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Predictive microbiology: towards the interface and beyond
T.A. McMeekin *, J. Olley, D.A. Ratkowsky, T. Ross
School of Agricultural Science, University of Tasmania, PO Box 252-54, Hobart, Tasmania 7001, Australia
Received 21 May 2001; accepted 9 August 2001
Abstract
This review considers the concept and history of predictive microbiology and explores aspects of the modelling process
including kinetic and probability modelling approaches. The journey traces the route from reproducible responses observed
under close to optimal conditions for growth, through recognition and description of the increased variability in responses as
conditions become progressively less favourable for growth, to defining combinations of factors at which growth ceases (the
growth/no growth interface). Death kinetics patterns are presented which form a basis on which to begin the development of
nonthermal death models. This will require incorporation of phenotypic, adaptive responses and may be influenced by factors
such as the sequence in which environmental constraints are applied. A recurrent theme is that probability (stochastic)
approaches are required to complement or replace kinetic models as the growth/no growth interface is approached and
microorganisms adopt a survival rather than growth mode. Attention is also drawn to the interfaces of predictive microbiology
with microbial physiology, information technology and food safety initiatives such as HACCP and risk assessment. D 2002
Elsevier Science B.V. All rights reserved.
Keywords:Predictive microbiology; History and process; Growth/no growth interface; Microbial physiology; IT and food safety
1. Introduction
Methods of food preservation such as salting, dry-
ing and fermentation have been carried out for thou-
sands of years representing an empirical approach to
the control of microbial populations in food. Theseprocesses continue to this day amongst indigenous
populations, and, one suspects, with traditional prod-
ucts produced in more sophisticated societies.
Early examples of the application of scientific
principles to food preservation include Pasteurs work
on the specificity of undesirable fermentations in wine
and the supply of lactic starter cultures by Hansens in
Denmark at the end of the 19th century. However,
while much of the fermentation industry (probably
because of large-scale production and the influence
of chemical engineers) has adopted quantitativeapproaches, large parts of food microbiology have
remained essentially qualitative or at best semiquanti-
tative. Thus shake and plate techniques allow
enumeration to within F 0.5 log, with minimum
levels of detection as high as 100 cfu/g. Furthermore,
most probable number techniques often have very
wide confidence limits and enrichment procedures
allow the presence (not necessarily the absence) of a
particular organism to be recorded in a sample. The
sample, of course, may be totally inadequate to
0168-1605/02/$ - see front matterD 2002 Elsevier Science B.V. All rights reserved.P I I : S 0 1 6 8 - 1 6 0 5 ( 0 1 ) 0 0 6 6 3 - 8
* Corresponding author. Tel.: +61-362-262636; fax: +61-362-
262642.
E-mail address:[email protected]
(T.A. McMeekin).
www.elsevier.com/locate/ijfoodmicro
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provide a true representation of the prevalence (prob-
ability of occurrence) of the organism in the product
lot, let alone a numerical indication of its density.
This qualitative/semiquantitative state of affairswill continue to impede the progress of food micro-
biology as a discipline that seeks to understand micro-
bial behaviour in foods and thus provide the scientific
basis upon which the food industry can supply safe
and wholesome food. The situation is encapsulated by
a quotation from the renowned physicist Lord Kelvin:
When you can measure what you are speaking about
and express it in numbers you know something about
it; but when you cannot measure it, when you cannot
express it in numbers, your knowledge is of a meagre
and unsatisfactory kind. In defence of food (and
probably other) microbiologists, deriving the quanti-
tative laws of physics that govern the natural world
was an exercise not unduly complicated by variability
inherent in biological systems and uncertainty about
the presence and potential of particular microorgan-
isms.
In many senses, the uncertainty factor is increasing
in a world characterised by condensation, stratifica-
tion and mobility of the human population. We are
experiencing an unprecedented rate of change as a
result of scientific and technological advances. Adap-
tation to and exploitation of change is a primarycharacteristic of microorganisms that, because of their
small size, speed of reproduction, phenotypic plasti-
city and genetic promiscuity, colonise almost every
conceivable habitat on earth. Thus, it is not surprising
that we are faced with the emergence and reemer-
gence of foodborne microbial pathogens (Lederberg,
1997).
Strategies to deal with these threats range from
reactive measures in which resources are mobilised
rapidly to address critical knowledge gaps to longer
term strategic measures. This longer term research isneeded to improve our ability to respond quickly to
new microbial threats and assist us to be more
proactive at anticipating and preventing emergence
(Buchanan, 1997). Important elements of a proactive
approach are the accumulation of quantitative infor-
mation on microbial behaviour in foods (predictive
microbiology) and an increased understanding of
microbial physiology (McMeekin et al., 1997).
Predictive microbiology (the quantitative microbial
ecology of foods) has, after a considerable gestation
period, emerged strongly as an essential element of
modern food microbiology. This contribution will
consider the development of predictive microbiology
with particular reference to interfaces. There areseveral connotations of interface that not only des-
cribe boundaries of scientific interest such as the
growth/no growth interface but also interfaces
between disciplines that have led to significant con-
ceptual and technological advances.
2. Concept and history of predictive microbiology
The concept of predictive microbiology is that a
detailed knowledge of microbial responses to environ-
mental conditions enables objective evaluation of the
effect of processing, distribution and storage opera-
tions on the microbiological safety and quality of
foods. It involves the accumulation of knowledge on
microbial behaviour in foods and its distillation into
mathematical models. Application of this condensed
knowledge is through devices that store and match the
information with the environmental conditions expe-
rienced by microorganisms in foods. These provide
cost-effective surrogates for traditional microbiologi-
cal testing to estimate shelf life and safety and, when
properly constructed and applied, predictive modelsmay be viewed as potentially the ultimate rapid
method.
As indicated in the Introduction, methods for the
preservation of foods have been practised for thou-
sands of years and with the passage of time, many
preservation methods have been characterised and
their scientific basis determined. An early example
of a predictive model is found in the thermal process-
ing of foods where a heat process sufficient to destroy
1012 spores ofClostridium botulinum type A is used.
The process is characterised by a predictive modeldeveloped by Esty and Meyer (1922) and despite
potential complications of shoulders and tails, the
efficacy of the process is widely accepted by the
canning industry. In large part, this arises from
the magnitude of the safety factor built into the
model.
Heat processes have also been determined to
ensure the thermal destruction of nonspore-forming
organisms such as milk pasteurisation protocols for
Mycobacterium tuberculosis and more recently for
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Salmonella in roast beef and psychrotropic pathogens
in sous-vide products. Where protocols are selected to
minimise processing and the safety factor is reduced,
more rigorous selection and validation of models isrequired. In the case of thermal processes, oversim-
plifying description of the response on the basis of
log linear kinetics may be inappropriate and the
effect of shoulders and tails requires consideration.
When nonthermal constraints are proposed to reduce
numbers of low infective dose pathogens through
several log cycles, such as in meat fermentations, an
exact description of pathogen behaviour including
variability in response, must be incorporated in the
model if it is to be used with certainty.
While the botulinum cook may have been the first
predictive model (albeit only recently recognised as
such) to find widespread utility in the food industry,
reference to the potential use of predictive micro-
biology to describe microbial growth can be found
in the 1930s when Scott (1937) wrote: A knowledge
of the rates of growth of certain microorganisms at
different temperatures is essential to studies of the
spoilage of chilled beef. Having these data it should
be possible to predict the relative influence on spoil-
age exerted by the various organisms at each storage
temperature. Further, it would be possible to predict
the possible extent of the changes in populationsthat various organisms may undergo during the
initial cooling off of the sides of beef in the meat-
works when the meat surfaces are frequently at
temperatures very favourable to microbial prolifer-
ation.
Clearly, Scott understood the potential to use
accumulated kinetic data on microbial growth res-
ponses to predict the shelf life and safety of foods.
Despite being unable to realise its full potential due to
lack of computing power, it is salient to note that
Scotts work on the effects of temperature, wateractivity and CO2 concentration enabled shipments of
nonfrozen beef carcasses and quarters from the anti-
podes to the UKan early example of the Hurdle
Concept in action.
The literature remained relatively silent on predic-
tive microbiology until the 1960s and 1970s when
manuscripts began to appear addressing food spoilage
and food poisoning problems. The former issues were
investigated using kinetic models (Spencer and
Baines, 1964; Nixon, 1971; Olley and Ratkowsky,
1973a,b). An important theme in any scientific dis-
cipline is the recognition of overarching similarities as
a first step in the development of a mechanistic
understanding of the process involved. In investigat-ing the microbial spoilage of fish, Olley and Ratkow-
sky (1973a,b) recognised the fundamental similarity
of the response to temperature of many spoilage
processes and proposed a universal spoilage curve.
From this curve, these authors conceived the relative
rate concept that has become the keystone in the
application of predictive models and a forerunner to
variants such as the gamma concept (Zwietering et al.,
1996). The second area of research in predictive
microbiology in the 1970s that dealt with prevention
of botulism and other microbial intoxications was
based on probability models (Genigeorgis, 1981;
Roberts et al., 1981).
The 1980s saw a marked increase in interest in
predictive microbiology as a result of major food
poisoning outbreaks and consequent public (and polit-
ical) awareness of the requirement for a safe and
wholesome food supply. Both traditional pathogens
and foods (Salmonella in eggs) and emerging
pathogens (Listeria monocytogenes) with unusual
characteristics (psychrotrophy) contributed to the
prioritisation of food safety research by governments
in the USA, UK, other EU countries and Australia andNew Zealand.
Through the 1980s and a large part of the 1990s,
kinetic modelling approaches dominated the predic-
tive microbiology scene, but more recently, a return to
probability modelling has been evident.
This trend can be attributed to the following.
(i) Recognition that variability in response time
(generation time and lag phase duration) estimates are
not normally distributed but are usually described by a
gamma or even inverse Gaussian distribution where
response time variance is proportional to the square orthe cube of the mean response time (Ratkowsky et al.,
1996).
(ii) Emergence of dangerous pathogens (particu-
larly Escherichia coli 0157:H7) with very low infec-
tive doses where the knowledge base required
description of conditions to prevent their proliferation
or which lead to their inactivation.
(iii) Increased awareness of stochastic approaches
as a result of quantitative microbial risk assessment
studies.
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3. The modelling process
Predictive microbiology is concerned with the
accumulation and synthesis of knowledge. Ideally,all published, or otherwise archived knowledge on
microbial behaviour in foods should be accessible to
and accessed by researchers wishing to confirm or
advance the state of knowledge.
Clearly, this is not always (perhaps not often) the
case and numerous instances can be cited where
old papers were not located in literature searches,
for example, square root-type temperature dependence
models (Ratkowsky et al., 1982, 1983) were originally
proposed as a power function by Belehradek (1926).
This oversight was subsequently corrected with a
special tribute to Professor Jan Belehradek in the
Preface to the monograph Predictive Microbiol-
ogy: Theory and Application (McMeekin et al.,
1993).
Researchers and funding agencies should be aware,
despite the limitations of some publications, of the
cost benefits available from judicious use of published
work rather than total reliance on de novo generation
of data (Ross, 1999a). Optimum benefit is derived
when the retrieved knowledge is thoroughly and
systematically analysed to exclude that which is
patently erroneous or has been misinterpreted. Lackof critical evaluation during the review process or
when citing references may lead to legitimising con-
cepts and procedures that will subsequently inhibit the
acceptance of predictive microbiology as an effective
and reliable procedure to judge the microbial safety
and quality of foods.
Ross et al. (2000) in considering the theory and
philosophy of mathematical modelling drew attention
to the competing claims of empirical and mechanistic
models. The former are pragmatic in nature and
describe the data in a useful mathematical relation-ship. On the other hand, mechanistic models are
derived from a theoretical basis, provide interpretation
of the response observed in terms of the underlying
mechanisms and are more amenable to refinement as
knowledge of the system increases. Among the mod-
els commonly used in predictive microbiology, none
are purely mechanistic, many have some underlying
basis and some are simply curve-fitting exercises that
at the extreme are unique to the data used to generate
the model.
During the kinetic modelling boom of the 1980s,
two major modelling approaches were used.
(i) Models based on the sequential determination of
the effect of individual factors or growth rates, forexample, a square root or Arrhenius model for temper-
ature dependence to which terms for water activity,
pH etc. were added. Characteristically, the experimen-
tal methods involved close interval determinations for
each environmental factor tested.
(ii) Polynomial models based on response surface
methodology where experiments usually involved
simultaneous determination of the effects of several
factors on microbial behaviour. The selection of the
variables on the response surface was often deter-
mined by a central composite experimental design.
This suffered from an inability to determine ade-
quately the effect of sufficient factor combinations
across the entire multidimensional surface under con-
sideration, particularly at the edges.
While both approaches are empirical, proponents
of the former argue that they contain parameters with
biological relevance, whereas response surface, poly-
nomial models represent a black box. In these,
biological significance is hidden and cross product
and other terms that are needed to describe responses
may make the model a unique description of the data
set used for its generation. Recent trends indicatingincreased use of computational neural networks
advance the black box approach and may inhibit
the search for mechanistic and biologically relevant
models.
Ross et al. (2000) also commented on aspects of
practical model building including the range of char-
acteristics investigated (growth, death, survival, toxin
formation) and the variables modelled that often
include temperature, water activity, pH, nitrite con-
centration and gaseous atmosphere, and on occasions,
organic acid or other preservative concentrations. Thesequential process adopted in modelling usually con-
sists of developing a primary model to determine the
magnitude of the responses of interest such as max-
imum specific growth rate, lag phase duration, time to
reach a specified level (cell numbers or metabolites)
or death rate. A secondary model is then constructed
to show the dependence of these factors on environ-
mental conditions, and on occasions, the algorithm is
incorporated into computer software packages to
generate a tertiary model.
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At various stages within national predictive micro-
biology projects, for example, the UK MAFF Food
Micromodel Program, quality assurance committees
were established to prescribe the minimum standardsfor model development and validation. Several
authors have also defined experimental protocols
(e.g. McMeekin et al., 1993). Perhaps the occasion
of the 3rd International Conference on Predictive
Microbiology should reactivate the need to develop
minimum experimental standards. Bacterial taxono-
mists prescribe the minimum amount of experimental
data required to describe a new bacterial species. A
similar set of guidelines by experts in predictive
modelling may allow reviewers and editors to exam-
ine more closely journal submissions purporting to
contain predictive models.
4. Towards the growth/no growth interface
Monod (1949) in his classic review The Growth
of Bacterial Cultures stated that The growth of
bacterial cultures, despite the immense complexity
of the phenomena to which it testifies, generally obeys
relatively simple laws which make it possible to
define certain quantitative characteristics of the
growth cycle, essentially the three growth constants:total growth (G), exponential growth rate (R) and
growth lag (L). That these definitions are not purely
arbitrary and do correspond to physiologically distinct
elements of the growth cycle is shown by the fact that,
under appropriately chosen conditions, the value of
any one of the three constraints may change widely
without the other two being significantly altered. The
accuracy, the ease, the reproducibility of bacterial
growth constant determinations is remarkable and
probably unparalleled so far as biological quantitative
characteristic are concerned.Such an opinion from a Nobel Laureate would
have provided encouragement for early proponents of
predictive microbiology for whom a basic premise
was that the responses of microbial populations to
environmental factors are reproducible. Clearly, with-
out reproducible responses it would not be possible,
from past observations, to predict future behaviour.
However, Monod (1949) was primarily concerned
with defining the general shape of the bacterial growth
curve (a primary model) for organisms growing under
well-controlled laboratory conditions including stud-
ies of diauxie in which a series of growth phases could
be induced. His review did not extend to analysing the
effect of environmental factors on the magnitude ofthe three variables (secondary models) although this
possibility was foreshadowed: Under certain specific
conditions quantitative interpretations of the primary
effect of the agent studied may even be possible.
As we are now aware from predictive modelling
studies, growth rates under conditions that permit
rapid population development are remarkably repro-
ducible. We are also aware that estimates of lag phase
duration show greater variability and that as a pop-
ulation experiences progressively harsher conditions,
response times become longer and variability in-
creases markedly. Recognition of this variability and
its characterisation by a particular distribution was an
important step in the development of predictive mod-
elling (Ratkowsky et al., 1996). These observations
are entirely consistent with the general rule that bio-
logical processes display variability that must be
characterised if the ecology of organisms in any
environment is to be understood. Thus, as a microbial
population moves progressively towards conditions
that will eventually preclude growth (the growth/no
growth interface), the ability of kinetic models to
provide an accurate description becomes increasinglylimited. An appropriate strategy in this circumstance
is to select a response time consistent with the severity
of the microbial hazard and estimate the probability
that the population will respond more quickly than the
selected level (McMeekin et al., 1993).
5. At the growth/no growth interface
A consistent observation from many studies in
predictive microbiology is that there is a minimumfinite rate of growth beyond which population devel-
opment does not occur even with markedly extended
periods of incubation. This boundary may be set by a
single factor such as temperature or a combination of
factors, for example, temperature, water activity, pH
etc. Generally, when more than one factor constrains
population development, the absolute level of each
factor required to prevent growth is lessened. This is
the essence of the Hurdle Concept advocated for
many years by Professor Leistner and his colleagues
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at the Federal Centre for Meat Research in Kulmbach,
Germany (Leistner, 1978, 1992). The Hurdle Concept
seeks to determine the minimum set of conditions to
prevent the growth of pathogens, or better still, tocause inactivation. The goal is to produce foods that
can remain stable and safe (even without refrigeration)
and are acceptable organoleptically and nutritionally
due to the mild processes applied.
A commonly used analogy, introduced by Dr. M.
Cole, to describe that set of minimal processing
conditions is the Food Safety Cliff. The cliff edge
represents those sets of product formulations beyond
which foods are potentially unsafe and the top of the
cliff represents the set of conditions that just prevent
pathogenic microorganisms from growing. At a long
distance from the cliff edge, there is great certainty
that the food will be safe as pathogens have been
eliminated or are unable to grow. That confidence
decreases markedly as the cliff edge is approached.
Conditions distant from the cliff edge represent highly
processed foods, those nearer the edge are more
natural products including minimally processed foods.
Thus, knowledge of the position of the cliff edge can
be used to design foods that just prevent microbial
growth. This knowledge will be invaluable in opti-
mising the amount and stringency of processing so
that the aesthetic changes to the quality of the food areminimised.
Further, while the Hurdle Concept is widely accep-
ted as a food preservation strategy, its potential has
not been fully realised as it is a largely qualitative
concept, the application of which is often empirical.
The intelligent selection of hurdles in terms of the
number required, the intensity of each and the
sequence of application to achieve a specified out-
come provides significant potential to approach the
edge of the food safety cliff with certainty.
There are many possible physiological explana-tions to explain the cessation of growth including
denaturation of ribosomes, membrane lipid phase
changes, and energy diversion to deal with environ-
mental insults to the point where insufficient energy
remains to fuel biosynthetic processes (Knochel and
Gould, 1995). While the prospect of a new generation
of mild but effective processing techniques will
require a thorough understanding of microbial phys-
iology, considerable advances can be achieved by
modelling the growth/no growth interface. In effect,
this type of modelling quantifies the hurdle con-
cept.
Early attempts to define nongrowth conditions
were based on + or
observations (Christian andWaltho, 1962) with some of these studies used to
develop probability models for growth. A more sys-
tematic approach to interface modelling was reported
by Ratkowsky and Ross (1995) to predict the growth/
no growth interface forShigella flexnerias affected by
temperature, pH, water activity and nitrite concentra-
tion. The procedure involved modifying a growth rate
model by taking the logarithm of both sides of the
equation and replacing the left-hand side with a logit
term (logit p), where p is the probability of growth
occurring. This or similar approaches were subse-
quently used by Presser et al. (1998) for E. coli,
Bolton and Frank (1999) forL. monocytogenes, Ross
(1999a) forKlebsiella oxytoca, Salter et al. (2000) for
E. coliand Tiengunoon et al. (in press) for L. mono-
cytogenes.
6. The lag phase and fluctuating conditions
The growth/no growth interface represents a boun-
dary at which the growth rate is zero and the lag phase
is infinite. Probably more than any other factor,accurate determination of the lag phase has created
problems for predictive microbiologists. Indeed in
many practical applications of predictive models such
as the hygienic assessment of meat processing oper-
ations (e.g. Gill et al., 1991), the lag phase is ignored.
The great difficulty is that cells contaminating a food
product range in physiological competence from those
that are actively dividing, to those that display a
physiological lag phase, to those that are damaged
and require repair before resolving lag, to those that
have entered a state of suspended animation (viablebut nonculturable), to those that are dead. Further
modelling complications may arise when fluctuations
in environmental conditions are of sufficient magni-
tude or rapidity to induce a population that has
resolved its lag phase to once again enter one of the
lag states listed above.
The duration of the phase is affected by factors
such as the identity and phenotype of the bacterium
(Buchanan and Cygnarowicz, 1990), inoculum size
(Baranyi and Roberts, 1994), the physiological history
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of the population (McMeekin et al., 1993) and by
changes in the physiochemical environment such as
temperature (Zwietering et al., 1994), pH, water
activity and nutrient availability (Buchanan and Cyg-narowicz, 1990).
While studying the effect of temperature shifts and
fluctuations on growth rate, several authors have
noted effects on the lag phase (Walker et al., 1990;
Fu et al., 1991; Duh and Schaffner, 1993; Blackburn
and Davies, 1994; Membre et al., 1999). It has often
been observed that lag time is inversely proportional
to the maximum specific growth rate (Smith, 1985;
McMeekin et al., 1993; Baranyi and Roberts, 1994).
The time required to resolve the growth lag
depends on the growth rate of the organism, which
is dictated by the growth environment. Lag time
duration has often been considered erratic and evalu-
ation of predictive models has shown that lag times
are less reliably predicted than generation times. This
has usually been attributed to the effect of the prior
history of cells on the duration of the lag time.
Robinson et al. (1998) formalised a concept of the
lag time as being dictated by two elements:
(i) the amount of work required of the cell to adjust
to a new environment and/or repair injury due to the
shift to the new environment, and
(ii) the rate at which those repairs and adjustmentscan be made. The latter is presumed to respond to the
environment in the same way, relatively, that gener-
ation time does (i.e. if the environment causes the
generation time to double, the lag time will also
double).
In effect, physiological lag times before exponen-
tial growth commences reduce the potential growth of
an organism during a given period of time. The
potential exists to force an organism into a long lag
by manipulation of mild environmental change. More
severe environmental changes may lead to cell injuryor even death.
In situations characterised by variability and uncer-
tainty, the development of good mechanistic models is
impossible and of good empirical kinetic models
improbable. As was the case with kinetic growth
models near the growth/no growth interface, the
adoption of a stochastic or probability has proved to
be an effective option (Ross, 1999a). This work
demonstrated that the apparent variability in lag phase
duration can be reduced by introducing the concept of
relative lag times (RLTs) or generation time equiv-
alents, that is, the ratio of lag time to generation time.
Using this approach, a common pattern of distribution
of RLTs for a wide range of species across a widerange of conditions has emerged.
The introduction of the stochastic modelling
approach to describe lag phase duration will have a
profound effect on the application of predictive micro-
biology allowing operators to move away from the
worst-case scenario. We also foreshadow that the
stochastic procedures now widely used in microbial
risk assessments will find considerable utility in the
description of specific food-processing operations.
7. Beyond the growth/no growth interface
Beyond the growth/no growth interface, rapid
death induced by thermal energy or irradiation has
been relatively well characterised. However, pat-
terns of nonthermal death are less well established
and, as was the case with growth kinetics, slow
rates of decline are likely to display considerable
variability.
The general pattern observed when death is
induced by low water activity conditions is a rapid
phase followed a more gradual phase of decline.Generally, the magnitude of the rapid phase increases
with the severity of the challenge, but thereafter, the
rate of decline proceeds at approximately the same
rate. Under many circumstances, complete extinction
of the population is not achieved. With low pH-
induced death, a third more rapid decline phase is
observed that may be attributed to energy depletion as
a result of proton pumping to maintain cytoplasmic
pH homeostasis.
The importance of energy status is also seen in
markedly different responses to the sequence of wateractivity and pH challenges (Shadbolt et al., 2001).
Reduced water activity followed by reduced pH leads
to a gradual decline, whereas the reverse sequence
causes rapid death on application of the second
hurdle. Again this may be explained by postulating
that the initial acid challenge depletes the cells energy
reserves to the point where it is unable to deal with a
subsequent water activity challenge. Conversely, the
less energetically demanding water activity constraint
(Krist et al, 1998a) when applied first allows the cell
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to retain sufficient energy reserves to deal more
effectively with a subsequent acid challenge.
8. The interface between predictive microbiology
and microbial physiology
Monod (1949) was also aware that the quantitative
description of microbial population behaviour (ecol-
ogy) was inextricably linked to the underlying phys-
iology of the cell when he wrote:
There is little doubt that as a further advances are
made towards a more integrated picture of cell phys-
iology, the determination of growth constants will
have a much greater place in the arsenal of micro-
biology. Further he counselled The fallacy of con-
sidering certain naive mechanistic schemes, however,
as appropriate interpretations of unknown, complex
phenomena should be avoided.
The former statement reflects the development of
predictive microbiology in which the patterns of
responses observed provide clues to underlying phys-
iological events in the cell.
As an example, consider a typical Arrhenius plot of
bacterial growth. Theory predicts that a plot of the
natural logarithm of growth rate versus the reciprocal
of absolute temperature will yield a linear relation-ship, the slope of which is the apparent energy of the
reaction. While this is true for simple chemical reac-
tions, complex biological phenomena such as micro-
bial growth display continually downward sloping
curves. On occasions, these were interpreted as rep-
resenting two linear regions with different activation
energies (Mohr and Krawiec, 1980) where it is tempt-
ing to suggest that the discontinuity indicates a major
physiological change (e.g. membrane lipid phase
change) in the cell: perhaps an example of Monods
fallacy of a naive mechanistic scheme.What can be deduced from a typical Arrhenius plot
for bacterial growth is that there is a normal physio-
logical range where Arrhenius kinetics provide a
reasonable description of the observed response and
where a constant activation energy is appropriate.
Beyond that, region activation energy estimates
change continually: in the high-temperature region
due to irreversible denaturation and in the low-temper-
ature region due to reversible denaturation of macro-
molecules.
An alternative description of the effect of temper-
ature on microbial growth rates was provided by
Belehradek (1926) and revived by Ratkowsky et al.
(1982) as the square root model. In this model, asquare root transformation of data is preferred to a
logarithmic transformation resulting in a linear
response that is extrapolated to the theoretical mini-
mum temperature for growth (Tmin), that is, where the
regression line intersects the temperature axis of a
square root plot.
Belehradek (1930) was dismissive of the applica-
tion of chemical kinetics to biological processes when
he wrote: The problem of temperature coefficients in
biology was initiated by chemists and has suffered
from the beginning from this circumstance. Attempts
to apply chemical temperaturevelocity formulae (the
Q10 rule and the Vant HoffArrhenius law) to bio-
logical processes failed because some of the temper-
ature constants used in chemistry (Q10,m) can be saidnot to hold good in biological reactions. Neverthe-
less, while Belehradek-type kinetics provide a good fit
to data, a square root plot is perhaps less informative
of the changing energy demands outside the normal
physiological range that can be deduced from an
Arrhenius plot.
Observed patterns of response to lowered water
activity and pH also provide clues to the mechanismsby which these hurdles affect the microbial cell. As an
example, the constants of the microbial growth curve
respond consistently to decreasing water activity lev-
els viz.: the growth rate constant decreases, lag phase
duration increases and cell yield remains constant
until near the limiting level for growth. At this point,
a marked reduction in yield is observed.
When the information contained in the primary
model is transformed into a secondary model, the
optimum water activity is revealed together with a
linear response to decreasing water activity in thesuboptimal range (e.g. see Troller and Christian, 1978
forS. aureusand Krist et al., 1998a forE. coli). When
experiments are carried out with different humectants,
specific solute effects are also noted (Troller and
Christian, 1978).
Further, as water activity conditions become pro-
gressively harsher, a common observation is that the
minimum temperature for growth increases (e.g.
McMeekin et al., 1987). This observation could be
explained by invoking an energy diversion hypothesis
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(Csonka, 1989; Knochel and Gould, 1995). That is,
energy required to deal with the water activity hurdle
is unavailable to overcome the concurrent temperature
barrier to growth, and as a result, the minimumtemperature for growth must increase.
While superficially attractive, this explanation is
not consistent with the primary water activity/cell
yield response that indicates that over a wide water
activity range, all available substrate is converted into
approximately the same amount of biomass (Krist et
al., 1998a). A similar observation is made for temper-
ature/cell yield responses, and for both constraints, the
growth rate constant declines sequentially as temper-
ature and water activity decrease in the suboptimal
region.
Conversely, at lowered pH levels, cell yield de-
clines progressively but the growth rate constant is
maintained across a wide pH range (Krist et al.,
1998a). This response reflects the well-documented
requirement for cells to maintain a constant internal
pH consistent with efficient operation of enzymes and
the need to expend energy pumping protons from the
cytoplasm.
The mechanism of microbial response to low-water
activity stress involves the synthesis or accumulation
of compatible solutes. These compounds stabilise
enzyme structure and maintain them in an activeconfiguration. Compatible solutes are also known to
confer protective effects against low-temperature
stress (Ko et al., 1994), an observation consistent with
the similar yield and growth rate constant responses
observed at reduced temperatures and at reduced
water activities.
While Krist et al. (1998a) discounted major energy
diversion as a growth-limiting mechanism at lowered
water activity, the concept of a critical activation
energy was proposed (Krist et al., 1998b). This
hypothesis was derived from observations on E. coligrown without water activity limitation (0.997) and
under stressful conditions (0.977) with and without
the compatible solute, glycine betaine.
The normal physiological temperature range was
reduced by appropriately 50% ataw = 0.977 compared
with aw = 0.997 but by approximately 25% at aw =
0.977 in the presence of glycine betaine. The observed
minimum temperature for growth at aw = 0.977 was
25.8C from which a critical activation energy of 178kJ/mol was computed using the Arrhenius-based ther-
modynamic model of Ross (1999b). Applying this
critical activation energy value to the other conditions,
a minimum growth temperature of 12.1 C was
calculated at aw = 0.997 and 17.8 C at aw = 0.977plus glycine betaine. Both values were close to (f 1
C) of the observed minimum temperature.Above we described a method to model the
growth/no growth interface that is characterised by a
sharp delineation between growth and no growth
conditions. A physiological explanation for this obser-
vation may be embodied in the concept of a critical
activation energy for growth. In the case of water
activity and temperature hurdles, this may reflect
the degree of enzyme unfolding that is ameliorated
in the presence of compatible solutes. It would there-
fore be interesting to compare the stability of selected
enzymes at the same critical activation energy
achieved by various water activity/temperature com-
binations in the presence/absence of compatible
solutes. Furthermore, the critical activation energy
hypothesis should be extended by measurement of
the ATP expenditure required to maintain internal pH
homeostasis.
When considering survival and death kinetics, it is
important also to take into account the physiological
state of the organism and adaptive responses that
enhance resistance to unfavourable conditions. Thephenomenon of acid habituation provides a good
example of the phenotypic plasticity of microorgan-
isms.
Brown et al. (1997) provided, in part, a physio-
logical explanation for increased acid tolerance in
response to mild stress by characterising an increase
in the level of cyclopropane fatty acids in the cell
membrane. Production of these compounds is ener-
getically expensive (three ATPs per mole synthesised)
and membrane composition and acid tolerance return
to approximately that of unstressed cells when theacid constraint is removed. While an increase in
cyclopropane fatty acids per se may not be responsible
directly for increased acid tolerance, it is of interest to
note that in acidophiles such as Thiobacillus, >60%
of membrane lipid fatty acids are of the cyclopropane
variety (Levin, 1971).
In keeping with the interface theme of this paper, it
is clear that the bacterial cell membrane is a crucial
interface between the cell and the surrounding en-
vironment. In relation to growth at reduced pH levels,
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active transport of protons across the membrane is
essential and for survival rearrangement of mem-
brane fatty acid composition appears to have a central
role.Advances in instrumentation that can monitor
membrane-related events in real time offer the pros-
pect of increased understanding of the physiological
processes that underlie the patterns of growth and
death embodied in predictive models. Examples
include fluorescence ratio imaging techniques that
allow real time observation of changes in internal
pH in response to environmental insults (Siegumfeldt
et al., 2000) and the MIFEk System that provides
direct measurement of ion fluxes across cell mem-
branes. Originally designed for use with plants cells
(Shabala et al., 1997; Shabala, 2000), the MIFEk
System has recently been adapted for use with large
microbial cells (Shabala et al., 2001b) and microbial
films deposited or grown on glass surfaces (Shabala et
al., 2001a). When used in tandem, fluorescence ratio
imaging and the MIFEk System will provide a
powerful combination to assess the efficacy of proto-
cols to disturb intracellular homeostasis and the role
of membrane transport systems in maintaining
homeostasis. Together, the techniques have the poten-
tial to provide information that will be the basis of a
new generation of mild but effective food preservationprocedures. The speed at which information on the
efficacy of antimicrobial combinations will accumu-
late will be measured in hours rather than days or
weeks required using conventional microbiology. As
an example, using the MIFEk System, we have
demonstrated in 2 3 h that proton efflux from a
Thraustochytrid sp. ceases at 8 C. Collapse of thisessential physiological process presumably correlates
with crystallisation of the cell membrane and effec-
tively indicates the minimum temperature for growth
of the organism. By contrast, temperature gradientincubator experiments to determine the minimum
temperature for growth can continue for up to 90 days.
9. The interface with information technology
Although Scott (1937) had devised the concept of
predictive microbiology, in reality, the development of
predictive models was constrained until the advent of
the computer and information technology age. Sim-
ilarly, the application of predictive models is largely
through the use of information technology. Impor-
tantly, this resource allows the continual accumulation
of knowledge and, as a consequence, should lead todevelopment of better models and greater scope for
their application.
As an example, consider the work of Gill et al. (e.g.
Gill et al., 1991) on modelling the hygienic efficacy
of meat processing operations. Gills original model
was based only on the temperature response of
E. coliusing a limited data set. Application using the
Delphik temperature logging system relied solely on
temperature history information and ignored other
effects (such as water activity) known to limit micro-
bial growth on meat carcasses during chilling. This
is a typical worst-case scenario but nevertheless led to
a useful concept, the process hygiene index (PHI),
based on the potential growth ofE. coli at the slowest
cooling point of the carcass. The criteria for the three-
class sampling plan devised as a decision support
system for the PHI were derived on the basis of
cooling regimes known to produce meat of adequate
hygienic quality. From this beginning, Gill and his
colleagues (Gill et al., 1991) in New Zealand and
Canada developed PHI recommendations for spray-
chilled carcasses, hot boned product, offal handling
and the transport and distribution of meat.Models forE. coli growth developed subsequently
are based on much more extensive data sets and
include the effect of water activity, pH and lactate
concentration (Presser et al., 1997). This emphasises
that knowledge is cumulative, can be stored, retrieved
and interpreted and provides greater precision in
describing the quantitative microbial ecology of
foods.
The accumulation of knowledge is also the corner-
stone of quantitative microbial risk assessment. This
procedure has been trialed as a measure of thehygienic equivalence of foods in international trade
and involves hazard identification, exposure assess-
ment, dose response assessment and risk character-
isation. To date, most microbial risk assessments have
been big picture attempts to quantify the risk of
disease arising from certain microorganism/food com-
binations (Cassin et al., 1998). While these may be
valuable in a comparative sense and indicate where
knowledge is lacking, they are always characterised
by variability and uncertainty. The latter category
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places a particular constraint on achieving a definitive
outcome from a quantitative risk assessment.
If uncertainty is removed (and variability mini-
mised), the stochastic approaches embodied in riskassessment techniques should have the potential to
characterise the microbiological consequences of a
food-processing operation. To test this hypothesis,
we selected production of fresh salmon fillets and
attempted to define those factors mainly responsible
for limiting shelf life (Rasmussen et al., 2001).
Characterisation of the harvesting and processing
operations allowed development of a process risk
model to quantify the risk that the stated shelf life
will not be achieved. Bacterial numbers in water and
ice and on fish and contact surfaces were collected
over a period of 9 months and fitted to distribution
functions. The model constructed using Analytica 2.0
predicted mean ice slurry water counts of log 3.36/ml
(observed 3.35/ml), fish surface contamination levels
to be log 3.31/ml (observed log 3.23/ml). The average
predicted shelf life at 4C was 6.5 days (observed 6.2days). An importance analysis carried out on the
model using Analytica demonstrated that storage
temperature had a much greater influence on shelf
life than contamination levels.
This demonstrates clearly that when sufficient
information is available and uncertainty is eliminated,a stochastic approach can provide an accurate micro-
bial profile of a specific processing operation. We
predict that stochastic modelling packages such as @
Risk and Analytica will be used increasingly to
characterise food-processing operations and to sug-
gest effective strategies to achieve food safety and/or
food quality objectives.
10. The interface with food safety initiatives
Predictive microbiology through interfaces with
many other disciplines has emerged as a paradigm
of modern food microbiology. It provides a scientific
basis to underpin the HACCP concept and quantita-
tive microbial risk assessment.
A dynamic interaction exists between HACCP (the
tool by which safety is built into food-processing
operations) and risk assessment (a measure of the
effectiveness of HACCP on other safety assurance
programs). This interaction may be facilitated by
developing food safety objectives but cannot occur
effectively without quantitative information.
Predictive microbiology assists the formulation of
HACCP plans by identifying hazards and criticalcontrol points and in specifying limits and corrective
action (Miles and Ross, 1999). With QMRA, predic-
tive models have a particular role as a cost-effective
means to provide the exposure assessment informa-
tion, a critical element in risk assessment.
11. Conclusions
Microbial food safety is of concern to industry,
government and the population at large with each
group anticipating the provision of a safe and whole-
some food supply as a basic tenet of a developed
society.
It is clear that predictive microbiology has a major
role to play in meeting this aspiration and that already
it has become an essential element of modern food
microbiology. This status has been achieved by con-
tinually improving our understanding of the quantita-
tive microbial ecology of foods and by developing
interfaces with other disciplines to apply the knowl-
edge contained in predictive models. Its utility will be
further enhanced when predictive microbiology isrecognised as an effective rapid method.
We foreshadow that consolidation of existing and
development of new interfaces will lead to acceptance
of predictive microbiology as a mature subdiscipline
of microbiology. In particular, alignment of quantita-
tive knowledge of microbial behaviour in foods with
understanding of underlying physiological processes
offers the prospect of a new generation of mild, but
effective, food preservation procedures.
Acknowledgements
The authors thank the many postgraduate students
and colleagues for contributions to predictive micro-
biology research at the University of Tasmania over a
period of 25 years. We particularly acknowledge the
continuing financial support of Meat and Livestock
Australia and assistance from the Department of
Industry Science and Resources to attend the 3rd
International Conference on Predictive Modelling in
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Foods, Leuven, Belgium, September 2000. Copies of
the oral presentation at Leuven on which this paper is
based are available electronically in Power-Point
format from the corresponding author.
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