equations were developed for use in the evaluation of dilution

Transcription

1 IV. APPLICATION OF STATISTICS TO PROBLEMS IN BACTERIOLOGY EXPERIMENTAL COMPARISON OF THE DILUTION METHOD, THE PLATE COUNT, AND THE DIRECT COUNT FOR THE DETERMINATION OF BACTERIAL POPULATIONS N. R. ZIEGLER AND H. 0. HALVORSON Department of Bacteriology and Immunology, Untiersity of Minnesota, Minneapolis Received for publication December 24, 1934 In previous publications (1933 a, b and c) we have presented certain theoretical considerations in regard to the dilution method of estimating bacterial populations. In the first of these publications, equations were developed for use in the evaluation of dilution data. The second publication was concerned with the accuracy of data obtained by using several tubes of a single dilution. The third paper was concerned with the accuracy of data obtained when several tubes of each of several dilutions were used. It was shown that with several dilutions it is possible to evaluate the limits of accuracy of the data obtained. To check the theoretical considerations with experimental data, we have determined bacterial populations by means of the dilution method, the plating method, and the direct count in order to compare the results obtained by the three methods. This paper is concerned primarily with the presentation of these experimental data. METHOD To determine the population of a heavy suspension of bacteria, it is necessary first to dilute the original suspension. The least dilution is required for the direct microscopic count, and the greatest for the dilution method. Sterile tap water adjusted to ph 7.0 was used as a diluent. We were guided in this by the work of Wilson (1922). To avoid the error which may occur as a result of evaporation of the measured diluent during autoclaving, the 609

2 610 N. R. ZIEGLER AND H. 0. HALVORSON sterile tap water was measured aseptically into sterile Erlenmeyer flasks by means of a 99-cc. sterile pipette or a 50-cc. sterile burette, depending upon the volume of water desired. A uniform suspension of the material to be examined was secured for all experiments by shaking it for five minutes with '-inch glass beads in a 500-cc. Erlenmeyer flask. In addition, the first dilution of the material was shaken with beads for about two minutes. Stein (1918) found that shaking of crude sewage for longer than five minutes did not further increase the bacterial count. Dilutions were made in powers of 10. For this purpose, 10-cc. volumetric pipettes graduated to deliver 0.1 cc. were used for measuring amounts greater than 1 cc., and 1-cc. volumetric pipettes were used when only 1 cc. was required. The first dilution was always made by adding 10 cc. of the material to 90 cc. of sterile tap water. Further dilutions were made by adding 1 cc. of this initial dilution to 99 cc. of diluent. Intermediate dilutions of 1:10 were made by adding 5 cc. of one dilution to 45 cc. of sterile water to secure the dilution with the next higher power of 10. The direct count. For the direct count we used a combination of the method of Breed and Brew (1925) and that of Benians (1916), as described by Henrici (1923). One cubic centimeter of the 1:10 dilution of the bacterial suspension was thoroughly mixed with an equal volume of a 2 per cent aqueous solution of Congo red. Instead of using ruled squares on a slide, it was found more convenient to spread the mixture over a definite circular area. The circular area can be outlined on a glass slide more accurately than a square. For this purpose circles having a radius of cm. were inscribed on 1.5-by-3-inch glass slides by means of a pair of dividers, to one arm of which a diamond pointed pencil was attached. The diameter was checked by means of a mechanical stage which could be read to 0.01 cm. These circles then had an area of 5 sq. cm. With a calibrated capillary pipette, 0.01 cc. of the bacteria Congo-red mixture was removed and spread as uniformly as possible over the circular area. The use of the circular area instead of a square removed the difficulty of spreading the material into corners. This should

3 APPLICATION OF STATISTICS IN BACTERIOLOGY increase the accuracy of the method. The slides were dried in the air, after which they were fixed in a 1 per cent solution of hydrochloric acid in 95 per cent alcohol, which also served to convert the dye to the blue form. When the alcohol had evaporated, the bacteria were counted. Counting was facilitated by the use of an eyepiece micrometer which was ruled in 10 squares each way, thus making 100 small squares. This eyepiece micrometer was used with a Leitz oil immersion objective (1/12) and a no. 5 ocular. The eyepiece micrometer was calibrated against a stage micrometer. For this calibration, we used a tube of such length that a distance of 0.1 mm. on the stage micrometer corresponded to the width of the large square of the micrometer eyepiece. Thus the area of the eyepiece micrometer represented an area of sq. cm. on a slide to be examined. Since the area of the bacterial film to be examined was 5 sq. cm., the total number of fields in this area was 5/ The average number of bacteria (n) per field (large square) times the number of fields gives the number of bacteria in the volume (1/200 cc.) of the 1:10 suspension used in making the film. Then (n X 5 X 200)/ = n- 107 bacteria per cubic centimeter in the dilution used in making the slides, or n 108 for the undiluted material. Usually 100 fields were counted on each slide along the diameter of the circular area, although sometimes 50 fields were counted on each of two slides. The number of slides made and the number of fields counted varied with the different experiments. The plating method. The Koch plating method was used. Petri plates were inoculated by delivering 1 cc. of the proper dilution into each plate from a 10 cc. volumetric pipette graduated in 0.1 cc. Standard beef extract agar was melted and brought to a temperature of 420, ±10C. The agar was then poured into the inoculated plate and rotated several times to secure a uniform distribution of the inoculum in the agar. After the agar had solidified, the plates, with one exception to be mentioned later, were inverted and incubated at 370C. for forty-eight hours. All the colonies on the plate were counted by the aid of a Wolffhuegel counting apparatus. The dilution method. Sets of ten tubes or multiples of ten tubes 611

4 612 N. R. ZIEGLER AND H. 0. HALVORSON were inoculated with each of three dilutions. The inoculation of large numbers of tubes was facilitated by using a test tube rack similar to that used by McCrady (1915) and by Wells (1918). These racks were made of heavy tin and were of such a size as to hold six 150-by-16 mm. straight-walled culture tubes. The inside dimensions of these racks were 10 cm. long, 1.6 cm. wide, and 10 cm. deep. The sides were open except for a strip of tin at the top, 4.5 cm. wide. The cover was 10.2 cm. long, 1.9 cm. wide, and 2.5 cm. deep. A layer of cotton was cut to fit snugly in the top of the cover. Similar racks containing 11 tubes have been used in later work. Because of variation in the diameter of the tubes, the cover was made of the above size, which enabled us to remove and replace it easily. The cover was held in position by a heavy rubber band. The rack, as shown in figure 1, has several advantages over the types formerly described. The tubes are held in a single row, and the bottoms are clearly visible, permitting positive and rapid observations. This is particularly advantageous in the case of certain organisms which form a sediment. The medium used depended upon the organism or type of material studied. In the present investigation, only liquid mediums were used. About 10 cc. of the medium were placed in each tube. The apparatus was sterilized at 15 pounds for fifteen minutes. The dilutions were so selected that the volume of the inoculum remained constant at 1 cc. This tended to decrease errors caused by the measurement of small volumes. In fact, if smaller volumes of the same dilution are used instead of the same volume of the next higher dilution, considerable error may be introduced because of the greater chance that organisms may adhere to the wall of the culture tubes in the process of inoculation. The sixth tube in each rack was used as a control to determine the chance of contamination when using this type of rack. Of the 6100 tubes used in the course of this work, 1160 were controls. Two of these controls were found to be contaminated. By using the system described above, it was possible to inoculate about 5 tubes per minute. The inoculated tubes were incubated at 370C. for forty-eight hours, except in a special case to be mentioned later.

5 APPLICATION OF STATISTICS IN BACTERIOLOGY For the first part of this study it was desirable to use an organism which was known to give a uniform suspension and as accurate a plate count as possible. Some preliminary tests were made to determine the dilution which would give a plate with an optimum number of colonies, and also to determine the dilutions which would, respectively, cause growth in nearly all tubes, cause growth in about half the tubes, and cause growth in but few of the tubes. To obviate the daily repetition of these preliminary FIG tests, we used a culture which had been transferred daily to a 1 per cent peptone solution for a period of thirty days. In this way a nearly constant population of the organism was maintained in the twenty-four-hour cultures. For example, when Escherichia coli was the test organism, preliminary experiments showed that the desired results were obtained when 6 cc. of a 1: 10 dilution of a twenty-four-hour culture were added to 94 cc. sterile tap water, and this diluted to 105 for plating, and to 106, 107, and 108 for the

6 614 N. R. ZIEGLER AND H. 0. HALVORSON dilution method. The dilutions used in the experiments are given in the appendices. EXPERIMENT 1 From the 1:10 dilution of the twenty-four-hour E. coli culture, three 1-cc. samples were removed and each mixed with 1 cc. of Congo red for the direct count. From each of these mixtures, 10 slides were made as described above. A hundred fields were counted on each of these slides. The data are given in Appendix I. Six cubic centimeters of the same 1:10 dilution of the twentyfour-hour E. coli culture were added to 94 cc. of sterile tap water. Further dilutions were made as described earlier. Ninety-two l-cc. samples were removed from the 105 dilution for plating as described. One hundred sixty 1-cc. samples were removed from the 106 dilution and inoculated into 16 sets of 10 tubes each containing peptone solution. Similarly, 16 sets were inoculated from the 107 and 108 dilutions. The results of these experiments are found in Appendices II and III respectively for plate counts and dilution data. Of the tubes inoculated from the 106 dilution, 158 showed growth and 2 no growth; from the 107 dilution, 61 tubes showed growth and 99 no growth; from the 108 dilution, 8 tubes showed growth and 152 no growth. The most probable number of organisms present in 1 cc. of the 107 dilution, as determined by means of equation 8 in earlier publications (1933 a, b), is found to be It has also been shown in an earlier publication (1933c) that the likely limits of accuracy can be evaluated. We find in this experiment that the actual population in the 107 dilution of the stock suspension, within reasonable probability, lies between X 107 and X 107. In the appendices this is referred to as the range. The values are determined from the curve presented in the third paper of this series. Since the stock suspension represents a 1:166k dilution of the original suspension, the population of the suspension, as determined by the dilution method, is X 109, and the limits of variation are X 109 and X 109. From the direct counts given in Appendix I, we have calculated

7 APPLICATION OF STATISTICS IN BACTERIOLOGY the mean values of the individual slides. These are presented in table 1. The mean of the 30 slides is The number of organisms per cubic centimeter in the original material is then X 109. From the standard deviations of the means of 30 slides, the limits of variation based upon a criterion of twice the standard deviation have been calculated. Therefore, from the direct count data, we find that the actual population lies somewhere between X 109 and X 109. TABLE 1 Mean values of individual direct counts of Escherichia coli in experiment N... = 30 Mean = Standard deviation of means of individual slides... = Coefficient of variation of means of individual slides...= per cent Standard deviation of means of 30 slides... = Coefficient of variation of means of 30slides.= 5.13 per cent The values obtained from the plates are found in Appendix II. It is to be observed that the mean value of 92 plates is colonies per plate with a 105 dilution of the stock suspension. The standard deviation of the mean is ± Again, using twice the standard deviation as a criterion of accuracy, we find that the actual population in the stock suspension as determined by the plate method is somewhere between 47.0 X 105 and 50.4 X 105. The stock suspension represents a dilution of 1: 1661 of the original suspension. Therefore the number of organisms per cubic centimeter in the original suspension, as determined by the plate count is X 109. The true value in the original sus- 615

8 616 N. R. ZIEGLER AND H. 0. HALVORBON pension will then lie somewhere between X 109 and X 109. The results are summarized in table 2. It can be seen from this table that the values obtained by the dilution and plating methods agree, but that the direct count gives a value which is significantly higher. EXPERIMENT 2 This experiment was essentially a repetition of experiment 1, except that a pure culture of Bacillus subtilis was used instead of Escherichia coli, and no direct count was made. B. subtilis was grown in beef extract broth, and transferred daily for 15 to 20 generations in order to obtain a uniform actively growing culture with a relatively constant population. The plates and tubes were inoculated as in the previous experiment. The medium used for the dilution experiment was beef-extract broth adjusted to ph 7.2. Because of the aerobic nature of the organisms to be used, only 5 to 6 cc. of medium were placed in each tube. The results of these experiments are found in Appendices II and III. The data were analyzed in the same manner as for experiment 1. The results are summarized in table 3. These data show, as in experiment 1, that there is no significant difference in the values obtained by the two methods. In the two following experiments, mixed cultures were used. It is well known that some bacteria are antagonistic to others. Pseudomonas pyocyanea is known to exert this antagonistic effect on E. coli. It is a common opinion that on plates made from mixed cultures containing nearly equal numbers of different organisms, one or more of which is antagonistic to the others, colonies of one predominate. It would appear that the plate counts of such mixtures would be abnormally low. It was therefore considered of importance to determine whether the dilution method would give a better measure of bacterial population than the plating method in such a mixed culture. Experiment 3 was therefore done on a mixture of two organisms, one of which is known to be antagonistic to the other. As a control, experiment 4 was carried out with a mixture of two

9 APPLICATION OF STATISTICS IN BACTERIOLOGY 617 organisms which are supposed to be non-antagonistic toward each other. In these experiments determinations were made not only on the mixed cultures but also on the pure cultures of the individual organisms before they were mixed in order to secure accurate information regarding the number of each kind of organism present in the mixture. For experiment 3, twenty-fourhour cultures of E. coli and Pseudomonas pyocyanea in peptone solution were used. For experiment 4, twenty-four-hour cultures TABLE 2 Summary of experiment 1 MOST PROBABLE POPULATION PER METHOD CUB ICCENTMETER IN THE ORIGINAL CULTURE REASONABLY CERTAIN LIMITS OF TRUE VALUE Direct count... 1,705,000,000 1,618,000,000-1,792,000,000 Plate count ,000, ,000, ,000,000 Dilution method ,200, ,000, ,000,000 TABLE 3 Summary of experiment 2 MOST PROBABLE METHE{OD POPULATION PER REASONABLY CERTAIN LIMITS OF CUBIC CENTIMETER IN THE TRUE VALUE ORIGINAL CULTURE Plate count ,000, ,000, ,000,000 Dilution method ,000, ,000, ,000,000 of E. coli and Staphylococcus aureus were used. As in previous experiments, each culture was transferred daily into peptone solution, except that beef extract broth was used for S. aureus. EXPERIMENT 3 Twenty-four-hour cultures of Ps. pyocyanea and E. coli in peptone solution were each shaken with beads for five minutes. Ten cubic centimeters of the E. coli culture were then added to 90 cc. of sterile tap water in a 500-cc. flask containing beads. Additional dilutions were made as indicated by preliminary experiments. The remainder of the 1:10 dilution was saved for the mixed culture. Five cubic centimeters of the culture of Ps.

10 618 N. R. ZIEGLER AND H. 0. HALVORSON pyocyanea were added to 45 cc. of sterile tap water and shaken as usual, after which, further dilutions were made. The mixed culture was prepared by adding 5 cc. of the 1:10 dilution of E. coli, prepared above, and 12 cc. of the original culture of Ps. pyocyanea to 83 cc. of sterile tap water. This mixture was shaken for five minutes. One cubic centimeter was then added to 99 cc. of water, and again shaken for five minutes. The part of this experiment involving the pure culture of E. coli will be referred to as experiment 3a, and that involving Ps. pyocyanea as experiment 3b. The data from these experiments are given in Appendices II and III. The data were analyzed, as for the previous experiment,and the results are summarized in table 4. The values summarized in table 4 under the heading "mixed culture calculated from pure culture data" were obtained by calculating the number of organisms that should have been present in the mixture from data obtained in the pure cultures. For example, in this mixture 5 cc. E. coli and 12 cc. Ps. pyocyanea were added to sterile tap water to make a total volume of 100 cc. From the plate counts, then, the mixture should have contained 0.5 X X X X 109 per cubic centimeter 100 organims This gives 30,990,000 organisms per cubic centimeter in the mixture. For the mixed culture, the dilution data give a value significantly greater than that obtained by the plating method. The same results are obtained in the pure culture of Ps. pyocyanea. With the pure culture of E. coli, however, the results obtained by the two methods are in agreement, as was found in experiment 1. There has been an apparent decrease in viable organisms in the mixed culture as compared with the values obtained for the pure cultures. These changes are sufficiently great to be significant, regardless of the method of counting. This decrease in the number of viable organisms is not explainable on the basis of longer contact of organisms in the mixed cultures because the inoculations were made first from the mixed culture. It is possible that some growth may have taken place in the pure culture during the time required to complete the inoculation of

11 APPLICATION OF STATISTICS IN BACTERIOLOGY the mixed cultures. We believe that this would not account for the entire discrepancy since the pure cultures were kept in the ice box during the three hours required to inoculate the mixed culture. Furthermore, -the cultures were cooled to ice box temperature before the mixture was made. It is not possible, from these data, to determine whether this decrease in viable organisms is due to the toxic effect of Ps. pyocyanea upon E. coli or upon itself. METHOD TABLE 4 Summary of experiments 3, Sa and Sb MOST PROBABLE NUMBER OF ORGAN- ISMS PER CUBIC CENTIMETER Found experi mentally Calculated from pure culture data Mixed culture REASONABLY CERTAIN LIMITS OF THE TRUE VALUE Plate count... 16,730,000 30,990,000 16,140,000-17,320,000 Dilution method... 36,420,000 61,390,000 30,350,000-45,500,000 Pure culture of E. coli Plate count... 1,343,000,000 1,200,000,000-1,390,000,000 Dilution method... 1,118,000, ,000,000-1,803,000,000 Pure culture of Ps. pyocyanea 619 Plate count ,300, ,300, ,300,000 Dilution method ,000, ,100,000-1,453,000,000 A discrepancy is observed between the plate count and the dilution count in both the pure culture of Ps. pyocyanea and in the mixed culture. Since the mixture contains many more Ps. pyocyanea than E. coli, the discrepancy for the mixture may be caused by the same factors which are operating in the pure culture of Ps. pyocyanea. EXPERIMENT 4 This experiment was done as a control for experiment 3. E. coli and S. aureus were used because they are not ordinarily considered to be antagonistic toward each other when grown together

12 620 N. R. ZIEGLER AND H. 0. HALVORSON in a mixed culture. S. aureus was subcultured on beef-extract broth and E. coli on peptone solution. Beef-extract broth was used in this experiment for the dilution method in order to provide a medium in which both organisms would grow well. Standard nutrient agar was used for plating. The proper dilutions for the individual pure cultures and for the mixed cultures were determined by preliminary experiments. The mixed culture was made by adding 5 cc. of the E. coli culture and 7 cc. of the S. aureus culture to 88 cc. of sterile tap water. The parts of this experi- METHOD TABLE 5 Summary of experiments 4, 4a and 4b MOST PROBABLE NUMBER OF ORGAN- ISMS PER CUBIC CENTIMETER mentally Found experi- Calculated culture Mixed culture of E. coli and S. aureus REASONABLY CERTAIN LIMITS OF THE TRUE VALUE Plate count... 54,750,000 61,170,000 53,000,000-56,500,000 Dilution method... 54,880,000 68,368,000 45,700,000-68,600,000 Pure culture of E. coli Plate count ,000, ,000, ,000,000 Dilution method... 1,030,800, ,000,000-1,663,000,000 Pure culture of S. aureus Plate count ,400, ,000, ,000,000 Dilution method ,400, ,000, ,000,000 ment dealing with pure cultures of E. coli and S. aureus will be designated as experiments 4a and 4b respectively. The results are given in Appendices II and III. The data of experiment 4 are summarized in table 5. The data obtained in this experiment are in agreement both on the pure cultures and on the mixed cultures. There is, however, as in experiment 3, some indication of a decrease in the number of viable organisms in the mixed culture. The decrease in this case, however, may not be sufficiently great to be significant.

13 APPLICATION OF STATISTICS IN BACTERIOLOGY 621 EXPERIMENT 5 In experiment 3, with a mixed culture of E. coli and Ps. pyocyanea, we found that the dilution method gave higher values than the plate count. This was also true with the pure culture of Ps. pyocyanea. The mixture contained about five times as many Ps. pyocyanea as E. coli, so the lack of agreement in the case of the mixture might have been due to the excessive numbers of this organism. To verify this point, we repeated experiment 3, but with a mixture containing about equal numbers of the two species. For experiment 5, suspensions of E. coli and of Ps. pyocyanea were prepared as in experiment 3. The mixed culture was prepared by adding 5 cc. of each of the above cultures to 90 cc. of sterile tap water. The mixture was shaken for five minutes. Additional dilutions of 101 for plating and 106, 107, and 108 for the dilution method were made. The part of this experiment involving the pure culture of E. coli will be referred to as experiment 5a, and that involving Ps. pyocyanea as experiment 5b. The data resulting from these experiments are found in Appendices II and III, and are summarized in table 6. The tendencies revealed in experiment 3 are apparent in the above data. With the pure culture of Ps. pyocyanea the dilution method gave counts significantly higher than the plate count. With the pure culture of E. coli, there is again a fair agreement in the results of the two methods. This time, however, the mixture contained a few more E. coli than Ps. pyocyanea, and the difference between the dilution method and the plate method is not sufficiently great to allow us to state that it is significant. It appears from this that the discrepancy between the two methods, as observed in experiment 3, was due to the fact that the mixture contained considerably more Ps. pyocyanea than E. coli. The discrepancy is apparently not due to the toxic effect of Ps. pyocyanea on E. coli but is rather a phenomenon which is characteristic of Ps. pyocyanea itself. We were interested in determining whether the discrepancy between the calculated number of organisms in the mixture and

14 622 N. R. ZIEGLER AND H. 0. HALVORSON the number found in experiment 3 could be due to Ps. pyocyanea alone. In doing experiment 5, therefore, a record was kept of the number of tubes which showed a green pigment indicating growth of Ps. pyocyanea. All other tubes were regarded as showing no growth in respect to this organism. The results are recorded in table 7. In table 8 the population of Ps. pyocyanea in the mixture from experiment 5 was obtained as a direct value by counting the number of tubes which showed a green pigment. This is recorded METHOD TABLE 6 Summary of experiments 5, 5a and 5b MOST PROBABLE NUMBER OF ORGANISMS PER CUBIC CENTIMETER Found ex r- Calculated mental~ frompr cuturte data Mixed culture REASONABLY CERTAIN LIMITS OF THE TRUE VALUE Plate count....21,500,000 28,570,000 20,800,000-22,200,000 Dilution method... 23,410,000 30,900,000 19,500,000-29,500,000 Pure culture of E. coli Plate count ,400, ,000,00-483,000,000 Dilution method ,000, ,000, ,000,000 Pure culture of Ps. pyocyanea Plate count ,000, ,000, ,000,000 Dilution method ,000, ,000, ,000,000 as Ps. pyocyanea experiment 5c. In experiment 5 we obtained the total number of organisms. The difference between the total number of organisms and the number of Ps. pyocyanea we assume to be E. coli, and it is recorded in table 8 as E. coli, experiment 5c. The Ps. pyocyanea population was also calculated from data obtained with the pure culture. The number that should have been present in the mixed culture, as calculated from these data, is recorded in table 8 as Ps. pyocyanea, experiment 5b. Likewise, the population of E. coli which should have been present in the mixed culture is recorded as the coli population in experiment 5a.

15 APPLICATION OF STATISTICS IN BACTERIOLOGY 623 It is apparent that the Ps. pyocyanea populations as calculated and as found experimentally are in agreement, while the corre- TABLE 7 Dilution data showing growth and no growth of Ps. pyocyanea in mixed culture used in experiment a SET pi qi p2 q2 pq Totals Calculated mode = 1.57 Range = TABLE 8 Table showing the relationship between the experimental and calculated values for the bacterial populations studied in experiments 6, 5a and 5b MOST PROBABLE NUMBER OF CUBICCENTIMETER IN MIXTURE RAOAL ETI LIMITS OF TRE TRUE VALUE Experiment 5a: E. coli (calculated value) 18,900,000 12,900,000-30,500,000 Experiment 5c: E. coli (by difference) 7,710,000 6,400,000-9,700,000 Experiment 5b: Ps. pyocyanea (calculated value).11,960,000 8,140,000-19,300,000 Experiment 5c: Ps. pyocyanea (experimental value).5l,700,000 13,100,000-19,800,000 sponding E. coli populations do not agree. The data show that when E. coli and Ps. pyocyanea are mixed, there is an immediate

16 624 N. R. ZIEGLER AND H. 0. HALVORSON destruction of a large number of E. coli, and that this destruction is sufficient to account for the entire discrepancy between the number of organisms found in the mixture and the number which should have been present, as apparent from data calculated from the respective pure cultures. EXPERIMENTS 6 TO 16 In order to obtain additional data on the accuracy of the dilution method as compared with the plate count and the direct count, a series of experiments was carried out on suspensions of E. coli containing different numbers of bacteria per cubic centimeter. Experiments 6 to 9 inclusive were carried out in the following manner. A twenty-four-hour culture in peptone solution was shaken as in previous experiments to secure a uniform suspension. A 1:10 suspension was then made by adding 10 cc. of the culture to 90 cc. of sterile tap water. From this suspension, 1, 2, 3, 4, and 5 cc. were removed and each diluted to 100 cc. in sterile tap water. Each of the five dilutions was then used as a stock suspension for a series of dilutions, of which the suitable ones were used for making plates and for the inoculation of tubes in the dilution method. Four plates and four sets of 10 tubes in 3 dilutions were used in each determination. From the 1:10 dilution of the original culture, one 1-cc. sample was removed, and slides 31, 32, 33 and 34 were made for the direct count, as described previously. On each of these slides, 100 fields were counted. Experiments 10 to 16 were carried out in the same manner, except that another twenty-four-hour culture was used, and amounts of the 1:10 dilution varying from 6 cc. to 11 cc. were diluted to 100 cc. as a starting point for the additional dilutions needed. Determinations of the bacterial population were made on each of these, as in the former experiments. From the original 1:10 dilution of this series, two 1-cc. samples were removed, and two slides made from each for the direct count. These were numbered 35a, 35b, 36a, and 36b. Fifty fields were counted from each slide. The data obtained from these experiments are given in Appendices I, II, and III, and are summarized in table 9.

17 TABLE 9 Summary of experiments 6 to 16 NUMBER OF EX- MOST PROBABLE ORGANISMS PER PERI- NUMBER OF CUBIC CENTIMETER ME.NT ~~~~ORGANISMS PER REASONABLY CERTAIN OF ORIGINAL MERT CUBIC CENTI- LIMITS OF THE TRUE VALUE CULTURE,AS MUTER OF STOCK BER SUSPENSION 6{ 7 ( 8( ( 10 { 11 { ( 13 { 14 { 15 { 16 { Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... Direct count... Plate count... Dilution method... CALCULATED FROM EACH EXPERIMENT I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1,611,000 1,010, ,900 3,222,000 2,307,500 2,528,000 4,833,000 3,925,000 3,991,000 6,444,000 7,700,000 8,833,000 8,055,000 8,375,000 7,850,000 8,826,000 9,150,000 7,810,000 10,297,000 10,925,000 9,490,000 11,768,000 12,125,000 16,740,000 13,239,000 14,675,000 13,880,000 14,710,000 17,475,000 13,850,000 16,181,000 18,925,000 18,610, ,339,000-1,883, ,600-1,104, ,100-1,366,000 2,678,000-3,766,000 2,213,100-2,401,900 1,720,000-4,077,000 4,017,000-5,640,000 2,981,000-4,869,000 2,715,000-6,437,000 5,356,000-7,532,000 6,756,000-8,644,000 6,009,000-14,247,000 6,695,000-9,415,000 7,431,000-9,319,000 5,340,000-12,661,000 6,000,000-11,652,000 8,206,000-10,094,000 5,310,000-12,600,000 7,000,000-13,594,000 9,981,000-11,869,000 6,460,000-15,310,000 8,000,000-15,536,000 11,181,000-13,069,000 11,390,000-27,000,000 9,000,000-17,478,000 13,731,000-15,619,000 9,440,000-22,239,000 10,000,000-19,420,000 16,531,000-18,419,000 9,420,000-22,340,000 11,000,000-21,362,000 17,981,000-19,869,000 12,660,000-30,020,000 1,611,000,000 1,010,000, ,900,000 1,611,000,000 1,153,750,000 1,264,000,000 1,611,000,000 1,308,300,000 1,330,300,000 1,611,000,000 1,925,000,000 2,208,250,000 1,611,000,000 1,675,000,000 1,570,000,000 1,471,000,000 1,525,000,000 1,301,700,000 1,471,000,000 1,560,700,000 1,355,700,000 1,471,000,000 1,515,600,000 2,093,300,000 1,471,000,000 1,630,600,000 1,542,200,000 1,471,000,000 1,747,500,000 1,385,000,000 1,618,100,000 1,865,4C0,00o 1,691,800,000

18 626 N. R. ZIEGLER AND H. 0. HALVORSON In the first two experiments of this series, 6 and 7, the direct count gives a value significantly greater than that obtained by the other two methods. This is in agreement with the results obtained in experiment 1. In experiments 8 to 16, the results of the three methods agree. There is a possibility here that slight growth may have favored the count obtained by the plate and dilution methods. However, we believe that the agreement in these latter experiments is due to a more efficient breaking up of clumps because of the fact that larger amounts of the original stock suspension were used. This appears to be the case because experiments 11 and 12 are comparable to 6 and 7 in that no appreciable time was permitted during which growth could occur. Nevertheless, in experiments 11 and 12, there is an agreement between the direct count and that obtained by the other methods. These data suggest that the most accurate results are to be expected when a comparatively large amount of the original culture is used in making the stock or starting suspension. This dilution should then be shaken with beads before further dilutions are made. When this precaution is taken, we believe that the direct count will give results in agreement with those of the plate count and dilution method, provided the comparisons are made upon cultures before they have entered the death phase. EXPERIMENT 17 As pointed out in the first publication of this series, our interest in this problem arose from a discrepancy observed between the plate count and the direct microscopic count on "curing pickle" used in packing houses. An experiment was therefore planned in which the plating method could be compared accurately with the dilution method to determine whether the latter would give the higher values. The material chosen to be examined was curing pickle which had been in use about 30 days. The high salt content of this material, made it advisable to use a medium of similar composition. Used curing pickle which contained rather large amounts of salt and protein was obtained and sterilized in the autoclave. This precipitated the protein and at the same time clarified the

19 APPLICATION OF STATISTICS IN BACTERIOLOGY medium. The medium was then filtered, and the salt concentration was adjusted to 6 per cent by dilution with tap water. The sugar content was increased by the addition of about 1 gram of glucose per liter. The reaction was then adjusted to neutrality and part of the "salt broth" tubed for use in the dilution method. To another portion, 15 grams of Difco agar per liter were added to make a solid medium. After tubing, both the "salt broth" and "salt agar" were sterilized for twenty minutes at 15 pounds. The material to be studied was diluted for use in the dilution method and for plating as indicated in Appendices II and III. Two series of plates were made, one using nutrient agar with a beef-extract base, and the other the "salt agar" described above. Because of the low temperature at which organisms associated with curing pickle are growing (3.30 to 4.40C.), and their rather TABLE 10 Summary of experiment MOST PROBABLE NUMBER OF REASONABLY CERTAIN METHOD ORGANISMS LIMITS OF THE TRUE PER CUBIC VALUE CENTIMETER Plate count (standard nutrient agar)...350, , ,000 Plate count (salt agar) , , ,000 Dilution method , ,600-1,096,800 slow growth, the plates and tubes in this experiment were incubated at 250C. for four days. The plates could not be left longer than this because of overgrowth of molds. The data obtained in this experiment are given in Appendices II and III, and are summarized in table 10. The data show that salt agar gives a higher count than standard nutrient agar and that the dilution method gives a count which is significantly higher than the plate count on salt agar. CONCLUSIONS The experimental data presented show that the plate count and dilution counts give the same results on the pure culture studied, with the exception of Ps. pyocyanea. In the case of Ps. pyocyanea and of certain mixed cultures of Ps. pyocyanea and

20 628 N. R. ZIEGLER AND H. 0. HALVORSON E. coli, and in the case of orgnism found in curing pickle, the dilution method gives higher values than the plate count. If proper care is taken to break up clumps of bacteria, the direct count gives the same value as the plating and dilution methods when used upon cultures before they have entered the death phase. The dilution method offers a new method of studying the antagonistic effect of one organism upon another. The fact that the dilution method agrees with other methods appears to us to justify the use of Poisson's series for the development of the fundamental equations found in earlier papers of this series. SUMMARY Experimental data are reported which have been obtained by direct microscopic count of bacterial populations, by the plate count, and by means of the dilution method. These determinations have been made on a pure culture of E. coli, B. subtilis, Ps. pyocyanea, and S. aureus, and upon mixed cultures of E. coli and Ps. pyocyanea, E. coli and S. aureus, as well as upon the mixed culture found in packing house curing pickle. REFERENCES BENIANS, T. H. C Brit. Med. Jour., 2: 722. BREED, R. S., AND BREW, J. D Circular of the New York State Agr. Exp. Station, Geneva, second reprint, 58: HALVORSON, H. O., AND ZIEGLER, N. R. 1933a Jour. Bacteriol., 25: HALVORSON, H. O., AND ZIEGLER, N. R. 1933b Jour. Bacteriol., 26: HALVORSON, H. O., AND ZIEGLER, N. R. 1933c Jour. Bacteriol., 26: HENRICI, A. T Proc. Soc. Exper. Biol. Med., 20: MCCRADY, M. H Jour. Infect. Dis., 17: STEIN, M. F Amer. Jour. Pub. Health, 8: WELLS, W. F Amer. Jour. Pub. Health, 8: WILSON, G. S Jour. Bacteriol., 7:

21 APPENDIX I Table of data obtained by direct count SLIDE 1 SLIDE 2 SLIDE 3 SLIDE 4 SLIDE 5 SLIDE 6 11i N 100 A B h C 78.35% SLIDE N 100 A B C 78.31% SLIDE % SLIDE : % SLIDE *I % SLIDE :1: % % SLIDE : % h % SLIDE :1: % 1- -I SLIDE 15 SLIDE 16 SLIDE h % SLIDE t % SLIDE N A B h L5.944 : C % 53.61% % 99.31% % 79.30% N = number of microscopic fields counted. A = mean number of bacteria per microscopic field. B = standard deviation of the counts of individual fields. C = coefficient of variation of the counts of individual fields. * = number of organisms per field. 629 JOURNAL OF BACTERIOLOGY, VOL. 29, NO. 6

22 APPENDEX I-Concluded Table of data obtained by direct count-concluded SLIDE 19 SLIDE 20 SLIDE 21 SLIDE 22 SLIDE 23 SLIDE 24 8* N 100 A B ±6.166 C 75.33% SLIDE N 100 A B C % SLIDE N 100 A B ±9.666 C % ± % SLIDE ± % SLIDE ± % ±t %~o SLIDE ± % SLIDE ± % ± % SLIDE ± % SLIDE ± % % SLIDE ± % SLIDE 35a SLIDE 35b % ± %,O SLIDE ± % SLIDE 36a SLIDE 36b ± % N = number of microscopic fields counted. A = mean number of bacteria per microscopic field. B = standard deviation of the counts of individual fields. C = coefficient of variation of the counts of individual fields. 630

23 EXPERIMENT 1 Dilution 10l 60* N 92 A B ±8.178 C 33.58% D ±0.857 E 3.52% F APPLICATION OF STATISTICS IN BACTERIOLOGY APPENDIX II Table of data obtained by plating EXPERIMENT 2 EXPERIMENT 3 Dilution ± % ± % Dilution ± % ± % EXPERIMENT 4 Dilution % ± % EXPERIMENT 5 Dilution 10' ± % % EXPERIMENT 3a EXPERIMENT 3b EXPERIMENT 4a EXPERIMENT 4b EXPERIMENT Sn EXPERIMENT 5b Dilution 107 Dilution 106 Dilution 107 Dilution 106 Dilution 107 Dilution * N A D : : :4:2.361 :1:5.129 E 4. 06% 13.36% 7.11% 6.27% 10.84% 7.54% F EXCPERIMENT 6 EXPERIMENT 7 8 EXT EIEN XPERIMEN EXPERIMENT EXPERIMENT Dilution 104 Dilution 104 Dilution 106 Dilution 105 Dilution 105 Dilution 10' Dilution * A D :14.72 ±44.72 : ±44.72 E 9.35% 4.09% 24.05% 12.26% 11.27% 10.32% 8.64% F

24 632 N. R. ZIEGLER AND H. 0. HALVORSON APPENDIX II-Concluded Table of data obtained by plating-concluded EXPERIMENT 13 EXPERIMENT 14 EXPERIMENT 15 EXPERIMENT 16 EXPERIMENT Dilution 105 Dilution 105 Dilution 105 Dilution 105 Dilution 103 Dilution * N A D : ± ±4.72 ±14.60 ±10.47 E 7.78% 6.43% 5.40% 4.99% 7.31% 5.97% F N = number of plates. A mean number of colonies per plate. B standard deviation of individual plate counts. C coefficient of variation of individual plate counts. D = standard deviation of the means. E coefficient of variation of the means. F = the range which will include 97 per cent of the means. * Number of colonies per plate. Downloaded from on June 20, 2017 by guest