Most+probable+number


 * MOST PROBABLE NUMBER**


 * __Introduction__**

Most probable number (MPN) is a method used to estimate the number of viable microorganisms living in a test sample. It is based upon the application of probability to the number of observed positive growth responses to a series of standard dilutions. It offers an effective means to estimate the number of microorganims in a test sample without direct count by such techniques as microscopy. MPN is commonly used in heterogeneous samples such as soil, water, and agricultural products in which exact cell numbers of individual microorganims may be impossible to determine.

The methodology for MPN uses dilution and incubation of duplicate cultures across many serial dilution intervals. This particular technique relies on various patterns of positive and negative growth aftter the inocculation of a desirable media in an appropriate vessel such as a test tube or microwell plates (shown below). The results used to infer an estimate of the population size are based on a rather complicated mathematical formula developed by Halvorson and Ziegler in 1933; though an MPN table or calculator which show accurate estimates are commonly used today (Halvorson and Ziegler, 1933).


 * __Materials and Methods__**

To begin this procedure it is best to know the dilution ratio (such as ten-fold dilutions), the number of replicates at each ratio as well as the initial dilution volume and inocculation volume.

The example that will be used as to give a clearer understanding on how the MPN method works uses a hypothetical scenario using a ten-fold dilution series consisitng of a water sample in which one ml of the dilution is inocculated into a separate test tube with an appropriate medium. Although this is only a hypothetical example MPN can be used for just about any dilution series depending on the durability of the microorganism in use.

The picture above shows a ten-fold serial dilution after prolonged period of incubation and can be replicated as follows:


 * 1)** An original undiluted sample which contains the microorganism(s) from which the dilution series can be made is needed.


 * 2)** Using a Beral pipette, alloquot one ml from the undiluted sample to a sanitized test tube containing an appropriate media of an appropriate volume.


 * 3)** Shake or vortex the newly inocculated test tube for at least 10 seconds to be certain that all contents are thoroughly mixed.


 * 4)** Using a Beral pipette, alloquot one ml from the well mixed test tube to a sanitized test tube containing the same media and volume as the first test tube before it was inocculated.


 * 5)** After the second test tube has been inocculated, shake or vortex the tube as in step **3.

6)** Follow steps **2,3,** and **4** for the rest of the tubes until the dilution series is finished.


 * 7)** Once the dilution series has been inocculated let the test tubes incubate until growth or no growth is observed (the amount of time for growth to occur may depend on the organism).


 * 8)** Once growth is observed, then the amount of organisms contained in the original sample may be estimated.

The picture above shows that all dilutions up to 10^-3 showed signs of growth but dilutions starting at 10^-4 showed no signs of growth whatsoever. Given this scenario it is possible to say that there are 1x10^3 organisms per ml in the orignal sample but less then 1x10^4 organims per ml. To increase the statistical accuracy of MPN more then one test tube can be inocculated per each dilution. MPN has historically used 3,5, or 10 test tubes per dilution with each tube being assigned a positive (+) or negative (-) based on any presence of growth (Woomer et al., 1990).



To estimate the number of microorganisms with multiple test tubes growth must be recorded in the order the dilutions were made (10^-1, 10^-2, 10^-3 etc). Once growth has been recorded for each succeding dilution it is then possible to compare the results obtained with that of a MPN Table, or enter the results in a MPN Calculator to obtain the desired results ( A sample MPN Table is shown below).




 * __References__**

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. Journal of Bacteriology. **25**:101-121.

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