An inhibitor can bind the free enzyme (competing with substrate for the active site), the enzyme-substrate complex, or both. The general modified Michaelis-Menten rate law used here:
v = Vmax[S] / ( Km(1+[I]/Ki) + [S](1+[I]/Ki′) )
Competitive: Ki′ → ∞ (Ki′ has no effect)
Uncompetitive: Ki → ∞ (Ki has no effect)
Noncompetitive: Ki = Ki′
Mixed: Ki ≠ Ki′, both finite
The Lineweaver-Burk plot linearizes this as 1/v = [Km(1+[I]/Ki)/Vmax]·(1/[S]) + (1+[I]/Ki′)/Vmax — so a competitive inhibitor changes the slope but leaves the y-intercept (1/Vmax) fixed, while a pure noncompetitive inhibitor changes the y-intercept but leaves the x-intercept (-1/Km) fixed. The time-course panel numerically integrates dS/dt = -v(S) with RK4 to show how substrate actually depletes and product accumulates over real time under the chosen inhibition regime — the saturation curve alone only shows instantaneous rate, not the reaction's full progress.