SOP: Calculation of Most Probable Numbers (MPN)

GIFSQ — Global Institute for Food Safety & Quality

Principle

The most probable number (MPN) estimates the number of bacteria (coliforms in the coliform test) per unit of test material from the pattern of gas-positive tubes across a three-dilution series of five tubes each. The number of positive tubes in each of the three dilutions is read off as a three-figure combination from Table I, which is adapted for test portions of 10, 1.0 and 0.1 ml (g), and the table value is corrected by the dilution factor of the middle dilution set.

Apparatus required

• Table I — Most Probable Number (MPN) of Bacteria per 100 g (ml) of test material, using 5 tubes
• Table II — Dilutions to be used and calculations of MPN per g or ml of test material

Procedure

• Count and record the number of gas-positive tubes in every dilution set
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• Choose three consecutive dilutions for the calculation: if only three dilutions were made, use those three; if more than three dilutions were made, use the highest dilution in which all five tubes are positive plus the two next higher dilutions; if more than three dilutions were made but no dilution has all five tubes positive, use the first three dilutions
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• If a positive tube occurs in a dilution higher than the three chosen, add the number of such positive tubes to those of the next lower dilution
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• If the tubes of all sets of the dilution series are positive, use the three highest dilutions and mark the MPN with a “greater than” symbol (>)
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• Look up the combination of positive tubes (for example 5-1-0) in Table I and read the corresponding number of microorganisms
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• Multiply the Table I value by the dilution factor of the middle set of tubes to obtain the MPN per 100 ml (g)
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• If the result must be expressed per g (ml), divide the MPN per 100 by 100

Worked example

• Five tubes with 10 ml of a 1:10 dilution of test material: all 5 positive
• Five tubes with 1 ml of a 1:10 dilution of test material: 1 positive
• Five tubes with 1 ml of a 1:100 dilution of test material: none positive
• The quantities in each of the five tubes of the three dilution series represent 1, 0.1 and 0.01 g (ml) of the test material respectively
• A reading of 5-1-0 gives a value of 33 according to Table I, which applies to 10, 1 and 0.1 g (ml) respectively
• Since only 1/10 of these amounts was actually used in the analysis, the value of 33 obtained from Table II is multiplied by 10, giving 33 × 10 = 330 organisms per 100 g (ml) of test material
• Expressed per g (ml), the MPN is 330 ÷ 100 = 3.3
• When higher dilutions are used, the same procedure is followed, but the multiplier (dilution factor) is enlarged to relate the amount of test material actually present to the values given for 10, 1.0 and 0.1 g (ml) in Table I

Calculation

MPN/100 ml (g) = No. microorganisms (Table I) × dilution factor of the middle set of tubes

Where,

• MPN/100 ml (g) = most probable number of organisms per 100 ml (g) of test material
• No. microorganisms (Table I) = the value read from Table I for the observed positive-tube combination
• Dilution factor of the middle set of tubes = reciprocal of the dilution of the analytical unit, taken for the middle set of the three dilutions selected

MPN per g (ml) = (MPN/100) ÷ 100

Precautions

• Table I is adapted from a conversion table prepared for the analysis of drinking waters, where 10, 1.0 and 0.1 ml of the water under test are used as test portions. When other sized portions of the test material are placed in the tubes, multiply the table values by an appropriate number to correct for the actual amount of test material in the tubes and to obtain the MPN per g (ml) as is usually done for foods, rather than per 100 ml (g) for which the values are given in the table.
• Ignore the volume of diluent added to the tubes (which accompanies the test material) when calculating the MPN.

Table I

Most Probable Number (MPN) of Bacteria Per 100 g (ml) of Test Material — Using 5 Tubes — With 10, 1 and 0.1 ml or g of Test Material

Pos = Number of positive tubes with each of 3 volumes used.

Table II

Dilutions to be used and calculations of MPN per g or ml of test material

Dilutions to be used are underlined. (pos/tot) = No. of positive tubes / No. of tubes inoculated.

References

• Appendix D — Calculation of Most Probable Numbers (MPN), Compendium of Analytical Methods, Volume 1, January 1993, Health Products and Food Branch, Ottawa.