Drug response curve

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I now have comprehensive content from both Katzung and Lippincott textbooks with all the key diagrams. Here is the full response:

Drug Response Curves

A drug response curve (dose-response curve) is a graphical representation of the relationship between the dose (or concentration) of a drug and the magnitude of its pharmacological effect. There are two main types: graded and quantal.

1. Graded Dose-Response Curve

As the concentration of a drug increases, its pharmacological effect gradually increases until all receptors are occupied (the maximum effect, E~~max~~). When plotted on a linear scale, the curve is hyperbolic; on a semi-logarithmic scale (log dose on x-axis), it becomes the classic sigmoidal (S-shaped) curve, which is easier to interpret across a wide range of doses.

Graded dose-response curve - linear (A) and semi-log (B) plots showing EC50 for Drug A vs Drug B

Figure: Panel A = linear plot; Panel B = semi-log (sigmoidal) plot. Drug A has a lower EC50 than Drug B, so Drug A is more potent. - Lippincott Illustrated Reviews: Pharmacology, p. 95

Key Parameters from the Graded Curve

A. Potency

Potency is a measure of how much drug is needed to produce a given effect.
Quantified by the EC50 (effective concentration producing 50% of maximal response) or ED50 (effective dose).
A smaller EC50 = more potent drug (curve shifted to the left).
Potency depends on receptor affinity (Ka) and efficiency of receptor coupling to the response.
Clinically, potency matters for dosing (e.g., candesartan is dosed at 4-32 mg while irbesartan requires 75-300 mg for the same antihypertensive effect - candesartan is more potent).

B. Maximal Efficacy (Emax)

The ceiling effect - the maximum response a drug can produce regardless of dose.
Determined by the drug's intrinsic activity (ability to activate the receptor after binding).
Reflects the limit of the dose-response curve on the response axis.
Clinically more important than potency: morphine has greater efficacy than naproxen and can treat severe cancer pain, whereas naproxen cannot - even though both may be equipotent for mild pain.

Dose-response curves comparing potency and efficacy: Drug A more potent than B (same efficacy); Drug C lower potency AND lower efficacy than A and B

Figure: Drug A is more potent than B (left-shifted EC50) but both have the same Emax. Drug C has both lower potency and lower efficacy. - Lippincott Illustrated Reviews: Pharmacology, p. 96-97

Graded Curves and Drug Types

Four graded dose-response curves (A, B, C, D) illustrating different potencies and efficacies

Figure: Drugs A, C, D = equal maximal efficacy (full agonists). Drug B = lower Emax (partial agonist). Drugs B > A in potency (lower EC50), but Drug A achieves higher response at high doses. Curve D = steep slope (clinical danger if upper portion = toxicity). - Katzung's Basic & Clinical Pharmacology, p. 64

Drug Type	Intrinsic Activity	Emax	EC50 / Position
Full agonist	= 1	Same as endogenous ligand	Variable
Partial agonist	0 < α < 1	Lower than full agonist	May be lower (more potent)
Antagonist	0	Zero (blocks, no activation)	-
Inverse agonist	Negative	Suppresses below baseline	-

Important distinction:

A drug can be more potent but less efficacious than another (e.g., Drug B vs Drug A above).
A drug with greater efficacy is clinically more useful when a strong effect is needed.

Slope of the Curve

Extremely steep curves (like curve D in the Katzung figure) have major clinical implications. A small dose increment can push the response from therapeutic to toxic (e.g., sedative-hypnotics causing coma). Steep slopes can result from cooperative interactions across multiple systems (e.g., a drug simultaneously affecting brain, heart, and vessels to lower blood pressure). - Katzung's Basic & Clinical Pharmacology, p. 65

2. Quantal Dose-Effect Curve

Used when the response is all-or-nothing (quantal) - e.g., prevention of seizures, arrhythmia, or death. Rather than measuring intensity of effect in one individual, quantal curves measure the fraction of a population that responds to a given dose.

Constructed by:

Determining the dose needed to produce a specified effect in each individual
Plotting cumulative % of responders vs. log dose
The resulting curve is sigmoidal (cumulative frequency distribution)

Quantal dose-effect curve showing ED50 (~5 mg) and LD50 (~160 mg), with frequency histograms

Figure: Blue curve = cumulative therapeutic responders; Red curve = cumulative lethal effect. ED50 = ~5 mg; LD50 = ~160 mg. The wide separation = wide therapeutic index. - Katzung's Basic & Clinical Pharmacology, p. 65-66

Key Parameters from the Quantal Curve

Parameter	Definition
ED50	Dose at which 50% of the population exhibits the desired effect
TD50	Dose at which 50% exhibit a specified toxic effect
LD50	Dose lethal to 50% (animal studies)
Therapeutic Index (TI)	TI = LD50 / ED50 (animal) or TD50 / ED50
Therapeutic Window	Range between minimum toxic dose and minimum effective dose

A high TI = wide safety margin (e.g., penicillin). A low TI = narrow margin requiring monitoring (e.g., digoxin, warfarin, lithium, aminoglycosides).

Note: The slopes of the dose-response curves matter. Even if ED50 and LD50 are well-separated, if the upper tail of the therapeutic curve overlaps the lower tail of the lethal curve, some patients at therapeutic doses may experience toxicity. - Goodman & Gilman's Pharmacological Basis of Therapeutics

3. Graded vs Quantal: Key Comparison

Feature	Graded	Quantal
Measured in	One individual or preparation	A population
Response type	Continuous (intensity)	All-or-nothing (yes/no)
X-axis	Log dose / concentration	Log dose
Y-axis	% maximal effect	% individuals responding
Key parameters	EC50, Emax, potency, efficacy	ED50, LD50, therapeutic index
What it shows	Potency + maximal efficacy	Population variability + safety margin

4. Receptor Occupancy and the Hill Equation

The relationship between drug concentration and receptor binding follows the law of mass action:

Drug + Receptor ⇌ Drug-Receptor Complex → Biological Effect

The fraction of occupied receptors is:

[DR]/[R_total] = [D] / (K_d + [D])

Where K_d = equilibrium dissociation constant. A lower K_d = higher affinity. The Hill-Langmuir equation extends this to describe the dose-response relationship mathematically (the basis for the sigmoidal curve). - Lippincott Illustrated Reviews: Pharmacology, p. 99-100

5. Variation in Drug Responsiveness

Individuals vary considerably in their response to the same drug due to:

Hyporeactivity / hyperreactivity - reduced or increased response compared to most individuals
Tolerance - diminishing response with continued use (e.g., opioids, nitrates)
Tachyphylaxis - rapid tolerance after just a few doses
Idiosyncratic responses - genetic polymorphisms in drug metabolism (e.g., CYP450 variants) or immunologic reactions
Age, sex, body size, comorbid disease states, and drug-drug interactions

These factors explain why the quantal curve shows a bell-shaped frequency distribution (Gaussian) around the ED50 rather than a sharp threshold. - Katzung's Basic & Clinical Pharmacology, p. 66

Sources:

Lippincott Illustrated Reviews: Pharmacology, Chapter 2, pp. 95-100
Katzung's Basic & Clinical Pharmacology, 16th Ed., Chapter 2, pp. 64-66
Goodman & Gilman's Pharmacological Basis of Therapeutics, Introduction

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