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United States Department of Agriculture

Agricultural Research Service

Title: A Simple Maximum Probability Resolution Algorithm for Most Probable Number Analysis Using Microsoft Excel

Authors
item Irwin, Peter
item Fortis, Laurie
item Tu, Shu-I

Submitted to: Journal of Rapid Methods and Automation in Microbiology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 13, 2001
Publication Date: N/A

Interpretive Summary: The contamination of foods with pathogenic bacteria (e.g., Salmonella or E. coli 0157:H7) may lead to substantial food poisoning epidemics. To minimize outbreaks of food poisoning, sensitive detection and effective intervention procedures should be developed. The level of bacterial contamination in foods is usually very low (e.g., only a few cells in a large volume). The most sensitive process for the detection of food-borne bacteria involves taking multiple samples from several dilutions (the "dilution method") and uses a mathematically protocol called "most probable number" (MPN) analysis to estimate the level of bacteria in the original sample. In this report we describe a new, but considerably less complicated, approach to estimating the MPN. Results indicated that the new method's estimations more closely approached a value predicted from fundamental enumeration pathogenic bacteria in foods using the dilution method.

Technical Abstract: Traditional most probable number (MPN) methods are executed using one of two schemes. The direct maximum probability resolution (DMPR) technique involves calculating the binomial probability distribution array, P (Product p i), as a function of cell density (Delta) and finding the value of Delta which corresponds to the maximum in P (the MPN). Alternatively, indirect MPR methods seeks the solution to a non-linear equation, related to p i, by altering Delta. We describe herein a simple maximum probability resolution (SMPR) method of the second type which involves the repeated calculation (j cycles) of Delta j+i by the addition of a term, related to the partial first derivative of p i with respect to Delta, to Delta j until the MPN is reached. Using this SMPR algorithm and comparing our results with a DMPR procedure (n = 5, 10, or 96; 10,000 point per p i), another indirect computer-based MPR method (n = 10 or 96), or published MPN tables (n = 5) we found that there was agreement to 3-5 significant figures. The SMPR approach also outperformed all other computer-based MPR techniques tested.

Last Modified: 11/26/2014
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