BACKGROUND THEORY

BACTERIAL GROWTH

Bacterial cells reproduce by dividing in two. If growth is not limited, doubling continues at a constant rate so both the number of cells and the rate of population increase doubles with each consecutive time period. For this type of exponential growth, plotting the natural logarithm of cell number against time produces a straight line. The slope of this line is the specific growth rate of the organism, which is a measure of the number of divisions per cell per unit time. In food, bacteria cannot grow continuously as the amount of nutrient available will be finite and waste products will accumulate. In these conditions growth curves tend to be sigmoidal.

A simple sigmoid growth curve (as shown in Figure 1) can be divided into three parts:

1. The lag phase
   Initially the number of cells does not increase. On finding themselves in a new environment, cells will take time to adjust. They may need to synthesise new enzymes, repair any cell damage and initiate plasmid or chromosomal replication.
2. The exponential phase
   This period is characterised by cell doubling. The maximum slope of the curve will be the specific growth rate of the organism in that particular environment.
3. The stationary phase
   Growth will slow down and eventually stop as nutrients become depleted or inhibitory metabolites build up

MODELLING

The number of pathogenic and spoilage bacteria present in food has both health and financial implications and is of concern to everybody from food producers and processors to retailers and consumers.

Traditional methods for enumerating bacteria are not instantaneous so you can only gain information on the number of organisms that were present at the sampling time. It is often desirable to know the current bacterial population or the number that will be present in the future if a product is subjected to particular treatments. Information on initial levels of contamination combined with knowledge on how bacteria number change allows present and future levels to be predicted.

Such predictive microbiology is based on the hypothesis that growth is an intrinsic characteristic of the organism and will occur reproducibly in the same environment. Thus by measuring growth once you can tell how a future population will develop under the same conditions. In its simplest form, these types of predictions can be made from graphs showing the number of bacteria measured in samples taken during growth against time. The points on the growth curve will show a trend allowing the population at any time to be estimated by interpolation. The trend can also be described mathematically by a growth function. The mathematical formula for the applied growth function is called a primary model. Such a model is only applicable for the environmental conditions under which the growth curve it describes was measured. Secondary models describe how the parameters of primary models depend on environmental factors such as temperature, pH and water activity. Predictive models of growth usually combine primary and secondary models. Using these for interpolation, growth against time can be predicted for any combination of conditions.

A sigmoid growth curve is commonly described by four parameters:

1. The natural logarithm of the initial cell concentration (y₀).
   The initial concentration is a random variable that is specific to each food and not related to the current environment.
2. The time in lag phase (l).
   The length of the lag phase will depend on the intrinsic characteristics of the bacteria, the current environmental conditions and the physiological history of the cells. Cells that have come from a different environment or are damaged (for example after heat treatment or freezing) may require more time to synthesise macromolecules and repair damage before they can divide than undamaged cells from a similar environment.
3. The maximum specific growth rate (µ_max).
   This represents the steepest slope of the curve. It is considered to be an intrinsic characteristic of the organism dependent on the current environment but not affected by the cell history.
4. The natural logarithm of the maximum cell concentration (y_max).
   The final concentration is of little interest in food safety as food is spoilt before the maximum bacterial concentration is reached.

Figure 1. A sigmoid bacterial growth curve can be characterised by four parameters.

Although modelling the lag time is very important, to date predictive modelling has primarily concentrated on growth rates. This is because the lag phase is technically difficult to study, so quantitative data is lacking, and lag is more difficult to model as it depends not only on the current conditions but also on the history, or initial physiological state, of the cells (See Figure 2). The effect of history can vary from cell to cell so improved predictions of lag time, and thus growth of bacteria in food, will require the use of stochastic modelling techniques that are missing from current predictive microbiology.

Figure 2. The number of cells present at a given time will depend not only on the maximum specific growth rate but also on the lag time which is history-dependent. These growth curves are from replicate experiments, except that the inoculation was prepared differently and led to different physiological states of the primary culture. The maximum specific growth rates are the same while the lag periods are different because the latter parameter depends on the history of the cells.

 

LAG TIMES OF INDIVIDUAL CELLS

Hundreds or thousands of organisms need to be present before they can be detected by standard counting method thus growth curves show the population lag time. Each individual cell will have its own lag time before it can start to multiply and it is the joint effect of all these individual lag times that make the lag time of the population growth. The BACANOVA project aims to look at the variability of the lag times of individual cells that make up the population lag.

The reasons for this are:

1.The lag of the population can be deduced from the lag of individual cells but not vice versa.
The total population at any time will be the sum of the bacteria present initially and the offspring they have produced in that time. Knowing the growth curves of the subpopulations generated by individual cells, a population growth curve can be constructed of the total population for any initial number of bacteria. However, population growth curves cannot be used to obtain information on the growth of individual bacteria. If a population consists of cells with differing lag times, the contribution each cell makes to the final cell number will not be equal; the subpopulations derived from cells that start to multiply fastest will make a greater contribution to the total population than those from the slow growing cells. As the contribution from each cell to the final population is not the same, one cannot use observations made at the population level to deduce the distribution of lag times amongst individual cells, or even the average lag time.

Consider two bacterial populations with individual cell lag time distributions A and B (Figure 3). The means of the lag times of the cells in each population are the same but the lag times of the two populations are markedly different (but not their maximum specific growth rates).

Figure 3.

The reason the population growth curves differ lies in the left hand tail of the distribution. Well adapted cells, with shorter lag times, will dominate growth so increasing the number of these cells reduces the population lag time. On the other hand, if the difference in the distributions appears mainly at the right hand tail, as in the case of distributions C and D (the mirror images of A and B), the two generated growth curves are indistinguishable, as shown in the second pair of plots.

In addition, knowing the number of cells with long lag times can be important when trying to determine the number of bacteria present in a sample. Cells with long lag may remain undetected by standard viable count procedures. This will lead to the probability of survival being underestimated.

2.When there are low numbers of cells, the distribution of the "time to a specific concentration" will be more closely related to the distribution of the lag phase of individual cells than lag of large populations.
This is particularly important for pathogens that can be present at very low levels. Consider a food where a small amount of contaminated sample has found its way into a large batch of product. When the food is divided into packets each packet will contain very low numbers of the contaminating organism. If the packs contain a single cell, the time before numbers start increasing in the pack will be the same as the lag phase of the cell in that pack and the distribution of times to a specific concentration will be the same as the distribution of lag times for individual cells. In this case, the probability of cell concentration reaching an infective dose by the time of consumption is the same as the distribution of individual lag times.

3.By determining the distribution of lag phase you may be able to determine the prehistory of the cells and improve modelling.
Current predictive models for bacterial growth in foods are based only on the conditions in the food and its environment, ignoring the initial physiological state of the bacterial cells. The past of a cell, such the conditions under which it was grown and any treatments like heating or freezing to which it has been subjected, will effect the ability of the cell to grow. If the variability of individual cells within a microbial population reflects the history of those cells, it may be possible to use that variability as an indication of cell history. Combining the effects of history with those of the actual environment would lead to improved models.

By understanding how the process history can effect the distribution of lag times, it may also be possible to adjust the historical treatments to improve processing. Figure 3 illustrates how small changes to the individual cell lag time distributions can alter the lag time of the population. Understanding and quantifying this phenomenon should help to optimise the microbiological quality and safety of food.

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