductory and undergraduate biochemistry. It simplifies by ignoring reverse reactions, product inhibition, allosteric cooperativity and changing temperature or pH, so it is a teaching tool rather than a research-grade kinetic solver.