1-s2.0-s0168160501006638-main

8/13/2019 1-s2.0-S0168160501006638-main

1/13

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

International Journal of Food Microbiology 73 (2002) 395407

8/13/2019 1-s2.0-S0168160501006638-main

2/13

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

T.A. McMeekin et al. / International Journal of Food Microbiology 73 (2002) 395407396

8/13/2019 1-s2.0-S0168160501006638-main

3/13

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.

T.A. McMeekin et al. / International Journal of Food Microbiology 73 (2002) 395407 397

8/13/2019 1-s2.0-S0168160501006638-main

4/13

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.


8/13/2019 1-s2.0-S0168160501006638-main

5/13

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


8/13/2019 1-s2.0-S0168160501006638-main

6/13

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


8/13/2019 1-s2.0-S0168160501006638-main

7/13

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


8/13/2019 1-s2.0-S0168160501006638-main

8/13

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


8/13/2019 1-s2.0-S0168160501006638-main

9/13

(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,


8/13/2019 1-s2.0-S0168160501006638-main

10/13

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


8/13/2019 1-s2.0-S0168160501006638-main

11/13

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


8/13/2019 1-s2.0-S0168160501006638-main

12/13

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.

References

Baranyi, J., Roberts, T.A., 1994. A dynamic approach to predicting

bacterial growth in food. Int. J. Food Microbiol. 23, 277 294.

Belehradek, J., 1926. Influence of temperature of biological pro-

cesses. Nature (London) 118, 117 118.

Belehradek, J., 1930. Temperature coefficients in biology. Biol.

Rev. Biol. Proc. Cambridge Philos. Soc. 5, 3058.

Blackburn, C., Davies, A.R., 1994. Effects of pre-conditioning on

pathogenic bacteria in foods. Food Technol. Int., 37 40.

Bolton, L.F., Frank, J.F., 1999. Defining the growth of Listeria

monocytogenes in Mexican-style cheese based on salt, pH and

moisture content. J. Food Prot. 62, 601609.

Brown, J.L., Ross, T., McMeekin, T.A., Nichols, P.D., 1997. Acid

habituation ofEscherichia coli and the potential role of cyclo-

propane fatty acids in low pH tolerance. Int. J. Food Microbiol.

37, 163173.

Buchanan, R.L., Cygnarowicz, M.L., 1990. A mathematical ap-

proach toward defining and calculating the duration of the lag

phase. Food Microbiol. 7, 237 240.

Buchanan, R.L., 1997. Identifying and controlling emerging food

borne pathogens. Emerg. Infect. Dis. 3, 517 522.

Cassin, M.H, Lammerding, A.M., Todd, E.C.D., Ross, W., McColl,

R.S., 1998. Quantitative risk assessment for Escherichia coli

O157:H7 in ground beef hamburgers. Int. J. Food Microbiol.41, 21 44.

Christian, J.H., Waltho, J.A., 1962. The water relations of staph-

ylococci and micrococci. J. Appl. Bacteriol. 25, 369377.

Csonka, L.N., 1989. Physiological and genetic responses of bacteria

to osmotic stress. Microbiol. Rev. 53, 121147.

Duh, Y.-H., Schaffner, D.W., 1993. Modelling the effect of temper-

ature on the growth rate and lag time ofListeria monocytogenes.

J. Food Prot. 56, 205 210.

Esty, J.R., Meyer, K.F., 1922. The heat resistance of the spore ofB.

botulinus and allied anaerobes XI. J. Infect. Dis. 31, 650663.

Fu, B., Taoukis, P.S., Labuza, T.P., 1991. Predictive microbiology

for monitoring spoilage of dairy products with temperature func-

tion integrators. J. Food Sci. 56, 12091215.

Genigeorgis, C.A., 1981. Factors affecting the probability of growthof pathogenic microorganisms in foods. J. Am. Vet. Med. As-

soc. 179, 14101417.

Gill, C.O., Harrison, J.C.L., Phillips, D.M., 1991. Use of temper-

ature function integration technique to assess the hygienic effi-

ciency of a beef carcass cooling process. Food Microbiol. 8,

8394.

Knochel, S., Gould, G., 1995. Preservation microbiology and safety:

quo vadis? Trends Food Sci. Technol. 6, 127131.

Ko, R., Smith, L.T., Smith, G.C., 1994. Glycine betaine confers

enhanced osmotolerance and cryotolerance on Listeria monocy-

togenes. J. Bacteriol. 176, 426431.

Krist, K., Ross, T., McMeekin, T.A., 1998a. Final optical density

and growth rate: effects of temperature and NaCl differs from

acidity. Int. J. Food Microbiol. 43, 195204.

Krist, K., Ross, T., Olley, J., 1998b. A mechanism for the limitation

of microbial growth by temperature and water activity. Proc.Poster Sessions, ISOPOW 7, MayJune 1998, Helsinki, Fin-

land. Hakapaino Oy, Helsinki, pp. 3741.

Lederberg, J., 1997. Infectious disease as an evolutionary paradigm.

Emerging Infect. Dis. 3, 417423.

Leistner, L., 1978. Hurdle effect and energy saving. In: Downey,

W.K. (Ed.), Food Quality and Nutrition. Applied Science Publ.,

London, pp. 553557.

Leistner, L., 1992. Food Preservation by combined methods. Food

Res. Int. 25, 151 158.

Levin, R.A., 1971. Fatty acids of Thiobacillus thioxidans. J. Bacter-

iol. 108, 992 995.

McMeekin, T.A., Chandler, R.E., Doe, P.E., Garland, C.D., Olley,

J., Putro, S., Ratkowsky, D.A., 1987. Model for the combined

effect of temperature and water activity on the growth rate of

Staphylococcus xylosus. J. Appl. Bacteriol. 62, 543550.

McMeekin, T.A., Olley, J., Ross, T., Ratkowsky, D.A., 1993. Pre-

dictive Microbiology: Theory and Application. Research Stud-

ies Press, Taunton, UK.

McMeekin, T.A., Brown, J.L., Krist, K., Miles, D., Nuemeyer, K.,

Nichols, D.S., Olley, J., Presser, K., Ratkowsky, D.A., Ross, T.,

Salter, M., Soontranon, S., 1997. Quantitative microbiology: a

basis for food safety. Emerging Infect. Dis. 3, 541 549.

Membre, J.-M., Ross, T., McMeekin, T.A., 1999. Behaviour of

Listeria monocytogenes under combined chilling processes.

Lett. Appl. Microbiol. 28, 216220.

Miles, D.W., Ross, T., 1999. Identifying and quantifying risks in the

food production chain. Food Aust. 51, 298303.Mohr, P.W., Krawiec, S., 1980. Temperature characteristics and

Arrhenius plots for nominal psychrophiles, mesophiles and ther-

mophiles. J. Gen. Microbiol. 121, 311 317.

Monod, J., 1949. The growth of bacterial cultures. Annu. Rev.

Microbiol. 3, 371394.

Nixon, P.A., 1971. Temperature integration as a means of assessing

storage conditions. Report on Quality in Fish Products, Seminar

No. 3. Fishing Industry Board, Wellington, New Zealand, pp.

3444.

Olley, J., Ratkowsky, D.A., 1973a. Temperature function integration

and its importance in storage and distribution of flesh foods

above the freezing point. Food Technol. Aust. 25, 6673.

Olley, J., Ratkowsky, D.A., 1973b. The role of temperature integra-

tion in monitoring fish spoilage. Food Technol. N. Z. 8, 147153.

Presser, K., Ratkowsky, D.A., Ross, T., 1997. Modelling the growth

rate ofEscherichia coli as a function of pH and lactic acid

concentration. Appl. Environ. Microbiol. 63, 2355 2360.

Presser, K., Ross, T., Ratkowsky, D.A., 1998. Modelling the growth

limits (growth/no growth) interface of Escherichia coli as a

function of pH, lactic acid and temperature. Appl. Environ.

Microbiol. 64, 17331779.

Rasmussen, S.K.J., Ross, T., Olley, J., McMeekin, T.A., 2001. A

process risk model for the shelf life of Atlantic salmon fillets.

Int. J. Food Microbiol., in press.


8/13/2019 1-s2.0-S0168160501006638-main

13/13

Ratkowsky, D.A., Ross, T., 1995. Modelling the bacterial growth/no

growth interface. Lett. Appl. Microbiol. 20, 2933.

Ratkowsky, D.A., Olley, J., McMeekin, T.A., Ball, A., 1982. Rela-

tionship between temperature and growth rate of bacterial cul-

tures. J. Bacteriol. 149, 15.Ratkowsky, D.A., Lowry, R.K., McMeekin, T.A., Stokes, A.N.,

Chandler, R.E., 1983. Model for bacterial culture growth rate

throughout the entire biokinetic temperature range. J. Bacteriol.

154, 1222 1226.

Ratkowsky, D.A., Ross, T., Macario, N., Dommett, T.W., Kam-

perman, L., 1996. Choosing probability distributions for mod-

elling generation time variability. J. Appl. Bacteriol. 80, 131

137.

Roberts, T.A., Gibson, A.M., Robinson, A., 1981. Prediction of

toxin production by Clostridium botulinum in pasteurised pork

slurry. J. Food Technol. 16, 337355.

Robinson, T.P., Ocio, M.J., Kaloti, A., Mackey, B.M., 1998. The

effect of growth environment on the lag phase ofListeria mono-

cytogenes. Int. J. Food Microbiol. 44, 8392.

Ross, T., 1999a. Predictive Microbiology Models in the Meat In-

dustry. Meat and Livestock Australia, Sydney, Australia, 196

pp.

Ross, T., 1999b. Assessment of a theoretical model for the effects of

temperature on bacterial growth rate. Proc. Conf. No. 1997/2 of

Commission C2, Quimper, France. Int. Inst. Refrig., Paris, pp.

6471.

Ross, T., McMeekin, T.A., Baranyi, J., 2000. Predictive microbiol-

ogy and food safety. In: Robinson, R.K., Batt, C.A., Patel, P.D.

(Eds.), Encyclopedia of Food Microbiology. Academic Press,

San Diego, pp. 16991710.

Salter, M.A., Ross, T., Ratkowsky, D.A., McMeekin, T.A., 2000.

Modelling the combined temperature and salt (NaCl) limits forgrowth of a pathogenic Escherichia colistrain using generalised

non-linear regression. Int. J. Food Microbiol. 61, 159167.

Scott, W.J., 1937. The growth of microorganisms on ox muscle: II.

The influence of temperature. J. Counc. Sci. Ind. Res. Aust. 10,

338350.

Shabala, S., 2000. Ionic and osmotic components of salt stress

specifically modulate net ion fluxes from bean leaf mesophyll.

Plant, Cell Environ. 23, 825837.

Shabala, S.N., Newman, I.A., Morris, J., 1997. Oscillations in H +

and Ca2 + ion fluxes around the elongation region of corn roots

and effects of external pH. Plant Physiol. 113, 111 118.

Shabala, L., Ross, T., Newman, I., McMeekin, T.A., 2001a. Mea-

surements of net ion fluxes and intracellular concentration

changes of H+

, Ca2 +

, K+

and NH4 +

inEscherichia coli usingion-selective microelectrodes. J. Microbiol. Methods 46, 119

129.

Shabala, L., Shabala, D., Ross, T., McMeekin, T.A., 2001b. Mem-

brane transport activity and ultradian ion flux oscillations asso-

ciated with the cell cycle of Thraustochytridiumsp Aust. J. Plant

Physiol. 28, 8799.

Shadbolt, C., Ross, T., McMeekin, T.A., 2001. Differentiation of the

effects of lethal pH and water activity: food safety implications.

Lett. Appl. Microbiol. 32, 99102.

Siegumfeldt, H., Techinger, K.B., Jakobsen, M., 2000. Dynamic

changes of intracellular pH in individul lactic acid bacterium

cells in response to a rapid drop in extracellular pH. Appl.

Environ. Microbiol. 66, 23302335.

Smith, M.G., 1985. The generation time, lag time and minimum

temperature of growth of coliform organisms on meat, and the

implications for codes of practice in abattoirs. J. Hyg. Camb. 94,

289300.

Spencer, R., Baines, C.R., 1964. The effect of temperature on the

spoilage of wet fish: I. Storage at constant temperature between

1C and 25 C. Food Technol. Champ. 18, 769772.

Tiengunoon, S., Ratkowsky, D.A., McMeekin, T.A., Ross, T., 2000.

Growth limits ofListeria monocytogenes as a function of tem-

perature, pH, NaCl, and lactic acid. Appl. Environ. Microbiol.

66, 4979 4987.

Troller, J.A., Christian, J.H.B., 1978. Water Activity and Food.

Academic Press, New York.

Walker, S.J., Archer, P., Banks, J.G., 1990. Growth limits ofListeriamonocytogenes at refrigeration temperatures. J. Appl. Bacteriol.

68, 157162.

Zwietering, M.H., deWit, J.C., Cuppers, H.G.A.M., vant Reit, K.,

1994. Modeling of bacterial growth with shifts in temperature.

Appl. Environ. Microbiol. 60, 204213.

Zwietering, M.H., deWit, J.C., Notermans, S., 1996. Application of

predictive microbiology to estimate the number ofBacillus cer-

eus in pasteurised milk at the point of consumption. Int. J. Food

Microbiol. 30, 5570.


1-s2.0-s0168160501006638-main

Documents