- Email: [email protected]
Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study
FBP-436; No. of Pages 7
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Contents lists available at ScienceDirect
Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp
Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study Corina Neagu a , Daniela Borda a,∗ , Osman Erkmen b a b
˘ “Dunarea de Jos” University of Galat¸i, Faculty of Food Science and Engineering, 111 Domneasca Street, 800201 Galati, Romania Department of Food Engineering, Faculty of Engineering, University of Gaziantep, 27310 Gaziantep, Turkey
a b s t r a c t The aim of this research was to analyze and model the combined effect of pressure and temperature upon Aspergillus ochraceus spores exposed to high pressure carbon dioxide (HPCD) treatment and to estimate the kinetic parameters. Lately, many empirical or semi-empirical mathematical models were presented and discussed for different microorganisms, mainly bacteria, demonstrating an increased need for tools able to quantify the parameters of the microbial inactivation. A. ocharaceus HPCD inactivation was adequately described by first order reaction kinetics and a synergic effect of pressure and temperature was noticed for the experimental range where pressure varied from 5.4 to 7.0 MPa and temperature varied from 30 to 50 ◦ C. The decimal reduction time (D) ranged from 47.07 min at 5.4 MPa and 30 ◦ C to 5.04 min at 7.0 MPa and 50 ◦ C. In this study three mathematical models were evaluated in order to find the best one that describes accurately the influence of pressure and temperature on the studied microbial response. An empirical exponential equation, that described pressure and temperature influence in the form of a polynomial equation, was found to best describe the dependence of A. ochraceus HPCD inactivation in the range 5.4–7.0 MPa and 30–50 ◦ C. This work adds insight to moulds inactivation at the already existing body of knowledge on bacteria inactivation with HPCD and provides support to potential industrial applications of the minimal–thermal methods that combine high pressure and mild temperature with carbon dioxide for different food matrixes. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: High pressure carbon dioxide; Inactivation; Aspergillus ochraceus; Mathematical model; Spores; Kinetics
1.
Introduction
Thermal food preservation is a well known classical treatment for reducing the microorganisms in foods. This technique is adapted to equilibrate the difficult balance between overheating (reducing the foods’ sensorial properties) and underheating (leading to unsafe and low-quality food products). As consumers are demanding minimally processed and fresh-like food products the application of alternative methods to thermal treatment known as cold pasteurization processes is gaining ground. In the past decades, a noticeable inactivation effect of high-pressure carbon dioxide (HPCD) on microorganisms in liquid foods at low temperatures and pressures below 20 MPa has been proved effective for food preservation (Enomoto et al., 1997; Erkmen, 2000; Hong and Pyun, 2001; Liao et al., 2007). In the HPCD technique food
is in contact with pressurized either sub- or supercritical CO2 for a certain amount of time in a batch, semi-batch or continuous manner. The different steps in the inactivation mechanism can be summarized as follows: (1) solubilization of pressurized CO2 in the external liquid phase decreasing the extracellular pH (pHex ), (2) cell membrane modification due to diffusion of CO2 into the cellular membrane, (3) cellular penetration of CO2 decreasing the intracellular pH (pHin ), (4) key enzyme inactivation/cellular metabolism inhibition due to pHin lowering, (5) direct (inhibitory) effect of molecular CO2 and HCO3 − on cell metabolism, (6) precipitation of CO3 2− with inorganic electrolytes and Ca2+ binding proteins causing the intracellular electrolyte imbalance and (7) removal of vital constituents from cells and cell membranes (Damar and Balaban, 2006; Spilimbergo et al., 2003; Garcia-Gonzalez et al., 2007).
∗
Corresponding author. Tel.: +40 336130177; fax: +40 236460165. E-mail address: [email protected] (D. Borda). Received 2 February 2013; Received in revised form 4 August 2013; Accepted 22 August 2013 0960-3085/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fbp.2013.08.011 Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
2
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Microbial inactivation achieved by HPCD ranges from 2 to 12 logs using pressures below 50 MPa and temperatures between 5 and 60 ◦ C (Damar and Balaban, 2006). Exposure time, pressure, temperature, initial number of cells, pressure cycling, initial pH of medium, water activity, cell growth phase or generation time, species of microorganisms and type of treatment all influence microbial inactivation by HPCD (Arreola et al., 1991; Dillow et al., 1999; Kamihira et al., 1987; Lin et al., 1993; Spilimbergo et al., 2003). In spite of intensified research efforts in the last years and presence of patents on the market (Balaban, 2004; Balaban et al., 1995; Connery et al., 2005) the HPCD technique has limited applications at industrial scale up to now (Ferrentino and Spilimbergo, 2011). The scaling up of the novel technologies based on various HPCD applications needs however more extensive studies on fundamental and mechanistic models able to better describe the microbial inactivation (Ferrentino and Spilimbergo, 2011). While bacteria inactivation under pressure and carbon dioxide treatment was extensively studied (Dillow et al., 1999; Kamihira et al., 1987; Oulé et al., 2006; Spilimbergo et al., 2003) less work was reported for moulds (Shimoda et al., 2002), although the total microbial flora inactivation by HPCD was reported (Calvo and Torres, 2010; Ferrentino et al., 2008, 2013; Matsufuji et al., 2009). The general objective of this research was to investigate the HPCD inactivation kinetics of Aspergillus ochraceus spores, which is an important contaminant of diverse food matrixes such as cereals, wines, coffee, grapes and derivates, being capable to produce nephrotoxic metabolites such as mycotoxins. Aspergillus ochareceus presence in foods is related to the dietary exposure to a toxic secondary metabolite – ochratoxin A (OTA) (Amézqueta et al., 2012). The specific objectives of this study were to analyze the effect of HPCD at different pressures (5.4, 6.0 and 7.0 MPa) and temperatures (30, 40 and 50 ◦ C) on A. ochraceus inactivation and to select the best general model that accurately describes the mould response to HPCD treatment.
2.
Materials and methods
2.1.
Preparation of A. ochraceus spores
A. ochraceus 151 strain was obtained from USAMV (University of Agronomic Science and Veterinary Medicine, Bucharest, Romania) collection. The mould strain was activated on potato dextrose agar (PDA; Merck, Darmstadt) slant and a stock culture was prepared on the PDA slant by incubating at 25 ◦ C for 3 days. The mould cultures for experiments were subcultured from stock culture using PDA plates at 25 ◦ C for 6 days. The spores were collected by washing the surface of the agar plate cultures using potato dextrose media (PDB; Difco, Detroit) containing 0.1% Tween 80 (pH = 5.6). The spore suspension was filtered through three layers of sterile cheesecloth to remove the hyphae under aseptic conditions. Finally, the number of spores in the filtrate was brought to about 106 spores × ml−1 by adding the necessary amount of physiological saline solution. The initial number of spores in the suspension was counted by direct microscopic counting method using Neubauer improved chamber (Erkmen, 2001b). The spore suspension used in all experiments was freshly prepared every day and stored in a refrigerator at 4 ◦ C during the experiments.
Fig. 1 – Schematic diagram of the apparatus used for high pressure CO2 .
2.2.
Equipment
The high-pressure installation used for experimental treatments is shown in Fig. 1. A cylindrical pressure vessel (maximum pressure tolerance level of 100 MPa) with the internal volume of 266 ml was used for CO2 pressurization as previously described (Erkmen, 2000, 2001a). The vessel closure has gas impermeable connections for the temperature and pressure sensors and gas inlet and outlet. A pressure manometer (Klauser Fisher, 28124-1; Brothers Commercial, Gaziantep, Turkey) and chromel (90% nickel and 10% chromium) thermocouple (Heraeus, 24313651; Teknim, Ankara, Turkey) were installed to monitor the pressure and the temperature of gas in the pressure vessel. A line filter packed with silica gel (60/80 mesh, Alltech, USA) was also mounted in the CO2 outlet of the vessel to reduce the pressure release rate. After each run the pressure vessel was disinfected with 0.1% H2 O2 solution and rinsed with sterile distilled water.
2.3.
Pressure treatments
Two samples containing 5 ml of daily prepared spore suspension (106 spores × ml−1 ) were placed into loosely capped (sterile metallic cap standing at fixed position) sterile test cylindrical tubes (110 mm × 14 mm) and the tubes were gently shacked. The tubes were placed into the pressure vessel and the vessel was tightly closed and immersed in a thermostatic water bath (ST-402; Nüve, Sanayii ve Malzemeleri I˙malat ve Ticaret A.S¸., I˙stanbul, Turkey) at constant temperatures (30, 40 and 50 ◦ C). When the temperature was equilibrated (within 1 min) and all tubing connections were secured, commercially available CO2 (purity 99.990%, FNA 84-37-611; Koc¸erler, Industrial and Medical Gas Producing and Marketing Commercial Limited Company, Gaziantep, Turkey) was injected through the gas inlet valve from the gas cylinder into the vessel, reaching the desired pressures (5.4, 6.0 and 7.0 MPa) within 1 min. After being exposed to CO2 pressure for a designated time period at a temperature of 30, 40 or 50 ◦ C, the pressure was lowered to atmospheric pressure (within 1 min) by opening the gas outlet valve slowly and the duplicate tubes were pulled out. A blank tube containing 5 ml of sample with the same concentration of spore suspension as the regular samples was incubated under atmospheric pressure in the water bath. After the treatment, 1 ml of spore suspension was immediately taken out from each of the two tubes and the samples were examined for surviving A. ochraceus
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
ARTICLE IN PRESS 3
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
spores. Three experiments were repeated for each experimental condition with freshly prepared inoculum that was prepared and stored in the same conditions as the initial one.
2.4.
2.5.
Modelling and statistical analysis
2.5.1.
Primary models
The inactivation of A. ochraceus spores was described using a first order kinetic model. Hence the general inactivation equation for spores is (Peleg and Normand, 2004): dN(t) = −k · t N(t)
N(t) = exp(−k · t) N0
(2)
where N(t) is the number of spores at time t (CFU ml−1 ), N0 is the number of spores at time 0 (CFU ml−1 ), k is the rate constant (min−1 ) and t is the time (min). For microorganisms’ inactivation, first order inactivation models or linearized models, equivalent to Eq. (2), are frequently applied to estimate the inactivation rate and the decimal reduction time, depending on the microbial load and time (Eq. (3)). Linear regression procedures were performed with SAS Windows 9.1 software (Cary, NC, SUA). The liniarized Eq. (2) is:
N N0
= −k · t
(3)
where N is the number of spores at time t (CFU ml−1 ), N0 is the number of spores at time 0 (CFU ml−1 ) and t is the time (min). The decimal reduction time (D (min)) is calculated with Eq. (4) (Bigelow, 1921):
2.6.
2.303 k
ln 10 ln 10 ln 10 (T − Tref ) ·exp ·exp (P − Pref ) Asym Dref z zP (5)
where k(T,P) is the inactivation rate constant as a function of pressure and temperature (min−1 ), z is the change in temperature (◦ C) required to achieve a 10-fold change in Asym Dref (min) value and zP is the change in pressure (MPa) required to achieve a 10-fold reduction in Asym Dref value. The Asym Dref represents the negative inverse of the loglinear part of the inactivation slope, after the shoulder region (Adekunte et al., 2010). The reference values of temperature and pressure were selected in the middle of processing conditions (Tref = 40◦ C and Pref = 6.0 MPa). Replacing the rate constant from Eq. (2) with the number of spores, a single general equation was obtained – Eq. (6):
ln
N N0
=−
ln 10 Asym Dref
·exp
(1)
which, when the reaction order is one, can be integrated under isothermal conditions into:
D=
k(T, P) =
Enumeration of A. ochraceus spores
Each treated sample was serially diluted with sterile physiological saline solution. The initial and the surviving A. ochraceus spores were counted by spread plating 1 ml of diluted and non diluted samples on duplicate plates of PDA (pH = 5.6). The plates were incubated at 25 ◦ C for 3 days, after which all the visible A. ochraceus colonies on PDA plates were counted (Erkmen, 2000). The number of survivors was expressed as log colony forming unit (CFU ml−1 ).
ln
from the Bigelow model. The current study adapted the equation proposed by Adekunte et al. (2010) and the result is Eq. (5):
ln 10 zP
· exp
ln 10 z
(P − Pref )
(T − Tref )
·t
(6)
This procedure brings the advantage of avoiding a considerable reduction of the data set when first estimating the reaction rate (k) and also the advantage of avoiding error multiplication from one regression equation (Eq. (2)) to another (Eq. (5)). The second model is based on the kinetic equation successfully applied by Boulekou et al. (2010) that describes the effect of pressure and temperature on enzyme inactivation. However, considering the concerns expressed by researchers on using certain kinetic parameters from the chemical reactions to describe the microbial inactivation or growth such as the activation energy, the activation volume but also the universal gas constant (van Boekel, 2008; Peleg and Normand, 2004), these parameters were replaced with general symbols denominated with alphabetical letters and no physical signification nor measurement units were attributed to the estimated parameters. The usefulness of a general kinetic model was verified for the fungal HPCD inactivation. Eq. (7) resulted from these changes:
ln
N N0
= −k0 · exp
A · exp[−B(P − Pref )] ·
P − Pref −(C(T − Tref ) + D) · T
·t
1 T
−
1 Tref
(7)
(4)
General models
In order to describe A. ochraceus spores HPCD inactivation as a function of pressure and temperature, three general semiempirical models adapted from the literature (Adekunte et al., 2010; Boulekou et al., 2010; Juliano and Knoerzer, 2009) were tested and compared. In the model proposed by Adekunte et al. (2010) the maximum inactivation rate constant is expressed as a function of temperature and amplitude, based on a equation developed
where k0 , A, B, C and D are model parameters. The third model tested was the one applied by Juliano and Knoerzer (2009) for the inactivation of Clostridium botulinum in dynamic conditions using a high pressure high thermal treatment. This model with 6 terms described the rate constant as an exponential function of pressure and temperature. The current approach applied only the terms of a polynomial equation with second order terms and replaced the rate constant from Eq. (2) in order to be able to use the entire data set (n = 68). The equation resulting from these changes
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
ARTICLE IN PRESS
FBP-436; No. of Pages 7
4
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
is Eq. (8):
ln
N N0
Table 1 – D values (min) for the A. ochraceus inactivation. P (MPa) T (◦ C) = −exp [(A0 + A1 · (P − Pref ) + A2 · (T − Tref ) 2
+A3 · (P − Pref ) + A4 · (T − Tref )
30
2
+A5 · (P − Pref ) · (T − Tref ))] · t
(8)
5.4 6.0 7.0 a
where A0 , A1 , A2 , A3 , A4 and A5 are model parameters. For Eqs. (7) and (8) the reference values of temperature and pressure were considered as for the Eq. (6) in the middle of processing conditions (Tref = 40 ◦ C and Pref = 6.0 MPa). Using non-linear regression procedure (SAS software, version 9.1, Cary, NC, USA) the parameters of Eqs. (6)–(8) were estimated for all the pressure temperature combinations with the entire data set (n = 68). As a basis for model discrimination root mean square error value was calculated and the goodness of fit that correlates the experimental and the predicted model values was assessed for all the tested models. RMSE (root mean square error)
RMSE =
ni i=1
(yexp (ti ) − y(ti , pis ))
2
nt − np
(9)
where yexp (ti ) denotes the experimental observations, y(ti ,pis ) the predicted values, nt the total number of data points and np the number of estimated model parameters. Standard deviation of the estimated parameters was also a good indicator for the contribution of the individual parameters to the model.
3.
Results and discussion
3.1.
Inactivation kinetics – primary models
The survival curves of A. ochraceus spores using HPCD treatment were fitted by the primary linear model (Eq. (3)) at different temperatures (30, 40 and 50 ◦ C) combined with different pressures (5.4, 6.0 and 7.0 MPa). At 5.4 MPa and 30 ◦ C the inactivation of spores takes place slowly, while at 40 ◦ C a 4.44 log reduction of the number of spores was noticed after 120 min of treatment. At 50 ◦ C after 120 min of treatment the total inactivation of the spores was obtained. It can be noticed that the inactivation effect of HPCD increased with the increase of temperature from 30 to 50 ◦ C. Linear inactivation was achieved at 6.0 MPa when inactivation curves were plotted as a function of time on a log linear scale, indicating first order kinetics for the entire experimental domain ranging from 30 to 50 ◦ C (data not shown). At 30 ◦ C and 6.0 MPa a very significant (R2 = 0.99) inactivation occurs after 120 min, but, generally, the inactivation goes slowly. At 40 ◦ C and 6.0 MPa a 2.81 log reduction of the initial number of viable spores was registered after 60 min of treatment. At 50 ◦ C and 6.0 MPa the number of viable spores had a 5.07 log reduction after 60 min of treatment and after 75 min total inactivation was obtained. At 7.0 MPa, after 90 min of treatment at 30 ◦ C, the number of viable spores was reduced with 2.87 log units. A 99.99% reduction in the number of viable spores was observed after 90 min of treatment at 40 ◦ C and 7.0 MPa. Inactivation at the same pressure and 50 ◦ C took place quickly and after 10 min of
b
40
50
47.07 ± 0.91a (0.93b ) 27.27 ± 0.37 (0.98) 19.01 ± 1.17 (0.97) 39.22 ± 1.10 (0.98) 17.12 ± 0.01 (0.98) 11.33 ± 0.28 (0.99) 27.43 ± 0.67 (0.99) 13.28 ± 0.52 (0.98) 5.04 ± 0.34 (0.96)
Standard error of regression. Square correlation coefficient.
treatment a 3.17 log reduction of the number of viable spores was noticed while after 30 min total inactivation was obtained. Inactivation of microorganisms by high-pressure carbon dioxide is governed essentially by the dissolution of CO2 into the cells (Erkmen, 2000; Hong and Pyun, 1999) and its effectiveness can be improved by the enhancement of the transfer rate. Principally, pressure controls the solubilization rate of CO2 and its solubility in a suspension medium (Ballestra and Cuq, 1988; Hong and Pyun, 1999). Shimoda et al. (2002) reported that the death kinetics of Aspergillus niger spores (expressed as the decimal reduction time, D) was linearly related to the treatment temperature and the concentration of dissolved CO2 , with an observed significant interaction between these two parameters. In the present study the decimal reduction time (D) was reduced by 1.7-fold from 47.07 min to 27.27 min for an increase in pressure from 5.4 to 7.0 MPa at 30 ◦ C and by 2.5-fold from 47.07 min to 19.01 min for an increase in temperature from 30 to 50 ◦ C (Table 1) at constant pressure (5.4 MPa). The stimulating effect of temperature on the microbial inactivation of HPCD has been frequently reported, as reviewed in Garcia-Gonzalez et al. (2007). An increase in temperature may stimulate the diffusivity of CO2 acting on the integrity of the cellular membrane and increasing its fluidity (Lin et al., 1993; Hong and Pyun, 2001; Oulé et al., 2006). The stimulating effect of temperature on mould inactivation can be in part counteracted by its inhibiting effect on CO2 solubility. In the present study, for the entire experimental domain a synergistic effect of temperature and pressure could be noticed and D value was reduced 9.3-fold from 47.06 min at 30 ◦ C and 5.4 MPa to 5.04 min at 50 ◦ C and 7.0 MPa. The correlation coefficients of the regression curves for all the temperatures and pressures studied were higher than 0.93 (Table 1).
3.2.
General models
To express the pressure–temperature dependence of A. ochraceus spores inactivation several models were assessed and compared. The parameters of the model estimated by Eq. (6) are presented in Table 2. The main advantage when applying this
Table 2 – Values of the parameters estimated by the nonlinear regression based on Eq. (6). Parameter
Value
Asym Dref (min) z (◦ C) zP (MPa)
21.06 ± 0.49 35.36 ± 1.62 4.29 ± 0.29
a
a
RMSE
p
1.437
<0.0001
Standard error of regression.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
ARTICLE IN PRESS
FBP-436; No. of Pages 7
5
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Table 3 – Values of the parameters estimated by the nonlinear regression based on Eq. (7).
Table 5 – Values of the parameters estimated by the nonlinear regression based on Eq. (8).
Parameter
Value
A B C D ko
617.95 × 101 −2.81 × 10−1 45.71 × 10−1 −38.20 × 101 3.78 × 10−1
a
± ± ± ± ±
18.72 × 101 a 1.22 × 10−1 36.72 × 10−1 188.03 × 101 0.14 × 10−1
RMSE
p
Parameter
Values
0.902
<0.0001
A0 A1 A2 A5
−21.88 × 10−1 5.66 × 10−1 6.40 × 10−2 3.08 × 10−2
a
0.14 × 10−1 a 0.2 × 10−1 0.17 × 10−2 0.27 × 10−2
p
0.773
<0.0001
Standard error of regression.
Standard error of regression.
model is considered its versatility in describing the kinetics of microbial inactivation with non-thermal technologies, in general (Adekunte et al., 2010). Moreover, the model is taking into account the non-linear regions that are often present on the microbial inactivation curves. The Asym Dref value of 21.06 min obtained in this case suggests a relatively slow HPCD inactivation process for A. ocharaceus in the studied pressure and temperature range. Much lower Asym Dref values were reported for Cronobacter sakazakii inactivation when applying combined ultrasound and temperature treatment (Adekunte et al., 2010). However, a strong dependence to pressure is shown by the current inactivation model where the estimated zP value is of 4.29 MPa (Table 2). The RMSE (1.437) value does not necessarily suggest a very good fit of the model with the experimental data, however the standard deviation for all the parameters is less than 7% of the estimated value. The correlation between the logarithm of the experimental values (ln(N/N0 )) and the predicted ones given by Eq. (6) indicates a good value of the correlation (R2 = 0.94). Another semi-empirical model that takes into consideration the effect of pressure and temperature on the inactivation rate was described by Eq. (7). The model has a lower RMSE (Table 3) value (0.902), indicating a better fitting capacity than the one of the model described by Eq. (6). However, the initially estimated parameter C had a high standard deviation (45.71 × 10−1 ± 36.72 × 10−1 ), thus aiming at high parameter accuracy, the term that described the temperature dependence was eliminated. The parameters obtained from the non-linear regression after the elimination of parameter C are indicated in Table 4. The removal of the parameter describing the influence of temperature from the initial model produced a significant decrease of the standard deviation for all of the remaining parameters to less than 9% of the estimated value and a decrease of the RMSE value to 0.869, suggesting a better model compared to the previous one. The parity correlation of the predicted with the experimental values has a very good R2 value (0.96) suggesting a tight distribution of the points around the line of equivalence.
Table 4 – Values of the parameters estimated by the nonlinear regression based on Eq. (7) after the removal of the term (T − Tref ). Parameter
Value
A B D ko
608.24 × 101 −4.51 × 10−1 −36.45 × 101 3.82 × 10−1
a
± ± ± ±
RMSE
± ± ± ±
Standard error of regression.
18.39 × 101 a 0.39 × 10−1 1.76 × 101 0.14 × 10−1
RMSE
p
0.869
<0.0001
The third model tested was implemented by Juliano and Knoerzer (2009) in a computational model that described the kinetics of C. botulinum inactivation with high pressure high thermal processing. This empirical model is an exponential function with second order polynomial terms as exponent. The polynomial exponent shows the dependence of the inactivation to pressure and temperature. The model described by Eq. (8) is considered to better describe the rate of inactivation than the classic log-linear kinetics (Juliano and Knoerzer, 2009). Eq. (8) was applied and, aiming at the most parsimonious model with the minimum number of parameters, all the second order parameters were eliminated due to having standard error values higher than the estimated parameters. Thus, besides the intercept, the polynomial exponent included only terms in P, T and P × T (Table 5). The resulting equation had a very good RMSE value −0.773, indicating a high accuracy of the model in describing A. ocharaceus inactivation. The standard deviation of all estimated parameters was less than 9%. A very good correlation R2 value (0.97) between the experimental and the predicted model values is suggesting a better interpolating capacity of this model – Eq. (8) compared to Eq. (7) and (6) where the R2 values were 0.96 respectively 0.94. Even though all the tested models proved to be reliable in describing the inactivation of A. ochareceus with high pressure carbon dioxide treatment in the temperature range 30–50 ◦ C combined with pressure in the range 5.4–7.0 MPa there are specific differences between the three models studied that can help discriminate them. The advantage of applying the Adekunte et al. (2010) kinetic model is linked to its versatility of describing linear and nonlinear kinetic processes and in bringing physical signification to the model parameters such as Asym Dref , z and zP . In this case the inactivation of A. ochraceus in the studied range was described by Eq. (6) which presented the highest RMSE value among all the analyzed models. The estimated values for Asym Dref , z and zP are characteristic for microbial inactivation. Validation studies on different strains are required prior to selecting this model as a tool for quantitative prediction of moulds spores’ survival. The Boulekou et al. (2010) model derived from Arrhenius and Eyring equations, described by Eq. (7) was successfully applied to describe the inactivation of A. ocharecus. However, researchers should avoid, when using models from enzyme kinetics, to attach physical signification for the estimated parameters such as the activation energy. Figs. 2–4 presents the experimental values as ln(N/N0 ) vs. time and the ones predicted by the three studied models, demonstrating that although all models describe well the inactivation of A. ochraceus the one that describes most accurately the experimental results is Eq. (8).
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
6
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
4.
Fig. 2 – Inactivation kinetics for A. ochraceus at 5.4 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data.
Conclusions
Inactivation of the A. ochraceus spores in PDA media with HPCD was obtained in the pressure range 5.4–7.0 MPa combined with temperatures from 30 to 50 ◦ C. The fastest inactivation rate was obtained for 7.0 MPa combined with 50 ◦ C treatment, where the D value achieved was 5.04 min. A power law model was the best HPCD predicting model of A. ochraceus spores in the experimental range. The advantages of directly using ln(N/N0 ) values in the general model is the linked with the use of the entire data set to estimate the pressure and temperature dependency without multiplying the errors form the primary to the secondary models. Statistical parameters such as RMSE, standard deviation for the parameters and the goodness of fit correlation indices enabled the selection of the best model that predicts A. ochraceus inactivation. Further studies are required to validate this model for the HPCD inactivation of other mould strains and in different food matrixes.
Acknowledgements This paper was supported by Gaziantep University Research Fund and PN-II-RU-ID-647 314 – Romania.
References
Fig. 3 – Inactivation kinetics for A. ochraceus spores at 6.0 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data.
Therefore, the best semi-empirical mathematical model for A. ochraceus inactivation considering the goodness of fit, the RMSE values and the standard deviation for the model parameters was found to be the equation that has a polynomial exponent, based on the equation suggested by Juliano and Knoerzer (2009) that linked directly the surviving mould spores to the pressure and temperature of the HPCD treatment.
Fig. 4 – Inactivation kinetics for A. ochraceus spores at 7.0 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data. treatment.
Adekunte, A., Valdramidis, V.P., Tiwari, B.K., Slone, N., Cullen, P.J., O‘Donnell, C.P., Scannell, A., 2010. Resistance of Cronobacter sakazakii in reconstituted powdered infant formula during ultrasound at controlled temperatures: a quantitative approach on microbial responses. Int. J. Food Microbiol. 142, 53–59. Amézqueta, S., Schorr-Galindo, S., Murillo-Arbizu, M., ˜ González-Penas, E., López de Cerain, A., Guiraud, J.P., 2012. OTA-producing fungi in foodstuffs: a review. Food Control 26 (2), 259–268. Arreola, A.G., Balaban, M.O., Wei, C.I., Peplow, A., Marshall, M., Cornell, J., 1991. Effect of supercritical carbon dioxide on microbial populations in single strength orange juice. J. Food Quality 14, 275–284. Balaban, M.O., 2004. Method and apparatus for continuous flow reduction of microbial and/or enzymatic activity in liquid products using carbon dioxide. US Patent 6,723,365 B2 (April 20, 2004) and US Patent Application 2004/0131739 A1 (July 8, 2004). Balaban, M.O., Marshall, M.R., Wicker, L., 1995. Inactivation of enzymes in foods with pressurized CO2 . US Patent 5,393,547 (February 28, 1995) and WO Patent 90/02799 (March 22, 1990). Ballestra, P., Cuq, J.-L., 1988. Influence of pressurized carbon dioxide on the thermal inactivation of bacterial and fungal spores. LWT-Food Sci. Technol. 31, 84–88. Bigelow, W.D., 1921. The logarithmic nature of thermal death time curves. J. Infect. Dis. 29, 528–536. van Boekel, M.A.J.S., 2008. Kinetic modeling of food quality: a critical review. Compr. Rev. Food Sci. Food Safety 7, 144–158. Boulekou, S.S., Katsaros, G.J., Taoukis, P.S., 2010. Inactivation kinetics of peach pulp pectin methylesterase as a function of high hydrostatic pressure and temperature process conditions. Food Bioprocess Technol. 3, 699–706. Calvo, L., Torres, E., 2010. Microbial inactivation of paprika using high-pressure CO2 . J. Supercrit. Fluids 52, 134–141. Connery, K.A., Shah, P., Coleman, L., Hunek, B., 2005. Commercialization of Better than Fresh Dense Phase Carbon Dioxide Processing for Liquid Food. ISSF, Orlando, FL, USA. Damar, S., Balaban, M.O., 2006. Review of dense phase CO2 technology: microbial and enzyme inactivation, and effects on food quality. J. Food Sci. 71, 1–11.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Dillow, A.K., Dehghani, F., Hrkach, J.S., Foster, N.R., Langer, R., 1999. Bacterial inactivation by using near- and supercritical CO2 . Proc. Natl. Acad. Sci. U. S. A. 96, 10344–10348. Enomoto, A., Nakamura, K., Hakoda, M., Amaya, N., 1997. Lethal effect of high-pressure carbon dioxide on a bacterial spore. J. Ferment. Bioeng. 83, 305–307. Erkmen, O., 2000. Antimicrobial effects of pressurized carbon dioxide on Brochothrix thermosphacta in broth and foods. J. Sci. Food Agric. 80, 1365–1370. Erkmen, O., 2001a. Antimicrobial effect of pressurized carbon dioxide on Yersinia enterocolitica in broth and foods. Food Sci. Technol. Int. 3, 245–250. Erkmen, O., 2001b. Mathematical modeling of Escherichia coli inactivation under high-pressure carbondioxide. J. Biosci. Bioeng. 92, 39–43. Garcia-Gonzalez, L., Geeraerd, A.H., Spilimbergo, S., Elst, K., Van Ginneken, L., Debevere, J., Van Impe, J.F., Devlieghere, F., 2007. High pressure carbon dioxide inactivation of microorganisms in foods: the past, the present and the future. Int. J. Food Microbiol. 117, 1–28. Ferrentino, G., Ferrari, G., Poletto, M., Balaban, M.O., 2008. Microbial inactivation kinetics during high-pressure carbon dioxide treatment: nonlinear model for the combined effect of temperature and pressure in apple juice. J. Food Sci. 73 (8), 389–395. Ferrentino, G., Spilimbergo, S., 2011. High pressure carbon dioxide pasteurization of solid foods: current knowledge and future outlooks. Trends Food Sci. Technol. 22, 427L 441. Ferrentino, G., Balzan, B., Spilimbergo, S., 2013. Optimization of supercritical carbon dioxide treatment for the inactivation of the natural microbial flora in cubed cooked ham. Int. J. Food Microbiol. 161, 189–196. Hong, S.I., Pyun, Y.R., 1999. Inactivation kinetics of Lactobacillus plantarum by high pressure carbon dioxide. J. Food Sci. 64, 728–733.
7
Hong, S.I., Pyun, Y.R., 2001. Membrane damage and enzyme inactivation of Lactobacillus plantarum by high pressure CO2 treatment. Int. J. Food Microbiol. 63, 19–28. Juliano, P., Knoerzer, K., 2009. C. botulinum inactivation kinetics implemented in a computational model of a high-pressure sterilization process. Biotechnol. Prog. 25, 163–174. Kamihira, M., Taniguchi, M., Kobayashi, T., 1987. Sterilization of microorganisms with supercritical carbon dioxide. Agric. Biol. Chem. 51, 407–412. Liao, H.M., Hu, X.S., Liao, X.J., Chen, F., Wu, J.H., 2007. Inactivation of Escherichia coli inoculated into cloudy apple juice exposed to dense phase carbon dioxide. Int. J. Food Microbiol. 118, 126–131. Lin, H.M., Yang, Z.Y., Chen, L.F., 1993. Inactivation of Leuconostoc dextranicum with carbon dioxide under pressure. Chem. Eng. J. 52, B29–B34. Matsufuji, H., Furukawa, S., Teranishi, K., Kawaharada, K., Chino, M., Yamagata, K., Ogihara, H., Yamasaki, M., 2009. Effects of non-thermal processes on the inactivation of microorganisms and antioxidants in minimally processed vegetables. Food Sci. Technol. Res. 15, 153–162. Peleg, M., Normand, M.D., 2004. Calculating microbial survival parameters and predicting survival curves from non-isothermal inactivation data. Crit. Rev. Food Sci. Nutr. 44, 409–418. Oulé, M.K., Tano, K., Bernier, A.-M., Arul, J., 2006. Escherichia coli inactivation mechanism by pressurized CO2 . Can. J. Microbiol. 52, 1208–1217. Shimoda, M., Kago, N.H., Kojima Miyake, M., Osajima, Y., Hayakawa, I., 2002. Accelerated death kinetics of Aspergillus niger spores under high pressure carbonation. Appl. Environ. Microbiol. 68, 4162–4167. Spilimbergo, S., Dehghani, F., Bertucco, A., Foster, N., 2003. Inactivation of bacteria and spores by pulse electric field and high pressure CO2 at low temperature. Biotechnol. Bioeng. 82, 118–125.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Contents lists available at ScienceDirect
Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp
Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study Corina Neagu a , Daniela Borda a,∗ , Osman Erkmen b a b
˘ “Dunarea de Jos” University of Galat¸i, Faculty of Food Science and Engineering, 111 Domneasca Street, 800201 Galati, Romania Department of Food Engineering, Faculty of Engineering, University of Gaziantep, 27310 Gaziantep, Turkey
a b s t r a c t The aim of this research was to analyze and model the combined effect of pressure and temperature upon Aspergillus ochraceus spores exposed to high pressure carbon dioxide (HPCD) treatment and to estimate the kinetic parameters. Lately, many empirical or semi-empirical mathematical models were presented and discussed for different microorganisms, mainly bacteria, demonstrating an increased need for tools able to quantify the parameters of the microbial inactivation. A. ocharaceus HPCD inactivation was adequately described by first order reaction kinetics and a synergic effect of pressure and temperature was noticed for the experimental range where pressure varied from 5.4 to 7.0 MPa and temperature varied from 30 to 50 ◦ C. The decimal reduction time (D) ranged from 47.07 min at 5.4 MPa and 30 ◦ C to 5.04 min at 7.0 MPa and 50 ◦ C. In this study three mathematical models were evaluated in order to find the best one that describes accurately the influence of pressure and temperature on the studied microbial response. An empirical exponential equation, that described pressure and temperature influence in the form of a polynomial equation, was found to best describe the dependence of A. ochraceus HPCD inactivation in the range 5.4–7.0 MPa and 30–50 ◦ C. This work adds insight to moulds inactivation at the already existing body of knowledge on bacteria inactivation with HPCD and provides support to potential industrial applications of the minimal–thermal methods that combine high pressure and mild temperature with carbon dioxide for different food matrixes. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: High pressure carbon dioxide; Inactivation; Aspergillus ochraceus; Mathematical model; Spores; Kinetics
1.
Introduction
Thermal food preservation is a well known classical treatment for reducing the microorganisms in foods. This technique is adapted to equilibrate the difficult balance between overheating (reducing the foods’ sensorial properties) and underheating (leading to unsafe and low-quality food products). As consumers are demanding minimally processed and fresh-like food products the application of alternative methods to thermal treatment known as cold pasteurization processes is gaining ground. In the past decades, a noticeable inactivation effect of high-pressure carbon dioxide (HPCD) on microorganisms in liquid foods at low temperatures and pressures below 20 MPa has been proved effective for food preservation (Enomoto et al., 1997; Erkmen, 2000; Hong and Pyun, 2001; Liao et al., 2007). In the HPCD technique food
is in contact with pressurized either sub- or supercritical CO2 for a certain amount of time in a batch, semi-batch or continuous manner. The different steps in the inactivation mechanism can be summarized as follows: (1) solubilization of pressurized CO2 in the external liquid phase decreasing the extracellular pH (pHex ), (2) cell membrane modification due to diffusion of CO2 into the cellular membrane, (3) cellular penetration of CO2 decreasing the intracellular pH (pHin ), (4) key enzyme inactivation/cellular metabolism inhibition due to pHin lowering, (5) direct (inhibitory) effect of molecular CO2 and HCO3 − on cell metabolism, (6) precipitation of CO3 2− with inorganic electrolytes and Ca2+ binding proteins causing the intracellular electrolyte imbalance and (7) removal of vital constituents from cells and cell membranes (Damar and Balaban, 2006; Spilimbergo et al., 2003; Garcia-Gonzalez et al., 2007).
∗
Corresponding author. Tel.: +40 336130177; fax: +40 236460165. E-mail address: [email protected] (D. Borda). Received 2 February 2013; Received in revised form 4 August 2013; Accepted 22 August 2013 0960-3085/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fbp.2013.08.011 Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
2
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Microbial inactivation achieved by HPCD ranges from 2 to 12 logs using pressures below 50 MPa and temperatures between 5 and 60 ◦ C (Damar and Balaban, 2006). Exposure time, pressure, temperature, initial number of cells, pressure cycling, initial pH of medium, water activity, cell growth phase or generation time, species of microorganisms and type of treatment all influence microbial inactivation by HPCD (Arreola et al., 1991; Dillow et al., 1999; Kamihira et al., 1987; Lin et al., 1993; Spilimbergo et al., 2003). In spite of intensified research efforts in the last years and presence of patents on the market (Balaban, 2004; Balaban et al., 1995; Connery et al., 2005) the HPCD technique has limited applications at industrial scale up to now (Ferrentino and Spilimbergo, 2011). The scaling up of the novel technologies based on various HPCD applications needs however more extensive studies on fundamental and mechanistic models able to better describe the microbial inactivation (Ferrentino and Spilimbergo, 2011). While bacteria inactivation under pressure and carbon dioxide treatment was extensively studied (Dillow et al., 1999; Kamihira et al., 1987; Oulé et al., 2006; Spilimbergo et al., 2003) less work was reported for moulds (Shimoda et al., 2002), although the total microbial flora inactivation by HPCD was reported (Calvo and Torres, 2010; Ferrentino et al., 2008, 2013; Matsufuji et al., 2009). The general objective of this research was to investigate the HPCD inactivation kinetics of Aspergillus ochraceus spores, which is an important contaminant of diverse food matrixes such as cereals, wines, coffee, grapes and derivates, being capable to produce nephrotoxic metabolites such as mycotoxins. Aspergillus ochareceus presence in foods is related to the dietary exposure to a toxic secondary metabolite – ochratoxin A (OTA) (Amézqueta et al., 2012). The specific objectives of this study were to analyze the effect of HPCD at different pressures (5.4, 6.0 and 7.0 MPa) and temperatures (30, 40 and 50 ◦ C) on A. ochraceus inactivation and to select the best general model that accurately describes the mould response to HPCD treatment.
2.
Materials and methods
2.1.
Preparation of A. ochraceus spores
A. ochraceus 151 strain was obtained from USAMV (University of Agronomic Science and Veterinary Medicine, Bucharest, Romania) collection. The mould strain was activated on potato dextrose agar (PDA; Merck, Darmstadt) slant and a stock culture was prepared on the PDA slant by incubating at 25 ◦ C for 3 days. The mould cultures for experiments were subcultured from stock culture using PDA plates at 25 ◦ C for 6 days. The spores were collected by washing the surface of the agar plate cultures using potato dextrose media (PDB; Difco, Detroit) containing 0.1% Tween 80 (pH = 5.6). The spore suspension was filtered through three layers of sterile cheesecloth to remove the hyphae under aseptic conditions. Finally, the number of spores in the filtrate was brought to about 106 spores × ml−1 by adding the necessary amount of physiological saline solution. The initial number of spores in the suspension was counted by direct microscopic counting method using Neubauer improved chamber (Erkmen, 2001b). The spore suspension used in all experiments was freshly prepared every day and stored in a refrigerator at 4 ◦ C during the experiments.
Fig. 1 – Schematic diagram of the apparatus used for high pressure CO2 .
2.2.
Equipment
The high-pressure installation used for experimental treatments is shown in Fig. 1. A cylindrical pressure vessel (maximum pressure tolerance level of 100 MPa) with the internal volume of 266 ml was used for CO2 pressurization as previously described (Erkmen, 2000, 2001a). The vessel closure has gas impermeable connections for the temperature and pressure sensors and gas inlet and outlet. A pressure manometer (Klauser Fisher, 28124-1; Brothers Commercial, Gaziantep, Turkey) and chromel (90% nickel and 10% chromium) thermocouple (Heraeus, 24313651; Teknim, Ankara, Turkey) were installed to monitor the pressure and the temperature of gas in the pressure vessel. A line filter packed with silica gel (60/80 mesh, Alltech, USA) was also mounted in the CO2 outlet of the vessel to reduce the pressure release rate. After each run the pressure vessel was disinfected with 0.1% H2 O2 solution and rinsed with sterile distilled water.
2.3.
Pressure treatments
Two samples containing 5 ml of daily prepared spore suspension (106 spores × ml−1 ) were placed into loosely capped (sterile metallic cap standing at fixed position) sterile test cylindrical tubes (110 mm × 14 mm) and the tubes were gently shacked. The tubes were placed into the pressure vessel and the vessel was tightly closed and immersed in a thermostatic water bath (ST-402; Nüve, Sanayii ve Malzemeleri I˙malat ve Ticaret A.S¸., I˙stanbul, Turkey) at constant temperatures (30, 40 and 50 ◦ C). When the temperature was equilibrated (within 1 min) and all tubing connections were secured, commercially available CO2 (purity 99.990%, FNA 84-37-611; Koc¸erler, Industrial and Medical Gas Producing and Marketing Commercial Limited Company, Gaziantep, Turkey) was injected through the gas inlet valve from the gas cylinder into the vessel, reaching the desired pressures (5.4, 6.0 and 7.0 MPa) within 1 min. After being exposed to CO2 pressure for a designated time period at a temperature of 30, 40 or 50 ◦ C, the pressure was lowered to atmospheric pressure (within 1 min) by opening the gas outlet valve slowly and the duplicate tubes were pulled out. A blank tube containing 5 ml of sample with the same concentration of spore suspension as the regular samples was incubated under atmospheric pressure in the water bath. After the treatment, 1 ml of spore suspension was immediately taken out from each of the two tubes and the samples were examined for surviving A. ochraceus
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
ARTICLE IN PRESS 3
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
spores. Three experiments were repeated for each experimental condition with freshly prepared inoculum that was prepared and stored in the same conditions as the initial one.
2.4.
2.5.
Modelling and statistical analysis
2.5.1.
Primary models
The inactivation of A. ochraceus spores was described using a first order kinetic model. Hence the general inactivation equation for spores is (Peleg and Normand, 2004): dN(t) = −k · t N(t)
N(t) = exp(−k · t) N0
(2)
where N(t) is the number of spores at time t (CFU ml−1 ), N0 is the number of spores at time 0 (CFU ml−1 ), k is the rate constant (min−1 ) and t is the time (min). For microorganisms’ inactivation, first order inactivation models or linearized models, equivalent to Eq. (2), are frequently applied to estimate the inactivation rate and the decimal reduction time, depending on the microbial load and time (Eq. (3)). Linear regression procedures were performed with SAS Windows 9.1 software (Cary, NC, SUA). The liniarized Eq. (2) is:
N N0
= −k · t
(3)
where N is the number of spores at time t (CFU ml−1 ), N0 is the number of spores at time 0 (CFU ml−1 ) and t is the time (min). The decimal reduction time (D (min)) is calculated with Eq. (4) (Bigelow, 1921):
2.6.
2.303 k
ln 10 ln 10 ln 10 (T − Tref ) ·exp ·exp (P − Pref ) Asym Dref z zP (5)
where k(T,P) is the inactivation rate constant as a function of pressure and temperature (min−1 ), z is the change in temperature (◦ C) required to achieve a 10-fold change in Asym Dref (min) value and zP is the change in pressure (MPa) required to achieve a 10-fold reduction in Asym Dref value. The Asym Dref represents the negative inverse of the loglinear part of the inactivation slope, after the shoulder region (Adekunte et al., 2010). The reference values of temperature and pressure were selected in the middle of processing conditions (Tref = 40◦ C and Pref = 6.0 MPa). Replacing the rate constant from Eq. (2) with the number of spores, a single general equation was obtained – Eq. (6):
ln
N N0
=−
ln 10 Asym Dref
·exp
(1)
which, when the reaction order is one, can be integrated under isothermal conditions into:
D=
k(T, P) =
Enumeration of A. ochraceus spores
Each treated sample was serially diluted with sterile physiological saline solution. The initial and the surviving A. ochraceus spores were counted by spread plating 1 ml of diluted and non diluted samples on duplicate plates of PDA (pH = 5.6). The plates were incubated at 25 ◦ C for 3 days, after which all the visible A. ochraceus colonies on PDA plates were counted (Erkmen, 2000). The number of survivors was expressed as log colony forming unit (CFU ml−1 ).
ln
from the Bigelow model. The current study adapted the equation proposed by Adekunte et al. (2010) and the result is Eq. (5):
ln 10 zP
· exp
ln 10 z
(P − Pref )
(T − Tref )
·t
(6)
This procedure brings the advantage of avoiding a considerable reduction of the data set when first estimating the reaction rate (k) and also the advantage of avoiding error multiplication from one regression equation (Eq. (2)) to another (Eq. (5)). The second model is based on the kinetic equation successfully applied by Boulekou et al. (2010) that describes the effect of pressure and temperature on enzyme inactivation. However, considering the concerns expressed by researchers on using certain kinetic parameters from the chemical reactions to describe the microbial inactivation or growth such as the activation energy, the activation volume but also the universal gas constant (van Boekel, 2008; Peleg and Normand, 2004), these parameters were replaced with general symbols denominated with alphabetical letters and no physical signification nor measurement units were attributed to the estimated parameters. The usefulness of a general kinetic model was verified for the fungal HPCD inactivation. Eq. (7) resulted from these changes:
ln
N N0
= −k0 · exp
A · exp[−B(P − Pref )] ·
P − Pref −(C(T − Tref ) + D) · T
·t
1 T
−
1 Tref
(7)
(4)
General models
In order to describe A. ochraceus spores HPCD inactivation as a function of pressure and temperature, three general semiempirical models adapted from the literature (Adekunte et al., 2010; Boulekou et al., 2010; Juliano and Knoerzer, 2009) were tested and compared. In the model proposed by Adekunte et al. (2010) the maximum inactivation rate constant is expressed as a function of temperature and amplitude, based on a equation developed
where k0 , A, B, C and D are model parameters. The third model tested was the one applied by Juliano and Knoerzer (2009) for the inactivation of Clostridium botulinum in dynamic conditions using a high pressure high thermal treatment. This model with 6 terms described the rate constant as an exponential function of pressure and temperature. The current approach applied only the terms of a polynomial equation with second order terms and replaced the rate constant from Eq. (2) in order to be able to use the entire data set (n = 68). The equation resulting from these changes
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
ARTICLE IN PRESS
FBP-436; No. of Pages 7
4
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
is Eq. (8):
ln
N N0
Table 1 – D values (min) for the A. ochraceus inactivation. P (MPa) T (◦ C) = −exp [(A0 + A1 · (P − Pref ) + A2 · (T − Tref ) 2
+A3 · (P − Pref ) + A4 · (T − Tref )
30
2
+A5 · (P − Pref ) · (T − Tref ))] · t
(8)
5.4 6.0 7.0 a
where A0 , A1 , A2 , A3 , A4 and A5 are model parameters. For Eqs. (7) and (8) the reference values of temperature and pressure were considered as for the Eq. (6) in the middle of processing conditions (Tref = 40 ◦ C and Pref = 6.0 MPa). Using non-linear regression procedure (SAS software, version 9.1, Cary, NC, USA) the parameters of Eqs. (6)–(8) were estimated for all the pressure temperature combinations with the entire data set (n = 68). As a basis for model discrimination root mean square error value was calculated and the goodness of fit that correlates the experimental and the predicted model values was assessed for all the tested models. RMSE (root mean square error)
RMSE =
ni i=1
(yexp (ti ) − y(ti , pis ))
2
nt − np
(9)
where yexp (ti ) denotes the experimental observations, y(ti ,pis ) the predicted values, nt the total number of data points and np the number of estimated model parameters. Standard deviation of the estimated parameters was also a good indicator for the contribution of the individual parameters to the model.
3.
Results and discussion
3.1.
Inactivation kinetics – primary models
The survival curves of A. ochraceus spores using HPCD treatment were fitted by the primary linear model (Eq. (3)) at different temperatures (30, 40 and 50 ◦ C) combined with different pressures (5.4, 6.0 and 7.0 MPa). At 5.4 MPa and 30 ◦ C the inactivation of spores takes place slowly, while at 40 ◦ C a 4.44 log reduction of the number of spores was noticed after 120 min of treatment. At 50 ◦ C after 120 min of treatment the total inactivation of the spores was obtained. It can be noticed that the inactivation effect of HPCD increased with the increase of temperature from 30 to 50 ◦ C. Linear inactivation was achieved at 6.0 MPa when inactivation curves were plotted as a function of time on a log linear scale, indicating first order kinetics for the entire experimental domain ranging from 30 to 50 ◦ C (data not shown). At 30 ◦ C and 6.0 MPa a very significant (R2 = 0.99) inactivation occurs after 120 min, but, generally, the inactivation goes slowly. At 40 ◦ C and 6.0 MPa a 2.81 log reduction of the initial number of viable spores was registered after 60 min of treatment. At 50 ◦ C and 6.0 MPa the number of viable spores had a 5.07 log reduction after 60 min of treatment and after 75 min total inactivation was obtained. At 7.0 MPa, after 90 min of treatment at 30 ◦ C, the number of viable spores was reduced with 2.87 log units. A 99.99% reduction in the number of viable spores was observed after 90 min of treatment at 40 ◦ C and 7.0 MPa. Inactivation at the same pressure and 50 ◦ C took place quickly and after 10 min of
b
40
50
47.07 ± 0.91a (0.93b ) 27.27 ± 0.37 (0.98) 19.01 ± 1.17 (0.97) 39.22 ± 1.10 (0.98) 17.12 ± 0.01 (0.98) 11.33 ± 0.28 (0.99) 27.43 ± 0.67 (0.99) 13.28 ± 0.52 (0.98) 5.04 ± 0.34 (0.96)
Standard error of regression. Square correlation coefficient.
treatment a 3.17 log reduction of the number of viable spores was noticed while after 30 min total inactivation was obtained. Inactivation of microorganisms by high-pressure carbon dioxide is governed essentially by the dissolution of CO2 into the cells (Erkmen, 2000; Hong and Pyun, 1999) and its effectiveness can be improved by the enhancement of the transfer rate. Principally, pressure controls the solubilization rate of CO2 and its solubility in a suspension medium (Ballestra and Cuq, 1988; Hong and Pyun, 1999). Shimoda et al. (2002) reported that the death kinetics of Aspergillus niger spores (expressed as the decimal reduction time, D) was linearly related to the treatment temperature and the concentration of dissolved CO2 , with an observed significant interaction between these two parameters. In the present study the decimal reduction time (D) was reduced by 1.7-fold from 47.07 min to 27.27 min for an increase in pressure from 5.4 to 7.0 MPa at 30 ◦ C and by 2.5-fold from 47.07 min to 19.01 min for an increase in temperature from 30 to 50 ◦ C (Table 1) at constant pressure (5.4 MPa). The stimulating effect of temperature on the microbial inactivation of HPCD has been frequently reported, as reviewed in Garcia-Gonzalez et al. (2007). An increase in temperature may stimulate the diffusivity of CO2 acting on the integrity of the cellular membrane and increasing its fluidity (Lin et al., 1993; Hong and Pyun, 2001; Oulé et al., 2006). The stimulating effect of temperature on mould inactivation can be in part counteracted by its inhibiting effect on CO2 solubility. In the present study, for the entire experimental domain a synergistic effect of temperature and pressure could be noticed and D value was reduced 9.3-fold from 47.06 min at 30 ◦ C and 5.4 MPa to 5.04 min at 50 ◦ C and 7.0 MPa. The correlation coefficients of the regression curves for all the temperatures and pressures studied were higher than 0.93 (Table 1).
3.2.
General models
To express the pressure–temperature dependence of A. ochraceus spores inactivation several models were assessed and compared. The parameters of the model estimated by Eq. (6) are presented in Table 2. The main advantage when applying this
Table 2 – Values of the parameters estimated by the nonlinear regression based on Eq. (6). Parameter
Value
Asym Dref (min) z (◦ C) zP (MPa)
21.06 ± 0.49 35.36 ± 1.62 4.29 ± 0.29
a
a
RMSE
p
1.437
<0.0001
Standard error of regression.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
ARTICLE IN PRESS
FBP-436; No. of Pages 7
5
food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Table 3 – Values of the parameters estimated by the nonlinear regression based on Eq. (7).
Table 5 – Values of the parameters estimated by the nonlinear regression based on Eq. (8).
Parameter
Value
A B C D ko
617.95 × 101 −2.81 × 10−1 45.71 × 10−1 −38.20 × 101 3.78 × 10−1
a
± ± ± ± ±
18.72 × 101 a 1.22 × 10−1 36.72 × 10−1 188.03 × 101 0.14 × 10−1
RMSE
p
Parameter
Values
0.902
<0.0001
A0 A1 A2 A5
−21.88 × 10−1 5.66 × 10−1 6.40 × 10−2 3.08 × 10−2
a
0.14 × 10−1 a 0.2 × 10−1 0.17 × 10−2 0.27 × 10−2
p
0.773
<0.0001
Standard error of regression.
Standard error of regression.
model is considered its versatility in describing the kinetics of microbial inactivation with non-thermal technologies, in general (Adekunte et al., 2010). Moreover, the model is taking into account the non-linear regions that are often present on the microbial inactivation curves. The Asym Dref value of 21.06 min obtained in this case suggests a relatively slow HPCD inactivation process for A. ocharaceus in the studied pressure and temperature range. Much lower Asym Dref values were reported for Cronobacter sakazakii inactivation when applying combined ultrasound and temperature treatment (Adekunte et al., 2010). However, a strong dependence to pressure is shown by the current inactivation model where the estimated zP value is of 4.29 MPa (Table 2). The RMSE (1.437) value does not necessarily suggest a very good fit of the model with the experimental data, however the standard deviation for all the parameters is less than 7% of the estimated value. The correlation between the logarithm of the experimental values (ln(N/N0 )) and the predicted ones given by Eq. (6) indicates a good value of the correlation (R2 = 0.94). Another semi-empirical model that takes into consideration the effect of pressure and temperature on the inactivation rate was described by Eq. (7). The model has a lower RMSE (Table 3) value (0.902), indicating a better fitting capacity than the one of the model described by Eq. (6). However, the initially estimated parameter C had a high standard deviation (45.71 × 10−1 ± 36.72 × 10−1 ), thus aiming at high parameter accuracy, the term that described the temperature dependence was eliminated. The parameters obtained from the non-linear regression after the elimination of parameter C are indicated in Table 4. The removal of the parameter describing the influence of temperature from the initial model produced a significant decrease of the standard deviation for all of the remaining parameters to less than 9% of the estimated value and a decrease of the RMSE value to 0.869, suggesting a better model compared to the previous one. The parity correlation of the predicted with the experimental values has a very good R2 value (0.96) suggesting a tight distribution of the points around the line of equivalence.
Table 4 – Values of the parameters estimated by the nonlinear regression based on Eq. (7) after the removal of the term (T − Tref ). Parameter
Value
A B D ko
608.24 × 101 −4.51 × 10−1 −36.45 × 101 3.82 × 10−1
a
± ± ± ±
RMSE
± ± ± ±
Standard error of regression.
18.39 × 101 a 0.39 × 10−1 1.76 × 101 0.14 × 10−1
RMSE
p
0.869
<0.0001
The third model tested was implemented by Juliano and Knoerzer (2009) in a computational model that described the kinetics of C. botulinum inactivation with high pressure high thermal processing. This empirical model is an exponential function with second order polynomial terms as exponent. The polynomial exponent shows the dependence of the inactivation to pressure and temperature. The model described by Eq. (8) is considered to better describe the rate of inactivation than the classic log-linear kinetics (Juliano and Knoerzer, 2009). Eq. (8) was applied and, aiming at the most parsimonious model with the minimum number of parameters, all the second order parameters were eliminated due to having standard error values higher than the estimated parameters. Thus, besides the intercept, the polynomial exponent included only terms in P, T and P × T (Table 5). The resulting equation had a very good RMSE value −0.773, indicating a high accuracy of the model in describing A. ocharaceus inactivation. The standard deviation of all estimated parameters was less than 9%. A very good correlation R2 value (0.97) between the experimental and the predicted model values is suggesting a better interpolating capacity of this model – Eq. (8) compared to Eq. (7) and (6) where the R2 values were 0.96 respectively 0.94. Even though all the tested models proved to be reliable in describing the inactivation of A. ochareceus with high pressure carbon dioxide treatment in the temperature range 30–50 ◦ C combined with pressure in the range 5.4–7.0 MPa there are specific differences between the three models studied that can help discriminate them. The advantage of applying the Adekunte et al. (2010) kinetic model is linked to its versatility of describing linear and nonlinear kinetic processes and in bringing physical signification to the model parameters such as Asym Dref , z and zP . In this case the inactivation of A. ochraceus in the studied range was described by Eq. (6) which presented the highest RMSE value among all the analyzed models. The estimated values for Asym Dref , z and zP are characteristic for microbial inactivation. Validation studies on different strains are required prior to selecting this model as a tool for quantitative prediction of moulds spores’ survival. The Boulekou et al. (2010) model derived from Arrhenius and Eyring equations, described by Eq. (7) was successfully applied to describe the inactivation of A. ocharecus. However, researchers should avoid, when using models from enzyme kinetics, to attach physical signification for the estimated parameters such as the activation energy. Figs. 2–4 presents the experimental values as ln(N/N0 ) vs. time and the ones predicted by the three studied models, demonstrating that although all models describe well the inactivation of A. ochraceus the one that describes most accurately the experimental results is Eq. (8).
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
6
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
4.
Fig. 2 – Inactivation kinetics for A. ochraceus at 5.4 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data.
Conclusions
Inactivation of the A. ochraceus spores in PDA media with HPCD was obtained in the pressure range 5.4–7.0 MPa combined with temperatures from 30 to 50 ◦ C. The fastest inactivation rate was obtained for 7.0 MPa combined with 50 ◦ C treatment, where the D value achieved was 5.04 min. A power law model was the best HPCD predicting model of A. ochraceus spores in the experimental range. The advantages of directly using ln(N/N0 ) values in the general model is the linked with the use of the entire data set to estimate the pressure and temperature dependency without multiplying the errors form the primary to the secondary models. Statistical parameters such as RMSE, standard deviation for the parameters and the goodness of fit correlation indices enabled the selection of the best model that predicts A. ochraceus inactivation. Further studies are required to validate this model for the HPCD inactivation of other mould strains and in different food matrixes.
Acknowledgements This paper was supported by Gaziantep University Research Fund and PN-II-RU-ID-647 314 – Romania.
References
Fig. 3 – Inactivation kinetics for A. ochraceus spores at 6.0 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data.
Therefore, the best semi-empirical mathematical model for A. ochraceus inactivation considering the goodness of fit, the RMSE values and the standard deviation for the model parameters was found to be the equation that has a polynomial exponent, based on the equation suggested by Juliano and Knoerzer (2009) that linked directly the surviving mould spores to the pressure and temperature of the HPCD treatment.
Fig. 4 – Inactivation kinetics for A. ochraceus spores at 7.0 MPa and different temperatures. The lines represent the fit of the general inactivation equations: Eq. (6) —, Eq. (7) - - - · and Eq. (8) – · · to the experimental data. treatment.
Adekunte, A., Valdramidis, V.P., Tiwari, B.K., Slone, N., Cullen, P.J., O‘Donnell, C.P., Scannell, A., 2010. Resistance of Cronobacter sakazakii in reconstituted powdered infant formula during ultrasound at controlled temperatures: a quantitative approach on microbial responses. Int. J. Food Microbiol. 142, 53–59. Amézqueta, S., Schorr-Galindo, S., Murillo-Arbizu, M., ˜ González-Penas, E., López de Cerain, A., Guiraud, J.P., 2012. OTA-producing fungi in foodstuffs: a review. Food Control 26 (2), 259–268. Arreola, A.G., Balaban, M.O., Wei, C.I., Peplow, A., Marshall, M., Cornell, J., 1991. Effect of supercritical carbon dioxide on microbial populations in single strength orange juice. J. Food Quality 14, 275–284. Balaban, M.O., 2004. Method and apparatus for continuous flow reduction of microbial and/or enzymatic activity in liquid products using carbon dioxide. US Patent 6,723,365 B2 (April 20, 2004) and US Patent Application 2004/0131739 A1 (July 8, 2004). Balaban, M.O., Marshall, M.R., Wicker, L., 1995. Inactivation of enzymes in foods with pressurized CO2 . US Patent 5,393,547 (February 28, 1995) and WO Patent 90/02799 (March 22, 1990). Ballestra, P., Cuq, J.-L., 1988. Influence of pressurized carbon dioxide on the thermal inactivation of bacterial and fungal spores. LWT-Food Sci. Technol. 31, 84–88. Bigelow, W.D., 1921. The logarithmic nature of thermal death time curves. J. Infect. Dis. 29, 528–536. van Boekel, M.A.J.S., 2008. Kinetic modeling of food quality: a critical review. Compr. Rev. Food Sci. Food Safety 7, 144–158. Boulekou, S.S., Katsaros, G.J., Taoukis, P.S., 2010. Inactivation kinetics of peach pulp pectin methylesterase as a function of high hydrostatic pressure and temperature process conditions. Food Bioprocess Technol. 3, 699–706. Calvo, L., Torres, E., 2010. Microbial inactivation of paprika using high-pressure CO2 . J. Supercrit. Fluids 52, 134–141. Connery, K.A., Shah, P., Coleman, L., Hunek, B., 2005. Commercialization of Better than Fresh Dense Phase Carbon Dioxide Processing for Liquid Food. ISSF, Orlando, FL, USA. Damar, S., Balaban, M.O., 2006. Review of dense phase CO2 technology: microbial and enzyme inactivation, and effects on food quality. J. Food Sci. 71, 1–11.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011
FBP-436; No. of Pages 7
ARTICLE IN PRESS food and bioproducts processing x x x ( 2 0 1 3 ) xxx–xxx
Dillow, A.K., Dehghani, F., Hrkach, J.S., Foster, N.R., Langer, R., 1999. Bacterial inactivation by using near- and supercritical CO2 . Proc. Natl. Acad. Sci. U. S. A. 96, 10344–10348. Enomoto, A., Nakamura, K., Hakoda, M., Amaya, N., 1997. Lethal effect of high-pressure carbon dioxide on a bacterial spore. J. Ferment. Bioeng. 83, 305–307. Erkmen, O., 2000. Antimicrobial effects of pressurized carbon dioxide on Brochothrix thermosphacta in broth and foods. J. Sci. Food Agric. 80, 1365–1370. Erkmen, O., 2001a. Antimicrobial effect of pressurized carbon dioxide on Yersinia enterocolitica in broth and foods. Food Sci. Technol. Int. 3, 245–250. Erkmen, O., 2001b. Mathematical modeling of Escherichia coli inactivation under high-pressure carbondioxide. J. Biosci. Bioeng. 92, 39–43. Garcia-Gonzalez, L., Geeraerd, A.H., Spilimbergo, S., Elst, K., Van Ginneken, L., Debevere, J., Van Impe, J.F., Devlieghere, F., 2007. High pressure carbon dioxide inactivation of microorganisms in foods: the past, the present and the future. Int. J. Food Microbiol. 117, 1–28. Ferrentino, G., Ferrari, G., Poletto, M., Balaban, M.O., 2008. Microbial inactivation kinetics during high-pressure carbon dioxide treatment: nonlinear model for the combined effect of temperature and pressure in apple juice. J. Food Sci. 73 (8), 389–395. Ferrentino, G., Spilimbergo, S., 2011. High pressure carbon dioxide pasteurization of solid foods: current knowledge and future outlooks. Trends Food Sci. Technol. 22, 427L 441. Ferrentino, G., Balzan, B., Spilimbergo, S., 2013. Optimization of supercritical carbon dioxide treatment for the inactivation of the natural microbial flora in cubed cooked ham. Int. J. Food Microbiol. 161, 189–196. Hong, S.I., Pyun, Y.R., 1999. Inactivation kinetics of Lactobacillus plantarum by high pressure carbon dioxide. J. Food Sci. 64, 728–733.
7
Hong, S.I., Pyun, Y.R., 2001. Membrane damage and enzyme inactivation of Lactobacillus plantarum by high pressure CO2 treatment. Int. J. Food Microbiol. 63, 19–28. Juliano, P., Knoerzer, K., 2009. C. botulinum inactivation kinetics implemented in a computational model of a high-pressure sterilization process. Biotechnol. Prog. 25, 163–174. Kamihira, M., Taniguchi, M., Kobayashi, T., 1987. Sterilization of microorganisms with supercritical carbon dioxide. Agric. Biol. Chem. 51, 407–412. Liao, H.M., Hu, X.S., Liao, X.J., Chen, F., Wu, J.H., 2007. Inactivation of Escherichia coli inoculated into cloudy apple juice exposed to dense phase carbon dioxide. Int. J. Food Microbiol. 118, 126–131. Lin, H.M., Yang, Z.Y., Chen, L.F., 1993. Inactivation of Leuconostoc dextranicum with carbon dioxide under pressure. Chem. Eng. J. 52, B29–B34. Matsufuji, H., Furukawa, S., Teranishi, K., Kawaharada, K., Chino, M., Yamagata, K., Ogihara, H., Yamasaki, M., 2009. Effects of non-thermal processes on the inactivation of microorganisms and antioxidants in minimally processed vegetables. Food Sci. Technol. Res. 15, 153–162. Peleg, M., Normand, M.D., 2004. Calculating microbial survival parameters and predicting survival curves from non-isothermal inactivation data. Crit. Rev. Food Sci. Nutr. 44, 409–418. Oulé, M.K., Tano, K., Bernier, A.-M., Arul, J., 2006. Escherichia coli inactivation mechanism by pressurized CO2 . Can. J. Microbiol. 52, 1208–1217. Shimoda, M., Kago, N.H., Kojima Miyake, M., Osajima, Y., Hayakawa, I., 2002. Accelerated death kinetics of Aspergillus niger spores under high pressure carbonation. Appl. Environ. Microbiol. 68, 4162–4167. Spilimbergo, S., Dehghani, F., Bertucco, A., Foster, N., 2003. Inactivation of bacteria and spores by pulse electric field and high pressure CO2 at low temperature. Biotechnol. Bioeng. 82, 118–125.
Please cite this article in press as: Neagu, C., et al., Mathematical modelling of Aspergillus ochraceus inactivation with supercritical carbon dioxide – A kinetic study. Food Bioprod Process (2013), http://dx.doi.org/10.1016/j.fbp.2013.08.011