Dilution Theory – Page 3:

The Most Probable Number Method

• This page and the associated pages on microbial enumeration are intended to address the use and interpretation of dilution theory techniques (plating and MPN) for educational purposes and may not be authoritative in applied or research situations. Familiarity of the author with any applied or research aspect is not to be implied. I can only address the method described herein and cannot advise on variations or similar dilution and inoculation methods.
  
  
• An essential reference which traces the development of the most-probable number technique and cites numerous important but hard-to-find literature on the subject is:  J. L. Oblinger and J. A. Koburger. 1975. "Understanding and Teaching the Most Probable Number Technique." J. Milk Food Technol. 38(9): 540-545.
   A downloadable copy of this hard-to-find paper is here.
  
  
• A related method which utilizes spot-inoculated plates – the Harris & Sommers Plate-Dilution Frequency Technique – is illustrated and referenced here.

To envision the theoretical basis for the Most Probable Number (MPN) Method, think of a ten-fold dilution series being made of a water sample with one ml of each dilution being inoculated into a separate tube of an all-purpose broth medium.

After incubation, the broth tubes are observed for the presence or absence of growth. Theoretically, if at least one organism had been present in any of the inocula, visible growth should be seen for that particular tube. If the broth inoculated from the 10^–3 dilution shows growth, but the broth from the 10^–4 does not, it is then possible to say that there were greater than 1X10³ organisms per ml of the original sample but less than 1X10⁴ per ml.

Bacteria are rarely, if ever, distributed evenly in a sample. For example, if a 10 ml sample contains a total of 300 organisms, not every one ml aliquot (a good term to know the correct definition of; look it up!) will contain 30 organisms; some will contain more or fewer, but the average of all ten aliquots in the entire 10 ml sample will be 30. This also applies to any of the dilution tubes from which inocula are taken.

To increase the statistical accuracy of this type of test, more than one broth tube can be inoculated from each dilution. Standard MPN procedures use a minimum of 3 dilutions and 3, 5 or 10 tubes per dilution. The statistical variability of bacterial distribution is better estimated by using as many tubes as possible or practical. After incubation, the pattern of positive and negative tubes is noted, and a standardized MPN Table is consulted to determine the most probable number of organisms (causing the positive results) per unit volume of the original sample.

In the following example, a set of 3 tubes of an all purpose broth medium is inoculated from each of the ten-fold dilutions, with each tube being inoculated with one ml.

After incubation, the number of tubes showing growth is recorded. As the succeeding dilutions were made, the organisms were diluted to such an extent that none were in the inocula of seven of the tubes (marked negative). In order to estimate the number of organisms per ml of the sample which would cause this kind of growth response, we locate the three sets of tubes which show dilution of the organisms "to extinction" – i.e., those tubes which were inoculated from the 10^–2, 10^–3 and 10^–4 dilutions.

The Neapolitan ice cream-colored table running along the right-hand side of the screen is the 3-tube MPN Table we have been using in our courses for decades (original source unknown). The heading of the last column tells us that this combination of results (in order: 3-2-0) suggests an average of 0.93 organisms being inoculated into each of the tubes of the middle set (of the three sets of tubes chosen) – i.e., those inoculated with one ml of a 10^–3 dilution. Therefore, the most-probable number of organisms per one ml of the original, undiluted sample would be 0.93 X 10³ or 9.3 X 10².

A 5-tube MPN table can be found by clicking here.

This method, with the associated table, only works if there is a succession of 1/10 dilutions being tested (in an appropriate medium) for growth, and the tubes chosen to compare with the table are in consecutive order of increasing dilution.

Some things to keep in mind:

• Other amounts than one ml can be inoculated into the broth tubes. For example, inoculating 0.1 ml of a 10^–3 dilution is equivalent to inoculating 1 ml of a 10^–4 dilution; the "plated dilution" (10^–4) is the same in each case.
  
• It doesn't matter what amount of medium there is in the tubes being inoculated. For example, the same growth response should be evident if we doubled the amount of broth in each tube.
  
• Also, we don't have to inoculate our tubes from dilutions. For example, one can set up a series of tubes where 10 grams are inoculated into each tube in the first set, 1 gram is inoculated into each tube in the second set, and 0.1 gram is inoculated into each tube in the third set. The sequence of decimally-decreasing amounts is maintained. (Recall how the so-called "plated dilution" represents the actual amount of sample being inoculated.) See the second sample problem below.
  

Here are a couple examples of MPN problems.

I.  (This is based on a problem from Bacteriology 102.)  From a water sample obtained from beautiful Lake Splammo, you inoculated 10 ml into 90 ml of sterile diluent; this is the "first dilution" indicated in the table below. After thorough mixing, 1 ml of this dilution was added to 99 ml of sterile diluent, and a third dilution was made the same way. From each of these dilutions, tubes of Glucose Fermentation Broth were inoculated with amounts as shown in the table below. After appropriate incubation, the tubes were checked for growth and acid production, and the data are summarized below.

What was the most probable number of glucose-fermenters per ml of the original sample of water? Here is one way of finding the solution:

• Choose the three consecutive sets of tubes that show "dilution to extinction" of glucose-fermenting organisms – i.e., sets C, D and E. We can indicate "3-1-0" to represent the number of positive tubes.
  
• Checking the MPN table, 3-1-0 indicates that an average of 0.43 organism (causing the determining reaction) was inoculated into each of the tubes in the middle set (D) – i.e., the tubes inoculated with 0.1 ml of the 10^–3 dilution. (As a side note, the so-called "plated dilution" would then be 10^–4 and the "dilution factor" would be 10⁴. Recall from the previous dilution theory pages that the "plated dilution" represents the amount of undiluted sample being inoculated, so you can imagine 10^–4 ml of water sample being inoculated into each tube of set D.)
  
• Using basic math, if 0.43 was in 0.1 ml of the 10^–3 dilution, this is equivalent to 4.3 being in 1 ml of the same 10^–3 dilution.
  
• Therefore the most-probable number of glucose-fermenting organisms per ml of the original, undiluted sample was 4.3 X 10³.

An alternate (easier) method would be to multiply the MPN value from the table (0.43) by the dilution factor of the "D" set of tubes which is 10⁴. The result is the same: 0.43 X 10⁴ = 4.3 X 10³.

II.  (This is based on a problem from Bacteriology 324.)  A sample of raw hamburger was divided aseptically, and weighed portions were added to flasks of enrichment broth utilized in the traditional FDA Salmonella isolation and identification procedure. The amounts utilized are indicated in the results table below. The entire FDA procedure was done from each flask, and the number of flasks from which confirmed isolates of Salmonella were obtained is indicated below.

Calculate the Salmonella count per gram of the hamburger.

• Checking the table, 3-3-1 indicates an average of 4.6 organisms (in this case, Salmonella) were inoculated into each of the middle set of flasks – i.e., those inoculated with 2 grams of hamburger.
  
• If 4.6 were in 2 grams of the hamburger, this is equivalent to 2.3 being in 1 gram.

Note that there are no dilutions made, but there are still decimally decreasing amounts of sample being inoculated. The smaller the number of organisms you expect, the less you want to dilute a sample. To "go in the opposite direction" from dilution, you need to take decimally larger portions of the undiluted sample as we have seen in this example.

Here is a set of practice problems "for the general public" involving dilution plating and the MPN method. Solutions are given on a separate page.

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" Mike Curiale's MPN Calculator.

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These general microbiology pages have copyright by John Lindquist
and found their permanent sanctuary here circa 2001.
Copies found elsewhere are neither authorized nor up to date.
Page content was last modified on 8/27/12 at 11:30 AM, CDT.
John Lindquist, Department of Bacteriology,
University of Wisconsin – Madison