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Methods and Principles in Medicinal Chemistry - Mannhold R.

Mannhold R., Kubinyi H., Timmerman H. Methods and Principles in Medicinal Chemistry - Wiley-VCH, 2001. - 155 p.
Download (direct link): pharmacokinetiksmedicanalchemistri2001.pdf
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[R] Ef/Em = [RL]/[R]t (2.19)
where EF is the fractional response, EM is the maximal response, [RL] is the concentration of receptor-ligand complex and [R]T is the total receptor concentration. At equilibrium, R + L ^ RL, such that the affinity constant KA can be defined as KA = [RL]/[L][R]. This is the same equation as that derived from Langmuir’s saturation isotherm, which derives from the law of mass action. It is possible to describe the occupancy theory in the following way:
• the receptor/ligand (RL) complex is reversible
• association is a bimolecular process
• dissociation is a monomolecular process
• all receptors of a given type are equivalent and behave independently of one another
• the concentration of ligand is greatly in excess of the receptor and therefore the binding of the ligand to the receptor does not alter the free (F) concentration of the ligand
• the response elicited by receptor occupation is directly proportional to the number of receptors occupied by the ligand
The equilibrium dissociation constant Kd gives a measure of the affinity of the ligand for the receptor.
Kd=([R][L])/[RL] (2.20)
Kd can also be defined by the two microconstants for rate on and off k+1 and k-1 so that Kd = k-1/k+1, where Kd is the concentration of the ligand (L) that occupies 50 % of the available receptors.
26 | 2 Pharmacokinetics
Antagonist ligands occupy the receptor without eliciting a response, thus preventing agonist ligands from producing their effects. Since this interaction is usually competitive in nature, an agonist can overcome the antagonist effects as its concentration is increased. The competitive nature of this interaction allows the determination of a pA2 value, the affinity of an antagonist for a receptor as shown below.
pA2 = -log Kb (2.21)
where Kb = the dissociation constant for a competitive antagonist and is the ligand concentration that occupies 50 % of the receptors.
We thus have a series of unbound drug affinity measures relating to the action of the drug. The values are those typically obtained by the pharmacologist and form the basis of the structure-activity relationships which the medicinal chemist will work on. It is possible to extend this model to provide a pharmacokinetic phase as shown in Figure 2.9.
Here we assume that:
• free drug is in equilibrium across the system
• only free drug can exert pharmacological activity (see above)
• drug is reversibly bound to tissues and blood
• only free drug can be cleared
To examine the validity of this model, data from a number of 7 transmembrane (7TM) receptor antagonists (antimuscarinics, antihistaminics, р-adrenoceptor blockers etc.) were examined. The Kb values for these drugs were compared to their free (unbound) plasma concentration. To simplify the analysis the plasma concentration data was taken from patients at steady state on therapeutic doses. Steady state means that the dosing rate (rate in) is balanced by the clearance rate (rate out). This concept is exactly as described earlier for intravenous infusion, however the steady state is an average of the various peaks and troughs that occur in a normal dosage regimen. The relationship between the values was very close and the in vitro potency values can be adjusted to 75 % receptor occupancy (RO) rather than 50% using Eq. (2.21) shown below (where the ligand concentration is represented by L):
RO = [L]/[Kb + L]
(2.21)
2.10 Unbound Drug Model and Barriers to Equilibrium 27
Fig. 2.10 Correlation of in vitro potency with plasma free drug concentration required for efficacy.
When this relationship is plotted, a 1:1 relationship is seen as shown in Figure 2.10. Thus the free concentration present in plasma is that actually seen at the receptor. Moreover, the in vitro values (KB) determined from receptor binding actually represent the concentration required in the patient for optimum efficacy.
We can thus see that the traditional indicators of potency that drive synthetic chemistry, such as pA2 values, can have direct relevance to the plasma concentration (free) required to elicit the desired response. If we extend this example further it is unlikely that in all cases there is a simple direct equilibrium for all compounds between the free drug in plasma and the aqueous media bathing the receptor. The concentration of the free drug in the plasma is in direct equilibrium with the interstitial fluid bathing most cells of the body, since the capillary walls contain sufficient numbers of pores to allow the rapid passage of relatively small molecules, regardless of physicochemistry. Most receptor targets are accessed extracellularly. We can expect therefore that all drugs, regardless of their physicochemistry, will be in direct equilibrium at these targets, with the free drug in plasma. For instance the G-protein-coupled receptors have a binding site which is accessible to hydrophilic molecules.
This is exemplified by the endogenous agonists of these receptors that are usually hydrophilic by nature. Adrenalin, dopamine and histamine are representative and have log D74 values of - 2.6, - 2.4 and - 2.9 respectively.
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