APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Mar. 1977, p. 675-680Copyright © 1977 American Society for Microbiology

Vol. 33, No. 3Printed in U.S.A.

Microtechnique for Most-Probable-Number AnalysisR. ROWE, R. TODD,* AND J. WAIDE

Institute of Ecology and Department of Agronomy, University of Georgia, Athens, Georgia 30601,* andDepartment of Zoology, Clemson University, Clemson, South Carolina 29631

Received for publication 20 September 1976

A microtechnique based on the most-probable-number (MPN) method hasbeen developed for the enumeration of the ammonium-oxidizing population insoil samples. An MPN table for a research design ([8 by 12] i.e., 12 dilutions, 8replicates per dilution) is presented. A correlation of 0.68 was found betweenMPNs determined by the microtechnique and the standard tube technique.Higher MPNs were obtained with the microtechnique with increased accuracy

in endpoint determinations being a possible cause. Considerable savings oftime,space, equipment, and reagents are observed using this method. The microtech-nique described may be adapted to other microbial populations using varioustypes of media and endpoint determinations.

Interest is increasing in the quantification ofmicrobial processes, such as nitrification anddenitrification, in natural and manipulatedecosystems. In such studies, direct determina-tions of microbial activity may be extremelydifficult, and indirect measurements must berelied upon. Such determinations usually in-volve the enumeration of microorganisms hav-ing the potential to carry out a certain biochem-ical reaction.The most-probable-number (MPN) technique

is one means of determining the potential activ-ity of a microbial population and has been usedby Alexander (1-3), Focht and Joseph (10),Smith et al. (21), and Todd et al. (22). Standardmethods of MPN analysis as used by these in-vestigators have proved time consuming andtedious.

Various microsystems have been developedto alleviate these problems. These microsys-tems originated for such uses as enumeration ofviable cells in bacterial cultures (6, 9), as aquick means of determining acid and gas pro-duction (12), for the study of heat destructionand bacterial spores (4), and for IMViC tests(12). Microsystem techniques have also beendeveloped for microbial analysis of food (11).Curtis et al. (7) describe an MPN microsystemfor assaying nitrifiers in water and sedimentsamples. Serial dilutions were made in testtubes, and aliquots were transferred to the mi-crowells of a 25-compartment "repli-plate" forincubation and assay using the MPN tablesdescribed by Alexander (2). Darbyshire et al.(8) developed a micromethod for estimating theMPN of total bacterial and protozoan popula-tions in soil using an 8 by 12 plate (12 dilutions,

8 replicates per dilution). In lieu of an MPNtable, a description of the statistical method,based on the Poisson distribution, used to com-pute the MPNs was provided.

In this communication we describe a microa-nalysis system designed for both serial dilutionand incubation. An MPN table designed for usewith this system in enumerating microbial pop-ulations is provided. Results of a direct compar-ison between the microsystem and the standardtube method for estimating the ammonium-oxidizing microbial population are also pre-sented.

MATERIALS AND METHODSMicrotiter system. A 0.05-ml aliquot of media is

placed into each of the 8 by 12 wells of a sterilemicroplate. Aliquots of the soil suspension (0.05 ml)to be tested are pipetted into each of the first eightwells. Serial dilutions are then performed by usingflame-sterilized loops calibrated to deliver 0.05 ml(Fig. 1). The loops are placed into the eight previ-ously inoculated wells, rotated rapidly, and thenmoved to the next eight wells where they are againrapidly rotated. This process is continued until se-rial dilutions have been carried out across the plate.The result is 12 twofold serial dilutions with eightreplicates at each dilution.

Nitrification method. Ammonium-calcium car-bonate medium as described by Alexander andClark (3) is placed in the wells. After inoculationand the performance of serial dilutions, the platesare covered with polypropylene tape and incubatedfor 3 weeks, as recommended by Alexander andClark M3). However, conflicting reports exist con-cerning the optimum incubation time for ammonia-and nitrite-oxidizing microorganisms (7, 18). At theend of the incubation period carried out at roomtemperature each plate is scored by adding an indi-

675

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from

676 ROWE, TODD, AND WAIDE

cator (0.2 g of diphenylamine in 100 ml of concen-trated H2SO4) to test for the presence of nitrate and/or nitrite (19). A blue color reaction indicates that

@" 0@.1 :| 1I

FIG. 1. A microplate with dilution loops.

these end products have formed, and the well isscored positive. The absence of a blue color is scorednegative (Fig. 2).MPN table. The statistical basis for the MPN

technique is well established (5, 14, 15). For anycombination of positive readings in a set of serialdilutions, it is possible to calculate the MPN esti-mate of population size, the standard error of theMPN, and its probability of occurrence. Table 1presents MPN values and standard errors for a two-fold dilution series with eight tubes per dilution.The codes (PI, P2, p3) represent the number of posi-tive tubes in three successive dilutions, where Picorresponds either to the highest dilution at whichall tubes gave positive readings, or to the dilutionshowing the highest number of positive tubes.

Table 1 was prepared following de Man (17) andParnow (20). For each possible code, from (0 0 1) to(n, n2 n3 -1), where nj is the number of tubes in thejth dilution, the MPN value was calculated. Thestandard error and the probability of occurrence ofthe MPN were also calculated. Then, for that MPNvalue, the probability of obtaining all codes from (0 00) to (n, n2 n3) were successively calculated andordered from largest to smallest. These probabilitiesdo not represent the probabilities of obtaining thegiven MPN, but rather the probability of obtainingthe various codes, assuming that the MPN is thetrue population size. If the code in question had thelargest probability of all codes of the MPN, then theMPN result was accepted. If not, then the code inquestion was consecutively compared with all codesin order of decreasing probabilities. If the code wasencountered before the sum of the probabilities wasgreater than or equal to 0.95, it was accepted; other-wise, it was rejected. This prevents the investigator

FIG. 2. The result of a nitrification test. Wells 1-12 represent twofold serial dilutions, and rows A-Hrepresent replicates.

APPL. ENVIRON. MICROBIOL.

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from

TABLE 1. Most probable numbersa

Pi P2 P3 MPN Standard error|p P2 P3 MPN Standard error

1 0 02 0 0.2 0 12 1 02 1 13 0 03 0 13 0 23 1 03 1 13 1 23 2 03 2 13 2 24 0 04 0 14 0 24 0 34 1 04 1 14 1 24 1 34 2 04 2 14 2 24 2 34 3 04 3 14 3 24 3 35 0 05 0 15 0 25 0 35 0 45 1 05 1 15 1 25 1 35 1 45 2 05 2 15 2 25 2 35 2 45 3 05 3 15 3 25 3 35 3 45 4 05 4 15 4 25 4 35 4 46 0 06 0 16 0 26 0 36 0 46 1 06 1 16 1 26 1 3

0.0370.0770.1170.1180.1600.1210.1630.2060.1650.2080.2530.2100.2560.3020.1680.2130.2590.3060.2160.2620.3100.3600.2650.3140.3650.4160.3180.3690.4220.4770.2210.2690.3190.3700.4230.2720.3230.3750.4290.4840.3270.3800.4350.4920.5500.3850.4410.4990.5590.6220.4470.5070.5680.6320.6990.2800.3320.3860.4420.5000.3360.3910.4490.508

1.0000.7080.5780.5780.5010.5790.5020.4490.5020.4990.4110.4500.4110.3810.5020.4500.4110.3820.4500.4120.3820.3580.4120.3820.3580.3380.3820.3580.3390.3220.4510.4120.3830.3590.3390.4130.3830.3590.3400.3230.3830.3600.3400.3230.3090.3600.3400.3240.3100.2980.3410.3240.3100.2980.2880.4140.3840.3600.3410.3240.3840.3610.3410.325

6666666666666666666666666677777777777777777777777777777777777777

1 4 0.5701 5 0.6352 0 0.3972 1 0.4552 2 0.5152 3 0.5792 4 0.6452 5 0.7153 0 0.4623 1 0.5243 2 0.5893 3 0.6573 4 0.7283 5 0.8034 0 0.5334 1 0.5994 2 0.6684 3 0.7424 4 0.8184 5 0.9015 0 0.6085 1 0.6805 2 0.7555 3 0.8355 4 0.9195 5 0.1010 0 0.3470 1 0.4040 2 0.4630 3 0.5251 0 0.4101 1 0.4701 2 0.5341 3 0.6011 4 0.6711 5 0.7462 0 0.4782 1 0.5432 2 0.6122 3 0.6842 4 0.7602 5 0.8412 6 0.9263 0 0.5523 1 0.6233 2 0.6963 3 0.7753 4 0.8583 5 0.9473 6 1.0424 0 0.6344 1 0.7104 2 0.7904 3 0.8774 4 0.9694 5 1.0684 6 1.1765 0 0.7245 1 0.8085 2 0.8965 3 0.9925 4 1.0965 5 1.2095 6 1.332

677

0.3110.2990.3610.3420.3260.3120.3000.2890.3420.3260.3120.3010.2900.2810.3270.3130.3010.2910.2820.2750.3140.3020.2920.2830.2760.2690.3860.3620.3430.3270.3630.3430.3270.3140.3020.2920.3430.3280.3150.3030.2930.2840.2770.3290.3150.3040.2940.2860.2780.2720.3160.3050.2950.2870.2800.2730.2680.3060.2960.2880.2810.2750.2700.266i

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from

TABLE 1- Continued

Pi P2 P3 MPN Standard error PI P2 P3 MPN Standard error

7 6 0 0.825 0.298 8 4 3 1.054 0.2877 6 1 0.917 0.290 8 4 4 1.171 0.2827 6 2 1.018 0.283 8 4 5 1.301 0.2787 6 3 1.126 0.278 8 4 6 1.444 0.2747 6 4 1.244 0.273 8 4 7 1.607 0.2727 6 5 1.376 0.269 8 5 0 0.870 0.3027 6 6 1.523 0.266 8 5 1 0.972 0.2958 1 0 0.495 0.346 8 5 2 1.085 0.2898 1 1 0.564 0.330 8 5 3 1.208 0.2848 1 2 0.637 0.317 8 5 4 1.346 0.2818 1 3 0.714 0.306 8 5 5 1.500 0.2788 1 4 0.796 0.296 8 5 6 1.679 0.2778 2 0 0.574 0.331 8 5 7 1.886 0.2778 2 1 0.648 0.318 8 6 0 0.999 0.2978 2 2 0.728 0.307 8 6 1 1.117 0.2928 2 3 0.812 0.297 8 6 2 1.248 0.2888 2 4 0.903 0.289 8 6 3 1.396 0.2858 2 5 1.001 0.283 8 6 4 1.565 0.2838 2 6 1.106 0.277 8 6 5 1.760 0.2838 3 0 0.662 0.319 8 6 6 1.993 0.2858 3 1 0.744 0.308 8 6 7 2.279 0.2888 3 2 0.831 0.299 8 7 0 1.153 0.2958 3 3 0.925 0.291 8 7 1 1.293 0.2918 3 4 1.027 0.285 8 7 2 1.452 0.2898 3 5 1.138 0.279 8 7 3 1.636 0.2898 3 6 1.259 0.275 8 7 4 1.855 0.2918 3 7 1.395 0.271 8 7 5 2.124 0.2948 4 0 0.759 0.310 8 7 6 2.465 0.3018 4 1 0.850 0.301 8 7 7 2.921 0.3128 4 2 0.947 0.293a pi, Number of positive wells in the least concentrated dilution in which either all of the wells are posi-

tive or the greatest number are positive; P2 andp3, number of positive wells in the next two higher dilutions,respectively.

from accepting statistically improbable results.Table 1 presents only those codes found to be

statistically acceptable, as described above. Also,those codes not operationally feasible are excludedfrom Table 1. For example, if 8, 8, 8, 7, and 4positive tubes were found in a twofold dilution se-

ries, then the sample would be scored as 8, 7, 4rather than 8, 8, 7. Also, if the number of positivetubes in the three highest dilutions of a series were

8, 8, and 7, it would indicate that the dilution seriesused was not adequate for estimating the populationsize.A program written for a Control Data Corpora-

tion Cyber 70/74 computer system was used to con-

struct Table 1. It will calculate MPN values for anyserial dilution series with any number of tubes per

dilution, not necessarily all equal. The table pre-

sented lists three codes (Pl, P2, p3). However, theprogram has the capacity to determine any num-

ber of codes from P, to P12- Copies of the program

may be obtained from the authors.MPN determination. A typical test result of enu-

merating ammonium-oxidizing bacteria in a sampleis depicted in Fig. 2. Microwells containing dark-colored solutions are positive tests for nitrate-ni-trite. Values for Pl, P2, and p3 are determined as

follows: Pi is the number of positive wells in theleast-concentrated dilution in which either all thewells are positive or the greatest number are posi-tive, and P2 and p3 are the number of positive wellsin the next two higher dilutions, respectively. InFig. 2, Pi 5 8, P2 = 6, and p3 = 4. These values givean MPN of 1.565 (Table 1). The MPN value is thenmultiplied by the dilution factor for P2, in this case64, to obtain a value of 100.16. To obtain the MPN in1 ml of the original inoculum, this number is multi-plied by 20 (20 x 100.16 = 2,003.2). Corrections mustalso be made for initial dilution factors and moisturecontent of samples.

RESULTS

The microplate technique was tested in acomparison with the standard tube techniqueas used by Alexander and Clark (3). Soil sam-ples were collected from three experimental wa-tersheds at the Coweeta Hydrologic Laboratoryin southwestern North Carolina. Samples weretaken from a watershed vegetated by an oak-hickory forest (watershed 18), a watershedwhich was planted in Eastern white pine in

APPL. ENVIRON. MICROBIOL.678 ROWE, TODD, AND WAIDE

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from

MICROTECHNIQUE FOR MPN ANALYSIS 679

DILUTION FACTOR

0 1o l 1 0

I 00af 2 A a* Ifr 4* '2 R*A i

A

I 0 la = 04

FIG. 3. Theoretical considerations in comparing endpoint determinations for the tube (10-fold dilutions)and microplate (2-fold dilutions) techniques. The dashed lines represent two population sizes (A and B).

1956 (watershed 17), and a watershed in the10th year of successional regrowth after theherbiciding of all vegetation in 1966 (watershed6). More complete watershed descriptions are

provided elsewhere (16).Three soil suspensions were prepared from

each sample, and the MPN of nitrifying orga-

nisms in each suspension was determined byboth the microplate and by the tube method.Results are given in Table 2. In both methodsthe highest number of nitrifiers was found on

the successional, grass-covered watershed.Numbers of nitrifiers on the hardwood wa-

tershed were higher than those on the pinewatershed in the suspensions analyzed by themicroplate technique, but lower in the standardtube analysis. A correlation of 0.68 was ob-tained between the two methods of analysis,which is statistically significant at the 90%level.

DISCUSSIONThe microplate technique gave consistently

higher MPNs than did the tube technique (Ta-ble 2). Increased accuracy in endpoint determi-nation in the twofold serial dilution of the mi-croplate technique as opposed to determinationin the 10-fold dilutions of the tube techniquemay account for this discrepancy. Consider thehypothetical situation depicted in Fig. 3. Thetube technique would give an MPN of 10 forboth A and B, since by the next serial dilutionof 100-fold both populations would have beendiluted to extinction. However, the microplatetechnique would give an MPN of 8 for popula-tion A and 64 for B. Cochran (5) discussed simi-lar aspects of the comparison of 2-fold and 10-fold dilution series.Reasons for the reversed order of the MPNs

on the pine and hardwood watersheds by thetwo different techniques remain obscure. Theextremely large standard error for the MPNestimate on the hardwood watershed using themicroplate technique may suggest that one ofthe suspensions for this sample gave anoma-

lous results. An increased sample size may re-

TABLE 2. Mean nitrifiers per gram of dry soil ±standard error in soil from three watershedsa

Mean nitrifiers/g of dry soil ± standard

Watershed error

Microplate Tube

Hardwood 2,009 ± 705 32± 4Pine 1,178 ± 82 269± 47Grass 3,261 ± 48 2,737± 0

a The mean represents three determinations ofeach sample.

sult in qualitatively similar results by the twotechniques. In any case, Table 2 reveals a fairlygood agreement between the two procedures,granting the potentially more accurate end-point determinations in the 1:2 dilutions of themicroplate method as discussed above.Advantages of the described MPN technique

are the ease with which large numbers of sam-ples may be processed, increased precision, im-proved sample replication (the microplate tech-nique gives eight replicates per sample as com-pared with five for the tube technique), andsavings in equipment, reagents, and incubationspace. For the past year, this technique hasbeen used in our laboratory for assessing theammonia-oxidizing bacterial populations in soilsamples from a variety of systems. The tech-nique has also been used for denitrifiers and forenumerating separate populations of ammoniaand nitrite oxidizers. Adaptations to other mi-crobial populations are possible using varioustypes of media and endpoint determinations.

LITERATURE CITED1. Alexander, M. 1965. Denitrifying bacteria, p. 1484-

1486. In C. A. Black et al. (ed.), Methods of soilanalysis, part 2. American Society Agronomy, Madi-son, Wis.

2. Alexander, M. 1965. Most probable number method formicrobial populations, p. 1467-1472. In C. A. Black etal. (ed.), Methods of soil analysis, part 2. AmericanSociety Agronomy, Madison, Wis.

3. Alexander, M., and F. E. Clark. 1965. Nitrifying bacte-ria, p. 1477-1483. In C. A. Black et al. (ed.), Methodsof soil analysis, part 2. American Society Agronomy,Madison, Wis.

VOL. 33, 1977

T U B E

PL ATEv o0 I z ts

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from

680 ROWE, TODD, AND WAIDE

4. Baldock, J. D., D. Y. C. Fung, and H. W. Walker. 1968.Rapid microtiter technique for study of heat destruc-tion of bacterial spores. Appl. Microbiol. 16:1627-1628.

5. Cochran, W. G. 1950. Estimation of bacterial densitiesby means of the "most probable number." Biometrics6:105-116.

6. Coneath, T. B. (ed.). 1972. Handbook of microtiter®9procedures. Dynatech Corp., Cambridge, Mass.

7. Curtis, E. J. C., K. Durrant, and M. M. J. Harman.1975. Nitrification in the Trent River Basin. WaterRes. 9:255-268.

8. Darbyshire, J. F., R. E. Wheatley, M. P. Graves, andR. H. E. Inkson. 1974. A rapid micromethod for esti-mating bacterial and protozoan populations in soil.Rev. Ecol. Biol. Sol 11:465-475.

9. Fung, D. Y. C., and A. A. Deaft. 1968. Microtitermethod for the evaluation of viable cells in bacterialcultures. Appl. Microbiol. 16:1036-1039.

10. Focht, D. D., and H. Joseph. 1973. An improved methodfor the enumeration of denitrifying bacteria. Soil Sci.Soc. Am. Proc. 37:698-699.

11. Fung, D. Y. C., and W. S. Lagrange. 1969. Microtitermethod for enumerating viable bacteria in milk. J.Milk Food Technol. 32:144-146.

12. Fung, D. Y. C., and R. D. Miller. 1970. Rapid procedurefor the detection of acid and gas production by bacte-rial cultures. Appl. Microbiol. 20:527-528.

13. Fung, D. Y. C., and R. D. Miller. 1972. Miniaturizedtechniques for IMVIC tests. J. Milk Food Technol.35:320-329.

14. Halvorson, H. O., and A. Moeglein. 1940. Application of

statistics to problems in bacteriology. V. The proba-bility of occurrence of various experimental results.Growth 4:157-168.

15. Halvorson, H. O., and N. R. Ziegler. 1933. Applicationof statistics to problems in bacteriology. I. A meansof determining bacterial populations by the dilutionmethod. J. Bacteriol. 25:101-121.

16. Johnson, P. L., and W. T. Swank. 1973. Studies oncation budgets in the southern Appalachians on fourexperimental watersheds with contrasting vegeta-tion. Ecology 54:70-80.

17. de Man, J. C. 1975. The probability of most probablenumbers. Euro. J. Appl. Microbiol. 1:67-78.

18. Matulewich, V. A., P. F. Strom, and M. S. Finstein.1975. Length of incubation of enumerating nitrifyingbacteria present in various environments. Appl. Mi-crobiol. 29:265-268.

19. Morgan, M. F. 1930. A simple spot-plate test for nitratenitrogen in soil and other extracts. Science 71:343-344.

20. Parnow, R. J. 1972. Computer program estimates bac-terial densities by means of the most probable num-bers. Food Technol. 26:56-62.

21. Smith, W. H., F. H. Bormann, and G. E. Likens. 1968.Response of chemoautotrophic nitrifiers to forest cut-ting. Soil Sc. 106:471-473.

22. Todd, R. L., W. T. Swank, J. E. Douglass, P. C. Kerr,D. L. Brockway, and C. D. Monk. 1975. The relation-ship between nitrate concentration in mountainstreams and terrestrial nitrifiers. Agro-ecosystems2:127-132.

APPL. ENVIRON. MICRODBIOL.

on March 8, 2020 by guest

http://aem.asm

.org/D

ownloaded from