Hill Langmuir Equation

INTRODUCTION
An antagonist is defined as a substance which can occupy a receptor binding site without eliciting a response, while preventing or reducing the response from agonist binding. There are many different molecules that serve as antagonists as well as many different ways by which antagonism can be achieved. One of the most direct ways by which one drug can reduce the effect of another (or of an endogenous mediator) is known as reversible competitive antagonism. Atropine is such an antagonist, which acts non-selectively at muscarinic receptors.
Reversible competitive antagonism is a form of receptor block by which a substance selectively binds to a particular type of receptor without eliciting a response, in such a way that also prevents
By rearranging this equation and taking logs we can form “log⁡(Par/(1-Par))=[A]-logKA” from which we can see that plotting log (Par/1-Par)) against log [A] forms what is known as a hill plot, which consists of a straight line with a slope of unity. If the relationship between drug concentration and tissue response is directly proportional, the relationship between occupancy and response can be denoted as Y/100= Par which can be substituted into the previous equation to provide log⁡(y/(100-y))=log⁡[A]-log⁡[KA]. This equation can now be used to predict the relationship between agonist concentration and tissue response. If this equation holds, and agonist concentration is directly proportional to tissue response, and the law of mass action applies, then after using a dose response curve to plot log(y/100-y) against log [A] we would get a hill plot with a straight line and a slope of
The schild equation also predicts the effect of a reversible competitive antagonist on a log agonist concentration response curve, which should cause a parallel shift to the right with no change in maximum response. This is because if the equation holds, the concentration ratio, r, is determined only by the values of [B] and Kb regardless of the concentration and even identity of the agonist (provided that it acts at the same receptor as the antagonist) [5]. A series of agonist concentration response curves, can be established, first in the absence of antagonist, then in the presence of increasing concentrations of antagonist. If a degree of parallelism is present in these curves, then a schild plot can be formed, with (r-1) (r being the dose ratio) plotted against antagonist concentration [B]. If the antagonism is reversible competitive, this should provide a schild plot of slope gradient 1. We would also expect the X intercept value to equal the dissociation constant of the