Mathematical modeling of Escherichia coli inactivation under high-pressure carbon dioxide

Inactivation curves of Escherichia coli under high carbon dioxide pressures (2.5, 5.1, 7.6 and 10.1 MPa) at different temperatures (20, 30, 40 and 45 degrees C) were analyzed using the modified Gompertz model. The phase disappearance (time for complete inactivation of all cells, lambda) and the inactivation rate (mu) of E. coli were inversely related. Inactivation rates (mu) of E. coli were higher at 45 degrees C under 10.1 MPa CO2 pressure than at 25, 30 and 40 degrees C under 2.5, 5.1 and 7.6 MPa CO2 pressure. Increased pressure and temperature had significant effects on the survival of E. coli. The temperature dependence of the inactivation rate constant was analyzed based on the Arrhenius, linear and square-root models. The temperature sensitivity (high E(mu)) determined based on the Arrhenius model was higher at high temperatures. E(mu) (activation energy) value was -186.56 Kjoule/mol at 10.1 Mpa, and -137.24, -167.25 and -183.80 Kjoule/mol at 2.5, 5.1 and 7.6 MPa, respectively. Results of this study enable the prediction of microbial inactivation exposed to different CO2 pressures and temperatures.     

Mathematical modeling of Saccharomyces cerevisiae inactivation under high‐pressure carbon dioxide

High‐pressure carbon dioxide inactivation curves of Saccharomyces cerevisiae at different temperatures were analysed using the modified Gompertz model. Comparable λ and μ values were obtained under pressure treatment as function of temperature. The phase of disappearance (λ) and the inactivation rate (μ) of S. cerevisiae were inversely related. Higher μ values were obtained at 50°C than at 40, 30, and 20°C under 10.0 MPa CO₂ pressure. Increased pressure and temperature had significant effects on the survival of S. cerevisiae. Arrhenius, linear and square‐root models were used to analyse the temperature dependence of the inactivation rate constant. For the Arrhenius model the activation energy (E_μ) was 56.49 kJ/mol at 10.0 MPa, and 55.70, 53.83, and 52.20 kJ/mol at 7.5, 5.0, and 2.5 MPa, respectively. Results of this study enable the prediction of yeast inactivation exposed to different CO₂ pressures and temperatures.     

Effect of temperature and/or pressure on lactoperoxidase activity in bovine milk and acid whey

At atmospheric pressure, inactivation of lactoperoxidase (LPO) in milk and whey was studied in a temperature range of 69-73 degrees C and followed first order kinetics. Temperature dependence of the first order inactivation rate constants could be accurately described by the Arrhenius equation, with an activation energy of 635.3 +/- 70.7 kJ/mol for raw bovine milk and 736.9 +/- 40.9 kJ/mol for diluted whey, indicating a very high temperature sensitivity. On the other hand, LPO is very pressure resistant and not or only slightly affected by treatment at pressure up to 700 MPa combined with temperatures between 20 and 65 degrees C. Both for thermal and pressure treatment, stability of LPO was higher in milk than in diluted whey. Besides, a very pronounced antagonistic effect between high temperature and pressure was observed, i.e. at 73 degrees C, a temperature where thermal inactivation at atmospheric pressure occurs rapidly, application of pressure up to 700 MPa exerted a protective effect. At atmospheric pressure, LPO in diluted whey was optimally active at a temperature of about 50 degrees C. At all temperatures studied (20-60 degrees C), LPO remained active during pressure treatment up to 300 MPa, although the activity was significantly reduced at pressures higher than 100 MPa. The optimal temperature was found to shift to lower values (30-40 degrees C) with increasing pressure.     

Inactivation of polyphenol oxidases in cloudy apple juice exposed to supercritical carbon dioxide

The inactivation of polyphenol oxidase (PPO) in cloudy apple juice exposed to supercritical carbon dioxide (SCCO₂) treatment was investigated. Higher pressure, higher temperature, and longer treatment time caused more inactivation of PPO. The maximum reduction of PPO activity reached more than 60% at 30 MPa and 55 °C for 60 min. The experimental data followed first-order reaction kinetics; the kinetic rate constant k and the decimal reduction time D were closely related to the pressure and temperature of SCCO₂ treatment. Higher pressures or higher temperatures resulted in lower D values (higher k), the D value of PPO was minimized to 145 min treated by the combination of 30 MPa and 55 °C. Activation energy of 18.00 kJ /mol, was significantly reduced by SCCO₂ treatment at 30 MPa, as compared to activation energy of 72.0 kJ/mol for identical treatment at atmospheric pressure. Pressure and temperature sensitivity of kinetic parameters were studied. Z_P at 55 °C was 66.7 MPa and Z_T at 30 MPa was 108 °C.     

EFFECT OF HIGH HYDROSTATIC PRESSURE ON SPORES OF GEOBACILLUS STEAROTHERMOPHILUS SUSPENDED IN SOYMILK

The inactivation of Geobacillus stearothermophilus spores (ATCC 7953) inoculated in soymilk was investigated using high hydrostatic pressure (550, 585 and 620 MPa) in combination with temperature (70, 80 and 90C) for selected times (2 s to 15 min). Inactivation of spores occurred at all selected treatments. Less than 10 CFU/mL of G. stearothermophilus were observed after 7 min of treatment at 620 MPa and 90C. An increase in the inactivation rate constant, at the highest pressure, was observed, resulting in a decrease in D values at all temperatures. D values were calculated as 10.6, 6.2 and 3.5 min for 70, 80 and 90C, respectively after pressurization at 620 MPa. z_p values decreased as temperature increased with values ranging from 142 to 238 MPa. The activation energy required for inactivation of G. stearothermophilus spores in soymilk, at the selected treatments, was in the range of 37.9–57.4 kJ/mol.     

High Pressure Inactivation of Polyphenoloxidases

Pressure stabilities of polyphenoloxidases (PPO) from apples, avocados, grapes, pears and plums were determined at pH 6-7. These PPOs differed in pressure stability, but all were rather pressure-stable. Inactivation of PPO from apple, grape, avocado and pear at room temperature (25°C) became noticeable at 600, 700, 800 and 900 MPa respectively, and followed first-order kinetics. Plum PPO was not inactivated at room temperature by pressures up to 900 MPa. For the two most pressure-stable PPOs, we investigated whether pressure stability would be reduced by the simultaneous application of mild heat. In case of plum PPO, activity reduction was detectable at 900 MPa and 50°C. Further temperature increase resulted in increase of the inactivation rate constant (E_a 63 kJ/mol). In case of pear PPO, temperature increase up to 35°C resulted in a 3-fold reduction of the inactivation rate constant. Only at higher temperatures, increase of the inactivation rate constant with increasing temperature was noted (Ea 120 kJ/mol).     

Inactivation of Escherichia coli inoculated into cloudy apple juice exposed to dense phase carbon dioxide

The inactivation of Escherichia coli in cloudy apple juice by dense phase carbon dioxide (DPCD) was investigated. With CO2 at 20 MPa and 37 degrees C or at 30 MPa and 42 degrees C, the inactivation of E. coli significantly increased (p<0.05) when increasing the exposure time, which conformed to a fast-to-slow two-stage kinetics. The two stages were well fitted to first-order reactions. Higher temperature or pressure significantly enhanced the bactericidal effect of DPCD (p<0.05), the maximum reduction was 7.66 log CFU at 45 MPa and 52 degrees C for 30 min. The survival curves against temperature or pressure were fitted using a linear equation with high regression coefficients (R2>0.94). The temperature inactivation rate (kT) and pressure inactivation rate (kP) were obtained. Higher kT or kP indicated higher susceptibility of E. coli to temperature or pressure. Moreover, there was good linear correlation of kT with pressure (R2=1.00). Also, kP increased with increasing temperature except for 37 degrees C. Greater inactivation of E. coli was obtained with 99.9% CO2 than with 99.5% CO2 or with the initial number of 10(5) CFU/mL than with that of 10(8) CFU/mL at 20 MPa and 37 degrees C.     

Kinetic study of high pressure microbial and enzyme inactivation and selection of pasteurisation conditions for Valencia Orange Juice

Keeping quality of fresh orange juice is highly dependent on pectinolytic enzyme activity and the growth of spoilage microorganisms. The inactivation kinetics of indigenous pectin methylesterase (PME) and of the two more pressure resistant species of spoilage lactic acid bacteria (LAB) Lactobacillus plantarum and L. brevis in freshly squeezed Valencia orange juice under high hydrostatic pressure (100–500 MPa) combined with moderate temperature (20–40 °C) was investigated. PME inactivation followed first order kinetics with a residual PME activity (15%) at all pressure–temperature combinations used. The values of activation energy and activation volume were estimated at each pressure and at each temperature, respectively. Values of 90 kJ/mol and ?30 mL/mol at reference pressure of 300 MPa and reference temperature of 35 °C were estimated respectively. The corresponding z_T and z_P values of LAB inactivation were also estimated at all conditions tested. Values of 19.5 °C and 95 MPa at reference pressure of 300 MPa and reference temperature of 30 °C were estimated respectively for L. plantarum, while the corresponding values for L. brevis were 40 °C and 82 MPa, respectively, at the same reference conditions. Pressure and temperature were found to act synergistically both for PME and LAB inactivation. The PME and LAB inactivation rate constants were expressed as functions of the temperature and pressure process conditions. These functions allow the determination of the pressure/temperature conditions that achieve the target enzyme and microbial inactivation at a selected processing time. The process conditions of 350 MPa at 35 °C for 2 min are proposed as effective for Valencia orange juice cold pasteurisation.     

High pressure thermal inactivation kinetics of a plasmin system

A crude plasmin extract was prepared from milk by ultracentrifugation and was partially purified using ammonium sulfate precipitation. Isothermal and high-pressure inactivation of this plasmin system at pH 6.7 could be described by a first-order kinetic model. As expected, the plasmin system displayed a high thermostability. High-pressure treatments were conducted in the 300- to 800-MPa pressure range, combined with temperatures from 25 to 65 degrees C. The plasmin system was very pressure stable at room temperature, but inactivation occurred with combined high-pressure/temperature-treatments. The influence of temperature at different constant pressures on the inactivation rate constant was quantified using the Arrhenius equation. At all temperatures studied, a synergistic effect of temperature and high pressure was observed in the 300- to 600-MPa pressure range. However, an antagonistic effect of temperature and pressure appeared at pressures above 600 MPa.     

Inactivation of hepatitis A virus by high-pressure processing: the role of temperature and pressure oscillation

Inactivation of hepatitis A virus (HAV) in Dulbecco's modified Eagle medium with 10% fetal bovine serum was studied at pressures of 300, 350, and 400 MPa and initial sample temperatures of -10, 0, 5, 10, 20, 30, 40, and 50 degrees C. Sample temperature during pressure application strongly influenced the efficiency of HAV inactivation. Elevated temperature (> 30 degrees C) enhanced pressure inactivation of HAV, while lower temperatures resulted in less inactivation. For example, 1-min treatments of 400 MPa at -10, 20, and 50 degrees C reduced titers of HAV by 1.0, 2.5, and 4.7 log PFU/ml, respectively. Pressure inactivation curves of HAV were obtained at 400 MPa and three temperatures (-10, 20, and 50 degrees C). With increasing treatment time, all three temperatures showed a rapid initial drop in virus titer with a diminishing inactivation rate (or tailing effect). Analysis of inactivation data indicated that the Weibull model more adequately fitted the inactivation curves than the linear model. Oscillatory high-pressure processing for 2, 4, 6, and 8 cycles at 400 MPa and temperatures of 20 and 50 degrees C did not considerably enhance pressure inactivation of HAV as compared with continuous high-pressure application. These results indicate that HAV exhibits, unlike other viruses examined to date, a reduced sensitivity to high pressure observed at cooler treatment temperatures. This work suggested that slightly elevated temperatures are advantageous for pressure inactivation of HAV within foods.     

Saccharomyces cerevisiae thermal inactivation kinetics combined with ultrasound.

Inactivation kinetics of Saccharomyces cerevisiae during thermal treatments at moderate temperatures (45.0, 47.5, 50.0, 52.5, or 55.0 degrees C) combined with application of 20 kHz of ultrasound were evaluated. S. cerevisiae inactivation under the combined effects of heat and ultrasound followed first-order reaction kinetics, with decimal reduction times (D) that varied from 22.3 to 0.8 min. D values in treatments that combined heat and ultrasound were significantly smaller (P < 0.05) than D values obtained for thermal treatments and were more noticeable at temperatures below 50 degrees C. The dependence of the D value on temperature had a significantly (P < 0.05) greater z value for combined treatments. Yeast heat inactivation kinetics revealed decreased thermal resistance caused by ultrasound.     

High Pressure Inactivation Kinetics of a Thermomyces lanuginosus Xylanase Evaluated as a Process Indicator

Abstract: The potential use of Thermomyces lanuginosus xylanase to develop a pressure–temperature–time integrator (PTTI) for high pressure processing was investigated. The combined effect of pressure and temperature on the inactivation of xylanase was studied in the pressure range of 100 to 600 MPa and temperature range of 50 to 70 °C. A synergistic effect of pressure and temperature was observed. Xylanase inactivation at the studied processing conditions followed first-order kinetics and was found to be very sensitive to changes in pressure and temperature. The values of activation energy and activation volume were estimated as 92.8 kJ/mol and −23.3 mL/mol at a reference pressure of 450 MPa and a reference temperature of 60 °C, respectively. A mathematical model of xylanase inactivation, having as variables time, pressure, and temperature allows the calculation of remaining enzyme activity at any combination of processing conditions within the studied domain. Practical Application: To ensure the optimization and control of high pressure processing, evaluation of the process impact on both safety and quality attributes of foods is essential. Enzymes can serve as effective tools in evaluating the impact of high pressure processes of foods.     

Combined pressure-thermal inactivation kinetics of Bacillus amyloliquefaciens spores in egg patty mince

Bacillus amyloliquefaciens is a potential surrogate for Clostridium botulinum in validation studies involving bacterial spore inactivation by pressure-assisted thermal processing. Spores of B. amyloliquefaciens Fad 82 were inoculated into egg patty mince (approximately 1.4 x 10(8) spores per g), and the product was treated with combinations of pressure (0.1 to 700 MPa) and heat (95 to 121 degrees C) in a custom-made high-pressure kinetic tester. The values for the inactivation kinetic parameter (D), temperature coefficient (zT), and pressure coefficient (zP) were determined with a linear model. Inactivation parameters from the nonlinear Weibull model also were estimated. An increase in process pressure decreased the D-value at 95, 105, and 110 degrees C; however, at 121 degrees C the contribution of pressure to spore lethality was less pronounced. The zP-value increased from 170 MPa at 95 degrees C to 332 MPa at 121 degrees C, suggesting that B. amyloliquefaciens spores became less sensitive to pressure changes at higher temperatures. Similarly, the zT-value increased from 8.2 degrees C at 0.1 MPa to 26.8 degrees C at 700 MPa, indicating that at elevated pressures, the spores were less sensitive to changes in temperature. The nonlinear Weibull model parameter b increased with increasing pressure or temperature and was inversely related to the D-value. Pressure-assisted thermal processing is a potential alternative to thermal processing for producing shelf-stable egg products.     

Heat inactivation of exogenous proteinases from Pseudomonas fluorescens. I. Possibility of inactivation in milk

The inactivation reaction of the proteinase of a P. fluorescens strain of biotype I in milk was investigated at 130-150 degrees C, also in milk and in buffer with and without added CaCl2 at temperatures below 100 degrees C. The decline in activity corresponded to first order kinetics in the UHT region; Ea = 115 kJ/mol. D values were 290 (130 degrees C), 124 (140 degrees C) and 54 s (150 degrees C); therefore, the usual temperature time combinations of UHT treatment are not sufficient to achieve the required rates of inactivation. At temperatures below 80 degrees C, inactivation corresponded increasingly to second order kinetics with considerably higher reaction rates; at 55 degrees C, an inactivation reaction corresponding to that induced by UHT treatment could be achieved at a thermal stress lower by a factor of 500. This "low temperature inactivation" was observed in a further 20 strains representing the spectrum of P. fluorescens. The average rates of inactivation following heat treatment in milk for 20 min are 47% at 55 degrees C and 44% at 60 degrees C. This can be regarded as the most effective temperature range for the inactivation of the proteinases in milk. Clear connections can be seen between the biotype groups and the optimum temperature for inactivation: biotype group I ca. 55 degrees C, group II (with a few exceptions) less than or equal to 50 degrees C and group III greater than or equal to 60 degrees C. The inactivation reaction is systematically influenced by the proteins and Ca++ ions present in milk.     

Inactivation of Escherichia coli and Listeria innocua in kiwifruit and pineapple juices by high hydrostatic pressure

Escherichia coli and Listeria innocua in kiwifruit and pineapple juices were exposed to high hydrostatic pressure (HHP) at 300 MPa for 5 min. Both bacteria showed equal resistance to HHP. Using low (0 degrees C) or sub-zero (-10 degrees C) temperatures instead of room temperature (20 degrees C) during pressurization did not change the effectiveness of HHP treatment on both bacteria in studied juices. Pulse pressure treatment (multiple pulses for a total holding time of 5 min at 300 MPa) instead of continuous (single pulse) treatment had no significant (p>0.05) effect on the microbial inactivation in kiwifruit juice; however, in pineapple juice pulse treatment, especially after 5 pulses, increased the inactivation significantly (p<0.05) for both bacteria. Following storage of pressure-treated (350 MPa, 20 degrees C for 60 s x 5 pulses) juices at 4, 20 and 37 degrees C up to 3 weeks, the level of microbial inactivation further increased and no injury recovery of the bacteria were detected. This work has shown that HHP treatment can be used to inactivate E. coli and L. innocua in kiwifruit and pineapple juices at lower pressure values at room temperature than the conditions used in commercial applications (>400 MPa). However, storage period and temperature should carefully be optimized to increase the safety of HHP treated fruit juices.     

Effect of high-hydrostatic pressure and temperature on rheological characteristics of glycomacropeptide

The influences of high pressure and temperature on the rheological characteristics of glycomacropeptide (GMP) were studied using a controlled rate rheometer. GMP dispersions at a concentration of 12.5% (w/w) were subjected to high pressure from 100 to 400 MPa for 30 min and temperature from 20 to 80 degrees C for 15 min followed by rheological measurements at a shear rate ranged between 0 and 200 s-1. Shear stress-shear rate data of both pressure and heat induced GMP samples fitted Herschel-Bulkley model well with yield stress. It exhibited shear-thinning behavior with flow behavior index ranged between 0.882 and 0.996. Consistency coefficient and apparent viscosity increased with pressure up to 300 MPa while those parameters decreased at 400 MPa. The rheology of GMP was influenced by temperature. The consistency coefficient and apparent viscosity at 100 s-1 obeyed the Arrhenius relationship with activation energies ranged between 8.17 to 12.38 kJ/mol. Lower activation energy signified lesser molecular aggregation or unfolding of protein molecules during thermal treatment of GMP.     

Temperature-assisted pressure inactivation of Listeria monocytogenes in turkey breast meat

Ready-to-eat turkey breast meat samples were surface-inoculated with a five-strain cocktail of Listeria monocytogenes cultures to a final concentration of approximately 10(7) CFU/g. The inoculated meat samples were vacuum-packaged and pressure treated at 300 MPa for 2 min, 400 MPa for 1 min, and 500 MPa for 1 min at initial sample temperatures of 1, 10, 20, 30, 40, 50, and 55 degrees C. L. monocytogenes was most resistant to pressure at temperatures between 10 and 30 degrees C. As temperature decreased below 10 degrees C or increased over 30 degrees C, its pressure sensitivity increased. This enhanced inactivation effect was more pronounced when meat samples were treated at higher temperature than at lower temperature. For example, a 1-min treatment of 500 MPa at 40 degrees C reduced the counts by 3.8 log(10), while at 1 and 20 degrees C the same treatment reduced counts by 1.4 and 0.9 log(10), respectively (P<0.05). The survival curves of L. monocytogenes were obtained at 300 MPa and 55 degrees C, 400 MPa and 50 degrees C, and 500 MPa and 40 degrees C. With increasing treatment time, the three survival curves showed a rapid initial drop in bacteria counts with a diminishing inactivation rate or tailing effect. The survival data were fitted with a linear and a nonlinear, Weibull, models. The Weibull model consistently produced better fit to the survival data than the linear model.     

A simplified approach for the kinetic characterization of acrylamide formation in fructose-asparagine model system.

The potential of acrylamide formation and degradation was studied in fructose-asparagine reaction system at different temperatures (120-200 degrees C). Kinetic data for concurrent formation and degradation of acrylamide was analysed based on a simplified form of chemical reaction in series in which acrylamide occurred as an intermediate. Experimental results revealed that the reaction proceeds zero order and first order with respect to asparagine and fructose, respectively. The thermal degradation of acrylamide was determined to be first order in fructose-glycine reaction system. The concurrent formation and degradation of acrylamide followed a typical kinetic pattern at the temperatures studied. Thermal degradation was observed within 60 min at T>150 degrees C, while only the accumulation was noted at T<150 degrees C. The mathematical model fitted to experimental data very well within temperature range of 120-200 degrees C. The temperature dependence of both acrylamide formation and degradation were found to obey Arrhenius law, and the activation energies were 52.1 kJ/mol and 72.9 kJ/mol, respectively.     

Conditions for high pressure inactivation of Vibrio parahaemolyticus in oysters

The objective of this study was to identify the high pressure processing conditions (pressure level, time, and temperature) needed to achieve a 5-log reduction of Vibrio parahaemolyticus in live oysters (Crassostrea virginica). Ten strains of V. parahaemolyticus were separately tested for their resistances to high pressure. The two most pressure-resistant strains were then used as a cocktail to represent baro-tolerant environmental strains. To evaluate the effect of temperature on pressure inactivation of V. parahaemolyticus, Vibrio-free oyster meats were inoculated with the cocktail of V. parahaemolyticus and incubated at room temperature (approximately 21 degrees C) for 24 h. Oyster meats were then blended and treated at 250 MPa for 5 min, 300 MPa for 2 min, and 350 MPa for 1 min. Pressure treatments were carried out at -2, 1, 5, 10, 20, 30, 40, and 45 degrees C. Temperatures >/=30 degrees C enhanced pressure inactivation of V. parahaemolyticus. To achieve a 5-log reduction of V. parahaemolyticus in live oysters, pressure treatment needed to be >/=350 MPa for 2 min at temperatures between 1 and 35 degrees C and >/=300 MPa for 2 min at 40 degrees C.     

Thermal kinetics of color degradation of mulberry fruit extract

The effects of temperature and pH on color degradation kinetics of the mulberry fruit extract were investigated. The absorbance at 510 nm was decreased with increase of heating time, but that at 420 nm was increased with the increase of heating time at 100 degrees C. The change of the browning index (A510/A420) was increased with increase of pH and was lower at pH 2.0 than that at pH 5.0. The browning index variation was adequately described by both the first-order and the zero-order kinetic. However, the zero-order kinetic model was proposed because of the better fit. According to the Arrhenius model, the activation energies for the browning index in the range of 80-100 degrees C for the four different pH values were 30.68 kJ/mol for pH 2.0, 35.87 kJ/mol for pH 3.0, 42.67 kJ/ mol for pH 4.0, and 43.49 kJ/mol for pH 5.0.