New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.     

Biphasic Thermal Inactivation Kinetics in Salmonella enteritidis PT4

The thermal inactivation kinetics of Salmonella enteritidis PT4 between 49 and 60°C were investigated. Using procedures designed to eliminate methodological artifacts, we found that the death kinetics deviated from the accepted model of first-order inactivation. When we used high-density stationary-phase populations and sensitive enumeration, the survivor curves at 60°C were reproducibly biphasic. The decimal reduction time at 60°C (D_60°C) of the tail subpopulation was more than four times that of the majority population. This difference decreased with decreasing temperature; i.e., the survivor curves became more linear, but the proportion of tail cells remained a constant proportion of the initial population, about 1 in 10⁴ to 10⁵. Z plots (log D versus temperature) for the two populations showed that the D values coincided at 51°C, indicating that the survivor curves should be linear at this temperature, and this was confirmed experimentally. Investigations into the nature of the tails ruled out genotypic differences between the populations and protection due to leakage from early heat casualties. Heating of cells at 59°C in the presence of 5 or 100 μg of chloramphenicol per ml resulted in reductions in the levels of tailing. These reductions were greatest at the higher chloramphenicol concentration. Our results indicate that de novo protein synthesis of heat shock proteins is responsible for the observed tailing. Chemostat-cultured cells heated at 60°C also produced biphasic survivor curves in all but one instance. Cells with higher growth rates were more heat sensitive, but tailing was comparable with batch cultures. Starved cells (no dilution input) displayed linear inactivation kinetics, suggesting that during starvation a rapid heat shock response cannot be initiated.     

Thermal Inactivation of Foot-and-Mouth Disease Viruses in Suspension

The heat resistance of foot-and-mouth disease virus (FMDV) strains isolated from outbreaks in Thailand was investigated in phosphate-buffered saline (PBS) at 50, 60, 70, 80, 90, and 100°C. The first-order kinetic model fitted most of the observed linear inactivation curves. The ranges of decimal-reduction time (D value) of FMDV strains at 50, 60, 70, 80, 90, and 100°C were 732 to 1,275 s, 16.37 to 42.00 s, 6.06 to 10.87 s, 2.84 to 5.99 s, 1.65 to 3.18 s, and 1.90 to 2.94 s, respectively. The heat resistances of FMDV strains at lower temperature (50°C) were not serotype specific. The effective inactivating temperature is approximately 60°C. Heat resistances of FMDV strains at 90 and 100°C were not statistically different (P > 0.05), while the FMDV serotype O (OPN) appeared to be the most heat resistant at 60 to 80°C. The other observed inactivation curves were linear with shoulder or tailing (biphasic curves). The shoulder effect was mostly observed at 90 and 100°C, while the tailing effect was mostly observed at 50 to 80°C. The adjusted D values in the case of shoulder and tailing effects did not affect the overall estimated heat resistance of these FMDV strains, so even unadjusted D values of deviant inactivation curves were legitimate. The z values of FMDV serotypes O, A, and Asia 1 were 21.78 to 23.26, 20.75 to 22.79, and 19.87°C, respectively. The z values of FMDV strains studied were not statistically significantly different (P > 0.05). The results of this study indicated that the heat resistance in PBS of FMDV strains from Thailand was much less than had been reported for foreign epidemic FMDV strains.     

Modeling the synergistic effect of high pressure and heat on inactivation kinetics of Listeria innocua: a preliminary study

The survival curves of Listeria innocua CDW47 by high hydrostatic pressure were obtained at four pressure levels (138, 207, 276, 345 MPa) and four temperatures (25, 35, 45, 50 degrees C) in peptone solution. Tailing was observed in the survival curves. Elevated temperatures and pressures substantially promoted the inactivation of L. innocua. A linear and two non-linear (Weibull and log-logistic) models were fitted to these data and the goodness of fit of these models were compared. Regression coefficients (R2), root mean square (RMSE), accuracy factor (Af) values and residual plots suggested that linear model, although it produced good fits for some pressure-temperature combinations, was not as appropriate as non-linear models to represent the data. The residual and correlation plots strongly suggested that among the non linear models studied the log-logistic model produced better fit to the data than the Weibull model. Such pressure-temperature inactivation models form the engineering basis for design, evaluation and optimization of high hydrostatic pressure processes as a new preservation technique.     

Effect of heat treatment on lactoperoxidase activity in caprine milk

Using isothermal conditions, inactivation of lactoperoxidase (LPO) in caprine milk was studied in a temperature range of 69–73 °C. In order to evaluate the effect of temperature on the reaction rate, the Arrhenius and thermal death time models were used for data analysis. Thermal inactivation of LPO can be accurately described by a first-order kinetic model, as indicated by the relationships obtained by plotting the retention values as a function of treatment time on a semi-logarithmic scale and confirmed by the high R²-values obtained. D- and k-values decreased and increased, respectively with increasing temperature, indicating a more rapid LPO inactivation at higher temperatures. The corresponding Z- and E_a-values calculated from the slope of the semi-logarithmic plots of D and k as a function of temperature were 9.45 °C and 225.98 kJ/mol, respectively.     

Accelerated Death Kinetics of Aspergillus niger Spores under High-Pressure Carbonation

The death kinetics of Aspergillus niger spores under high-pressure carbonation were investigated with respect to the concentration of dissolved CO₂ (dCO₂) and treatment temperature. All of the inactivation followed first-order death kinetics. The D value (decimal reduction time, or the time required for a 1-log-cycle reduction in the microbial population) in the saline carbonated at 10 MPa was 0.16 min at 52°C. The log D values were linearly related to the treatment temperature and the concentration of dCO₂, but a significant interaction was observed between them.     

Toward a multi-membrane model for potassium conduction in squid giant axon.

Possible physical mechanisms are considered which come close to a quantitative explanation for features of the potassium admittance magnitude. At 1–30 Hz there is an elevation of [Y] and positive phase above that obtained from the Hodgkin-Huxley model. Moreover there appears to be a slight negative phase for lower frequencies. An additional important feature for model fitting is the movement of the middle zero-phase crossing to the left with depolarization. Two general classes of subsystems are discussed. (1) Extracellular: potassium accumulation, barriers to diffusion near or adjacent to the excitable membrane, diffusion with volume flow, bulklimited diffusion through the Schwann cell layer and adsorption or absorption by the Schwann cells; (2) processes intrinsic to the excitable membrane: cyclic steady state, co-operative, inactivating and second order. A generalized potassium inactivation is treated in detail which provides fairly quantitative fits to transmembrane transfer data with a voltage-dependent inactivation time constant ranging between 40 and 100 ms. However, potassium accumulation coupled with hypothesized sorptive effects of the greater membrane, particularly the Schwann cell layer, also provide reasonable fits. Based on lack of experimental evidence for an inactivation, the choice is made for a multicompartment model. When an HH membrane element is combined with accumulation-depletion in an extracellular space and with a bulk limited or surface limited diffusion through the Schwann cells good agreement is obtained with measured admittance.     

Determination of Thermal Inactivation Kinetics of Hepatitis A Virus in Blue Mussel (Mytilus edulis) Homogenate

Hepatitis A virus (HAV) is a food-borne enteric virus responsible for outbreaks of hepatitis associated with shellfish consumption. The objectives of this study were to determine the thermal inactivation behavior of HAV in blue mussels, to compare the first-order and Weibull models to describe the data, to calculate Arrhenius activation energy for each model, and to evaluate model efficiency by using selected statistical criteria. The times required to reduce the population by 1 log cycle (D-values) calculated from the first-order model (50 to 72°C) ranged from 1.07 to 54.17 min for HAV. Using the Weibull model, the times required to destroy 1 log unit (t_{D = 1}) of HAV at the same temperatures were 1.57 to 37.91 min. At 72°C, the treatment times required to achieve a 6-log reduction were 7.49 min for the first-order model and 8.47 min for the Weibull model. The z-values (changes in temperature required for a 90% change in the log D-values) calculated for HAV were 15.88 ± 3.97°C (R², 0.94) with the Weibull model and 12.97 ± 0.59°C (R², 0.93) with the first-order model. The calculated activation energies for the first-order model and the Weibull model were 165 and 153 kJ/mol, respectively. The results revealed that the Weibull model was more appropriate for representing the thermal inactivation behavior of HAV in blue mussels. Correct understanding of the thermal inactivation behavior of HAV could allow precise determination of the thermal process conditions to prevent food-borne viral outbreaks associated with the consumption of contaminated mussels.     

Inactivation of Caliciviruses

The viruses most commonly associated with food- and waterborne outbreaks of gastroenteritis are the noroviruses. The lack of a culture method for noroviruses warrants the use of cultivable model viruses to gain more insight on their transmission routes and inactivation methods. We studied the inactivation of the reported enteric canine calicivirus no. 48 (CaCV) and the respiratory feline calicivirus F9 (FeCV) and correlated inactivation to reduction in PCR units of FeCV, CaCV, and a norovirus. Inactivation of suspended viruses was temperature and time dependent in the range from 0 to 100°C. UV-B radiation from 0 to 150 mJ/cm² caused dose-dependent inactivation, with a 3 D (D = 1 log₁₀) reduction in infectivity at 34 mJ/cm² for both viruses. Inactivation by 70% ethanol was inefficient, with only 3 D reduction after 30 min. Sodium hypochlorite solutions were only effective at >300 ppm. FeCV showed a higher stability at pH <3 and pH >7 than CaCV. For all treatments, detection of viral RNA underestimated the reduction in viral infectivity. Norovirus was never more sensitive than the animal caliciviruses and profoundly more resistant to low and high pH. Overall, both animal viruses showed similar inactivation profiles when exposed to heat or UV-B radiation or when incubated in ethanol or hypochlorite. The low stability of CaCV at low pH suggests that this is not a typical enteric (calici-) virus. The incomplete inactivation by ethanol and the high hypochlorite concentration needed for sufficient virus inactivation point to a concern for decontamination of fomites and surfaces contaminated with noroviruses and virus-safe water.     

State-dependent inactivation of K+ currents in rat type II alveolar epithelial cells

Inactivation of K+ channels responsible for delayed rectification in rat type II alveolar epithelial cells was studied in Ringer, 160 mM K-Ringer, and 20 mM Ca-Ringer. Inactivation is slower and less complete when the extracellular K+ concentration is increased from 4.5 to 160 mM. Inactivation is faster and more complete when the extracellular Ca2+ concentration is increased from 2 to 20 mM. Several observations suggest that inactivation is state-dependent. In each of these solutions depolarization to potentials near threshold results in slow and partial inactivation, whereas depolarization to potentials at which the K+ conductance, gK, is fully activated results in maximal inactivation, suggesting that open channels inactivate more readily than closed channels. The time constant of current inactivation during depolarizing pulses is clearly voltage-dependent only at potentials where activation is incomplete, a result consistent with coupling of inactivation to activation. Additional evidence for state-dependent inactivation includes cumulative inactivation and nonmonotonic from inactivation. A model like that proposed by C.M. Armstrong (1969. J. Gen. Physiol. 54: 553-575) for K+ channel block by internal quaternary ammonium ions accounts for most of these properties. The fundamental assumptions are: (a) inactivation is strictly coupled to activation (channels must open before inactivating, and recovery from inactivation requires passage through the open state); (b) the rate of inactivation is voltage-independent. Experimental data support this coupled model over models in which inactivation of closed channels is more rapid than that of open channels (e.g., Aldrich, R.W. 1981. Biophys. J. 36:519-532). No inactivation results from repeated depolarizing pulses that are too brief to open K+ channels. Inactivation is proportional to the total time that channels are open during both a depolarizing pulse and the tail current upon repolarization; repolarizing to more negative potentials at which the tail current decays faster results in less inactivation. Implications of the coupled model are discussed, as well as additional states needed to explain some details of inactivation kinetics.     

超高静压协同中温对凝结芽孢杆菌芽孢灭活动力学规律的研究

研究了超高静压协同中温对凝结芽孢杆菌芽孢在磷酸缓冲液和牛奶(经超高温灭菌)中灭活的动力学规律,并对超高静压的升压过程及相应的灭活效果进行了研究.结果表明,升压过程对凝结芽孢杆菌芽孢灭活的影响不能忽略,且随压力增加这种效果越强,最高使其下降1.77个数量级;凝结芽孢杆菌芽孢在牛奶中比在磷酸缓冲液中有更高的抗性;在3种拟合模型(线性、Weibull和Log-logistic模型)中,线性模型不适合模拟这些存活曲线,而Log-logistic模型能更好地模拟这些存活曲线,其次是Weibull模型.     

超高静压协同中温对凝结芽孢杆菌芽孢灭活动力学规律的研究

研究了超高静压协同中温对凝结芽孢杆菌芽孢在磷酸缓冲液和牛奶(经超高温灭菌)中灭活的动力学规律, 并对超高静压的升压过程及相应的灭活效果进行了研究。结果表明, 升压过程对凝结芽孢杆菌芽孢灭活的影响不能忽略, 且随压力增加这种效果越强, 最高使其下降1.77个数量级; 凝结芽孢杆菌芽孢在牛奶中比在磷酸缓冲液中有更高的抗性; 在3种拟合模型(线性、Weibull和Log-logistic模型)中, 线性模型不适合模拟这些存活曲线, 而Log-logistic模型能更好地模拟这些存活曲线, 其次是Weibull模型。     

Stochastic modeling of S. cerevisiae inactivation by supercritical CO2

Pasteurization of S. cerevisiae in a simple substrate with supercritical CO(2) was performed at 36 degrees C on a laboratory multibatch apparatus of a total volume of 150 mL. The pressure values ranged from 100 to 300 bar. The results show a clear dependence between inactivation ratio and increase of pressure. A mathematical modeling of the process was exploited to fit the experimental evidences: inactivation curves were analyzed using a stochastic model based on the multihit model (1). The nonlinear survival curve shows a shoulder and a tail which represent the lag and the resistant phase, respectively. The meaning of the nonlinear relationship between inactivation ratio and time is also discussed; the effect of pressure on the values assumed by the parameters of the model proposed was investigated.     

Specific Growth Rate Determines the Sensitivity of Escherichia coli to Thermal, UVA, and Solar Disinfection

Knowledge about the sensitivity of the test organism is essential for the evaluation of any disinfection method. In this work we show that sensitivity of Escherichia coli MG1655 to three physical stresses (mild heat, UVA light, and sunlight) that are relevant in the disinfection of drinking water with solar radiation is determined by the specific growth rate of the culture. Batch- and chemostat-cultivated cells from cultures with similar specific growth rates showed similar stress sensitivities. Generally, fast-growing cells were more sensitive to the stresses than slow-growing cells. For example, slow-growing chemostat-cultivated cells (D = 0.08 h⁻¹) and stationary-phase bacteria from batch culture that were exposed to mild heat had very similar T₉₀ (time until 90% of the population is inactivated) values (T_{90, chemostat} = 2.66 h; T_{90, batch} = 2.62 h), whereas T₉₀ for cells growing at a μ of 0.9 h⁻¹ was 0.2 h. We present evidence that the stress sensitivity of E. coli is correlated with the intracellular level of the alternative sigma factor RpoS. This is also supported by the fact that E. coli rpoS mutant cells were more stress sensitive than the parent strain by factors of 4.9 (mild heat), 5.3 (UVA light), and 4.1 (sunlight). Furthermore, modeling of inactivation curves with GInaFiT revealed that the shape of inactivation curves changed depending on the specific growth rate. Inactivation curves of cells from fast-growing cultures (μ = 1.0 h⁻¹) that were irradiated with UVA light showed a tailing effect, while for slow-growing cultures (μ = 0.3 h⁻¹), inactivation curves with shoulders were obtained. Our findings emphasize the need for accurate reporting of specific growth rates and detailed culture conditions in disinfection studies to allow comparison of data from different studies and laboratories and sound interpretation of the data obtained.     

Photodynamic Inactivation of the Na,K-ATPase Occurs via Different Pathways

The photodynamic, i.e., the light-induced, inactivation of the Na,K-ATPase in the presence of the sensitizer rose bengal was studied under different conditions. The shape of inactivation curves of the enzyme activity was analyzed as well as partial reactions of the pump cycle. Both experimental approaches showed the existence of two different time constants of inactivation of the ion pump, which reflect two pathways of a photodynamic modification. This is supported by the following observations: (1) The amplitude of the initial fast decay of enzyme activity was enhanced in the presence of D₂O and reduced in the presence of the singlet oxygen scavenger imidazole. (Similar results were found for the SR Ca-ATPase.) (2) Contrary to the fast enzyme inactivation the slow process shows an inverse dose-rate behavior. (3) Inactivation of the partial reactions of Na⁺-binding and of K⁺-binding to the membrane domain of the Na,K-ATPase showed only a single time constant, which corresponded to the slower time constant of enzyme inactivation. In the presence of high concentrations of singlet oxygen the fast time constant dominated the inactivation of the ATP-induced partial reaction for which the cytoplasmic domains of the enzyme play an important role. The data support the conclusion that fast inactivation is due to modification of the cytoplasmic domains and slow inactivation due to modifications of the membrane domain of the ion pumps.This revised version was published online in June 2005 with a corrected cover date.     

Kinetic modeling of thermal inactivation of the Bacillus sp. protease P7

Data from thermal stability of a keratinolytic protease produced by the Amazon isolate Bacillus sp. P7 was fitted to various mathematical models. Kinetic modeling showed that Weibull distribution was the best equation to describe the residual activity of protease P7 after heat treatment. The effects of temperature on equation parameters and on characteristics of the inactivation curves were evaluated. As expected, faster inactivation was observed at higher temperatures. The critical temperature to accelerate protease decomposition was about 70 °C. The reliable life (t _R) of the enzyme, analogous to the D value, ranged from 1,824 to 8 min at 45–65 °C. Within these temperatures, an increase of 8.81 °C was needed to lower enzyme t _R in one-log unit. Protease P7 is a potentially useful biocatalyst for various industrial bioprocesses, and therefore, kinetic modeling of thermal inactivation addresses an important topic aiming enzyme characterization and applications.     

Sunlight Inactivation of Enterococci and Fecal Coliforms in Sewage Effluent Diluted in Seawater

Inactivation (loss of culturability) by sunlight of enterococci and fecal coliforms within sewage effluent diluted in seawater was investigated in field experiments. In most experiments, 500-ml flasks of pure silica were used to confine activated sludge effluent diluted to 2% (vol/vol) in seawater. Inactivation of bacteria in these flasks (diameter, 0.1 m) was faster than in either open chambers (depth, 0.25 m) or patches of dyed effluent (depth of order, 1 m), probably because of the longer light paths in the latter two types of experiment, which caused greater attenuation of sunlight. Inactivation of 90% of enterococci generally required 2.3 times the insolation required for 90% inactivation of fecal coliforms, because of both the presence of larger initial shoulders on survival curves and a lower final inactivation rate. Two parameters are required to model inactivation of enterococci, a shoulder constant as well as a rate coefficient. The depth dependence of inactivation rate for both fecal indicators matched the attenuation profile of UV-A radiation at about 360 nm. Inactivation by UV-B radiation (290 to 320 nm), which penetrates much less into seawater, is of minor importance compared with the UV-A and visible radiation in sunlight, contrary to expectations in consideration of published action spectra for bacterial inactivation.     

Mechanisms of Inactivation by High-Voltage Atmospheric Cold Plasma Differ for Escherichia coli and Staphylococcus aureus

Atmospheric cold plasma (ACP) is a promising nonthermal technology effective against a wide range of pathogenic microorganisms. Reactive oxygen species (ROS) play a crucial inactivation role when air or other oxygen-containing gases are used. With strong oxidative stress, cells can be damaged by lipid peroxidation, enzyme inactivation, and DNA cleavage. Identification of ROS and an understanding of their role are important for advancing ACP applications for a range of complex microbiological issues. In this study, the inactivation efficacy of in-package high-voltage (80 kV [root mean square]) ACP (HVACP) and the role of intracellular ROS were investigated. Two mechanisms of inactivation were observed in which reactive species were found to either react primarily with the cell envelope or damage intracellular components. Escherichia coli was inactivated mainly by cell leakage and low-level DNA damage. Conversely, Staphylococcus aureus was mainly inactivated by intracellular damage, with significantly higher levels of intracellular ROS observed and little envelope damage. However, for both bacteria studied, increasing treatment time had a positive effect on the intracellular ROS levels generated.