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Dose-Response Relationship in General Pharmacology
The dose-response (D-R) relationship describes how the magnitude or probability of a drug's effect changes as the dose increases. It is one of the foundational concepts of pharmacodynamics.
1. Basic Principle
The pharmacologic effect of a drug depends on:
- Drug concentration at the receptor site (governed by pharmacokinetics)
- Receptor sensitivity (affinity, density, coupling efficiency)
As concentration increases, effect increases until all receptors are occupied (maximum effect, Emax).
"The magnitude of the drug effect depends on receptor sensitivity to the drug and the drug concentration at the receptor site, which, in turn, is determined by both the dose of drug administered and by the drug's pharmacokinetic profile."
- Lippincott Illustrated Reviews: Pharmacology
2. Types of Dose-Response Curves
A. Graded Dose-Response (Individual)
In a graded D-R, the magnitude of response in a single individual increases continuously with increasing dose. Plotting effect vs. dose gives a hyperbolic curve; on a log dose axis, it becomes a characteristic sigmoidal (S-shaped) curve.
Figure: Graded dose-response curves. Panel A = linear plot; Panel B = semi-log plot. EC50 is the dose producing 50% of maximal effect. Drug A (red) is more potent than Drug B (orange) because it achieves EC50 at a lower dose. - Lippincott Illustrated Reviews: Pharmacology
Two critical drug properties are read from this curve:
i. Potency
- Potency = amount of drug needed to produce a given effect
- Measured by the EC50 (concentration producing 50% of maximal response)
- Lower EC50 = more potent drug
- Example: candesartan (dose range 4-32 mg) is more potent than irbesartan (75-300 mg) for the same antihypertensive effect
- Potency determines the dose needed, but does not determine how useful a drug is clinically
ii. Efficacy (Intrinsic Activity)
- Efficacy = the maximum response a drug can produce (Emax)
- Depends on the number of drug-receptor complexes formed AND the intrinsic activity of the drug
- A drug with high efficacy achieves a greater Emax, even if it is less potent
- Clinical relevance: efficacy is more important than potency - morphine has greater efficacy than naproxen for pain (can treat cancer pain), whereas naproxen and ibuprofen have the same efficacy despite different potencies
B. Quantal Dose-Response (Population)
In a quantal D-R, the response is measured across a population - each individual either responds or does not (all-or-nothing). The percentage of individuals responding is plotted against dose, producing a sigmoidal curve.
Figure: Quantal concentration- and dose-response curves. Panel A: frequency distribution and cumulative dose-response (EC50 = 10 mg/L). Panel B: two quantal curves for therapeutic (hypnosis, blue) vs. lethal (death, green) effects. TI = LD50/ED50 = 400/100 = 4. - Goodman & Gilman's Pharmacological Basis of Therapeutics
Key quantal parameters:
| Parameter | Definition |
|---|
| ED50 | Dose effective in 50% of the population |
| LD50 | Dose lethal in 50% of the population |
| TD50 | Dose toxic in 50% of the population |
| Therapeutic Index (TI) | LD50/ED50 - higher = safer drug |
| Margin of Safety | LD1/ED99 - stricter safety measure |
| Therapeutic Window | Range of concentrations/doses giving efficacy with minimal toxicity |
A high TI (e.g., penicillin ~1000) means wide safety margin. A low TI (e.g., digoxin, warfarin, lithium ~2) demands careful monitoring.
3. Receptor Occupancy and the Law of Mass Action
Drug + Receptor ⇌ Drug-Receptor Complex → Biologic Effect
The fraction of bound receptors follows:
[DR]/[Rt] = [D] / (Kd + [D])
Where:
- [D] = free drug concentration
- Kd = equilibrium dissociation constant (inverse measure of affinity)
- Lower Kd = higher affinity (tighter binding)
This equation generates the same sigmoidal shape as the dose-response curve, confirming that receptor occupancy underlies the pharmacologic effect.
4. Agonist Types and Their Dose-Response Profiles
Figure: Full agonist achieves 100% receptor activity; partial agonist plateaus below 100% even at saturation; inverse agonist suppresses below baseline constitutive activity. - Lippincott Illustrated Reviews: Pharmacology
| Drug Type | Intrinsic Activity | Emax |
|---|
| Full agonist | = 1 | 100% (same as endogenous ligand) |
| Partial agonist | 0 < x < 1 | Less than full agonist; can act as partial antagonist when co-administered with full agonist |
| Antagonist | = 0 | 0 (blocks receptor without activation) |
| Inverse agonist | < 0 (negative) | Suppresses below baseline constitutive activity |
Clinical example: Aripiprazole is a partial agonist at dopamine receptors - it inhibits overactive dopaminergic pathways while stimulating underactive ones, explaining its utility in schizophrenia with low extrapyramidal risk.
5. Non-Monotonic Dose-Response Curves
Not all D-R curves are sigmoidal. From Goodman & Gilman:
- U-shaped curve: seen with hormones, vitamins, and essential metals - deficiency and excess are both harmful (e.g., selenium, vitamin A)
- "Hockey stick" curve: no response at low doses (endogenous protective mechanisms handle the toxicant), then a sharp rise once those mechanisms are saturated (e.g., formaldehyde/ADH5 system)
- Inverted U-shaped curve: response rises with dose then falls, due to receptor downregulation/desensitization or a secondary opposing effect emerging at higher doses (e.g., cannabidiol at high doses producing anxiogenic effects)
6. Clinical Relevance Summary
| Concept | Clinical Implication |
|---|
| Potency (EC50) | Determines tablet/dose size, not clinical superiority |
| Efficacy (Emax) | Determines what conditions a drug can treat |
| Therapeutic Index | Guides safe dosing; narrow TI drugs require plasma monitoring |
| Therapeutic Window | Range for clinical use; overlap of efficacy and toxicity curves in population |
| Partial agonism | Can reduce toxicity while providing partial effect (e.g., buprenorphine in opioid dependence) |
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