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Overview of Predictive Microbiology


Anticipating the behavior of microbial pathogens in food is an important goal of food safety managers. In this regard, the scientific field of predictive microbiology offers important tools to food safety mangers to estimate the consequences of food handling and processing operations on growth, survival and inactivation of foodborne pathogens.

Successful development and implementation of predictive models involves a series of steps that include experimental design, model development, model validation and production of an effective interface between the model and end-user. The net result is a tool that can be used in HACCP plans to define critical control points and critical limits, as well as to determine safe corrective actions when processing deviations occur.

Phases of Bacterial Growth

The level of bacteria in food is controlled by various factors, including the initial contamination level, the level of nutrients, temperature, pH, water activity, additives, and the presence of other microorganisms. Bacteria can increase in numbers (grow), decrease in numbers (inactivate or die) or remain at the same level (survive). Predictive models can be developed for each of these types of bacterial behavior.

A survey of the literature reveals that many models have been developed for microbial growth compared to inactivation or survival. Also, there are many more models for bacteria in defined microbiological media, such as broth, than for real food. In the majority of cases, microbial growth can be segmented into three different phases: lag phase, growth phase and stationary phase.

Lag Phase (Lag Phase Duration)

Lag Phase can be defined as the amount of time required for a cell to adjust to a new environment prior to replication (growth). Lag Phase is the most unpredictable part of a growth curve compared to Growth and Stationary phases. This is because Lag Phase will be different depending on the previous history of the microorganism. For example, the Lag Phase Duration (LPD) of bacteria grown at 37°C (98°F) in culture media and then transferred to raw ground beef at 10°C (50°F) will be different than the LPD of bacteria grown at 21.1°C (70°F) and then transferred to ground beef at 10°C (50°F). This is because the previous environment of the bacteria will result in different cellular changes that need to be made before the organism can grow in a new environment.

The LPD represents a distribution of lag times for individual cells within the microbial population. As you notice in most growth curves, this produces a curve between the Lag Phase and Growth Phase. Consequently, a portion of this curve is included in the calculated Lag Phase and a portion is included in the Growth Phase.

Growth Phase

The Growth Phase represents the replication (multiplication) of microorganisms. Growth is sometimes described in terms of Growth Rate or Generation (Doubling) Time. The Generation Time is the time (usually stated in hours or days) that it takes for one cell to divide and become two cells. To convert this to Growth Rate, simply divide 0.301 (the log10 value of 2) by the Generation Time. On the other hand, Growth Rate is the change in bacterial numbers over some period of time, typically expressed as log10 per hour or day. To convert Growth Rate to Generation (Doubling) Time, divide 0.301 by the Growth Rate.

For plotting growth data, we typically convert cell numbers to the log10 value and plot this as a function of time. This produces a plot showing a linear growth phase.

Stationary Phase and Maximum Population Density

The terms Stationary Phase and Maximum Population Density (MPD) refer to the maximum (highest) level that bacteria reach in the food. This level can be affected by the presence of other bacteria, such as food spoilage organisms, limiting nutrients, and/or the production of inhibitory factors. In most foods, a typical MPD is 9-10 log10 (1 billion to 10 billion) cells per gram or milliliter of food.

Death Phase

Although not always observed, bacteria can die in a food after an extended storage time. This normally occurs after reaching the Stationary Phase.

Phases of Bacterial Inactivation

Bacteria are inactivated, or killed, when conditions are adverse to bacterial survival. These environmental conditions can cause acute (fast) inactivation as with high temperature, or mild inactivation (slow), as observed with low levels of organic acids. The shape of the inactivation curve may vary, depending on the organism and environment. Conditions may cause an immediate linear (straight line) reduction in cell numbers, or a period of no change in cell numbers followed by a linear decrease.

Linear Phase

For inactivation scenarios, the log10 value of the cell number in normally plotted. In the linear phase of inactivation, the rate (slope of the line) of inactivation depends on the number of cell “targets” affected by the effector (such as heat). As the cell concentration declines, the probability of a “hit” on the cell target decreases, resulting in a proportional linear reduction in cell number.

Inactivation is commonly referred to in terms of the decimal reduction time, or D-value. Although D-values can be expressed for different levels of reduction, the most common representation is the time for the population to decrease by 90% (10-fold or 1.0 log10). The D-value equals the absolute value of the inverse of the rate (slope) of cell reduction.

A common secondary model of the D-value is referred to as the Z-value. This term describes the change in temperature that causes in a 90% (or 10-fold) change in the D-value. The Z-value is the inverse of the rate of change in the D-value.

The Z-value is commonly used to calculate process lethality. Process lethality can be expressed as the F-value which is an integrated calculation of time-dependent thermal effects on inactivation of cell numbers, and serves to measure the accumulated lethality effects with “come-up” and “come-down” thermal profiles, such as those used in the canning industry.

“Shoulders and Tails”

The kinetics of both thermal and non-thermal inactivation may display a lag-like period, sometimes referred to as a “shoulder,” that proceeds the linear inactivation phase. For thermal inactivation scenarios, this is more commonly observed at lower temperatures and when using higher cell concentrations. It is theorized that this represents a subpopulation of cells that are more thermotolerant, with a greater likelihood of being observed when high inoculum levels are used. In some cases, these shoulders may result from inaccurate measurements of the internal temperature of the matrix during temperature “come-up” time, the use of mixed cultures, cell clumping and cell multiple- hit mechanisms. The Weibull distribution is commonly applied to model such non-linear inactivation curves.

In some instances, the linear phase of inactivation does not intercept the x-axis, but instead transitions to a curve referred to as a “tail.” Such “tails” are more commonly observed with higher inoculum levels. Investigators theorize that “tails” represent a subpopulation of bacteria that are more thermally resistant.

Primary Factors that Affect Bacterial Behavior

Research shows that temperature, pH and water activity have very pronounced effects on the behavior of bacteria. Consequently, these factors can be adjusted to control both food spoilage and safety. For example, low temperature can be used to inhibit microbial growth during food storage; food pH can be reduced with organic acids to stop growth and cause microbial inactivation; and water activity can be lowered through the use of salts to extend shelf-life.


Temperature is an extrinsic factor of food that has a strong influence on the growth and inactivation of bacteria. In general, temperatures less than 5ºC halt the replication of microbial pathogens and retard spoilage, while temperature greater than 54ºC are lethal to pathogens.

In addition, there is a direct relationship among temperature, bacterial lag phase and growth rate, in that lag phase decreases and growth rate increases with increasing temperature.


High levels of acidity inhibit bacterial growth and can lead to the death of vegetative microorganisms. Some acidulants, such as lactic acid, have been shown to be effective inhibitors of Listeria monocytogenes.

Water Activity

Water activity is a measure of the amount of water that is not tightly bound to the food matrix and available to support the growth of bacteria, yeasts and moulds (fungi). This value varies from 0 to 1, with most hazardous foods being in the range of 0.85 to 0.99. Water activity is affected by various compounds in food, not simply NaCl.

Table 1 provides a general overview of the effects of temperature, pH and water activity on microbial growth.

Table 1. Temperature, pH and water activity (aw) parameters for microbial pathogens.

Salmonella spp. 5.2 / 35-43 / 46.2 3.8 / 7.0-7.5 / 9.5 0.94 / 0.99 / >0.99
Clostridium botulinum
A & B 10 - 50 4.7 - 9 >0.93
nonproteolytic B 5 - ? -b NRc
E 3.3 - 15-30 -b >0.965
F 4 - ? -b NRc
Staphylococcus aureus 7 / 37 / 48 4.0 / 6.0-7.0 / 10 0.83(0.9) / 0.98 / >0.99
Campylobacter jejuni 32 / 42-43 / 45 4.9 / 6.5-7.5 / ca9 >0.987 / 0.997 / -
Yersinia enterocolitica -1.3 / 25-37 / 42 4.2 / 7.2 / 9.6 - / - / 5% NaCl
Listeria monocytogenes -0.4 / 37 / 45 4.39 / 7.0 / 9.4 0.92 / - / -
Vibrio cholerae O1 10 / 37 / 43 5.0 / 7.6 / 9.6 0.970 / 0.984 / 0.998
V. cholerae non-O1 -b -b -b
Vibrio parahaemolyticus 5 / 37 / 43 4.8 / 7.8-8.6 / 11 0.940 / 0.981 / 0.996
Clostridium perfringen 4 / 43-47 / 50 5.5-5.8 / 7.2 / 8.0-9.0 0.97 / 0.95-0.96 / 0.93
Bacillus cereus 4 / 30-40 / 55 5.0 / 6.0-7.0 / 8.8 0.93 / - / -
Escherichia coli ca7-8 / 35-40 / ca44-46 4.4 / 6-7 / 9.0 0.95 / 0.995 / -
Shigella sonnei 6.1 / - / 47.1 4.9 / - / 9.34 - / - / 5.18% NaCl
Shigella flexneri 7.9 / - / 45.2 5.0 / - / 9.19 - / - / 3.78% NaCl
  • minimum / optimum / maximum values.
  • The value, though unreported, is probably close to other species of the genus.
  • NR denotes that no reported value could be found, but for most vegetative cells, an aW of >0.95 would be expected.
Values taken from:

ICMSF(1996) Microorganisms in Foods 5: Characteristics of Microbial Pathogens, Roberts, T. A., Baird-Parker, A. C. and Tompkin, R. B. (eds.), Blackie Academic & Professional, London [ISBN 0 412 47350 X]

Microbial Survival in the Environment, E. Mitscherlich and E.H. Marth (eds.), Springer-Verlag, Berlin and Heidelberg, 1984. [ISBN 3-540-13726-2 Springer-Verlag, Berlin, New York, Tokyo] [ISBN 0-387-13726-2 Springer-Verlag, Heidelberg, Berlin, Tokyo].

pH of Selected Foods

Table 2 provides pH values for a variety of common foods.

Table 2. Reported pH for various foods.

Foods pH Reference Foods pH Reference
apple juice 3.48-3.69 25 lemon juice 2.2 15
apple juice, Delicious 3.55-3.79 10 lemon filling 3.09-3.24 28
apple juice, Delicious 4.04-4.24 10
apple juice, Delicious 4.01-4.33 11 mangoes, alphonso 4.57 32
apple juice, Golden Delicious 3.78-3.94 10 milk cow whole pwd. recon. 6.5 21
apple juice, Golden Delicious 3.78 11 milk, imitation fluid recon 6.5 21
apple juice, Golden Delicious frz 3.61-3.93 10 milk, imitation fluid whole recon 6.1-7.2 21
apple juice, Jonathan 3.52-3.62 11 milk, imitation whole pwd. recon. 6.08-6.90 21
apple juice, Jonathan 3.49-3.51 10 milk, imitation base 6.9-7.3 21
apple juice, Jonathan frz 3.18-3.31 10
apple juice, Grimes 3.74-3.82 11 oats, rolled, raw 5.95 8
apple juice, Grimes 3.55-3.66 10 oats, rolled, cooked 5.95 8
apple juice, Grimes frz 3.53-3.63 10 orange filling 3.79-4.65 28
apple juice, Stayman 3.54-3.62 11 orange juice 4.2 15
apple juice, Willowtwig 3.28-3.37 10 orange juice, canned 3.69-3.53 24
apple juice, Willowtwig frz 3.20-3.27 10
apple juice, Winesap 3.57-3.65 10 peaches 3.8 30
apple juice, Winesap 3.57-3.62 11 pears, Bartlett 3.86 30
apple juice, Winesap frz 3.42-3.52 10 perch red sea, fresh 6.8 31
apricot filling 4.05-5.43 28 pineapple filling 3.42-3.62 28
asparagus, fresh 5.8 31 pork, LD 5.60-6.93 22
pork, normal 6.17 18
beef, frozen 5.25-5.30 16 pork, pale-soft-extrudative 5.88 18
beef, rectus abdominus 5.9-5.73 7 poultry, male, pectoralis major 5.8 1 9
beef, semitendinosus, 25C 5.57 9
beef, semitendinosus, raw 5.52 9 quince juice 3.63 25
beef, semitendinosus, 45C 5.59 9
beef steaks, LD rib, raw 5.5-5.9 27 raspberries, black 3.25 30
blackberry juice 3.84 25 raspberry juice, black 3.78 25
brandy, 10 Exposition 3.38-4.47 12 rhubarb 3.0 3
brandy, 19 Prorate 3.12-5.06 12 sheep, Marino, semitendinosus 5.60-7.0 2
carrots, Imperator, raw 6.1 29 sheep, Marino, biceps femoris 5.65-6.60 2
carrots, Imperator boiled 5.7 29 sheep, Marino, semimembranosus 5.60-4.47 2
cauliflower, frozen 6.20 16 spinach, frozen 6.15-6.60 16
cereal, wheat, darker, cooked 5.98-6.08 8 spinach, fresh 6.4 31
cereal, wheat, darker, raw 5.45-5.95 8 strawberries fresh mature 3.42-3.21 23
cereal, wheat, fine, wht, raw, cked 5.39-7.50 8 strawberries, frozen 3.30-3.55 16
cheese, cheddar 5.2-5.5 26 strawberries, overmature 3.60 23
cheese, cheddar 4.87 14 strawberries, immature 3.18 23
cherries 3.75 30 strawberry juice 3.44 25
cherry juice 3.50 25 strawberry filling 3.81-5.00 28
chocolate filling 6.39-5.00 5
coconut skim milk, spray-dried 7.05-7.09 13 tomato juice 4.30-4.39 6
corn, sweet, fresh 6.7 31 tomato juice 3.81-4.71 34
cranberry juice 3.42 25 tomatoes, ripe 4.2 17
currant juice 3.19 25 tomatoes(sliced), frozen 3.15-3.40 16
custard 6.73-6.84 5 turkey meat, dark 6.1 20
custard, standard 5.84-6.6 5 turkey meat, white 5.7 20
elderberry juice 4.27 25 wine, Albemarle 3.19 4
wine, burgundy, California 1917 3.86 33
grape juice 3.13-3.15 25 wine, Hunt 3.09 4
grapefruit juice 4.0 15 wine, Magoon 2.97 4
wine, Noble 3.29 4
wine, pink 3.52 1
wine, red 3.63 1
wine, Tarheel 3.44 4
wine, Thomas 3.04 4

Abbreviations: frz = frozen, wht = white, cked = cooked, pwd. = powdered, recon. = reconstituted, LD = longissimus dorsi muscle

  1. Amerine, M.A. and A.J. Winkler. 1941. Color in California wines. IV. The production of pink wines. Food Research 6:1.
  2. Bouton, P.E., P.V. Harris and W.R. Shorthose. 1971. Effect of ultimate pH upon the water-holding capacity and tenderness of mutton. Journal Food Science 36:435.
  3. Brown, E.J., H. Schuele, and F. Fenton. 1941. Loss of vitamin C during cooking of rhubarb. Food Research 6:1.
  4. Carroll, D.E., W.B. Nesbitt and M.W. Hoover. 1975. Characteristics of red wines of six cultivars of Vitis rotundifolia Michx. Journal Food Science 40:919.
  5. Cathcart, W.H. and A. Merz. 1942. Staphlococci and salmonella control in foods. III. Effect of on inhibiting growth of staphylococci. Food Research 7:98.
  6. Crandall, P.G. and P.E. Nelson. 1975. Effects of preparation and milling on consistency of tomato juice and puree. Journal Food Science 40:710.
  7. Dube, G., V.D. Bramblett, R.D. Howard, B.E. Homler, H.R. Johnson, R.B. Harrington, and M.D. Judge. 1971. Dietary effects on beef composition. 4. Processing and palatability attributes. Journal Food Science 36:147.
  8. Eklund, A.B. and V.R. Goddard. 1945. Stability of thiamin chloride (vitamin B1) in mineral and vitamin-fortified cereal. Food Res. 10:365.
  9. Fogg, N.E. and D.L. Harrison. 1975. Relationships of electrophoretic patterns and selected characteristics of bovine skeletal muscle and internal temperature. Journal Food Sci. 40:38.
  10. Forgacs, J., W.A. Ruth and F.W. Tanner. 1945. Freezing of apple juice. Food Research 10:149.
  11. Forgacs, J., W.A. Ruth, and F.W. Tanner. 1945. Examination of canned apple juices. Food Research 10:227.
  12. Guymon, J.F., N.E. Tolbert and M.A. Amerine. 1943. Studies with brandy. I. pH. Food Research 8:224.
  13. Hagenmaier, R.D., C.M. Cater and K.F. Mattil. 1975. Coconut skim milk as an intermediate moisture product. Journal Food Science 40:717.
  14. Hoecker, W.h. and B.W. Hammer. 1944. Salt migration in cheddar cheese curd and its effect on moisture content, pH, and bacterial content. Food Research 9:278.
  15. Joslyn, M.A. and A. Sedky. 1940. Effect of heating on the clearing of citrus juices. Food Research 5:223.
  16. Kaloyereas, S.A. 1947. Drip as a constant for quality control of frozen foods. Food Research 12:419.
  17. Kartesz, Z.I. 1938. Pectic enzymes. II. Pectic enzymes of tomatoes. Food Research 3:481.
  18. Kemp, J.D., R.E. Montgomery, and J.D. Fox. 1976. Chemical palatability and cooking characteristics of normal and low quality pork loins as affected by freezer storage. Journal Food Science 41:1.
  19. Khan, A.W. 1971. Effect of temperature during post-mortem glycolysis and dephosphorylation of high energy phosphates on poultry meat tenderness. Journal Food Science 36:120.
  20. Koonz, C.H. and J.M. Ramsbottom. 1938. Susceptibility of frozen-defrosted poultry meat to drip. Food Research 3:485.
  21. Kosikowski, F.V. 1971. Nutritive and organoleptic characteristics of nondairy imitation milks. Journal Food Science 36:1021.
  22. Krzywicki, K. 1971. Relation of ATPase activity and calcium uptake to postmortem glycolysis. Journal Food Science 36:791.
  23. Loeffler, H.J. 1946. Retention of ascorbic acid in strawberries during processing, frozen storage, and manufacture of velva fruit. Food Research 11:69.
  24. Nolte, A.J. and H.W. Van Loesecke. 1940. Chemical and physical characteristics of the petroleum ether soluble material of fresh and canned Florida Valencia orange juice. Food Research 5:457.
  25. Pederson, C.S. and H.G. Beattie. 1943. Buffering effect of fruit juices. Food Research 8:405.
  26. Personius, C., E. Boardman and A.R. Ausherman. 1944. Some factors affecting the behavior of cheddar cheese in cooking. Food Research 9:304.
  27. Ramsbottom, J., and C.H. Koonz. 1940. Relationship between time of freezing beef after freezing slaughter and amount of drip. Food Research 5:423.
  28. Ryberg, R.E. and W. H. Cathcart. 1942. Staphyloccoci and salmonella control in foods. II. Effect of pure fruit fillings. Food Research 7:10.
  29. Stephens, T.S., G. Saldana, H.E. Brown, and F.P. Griffiths. 1971. Stabilization of carreatment. Journal Food Science 36:36.
  30. Tanner, F.W., P.R. Beamer and C.J. Rickher. 1940. Further studies on development of Clostridium botulinum in refrigerated foods. Food Research 5:323.
  31. Theriault, F.R. and C.R. Fellers. 1942. Effect of freezing and of canning in glass and in tin on available iron content of foods. Food Research 7:503.
  32. Thomas, P. 1975. Effect of post-harvest temperature on quality, carotenoids and ascorbic acid content of Alphonso mangos on ripening. Journal Food Science 40:704.
  33. Winkler, A.J. and M.A. Amerine. 1938. Color in California wines. II. Preliminary comparisons of certain factors influencing color. Food Research 3:439.
  34. York, G.K., J.R. Heil, G.L. Marsh, A. Ansar, R.L. merson, T. Wolcott, and S. leonard. 1975. Thermobacteriology of canned whole peeled tomatoes. Journal Food Science 40:764.

Classes of Models

Primary Models

After the experimental protocol is established, time-versus-cell number data are collected for each of the test conditions. Next, curve-fitting programs are used to develop a best-fit line to the data. For growth data, the parameters normally include lag phase duration, growth rate and maximum population density. For inactivation data, parameters may reflect an initial “shoulder”, somewhat analogous to the lag phase, a linear reduction in cell count, and possibly a “tail.” In cases where probability-of-growth is relevant, such as at the growth/no-growth boundaries, data may be scored simply as growth or no-growth.

Secondary Models

Secondary models are derived from the primary model parameters (e.g., lag time, growth/inactivation rate, maximum population density). Secondary models predict the change in primary model parameters as a function of the environment. An example of a secondary model is predictions of growth rate as a function of temperature, or predictions of growth rate as a function of multiple environmental conditions such as salt, water activity and temperature. The z-value is another type of secondary model that describes the change in D-value as a function of temperature. Secondary models can be simple linear regressions or more complex polynomial models that require sophisticated computational software.

Various secondary models have been used to model growth and inactivation of bacteria. More commonly, lag time and growth rate have been modeled using square-root, gamma and cardinal approaches. The use of probability models for describing the likelihood of a microbial event in food is increasing in the literature. Applications include modeling growth/no-growth interfaces, the length of the lag phase for pathogens in formulated ready-to-eat foods, and the production of microbial toxins. Another model form that is increasingly reported is Artificial Neural Networks.

Tertiary Models

The next step of model development involves expressing secondary model predictions through a primary model. This is commonly done with spreadsheets (e.g., Microsoft Excel) and in stand-alone software, such as the US Department of Agriculture-Agricultural Research Service’s Pathogen Modeling Program (PMP; http://ars.usda.gov/Services/docs.htm?docid=6786) and the UK Institute of Food Research’s Growth Predictor (http://www.ifr.ac.uk/Safety/GrowthPredictor/default.html).

Importantly, predictions of microbial behavior are not 100% accurate. Variations and uncertainty are introduced through experimental error, strain variation, and primary and secondary models. Such error is typically expressed as upper and lower confidence levels. For example, model limits that include 95% of the observed data are referred to as 95% confidence intervals.