Inhibition

Why it matters

Most drugs are enzyme inhibitors: statins block HMG-CoA reductase, many HIV and hepatitis C drugs block viral proteases, and antibiotics such as penicillin inactivate bacterial cell-wall enzymes. Cells also regulate their own pathways by inhibiting enzymes. In drug discovery and basic research you will often get rate data with and without an inhibitor and need to say how it inhibits, because that tells you where it binds and how it will behave at the substrate levels in a cell.

Reversible inhibition types

Reversible inhibitors bind and unbind; irreversible ones (covalent inactivators) permanently disable the enzyme and are analysed differently. For reversible inhibition at inhibitor concentration [I] with inhibition constant KiThe inhibition constant, a property of the inhibitor that does not depend on substrate level., define α = 1 + [I]/Ki.

CompetitiveInhibition by a compound that binds the free enzyme at the active site: Km rises and Vmax is unchanged.: the inhibitor binds the free enzyme at the active site, competing with substrate.

• Apparent Km increases: Km,app = α · Km.
• Vmax is unchanged: enough substrate outcompetes the inhibitor.
• Lineweaver–Burk lines cross on the y-axis.

UncompetitiveInhibition by a compound that binds only the ES complex: Vmax and Km fall by the same factor.: the inhibitor binds only the ES complex.

• Both fall by the same factor: Vmax,app = Vmax / α' and Km,app = Km / α', where α' = 1 + [I]/Ki' and Ki' is the inhibitor's dissociation constant from ES.
• Lineweaver–Burk lines are parallel.

NoncompetitiveInhibition by a compound that binds E and ES equally well: Vmax falls and Km is unchanged. (pure): the inhibitor binds E and ES equally well, at a site other than the active site.

• Vmax falls: Vmax,app = Vmax / α. Km is unchanged.
• Lines cross on the x-axis.

MixedInhibition by a compound that binds E and ES with different affinities: Vmax falls and Km changes.: the inhibitor binds E and ES with different affinities. Vmax falls and Km changes (up or down). Lines cross off both axes. Pure noncompetitive inhibition is really a special case of mixed inhibition.

Reading the parameters

The cleanest approach is to fit Michaelis–Menten curves to each data set (no inhibitor, and one or more inhibitor concentrations), then compare the apparent parameters:

Vmax,app ≈ Vmax   and   Km,app > Km          → competitive
Vmax,app < Vmax   and   Km,app ≈ Km          → noncompetitive
Vmax,app < Vmax   and   Km,app < Km, same factor  → uncompetitive
anything else with Vmax,app < Vmax           → mixed

"≈" needs a tolerance, because real fits have error. A good analysis also fits a global model (all data sets at once, with Ki as a parameter) and compares models statistically, but comparing apparent parameters is the right first step.

Worked example

The same enzyme as the last lesson, assayed with and without 1 mM of three different compounds:

                 Vmax,app (µM/min)   Km,app (mM)
no inhibitor     99.2                2.48
compound X       104.9               8.20
compound Y       49.9                2.50
compound Z       50.0                1.31

• X: Vmax about the same (within the fit's error), Km up more than threefold → competitive.
• Y: Vmax halved, Km unchanged → noncompetitive.
• Z: Vmax and Km both roughly halved (ratios 0.50 and 0.53) → uncompetitive.

For competitive compound X, Ki follows from Km,app = Km (1 + [I]/Ki):

Km,app / Km = 8.20 / 2.48 = 3.31
Ki = [I] / (3.31 − 1) = 1 mM / 2.31 ≈ 0.43 mM

IC50 is not Ki

Screening assays often report IC50The inhibitor concentration that halves the rate under particular assay conditions., the inhibitor concentration that halves the rate under the assay conditions. For a competitive inhibitor, IC50 depends on how much substrate you used: IC50 = Ki (1 + [S]/Km) (the Cheng–Prusoff relation). Two labs with different substrate levels can report different IC50s for the same compound, so compare Ki values, or state the assay conditions.

Common mistakes

• Over-reading small differences. A 5 % change in Vmax is often within fit error. Use replicates and confidence intervals.
• Calling every Vmax decrease "noncompetitive" without checking Km.
• Testing only one inhibitor concentration for a publication-level claim. Use several.
• Ignoring tight-binding inhibitors. When Ki is close to the enzyme concentration, the simple equations fail.

Recap

• Competitive: Km up, Vmax same. Noncompetitive: Vmax down, Km same. Uncompetitive: both down together. Mixed: Vmax down, Km changes.
• Classify by comparing fitted apparent parameters, with sensible tolerances.
• Ki is a constant of the inhibitor; IC50 depends on assay conditions.

Try it

On the Do tab, finish a Python function that classifies inhibition type from fitted Vmax and Km values.