Most Probable Number (MPN): how it works, how to read its tables and when to use it instead of the plate count

Counting without seeing colonies

The plate count counts what can be seen: each colony on the agar is assumed to be one colony-forming unit, as explained in what CFUs are and how they are interpreted. The Most Probable Number (MPN) method reaches a figure by another route. It does not count colonies: it distributes the sample into several tubes of broth, observes which show growth and, from that combination of positives and negatives, calculates the concentration most likely to have produced that result.

Appendix 2 of the FDA Bacteriological Analytical Manual (BAM) credits McCrady, in 1915, with the first accurate estimate of viable bacteria by this route. It remains in use because it solves situations where the plate falls short: low concentrations, foods with particles that can be mistaken for colonies and microorganisms that need enrichment before they can be isolated.

The statistical principle

The idea is to dilute until some tubes receive at least one viable cell and others none. If the bacteria are randomly distributed, the number of cells that falls into each tube follows a Poisson distribution, and the probability that a tube receives no cells depends only on the concentration and the amount of sample inoculated. With several decimal dilutions and several tubes per dilution, the pattern of positive tubes makes it possible to estimate the original concentration. The MPN is, literally, the concentration value that makes the observed result most probable; the equation is solved by iteration.

The assumptions that must hold

The BAM lists four conditions for the estimate to be valid:

• The bacteria are randomly distributed in the sample.
• They are separate, not clustered, and do not repel each other.
• Every tube that receives even one viable organism produces growth or a detectable change.
• The tubes are independent of each other.

The third assumption is the most demanding: the medium must allow a single cell, sometimes injured, to grow in the presence of background flora. That is why the quality of the broth and of the enrichment step directly determines the result. In addition, the MPN only counts viable organisms. If the bacteria form chains or clusters that dilution does not separate, the BAM states that the result should be read as growth units or CFU, not as individual cells.

3-, 5- and 10-tube series

The most widely published design is three consecutive decimal dilutions with 3, 5, 8 or 10 tubes each; Appendix 2 provides tables for those designs, built for inocula of 0.1, 0.01 and 0.001 g. BAM Chapter 4, on coliforms and E. coli, states that the 3-tube series is used for most foods; that no fewer than 5 tubes per dilution should be used for bivalve molluscan shellfish; and that there is a 10-tube method for bottled water or samples not expected to be highly contaminated.

More tubes mean more information per dilution and therefore narrower intervals and a lower lower limit. With the BAM tables and inocula of 0.1, 0.01 and 0.001 g, the result with all tubes negative is reported as less than 3.0 MPN/g in the 3-tube series and less than 1.8 MPN/g in the 5-tube series. The upper confidence limit of that null result drops from 9.5 to 6.8 and, with 10 tubes, to 3.1 MPN/g.

How to read the tables

The result is expressed as a three-digit code: the number of positive tubes in each of the three selected dilutions. In the 3-tube table, code 3-1-0 corresponds to 43 MPN/g, with a 95% confidence interval of 9 to 180. If the inocula used were ten times smaller than those in the table (0.01, 0.001 and 0.0001 g), the value and its limits are multiplied by 10: 430 MPN/g. The same rule works downward: inoculating larger quantities lowers the limit of quantification.

When more than three dilutions are inoculated, the BAM describes a procedure for choosing the three that are taken to the table. In short, the highest dilutions that, together with the previous one, have all tubes negative are discarded, and the highest dilution with all tubes positive is sought. FDA also offers a calculation application and a spreadsheet for selecting dilutions.

The tables omit combinations so improbable that they suggest laboratory error or contamination. If the code obtained is not in the table, the BAM treats it as an improbable result: it may be due to interference in the low dilutions or to confirming too few colonies, and if the cause is unknown, the estimate may not be reliable.

Confidence intervals: the figure comes with a wide range

An MPN must always be read together with its interval. In the 5-tube series, code 5-2-0 gives 49 MPN/g with a 95% interval of 15 to 150: the true value can lie in a range spanning a factor of about ten. The BAM defines that interval as follows: before the tubes are inoculated, the probability that the resulting interval will contain the true concentration is at least 95%. The tables use a modification of the de Man method (1983); FDA's Excel spreadsheet uses a normal approximation to the logarithm of the MPN, so its intervals may not match those in the tables.

Several authors have described that the MPN tends to overestimate concentration. The BAM cites the work of Garthright (1993), who showed that this bias is not appreciable when results are expressed as logarithms, the usual way of comparing and combining data. To understand how uncertainty, the limit of detection and the compliance decision fit together, see limit of detection and measurement uncertainty.

Where MPN is used in the food industry

Coliforms and E. coli in foods

The classic BAM method has three phases. In the presumptive phase, the dilutions are inoculated into lauryl tryptose (LST) broth and incubated at 35 °C; gas production is recorded at 24 and 48 hours. In the confirmed phase for coliforms, each gassing tube is transferred to brilliant green lactose bile (BGLB) broth at 35 °C, and for fecal coliforms and E. coli, to EC broth at 44.5 °C. The completed phase for E. coli adds isolation on L-EMB agar and biochemical tests (IMViC). The MPN is calculated from the proportion of confirmed tubes in three consecutive dilutions. The chapter points out that coliform is not a taxonomic category but a working definition. What each group indicates in water is explained in total coliforms, E. coli and enterococci.

E. coli in bivalve molluscs: ISO 16649-3

This is the case in which MPN is the method set by the standard. Regulation (EC) No 2073/2005 establishes for live bivalve molluscs, and for live echinoderms, tunicates and marine gastropods, a food safety criterion for E. coli with n = 5, c = 1, m = 230 and M = 700 MPN per 100 g of flesh and intravalvular liquid, throughout the shelf life, with EN/ISO 16649-3 as the reference method. The batch is satisfactory if all five values are 230 or less, or if only one is between 230 and 700.

The generic protocol of the FAO Reference Centre, based on ISO 16649-3, describes the method as a two-stage 5-tube, 3-dilution MPN. First, the shellfish homogenate is inoculated into minerals modified glutamate broth and incubated at 37 °C for 24 hours; then the tubes showing acid production are subcultured onto agar with a chromogenic β-glucuronidase substrate (TBX) at 44 °C. The theoretical limit of detection is 18 E. coli per 100 g, and with three dilutions the maximum reportable result is greater than 18,000. β-glucuronidase-negative strains, such as E. coli O157, are not detected. The same document notes that Codex standard 292-2008 identifies this method, or an equivalent, for live or raw bivalve molluscs.

Quantitative Salmonella on carcasses and neck skin

For Salmonella, detection (absence in 25 g) answers whether the pathogen is present; MPN answers how much there is. Technical specification ISO/TS 6579-2:2012 describes a miniaturized MPN in 12-well plates: three wells per dilution, successive dilutions in buffered peptone water and subculture on semi-solid MSRV medium at 41.5 °C, with confirmation on XLD agar. The standard acknowledges its limitation: the limit of detection is approximately 1 CFU/g, compared with 1 CFU in 25 g (0.04 CFU/g) for the detection method, and it is not appropriate for samples with less than 1 CFU/g, for which it advises a conventional MPN.

A study published in Poultry Science in 2024 applied this miniaturized MPN to 96 pooled neck skin samples, representing 480 chicken carcasses. It found Salmonella in 97.9% of samples before chilling and in 85.4% after, with mean counts of 1.84 and 1.48 log MPN/g. A presence/absence result would not have shown that reduction. This type of quantification is useful for evaluating process steps, as seen in Salmonella in chicken meat.

Listeria monocytogenes in positive samples

BAM Chapter 10 calls for enumerating L. monocytogenes when a food tests positive, using a reserve portion and combining MPN and direct plating. The MPN is set up with 50 g of sample in 450 ml of buffered Listeria enrichment broth (BLEB) and four dilutions with three tubes each, equivalent to 10, 1, 0.1 and 0.01 g of sample. At 48 hours each tube is plated for isolation and confirmation, or screened with an approved rapid method and the presumptives confirmed; the result is interpreted with the Appendix 2 tables. If all tubes are positive, the direct plating count applies.

MPN versus plate count (CFU)

They are not rivals but tools for different ranges and matrices:

• Sensitivity at low counts. The BAM notes that the MPN is particularly useful for low concentrations, below 100 per gram, especially in milk and water. Each tube can receive several grams, which lowers the lower limit.
• Difficult matrices. In foods with particles that interfere with colony counting, the broth tube avoids the problem of distinguishing colonies from food debris.
• Recovery of injured cells. The broth works as a prior growth step, which favors cells stressed by heat, cold or disinfectants, provided the medium is appropriate.
• Precision. This is the weak point: MPN intervals are wide, so two results that look different may not differ statistically. A plate well counted within its useful range is generally more precise.
• Labor and time. Many tubes, several transfers and confirmations of 48 hours or more. Traditional plate culture is more direct if the expected load is high.
• Confirmation. In pathogen methods, a tube with growth is presumptive until confirmed (see presumptive vs. confirmed result).

Which TAAG kits relate to this method

TAAG does not have an MPN kit: its real-time PCR kits are qualitative (detection and identification) and do not give a number of microorganisms per gram. Where they can play a role is in reading tubes or wells, as BAM Chapter 10 allows for the Listeria MPN. The catalog includes kits for microorganisms that are quantified by MPN: Specio 1.3 E. coli (V-SF167), with declared matrices of foods, beverages and living and inert surfaces; Ampliora 1.3 E. coli (V-SF69), for leafy vegetables and surfaces; Ampliora 1.1 Salmonella spp. (V-SF97), with a declared sensitivity of 1 CFU/25 g in raw chicken thigh, frozen beef burger, sausage (longanicilla), mortadella and surface; and Ampliora 2.3 Listeria spp. and L. monocytogenes (V-SF46), for foods, beverages and surfaces. None declares bivalve molluscs as a validated matrix, and their associated enrichment media are not the broths of a standardized MPN (MMGB, BLEB or MSRV). Using a kit to read the tubes of an MPN requires validating that use with the specific broth and matrix; it is advisable to review it with TAAG before incorporating it into a procedure.