The Hill equation revisited: uses and misuses

Area of Science:

• Biochemistry
• Pharmacology
• Chemical Kinetics

Background:

• The Hill coefficient is widely used to quantify ligand-receptor binding and functional effects.
• Its application is limited, as it often fails to represent physically possible reaction schemes for receptors with multiple binding sites.
• The coefficient primarily reflects cooperativity rather than the exact number of binding sites.

Purpose of the Study:

• To evaluate the limitations of the Hill coefficient in modeling ligand-receptor interactions.
• To propose alternative, physically plausible reaction schemes for analyzing dose-response curves.
• To improve the accuracy of modeling ligand-receptor dynamics, particularly concerning stoichiometry.

Main Methods:

• Analysis of the mathematical constraints of the Hill equation for multi-site receptors.
• Development and simulation of several simple, physically realistic reaction schemes.
• Comparison of model-generated dose-response curves with observed phenotypes.

Main Results:

• The Hill equation inaccurately estimates binding sites for most multi-site receptors, except in cases of strong positive cooperativity.
• The Hill coefficient functions more accurately as an indicator of interaction or cooperativity.
• Proposed reaction schemes generate diverse, plausible dose-response curve phenotypes.

Conclusions:

• The Hill coefficient is an inadequate measure for determining the number of ligand binding sites in many biological systems.
• Alternative reaction schemes provide more accurate and physically meaningful models for ligand-receptor interactions.
• Accurate modeling benefits from incorporating independent information on ligand-receptor stoichiometry.