The calculation of microbial assays.

Microbial assays of the vitamins, and of other potency is adjusted for the known difference in nutrients such as amino acids, are still a research concentration of the two test solutions to obnecessity, despite the encroachment of physicotain the biologically effective content of the vitachemical techniques for standardization. Almin in each Unknown. Four conditions, dethough their role in standardization is shrinking, veloped primarily in studies of the vitamin Bn the need of industry for quantitative bioassays assay, are of general applicability and should inwith a measurable precision has produced some crease the reliability of microbial assays. They useful designs and calculations that the research may be considered in order. worker could adopt with profit. The quantitative A straight log-dose response curve. Apart from biological assays in U.S.P. XV, for example, technical details, which vary with the material have been reduced to a few basic patterns. Inunder test, much of the success of an assay decluded in this program are the two remaining pends upon the concentration of the test soluU.S. P. microbial assays for the vitamins, those tions. By covering a wide enough dosage range, for vitamin B12 and for calcium pantothenate. the growth response, in terms of y = 100 (per The methods developed there are by no means cent transmittance), can be plotted against the restricted to these two vitamins but are easily log-dose as a sigmoid curve, the response then adapted to the bioassay of all vitamins and amino increasing (instead of decreasing) with the dose. acids in which a growth response is measured in The curve for the pantothenic acid Standard in a limiting nutrient. By investing a little more figure 1 is an example. Its fiftyfold range (obeffort, the microbiologist can gain appreciable tained by using two or more concentrations of dividends in the form of more reliable and pretest solution) is far wider than the threefold to cise results. The purpose of this paper is to show fivefold range in a customary assay. how this may be done. An effective assay requires only the central linear portion of the complete curve. There may BASIC EXPERIMENTAL DESIGN exist some transformation of the response, based A standard pattern for a microbial assay is to upon a sigmoid function, which would plot as a pipette, into a replicated series of sterilized test straight line against the log-dose over the entire tubes, doses varying from 1.0 to 5.0 ml of test range, but we have yet to find such a "cure-all. " solution. The experimenter adds to each tube The angular or arc sine transformation of y 5.0 ml of basal medium stock solution and suffiextends the linear zone in figure 1 from a fivefold cient water to make 10 ml. The tubes are covered, to a tenfold range of dosages but not much more. sterilized in an autoclave, cooled, inoculated, Given an appropriate concentration of test soluand incubated for 16 to 24 hr at a constant temtion, and a suitable organism and medium, perature. The transmittance of the contents of enough of the complete curve will be linear for each tube, well mixed, is then measured in an assay purposes. electrophotometer at a specific wave length and With some nutrients, the lower part of the recorded as a percentage of the inoculated blank. curve yields a straight line when the growth reWith the aid of rough, preliminary assays or sponse is plotted against arithmetic dosage units, past experience, test solutions are prepared of leading to the so-called slope-ratio assays. These each sample or Unknown that have approxiare covered by a well-developed series of statismately the same concentration of vitamin, or tical techniques which need not be considered other nutrient, as the test solution of Standard. here (Bliss, 1952; Finney, 1952). Sometimes the The assay determines how much test solution of smaller growth responses can be converted to z = each Unknown will produce the same growth log y to obtain a straight line relating z to x, response, measured electrophotometrically, as where x = log-ml (loglo ml of solution taken). the test solution of the Standard. This relative Conversely, at dosage levels giving comparatively