National University of Singapore · FACULTY OF PHARMACOLOGY

PHC5005 Chap.8 Quantal Dose-Response, Therapeutic Index and Tolerance

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Chapter 8 of 10 · PHC5005

Quantal Dose-Response, Therapeutic Index and Tolerance

Why responses differ between people

The course closes its pharmacodynamics lecture by moving from a single receptor system to whole populations. It identifies four sources of individual variation in drug response. Pharmacodynamic variation concerns the amount or function of the target and its signalling components. Pharmacokinetic variation concerns absorption, distribution, metabolism and excretion.

Disease-induced variation arises when illness changes a drug's access to its target or its action there. Environment-induced variation comes from diet, toxins, supplements and complementary or alternative preparations.

Later lectures on pharmacogenetics and special populations expand the first two.

Graded and quantal responses

A graded response is continuous: the effect grows with concentration and can be measured in one subject. A quantal response is all or none, yes or no, such as prevention of convulsions, correction of an arrhythmia or death.

For these a graded curve cannot be built, so the population is studied instead: each subject's threshold dose is recorded, the thresholds form a log-normal distribution, and the cumulative plot shows the percentage of subjects responding at each dose.

Median doses and the therapeutic index

From quantal curves come three medians. ED50 is the dose that produces a predefined response in half the population.

TD50 is the dose at which half show toxic effects. LD50 is the dose that kills half of those exposed; cyanide's is very small. The therapeutic index, TD50 divided by ED50, summarises the risk-benefit ratio: the larger it is, the safer the drug in normal clinical use.

Penicillin and warfarin are the course's wide and narrow examples.

Hysteresis

Because most drugs must reach their site of action and then bind, effects lag behind changes in plasma concentration. The course defines hysteresis as the retardation of an effect behind its cause.

An anticlockwise loop in a plot of effect against concentration points to limited access to the site of action or slow receptor kinetics; a clockwise loop points to one of two related processes failing to keep pace with the other.

Changing responsiveness

Responses also change with exposure. Overexpression of receptors can exaggerate responses.

Desensitisation is a temporary loss of receptor responsiveness after repeated or continuous agonist exposure, with tachyphylaxis its most rapid form. Tolerance is a reduced response after prolonged use that requires higher doses. Down-regulation is a loss of surface receptors through endocytosis, with degradation or recycling. Together they explain why dose requirements can drift without any change in pharmacokinetics.

In this chapter

What this chapter covers

  • 01

    Pharmacodynamic, pharmacokinetic, disease and environmental sources of variation

  • 02

    Graded against quantal dose-response relationships

  • 03

    Log-normal distribution of individual threshold doses

  • 04

    ED50, TD50 and LD50 as population medians

  • 05

    The therapeutic index as a risk-benefit ratio

  • 06

    Anticlockwise and clockwise hysteresis

  • 07

    Desensitisation, tachyphylaxis, tolerance and down-regulation

Worked example · free

Reading a quantal study

Q [4 marks]. In a trial of a new sedative, half the subjects reach the target sedation score at 15 mg, and half show the first signs of respiratory toxicity at 90 mg. State which measures these are, calculate the therapeutic index and interpret it against a drug whose index is 2. The step weighting shown here is an AskSia study allocation and is not a University marking scheme.
Figure 8.1.Figure 8.1. Computed quantal curves for an illustrative drug: the dose that helps half the population is twenty times smaller than the dose that harms half.therapeutic effecttoxic effectED50 20TD50 4001010010000%50%100%dose, mg (log scale)population responding
Figure 8.1. Computed quantal curves for an illustrative drug: the dose that helps half the population is twenty times smaller than the dose that harms half.
  • 1Name the two measures.
  • 1Calculate the therapeutic index.
  • 2Compare the safety margins.
Fifteen milligrams is the ED50, the dose producing the predefined response in half the population, and 90 mg is the TD50, the dose at which half show toxic effects. The therapeutic index is TD50 divided by ED50, 90 divided by 15, which is 6. A drug with an index of 2 reaches its median toxic dose at only twice its median effective dose, so ordinary variation in exposure can push patients into toxicity; the new sedative has three times that margin and is safer under normal clinical use. Because both figures are medians, the index still does not describe the most sensitive patients.
Sia tip — Always divide toxic by effective. An index written the other way round is below 1 and reverses the conclusion.
Glossary

Key terms

Quantal Response
An all-or-none response in which the number of subjects responding, rather than the size of the effect, varies with dose.
ED50
The dose at which half of a population shows a response of a chosen intensity.
TD50
The dose at which 50 per cent of a population exhibits toxic effects.
LD50
The dose that kills 50 per cent of the population exposed to a drug.
Therapeutic Index
The ratio TD50 divided by ED50, a population measure of a drug's safety margin.
Hysteresis
A delay in which the effect trails behind the change in concentration that drives it.
Tachyphylaxis
The most rapid form of desensitisation, a quick loss of response to repeated doses.
Down-Regulation
Loss of receptors from the cell surface after prolonged agonist exposure, through internalisation.
FAQ

Quantal Dose-Response, Therapeutic Index and Tolerance FAQ

When is a quantal dose-response curve used instead of a graded one?

When the response cannot be graded because it is all or none, such as prevention of convulsions, stopping an arrhythmia or death. The study then records how many subjects respond at each dose and plots the cumulative percentage, which is why ED50 is a population figure rather than an individual one.

Why is a drug with a large therapeutic index considered safer?

The index divides the dose that is toxic in half the population by the dose that is effective in half. A large value means a wide gap between benefit and harm, so normal variation in dose or exposure is unlikely to cause toxicity.

What does an anticlockwise hysteresis loop tell you?

The effect is lagging behind plasma concentration: at the same plasma level there is less effect while concentrations rise than while they fall. The course attributes this to limited access to the site of action or to slow receptor kinetics.

How do tolerance and desensitisation differ?

Desensitisation is a short-lived loss of receptor responsiveness after repeated or continuous agonist exposure, fastest in tachyphylaxis. Tolerance is the body's reduced response after prolonged use, meaning larger doses are needed to match the earlier effect. Down-regulation, in which surface receptors are withdrawn, is one mechanism behind reduced responsiveness.

What are the four sources of variation in drug response?

Pharmacodynamic differences in targets and signalling, pharmacokinetic differences in absorption, distribution, metabolism and excretion, disease-induced changes in access to or action at the target, and environment-induced differences from diet, toxins, supplements and complementary preparations.

Why does pharmacodynamics matter in drug development?

The course lists its uses: understanding disorders better, identifying and validating new targets, optimising lead compounds, and explaining differences between preclinical and clinical response as well as adverse drug reactions and interactions.

Study strategy

Exam move

For every drug example in the pharmacology lectures, decide whether its safety depends on a wide or a narrow therapeutic index, and write the monitoring consequence beside it. The same classification reappears in excretion, dosing and special populations, so one list serves several topics.

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