Lecture 4: Drug-Receptor III

Overview of Drug Antagonists

• Antagonists comprise the majority of drugs that are used in clinical practice.

• An antagonist is defined as a drug that prevents the response of an agonist.

• Antagonism is categorized into five distinct classes:

  • Chemical antagonism

  • Pharmacokinetic antagonism

  • Physiological antagonism

  • Non-competitive antagonism

  • Competitive antagonism

Chemical Antagonism

• This occurs when substances combine in a solution resulting in the loss of the active drug's effects. The agonist is chemically altered by the antagonist.

• A primary example is the inactivation of heavy metals, such as mercury ($Hg$), lead ($Pb$), and cadmium ($Cd$).

• The toxicity of these heavy metals is reduced through the addition of a chelating agent, such as dimercaprol.

• The interaction follows the general principle: $\text{Heavy Metal} + \text{Chelator} \rightarrow \text{Inactivated Complex}$.

Pharmacokinetic Antagonism

• Pharmacokinetic antagonism involves a reduction in the amount of drug absorbed, metabolized, or excreted due to a change in drug metabolism caused by another substance.

• A clinical example involves patients taking warfarin, which is an anti-coagulant used to thin the blood and reduce the risk of heart attack and stroke.

• Care must be taken when treating these patients with certain antibiotics, as these antibiotics may stimulate the metabolism of warfarin.

• Increased metabolism leads to a reduction in the effective concentration of warfarin within the bloodstream.

Physiological Antagonism

• This involves the interaction of two drugs that produce opposing actions within the body.

• Example 1: Noradrenaline and Histamine on arterial blood pressure.

  • Noradrenaline raises arterial blood pressure by acting on the heart via $\beta_{1}$ receptors and on peripheral blood vessels via $\alpha_{1}$ receptors.

  • Histamine lowers arterial pressure by causing vasodilation via $H_{1}$ receptors.

• Example 2: Histamine and Omeprazole on gastric acid secretion.

  • Histamine, acting through $H_{2}$ receptors, increases acid secretion in the gut.

  • Omeprazole counteracts this effect by directly inhibiting the proton pump.

Non-Competitive Antagonism

• This type of antagonism blocks a step in the process between receptor activation and the observed response.

• Non-competitive antagonists do not compete with the agonist for the specific receptor binding site.

• Examples of non-competitive antagonists include:

  • Verapamil and Nifedipine: These inhibit $L$-type Calcium channels, leading to the relaxation of smooth muscle and a subsequent lowering of blood pressure.

  • Ketamine: This acts as a non-competitive inhibitor of NMDA receptors by blocking the channel pores.

Competitive Antagonists and Receptor Interaction

• Competitive antagonists bind to the same site on the receptor as the agonist.

• Agonist (Drug A) Interaction:

  • The binding of the drug ($A$) to the receptor ($R$) to form a complex ($AR$) is governed by affinity, specifically the association rate constant ($k_{+1}$) and the dissociation rate constant ($k_{-1}$).

  • The activation of the receptor ($AR \rightarrow AR^{*}$) is governed by efficacy ($\alpha$).

  • The overall response is determined by both affinity and efficacy.

• Antagonist (Drug B) Interaction:

  • The antagonist ($B$) binds to the receptor ($R$) to form a complex ($BR$) at the same site as the agonist.

  • Occupation is governed by affinity. A high affinity is characterized by a faster association ($k_{+1}$) and a slower dissociation ($k_{-1}$).

  • The antagonist possesses zero efficacy and therefore does not elicit a response ($BR \rightarrow \text{No Response}$).

Reversible Competitive Antagonism

• In reversible competitive antagonism, the antagonist competes with the agonist for occupancy of the receptor.

• Increasing the concentration of the antagonist causes a parallel rightward shift in the concentration-response curve of the agonist.

• There is no change in the maximum response ($E_{max}$) or the slope of the curve.

• Validation of this model is seen in the effects of Atropine on the response of Acetylcholine in the guinea-pig ileum.

Dose Ratio and Quantification of Parallel Shifts

• The parallel shift caused by a competitive antagonist is quantified using the Dose Ratio ($DR$).

• The Dose Ratio indicates how many more times the agonist concentration is required to achieve the same effect in the presence of an antagonist.

• $DR = \frac{[\text{Concentration of agonist in presence of antagonist}]}{[\text{Concentration of agonist in absence of antagonist}]}$

Schild Analysis and the Schild Equation

• The affinity of an antagonist ($K_{D}$) can be determined by measuring the Dose Ratio (shift) in the agonist concentration-response curve caused by increasing concentrations of a competitive antagonist.

• The Schild Equation is defined as:     $DR = \frac{[X_{b}]}{K_{D}} + 1$

  • $[X_{b}]$ represents the molar concentration of the antagonist.

  • $K_{D}$ represents the Antagonist Affinity Constant.

The Schild Plot and $pA_{2}$

• A Schild plot displays the relationship between $log_{10}(DR - 1)$ and $log_{10}([Antagonist])$.

• The equation can be rearranged to form a linear relationship:     $log_{10}(DR - 1) = log_{10}[X_{b}] - log_{10}(K_{D})$

• The term $pA_{2}$ is defined as the negative logarithm of the molar concentration of antagonist that produces a dose ratio of $2$.

• $pA_{2} = -log_{10}(K_{D})$

• Calculation steps for $pA_{2}$ and $K_{D}$:

  1. Measure the Dose Ratio ($DR$) for various antagonist concentrations ($[X_{b}]$).

  2. Calculate $log_{10}(DR - 1)$ and plot it against $log_{10}[X_{b}]$.

  3. The x-intercept of this plot gives the $pA_{2}$.

  4. The affinity constant $K_{D}$ is calculated as:         $K_{D} = 10^{-pA_{2}}$

• Example: If an antagonist has a $pA_{2} = 3$, then the affinity constant is $K_{D} = 10^{-3}\,M$.

Logic of the Schild Equation Rearrangement

• Starting with: $DR = \frac{[X_{b}]}{K_{D}} + 1$

• Subtracting 1: $DR - 1 = \frac{[X_{b}]}{K_{D}}$

• Expressed as a product: $DR - 1 = [X_{b}] \times \frac{1}{K_{D}}$

• Taking the logarithm of both sides: $log_{10}(DR - 1) = log_{10}[X_{b}] + log_{10}(\frac{1}{K_{D}})$

• Using log properties: $log_{10}(DR - 1) = log_{10}[X_{b}] - log_{10}(K_{D})$

• When the Dose Ratio is $2$ ($DR = 2$):

  • $log_{10}(2 - 1) = log_{10}[X_{b}] - log_{10}(K_{D})$

  • Since $log_{10}(1) = 0$, the equation becomes $0 = log_{10}[X_{b}] - log_{10}(K_{D})$

  • This results in $log_{10}[X_{b}] = log_{10}(K_{D})$

  • Taking the inverse log: $[X_{b}] = K_{D}$

Partial Agonists and Irreversible Antagonists

• Partial Agonists:

  • Partial agonists can behave like competitive antagonists by causing a rightward shift in the concentration-response curve of a full agonist.

  • They are distinguishable from pure competitive antagonists because a response may be observed even at the lowest tested concentrations of the full agonist in the presence of the partial agonist.

• Irreversible Competitive Antagonists:

  • This type of antagonism cannot be reversed by washing the tissue.

  • Irreversible antagonism is time-dependent.

  • Example: The alkylating drug dibenamine ($1\,nM$) acting on histamine responses in the guinea-pig ileum.

  • Increasing exposure time (e.g., $5$, $10$, $15$, or $20$ minutes) leads to a progressive depression of the maximum response.

  • In cases of irreversible antagonism, the reaction does not reach equilibrium, and therefore, Schild analysis cannot be used to measure $K_{D}$.