A General Theory for Plate Assay of Antibiotics with some Practical Applications

Abstract

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 a t 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.Although very good plate assay methods are available for penicillin and streptomycin, those described for the newer antibiotics are less satisfactory owing to a tendency for the zone edges to be poorly defined and to shift their position as incubation of the plates is continued. Unless a valid theoretical treatment of the nature of diffusion of an antibiotic from the cup into the surrounding agar gel is available, attempts to investigate the factors governing the nature of the zone edge and the slope of the dose-response curve for new antibiotics will be empirical and time-consuming. The only theoretical treatment of this problem of which we were aware was that given by Cooper & Woodman (1946), who discussed diffusion of antiseptics and of penicillin from a Heatley cup into agar, and claimed good agreement between predicted zone diameters and those which they observed in practice. They used, however, a formula derived from considerations of linear, not radial, diffusion, and assumed that the concentration of antibiotic in the cup was constant during the first 8 hr. These assumptions do not hold in plate assays as often performed, and we decided therefore to investigate the theoretical treatment from first principles. With the aid of certain assumptions, which are discussed below, a theoretical expression was derived, ...

Isolation of Auxotrophs of Penicillium chrysogenum and their Penicillin Yields

“…(Clutterbuck et al 1932) which interfered with colorimetric determinations. A biological assay was therefore used for strain H and its derivatives (Humphrey & Lightbown, 1952). Assay results were expressed in units of penicillin/ml.…”

Development and Validation of Microbial Bioassay for Quantification of Cephalexin in Pharmaceutical Preparations

“…The agar diffusion method widely used in antibiotic assay relates the size of the zone of inhibition to the dose of the antibiotic assayed. The relation of the diameter of inhibitory zones to concentration of antibiotic in a solution applied in cups has been considered theoretically 20,21. The ability of an antibiotic is to inhibit or to kill the growth of living microorganisms.…”

The Intracellular Accumulation of 14C-streptomycin by Escherichia Coli strain B in Relation to its Growth-Inhibitory Effect

“…The material, dissolved in 25 ml. of water, was assayed by the plate diffusion technique (Humphrey & Lightbown, 1952) against the International Standard of Streptomycin, and found to contain 700 i.u./ml. Radioactivity was determined in a Nuclear Chicago, Model D 47 ultrathin-window counter, giving background activity of less than 2 c.p.m.…”