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SUMMARY: The distribution of antibiotic (or other substance) in the agar around a container or around a hole in a punch-plate can be expressed theoretically by an equation involving: the initial quantity of antibiotic, the depth of the agar layer, the diffusion constant, the concentration at a given distance from the container, and the time of diffusion. The validity of the equation was confirmed by measurement of the diffusion constants of penicillin, streptomycin and aureomycin, and of the critical concentration of these substances required to inhibit test organisms, followed by the use of the values so obtained to predict the sizes of the inhibition zones produced experimentally by these antibiotics after varying periods of diffusion. The theory predicts that the square of the inhibition zone diameter will be proportional to the logarithm of the antibiotic concentration. This relationship was found to hold, when accurate assays were made, for a number of antibiotics but not for penicillin when tested with Bacillus subtilis. The most important factor determining the slope of the dose-response curve under given conditions is the diffusion constant of the antibiotic. The slope can, however, be increased by prolonging the time allowed for diffiusion. Particular factors which affected both the sharpness of the zone edge and the nature of the dose-response curve were production of small amounts of penicillinase by strains of B. subtilis used for penicillin assay, and uptake of streptomycin by organisms used for streptomycin assay. Measurements of adsorption of streptomycin by B. subtilis, B. pumilus and by Staphylococcus aureus were made, and were shown to fit equations of the Freundlich isotherm type.
Humphrey et al. (1952) studied this question.