Comprehensive Study Guide: Pharmacodynamics (PHAR 112)

PHAR 112: Introduction to Pharmacology and Therapeutics

Pharmacodynamics

Instructor: Dr. Stella Chan Institution: S.K. Yee School of Health Sciences

Learning Outcomes

By the end of this lecture, students should be able to:

• Describe a typical ligand concentration-occupancy curve.
• Describe and interpret a typical concentration-response curve for a drug, labeling positions used to define drug potency and efficacy.
• Define the terms $ED_{50}$, $LD_{50}$, $TD_{50}$, and therapeutic index ($TI$).
• Compare the efficacy and potency of two drugs based on their concentration-response curves.
• Predict and explain the effect of an antagonist in the presence and absence of an agonist.

Introduction to Pharmacodynamics

Pharmacodynamics is the study of what a drug does to the body. This field explores:

• The mechanisms by which drugs produce their biological effects.
• The interaction between drugs and their specific receptors.
• The quantitative relationship between the dose administered and the resulting effect.

Importance in Clinical Practice

Understanding pharmacodynamics is essential for safe dispensing:

• Variability in Potency: Different drugs can produce different effects even at the same dose; some require very small doses to be effective.
• Dosing Accuracy: Helps clinicians avoid under-dosing (inefficacy) and over-dosing (toxicity).
• Safety Margins: Some drugs possess a narrow margin between beneficial therapeutic effects and harmful toxic effects.

Drug-Receptor Binding: Mathematical Foundations

Fractions and Percentages

Binding is often expressed as fractions or percentages:

• A fraction of $0.5$ is equivalent to $50\%$ (half).
• If there are $10$ receptors and $5$ are occupied, the occupancy is: $\frac{5}{10} = 0.5 = 50\%$.

Affinity

Affinity is a measure of how tightly a drug binds to a receptor. It is the tendency of a ligand ($L$) to combine with a receptor ($R$) to form a complex ($LR$).

The Equilibrium Scheme:$L + R \rightleftharpoons LR$

• $k_{+1}$: Association rate constant.
• $k_{-1}$: Dissociation rate constant.

Equation 1 (The Equilibrium Dissociation Constant): The constant $K_d$ is numerically equal to the ratio of the dissociation rate constant to the association rate constant. It has the dimensions of Molarity ($mol/l$). $K_d = \frac{[k_{-1}]}{[k_{+1}]}$

Equation 2 (Law of Mass Action): At equilibrium, the rates of association and dissociation are equal: $K_d = \frac{[L][R]}{[LR]}$ Rearranged to find the concentration of the complex: $[LR] = \frac{[L][R]}{K_d}$

Equation 3 (Total Receptor Conservation): Assuming the total concentration of receptors ($R_0$) is constant: $[R_0] = [R] + [LR]$ Substituting Equation 2 into Equation 3: $[R_0] = [R] + \frac{[L][R]}{K_d} = [R] \times (1 + \frac{[L]}{K_d})$

Equation 4 (Fractional Occupancy): Solving for the fraction of binding sites occupied by a ligand ($L$) at equilibrium: $\text{Fractional Occupancy} = \frac{[LR]}{[R_0]} = \frac{[L]}{[L] + K_d}$ This interaction assumes the law of mass action is obeyed.

The Ligand Concentration-Occupancy Curve

Plotting drug responses allows for the visualization of drug effects across wide concentration ranges (e.g., nanomolar to millimolar).

Comparison: Linear vs. Semi-Log Scale

1. Linear Scale: Plotting Occupancy ($\%$) against Concentration ($[L]$). The resulting curve is a rectangular hyperbola. It is difficult to see changes at very low concentrations.
2. Semi-Log Scale: Plotting Occupancy ($\%$) against the logarithm of Concentration ($\log[L]$). The resulting curve is sigmoidal (S-shaped). This is the preferred method for comparing drug data.

Understanding Kd (The Dissociation Constant)

• Definition: $K_d$ is the concentration of ligand at which $50\%$ of available receptors are occupied.
• Proof: When $[L] = K_d$, the fractional occupancy is: $\frac{[LR]}{[R_0]} = \frac{[L]}{[L] + [L]} = \frac{[L]}{2[L]} = 0.5 = 50\%$
• Relationship with Affinity:     - Low $K_d$ = High Affinity: The drug binds tightly; less drug is needed to occupy receptors (Example: $K_d = 1\,nM$).     - High $K_d$ = Low Affinity: The drug binds weakly; more drug is needed (Example: $K_d = 1000\,nM = 1\,\mu M$).
• Graphical Interpretation: On a semi-log plot, the curve for Drug A (higher affinity) will be positioned to the left of Drug B (lower affinity).

Dose-Response Relationship and Agonism

The magnitude of a biological response is generally proportional to the concentration of receptors occupied by the drug.

Response Formula:$\text{Response} = [DR] = \frac{\text{Max. Response} \times [D]}{[D] + K_d}$ Where:

• $[D]$ is the concentration of free drug.
• $[DR]$ is the concentration of the drug-receptor complex.
• $[R]$ is the total receptor concentration.

Agonists

An agonist can be an exogenous drug or an endogenous ligand.

• Mechanism: Agonist binding to the primary (orthosteric) site alters receptor activity, initiating a series of intracellular steps that lead to a response.
• Saturation: Increasing agonist concentration increases response until all receptors are bound or a maximal plateau is reached.
• Molecular States: In most cases, the resting state ($R$) and the active drug-receptor complex ($DR^<em>$) are relevant. The intermediate unstable species ($R^</em>$ and $DR$) are quantitatively insignificant.

Drug Potency and Efficacy

Potency

Potency refers to the concentration or amount of drug required to produce a defined effect.

• $EC_{50}$: The molar concentration of an agonist that produces $50\%$ of its maximal possible effect. This can be a stimulatory or inhibitory effect.
• Inverse Relationship: A lower $EC_{50}$ indicates higher potency.
• Analogy: Potency is like the number of people needed to push a car. If fewer people are needed, those people are "more potent."
• Graphical Identification: The curve further to the left is more potent.     - Example: Drug A ($EC_{50} = 5\,nM$) is more potent than Drug B ($EC_{50} = 50\,nM$).

Efficacy ($E_{max}$)

Efficacy is the maximal response produced by a drug. It expresses the degree to which different agonists produce varying responses.

• Relationship: Higher $E_{max}$ indicates higher efficacy. Potency and efficacy are not intrinsically related; a drug can be highly potent but have low efficacy.
• Analogy: Efficacy is like how far the car moves. If it moves $100\,m$, it is more efficacious than one that moves $10\,m$.
• Graphical Identification: Look at the plateau (top) of the curve. A higher top indicates higher efficacy.     - Example: Drug A (reduces blood pressure by $40\,mmHg$) is more efficacious than Drug B (reduces BP by $20\,mmHg$).

Full Agonists, Partial Agonists, and Spare Receptors

Full Agonists

• Can produce maximal effects ($100\%$) even when occupying only a small fraction of the total receptor population.
• Possess high intrinsic activity.
• Analogy: Like a light switch (On/Off).

Partial Agonists

• Produce only submaximal effects ($< 100\%\text{ max}$) even when ALL receptors are occupied.
• By definition, they have lower maximal efficacy than full agonists and low intrinsic activity.
• Analogy: Like a dimmer switch.
• Example: In gut muscle contraction via muscarinic ACh receptors, Butyl and Hexyl trimethylammonium are full agonists, while Heptyl and Octyl derivatives are partial agonists.

Spare Receptors (Receptor Reserve)

• A system has spare receptors if a full agonist can reach maximal response while occupying only a fraction (e.g., $10\% - 50\%\%$) of receptors.
• Mechanism: Signal amplification allows a single receptor activation to trigger a massive cellular response.
• Example: Catecholamines can produce maximal heart muscle contraction even if $90\%$ of $\beta$-adrenoceptors are blocked by an irreversible antagonist.
• Note: Partial agonists have no spare receptors because they require $100\%$ occupancy just to reach their (submaximal) plateau.

Quantal Dose-Response and Drug Safety

While graded dose-response curves look at individuals, quantal curves examine population averages.

Key Definitions

• All-or-None Basis: Quantal responses observe the presence or absence of a response (e.g., sleep vs. awake, alive vs. dead).
• $ED_{50}$ (Median Effective Dose): Dose at which $50\%$ of subjects exhibit the therapeutic response.
• $TD_{50}$ (Median Toxic Dose): Dose at which $50\%$ of subjects experience toxicity.
• $LD_{50}$ (Median Lethal Dose): Dose at which $50\%$ of subjects die.

Therapeutic Index ($TI$)

$TI$ is a measure of drug safety representing the range between effective and toxic doses.

Formula:$TI = \frac{TD_{50}}{ED_{50}}$

• General Rule: The larger the $TI$, the safer the drug. A $TI > 10$ is considered to have a good safety profile.
• Wide Therapeutic Index (Safe): Penicillin ($TI > 100$). High doses can be given with low risk.
• Narrow Therapeutic Index Drugs (NTIDs - Dangerous):     - Warfarin: $TI \approx 2-3$. Small dose changes cause bleeding or clotting.     - Digoxin: $TI \approx 2$.     - Lithium: $TI \approx 2-3$.     - NTIDs require constant clinical monitoring.

Pharmacology of Antagonism

An antagonist is a molecule that inhibits the action of an agonist but has no effect in the absence of the agonist.

Types of Antagonists

1. Receptor Antagonists: Bind to active or allosteric sites.     - Competitive (Reversible): Compete for the active site.     - Noncompetitive (Irreversible or Allosteric): Block the site permanently or change its shape via an allosteric site.
2. Nonreceptor Antagonists:     - Chemical Antagonists: Bind directly to the agonist molecule.     - Physiological Antagonists: Use a different physiological pathway to produce an opposite effect.

Reversible Competitive Antagonists

• Binding of agonist and antagonist is mutually exclusive.
• Surmountable: The block can be overcome by increasing agonist concentration.
• Effect on Curve: Causes a parallel rightward shift. Potency decreases ($EC_{50}$ increases), but efficacy ($E_{max}$) remains unchanged.
• Affinity Metric ($pA_2$): The negative log of the antagonist concentration that requires doubling the agonist dose to reach the same effect.     - Formula: $pA_2 = -\log(K_B)$     - A higher $pA_2$ means higher affinity for the antagonist.

Noncompetitive Antagonists

• Insurmountable: Cannot be overcome by more agonist.
• Situation 1 (Irreversible): Antagonist binds covalently/tightly to the active site. Once spare receptors are used up, $E_{max}$ drops.
• Situation 2 (Allosteric): Antagonist binds elsewhere, preventing receptor activation.
• Effect on Curve: The curve shifts right and the maximum response ($E_{max}$) is reduced.
• Receptor Reserve Exception: At low doses, a noncompetitive antagonist might only cause a parallel shift if there is a large receptor reserve for the agonist. As dose increases, the plateau eventually drops.
• Example: Phenoxybenzamine (PBZ/BPZ) is an irreversible $\alpha$-adrenergic antagonist used for hypertension caused by catecholamine-releasing tumors (pheochromocytoma).

Chemical and Physiological Antagonists

• Chemical Antagonist Examples:     - Protamine: Positively charged; binds to acidic Heparin to neutralize it.     - Dimercaprol: A chelator used to bind toxic lead and other metals.
• Physiological Antagonist Examples:     - Insulin: Opposes the hyperglycemic effects of glucocorticoids (e.g., from an adrenal cortex tumor).     - $\beta$-blockers: Counteract tachycardia caused by thyroid hormone.

Inverse Agonists

Many receptors (specifically GPCRs and ion channels) have constitutive activity, meaning they are active even without a ligand.

• Mechanism: Inverse agonists preferentially bind to and stabilize the Inactive State ($R$) of the receptor.
• Efficacy: They have negative intrinsic activity (negative efficacy).
• Comparison:     - Agonist: Positive efficacy (shifts balance to $R^*$).     - Antagonist: Zero efficacy (blocks agonist but doesn't change basal activity).     - Inverse Agonist: Negative efficacy (reduces basal activity below resting levels).
• Example: Many drugs formerly called antagonists (e.g., antihistamines, $\beta$-blockers) are actually inverse agonists.

Questions & Exercises

True/False Questions

1. A partial agonist is one that, even at its highest dose, cannot achieve the same maximal response as a full agonist at the same receptor.

• Answer: True.
• Explanation: Partial agonists have low intrinsic ability to induce the necessary conformational change in the receptor.

2. A full agonist achieves a maximal response when all its receptors are occupied.

• Answer: False.
• Explanation: Many full agonists achieve maximal response at low occupancy due to "spare receptors."

Graph Identification Exercises

3. Comparing Drug X, Y, and Z:

• Drug X is more potent than Drug Y (X is further left).
• Drug Y is the least potent (furthest right).
• Drug X and Drug Y have the same efficacy ($E_{max}$ is equal).
• Drug Z has the least efficacy (lowest plateau).

4. Drug A with Antagonist A':

• The curve shifts Right.
• The dose required for $EC_{50}$ Increases.
• The maximum response ($E_{max}$) Can still be achieved.
• Conclusion: Antagonist A' is Competitive.

5. Drug B with Antagonist B':

• At $10\,nM$: Parallel rightward shift without reducing maximal response (due to receptor reserve).
• At $100\,nM$: Rightward shift with a drop in maximum response.
• Conclusion: Antagonist B' is Noncompetitive.