MOST PROBABLE NUMBER

Soil Microbiology

BIOL/CSES 4684




This webpage was created by Laura Kirk


I.  OVERVIEW OF MOST PROBABLE NUMBER COUNT METHODOLOGY

The most probable number (MPN) technique is an important technique in estimating microbial populations in soils, waters, and agricultural products.  Many  soils are heterogeneous, therefore exact cell numbers of an individual organism can be impossible to determine.  The MPN technique is used to estimate microbial population sizes in situations like this.  The technique does not rely on quantitative assessment of individual cells, instead it relies on specific qualitative attributes of the microorganism being counted.  The important aspect of MPN methodology is the ability to estimate a microbial population size based on a process-related attribute.

The MPN technique estimates microbial population sizes in a liquid substrate.  The methodology for the MPN technique is dilution and incubation of replicated cultures across several serial dilution steps.  This technique relies on the pattern of positive and negative test results following inoculation of a suitable test medium (usually with a pH sensitive indicator dye) such as tubes (upper left photo) and microwell plates (upper right photo).  The results are used to derive a population estimate based on the mathematics of Halvorson and Ziegler.  Here is the general equation for determining the MPN of organisms in a substrate after it is serially diluted and several units are inoculated of each dilution (Halvorson & Ziegler, 1933).

 [a1p1/(1-e^(-a) 1^x)] + ... + [akpk/(1-e^(-a) k^x)] = a1n1 + ... + aknk

     where
          a = the dilution level of each dilution,
          n = the number of inoculated units at each dilutions level,
          p = the number of positive units within each dilution level,
          k = the highest dilution level of the series,
          e = the base of the natural logarithm.

There are two assumptions underlying the mathematical solution.  First, it is assumed that organisms in the initial and all subsequent dilutions are randomly distributed.  Secondly, it is assumed that one or more organisms contained within an inoculant volume are capable of producing  a positive result.  If the second assumption is not satisfied, unusual patterns of positive and negative occurs.  The MPN techniques also assume that all test organisms occupy a similar volume.


II.  OVERVIEW OF MPN PROCEDURES

The are four main design features of a MPN determination that must be chosen before using the MPN procedure.  The first one is to select a base dilution ratio, and then to select the number of units at each dilution level.  The other two design features are to determine an initial dilution volume and its value and to select the inoculation volume.

Next the required materials must be gathered.  If you choose to use a procedure with six fivefold dilution steps and four units per dilution level, as the experiment in Paul L. Woomer?s "Most Probable Number Counts" article, you will need the following materials:  100 grams of soil, one sterile 1 L wide-neck Erlenmeyer flask and stopper containing 400 mL of sterile-N mineral nutrient diluent, one sterile 5 mL wide-mouth pipette, five sterile 5 mL pipettes, one sterile 1 mL pipette, one growth pouch rack, and twenty-four growth pouches containing nodulation legume seedlings previously selected for uniformity of root and shoot development.

Below is a dilution scheme for a most probable number count experiment.



To record your data, prepare a data sheet that assigns either a positive or a negative value for each experimental unit.  Figure 2 is an example of a data sheet where a (+) represents root nodulation.  After the data is recorded go the appropriate MPN table to assign a population estimate. Tables can be generated using MPNES software (Woomer et al., 1990).

Figure 2.  An example data sheet for recording the results of an MPN experimentation. This is taken from Paul L. Woomer?s "Most Probable Number Counts.

                                                       Replicate                                                  Total
-----------------------------------------------------------------------------------------------------
Dilution Level                       1          2          3          4
-----------------------------------------------------------------------------------------------------
5^-1                                          +         +          +          +                                         4
5^-2                                          +         +          +          +                                         4
5^-3                                          +         +          -           +                                         3
5^-4                                           -          -           +          -                                          1
5^-5                                           -          -           -           -                                          0
5^-6                                           -          -           -           -                                          0
------------------------------------------------------------------------------------------------------
Base dilution level (A)     5
Number of units per dilution level (N)   4
Experimental Results      4-4-3-1-0-0
Tabular MPN (TMPN)     165
Initial dilution (I)      NA
Inoculation volume (V)     1.0 mL
Probability of experimental outcome    0.106
Population estimate      165 cells per gram



III.  PROS AND CONS

There are many clear advantages of using the MPN technique.  MPN methodology results in more uniform recovery of a microbial population across different soil types than filter counts.  Furthermore, the detection of organisms through process-related attributes often results in the recovery of mixed populations with similar functional roles in soils.  For a more detailed study, the mixed populations can be separated into individual colonies.

Another advantage of MPN techniques is that, unlike direct quantitative procedures, it measures only live and active organisms.  Microscopic techniques sometimes confuse live and dead cells.  Also, MPN methodologies provide more realistic estimates of infective propagules of VA mycorrhizae in field soils than does the more conventional method of spore counts (Porter, 1979).

Despite the numerous advantages of using MPN methodology there are a few disadvantages to the method.  MPN procedures tend to require more labor and materials than microscopic procedures.  Also, MPN estimates often have a lower order of precision than do well-replicated direct counts.


IV.  ADDITIONAL SOURCES OF INFORMATION

Halvorson, H.O., and N.R. Ziegler.  1933. Applications of statistics to problems in bacteriology. I. A means of determining bacterial populations by the dilution method.  J. Bacteriol. 25:101-121.

Porter, W.M.  1979.  The "most probable number" method for enumerating infective propagules of vesicular arbuscular mycorrhizal fungi in soils.  Aust. J. Soil Res. 17:515-519.

Woomer, P., J. Bennet, and R. Yost. 1990. Overcoming the inflexibility of most-probable-number procedures Agron. J. 82:349-353.

Woomer, Paul L.  1994.  Most Probable Number Counts.  SSSA Book Series:  5:59-79.


V.  LINKS TO OTHER SITES ON MPN

MPN Calculator  MPN Calculator is designed as a reference to the MPN for coliform testing based on standard methods for the examination of water and wastewater.

MPN Groups  This site is a slide presentation by a student on the MPN technique.
 


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