Nonlogarithmic death rate calculations for Byssochlamys fulva and other microorganisms.

Survivor curves for heat-resistant ascospores of Byssochlamys fulva exposed to lethal heat were nonlogarithmic. At lower heating temperatures, the log survivor curves were characterized by a shoulder plus an accelerating death rate; with increased temperatures, the rate approached logarithmic death. The formula (log No -- log N)a = kt + C was adapted to linearize these data. No and N are the initial and surviving numbers of organisms at the time t. The death rate is given by k, and C is a constant for a set of data. The a value is derived from the least-squares slope of a plot of log (log No -- log N) against log time and is used to linearize the thermal death rate curves. This formula permitted calculations of parameters analogous to those for logarithmic death (D and z). Use of formula is illustrated for selected nonlinear microbial death rate curves from the literature.     

Thermal susceptibility of Streptococcus faecium strains isolated from frankfurters

The heat resistance of nine strains of Streptococcus faecium isolated from frankfurters was determined at 63 and 68 degrees C in brain heart infusion broth. Exponential-phase cultures (approximately 10(7) colonies/mL) were used as inoculants. The heat resistance of S. faecium DP2181, a moderately resistant isolate, was further examined in broth (55, 63, and 68 degrees C) and frankfurter emulsion (63 and 68 degrees C). The decimal reduction times (D values) were determined by regression. In broth, both time-temperature combinations resulted in a 3-4 log decline in bacterial numbers for the nine S. faecium strains tested. For S. faecium DP2181, the survivor curves deviated from the logarithmic order of death at all three heating temperatures. An initial slow period of death was evident at 55 degrees C and a resistant tail of organisms was observed at 55, 63, and 68 degrees C. The D55D63, and, D68 values for the logarithmic portion of the corresponding survivor curves were 105.6, 9.36, and 3.34 min, respectively. The survival of DP2181 was enhanced by the frankfurter emulsion. The results indicate that populations of S. faecium existed that were very heat resistant and could survive normal frankfurter processing if initially present in high numbers.     

Some Factors Affecting the Activity of Diethylpyrocarbonate as a Sterilant

Quantitative data indicated logarithmic death in 5 degrees Brix Concord grape juice when concentrations of cells under 10(7)/ml were exposed to diethylpyrocarbonate (DEPC). Species differed considerably in their resistance; e.g., 50 ppm reduced the viable count of Saccharomyces cerevisiae over nine log(10) cycles, whereas 200 ppm reduced the count of Byssochlamys fulva ascospores by only about 1 log. DEPC lethality was enhanced by higher temperatures; destruction at 40 C was 10- to 100-fold greater than at 20 C. Studies on death rates showed that most yeasts and fungal spores were killed during the first hour of exposure, whereas 24 h or longer was needed for maximal destruction of several lactic acid bacteria. Repair of DEPC-induced damage was believed responsible for the slower death rates of the lactics.     

Equilibrium and kinetics of the unfolding of alpha-lactalbumin by guanidine hydrochloride (IV): dependence of the N equilibrium A transconformation on the temperature.

The reversible unfolding from the native (N) state to the acid (A) state of alpha-lactalbumin by guanidine-HCl (0.8-2.0 M) was studied at 10-35 degrees C by means of difference spectra and pH-jump measurements. At each temperature, all points plotted as the logarithmic equilibrium constant log KNA of the N equilibrium A process against pH could fall on a curve independent of the denaturant concentration by shifting each point along the log KNA axis, where the shift factor f did not depend on temperature. Moreover, by shifting the points at each temperature along the log (KNA/f) axis, a master curve, independent of both temperature and the denaturant concentration, could be obtained for the pH-dependence of log KNA. From the dependence of the logarithmic rate constants on pH, master curves independent of both temperature and the denaturant concentration could also be made for the N leads to A and the A leads to A processes, where A mean the activated state. The results show the two-state character of the N equilibrium A process. The enthalpy changes and the differences in heat capacity for the N equilibrium A, N equilibrium A and A equilibrium A processes were determined from the accurate measurements of temperature dependence of the unfolding at pH 4.3 and 1.0 M guanidine-HCl. The results show that the disruption of hydrophobic interaction is caused mainly in the A leads to A process, while most of the changes in the pK values of the ionizing groups are caused in the N leads to A process.     

A model of microbial survival curves in water treated with a volatile disinfectant

AIM: To develop a method to calculate microbial survival parameters in water treated with a dissipating disinfectant and predict the inactivation patterns under different agent concentrations and decay rate regimes. METHODS AND RESULTS: It has been assumed that the survival curves of the organism, under (hypothetical) constant agent concentration conditions, follow the power law model log [N(t)/N0] = -btn with a concentration independent exponent, n. The concentration dependence of the 'rate parameter', b, has been assumed to obey a log logistic relationship. Under changing disinfectant concentration, the survival curve is constructed so that its local slope, i.e. momentary logarithmic inactivation rate of the organism, is the slope of the momentary 'constant concentration' curve at the momentary agent concentration, at the time which corresponds to the momentary survival ratio. The resulting differential equation was used to retrieve the survival parameters by numerical minimization procedures. Once these are calculated, the equation is solved numerically to produce the survival curve for almost any conceivable agent concentration history. The predictive ability of the method is demonstrated by using the survival parameters, calculated from published data obtained under one concentration profile, to predict survival curves under very different decay patterns. CONCLUSIONS: It is possible to calculate microbial survival parameters from data obtained in treatments where the unstable or volatile disinfectant progressively dissipates and use them to predict the outcome of different treatments. SIGNIFICANCE AND IMPACT OF THE STUDY: The proposed mathematical method will enable the prediction of microbial inactivation patterns in water treated with unstable and/or volatile chemical agents.     

Kinetics of Death of Bacterial Spores at Elevated Temperatures

The kinetics of death of Bacillus stearothermophilus spores (FS 7954) suspended in phosphate buffer (pH 7) were studied over a temperature range of 127.2 to 143.8 C and exposure times of 0.203 to 4.150 sec. These short exposure were achieved by use of a tubular flow reactor in which a suspension of spores was injected into a hot flowing stream at the entrance of the reactor. Thermal equilibria of the suspension with the hot stream was achieved within 0.0006 sec. After flow through a fixed length of reactor, the stream containing the spores was cooled by flash vaporization and then assayed for viable count. The death rate data were fitted by a logarithmic expression. However, logarithmic death rate was only approximated in the tail or high-kill regions of exposure. Death rate constants obtained from this portion of the data were found to correlate by Arrhenius as well as Absolute Reaction Rate Theory relationships. Thermal-death time curves were found to correlate the data rather poorly. The activation energy and frequency constant for an Arrhenius relationship fit of the data were found to be 83.6 kcal/gmole and 10^47.2 min^-1, respectively. The standard enthalpy and entropy changes for an Absolute Reaction Rate Theory relationship fit of the data were found to be 84.4 kcal/gmole and 157 cal/gmole-K, respectively.     

Kinetics of sterilization of Lactobacillus brevis cells by the application of high voltage pulses

The technique of irreversible electroporation has been successfully applied to cause a lethal effect on Lactobacillus brevis cells suspended in phosphate buffer solution, Na(2)HPO(4)/NaH(2)PO(4) . H(2)O (0.845/0.186 mM) between parallel plane electrodes. Tests were carried out at different temperatures (24,45,60, and 80 degrees C) to determine if there was a synergistic effect of temperature and electric pulse treatment on the destruction of L. brevis. Experimental results indicate that the viability (log N/N(0); where N(0) and N are the number of cells survived per milliliter before and after pulse voltage application, respectively) of L. brevis decreased with electric field strength E and temperature T and treatment time t(t). The relations between log(N/N(0)) and t(t) and log(N/N(0)) and E indicate that higher field strengths are more effective than higher treatment times in causing destruction of L. brevis cells. It was also found that as the temperature of the liquid medium containing L. brevis cells increased from 24 to 60 degrees C, the death rate of L. brevis cells increased with a decrease in the total treatment time t(t) (pulse width x number of pulses applied). The application of an electric field strength E = 25 kV/cm at 60 degrees C and treatment time t(t) = 10 ms resulted in very high destruction levels of L. brevis cells (N/N(0) = 10(-9)). In comparison with existing steam sterilization technology, this new method of sterilization using relatively low temperature and short treatment time could prove to be an excellent method to minimize thermal denaturation of important nutrient components in liquid media. (c) John Wiley & Sons, Inc.     

Predicting the stabilities of freeze-dried suspensions of Lactobacillus acidophilus by the accelerated storage test

The elevated temperatures of 50 ° C, 60 ° C, and 70 ° C were used in an accelerated storage test for predicting the stability of freeze-dried suspensions of L. acidophilus. The logarithmic death of bacteria at the above temperatures and the Arrhenius relationship obtained permitted predicting the rate of death at any storage temperature. The values predicted for storage stability of freeze-dried suspensions of L. acidophilus at 4 ° C and 20 ° C were confirmed by the actual values obtained after storage at these temperatures for 6, 15, and 19 mo.     

Nitrification in soil as a function of time

The dependence of nitrification on time may be expressed as ΣN=C/(m+1) ·t ^m+1 since its logarithmic form log ΣN=K logt+q suggests the possibility of a linear relationship between log ΣN and logt such as was found in more than 50 cases of nitrification in different soils. It was further shown that the equations for the integration curve and for the rate curve are of the same form, differing only in the constants.     

Effect of chill and freezing temperatures on survival of Vibrio parahaemolyticus inoculated in homogenates of oyster meat

Survival of Vibrio parahaemolyticus was determined in oyster meat homogenates at various temperatures. (4°C, 0°C, -18°C and -24°C) and bacterial levels (10², 10⁴, 10⁵ and 10⁷ ml^-1). In all cases, the numbers of V. parahaemolyticus were a logarithmic function of log time. This study indicates that high numbers of V. parahaemolyticus can be inactivated at low temperatures. The time of total inactivation depends on the initial number of micro-organisms and incubation temperature. It is possible to use this information to determine the storage time necessary to reduce V. parahaemolyticus hazards in fish.     

Patterns of bacterial destruction in solutions by microwave irradiation

The patterns of destruction of several kinds of bacterial cells suspended in solutions by microwave irradiation were studied. The survival curves of Escherichia coli and Staphylococcus aureus were similar and approximated a set of three linear phases. The curves of Pseudomonas fluorescens and Bacillus cereus spores shifted to the shorter and longer irradiation periods, respectively. The rate constant and initial time of destruction for each linear phase of the survival curve were compared among these organisms. When irradiated E. coli cells were incubated in an agar with a high salt level, fewer cells were recovered. The curve of E. coli cells in the logarithmic phase of growth shifted to shorter exposure periods. There were no significant differences in the survival curves of E. coli cells grown at temperatures of 22–36°C, whereas the curve of cells grown at 44°C shifted to longer periods.     

Thermal inactivation and injury of Moraxella-Acinetobacter cells in ground beef.

The thermal inactivation and injury (sensitivity to 0.8% NaCl) of a radiation-resistant culture of Moraxella-Acinetobacter mixed in minced beef were determined. Survival curves for Moraxella-Acinetobacter cells in beef had an initial shoulder preceding a logarithmic decline when the cells were heated at 65, 70, and 75 degrees C, but not at 80 degrees C. In all cases, the experimental points not included in the shoulder were linearized by means of a least-squares straight line, and the latter was used to determine D values. Shoulder values of 12.2, 4.1, and 0.6 min at temperatures of 65, 70, and 75 degrees C were added to the respective D values of 35.4, 6.6, and 1.4 min to determine the time required to destroy one log cycle. The Z value was 7.3 degrees C. Moraxella-Acinetobacter cells in meat were more rapidly injured than inactivated, on initial exposure to heat. The number of cells injured by this initial exposure increased as the temperature was increased. At 65 degrees C the percentage of injured cells increased more rapidly with exposure time than did the inactivated cells. As the temperature was increased, the rates of inactivation and injury became more and more similar.     

Determination of time of death in forensic science via a 3-D whole body heat transfer model

This study is focused on developing a whole body heat transfer model to accurately simulate temperature decay in a body postmortem. The initial steady state temperature field is simulated first and the calculated weighted average body temperature is used to determine the overall heat transfer coefficient at the skin surface, based on thermal equilibrium before death. The transient temperature field postmortem is then simulated using the same boundary condition and the temperature decay curves at several body locations are generated for a time frame of 24 h. For practical purposes, curve fitting techniques are used to replace the simulations with a proposed exponential formula with an initial time delay. It is shown that the obtained temperature field in the human body agrees very well with that in the literature. The proposed exponential formula provides an excellent fit with an R² value larger than 0.998. For the brain and internal organ sites, the initial time delay varies from 1.6 to 2.9 h, when the temperature at the measuring site does not change significantly from its original value. The curve-fitted time constant provides the measurement window after death to be between 8 h and 31 h if the brain site is used, while it increases 60–95% at the internal organ site. The time constant is larger when the body is exposed to colder air, since a person usually wears more clothing when it is cold outside to keep the body warm and comfortable. We conclude that a one-size-fits-all approach would lead to incorrect estimation of time of death and it is crucial to generate a database of cooling curves taking into consideration all the important factors such as body size and shape, environmental conditions, etc., therefore, leading to accurate determination of time of death.     

Kinetics of biocide kill

The efficient use of biocides to control microbial contamination is dependent upon selecting the most potent agent at the anticipated end-use concentration. This is based upon an accurate determination of two basic parameters:

• 1.(1) The time taken by the biocide to achieve a total kill (death rate or decimal reduction time).
• 2.(2) The effect of biocide concentration on the death rate or decimal reduction time.

The time taken to achieve a total kill can be calculated from the death rate. In the simplest case a plot of the natural logarithm of survivors declines linearly when plotted against time and the slope of that line is the death rate. However, the plot of the line of survivors against time is frequently non-linear. Concave curves may result from attempts to control a mixed population with different degrees of tolerance to the biocide; the shape of the curve being a combination of two or more different linear declines. Convex curves, or curves with a shoulder, may be due to one of three phenomena. The target organisms may adhere together in clumps of two or more; the nature of the reaction of biocide with the target organism is one where the organism first changes from a resistant to a susceptible state; or the nature of the biocide molecule is such that uptake is relatively slow and death only commences when a critical concentration has accumulated within the cell. With all such convex curves the decline eventually becomes linear and again the slope is the death rate.The relationship between death rate and biocide concentration is rarely proportional and usually exponential. Thus halving the concentration may cause a disproportionate increase in the decimal reduction time. This relationship is controlled by the concentration coefficient or concentration exponent. When the logarithm of concentration is plotted against the log of death rate or log of decimal reduction time, a linear relationship is obtained whose slope is the concentration coefficient. Thus if the death rates at two or more concentrations are known, the concentration coefficient can be determined and the effect of dilution predicted.The mathematical interpretation of these phenomena and their influence on biocide treatment are discussed.     

Equilbrium and kinetics of the unfolding of alpha-lactalbumin by guanidine hydrochloride (II).

The reversible unfolding of alpha-lactalbumin by guanidine hydrochloride, was studied at 25.0 degrees C in a relatively low concentration range of the denaturant (0.80-2.00 mol/l) by means of difference spectra and pH-jump measurements. The unfolding was shown to occur between two states, N and D, because apparent rate-constants of the unfolding and the refolding reactions depended only on pH. All curves plotted as the logarithmical equilibrium constant log KD against pH could fall on the same base curve by shifting each curve along the log KD axis. From the dependence of the logarithmic rate constant on pH, master curves could also be made for the forward and the backward reactions. The dependence of these master curves on pH indicates that the groups affecting the pH dependence of the unfolding are three residues with pKN = 3.3 and pKA = pKD = 4.4, one residue with pKN = pKA = 3.8 and pKD = 4.4, and one residue with pKN = 5.8 and pKA = pKD = 6.3, where A indicates the activated state. On the other hand, from the denaturant activity dependence of the shift factors required for making the master curves, the value of the intrinsic binding constant of the denaturant to the protein was found to be similar to that obtained from previous measurements at pH 5.5. Differences between the numbers of the binding sites of the denaturant on the denaturated and the native proteins, and between those on the activated and the native proteins were shown to be 5.3 and 2.1, respectively. The free energy of stabilization in the native-like environment also shows that the protein in the native state is more unstable than lysozyme.     

Temperature dependence of collagen fluorescence.

Dermal collagens have several fluorescent moieties in the UV and visible spectral regions that may serve as molecular probes of collagen. We studied the temperature-dependence of a commercial calf skin collagen and acid-extracted Skh-1 hairless mouse collagen at temperatures from 9 degrees C to 60 degrees C for excitation/emission wavelengths 270/305 nm (tyrosine), 270/360 nm (excimer-like aggregated species), 325/400 nm (dityrosine) and 370/450 nm (glycation adduct). L-tyrosine (1 x 10(-5) M in 0.5 M HOAc) acted as a "reference compound" devoid of any collagen structural effects. In general, the fluorescence efficiency of these fluorophores decreases with increasing temperature. Assuming that rate constant for fluorescence deactivation has the form k(d)(T) = k(d) degrees exp (-DeltaE/RT), an Arrhenius plot of log[(1/Phi) - 1] vs. 1/T affords a straight line whose (negative) slope is proportional to the activation energy, DeltaE, of the radiationless process(es) that compete with fluorescence. Because it is difficult to accurately measure Phi(f) for collagen-bound fluorophores, we derived an approximate formula for an activation parameter, DeltaE*, evaluated from an Arrhenius-like plot of log 1/I(N)vs. 1/T, (1/I(N)vs. is the reciprocal normalized fluorescence intensity). Tyrosine in dilute solution affords a linear Arrhenius plot in both of the above cases. Using the known value of Phi(f) = 0.21 for free tyrosine at room temperature, we determined that DeltaE* is accurate to approximately 25% in the present instance. Collagen curves are non-linear, but they are quasi-linear below approximately 20 degrees C, where the helical form predominates. Values of DeltaE* determined from the data at T < 20 degrees C ranged from 6.2-8.4 kJ mol(-1) (1.5-2.0 kcal mol(-1)) for mouse collagen and 10.3-11.4 kJ mol(-1) (2.5-2.7 kcal mol(-1)) for calf skin collagen, consistent with collisional deactivation of the fluorescent state via thermally enhanced molecular vibrations and rotations. Above 20 degrees C, log 1/I(N)vs. 1/T plots from Skh-1 hairless mouse collagen are concave-downward, suggesting that fluorescence deactivation from the denatured coil has a significant temperature-independent component. For calf skin collagen, these plots are concave-upward, suggesting an increase in activation energy above Tm. These results suggest that collagen backbone and supramolecular structure can influence the temperature dependence of the bound fluorophores, indicating the future possibility of using activation data as a probe of supramolecular structure and conformation.     

Sensitivity to ultraviolet radiation as a function of DNA content in Escherichia coli B/r.

Populations of Escherichia coli B/r A were grown to log phase at various growth rates determined by the richness of the medium. The genome content, G, was calculated from log phase doubling times by means of the Cooper-Helmstetter formula. Cell volumes were measured and found to vary linearly with this genome content. Cells with various DNA contents were prepared for ultraviolet irradiation and plated for dark repair under similar conditions. The resulting logarithmic survival curves were all similar in shape: convex up, with straight line portions having approximately the same slope (D0 = 11.4 +/- 0.2 J/m2). The shoulders however increase in width with calculated DNA content giving an extrapolation number which varies roughly as exp(G) or exp (0.6 Gmax).     

Computer analysis of sub-parameters of depurination and depolymerization rate constants in Feulgen DNA hydrolysis

Feulgen DNA hydrolysis curves derived from cytofluorometry at various temperatures and HCl concentrations were computer analyzed with least squares fit to Bateman function. By comparing the depurination (k1) and depolymerization (k2) rate constants at different hydrolysis conditions, it was found that the two parameters of temperature and HCl concentration can be expressed as k = AN2 X exp (-B/T), where A and B are constants, N is the HCl concentrations, and T is the absolute temperature. From the analysis of Feulgen hydrolysis curves with 2N HCl at various temperatures, it was calculated that A = 5.3590 X 10(14) and B = 12133.543, for k1, and A = 6.2401 X 10(14) and B = 12181.660, for k2 for mouse 4C hepatocytes fixed with absolute methanol. Computer generated theoretical hydrolysis curves using the above k1 and k2 values were compared with experimental curves at various temperatures and HCl-concentrations. The two types of hydrolysis curves coincided with each other when 1-3 N HCl was used at temperatures between 30-40 degrees C. The peak times of hydrolysis curves at different conditions determined by experimental analysis and theoretical estimations also coincided reasonably well with each other. The physico-chemical phenomena underlying the equation designating k1 and k2 values are discussed.     

Thermal death kinetics of egg and third instar Mediterranean fruit fly (Diptera: Tephritidae)

Two developmental stages of Ceratitis capitata (Wiedemann), 24-h-old eggs and third instars, 8 d after oviposition, were subjected to thermal exposures in a heating block system, at various temperatures of 46, 48, 50, and 52 degrees C to determine the thermal death kinetics of the insects. At these temperatures, 100% mortality was achieved by exposure of 300 C. capitata larvae for 60, 15, 4, and 1 min, respectively. The 0.5 order kinetic model had the best fit to the survival ratio for all the treatment temperatures, hence it was used for the prediction of the lethal times. The thermal death time (TDT) curves showed that the third instars were more heat-resistant than eggs, especially at the two low temperatures (46 and 48 degrees C). Under temperature-time combinations that did not result in complete kill, the thermal mortality for eggs was also significantly higher than that for third instars. The activation energy values calculated from the TDT curves were 490.6 and 551.9 kJ/mol, respectively, for thermal death of eggs and third instars.     

Heat resistance of Klebsiella pneumoniae in media with various sucrose concentrations

Summary The heat resistance of Klebsiella pneumoniae, an organism of widespread occurrence in nature has been determined in media containing various amounts of sucrose at temperatures between 47° and 59°C.In the presence of sucrose and at all temperatures the inactivation curves show a fast initial drop (logarithmic phase) in the number of survivors followed by a less rapid one (tail phase). The influence of the sucrose concentration can be described withln k _s = ln k _O – _T [sucrose] for media with more than 0.52 mol/l sucrose for the logarithmic as well as for the tail phase of inactivation.The heat-injured cells were recovered on various media to investigate the influence of the presence of small metabolites and nutrients on the shape of the inactivation curves and on the death rate. For cells heated in media without sucrose, the recovery on a rich medium was much better than on a poor one; for cells heated in media with more than 0.26 mol/l sucrose, no difference was observed between the various recovery media.The activation energies as determined on the various media are always nearly the same, which strongly suggests that the critical sites in the heat inactivation were not enzymes playing a key role in the synthesis of small molecules such as amino acids or nucleotides.