Binding Thermodynamics

Six small calculators for molecular recognition. Values update as you type; temperature is shared by all cards. Constants: R = 1.98720 cal·mol⁻¹·K⁻¹ (8.31446 J·mol⁻¹·K⁻¹).

Temperature °C

1Affinity ↔ pX ↔ ΔG°

Kd / Ki / IC50

pKd / pKi / pIC50

pX = −log₁₀(K / M) · ΔG° = RT·ln(Kd) · one log unit ≈ kcal/mol at this temperature.

2Cheng–Prusoff

Enzyme (competitive) Receptor binding

IC50

Substrate concentration [S]

3Ligand efficiency metrics

IC50 / Kd

SMILES (optional, fills the fields below with RDKit)

Heavy atoms

cLogP

MW (g/mol)

PSA (Å²)

LE = 1.37·pX / HA (≈ −ΔG/HA, kcal·mol⁻¹ per heavy atom; ≥ 0.3 is a common target) · LLE = pX − cLogP (≥ 5 desirable) · BEI = pX / MW(kDa) · SEI = pX / (PSA/100 Å²)

4ΔG° = ΔH° − TΔS°

Solve for: ΔG ΔH ΔS

ΔG° (kcal/mol)

binding

ΔH° (kcal/mol)

from ITC

ΔS° (cal·mol⁻¹·K⁻¹)

entropy

Enthalpy- vs entropy-driven binding is read from the sign of −TΔS°; ITC gives ΔH° and Ka directly, ΔS° follows.

5van ’t Hoff

Two temperatures → ΔH°, ΔS° Kd + ΔH° → Kd at T₂

Kd at T₁

T₁ (°C)

Kd at T₂

T₂ (°C)

ln(Ka₂/Ka₁) = −ΔH°/R · (1/T₂ − 1/T₁), assuming ΔH° is constant (ΔCp ≈ 0) between the two temperatures.

6Receptor occupancy

Free ligand concentration [L]

Hill coefficient n

θ = [L]ⁿ / ([L]ⁿ + Kdⁿ); the curve plots θ against log[L] with the current point marked. Ligand depletion is ignored.