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THE M ATHEM ATICS OF
Modeling Microbial Multiplication
No prediction of microbial behavior can ever be completely
accurate. Numerous variables—too many, in fact—
make it a difficult problem to model. During the last few
decades, however, the science of modeling and estimating
bacterial reproduction and inactivation processes has
blossomed into a major area of research that has been
dubbed “predictive microbiology.”
Part of the field’s rapid expansion has come from the
realization that researchers need to develop more complex
models to account for the effects on microbial multiplication
of factors including temperature, pH, preservatives, food
structure, water activity, and the presence of other organisms.
Quick, reasonable estimates of bacterial reproduction and
survival, although not infallible, have enabled researchers to
determine the shelf lives of foods, create new products,
highlight potential points of concern in production and
distribution processes, intelligently assess the influence of
environmental factors, and help formulate better safety
guidelines.
The specifics of the models that researchers and commercial
food processors use lie beyond the scope of this book,
but generally they try to predict the classic sigmoid or S-
shaped curve that describes the lag, exponential, and stationary
phases of bacterial reproduction over time (the onset of
bacterial death adds a downward slope to the sigmoid curve).
These predictive models fall into three main classes: primary,
secondary, and tertiary. Primary models seek to explain
the response of bacteria to a single set of conditions over
time. The oldest and simplest of these models, the log-linear
model, is based on the concept that for a specific temperature,
the rate at which bacteria die off remains constant over
time. The builders of more recent models, including versions
that are called (after their authors) the Baranyi, Buchanan, and
modified Gompertz models, have sought to refine their
predictions of bacterial replication curves by using experimental
data.
Secondary models predict environmental relationships,
such as the effect of temperature on the bacterial reproductive
rate, or more complicated interactions including how the
combination of salt and water activity affects the replication
rate as the temperature increases. Tertiary models are more
complicated still and combine aspects of primary and secondary
models. They typically require spreadsheets or
dedicated software programs to perform the calculations
involved.
Some of these software programs can be very useful to
chefs who design a particular food or food process. A company
that is creating a ready-to-eat food product that has
multiple ingredients and cooking steps can use the software
to find out if the process provides enough of a safety margin.
A firm that makes precooked corned beef, for example,
might predict the replication of Clostridium perfringens at
a given cooling rate. The software’s prediction might persuade
the company to change the mix in the corned beef
curing formula or to increase the cooling rate. In most cases,
of course, chefs will not care about this level of detail, but
particularly complex processes might be worth the trouble.
Many such food-pathogen software programs exist, but
two stand out. The Pathogen Modeling Program, or PMP, is
distributed for free by the U.S. Department of Agriculture.
As of 2010, the software was available online at
http://ars.usda.gov/services/docs.htm?docid=11550.
The second program, Growth Predictor, is distributed
for free by the U.K. Institute of Food Research at
http://www.ifr.ac.uk/Safety/GrowthPredictor. A version of
Growth Predictor can be used with a web interface as part of
the ComBase Initiative (a collaboration of agencies from the
U.S., the U.K., and Australia) and is available by filling in an
e-mail form at http://www.combase.cc/toolbox.html.
The Pathogen Modeling Program (PMP) is distributed for free.
146 VOLUME 1 · HISTORY AND FUNDAMENTALS
MICROBIOLOGY FOR COOKS 147