Measuring how strongly a drug acts: concentration–response

Receptor pharmacology measures how strongly and how effectively drugs act at a receptor. In a cell-based functional assay, cells that express the receptor are exposed to a range of drug concentrations in a multiwell plate, and a response is read from every well; here it is the rise in calcium inside the cells, reported by a fluorescent indicator.

Plotting the response against the logarithm of the concentration gives a concentration–response curve. Fitting it gives the potency of an agonist, its EC50 (usually reported as pEC50, the negative logarithm of the EC50 in molar units), and its maximal effect, Emax, which reflects efficacy. These terms and symbols follow the recommendations of the International Union of Pharmacology (Neubig et al., 2003).

A competitive antagonist shifts the agonist curve to the right without lowering its maximum. The size of the shift at several antagonist concentrations gives the antagonist's affinity by Schild analysis (Arunlakshana and Schild, 1959); a lowered maximum shows that the antagonism is not simply competitive.

Every compound is hypothetical. The simulator records the true values, so the effect of each choice, including any mistake, on the result is shown at the end. Nothing here is guidance on doses for people or animals.

Learning objectives

• Explain potency (EC50, pEC50), efficacy (Emax) and the Hill slope, and tell a full from a partial agonist
• Calculate a stock solution and a serial dilution scheme, and choose a concentration range that defines the whole curve
• Design a 96-well plate map with vehicle and reference controls, randomised positions and a rule for accepting plates set in advance
• Compute Z′ and normalise responses to the controls on each plate, and recognise uneven seeding and edge effects
• Fit the four-parameter logistic, apply acceptance criteria, and compare compounds across independent experiments with the experiment as the unit of analysis
• Use dose ratios and a Schild plot to tell competitive from non-competitive antagonism

Ethics and safety

Work with cell lines follows the institution's biosafety rules and the conditions under which the cell line was obtained; cells are handled in a biological safety cabinet with aseptic technique. Compounds of unknown activity are treated as hazardous: weighing is done in a ventilated enclosure, and nitrile gloves, a laboratory coat and eye protection are worn, especially with DMSO, which passes through skin and can carry dissolved compounds with it. Cell-based assays like this one are also a way to answer pharmacological questions without using animals (Replacement, one of the 3Rs). Plate maps, raw reader files, compound lot numbers and cell passage numbers are kept with the notebook, and the acceptance criteria and analysis are written down before the data are collected.

Key terms

• Concentration–response curve: The response measured at a series of drug concentrations, plotted against the logarithm of the concentration; usually S-shaped.
• EC50 and pEC50: The concentration that gives half of the drug's own maximal response, a measure of potency; pEC50 = −log10(EC50 in mol/L), so 100 nM is a pEC50 of 7.
• Emax: The largest response a drug can produce in the system, however high its concentration; it reflects efficacy and is given here as a percentage of the response to the reference full agonist.
• Partial agonist: An agonist that cannot produce as large a maximal response as another (full) agonist acting on the same receptor in the same cells, however high its concentration (Neubig et al., 2003); even a small but real shortfall makes it, strictly, a partial agonist.
• Hill slope: The steepness of the curve; with a slope of 1 the response rises from 10% to 90% of its maximum over about an 81-fold range of concentration.
• Four-parameter logistic: The equation fitted to the data: bottom, top (Emax), log EC50 and Hill slope.
• Stock solution: A concentrated, accurately made solution (here 10 mM in DMSO) from which all working concentrations are diluted.
• Serial dilution: A series made by carrying a fixed volume from each well into fresh solvent in the next, so each is the same fraction of the one before.
• Vehicle: The solvent without drug (here DMSO, 0.1% in the well; most cell assays keep it at or below about 0.1 to 0.5%); vehicle wells are the negative control and define 0% response.
• RFU: Relative fluorescence units: the plate reader's arbitrary unit of light; comparable only within a plate, hence normalisation to controls.
• Z′ factor: 1 − 3(σp + σn)/|μp − μn|, from the means (μ) and standard deviations (σ) of the positive and negative control wells; values of 0.5 or more indicate a clear separation (Zhang et al., 1999).
• Edge effect: A systematic difference of the outer wells of a plate, often from evaporation and uneven warming.
• Schild plot: log(dose ratio − 1) against log antagonist concentration. For a competitive antagonist it is a straight line of slope about 1; where it crosses the x-axis gives the pA2, which with a slope of 1 equals pKB, the negative logarithm of the antagonist’s equilibrium dissociation constant KB (Arunlakshana and Schild, 1959).
• Technical and biological replicates: Wells on one plate (technical) versus independent experiments on different days with different cell passages (biological, the unit of analysis).