Biochemical Pharmacology & Drug Discovery
Cheng-Prusoff Competitive K_i from IC50 Formula
Convert assay-dependent half-maximal inhibitory concentration IC_50 into intrinsic competitive inhibitor affinity K_i = IC_50 / (1 + [L] / K_d) and compute uncompeted vs competed target receptor occupancy.
Never compare raw IC50 values across labs running different substrate or radioligand loads!
In enzyme kinetics and radioligand binding screens, observed Half-Maximal Inhibitory Concentration IC_50 is NOT an intrinsic constant of a competitive drug candidate—increasing substrate or radioligand concentration [L] shifts IC_50 proportionally higher! Yung-Chi Cheng and William Prusoff (1973, Biochemical Pharmacology) derived the exact thermodynamic conversion to Intrinsic Inhibitor Dissociation Constant K_i: K_i = IC_50 / (1 + [L] / K_d), where K_d (or K_m for Michaelis-Menten enzymes) is the substrate/ligand dissociation constant! Once K_i is known, medicinal chemists predict Uncompeted Target Occupancy [I] / ([I] + K_i) vs Competed In-Vivo Occupancy [I] / ([I] + K_i * (1 + [L] / K_d)) at free plasma drug concentration [I]!
Verify on Measured_Assay_IC50 = 120.0 nM (B2), Assay_Ligand_Conc [L] = 30.0 nM (B3), Ligand_Dissociation_Kd = 10.0 nM (B4 -> Cheng-Prusoff Multiplier 1 + 30/10 = 4.00x in E2), and Free_Plasma_Drug_Conc [I] = 90.0 nM (B5): True Intrinsic Affinity is K_i = 120.0 / 4.00 = 30.00 nM (E3—4x tighter binding than raw IC_50 suggested!); Uncompeted Receptor Occupancy is 90 / (90 + 30) = 0.7500 (75.00% in E4); and Competed Occupancy at [L] = 30 nM is 90 / (90 + 120) = 0.4286 (42.86% in E5)! Test trace-ligand limit [L] = 0 nM: Correction Multiplier = 1.00 and K_i equals IC_50 (120.00 nM)!
| Lead-Optimization Pharmacology Metric (IC50=120 nM, [L]=30 nM, Kd=10 nM, [I]=90 nM) | Formula | Verified Output |
|---|---|---|
| Cheng-Prusoff Shift Factor | 1 + [L] / K_d | 4.0000x |
| Intrinsic Inhibitor Constant K_i (nM) | IC_50 / (1 + [L] / K_d) | 30.00 nM |
| Uncompeted Receptor Occupancy | [I] / ([I] + K_i) | 0.7500 (75.00%) |
| Competed Occupancy @ [L] = 30 nM | [I] / ([I] + IC_50) | 0.4286 (42.86%) |
Cheng-Prusoff Intrinsic K_i Formula
Validate IC_50 > 0, [L] >= 0, K_d > 0, and [I] >= 0!
=LET(ic_50, B2, lg_c, B3, kd_l, B4, dr_i, B5, IF(OR(ic_50 <= 0, lg_c < 0, kd_l <= 0, dr_i < 0), "Invalid Assay Input", ROUND(ic_50 / (1 + lg_c / kd_l), 2)))Uncompeted vs Competed Fractional Target Occupancy Formula
Notice that at [I] = IC_50 = 120 nM, Competed Occupancy [I] / ([I] + K_i * (1 + [L]/K_d)) equals 120 / (120 + 120) = 0.5000 (50.0% displacement by definition of IC_50)!
=IF(ISTEXT(E3), E3, ROUND(B5 / (B5 + B2), 4))Try the example
Use the original values or change them to test your understanding.