Del Castillo Katz model

Del Castillo Katz model is a mathematical model used in the field of pharmacology to describe the interaction between drugs and receptors. It was developed by Juan del Castillo and Bernard Katz in 1957.

Overview

The Del Castillo Katz model is an extension of the Langmuir isotherm and is used to describe the binding of ligands to receptors. It assumes that the receptor can exist in two states, active and inactive, and that the ligand can bind to both states. The model is characterized by four rate constants: the association and dissociation rates for the ligand binding to the active and inactive states.

Mathematical Formulation

The Del Castillo Katz model is described by the following set of differential equations:

• d[R]/dt = k1[L][R] - k2[LR] + k5[LR*] - k6[R]
• d[LR]/dt = k2[LR] - k1[L][R] + k4[LR*] - k3[LR]
• d[LR*]/dt = k3[LR] - k4[LR*] + k6[R] - k5[LR*]

where [R] is the concentration of the receptor in the inactive state, [LR] is the concentration of the ligand-receptor complex in the inactive state, [LR*] is the concentration of the ligand-receptor complex in the active state, [L] is the concentration of the free ligand, and k1, k2, k3, k4, k5, and k6 are the rate constants.

Applications

The Del Castillo Katz model is widely used in pharmacology to study the effects of drugs on the body. It can be used to predict the response of a receptor to a drug, and to design new drugs with desired properties. The model is also used in biochemistry to study the binding of ligands to proteins.

See Also

• Langmuir isotherm
• Pharmacodynamics
• Drug-receptor interaction

References

• Del Castillo, J., & Katz, B. (1957). Interaction at end-plate receptors between different choline derivatives. Proceedings of the Royal Society of London. Series B - Biological Sciences, 146(924), 369–381.