Pharmacokinetics made easy 10 Pharmacodynamics - the concentration-effect relationship
- D.J. Birkett
- Aust Prescr 1995;18:102-4
- 1 October 1995
- DOI: 10.18773/austprescr.1995.088
So far, this series has considered how drugs are absorbed, distributed and excreted by the body the pharmacokinetic phase of drug action. To produce therapeutic or toxic effects, drugs interact with receptors in the body the pharmacodynamic phase of drug action. The drug in the tissues, where drug-receptor interactions usually occur, is in equilibrium with the unbound drug in the plasma.
Drugs usually interact in a structurally specific way with a protein receptor. This activates a second messenger system which produces a biochemical or physiological response, e.g. changes in intracellular calcium concentrations result in muscle contraction or relaxation. The most common receptors are transmembrane receptors linked to guanosine triphosphate binding proteins (G proteins) which activate second messenger systems such as adenylylcyclase (beta adrenoceptors) or the inositoltriphosphate pathway (alpha adrenoceptors).
A drug which binds to a receptor and produces a maximum response is called a full agonist; a drug which binds and produces less than a maximal response is called a partial agonist. Drugs which bind but do not activate second messenger systems are called antagonists. Antagonists can only produce effects by blocking the access of the natural transmitter (agonist) to the receptor. Thus, beta blockers produce relatively little change in heart rate when given to subjects at rest as there is low sympathetic tone and little noradrenaline (the natural agonist) to be antagonised at the beta receptor. The effects of beta blockers are therefore measured after stimulating the sympathetic system (usually by exercise) e.g. the degree to which exercise induced tachycardia is blocked. Partial agonists produce an effect if no agonist is present, but act as antagonists in the presence of a full agonist. Pindolol, a beta blocker which is a partial agonist, produces less decrease in heart rate than pure antagonists such as propranolol.
Selectivity in drug action is related to the structural specificity of drug binding to receptors. Propranolol binds equally well to beta1 and beta2 adrenoceptors, whereas atenolol and metoprolol bind selectively to and block (are antagonists at) beta 1 adrenoceptors. Salbutamol is a selective beta2 adrenoceptor agonist and, in this case, additional selectivity is achieved by inhaling the drug directly to its site of action in the lungs.
The interaction of a drug with a receptor involves it binding to the receptor in the same structurally specific way that a substrate binds to the active site of an enzyme. The same equation and similar parameters are therefore used to describe the concentration effect relationship (Fig. 1). The affinity of the drug for the receptor is described by the EC50 , the concentration of the drug required to give half maximal response. The different actions of a drug, such as therapeutic and adverse effects, are often due to the drug binding to different receptors with different EC50 values. Ideally, adverse effects should occur at higher drug concentrations than therapeutic effects. The ratio adverse effect EC50 /therapeutic effect EC50 gives some measure of the safety of the drug and is called the therapeutic index.
Fig. 1A shows the drug concentration effect relationship. As drug concentration increases, the response rises to a maximum, at which point the receptor is saturated. Fig. 1B shows the curve replotted using a logarithmic concentration (x) axis. Concentration response curves are often plotted in this way as the part of the curve between 20% and 80% of maximal response is approximately linear and this section of the curve most often applies to drugs at therapeutic concentrations. Increasing drug concentration above 80% maximal response achieves very little in terms of extra therapeutic effects, but increases the risk of adverse effects.
This type of concentration-response curve is produced by measuring a continuous parameter, such as blood pressure or exercise-induced heart rate, at various drug concentrations. It is known as a graded concentration response curve.
After a single dose, drug concentration falls in an exponential manner with time - the logarithm of drug concentration is linear with time (see Fig. 2 and Article 3 'Half life' Aust Prescr 1988;11:57-9). From Fig. 1B it can be seen that the logarithm of drug concentration is also linear with response in the range 20-80% maximal response. In this range, therefore, response falls in a linear fashion with time (Fig. 2). If the dose of the drug is large enough to produce a concentration which causes a maximal response, the response will change very little until the drug concentration falls to that producing about 80% maximal response (Fig. 2). The duration of action can be prolonged by increasing the dose, but there is a risk of producing more adverse effects, unless the drug has a large therapeutic index. Beta blockers are usually given once or twice daily, despite having short elimination half lives. This is at least partly because they have a large therapeutic index and the doses used are large enough to produce a maximal effect for a significant part of the interval between doses.
The drug concentration-effect relationship is described by the same function as the enzyme velocity-substrate concentration relationship. E is the effect at drug concentration C, Emax is the maximal effect at high drug concentrations when all the receptors are occupied by the drug, and EC50 is the drug concentration to give the half-maximal effect. This is the simplest form of the concentration-effect relationship and more complex expressions are sometimes required to explain the observed effects.
When plotted on a semi-logarithmic plot, the curve from Fig. 1A becomes a sigmoidal shape, but is approximately linear between 20% and 80% of maximal effect, a range commonly observed for drugs used at therapeutic doses.
The time course of drug concentration and response after a single dose. Concentration decreases in an exponential manner. If the initial concentration is high enough to be in the region of maximal response (see Fig. 1), there is initially little change in effect as the concentration decreases. In this case, as drug concentration falls from 100 mg/L to 4 mg/L, the effect only falls from 99% to 80% of maximal effect. The decrease in effect is then approximately linear with time between 80% and 20% of maximal effect. If the dose had been such that the initial concentration was about 4 mg/L giving about 80% maximal effect, the decrease in effect would have been linear with time from immediately after the dose.
The parameters used were: initial drug concentration (Co) = 100 mg/L; Emax = 100; EC50 = 1 mg/L; elimination rate constant k = 0.35/hour (elimination half-life = 2 hours).
An alternative way of constructing a concentration effect curve is to determine the percentage of a population of patients showing a defined response at various drug concentrations. For example, with phenytoin, the therapeutic response might be defined as >80% decrease in the frequency of fits and the adverse effect defined as the proportion of patients developing nystagmus on looking sideways. These are called quantal (population) concentration response curves and have the same shape and parameters as the graded concentration response curves referred to above.
Fig. 3 shows quantal (population) concentration response curves as they might occur for the therapeutic and adverse effects of phenytoin with a therapeutic concentration range (window) of 1020 mg/L. At the top of the therapeutic range not all patients will have a therapeutic response and, within the 'therapeutic range', significant numbers of patients may have adverse effects. As therapeutic ranges are defined on a population basis, they need to be interpreted carefully in relation to individual patients.
Quantal (population) concentration-response curves and the concept of the therapeutic range (window). Quantal concentration-response curves are constructed by determining the cumulative percentage of a patient population with a discrete therapeutic or adverse effect. Such curves are shown for the anticonvulsant, phenytoin. Although some patients respond at lower concentrations, the therapeutic range most commonly used is
10-20 mg/L (shaded area), which gives a therapeutic response (reduction in fit frequency) in most patients with an acceptable incidence of adverse effects (e.g. nystagmus, ataxia).
i. Drugs used at concentrations which give a maximal response (Fig. 2).
ii. 'Hit and run' drugs. Some drugs act irreversibly e.g. the classical MAO inhibitors or the effect of aspirin on cyclooxygenase in platelets. Termination of these effects relies on synthesis of new MAO or platelets, so that there is no relationship between drug concentration and effect.
iii. Delayed distribution. The site of drug action is at a site to which the drug is slowly distributed. An example is digoxin (see Article 2 'Volume of distribution' Aust Prescr 1988;11:36-7). The effect increases as the drug concentration falls due to redistribution. Drug concentrations soon after a dose cause a smaller effect than the same concentrations cause later when distribution to the site of action has occurred.
This results in an anticlockwise hysteresis in the concentration effect relationship (Fig. 4A).
iv. The 'wrong' effect is measured. For example, after the first dose, the effect of warfarin on prothrombin time increases as the warfarin concentration decreases. The rate of onset of effect is measured by the rate of decay of existing clotting factors. However, the direct effect of warfarin is on the rate of clotting factor synthesis. If this is determined directly, warfarin concentration correlates well with response.
v. Acute tolerance (tachyphylaxis) develops. Examples are amphetamines or cocaine. Drug concentrations soon after a single dose cause a greater effect than the same concentrations cause at a later time. This results in a clockwise hysteresis in the concentration effect relationship (Fig. 4B).
Clockwise and anticlockwise hysteresis loops. The points are concentration response measurements made at varying times after a dose. The arrows show the direction of time after the dose.
An anticlockwise hysteresis loop occurs when the drug has to be distributed to its site of action. Response for a given plasma concentration is initially low, but increases as the drug is distributed out of the plasma to the site of action. An example is digoxin.
A clockwise hysteresis loop occurs when rapid tolerance (tachyphylaxis) develops. The response for a given plasma concentration is initially high, but decreases as tolerance rapidly develops. Examples are cocaine or indirectly acting sympathomimetic drugs such as pseudoephedrine.
Professor of Clinical Pharmacology, Flinders University of South Australia, Adelaide