Kapron, AI., Hehman, P. I,., 1x0. ENG. CHEXl., ANAL. ED. 17, 5 i 3
(14)
(20)
(1945).
Selidow, I., Diamond, R. M., J .
(15)
Phys. Chem. 5 9 , 710-18 (1955). (16) Sichols, RI. L., Rogers, L. H., IXD. E ~ GCHEX, . ANAL. ED. 16, 137 (1044). (1;) Pavelka, F., Loghi, A . , Xikrochernie z w . Mikrochinz. Acta 31, 138 (1943). (18)Pechard, E., Conipt. rend. 114, 173 (1 892). (19) Per&, D. D., S e w ZeaZand J . Sci. Technol. 28A, 183 (1946).
Piper, C. S.,Beckwith, R. S., J. SOC. Chem. Ind. (London) 67, 374 (1948).
(21)
Robinson, W. O., Soil Sci. 66, 317 (1948).
Sandell, E. R., “Colorimetric Determination of Traces of Metals,” Vol. 111, 2d ed., pp. 453-68, Interscience, New York, 1950. (23) Steiner, O., 2. anal. Chem. 81, 389 (22)
(1930). (24)
Swift, E. H., J . .4m. Chenz. SOC.46, 2375 (1924).
(25)
Thamer, 13. J., Voigt, A. F., Ibicl., 73,
(26)
Thamer, B.J., Voigt, A . F., J . Phys.
3197 (1951).
Chem. 56, 227 (1952).
Weissler. A , . IND. ESG. C I S ~ I. .~, A L ED. 17. 645 (1945). (28) Wells, J. ’E., Pemberton, R., d n d y s l (27)
72, 185 (1947).
RECEIVEDfor review October 8, 1056. . Accepted October 25, 1956. Work done under the auspices of the U. S. -1toniic Energy Commission.
Factors Influencing Validity and Confidence Limits
of Pantothenic Acid Estimation MicrobiologicaI Assay with Lactobacillus Casei MIRIAM F. CLARKE Department of Physiological Chemisfry, The Woman’s Medical College of Pennsylvania, Philadelphia, Pa.
Earlier work had demonstrated a linear relationship between the logarithm of pantothenate per tube and the amount of acid formed upon incubation with 1. casei, provided glucose was increased in the medium to a level that would eliminate i t as a limiting factor. Now a change in the media from peptone to enzymehydrolyzed casein yields a straight line but with a much greater slope. Factors affecting the slope of this logarithmic dose-response curve were examined critically: glucose content of the medium, size and method of preparation of the inoculum. Most favorable conditions for valid assays were found when 3% glucose and heavier inoculum (from enriched medium) were employed and when dosage corresponded to 0.125 to 0.25 y o f calcium pantothenate. Under these conditions, the slope of the doseresponse curves was between 13 and 18, and assays of 2 X 2 or 2 X 3 design, using 16 or 18 tubes, yielded confidence limits of 98 to 102%;.
S
on the original microbiological assay (19), in nhich L. casei n-as eniployed for the quantitative determination of pantothenic acid, suggested that the medium could be improved by the addition of one or more growth-stimulating substances present in rice polishings concentrate ( 6 ) as well as by a n increase in glucose and buffer content (5, 27). Yore recent n ork has s h o m that the (hired improvement in the medium for TUDICS
this organism could be attained by incipasing the peptone, or replacing the peptone, yeast extract, and acid-hgdrolyzed casein by a charcoal-treated enzymatic hydrolyzate of casein together with the usual vitamin, purine, and pyrimidine components, and nith appropriate increases in glucose and buffer (4, 16, 23). As the casein preparation mnde n-ith enzymes offered such marked improvement over the nitrogen sources in the earlier media, it became unnecessary, for practical assay purposes, to resort to concentrates of natural products to provide the necessary adjuvants to the medium. Moreover, use of the enzyme-hydrolyzed caqein in media containing pantothenate hut lacking one of several other vitamins had provided n basis for satisfactory assays (23). K h e n used for riboflavin assayq, this medium nith added glucose had alloned a long, steep doseresponse curve and a small experimental error which compared very favorably n i t h other media used for riboflavin
(4). Preliminary experiments with the Roberts-Snell medium n ith graded doses of pantothenate indicated that the charcoal treatment of the casein preparation varied somen hat in the degree of removal of pantothenic acid or of other substances capable of enhancing bacterial growth. High titrations were occasionally encountered in response to zero dose (blanks). Low “ceiling” or maximum acid output sometimes occurred \then preparations n-ere employed n hich yielded satisfactorily low blank titrations. The
.
size of tlic inoculum and the methotl used in its prepamtion had n. considerable effect upon the results obtained. The culture itself seemed to be providing significant amounts of growth stimulating substances but, of course, increases of pantothenate from this source rvere undesirable. Experiments n-ere therefore first directed ton-arc1 modifications of the inoculum. Clianges in the amount of glucose n-ere tried to see whether the higher maximum output of acid allo1Ted by 3 7 , glucose ~ o u l dgive as satisfacbory results with pantothenic acid assays as had heen the case with riboflavin. 1Iodifications n-ere sought which would yield a long dose-response curve of proved linearity and steep slope, and a reasonably m a l l experimental error. PROCEDURE
The Roberts and Snell (63) medium was the basis for these experiments. It contained, in the 10 ml. in each test tube: enzymatic casein preparation (23), 4 ml. (==200 mg. of casein, prepared from vitamin test casein, Xutritional Biochemicals Corp.); salt solution C (23), 0.2 ml.; glucose, 200 mg.; cystine. 1 mg.; sodium acetate, 200 mg. KHzPOl and K2HP04,25 mg. each ; adenine sulfate, guanine hydrochloride, and uracil, 100 y each; pyridoxine, 10 y ; nicotinic acid, thiamine, and riboflavin, 5 y each; p-aminobenzoic acid, 1 y ; biotin, 0.04, and folic acid, 0.02 y. The only modification of this medium which n-as investigated v-as the increase of glucose from 2 to 30/,, as indicated under results. Media nere prepared one day before their actual use in an assay. ant1 stored ~
r;
VOL. 29, NO. 1, JANUARY 1957
135
overnight in a refrigerator. The fol1on.ing morning they were more or less cloudy; hence filtration by gravity through Filter-Cel preceded the final distribution into assay tubes. Stab transfers of L. casei ATCC S o . 7469 were prepared in glucose-agaryeast extract tubes (23) a t biweekly intervals. For each group of assays, inoculum was prepared by transferring organisms from a freshly incubated stab to tubes containing 10 ml. of one of two media; (a) the Roberts-Snell complete liquid medium (above) with glucose increased to 300 mg., and ll-it’h 40 mg. of untreated Bacto yeast ext’ract, as in the riboflavin assays (4), or (6) the niedium \vit,h only 200 mg. of glucose and 5 y of calcium pantothenate per tube. I n either case, cultures incubated 20 to 24 hours were centrifuged, washed by suspension in sterile O.S& saline, centrifuged again, and resuspended to the original volume in saline. For certain experiments these suspensions were treated by further dilution with saline, so that the resulting preparations gave a reading between 90 and 100, or between 9 and 10, in a Klett-Summerson colorimeter equipped with filter No. 66. The inocula from the enriched medium (a) \\.ere designated >IC; those from the other ( b ) were designated RS. The letter H was used for heavy inoculum reconstituted to 10 ml. 11 and L were used for “medium” or “light” inocula reading 90 to 100 or 9 to 10, respectively. One drop of each inoculum was introduced aseptically into each tube, previously autoclaved. The tubes for assay were autoclaved only G minutes a t 15 pounds t’ominimize the change in color. Although the browning had no appreciable effect upon bacterial metabolism, the darker color after a longer autoclaving contributed t o the error of titration. KOevidence of incomplete destruction of microorganisms was obtained in unseeded, incubated control tubes. T o test each medium and inoculum, a stock solution of calcium pantothenate was diluted so that doses a t several levels were used. The dosage interval nxs 0.30103 or the log of 2 , each dose being twice the one next below. K h e n a concentrate was tested against calcium pantothenate standard, either this interval or a smaller one was used for unknown and standard. Duplicates were used a t all dose levels in the study of standard curves; in some assays three or four replicates were employed. The tubes were incubated at 37” C. for 70 to 72 hours in an incubator or a constant temperature water bath. Random arrangement of the tubes of all experiments was adhered t’o. After incubation they were remol-ed and titrated in random order to pH G.8 to 7.0 with 0.1S sodium hydroxide, using liromothymol blue as indicator. The st’atistical analysis of the data for the dose-response curves followed methods used heretofore ( d , 4 ) . An estiimte of standard error, slope, linearit,y, etc., ITas made from an analysis of data from the series with standard pantothenate. Application of the in136
ANALYTICAL CHEMISTRY
‘ O r -
n
*
t
I
I
I
t
0
1
L
I
t
I
I
1
4
,
1
I
I
(
LOG MICROGRAMS CALCIUM PANTOTHENATE 0 30103 DOSE I N T E R V A L S
Figure 1.
Dose-response curves
Points for each curve represent means of duplicate responses to 0.015625, 0.03125, 0.0625, 0.125, 0.25, and 0.507 of calcium pantothenate per test tube. Roberts-Snell medium with 2y0 glucose. Inoculum as indicated in test
formation so obtained to microbiological assays included tests for parallelism, curvature, and confidence limits of the estimated potency. METHOD OF CULTURING INOCULUM
Two methods of subculturing L. casei in liquid media were employed : (a) 3% glucose and 0.4% Bacto yeast extract and (b) 2% glucose with 5 y of calcium pantothenate per tube. The organisms were prepared so that medium and light inocula from (a)-i,e., MC-31 and h I C - b a n d from @)-Le., RS-?*I and RS-L-were used in seeding tubes prepared with the Roberts-Snell basal medium containing 2% glucose with graded doses of pantothenate. Figure 1 shows the longer and steeper linear portion of the dose-response curves 1% hen the inocula used had been prepared from the culture grown on the medium nith increased glucose and enriched with yeast extract. Similar results were obtained when this experiment was repeated using the same four inocula but with 3% glucose instead of 2’3 in the assay medium. As these experiments indicated that the length and slope of the dose-response curve nere limited by use of inoculum grown in unenriched medium, the latter procedure for culture of L . casei !vas not employed in subsequent experiments. Blank titrations all showed between 1.1 and 2.3 ml. of 0.1A17acid per tube in this series.
AMOUNT OF GLUCOSE IN ASSAY MEDIUM
4 number of curves were drawn from data obtained from experiments in which either 2 or 3% glucose had been incorporated in the medium. K i t h each medium, three inocula were used: XIC-H, MC-M., and MC-L.
,
Figure 2 shows the evpected increase in the maximum acid production IT hen the media contained 3% glucose. The range of linearity in all these euperiments seemed to he between 0.0625 and 0.25 y per tube, regardless of glucose content. The calculated slopes. b, n-ere greater with 3% glucose than when 2% glucose was used nith the corresponding inoculum (Table I).
SIZE OF INOCULUM
Increasing the size of the inoculum from just turbid (MC-L) to heav). (MC-H) affected the outcome by increasing the slope of the dose-response curve (Table I). The heavier inocula also tended to raise the amount of acid formed in response to zero dose, the “floor,” as Ivell as the maximum acid produced with maximum pantothenate, the “ceiling.” The largest sampling variance, s2, was found when the lightest inoculum was used with both glucose concentrntions. In combination 6, a smnll slope and a large sampling error point to the inadvisability of employing ?yo glricose with light inoculum in assays. K i t h combinations 5 and 6 much larger mean squares for departure from linearity (1.334 and 1.632, respectively) were obtained than with other combinations, d i i c h resulted in values varying from 0.023 to 0.468. Khen variance ratios for all combinations were calculated (using the mean square for departure from linearity and the mean square for error term, assay X doses, from the analysis of variance), no ex-idence of nonlinearity was obtained (8). Xoreover, when a more rigid t’est was applied, the ratio of mean square for departure from linearity to the error term computed from the difference b e h e e n duplicates (sampling variance),
Table I.
Combi- Glunation cose, No.
yo
1
3 3
3 4 5 6
3
2
2 2 2
Effect of Glucose Concentration and Inoculum Size on Dose-Response Curves and Related Statistics
Inoculum XIC-H PIIC-XI RIC-L 3IC-H
0
;\IC-L
0
hlC-XI
Acid Liean Slope, Produced Maximum Linear in Blanks, Acid Portion Test for Significance of Sampling SO. Range, Produced, of Curve, Departure from Linearity; Variance, s/ b, of Y nn. 0.LV RI1. 0.1.V b from Variance Ratiou ( 8 ) s2 Expts. 0625-0 25 1 0-5 9 19-24 15 65 Not significant 0 2239 0 0302 6 0 0858 0 0222 5 17-25 13 21 S o t significant 0625-0 25 1 7-4 2 13 36 N o t significant 0 2540 0 0 3 7 5 14-23 0625-0 25 1 4-3 i 18-19 14 35 X o t significant 0 0240 0 0108 4 0625-0 25 1 0-5 8 0 0433 0 0202 2 1 5-2 2 16-18 10 30 Significant i P = 0 051 0625-0 25 1.4-1.5 14-15 10.11 Approaching significance 0 -1118 ... 2 ( P between 0.2 and 0.1)
dpprou. Range of Linearity, 0 0 0
ITarinnre ratio computed from mean square for departure from linearity and sampling vnriance,
24
LOG MICROGRAMS CALCIUM PANTOTHENATE 0 30103 DOSE
Figure 2.
INTERVALS
Dose-response curves
Points for each curve represent pooled data for responses to 0.03125, 0.0625, 0.125, 0.25, and. 0 . 5 0 ~of calcium pantothenate per test tube. Inoculum as indicated in tevt A,B,C. 370 glucose D,E,F. 27, glucose
(Table I) no evidence of departure from linearity was adduced except in the case of combination 6, where the probability approached significant levels. (The error term for combination 6 is very large.) Although combined data thus support linear regression in combinations 1 to 4, examination of the individual graphs showed in some a tendency toward a steeper slope above 0.125 y than below this dose. These obsermtions suggest the use of a shorter portion of the dose-response curve in assayb and emphasize the importance of devices to test the validity of assay results. COMMERCIAL SOURCE OF ENZYMEHYDROLYZED CASEIN
TI\o idmtical self-contained expeiimeiits 11ere carried out in 17 hicli media ewctly alike, with the exception of the source of enzymatic casein preparation, were compared. Glucose iras incorporated a t 3% and the h e a ~ i e s t inoculum (NC-HI was usecl. Results shon- (Table 11)that the com-
mercial preparation, “vitamin-free” casein hydrolyzate (enzymatic), Sutritional Biochemicals Corp., gives a satisfactory dose-response curve with a very high maximum acid output. The linear portion is placed higher than is the curve from media with casein preparation, made from Nutritional Biochemicals Corp. “vitamin test casein” by the procedure of Roberts and Snell (93). Although the zero dose yields a very high titration, approximately 7 ml., suggesting possible pantothenate contamination, this commercial material has certain advantages. d s cnlculated in these t n o experiments, the slope, b, is greater; the sampling error, s2, and expected precision, A, are smaller when the commercial source is used. dssays using this casein preparation should yield valid results. ASSAYS
OF
92.
vitamins, prepared by Charlec C. Haskell and Co.), using combinations 1to 4 of medium and inoculum dcscribed aboT e. Because of the factorial design, it nas possible to use factorial coefficients ( 2 ) in analyzing the results. Some of these assays yielded reasonable values for potency but upon close examination proved to be unsatisfactory, because of very large experimental error when light inoculum was used, or nonvalidity due to departure from parallelism, to curvature of the combined curve. or to opposed curvatuie, as indicated by large variance from these sources compared with sampling variance. Valid assays were obtained simply by restricting doses to the upper portion of the dose-response curve. above 0.128 y of calcium pantothenate, avoiding the loner portion which studies with standard alone had indicated might have a smaller value for dope. Two designs were successful. I n a 2 x 2 assay, doses of 0.125 and 0.250 y of caiciuni pantothenate were compared M ith corresponding amounts of Pantabee (02.5 and 0.50 mg.). I n one 16-tube assay of this design the following were obtained: s2 = 0.1353; confidence limits, 98 to 10294 (P = 0.05). another design yielding valid results was a 2 x 3 assay using a dosage interval of 0.09691 instead of 0.30103 used heretofore. Doses of 0.16, 0.20, and 0.25 y of standard were compared Ivitli 0.512, 0.64, and 0.80 mg. of Pantabee. I n this design it \\as possible to demonstrate that there mas no departuie from parallelism, curvature of the conibined curve, or opposed curvature of the separate curves. I n a n 18-tube assay on a Pantabee sample using this design the following were obtained: common slope, b, = 18.40:s2 2 0.1403; confidence limit.. 98 to 10lyo ( P = 0.03.
VITAMIN PREPARATIONS
9 number of assays of free pantothenate potency ryere carried out on Syrup of Pantabee (an aqueous liver concentrate with added B-complex
DISCUSSION
Previously published curves relating dose of pantothenate to response, acid VOL. 2 9 , NO. 1 , JANUARY 1957
137
produced by L. casei, have been of two kinds. Pennington, Snell, and Williams (19) found a curvilinear relationship plotting dosage on an arithmetic scale. I n general, enrichment of their medium led to even greater curvature in the dose-effect curve, especially if glucose was increased simultaneously with the increase in growth-stimulating substances and buffer (6, 15, 16). On the other hand, a straight line relating arithmetic increment of dose and response has been reported by Strong and associates (27, 281,who, however, kept the glucose a t the 1% level of the original authors and thus provided rather strict limitation for acid production in a medium which mas otherwise considerably enriched. The media of Strong and associates, when used in a cooperative study of the microbiological assay of pantothenic acid using L. casei, led to extremely variable results (16). There are advantages to the assayer, if a greater difference between minimum and maximum response is obtained. If, however, this results in a curvilinear dose-response relationship, it becomes obvious that some transformation should be used, so that a straight line is made available with its advantages in testing validity and determining potency and confidence limits. Bliss observed (1, p. 562) that the “frequent occurrence of a slight convex curvature in the dosage-response curve is a major handicap in the wider adoption of sloperatio or log-ratio microbiological assays.” The use of curves in which the logarit,bm of pantothenate is related linearly to the acid produced by L. casei was suggested some time ago ( 6 ) . Best results were then obtained when the acid-hydrolyzed casein was replaced by a peptone preparation, the latter in greater proportion than had been used originally, and when glucose was so increased that it did not become a limiting factor for acid production. With such media there was a linear regression from approximately 0.04 to 2.56 7 , when log calcium pantothenate per tube was plotted against acid produced in 3 days. The slopes were usually between 9 and 11 (16). Replotting the data of Roberts and Snell, using log-dose and acid output as coordinates, also disclosed a sigmoid curve, the central portion of which, between 0.04 and 0.10 y, was apparently linear with a slope of about 10.5. I n the present experiments on pantothenic acid, lower “ceiling” and smaller values for slope were obtained when 2% glucose was employed instead of 3%. When the size of the inoculum and the amount of glucose were similar to those used by Roberts and Snell, a similar slope was found: 10.3 and 10.1 for combinations 5 and 6 (Table I), though adequate statistical support for linear
138
ANALYTICAL CHEMISTRY
regression was lacking under these experimental conditions. L. casei was also used for pantothenate assays by Clegg, Kodicek, and Mistry ( 6 ) , who employed a medium with acid-hydrolyzed casein, peptone, and 300 mg. of glucose. When the figures of these investigators were replotted, using the logarithm of the dose and the acid output in 3 days as coordinates, a very long, straight doseresponse curve emerged, apparently linear between 0.02 and 0.5 y and with an over-all slope of about 13.
Table II.
been suggested repeatedly (?‘, 9-11, 22, 24). The presence of stimulatory factors in this category in yeast extract @$), liver concentrates (12, 18, 26), and peptone (13, 21, 22) has been pointed out. Khile the identity and number of these compounds remain in doubt, their presence must be assured by incorporating some natural, convenient source into the medium. Even if they were all known, a cheap source would still be required. The enzymehydrolyzed casein seems to be the best answer to this problem.
Comparison of Values Obtained Using Enzyme-Hydrolyzed Casein Prepared in Laboratory vs. Commercial Product
(Medium: 3% glucose. Inoculum: MC-H) Source of Casein Preparation “Vitamin-free” Author’s casein preparationa hydrolyzate (83) (enzymatic)* Approximate range of linearity, y 0.0625-0.25 0.125-0.50 Maximum acid, ml. 0.1N 23 26-28 Slope of dose-response curve, b 16.65 17.67 Test for significance of departure from linearity; from variance ratioc (8) Not significant Not significant Sampling variance, s2 0.1460 0.0977 Expected precision, 0.0230 0.0177 No. of experiments 2 2 Q
b
Starting with vitamin test casein Nutritional Biochemicals Corp. From Nutritional Biochemicals dorp. See 5 , Table I.
It is obvious that the production of such useful curves depends t o a considerable degree upon the availability of sufficient glucose from which L. casei produces acid, and sufficient buffer so that the limiting effect of acid upon bacterial metabolism is offset. Vitamins must be present a t maximum levels. But also, sources of nitrogenvarious amino acids, certain purines and pyrimidines, and probably other compounds-must be available in large enough amounts to allow maximum performance. These substances, except for certain amino acids which are required, are not considered essential but possess definitely stimulating properties, Certain peptides have a stimulating effect upon lactobacilli, aside from their amino acid content (14, 32). Where maximum performance of L. cmei is expected, the necessity of incorporating sufficient ‘(strepogenin activity” is indicated. The amount of strepogenin found in trypsin-hydrolyzed casein (22, 25, 26) makes this material of unusual value in media for L. casei. That the “strepogenin activity” of specific peptides already identified may not represent the whole picture has
Treatment with charcoal, designed to remove traces of pantothenate, may also remove a portion of the peptidebound amino acids or other stimulating materials referred to above (18, 22). Evidence of this was obtained by extending certain dose-response curves so as to show both floor and ceiling, which tended to rise and fall together with the different batches of hydrolyzate. Thus, the maximum acid output depends not only upon maximum pantothenate available, but also upon other substances which potentiate this pantothenate. The desirability of low blanks has been stressed in various publications. These low titration values now appear t o be due not only to absence of pantothenate but also to removal of a portion of the stimulating substances, which, if present, increase the effect of minute traces of pantothenate. This is supported by the trailing off of the lower portion of doseresponse curves in a few experiments using a very wide range of dose. These substances, if present in the useful dosage range, increase this range and the slope. I n the author’s experience, the variability between batches of the casein
preparation with regard to these substances may have been the chief source of variation, betn-een assays, of the slope, the minimum, and the maximum acid output. The effect upon accuracy of assay values is probably small, as a standard curve is ah-ays used in every assay of unknowns. Even if the high blanks had been explainable on the basis of pantothenate Contamination alone, no harm would have arisen in assays carried out as planned herein. Both Bliss and Kood (1, p. 562; 29, 51) have suggested adding wficient vitamin to the basal medium to shift the resulting response values into the linear portion of the dose-response curve. The medium itself need not be depended upon solely for these stimulating compounds; some are available also in suitable inocula, prepared in enriched basal medium and of sufficient size. The importance of the inoculum in this regard has been pointed out (12, 24, 26). The total effect of these substances influencing the performance of L . casei is readily seen in the slope of the dose-response curves relating logdose to the arid produced during 3 days of incubation. In assays using the Roberts-Snell medium n ith increased glucose and with inocula designated aa “medium” or “heavy” (from enriched basal medium), slopes of the curves of response for the fortified liver concentrate tested were no steeper than those for the standard pantothenate. This had not been the case when the unaltered Pennington, Snell, and Williams medium had been used to assay vitamin concentrates. This observation had been the first hint of the inadequacy of this early medium. Mean slopes for pantothenate were 8.04, while those for rice polishings concentrate were 9.17; the difference was significant a t the 1% level ( 5 ) . Under the improved conditions described in this paper, slopes for standard and unknown, the latter a concentrated liver and vitamin preparation, usually lie between 13 and 18 with no tendency for a greater slope when the concentrate replaced pure pantothenate in constructing the doseresponse curve. The medium is also more sensitive to pantothenate, be cause maximum acid is produced using between 0.5 and 1.0 y of calcium pantothenate per tube, whereas formerly over 2 7 were required (16). It has been emphasized by Wood (SO, p. 632) that the “single-curve”
method commonly employed to estimate potency from experimental data “not only is theoretically unsound, but also may in practice give a result which is materially in error.” He proposed a “slope-ratio” method, R hich has been used by Bliss ( 1 , p. 569) to compute the potency of plant extracts n hich are dilute with respect to their pantothenate concentration. Loner doses of this vitamin may with certain media yield a straight line on an arithmetic scale over a limited range. I n the example cited by Bliss, full reference and description of the medium are not given. Moreover, the responses to standard are lower than \\-hat can be expected using improved media in 3-day assays. If this procedure and the slope-ratio of estimating potency are resorted to because of the dilute nature of test solutions or the presence of interfering substances, evidence as to completeness of the medium is extremely important. Should certain carbohydrates or specific peptides be present in sufficient concentration, they might influence acid output and the slope, if these substances were in borderline concentration in the basal medium. Because the mathematical procedures are simpler and offer certain safeguards u-hen the linear regression described in this paper is used, other methods need not be used when concentrates are assayed with L . casei. Moreover, aids in the calculations required for potency ratio and confidence limits are now readily available ( I , 3, 90). The experiments described and related statistical treatment have been offered as a useful procedure to test the validity and precision of these assays and not as any criticism of previously published media. Although applied here to assays in nhich L . caspi is used to estimate pantothenic acid, and, previously, riboflavin (4) potency, the steps suggested have general applicability for other microorganisms and growth principles. The time for a collaborative study of an assay method might well follow such an analysis as this, so that sources of variation and evidence of reliability might be evaluated readily. LITERATURE
CITED
( 1 ) Bliss, C. I., “Statistics of Bioassay,” Academic Press, Nen- Pork, 1952. (2) Bliss, C. I., Marks, H. P., Quart. J . Pharm. and Pharmacol. 12,82-110, 182-205 (1939). (3) Burn, J. H., Finney, D. J., Goodwin,
L. G., “Biological Standardization.” 2nd ed.. Oxford Universitv Pres’s, London; 1950. (Statistied analysis, pp. 26-176). (4) Clarke, &I. F., ANAL. CHEM. 25, 1247-52 (1953.)
( 5 ) Clarke, &I.F., Lechycka, M., Light, A. E., J . Biol. Chem. 142, 957-8 fl942). \ - -
--z
(6) Clegg, K. hI., Kodicek, E., Mistry, S. P., Biochent. J . 50, 326-31 (1951).
( 7 ) Dunn, AI. S., McClure, L. E., J . Biol.
Chem. 184, 223-33 (1950). (8) Fisher, R. A , , Yates, F., “Statistical Tables,” 4th ed., Oliver and Boyd, Edinburgh, 19.53. (Variance ratio, Table I-). (9) Kihara, H., llcCullough, W. G., Snell, E. E., J . Biol. Chem. 197, 783-9 (1952). (10) Kitay, E., Snell, E. E., J . Bacteriol. 60, 49-56 (1950). (11) Klungsgyr, M., Sirny, R. J., Elvehiem, C. A . , J . Biol. Chem. 189,55769 (’1951):
Kodicek, E., Rfistry, S.P., Biochem. J . 51, 108-12 (19523. Kodicek, E., Peppe r, ’C. R.,J . Gen. Microbiol. 2, 292-305. (1948). Krehl, W.A., Fruton, r. s., J . ~ i o z . Chem. 173. 4:79-85 (1948).
Light, A. E.‘, Clarke. M. F.. Zbid., 147, 739-47 (1943):
LOY, H . W., Jr., J . Assoc. O$lc. Agr. Chemists 28, 567-71 (1945).
Neal, A. L., Strong, F. M., IKD.EXG. CHEJI.. ANAL. ED. 15. 654-7 (1943): (18) Peeler, H. T., Daniel, L. J., Norris,
L. C., Heuser, G. F., J . Biol.
Chem. 177, 905-16 (1949). (19) Pennington, D., Snell, E. E., Williams, R. J., Ibid. 135, 213-22 (1940). (20) Pharmacopoeia of U. S. A, XV, Washington, 1950. (Design and analysis of biological assays, pp. 865-80.) (21) Pollack, M. A., Lindner, &I.,J . Biol. Chem. 147, 183-7 (1943). (22) Rege, D. V., Sreenivasan, .4., J . Rncferiol. .... ... 67. 680-5 (1954). (23) Roberta, E. C.: Snell, E. E.; J . Biol. Chem. 163, 499-509 (1946). (24) Scott. M. L., Korris, L. C., Heuser, G. F., Zbid: 166, 481-9 (1946). (25) Sprince, H., Woolley, D. W., J . Am. Clhem.. Soc. 67. 1734-6 119433. (26)
. ,
(27)
147,’483-4 ( 1943). (28) Strong, F. M., Feeney, R. E., Earle, A.. IND.ENG.CHEM...SSAL.ED. ._ 13; 566-70(1941). ’ (29) Wood, E. C., Analyst 71,l-14 (1946). (30) Wood, E. C., Nature 155, 632-3 ~, (1945). (31) Wood, E. C., Finney, D. J., QuarLJ. Pharm. and Pharmacol. 19, 112-27 (1946). (32) Woolley, D. W., J . Biol. Chern. 172, 71-81 (1948).
RECEIVED for review July 3, 1956. dccepted September 19, 1956.
VOL. 29, NO. 1, JANUARY 1957
139
