Enzyme kinetics

Choose a reversible inhibition model, set Vmax and Km, and calculate. For an inhibited model, also set the free inhibitor concentration I and its inhibition constant Ki. The S limit is under Plot range. Move the substrate probe or enter an exact free substrate concentration S; this changes the displayed rates without changing the curves. Clear result keeps the inputs. An S value beyond a reduced plot limit remains invalid until you correct it.

This is a comparison of chosen models, not a method for identifying an experimental inhibition mechanism. It describes single-substrate initial rates under fixed conditions, with free S and I effectively undepleted and negligible product-driven reverse reaction. It does not model progress over time, cooperativity, partial or irreversible inhibition, or fit experimental data. Vmax is in µM/s; S, I, Km and Ki are in µM.

The rate is v = Vmax·S/(α·Km + α′·S). Without inhibition, α = α′ = 1. Competitive inhibition has α = 1 + I/Ki and α′ = 1: S and I bind mutually exclusively, which does not necessarily mean the same binding site. Uncompetitive inhibition is associated with the enzyme–substrate complex and has α = 1, α′ = 1 + I/Ki. Pure noncompetitive inhibition has α = α′ = 1 + I/Ki, representing equal inhibitor affinity for free enzyme and enzyme–substrate complex.

The apparent parameters are Vmax,app = Vmax/α′ and Km,app = α·Km/α′. Competitive inhibition leaves Vmax unchanged and increases Km. Pure noncompetitive inhibition lowers Vmax and leaves Km unchanged. Uncompetitive inhibition lowers both by the same factor. Km is the substrate concentration at half the corresponding asymptotic rate; it is not generally an affinity or binding constant.

The dashed gray curve is the baseline and the blue curve is the chosen model. Diamonds mark (Km, Vmax/2), where these points lie within the plot. A short dotted line marks the model's asymptotic Vmax; the curve need not reach it at the right edge. A hollow gray circle and a blue dot show the rates at the chosen S. Inhibition is 100·(v without − v model)/(v without). At S = 0 both rates are zero, so this percentage is undefined.

Example: Vmax = 100 µM/s, Km = 25 µM, I = Ki = 50 µM and S = 100 µM give 80 µM/s without inhibition, approximately 66.6667 competitively, 40 in the pure noncompetitive case and 44.4444 uncompetitively. In the last case, Vmax,app = 50 µM/s and Km,app = 12.5 µM, so v = 25 µM/s at S = 12.5 µM.

The input limits are display limits: Vmax, Km, Ki and the S limit range from 0.001 to 10000 in their stated units; I ranges from 0 to 10000 µM and the probe from 0 to the S limit. These are not universal experimental validity ranges. Inputs are calculated locally in your browser.

Sources: IUBMB, Symbolism and Terminology in Enzyme Kinetics (1981); Assay Guidance Manual, Mechanism of Action Assays for Enzymes.