Overview of Predictive Microbiology

Introduction

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

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.

pH

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 (a_w) parameters for microbial pathogens.

pH of Selected Foods

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

Table 2. Reported pH for various foods.

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.