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**In this article we will discuss about predictive food microbiology. **

Understanding how different properties of a food, its environment and its history can influence the microflora that develops on storage is an important first step towards being able to make predictions concerning shelf-life, spoilage and safety.

The food industry is continually creating new microbial habitats, either by design in developing new products and reformulating traditional ones, or by chance, as a result of deviations in the composition of raw materials or in a production process.

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To be able to predict microbial behaviour in each new situation and determine its consequences for food safety and quality, we must first describe accurately the food environment and then determine how this will affect microbial growth and survival.

Characterization of a habitat in terms of its chemical and physical properties is generally straightforward, although problems can arise if a property is not uniformly distributed throughout the product. This can be a particular problem with solid foods, for example the local salt concentration may vary considerably within a ham or a block of cheese, how water can migrate through a mass of food.

A considerable amount of data is available on how factors such as pH, a_{w}, and temperature affect the growth and survival of micro-organisms. Much of this data was however acquired when only one or two factors had been changed and all the others were optimal or near- optimal.

In many foods a very different situation applies, micro-organisms experience a whole battery of sub-optimal factors which collectively determine the food’s characteristics as a medium for microbial growth. Leistner described this situation as the ‘hurdle effect, where each inhibitory factor can be visualized as a hurdle contributing to a food’s overall stability and safety (Figure 3.14).

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Scientific description of this multi-factorial technique for preserving foods may be relatively recent but the concept has been applied – empirically since antiquity in numerous traditional products such as cheese, cured meats, smoked fish and fruit preserves, all of which rely on a number of contributing factors for their stability and safety.

When confronted with this situation there are three basic approaches to predicting the fate of particular organisms. The first is to seek an expert judgement, based on the individual expertise of a food microbiologist and their interpretation of the published literature. While this can be useful qualitatively, it rarely provides reliable quantitative data.

To its credit, the food industry has generally not placed too great a reliance on this sort of approach but has resorted to the challenge trial. In this, the organism of concern is inoculated into the food material and its fate followed through simulated conditions of processing, storage, distribution, temperature abuse, or whatever is required.

Though it provides reliable data, the challenge trial is expensive, time consuming and labour intensive to perform properly. It also has extremely limited predictive value since its predictions hold only for the precise set of conditions tested. Any change in formulation or conditions of processing or storage will invalidate the predictions and necessitate a fresh challenge trial under the new set of conditions.

The third and increasingly popular approach is the use of mathematical models. A model is simply an object or concept that is used to represent something else and a mathematical model is one constructed using mathematical concepts such as constants, variables, functions, equations etc..

Mathematical models are not entirely new to food microbiology having been used with great success since the 1920s for predicting the probability of Clostridium botulinum spores surviving a particular heat process and enabling the design of heat processes for low acid canned foods with an acceptable safety margin.

The log-linear C. botulinum model is an inactivation model, describing microbial survival, but models predicting the potential for microbial growth to occur under a range of conditions can also be constructed. These are generally more complex but their development has been facilitated by the availability and accessibility of powerful modern computers.

**There are four essential steps in developing a model:**

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**(1) Planning:**

**This requires a clear definition of the problem:**

(i) Are we interested in spoilage or safety, which organisms are our main concern?

(ii) What is the appropriate response or dependent variable, e.g. growth rate, toxin production, time to spoilage?

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(iii) What are the relevant explanatory or independent variables, e.g. temperature, pH, a_{w}?

**(2) Data Collection:**

The response variable identified in the planning stage is measured for various levels of the explanatory variables. These should cover the full range in which we may be interested since the predictive value of the model is limited to situations where unknown values can be interpolated. Extrapolation into areas where there are no data points will not yield valid predictions.

**(3) Model Fitting:**

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Different models which relate the response variable to the explanatory variables are tested to see how well they fit the experimental data.

**(4) Model Validation:**

The model is evaluated using experimental data not used in building the model. A number of different types of model are commonly used. Probabilistic models give a quantitative assessment of the chance that a particular microbiological event will occur within a given time and are most suited to situations where the hazard is severe.

The event most often described in such models is the probability of toxin formation (i.e. growth) by C. botulinum. The work was initially prompted by the perceived need to reduce nitrite levels in cured meats such as hams and to assess quantitatively the relative importance of factors contributing to their safety.

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In the original work, the probability of toxin production, p, (the proportion of samples containing toxin within each treatment combination) was fitted to a logistic model to describe the relationship between the probability of toxin production and the level of factors/variables present (Figure 3.15). Any factor which tends to decrease µ in Figure 3.15 reduces the probability of toxin production.

Of the different factors included in the model, it can be seen that nitrite, incubation temperature and isoascorbate are more important in preventing toxin production than the others and that they are acting independently; there is no evidence of synergistic interactions between them.

Here the logistic equation is being used simply as a regression equation, a common practice in modelling situations where there are two possible outcomes to an event, e.g. pass/fail, toxin production/no toxin production. Its use in this context should not be confused with its use to represent the microbial growth curve.

One disadvantage of probabilistic models is that they do not give us much information about the rate at which changes occur. Models that predict times to a particular event such as growth to a certain level or detectable toxin production are termed response surface models.

**One such model for the growth of Yersinia enterocolitica at sub-optimal pH and temperature is described by the equation: **

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LTG = 423.8 —2.54(T) -10.97 (pH) + 0.0041(T)^{ 2 }+ 0.52(pH)^{ 2}+0.0129(pH) (T)* ……………………(3.25)

where LTG is the natural logarithm of the time for a 100-fold increase in numbers, T is temperature, pH is pH with acetic acid as acidulant. Terms marked with an asterisk have an insignificant contribution at the 5% confidence level.

Such models are derived by analysing the data for growth under different (known) conditions for a least squares fit to a quadratic equation. For many, the practical implications of equations are not immediately obvious and a graphical representation as a three dimensional response surface has more impact (Figure 3.16)

Although the model is simply a fitted curve and is not based on any assumptions about microbial growth, an interesting consequence of the Yersinia model is that the cross-product term is not significant. This means that the two preservative factors, temperature and pH appear to be acting independently; a fact that is also apparent from the graph where there is little or no curvature in the response surface.

Kinetic models take parameters which describe how fast a micro-organism will grow such as lag-phase duration and generation time and model these as the response variable. Such an approach is more precise than response-surface approaches since individual parts of the growth curve may respond differently to changing conditions.

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To derive these parameters from experimental growth data, the results are normally fitted to a mathematical function which describes the microbial growth curve.

**Some have used the logistic equation for this, but more commonly the Gompertz equation is used: **

y = a exp[-exp(b —ct)] ……………….. (3.26)

where y is bacterial concentration, a, b and c are constants, and t is time.

This equation was originally developed in the 19th Century to describe the growth of human populations, but the parameters a, b and c can be used to derive the lag time, growth rate and other properties of the microbial growth curve.

Once a large number of such values have been obtained under a variety of environmental conditions, their variation with factors such as temperature, salt, pH etc. can be modelled using response surface techniques to give a polynomial equation, usually of degree 2 or 3, i.e. a quadratic or cubic polynomial (Figure 3.17).

Some models have started off as attempts to model the effect of temperature on microbial growth and have been refined to incorporate other factors such as pH and a_{w}.

**The classical Arrhenius equation relates the rate constant (k) of a chemical reaction to absolute temperature T: **

k = A exp (-E/RT) ……………(3.27)

where E is the activation energy, A is the collision factor and R is the universal gas constant. If we assume that microbial growth is governed by a single rate-limiting enzyme, then we can interpret k as the specific growth rate constant and E as a temperature characteristic.

If this is the case and A and E are constant with temperature; then a plot of In k against 1/T (the absolute temperature) would give a straight line. In fact a concave downward curve is obtained indicating that the activation energy E increases with decreasing temperature.

**To improve the fit with observed behaviour, the basic equation has been modified by Davey to include a quadratic term: **

In k = C_{0}+ C_{1 }/T+C_{2}/T^{2} ……………….(3.28)

This can be further modified to include other parameters affecting k such as pH and a_{w}.

**For example: **

In A = C_{0} + C_{1 }/T + C_{2}/T^{2} + C_{3}a_{w} + C_{4 }a^{2}_{w} ………………….(3.29)

The Schoolfield equation is another variation of the Arrhenius model where additional terms have been added to the basic equation to account for the effects of high- and low-temperature inactivation on growth rate. Terms describing the effect of a_{w} and pH can also be incorporated here to give a considerably more complex equation.

**An alternative, rather simpler, approach which has met with some success is the square root model to describe growth at sub-optimal temperatures: **

√k=b (T-T_{min}) …………………………..(3.30)

where k is the rate of growth, T the absolute temperature (K), and T_{min} is a conceptual minimum temperature of no physiological significance since it is usually below the freezing point of microbiological media.

Application of this expression to describe microbial growth was first described by Ratkowsky, although it is now recognized as a special form of the Belehradek power function originally described nearly 70 years ago.

A plot of √k against T should give a straight line with an intercept on the T axis at T_{min} and this has been observed and reported by a number of authors monitoring growth in both laboratory media and foods (Figure 3.18).

To include the effects of other constraints on growth the square root equation has been extended separately to give similar equations including an a_{w} term and a pH term.

The fact that T _{min} is not affected by a_{w }or by pH over the ranges tested indicate that these factors act independently of temperature.

**Recently these two models have been combined to describe the growth of Listeria monocytogenes at sub-optimal pH, a _{w }and temperature using an equation of the form: **

Mathematical models of growth are not simply tools for use in development laboratories. For instance, by being able to predict accurately the response of microbial growth rate to temperature, the effect of a fluctuating temperature environment on microbial numbers throughout a distribution chain can be predicted.

The value of the technique where what might appear as slightly different temperature histories between depot and supermarket can have a dramatic effect on microbial numbers.

Time-temperature function integrators are available which integrate the temperature history of a batch of product and express it as time at some reference temperature. If the temperature of the product remains at the reference temperature, say 0°C, then they run as clocks recording real time.

If the temperature fluctuates, then they speed up or slow down depending on whether the temperature deviates above or below the reference temperature.

The relationship between rate and temperature used is the same as that between microbial growth rate and temperature. So quality loss as a result of microbial growth in a fluctuating temperature environment can be known with some accuracy and without the need for microbiological testing.

Mathematical models may play a part in the development of computer-based expert systems in food microbiology. The expert systems would provide advice and interpretation of results provided by mathematical models in the same way as human experts would but by embodying their expertise in the form of rules a computer can apply.

One expert system which is commercially available, developed at the UK’s Flour Milling and Baking Research Association, predicts the mould-free shelf life of bakery products.

Here a_{w} and temperature are the principal determinants of shelf-life and previous storage trials have shown that, at a given temperature, there is a linear relationship between the logarithm of the mould-free shelf-life and the a_{w}, expressed as equilibrium relative humidity (ERH).

**For example, at 27 °C: **

Log_{10}mould-free shelf-life = 6.42 – (0.0647xERH) …………………..(3.34)

The user is led through a series of screen menus, to choose a product type, and input the ingredients, their relative amounts, the weight loss during processing and the storage temperature. The programme then calculates the ERH of the product and uses the appropriate isotherm to calculate the mould-free shelf-life.