An interactive guide to double-reciprocal analysis in enzyme kinetics — from first principles to ping-pong mechanisms.
The Michaelis-Menten equation describes how reaction velocity V depends on substrate concentration [S]. The curve is a hyperbola — hard to extract precise values from. The Lineweaver-Burk transformation inverts both sides, turning the hyperbola into a straight line whose intercepts directly reveal Vmax and Km.
Adjust Vmax and Km below and watch both the Michaelis-Menten curve and its Lineweaver-Burk transformation update in real time.
Different inhibitors shift the Lineweaver-Burk line in characteristic ways. Click through each type to see the diagnostic pattern.
Baseline: a single straight line defined by Vmax and Km.
Same y-intercept (Vmax unchanged), but the slope increases — the apparent Km rises because the inhibitor competes for the active site. Lines converge at the y-axis.
Parallel lines — both slope and y-intercept change proportionally. The inhibitor only binds the ES complex, reducing both apparent Vmax and Km by the same factor.
Same x-intercept (Km unchanged), but Vmax decreases. The inhibitor binds enzyme regardless of substrate, reducing max velocity without affecting affinity.
In a ping-pong (double displacement) reaction, the enzyme bounces between two states — it binds substrate A, releases product P, then binds substrate B and releases product Q. The enzyme itself is chemically modified between the two half-reactions (e.g. aminotransferases).
Step 1: E + A → E* + P
Step 2: E* + B → E + Q
The enzyme alternates (ping-pongs) between forms E and E*. Crucially, substrate A leaves before substrate B binds — no ternary complex is formed.
Vary [A] at several fixed concentrations of [B]. On a Lineweaver-Burk plot, ping-pong gives a family of parallel lines — identical slopes, different y-intercepts. This is because the apparent Vmax changes with [B] but Km/Vmax stays constant.