General Principles Of Pharmacology/Binding and response
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A complete description of a receptor-drug interaction includes an analysis of the binding step and an analysis of the coupling between the binding and the biological response. Both steps of the analysis can be very complicated. In the case of the binding step, the receptor molecule may exist in more than one conformational state each of which exhibit different affinities for the drug. A complete description of the binding mechanism would include a characterization of the affinity of the drug for each conformational state as well as a description of the isomerization between conformational states. The coupling between the binding and the biological response is difficult to discuss in general terms because it is highly dependent upon the tissue under study. Nevertheless, a number of strategies have been developed that are useful in a variety of cases.
R + D ⇔ RD → → → effect
Binding Response
R= Receptor
D= drug
RD= Receptor-Drug complex
R + D ⇔KD RD
KD = ![\frac{[R][D]}{[RD]}](/images/math/0b14f98194af3adaaeac52d33f594fb6.png)
KD = Equilibrium dissociation constant
R= Receptor
D= drug
RD= Receptor-Drug complex
A measure of the affinity of the receptor for the drug is given by the equilibrium dissociation constant. In order to make these concepts useful, an equation relating the number of receptors present and the affinity of those receptors for the drug to measurable parameters must be developed. The following derivation attempts to relate the total concentration of receptors and the KD to the concentration of free drug and of receptor-drug complex. The total concentration of receptors, [Rt], is by definition the sum of the bound and free receptor concentrations:
[Rt] = [R]+ [RD]
From the definition of the equilibrium dissociation constant:
[RD] = [R][D]/KD
A saturation function can be defined as follows
[RD]/[Rt] = Y-- =[RD]/[RD]+[R]=[R][D]/KD / [R][D]/KD+[R] = [D]/KD/[D]/KD+1 =[D] /[D]+ KD
This is the equation for the simple bimolecular interaction between receptor and drug and is true only following equilibration of all species. In practice, receptor-drug interactions are often much more complicated than this simple description; however, the principles used to derive the relationships for the equilibrium state are the same.
The relationship of the concentration of bound drug to free drug can be described by the Langmuir isotherm, which is a rectangular hyperbola as shown below. Note that the KD is the equal to the concentration of free drug at half maximal saturation (0.5*[Rt]) and that the plateau for the bound drug is reached at a value equal to [Rt].
The relationship of the concentration of bound drug to free drug is often plotted on a semi logarithmic scale. This representation shows more clearly any differences in affinity between two binding curves over a wide range of concentrations.
Fig.2.3 Binding and Response of drugs
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