Most probable number

There are many discrete entities that are easily detected but difficult to count. Any sort of amplification reaction or catalysis reaction obliterates easy quantification but allows presence to be detected very sensitively. Common examples include microorganism growth, enzyme action, or catalytic chemistry. The MPN method involves taking the original solution or sample, and subdividing it by orders of magnitude (frequently 10× or 2×), and assessing presence/absence in multiple subdivisions.

The degree of dilution at which absence begins to appear indicates that the items have been diluted so much that there are many subsamples in which none appear. A suite of replicates at any given concentration allow finer resolution, to use the number of positive and negative samples to estimate the original concentration within the appropriate order of magnitude.

In microbiology, the cultures are incubated and assessed by eye, bypassing tedious colony counting or expensive and tedious microscopic counts. Presumptive, confirmative and completed tests are a part of MPN.

In molecular biology, a common application involves DNA templates diluted into polymerase chain reactions (PCR). Reactions only proceed when a template is present, allowing for a form of quantitative PCR, to assess the original concentration of template molecules. Another application involves diluting enzyme stocks into solution containing a chromogenic substrate, or diluting antigens into solutions for ELISA (Enzyme-Linked ImmunoSorbent Assay) or some other antibody cascade detection reaction, to measure the original concentration of the enzyme or antigen.

The major weakness of MPN methods is the need for large numbers of replicates at the appropriate dilution to narrow the confidence intervals. However, it is a very important method for counts when the appropriate order of magnitude is unknown a priori and sampling is necessarily destructive.

• Dilution assay

• A downloadable MPN calculator to take your data and get estimates
• A five-replicate MPN table
• Details of practical implementation, but not theory
• US FDA article on MPN method
• Information on the MPN method and ballast water treatment
• Downloadable EXCEL program for the determination of the Most Probable Numbers (MPN), their standard deviations, confidence bounds and rarity values according to Jarvis, B., Wilrich, C., and P.-T. Wilrich: Reconsideration of the derivation of Most Probable Numbers, their standard deviations, confidence bounds and rarity values. Journal of Applied Microbiology 109 (2010), 1660 – 1667

• Oblinger, J.L., and J. A. Koburger, J.A. (1975) "Understanding and Teaching the Most Probable Number Technique." J. Milk Food Technol. 38(9), 540–545.