www.elsevier.com/locate/ijfoodmicro

International Journal of Food Microbiology 98 (2005) 89–105

A fuzzy logic-based model for the multistage high-pressure

inactivation of Lactococcus lactis ssp. cremoris MG 1363

K.V. Kilimanna, C. Hartmanna, A. Delgadoa, R.F. Vogelb, M.G. Ganzleb,*

aLehrstuhl fur Fluidmechanik und Prozessautomation, Technische Universitat Munchen, Weihenstephaner Steig 23,

D-85350 Freising, GermanybLehrstuhl fur Technische Mikrobiologie, Technische Universitat Munchen, Weihenstephaner Steig 16, D-85350 Freising, Germany

Received 22 April 2003; received in revised form 29 October 2003; accepted 9 May 2004

Abstract

The high-pressure inactivation (200 to 600 MPa) of Lactococcus lactis ssp. cremorisMG 1363 suspended in milk buffer was

investigated with both experimental and theoretical methods. The inactivation kinetics were characterised by the determination

of the viable cell counts, cell counts of undamaged cells, LmrP activity, membrane integrity, and metabolic activity. Pressures

between 200 and 600 MPa were applied, and pressure holding times were varied between 0 and 120 min. Experiments were

carried out in milk buffer at pH values ranging between 4.0 and 6.5, and the effect of the addition of molar concentrations of

NaCl and sucrose was furthermore determined.

The inactivation curves of L. lactis, as characterised by viable cell counts, exhibited typical sigmoid asymmetric shapes.

Generally, inactivation of the membrane transport system LmrP was the most sensitive indicator of pressure-induced sublethal

injury. Furthermore, the metabolic activity was inactivated concomitant with or prior to the loss of viability. Membrane integrity

was lost concomitant with or later than cell death. For example, treatments at 200 MPa for 60 min in milk buffer did not

inactivate L. lactis, but fully inactivated LmrP activity and reduced the metabolic activity by 50%. The membrane integrity was

unaffected. Thus, the assay systems chosen are suitable to dissect the multistep high-pressure inactivation of L. lactis ssp.

cremoris MG 1363.

A fuzzy logic model accounting for the specific knowledge on the multistep pressure inactivation and allowing the

prediction of the quantities of sublethally damaged cells was formulated. Furthermore, the fuzzy model could be used to

accurately predict pressure inactivation of L. lactis using conditions not taken into account in model generation. It consists of

160 rules accounting for several dependent and independent variables. The rules were generated automatically with fuzzy

clustering methods and rule-oriented statistical analysis. The set is open for the integration of further knowledge-based rules. A

very good overall agreement between measured and predicted values was obtained. Single, deviating results have been

identified and can be explained to be measurement errors or model intrinsic deficiencies.

D 2004 Elsevier B.V. All rights reserved.

Keywords: High-pressure treatment; Multistep inactivation; Fuzzy modelling

0168-1605/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.ijfoodmicro.2004.05.010

* Corresponding author. Tel.: +49-8161-713204; fax: +49-

8161-713327.

E-mail address: michael.gaenzle@wzw.tum.de (M.G. Ganzle).

1. Introduction

The treatment of food and biological matter with

high hydrostatic pressures (HP) up to 1 GPa is

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–10590

generally carried out at ambient temperature in a batch

process, where the sample is compressed to the desired

pressure level which is maintained for several minutes.

High hydrostatic pressure has multiple effects on

biological systems, such as phase transitions of water

and biopolymers, the denaturation of proteins, the

inactivation of enzymes, and the inactivation of micro-

organisms, whereas levels of aroma compounds and

vitamins remain unchanged (Wouters et al., 1998).

Consequently, high-pressure effects allow a wide

spectrum of potential applications in food technology.

In addition to the bactericidal effect of high-pressure

treatment (Knorr, 1996), sensorial properties, func-

tional properties, and shelf life may be affected (Butz

et al., 2002; Harte et al., 2002; Krebbers et al., 2002).

Changes in the texture or the colour of foods are often

related to the denaturation of proteins and modifica-

tions of the activities of enzymes during the HP

treatment (Fachin et al., 2002).

High-pressure treatment is used as an alternative

food preservation process for the inactivation of

spoilage microorganisms and pathogens that has less

detrimental effects on sensorial and nutritional quali-

ties of food when compared to thermal processing.

The wide application of pressure processing for food

preservation requires the availability of reliable math-

ematical models based on adequate knowledge on

those aspects of bacterial physiology governing inac-

tivation by pressure (Smelt et al., 2002).

Moderately high pressures are shown to cause a

sublethal injury, from which the organisms recover

only on nonselective media (Kalchayanand et al.,

1994; Patterson et al., 1995; Hauben et al., 1996;

Ulmer et al., 2000). Many foods are selective media

due to their particular properties, such as pH value and

presence of antimicrobial compounds, as well as their

thermal history. In those foods, pressure inactivation

of specific resistance mechanisms required for growth

or survival in these products is sufficient for preser-

vation (Garcia-Graells et al., 1998; Molina-Gutierrez

et al., 2002b; Ulmer et al., 2002). On the other hand,

food components may reduce the bactericidal effects

of pressure or fully counteract pressure effects on

microbial viability (Hauben et al., 1998; Molina-

Gutierrez et al., 2002a).

Damage to bacterial membranes and membrane-

bound enzyme systems is assumed to be a major cause

of pressure-induced cell death (Pagan and Mackey,

2000; Smelt et al., 2002; Ulmer et al., 2002). Inacti-

vation of membrane-bound enzymes involved in pH

homeostasis accounts for the loss of acid resistance in

lactic acid bacteria and Escherichia coli (Wouters et

al., 1998; Pagan and Mackey, 2000; Molina-Gutierrez

et al., 2002b). Sublethal pressure treatments inactivate

HorA, an ATP-dependent MDR transport enzyme

involved in hop resistance of Lactobacillus plantarum

(Ulmer et al., 2002). Furthermore, HP also affects the

metabolic activity and induced morphological modifi-

cations. Ribosomal destruction in E. coli and Listeria

monocytogenes results in metabolic malfunctions con-

tributing to cell death (Isaacs et al., 1995). In Lacto-

bacillus viridescens were observed cavities between

cytoplasmic membrane and outer cell wall after HP at

400 MPa (Park et al., 2001).

The increasing knowledge base concerning the

various effects of pressure, pressure holding time,

temperature, and additives is a prerequisite for predic-

tive models of bacterial inactivation during HP pro-

cessing and its application in the food industry. Current

modelling of high-pressure inactivation mostly relies

on differential equation models, where kinetics of

surviving cells or kinetics of the inactivation of im-

portant enzymes as a function of pressure, temperature,

and time (Ludikhuyze et al., 1997; Erkmen, 2001; Lee

et al., 2001; Fachin et al., 2002) are used to describe the

whole inactivation process. The integration of further

knowledge into these models requires the formulation

of further differential equations with additional param-

eters that have to be quantified by experimental inves-

tigations. This is probably one reason why the present

approaches do not regard the physiological activities of

the examined population, whereas the examination of

the physiological status may give important indications

for using HP more effectively. Furthermore, it has been

shown that the formulation of the dependency of

kinetic parameters on pressure and temperature by

Arrhenius relationships sometimes fails. This has pro-

moted the use a kinetic parameter prediction based on

artificial neural networks. The knowledge-based data

analysis promised good results of prediction. The

drawback of artificial neural networks is the black

box approach, which does not allow the detection of

biological and physiological mechanisms of micro-

organisms during HP (Geeraerd et al., 1998).

A Fuzzy logic approach potentially avoids the

drawbacks of those modeling approaches currently

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 91

used to predict pressure effects on enzymes and

cellular systems. Fuzzy logic allows the simple

integration of expert knowledge. It compensates a

large bandwidth in the experimental data arising

from variable experimental conditions. Obvious

errors in the experimental data can be eliminated

without changing the overall structure of the model.

A multivariable prediction as mentioned above can

be easily realised. This functionality comprises the

potential to detect correlations between different

state variables. Finally, many high pressure-induced

effects are still unexplained, and therefore, a deter-

ministic approach based on clear microbiological

and physical concepts seems to be not feasible at

present.

It was the aim of this work to provide a knowledge

and data-based model approach for the pressure-in-

duced inactivation of Lactococcus lactis that allows

the integration of the current knowledge on the

multistage inactivation of this organism on the basis

of fuzzy logic rules.

The model aimed to predict the viability and

sublethal injury of L. lactis as well as the activity of

LmrP, a proton motive force dependent multidrug

transport enzyme, the membrane integrity, and the

metabolic activity of L. lactis as a function of pressure

level, pressure holding time, and several substrate

additives. It is based on experimental data covering

the pressure range of 200 to 600 MPa, pH values

between 4.0 and 6.5, and the presence of additives

known to exert a protective effect towards pressure-

induced inactivation.

2. Materials and methods

2.1. Microorganisms and media

L. lactis ssp. cremoris MG 1363 was grown at 30

jC in M17 broth (Merck, Darmstadt, Germany)

supplemented with 1% glucose. Cells of an overnight

culture were harvested by centrifugation, washed, and

resuspended in buffer to cell counts of about 109 cells

ml� 1. This buffer was designated ‘‘milk buffer’’

because it was intentionally set up to resemble whey

(Molina-Gutierrez et al., 2002a) and contained the

following compounds (in g l� 1): KCl, 1.1;

MgSO4�7H2O, 0.7110; NaH2PO4�2H2O, 1.874;

CaSO4�2H2O, 1.0; CaCl2�2H2O, 0.99; citric acid,

2.0; lactose, 52.0. The pH was adjusted to pH 6.5.

Where indicated, the following compounds were

added to the buffer: mannitol (1 M); sucrose (0.5,

1.0, 1.5 M), NaCl (1, 2, 3, or 4 M) or milk buffer was

varied by different pH values.

2.2. High-pressure treatments

Pressure treatment was carried out at a pressure of

200, 300, and 600 MPa in different buffer systems for

model establishment. All parameter combinations

used for model establishment are given in Table 1.

The fuzzy model was validated by experiments car-

ried out at pressures of 200, 250, 350, 400, and 500

MPa. In all pressure treatments, the compression/

decompression rate was 200 MPa min� 1, the pressure

temperature was 20 jC, and various time intervals

(0–120 min) were used. For each high-pressure

inactivation kinetic, untreated cultures and cultures

sterilised by treatment with 80 jC heated water for 15

min were used to design control values and calibration

samples containing 100%, 50%, 25%, 12.5%, 6.25%,

3.125%, 1.5625%, and 0% viable cells. All pressure

inactivation kinetics were performed at least in dupli-

cate, and results are reported as meanF standard

deviation.

2.3. Colony-forming units and counts of undamaged

cells

After pressure treatment, cell suspensions of each

vial were diluted and plated on M17 agar (Merck) or

M17 agar containing 3% NaCl for the determination

of viable and undamaged cell counts, respectively.

The plates were incubated for 24 h at 30 jC under

aerated conditions and for 48 h to assess undamaged

cells under same conditions as described above.

2.4. Metabolic activity

The determination of metabolic activity of pres-

sure-treated L. lactis was carried out according to

Ulmer et al. (2000). Cells from 1 ml pressure-

treated cultures were harvested by centrifugation.

The supernatant was removed and the pellet resus-

pended in 1 ml phosphate buffer [PBO (g l� 1):

H2KPO4, 6.8; MgSO4�7H2O, 0.1; MnSO4�1H2O,

Table 1

Parameter combinations used for model establishment

Pressure Parameters analysed Additive

200 MPa Cell counts, undamaged

cell counts, MI, MA,

LmrP activitya

None

Cell counts, LmrP

activity

0.5 M sucrose

Cell counts, undamaged

cell counts

1 M mannitol

Cell counts, undamaged

cell counts, LmrP activity

4 M NaCl

300 MPa Cell counts, undamaged

cell counts, MI,

MA, LmrP activitya,b

None

Cell counts, undamaged

cell countsbpH 6.0

Cell counts, undamaged

cell countsbpH 5.0

Cell counts, undamaged

cell countsbpH 4.0

Cell counts, undamaged

cell counts

0.5 M

sucrose

Cell counts, undamaged

cell counts

pH 6.0 and

0.5 M sucrose

Cell counts, undamaged

cell counts

pH 5.0 and

0.5 M sucrose

Cell counts, undamaged

cell counts

pH 4.0 and

0.5 M sucrose

Cell counts 1 M NaCl

Cell counts, LmrP activitya 4 M NaCl

MI, MAa Milk serumc

400 MPa Cell countsa None

Cell countsa 0.5 M sucrose

Cell countsa 1 M sucrose

Cell countsa 1.5 M sucrose

Cell countsa 1 M NaCl

Cell countsa 2 M NacCl

Cell counts 1 M NaCl and

2.5 mM glycine

betaine

Cell countsa 2 M NaCl and

2.5 mM glycine

betaine

Cell counts 3 M NaCl and

2.5 mM glycine

betaine

600 MPa Cell countsa None

Cell counts 0.5 M sucrose

Cell counts 1 M sucrose

Cell counts, MI, MA,

LmrP activity

1.5 M sucrose

Cell counts 1 M NaCl

Cell counts 2 M NaCl

Cell counts 3 M NaCl

Table 1 (continued )

Pressure Parameters analysed Additive

600 MPa Cell counts, MI, MA,

LmrP activity

4 M NaCl

Cell counts 2 M NaCl and

2.5 mM

glycine betaine

Cell counts 4 M NaCl and

2.5 mM glycine

betaine

Inactivation kinetics were determined at each combination of

pressure level and additives, and for each kinetics, samples taken

after eight or more different pressure holding times were

characterised as indicated. Data from Molina-Hoppner (2002).a Experimental data published by Molina-Guttierrez et al.

(2002a).b Experimental data published by Molina-Gutierrez et al.

(2002b).

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–10592

0.05]. A stock solution of tetrazolium was prepared

mixing 4-iodonitrotetrazolium violet [INT, 2-(4-

iodophenyl)-3-(-4-nitrophenyl)-5-phenyltetrazolium

chloride] and glucose in PBO. The final concentra-

tion of each was 4 and 20 mM, respectively. The

bacterial cell suspensions (100 Al each) were mixed

with 100 Al of the stock solution. The absorbance

was measured at 590 nm with a spectrafluor micro-

titer plate reader (TECAN, Grodig, Austria). A

calibration curve was established for each inactiva-

tion kinetics using the calibration samples described

above, and the results are reported as percent meta-

bolic activity (MA).

2.5. Membrane integrity

The determination of the membrane integrity of

pressure-treated L. lactis was carried out with the

LIVE/DEADR BacLightk kit (Molecular probes,

Eugene, USA) with propidium iodide as membrane-

impermeant probe essentially according to the instruc-

tions of the manufacturer. One milliliter pressurised

cell suspension was harvested by centrifugation. The

supernatant was removed, and the pellet resuspended

in 1 ml PBO. A stock solution of LIVE/DEADRBacLightk was prepared, the final concentration of

each dye was 33.4 AMSytoR 9 and 200 AMpropidium

iodide (PI). The bacterial cell suspensions (100 Al each)were mixed in 100 Al of the stock solution, mixed

thoroughly, and incubated for 5 min in the dark at 30

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 93

jC. The fluorescence intensities of SytoR 9 and PI

were measured with excitation and emission wave-

lengths of 485 and 520 nm, and 485 and 635 nm,

respectively, using a spectrafluor microtiter plate read-

er (TECAN). The ratio of SytoR 9 to PI fluorescence

intensity was used as measurement for membrane

integrity. A calibration curve was established for each

inactivation kinetic using the calibration samples de-

scribed above, and the results are reported as percent

intact membrane (MI).

2.6. LmrP activity

Ethidium bromide (EB) is a substrate for the mem-

brane-bound enzyme LmrP and other multidrug resis-

tance transport enzymes. L. lactisMG1363 contains at

least four drug extrusion activities (Yokota et al., 2000).

Because extrusion of EB by L. lactis MG1363 occurs

predominantly by the LmrP transporter and is fully

inhibited by ionophores that dissipate the proton mo-

tive force (Bolhuis et al., 1994, 1995, 1996), EB efflux

activity was reported as LmrP activity. EB stock

solutions were prepared by dissolving 40 Amol of EB

l� 1 in PBO. Cells were washed then harvested by

centrifugation and resuspended in a stock solution of

PBO and EB, the final concentration was 20 Amol l� 1.

After this treatment, the cell suspension was stained for

2 h at 30 jC in the dark without an energy source. Then,

glucose was added to a final concentration of 20 g l� 1.

Cells reenergised with glucose export EB, resulting in a

lower fluorescence of the EB–DNA complex. Imme-

diately after glucose addition, the fluorescence of the

EB–DNA complex was measured over 30 min in a

spectrafluor microtiter plate reader (TECAN) using

excitation and emission wavelengths of 485 and 595

nm. The initial rate of EB efflux, as measured by the

decrease of EB fluorescence intensity upon glucose

addition, was calculated as described (Ulmer et al.,

2002) and reported as LmrP activity.

3. The development of a fuzzy logic model

The Principal objective of fuzzy modelling was the

definition of a rule base that is able to predict depen-

dent variables as a function of independent variables

by application of the fuzzy (nonbinary) logic. In this

work, the software tools WinROSA and DataEngine

(both MIT GmbH, Aachen, Germany) were used for

fuzzy modelling.

The first step of the determination of the rule base

was the ‘‘fuzzyfication’’. Sharp data were described

with linguistic variables. For example, in the current

context pressure values between 50 and 300 MPa

were described with the linguistic variable ‘‘low’’,

while the linguistic variable ‘‘high’’ was associated to

the pressure range between 300 and 600 MPa. The

association of linguistic variables to a variable range

was achieved by the use of a membership function

that took on values larger than zero if the pressure

value was located completely within this range and

equals to zero if the pressure value was completely out

of this range. Several membership functions were

used to associate linguistic variables to the complete

range of the variable. This procedure was applied to

all dependent and independent variables. A graphical

representation of these membership functions (subse-

quently called fuzzy classifiers) is given for pressure,

time, and substrate additives in Fig. 1. In order to

avoid gaps in the parameter definition, the ranges of

the individual fuzzy classifiers were overlapping.

The geometrical form of the membership functions

and their definition range may be determined intui-

tively by the experienced modeller. A more sophisti-

cated method to identify structures in complex data is

the fuzzy C-means clustering, which has been

employed in the current work (Anonymous, 2001).

The method allowed the identification of data clusters

and gave the cluster centres as well as a class

membership value for each data point as a result.

To start the algorithm, a number of classes was

estimated. At the beginning of the search, classes

were chosen randomly by the algorithm, and once

defined, classes were enhanced by the application of

the algorithm. The method stopped if a predefined

difference between the membership value of the

previous and of the present iteration was smaller

than a given limit of convergence e. The obtained

class centres and membership values represented

typical clusters of the measurands.

The obtained cluster membership values were

further analysed with respect to their dependency on

the in- and output variables. From the characteristics

of these transfer functions, the geometrical shape of

the fuzzy classifiers l(x) was obtained for all input

and output variables (Zimmermann, 1993). Fig. 1

Fig. 1. Graphic representation of fuzzyfication using input variables pressure, pressure holding time, and additives and the output variable LmrP-

activity.

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–10594

shows fuzzy classifiers for pressure, pressure holding

time, additives, and for the physiological state of

LmrP. Based on the transfer function analysis, a

trapezoid function was chosen for the physiological

state variables and for the pressure holding time. For

the additives, a punctiform geometry was chosen

because of the strongly varying influence of different

additives on the inactivation. Overlapping of the

classifiers has to be excluded in this case, because

each of them affects the physiology of L. lactis

differently. For the pressure, a triangular form was

chosen.

The next step in the setup of the fuzzy logic model

was the detection and formulation of rules for the

dependency of output parameters on input parameters.

We used the Fuzzy Rule-Oriented Statistic Analysis

(ROSA) algorithm, which represented an evolutionary

search algorithm that allows the automatic generation

of fuzzy rules from the data. Therefore, the previously

obtained fuzzyfication must be imported into the

software, which then found correlations between data

and fuzzyfication. The results were fuzzy rules having

an IF–THEN structure (see examples below). The

fuzzy ‘‘IF’’ part described the premise, the fuzzy

‘‘THEN’’ part the conclusion of the rule. A validity

value is between 0 and 1 and was automatically

associated to a rule describing the validity of the rule

with respect to the investigated data. The obtained

rules were checked by an expert on plausibility, and

further rules were introduced based on (human) expert

knowledge when the set of rules generated by the

Fuzzy ROSA algorithm failed to adequately describe

the experimental data. All rules together represented

the fuzzy logic model (Krone and Kiendl, 1996).

The evaluation of the rule sets requires the com-

bination of rules that apply to a given set of input

variables. This was done in a step denominated the

inference. For a given parameter set of sharp (input)

data, the membership function values to the

corresponding linguistic variables were determined

by the evaluation of the fuzzy classifiers. These values

were associated to the premise of each rule that

applies to the present input parameters (aggregation).

From the rule and evaluation of the classifiers of the

output variable, the membership value of the conclu-

sion was obtained. This value was always one in the

present case but might adopt other values in general.

Both membership values were combined (activation)

and weighted by the validity function of the rule

(accumulation). One obtains a value for each of the

rules representing the degree of application of the rule

for the specific set of parameter values.

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 95

The values of all the rules referring to a specific

output value were collected and analysed with its

classifier function. Each rule addresses a specific

linguistic variable of the output variable. The value

of the rule was used to weigh the linguistic variable.

In order to obtain a sharp value of the output variable,

the center of gravity method was applied (Kiendl,

1997). The following example illustrates the operation

of the fuzzy rule base (Fig. 2).

The sharp input data consist of a value for the

pressure of 430 MPa, a pressure holding time of 20

min and no substrate additive (pure milk buffer). From

the rule base, only two rules apply to this case of input

parameter values:

Rule 1: IF ‘‘pressure’’ is ‘‘high’’ AND ‘‘time’’ is

‘‘middle + ’’ THEN ‘‘cell count’’ is ‘‘very low’’

with a validity of 1.0.

Rule 2: IF ‘‘pressure’’ is ‘‘very high’’ AND

‘‘additive’’ is ‘‘milk buffer’’ THEN ‘‘cell count’’

is ‘‘zero’’ with a validity of 1.0.

In terms of the classifiers (Fig. 2), pressure is

‘‘high’’ with a truth value of 0.7 and ‘‘very high’’

with a truth value of 0.2. The pressure holding time is

‘‘middle + ’’ with a truth value of 1.0. The additive is

Fig. 2. Fuzzyfication of the fuzzy variables. Defuzzyfication of the r

‘‘zero’’ with a validity function of 1.0 as well. Both

involved rules have a previously determined validity

value of 1.0.

Thus, Rule 1 applies with a truth value of 0.7, and

Rule 2 applies with a truth value of 0.2. Both truth

values are then applied as a weight factor to the fuzzy

classifiers of the conclusion. This leads to a member-

ship function with a maximum value of 0.2 for ‘‘zero’’

cell counts and a maximum value of 0.7 for ‘‘very

low’’ cell counts. In order to obtain a sharp value for

the logarithmic cell count to be expected for the

abovementioned parameters, the center of gravity is

determined to 3.4 log cycles and taken as the result of

the variable cell count. While the present example is

based on two rules only, the complete rule base covers

approximately 160 rules for all known physiological

states.

4. Results

4.1. Model establishment

The pressure-induced inactivation of L. lactis ssp.

cremoris MG 1363 was characterised by the identi-

fication of the cell counts on selective and nonselec-

ules for the present case; number of viable cells are detected.

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–10596

tive medium and measurements of the LmrP activity,

the membrane integrity as well as its metabolic

activity as a function of pressure, pressure holding

time, and different additives to milk buffer. The

additives to the buffer were glycine betaine, manni-

tol, sodium chloride, and sucrose in different con-

centrations. Furthermore, the pH value was varied in

the range of 4.0 to 6.5. Pressure holding time ranges

from 0 to 120 min and pressures of 0.1, 200, 300,

and 600 MPa were applied. Temperature changes

during compression were less than 6 jC and were

considered irrelevant. The data set was compiled over

a period of 3 years by Molina-Hoppner (2002) and

Molina-Gutierrez et al. (2002a, b), and all experi-

ments used to establish the model are compiled in

Table 1. At least eight different pressure holding

times were analysed for each kinetic. Fewer data

points were analysed in those kinetics where no

inactivation in the analysed parameters was observed

within 120 min. The data sets are based on experi-

mental work that was completed before the model-

ling procedure started, and the raw data have been

used in a straightforward manner for the model

establishment.

Fig. 3A, B, and C illustrate the agreement between

experimental data used for the model establishment

and data predicted by the fuzzy model. Fig. 3A shows

the parity plot for both the logarithm of the cell counts

(CFU) on full medium and the logarithm of the cell

counts on selective medium (CFUsub). The predicted

values agree with the experimental data within the

range of the experimental error of one log cycle.

Stronger deviations are related to a significant in-

crease in the CFU with increasing pressure application

time at constant pressure. Because growth of L. lactis

is fully inhibited at pressure levels greater than 50

MPa, increasing cell counts during pressure holding

time at 200 MPa or greater are brought about by

experimental error. Virtually all data points are in the

range of experimental standard deviation for the

parameters membrane integrity and metabolic activity

(Fig. 3B). Likewise, virtually all predicted values of

LmrP activity are within experimental error of mea-

sured values (Fig. 3C). The eight deviating data points

marked by circles in Fig. 3C can be identified as

control values without pressure application in the

presence of 1, 2, and 4 M NaCl and 1 M mannitol.

These additives alone reduced LmrP activity in un-

treated cells by more than 60% compared to cells in

milk buffer because of the detrimental effect of these

additives on the internal pH. Because this effect of

additives alone on the intracellular pH and on LmrP

activity in untreated cells was not incorporated in the

model, predicted values are higher than the values

determined experimentally.

4.2. Model validation

The prediction quality of the model was evaluated

on the basis of data that were not previously used for

the generation of the model. For this reason, further

experiments were carried out at pressures of 200, 250,

350, 400, and 500 MPa and different pressure holding

times and selected additives (milk buffer with an pH

value of 4.0, 5.0, 6.0, or 6.5, or milk buffer containing

0.5 or 1.5 M sucrose, or 3 or 4 M NaCl). The

agreement between measured and predicted values

is illustrated in Fig. 4A, B, and C for CFU and

CFUsub, metabolic activity and membrane integrity,

as well as LmrP activity, respectively. None of these

experimental data were used for the establishment of

the model. The quality of the agreement is even better

in this case than in the case of data used for modeling.

This improved quality of fit is a result of the exper-

imental procedures. Whereas the data set for model

establishment was obtained over a period of 3 years

using an experimental design aimed to test different

hypotheses (effects of NaCl, sucrose, or pH on

various aspects of inactivation), the data set for model

validation was obtained in a short period using the

finalised methods. A more detailed comparison of

predicted values and experimental values from indi-

vidual high-pressure inactivation kinetics of L. lactis

used for model validation is presented in the follow-

ing paragraphs.

4.3. Evaluation of cell counts on full and selective

medium

The largest amount of data were available for the

cell counts on M17 agar (CFU) and the cell counts

on M17 agar with 3% NaCl (CFUsub). The CFU-

sub are generally lower than the CFU. The differ-

ence between CFU and CFUsub indicates the

number of cells that suffered a sublethal injury but

remained viable. CFUsub presents counts of undam-

Fig. 3. Comparison of measured and predicted data for model establishment. Shaded areas indicate the deviation explained by overall experimental

errors the methods for determination of CFU, CFUsub, MI, MA, and LmrP activity. (A) Cell counts (CFU) and undamaged cell counts (CFUsub).

(B) Membrane integrity (MI) and metabolic activity (MA). (C) LmrP activity. Highlighted by circles are values for LmrP activity of untreated

cultures where the LmrP activity was reduced because of the presence of high NaCl or mannitol concentrations (see text for details).

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 97

Fig. 4. Comparison of predicted data and data measured for model validation after model establishment. Shaded areas indicate the deviation

explained by overall experimental errors the methods for determination of CFU, CFUsub, MI, MA, and LmrP activity. Experimental data

presented in the graph were not used for model establishment. (A) Cell counts (CFU) and undamaged cell counts (CFUsub). (B) Membrane

integrity (MI) and metabolic activity (MA). (C) LmrP activity.

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–10598

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 99

aged cells that are totally resistant against HP at the

given conditions.

Cell counts were generally reproducible with a

deviation of F 1 log cycle, and the limit of detection

was 103 cfu/ml. The numerical value for cell counts

below the detection limit was arbitrarily set to 32 cfu/

ml. In Fig. 5, CFU are compared with those measured

and predicted values obtained with HP treatments at

200 MPa with pH values of 4 and 6, as well as 400

MPa and 3 and 4 M sodium chloride as an additive.

The effect of various pH on high-pressure inactivation

of L. lactis is apparent both in experimental and in

model data. At 200 MPa and a pH value of 6.0, a

reduction of the CFU of two log cycles was achieved

after 120 min. At a pH of 4.0, treatment with 200 MPa

resulted in a reduction of cell counts by more than

four log cycles within 20 min. In the presence of 3 M

NaCl, treatment of L. lactis for 10 min at 400 MPa

reduced the cell counts by three logs (Fig. 5), whereas

in milk buffer, a reduction of cell counts by more than

four logs is achieved by compression/decompression

without any pressure holding time (data not shown),

indicating a strong baroprotective effect of 3 M NaCl.

This baroprotective effect of NaCl is more pro-

nounced in the presence of 4 M NaCl, where a

Fig. 5. Cell counts of L. lactis after pressure treatment at various pressure le

model validation (meansF standard deviation of two independent experim

at 200 MPa, pH 4.0 (.,U) and pH 6 (o,---), at 400 MPa, 3 M NaCl (E

reduction of less than one log was observed within

1 h of pressure treatment. The model is able to

account for these synergistic and antagonistic effects

of pressure and low pH or high NaCl, respectively. A

large deviation between predicted and the measured

value at 400 MPa, 3 M NaCl, and 60 min pressure

holding time can be identified. Analysis of these data

suggests that this strong increase of CFU is a mea-

surement error that cannot be accounted for by the

model.

Fig. 6 shows the cell counts on selective medium

after HP treatment of L. lactis at 200 MPa with pH

values of 5.0 and 6.5. Inactivation curves of L. lactis

were generally characterised by sigmoid asymmetric

shapes. Because of sublethal injury inflicted by HP

treatment, the cell counts of undamaged cells on

selective medium are reduced more rapidly than

viable cell counts. The data set used for model

establishment contained inactivation kinetics at pH

values other than pH 6.5 at a pressure level of 300

MPa only. Therefore, prediction of pH effects on the

inactivation of L. lactis at 200 MPa as shown in Figs.

5 and 6 represents an extrapolation from those data

used to establish the model. Nevertheless, for inacti-

vation at 200 MPa and pH values of 4.0, 5.0, 6.0, and

vels. Symbols represent experimental data from the data set used for

ents), lines represent predicted values. Shown are data for treatments

,��-�-) and at 400 MPa, 4 M NaCl (D,: : :).

Fig. 6. Cell counts of undamaged cells of L. lactis after pressure treatment at 200 MPa. Symbols represent experimental data from the data set

used for model validation (meansF standard deviation of two independent experiments), lines represent predicted values. Shown are data for

treatment at pH 5.0 (.,U) and pH 6.5 (o,---).

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105100

6.5 (Figs. 5 and 6 and data not shown), an excellent

agreement between predicted and measured data were

obtained.

4.4. Metabolic activity and membrane integrity

The measurement of the metabolic activity (MA)

provides information on the glycolytic activity of L.

lactis. The rate of tetrazolium reduction to formazan

is dependent on cofactor regeneration in glycolysis.

For model generation, data from experiments at

pressures of 0.1, 200, 300, and 600 MPa, at pressure

holding times between 0 and 60 min for milk buffer,

milk ultrafiltrate, and milk buffer with the additives

1.5 M sucrose or 4 M NaCl were used. The

experimental error for the determination of metabolic

activity generally was xF 15% or less, where x

represents the average value (see Fig. 3B). The

quality of the model with respect to the prediction

of the MA was investigated at pressures of 250, 350,

and 500 MPa using milk buffer or milk buffer

containing either 0.5 M sucrose, 1.5 M sucrose or

4 M NaCl.

Furthermore, the membrane integrity (MI) of pres-

sure-treated L. lactis was characterised. The model

was created based on data of MI obtained at pressures

of 0.1, 200, 300, and 600 MPa using the same

additives and pressure holding times as for MA (see

above). The experimental error for the determination

of membrane integrity generally was xF 10% or less

(see Fig. 3B). The quality of the model with respect to

the prediction of the MI has been investigated at

pressures of 250, 350, and 500 MPa using milk buffer

or milk buffer containing either 0.5 M sucrose, 1.5 M

sucrose, or 4 M NaCl.

Selected results for predicted data for MA and MI

are shown in Figs. 7 and 8. Generally, the predicted

values are within experimental error of the data.

Fig. 7 illustrates measurements and model predic-

tions of MA and MI at pressures of 250 and 500 MPa

for milk buffer with an additive of 4 M NaCl as a

function of the pressure application time. In Fig. 8,

data for milk buffer and milk buffer with 1.5 M

sucrose are shown.

From Figs. 7 and 8, it can be observed that the

membrane integrity remains unaffected at pressures of

250 MPa even under conditions reducing viable cell

counts by more than two logs (250 MPa, milk buffer,

60 min pressure holding time). At HP of 500 MPa in

the presence of 1.5 M sucrose or 4 M NaCl, the

membrane integrity remains higher than 40% after

pressure treatments for up to 1 h. These data confirm

Fig. 7. Membrane integrity (MI) and metabolic activity (MA) of L. lactis after pressure treatment. Symbols represent experimental data from the

data set used for model validation (meansF standard deviation of two independent experiments), lines represent predicted values. Shown are

data for MA after treatments at 250 MPa, 4M NaCl (.,U) and at 500 MPa, 4M NaCl (o,-��-), and data for MI after treatments at 250 MPa, 4 M

NaCl (E,---) and at 500 MPa, 4M NaCl (D,: : :).

Fig. 8. Membrane integrity (MI) and metabolic activity (MA) of L. lactis after pressure treatment. Symbols represent experimental data from the

data set used for model validation (meansF standard deviation of two independent experiments), lines represent predicted values. Shown are

data for MA after treatment at 250 MPa, milk buffer (.,U) and at 500 MPa, 1.5 M sucrose (o,-��-), and data for MI after treatment at 250 MPa,

milk buffer (E,---) and at 500 MPa, 1.5M sucrose (D,: : :).

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 101

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105102

the protective effect of sucrose and NaCl on mem-

brane integrity observed previously (Molina-Gutierrez

et al., 2002a).

The metabolic activity was strongly dependent on

the presence of additives. Treatment of L. lactis in

milk buffer reduced the MA to 20% after 60 min at

250 MPa (Fig. 8). Using 4 M NaCl as additive at the

same pressure level leads to a slightly increased MA

(Fig. 7). Pressure treatments at 500 MPa revealed

differences between the protective effect of sucrose

and NaCl. Each additive prevented a reduction of cell

counts within 20 min at 500 MPa. In the presence of 4

M NaCl, a complete loss of metabolic activity was

observed after 4 min of pressure treatment, whereas

cells retained more than 20% of the metabolic activity

after pressure treatment for 20 min in the presence of

sucrose.

Taken together, the membrane integrity of L. lactis,

as judged by propidium iodide permeability, is less

sensitive to pressure application than viability and

metabolic activity. The membrane integrity and the

metabolic activity are protected both by NaCl and

sucrose addition, whereas the metabolic activity is

protected only by sucrose. This confirms the theory of

multistage inactivation of L. lactis and a specific

effect of the different additives on physiological states

of L. lactis during high pressure inactivation.

4.5. LmrP activity

Membrane-bound enzymes are generally consid-

ered a sensitive indicator of bacterial sublethal

injury, and Ulmer et al. (2002) reported that suble-

thal injury of L. plantarum after high-pressure treat-

ment corresponded to the inactivation of HorA, an

ATP-dependent multidrug-resistance enzyme. In this

work, the activity of LmrP was determined, an pmf-

dependent MDR tranporter functionally but not

structurally related to HorA. The determination of

LmrP activity of pressure-treated L. lactis was re-

producible with an experimental error of xF 10% or

less (see Fig. 3C). Experimental data obtained in

milk buffer or milk buffer with sucrose, NaCl, or

mannitol at pressures of 0.1, 200, 300, and 600 MPa

and pressure holding times of 0 to 120 min were

used for the establishment of the model. Fig. 9

depicts results of model prediction of experimental

data obtained for the inactivation of L. lactis at 250

MPa in milk buffer and 500 MPa in milk buffer

with 1.5 M sucrose.

Predicted values for LmrP activity differ from the

measured data within the experimental error. At any

combination of pressure level, pH, and additives

employed, a complete inactivation of LmrP was

observed prior to cell death and loss of metabolic

activity. For example, after pressure application of 250

MPa for 8 min in milk buffer, cell counts and

undamaged cell counts remain virtually unaffected,

whereas LmrP is fully inactivated. Sucrose provided

protection towards LmrP inactivation; however, al-

though cell counts remained unaffected by application

of 500 MPa for 1 h in the presence of 1.5 M sucrose,

LmrP was fully inactivated after 4 min of pressure

application.

5. Discussion

The pressure inactivation process of L. lactis ssp.

cremoris MG 1363 is considered as a multistage

inactivation process (Molina-Hoppner, 2002). Pres-

sure treatment reversibly dissipates the transmem-

brane potential, and membrane transport systems

related to pH homeostasis are irreversibly inactivated

prior to cell death (Molina-Gutierrez et al., 2002b). In

this study, the activity of the membrane-bound trans-

port enzyme LmrP was found to be a sensitive

indicator of pressure-induced sublethal injury. The

metabolic activity of L. lactis was inactivated con-

comitant with or earlier than cell death. After pressure

inactivation in milk buffer, the membrane remained

impermeable to propidium iodide even under condi-

tions that reduced viable cell counts by more than

99%. A reduction of the pH value or the addition of

NaCl or sucrose order in molar concentrations exerted

synergistic and antagonistic effects on pressure inacti-

vation, respectively. These different additives exerted

specific effects on individual stages of pressure inac-

tivation of L. lactis.

A fuzzy logic model was formulated that predicts

the membrane integrity, the metabolic activity, con-

centrations of surviving damaged and undamaged

cells, and the activity of the membrane transport

system LmrP as a function of a pressure level ranging

from 0.1 to 600 MPa, pressure holding time up to 2 h,

and for different additives to the fluid medium. The

Fig. 9. LmrP-activity (LmrP) of L. lactis after pressure treatment. Symbols represent experimental data from the data set used for model

validation (meansF standard deviation of two independent experiments), lines represent predicted values. Shown are data for LmrP after

treatment at 500 MPa, 1.5 M sucrose (.,U) and at 250 MPa, milk buffer (o,-��-).

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105 103

predictive performance of the model was determined

using experimental data that were generated after

model establishment at conditions not taken into

consideration for model establishment. The values

predicted by the fuzzy model are in excellent agree-

ment with the experimental data sets used for model

establishment and model validation.

At several data points, a significant deviation be-

tween predicted and measured results was recognised.

The following reasons explain these deviations: first,

in some cases, experimental values for a given param-

eter (e.g., CFU) increase with increasing pressure

treatment times, although a monotonously decreasing

characteristics has to be expected because cell death is

irreversible. Thus, such data are assumed to be mea-

surement errors and the model was set up to generate

monotonously decreasing values with increasing pres-

sure treatment times for all parameters analysed. Sec-

ond, a source of error lies in the centre-of-gravity

defuzzyfication method (COG method) that connects

by mistake nonneighbouring fuzzy classifiers that are

not connected for the determination of the COG in

those few cases where a strong inactivation of a

parameter is observed within a short period of time.

For example, the fuzzy classifier ‘‘middle‘‘ was used to

describe pressure treatment times between 7 to 15 min.

During pressure treatment at 250 MPa, cells counts are

reduced from 109 to 105 cfu/ml within this period of

time. The output of defuzzyfication results in a wrong

determination of the COG and an underestimation of

the value of the output variable. Third, deviations

result from the experimental error in the data used

for model generation. All data used were obtained

from experiments that were performed at least in

duplicate. The model generation was based on all of

these data rather than mean values of independent

experiments. When the output variable of the two

experiments performed under identical conditions

was assigned to two different fuzzy classifiers, two

sets of rules were generated. To reduce the set of rules

required for accurate prediction, one of these two sets

of rules was ignored. These resulting model deficien-

cies can be overcome by the addition of further fuzzy

rules or the incorporation of expert knowledge-based

rules, e.g., the requirement of a monotone decrease of

CFU with time.

In conclusion, a model based on fuzzy logic rules

was established which accounts for the specific

knowledge on the multistep pressure inactivation of

L. lactis, and which allows the prediction of the

quantities of lethally and sublethally damaged cells

after pressure treatment. The fuzzy model accurately

K.V. Kilimann et al. / International Journal of Food Microbiology 98 (2005) 89–105104

predicts pressure inactivation of L. lactis using con-

ditions not taken into account in model generation.

Because fuzzy type models are increasingly used to

control unit operations in food production, the devel-

opment of models that include the prediction of

microbial behaviour during food production can be

envisaged in the future. Additionally, it may serve as a

tool for model and measurement-based analysis of

correlations between the various physiological states

of L. lactis during pressure treatment in order to

improve the understanding of the complex process

of bacterial inactivation by high pressure.

Acknowledgements

This work was supported by the Deutsche

Forschungsgemeinschaft Grant No. For 358/2.

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