Ki (Inhibition Constant) Calculators

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The inhibition constant Ki is the dissociation constant for the enzyme-inhibitor complex — it measures how tightly an inhibitor binds to its enzyme target. A lower Ki means tighter binding and a more potent inhibitor. Ki is defined as Ki = [E][I] / [EI], where [E] is free enzyme, [I] is inhibitor, and [EI] is enzyme-inhibitor complex. Ki is related to but distinct from IC₅₀ (the concentration giving 50% inhibition, which depends on substrate concentration). Ki is a fundamental parameter in drug discovery and is used to rank inhibitor potency independently of assay conditions.

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Ki Formula

Ki = [E][I] / [EI]

Units: mol/L (M). Lower Ki = tighter binding = more potent inhibitor. Ki is related to IC₅₀ by the Cheng-Prusoff equation:

Ki = IC₅₀ / (1 + [S]/Km) (for competitive inhibition)

Ki = IC₅₀ (for noncompetitive inhibition, since [S] doesn't affect binding)

This relationship shows why IC₅₀ depends on assay substrate concentration while Ki does not — Ki is the condition-independent constant.

Determining Ki Experimentally

Method 1 — Dixon plot: measure v at multiple [I] values for two or more [S] values; plot 1/v vs. [I]; lines intersect at −Ki on the x-axis (competitive) or at Ki below the x-axis (noncompetitive). Method 2 — from IC₅₀: run a dose-response curve at known [S] and Km, then apply Cheng-Prusoff. Method 3 — Lineweaver-Burk with inhibitor: analyze how Km and Vmax change at different [I] to determine inhibition type and Ki.

Ki in Drug Design

In medicinal chemistry, lead optimization aims to reduce Ki (increase potency). Ki < 1 nM is considered very potent. Ki 1–100 nM is typical for approved drugs. Ligand efficiency (LE = ΔG / heavy atoms) normalizes Ki by molecular size. Selectivity ratio (Ki for off-target / Ki for target) guides selectivity optimization.

Glossary

Ki (Inhibition Constant)
The dissociation constant for the enzyme-inhibitor complex: Ki = [E][I]/[EI]; lower Ki = tighter binding = more potent inhibitor; independent of assay substrate concentration.
Cheng-Prusoff Equation
Ki = IC₅₀/(1+[S]/Km) for competitive inhibitors; converts IC₅₀ to the condition-independent Ki; essential for comparing inhibitor potency across different assay conditions.
IC₅₀
Inhibitor concentration causing 50% reduction in enzyme activity or cell viability under specific assay conditions; depends on [S] and Km for enzyme assays; converted to Ki via Cheng-Prusoff.

Frequently Asked Questions

Ki is the dissociation constant for the enzyme-inhibitor complex — a thermodynamic measure of binding affinity that is independent of assay conditions. IC₅₀ is the inhibitor concentration reducing enzyme activity by 50% under specific assay conditions — it depends on substrate concentration and enzyme concentration. They relate through the Cheng-Prusoff equation: Ki = IC₅₀/(1+[S]/Km) for competitive inhibitors. A drug with very low Ki may appear to have a higher IC₅₀ if the substrate concentration in the assay is well above Km.

Two common methods: (1) Dixon plot — measure enzyme velocity at multiple inhibitor concentrations and multiple substrate concentrations; plot 1/v vs. [I]; parallel lines = noncompetitive inhibition (Ki read from intersection below x-axis); converging lines at x-axis = competitive (x-intercept = −Ki). (2) Cheng-Prusoff correction of IC₅₀: measure IC₅₀ in a dose-response assay at known [S] and Km, then Ki = IC₅₀/(1 + [S]/Km) for competitive inhibition. Always report both the inhibition type and Ki value.

Ki is inversely related to inhibitor potency — lower Ki = tighter binding = more potent inhibitor. ΔG of binding = RT × ln(Ki) ≈ 1.38 kcal/mol per 10-fold decrease in Ki at 25°C. Clinical drug Ki ranges: enzyme inhibitor drugs typically have Ki 1–100 nM; extremely potent drugs like irreversible inhibitors may have effective Ki < 0.1 nM. A 10-fold decrease in Ki represents ~1.4 kcal/mol improvement in binding affinity — equivalent to one optimized H-bond or hydrophobic contact added in drug design.

In competitive inhibition, the inhibitor competes with the substrate for the active site — increasing [S] can overcome the inhibition. Ki is the true dissociation constant for the EI complex. The apparent Km increases as Ki = Km_apparent × [E]free/(Km+[I]), but Vmax is unchanged. Km_apparent = Km × (1 + [I]/Ki). In noncompetitive inhibition, the inhibitor binds a different site; Ki describes EI binding; both Km and Vmax are affected. In uncompetitive inhibition, the inhibitor binds only to the enzyme-substrate complex — Ki' = Km_apparent = Km/(1+[I]/Ki').