Development of a global stochastic model relating the distribution of individual cell and population physiological states

Our ability to predict the lag (λ) prior to growth of foodborne pathogens is limited by our lack of understanding of the physiological changes taking place in the individual cell during the adaptation process. Theoretical models have been developed to describe the stochastic nature of individual cells, and probability distributions have been used to assign hypothetical values of the physiological state to individual cells (p_i). The aim of this study is to develop a polynomial model which will link distributions of p_i values to the physiological state of the population (h₀), and thus to the λ. Risk analysis software was used to simulate values of p_i for populations of cells drawn from lognormal distributions with parameters and β, and growth curves were simulated using a modified continuous-discrete-continuous (CDC) model. Values for h₀ were then obtained for each growth curve by fitting with the heterogeneous population model (HPM). Multiple regression analysis was used to develop a polynomial function which described the subsequent h₀ value as a function of and β (R²=0.9957). Outputs from simulations using the polynomial model agree well with results from related stochastic models, and suggest that distributions can accurately describe the physiological state of cell populations.     

A model of the specific growth rate inhibition by weak acids in yeasts based on energy requirements

Zygosaccharomyces bailii, a spoilage yeast, capable of metabolic activity in food environments with low pH, low a_w and in the presence of weak acid preservatives was chosen for a study on the effect of benzoic acid on growth parameters. In batch cultures, under controlled pH, this food preservative inhibited growth, decreasing the specific growth rate (μ) and the yield coefficient (Y_S) on glucose. Data obtained at pH 3.5, 4.0 and 4.5 showed that this inhibition was exclusively promoted by the undissociated form of the acid since the effect was independent of pH when the concentration of the acid was expressed in this form. Moreover, the relationship between the values for μ and Y_S, provided evidence that the specific consumption rate of glucose (q_S) was not affected by benzoic acid, indicating that the inhibition of growth should be completely explained by a decrease of Y_S. The outcome of parallel experiments performed in continuous culture was that the decrease of Y_S was due to an increase of the maintenance coefficient (m), defined as the fraction of q_S diverted from growth to cope with stress, represented in this case by the presence of the preservative. Based on these results a model was built, assuming that m increased hyperbolically with the concentration of benzoic acid, from zero in the absence of the acid up to q_S when growth was completely inhibited. The concentration of the acid, for which m=q_S/2, is a constant (K_W), and represents a measure of the tolerance for a preservative, in this case benzoic acid. The simple equation μ/μ₀=1+W/K_W predicts the value of μ for a concentration (W) of the preservative, requiring the knowledge of two parameters: the specific growth rate in the absence of the preservative (μ₀) and K_W. The equation fitted very well the data of the effect of benzoic acid on the specific growth rate of Z. bailii, having K_W=0.96 mM benzoic acid. The model was also validated with other spoilage yeasts grown in the presence of benzoic acid in microtiter plates in an automated spectrophotometer. The values obtained for K_W under these conditions confirm Z. bailii as the most tolerant (K_W=2.1 mM) followed by Pichia sp. (K_W=0.78 mM), Saccharomyces cerevisiae (K_W=0.53 mM) and Debaryomyces hansenii (K_W=0.11 mM).     

Modelling the effect of a temperature shift on the lag phase duration of Listeria monocytogenes

The aim of this work is to study and model the effect of a temperature shift on h₀, the product of the growth rate by the lag phase duration (μλ). Our work is based on the data of Whiting and Bagi [Int. J. Food Microbiol. 73 (2002) 291], who studied the influence of both the pre-incubation temperature (T_prior) and the growth temperature (T_growth) on λ values of Listeria monocytogenes. We introduce a new model to describe the evolution of the parameter h₀ as a function of T_prior and T_growth, and compare it to Whiting and Bagi's published polynomial model that describes the influence of T_prior and T_growth on λ independently of μ. For exponential as well as stationary phase cells, h₀ increases almost linearly with the magnitude of the temperature shift. A simple linear model of h₀ turns out to be more suitable to predict λ values than a polynomial model of λ.     

Physical changes of significance for early post mortem water distribution in porcine M. longissimus

The post mortem changes in water mobility and distribution were followed in porcine muscle (M. longissimus dorsi) samples using continuous low-field NMR relaxation measurements and simultaneous measurement of changes in muscle impedance as an indirect measure of membrane integrity as well as muscle contraction measurements using a rigormeter instrument. Distributed exponential fitting analysis of NMR T₂ relaxation data revealed the presence of three distinct water populations (T₂₀, T₂₁, T₂₂) within the muscle during its conversion to meat. Comparison of T₂ relaxation patterns and contraction data indicates that rigor development affects the attributes of the T₂₁ water population and thereby contributes to myofibrillar water characteristics post mortem, as the T₂₁ water population is believed to reflect inter/intra-myofibrillar water. The volume of the water population believed to reflect extra-cellular water (T₂₂) in the living muscle. Early post mortem T₂₂ decreased slightly within the first 2–3 h post mortem followed by an increase and a change in its characteristic time constant. This was ascribed to an initial muscle cell swelling followed by water being expelled from the cellular space into the extra-myofibrillar space. Comparison of changes in the T₂₂ water population and impedance characteristics within the muscle during its conversion to meat revealed close relationship between progresses in the two attributes. Obtained data strongly support that the post mortem reorganization of water is closely associated with membrane properties, which moreover was found to affect the final water-holding capacity of the meat. Finally, a model for early post mortem events leading to changes in the distribution of water within muscles is proposed.     

Relationships between sensory perception and water distribution determined by low-field NMR T(2) relaxation in processed pork - impact of tumbling and RN(-) allele

The relationships between water distribution, measured with low-field NMR (LF-NMR) transverse (T₂) relaxometry and sensory properties in tumbled and non-tumbled cured-smoked loins from 30 female Hampshire crossbred pigs were investigated. Upon distributed analysis of the T₂ relaxation, three populations centred at about 2, 40 and 600–800 ms, respectively, were detected. Clear differences in the characteristics of the intermediate population (T₂₁) were observed between loins from carriers and non-carriers of the RN⁻ allele, which implies differences in water–protein interactions between the two genotypes. PLS regressions between NMR T₂ variables and sensory attributes revealed significant correlations between NMR T₂ variables and the sensory attributes juiciness, acidulous taste and meat taste, which mainly could be ascribed to the T₂₁ time constant. In addition, the number of unappealing pores assessed by the sensory panel was highly related to the relative T₂ populations, implying that the microstructure is directly reflected in the NMR T₂ populations. However, prediction of the processing yield from NMR T₂ variables was poor. The correlation improved when RN genotypes and tumbling conditions were included as predictors. Thus, other effects of tumbling treatments and RN genotypes unrelated to NMR T₂ relaxation were observed.     

Effect of temperature and relative humidity on yellowing rate of paddy

The effects of temperature and relative humidity (or water activity) in storage chambers on yellowing rate of paddy were investigated and then an empirical equation for predicting the yellowing rate was developed. Paddy was conditioned using saturated salt solutions at relative humidities ranging from 0.80 to 0.95 and temperatures of 35, 45, 55, 60 and 65°C. The yellowing rate was found to follow the zero order kinetics. The yellowing constant value (k) increased exponentially with temperature and increased linearly with water activity. The magnitude of apparent activation energy varied from 130–145 kJ/mol. A predictive equation for determining yellowing rate was ln k=−δa_w−/T+(γa_w)/T where a_w was water activity (valid from 0.80 to 0.95), T was absolute temperature (valid from 308 to 338 K) and , δ, and γ were constants. The results of variance analysis showed that temperature, water activity and their interaction significantly influenced the yellowing rate of paddy.     

Thermal inactivation of the frozen thawed traditional meat starter culture, Pediococcus pentosaceus, in a meat model system

The equation, y_(t) = y₍₀₎e^kt, was fitted (R = 0.9281, 0.9220 and 0.9117, respectively) to thermal inactivation data (55, 60 and 65 °C) of the traditional meat starter culture Pediococcus pentosaceus (10⁷ cfu/ml) in a meat model system. The population reduction constant (‘k’) increased (about 2.5- and 3-fold) with an increase in the treatment temperature (from 55 to 60 °C and from 60 to 65 °C, respectively). The Q₁₀ (55–65 °C) for ‘k’ was 7.63. Thermal treatments of 19.1, 9.0 and 3.1 min (55, 60 and 65 °C, respectively) reduced the population of P. pentosaceus by 2.0 logs. The value of ‘k’ and the duration of the thermal treatment played an important role in the extent of the inactivation of the culture. The “zero inactivation” temperature (T₀) for P. pentosaceus was 49.9 °C. About 5 logs of the culture would be destroyed at 63 and 68 °C within about 15.5 and 6.5 min, respectively.     

Enthalpy-Entropy compensation in food vapor adsorption

Enthalpy-entropy compensation was analysed for sorption isotherms of potatoes, macadamia nuts, apricots, figs, currants, prunes and raisins. Plots of (ΔH_dif)_T vs (ΔS_dif)_T for potatoes and macadamia nuts presented two isokinetic temperatures: T_B1 = 272.0 ± 57.7 K (− 1 °C) for potatoes, T_B1 = 265.0 ± 18.8 K (− 8 °C) for macadamia nuts and T_B2 = 382.5 ± 7.3 K (109.5 °C) for both products. The first isokinetic temperature (T_B1) appeared only at the upper portion of the temperature range tested (50, 60 and 70 °C for potatoes and 50 and 60 °C for macadamia nuts). The two isokinetic temperatures observed for potatoes and macadamia nuts suggested that during the initial stages at low a_w T_B1 is controlled by changes in the entropy of water, whereas the second isokinetic temperature (T_B2) is considered to be enthalpy-controlled. Dried fruits presented only one isokinetic curve T_B = 315.7 ± 3.5 K (42.7 °C), for raisins, currants and figs (75.2–82.3% d.b. sugars) and T_B = 317.7 ± 4.6 K (44.7 °C) for prunes and apricots (51.5–54.5% d.b. sugars), indicating an enthalpy-controlled adsorption process for the whole range of moisture contents covered.     

The significance of cooling rate on water dynamics in porcine muscle from heterozygote carriers and non-carriers of the halothane gene-a low-field NMR relaxation study

The post mortem changes in the chemical/physical state distribution of water were followed in pig muscle (M. longissimus dorsi) from heterozygote (n=12) and non-carriers (n=12) of the halothane gene exposed to two different cooling profiles using continuous low-field NMR relaxation measurements. T₂ relaxation data were analyzed using distributed exponential fitting analysis. Independent of genotype post mortem changes were observed in the two water populations characterizing water within the myofibrillar space (T₂₁) and the extra-myofibrillar space (T₂₂), respectively, as a function of chilling regime. The effect was most pronounced in samples from heterozygote carriers of the halothane gene. The obtained results strongly suggest that improved water-holding capacity of muscles upon fast chilling can be ascribed to a reduced accumulation of extra-myofibrillar water in the meat post mortem, and it is hypothesized that differences in the accumulation of extra-myofibrillar water post mortem can be ascribed largely to the time at which disruption of cell membrane integrity takes place.     

Water status of cooked white salted noodles evaluated by MRI

Transverse relaxation time (T₂)-weighted images and T₂ maps of white salted noodles (WSN) were investigated by magnetic resonance imaging technique. T₂-weighted images and T₂ maps clearly showed the differences in water status between noodles. The migration of moisture from surface regions to central regions of boiled WSN at different migration rates were investigated during storage. The distribution of T₂ values changed differently depending on the cooking and storage times. The small differences in T₂ values between surface region and central region of noodles cooked for 5 and 15 min were attributed to the limited water absorption during short cooking time, which resulted in high firmness. The changes in starch granules morphology observed under scanning electron microscope and the increase of noodle firmness measured by texture analyzer were significantly affected by the water status in noodles. The water status can be controlled by the cooking time.     

Partial characterization of starches from Dioscorea opposita Thunb. cultivars

The physicochemical, morphological, thermal and crystal properties of the starches separated from four different Dioscorea opposita Thunb. cultivars (Yongji, Anguo, Jinpingyao and Shandongniutuimi) were studied. Amylose content of D. opposita Thunb. starches from different cultivars were in the range of 19.38–22.02%. Moisture content, swelling power, solubility and water-binding capacity of starches differed significantly. Scanning electron micrographs revealed the presence of smooth or rough surface, oval to spherical shaped granules, with mean particle size in the range of 29.2–36.96 μm. The gelatinization transition temperatures (T_o, T_p and T_c) and enthalpy of gelatinization (ΔH_gel), peak height index (PHI) and gelatinization temperature range (R) were determined. T_o, T_p, T_c of D. opposita Thunb. starches ranged from 70.2 to 75.8, 77.5 to 81.1, and 82.8 to 86.9 °C, respectively. D. opposita cv. Anguo starch showed the highest ΔH_gel values (12.47 J/g) while D. opposita cv. Shandongniutuimi starch showed the lowest values (10.54 J/g). The crystal type of starches separated from different D. opposita Thunb. cultivars was a typical C-type X-ray diffraction pattern. The relative crystallinity of the starches ranged from 34.3% to 43.1%.     

Effect of environmental stresses on the mean and distribution of individual cell lag times of Escherichia coli O157:H7

The effect of starvation, heat or acid stress on duration of individual cell lag time (τ) and standard deviation (SD) of τ was investigated using Escherichia coli O157:H7. Cells were stressed by exposure to acid (pH 3.5), heat (50 °C), or starvation in either glucose-free mineral medium (MOPS), tryptic soy broth (TSB) or Luria broth (LB). Stressed cells were then diluted into wells of a Bioscreen plate to obtain single cells per well. Replicate time to detection (t_d) values were obtained using the Bioscreen and used to calculate the τ and SD. Significant (P ≤ 0.05) increases in τ over untreated controls were found for the following treatments: 14 days in acid; 2 h of heating; 3 days starvation in MOPS; and 2 days starvation in either TSB or LB. The largest increase in τ was > 2-fold from 2.5 to 5.6 h observed with the heat treatment. MOPS starvation was more detrimental to the cells than was acid treatment over the same time period. A significant increase in SD was found with 21 days acid treatment, and 2 days starvation in either TSB or LB. No significant increase in SD was found for MOPS starvation or heat treatment. Lognormal, Gamma, ExtremeValue and Weibull distributions were fitted to the τ data using BestFit. The results suggest that the Lognormal distribution is suitable for fitting τ data from either stressed or unstressed cells.     

NMR relaxometry and differential scanning calorimetry during meat cooking

By combining simultaneous nuclear magnetic resonance (NMR) T₂ relaxometry and differential scanning calorimetry (DSC) on pork samples heated to nine temperature levels between 25 and 75 °C, the present study investigates the relationship between thermal denaturation of meat proteins and heat-induced changes in water characteristics. Principal component analysis (PCA) on the distributed ¹H NMR T₂ relaxation data revealed that the major changes in water characteristics during heating occur between 40 and 50 °C. This is probably initiated by denaturation of myosin heads, which however, could not be detected in the DSC thermograms obtained directly on the meat. In contrast, the DSC thermograms revealed endothermic transitions at 54, 65 and 77 °C, probably reflecting the denaturation of myosin (rods and light chain), sarcoplasmic proteins together with collagen and actin, respectively. Simultaneous modelling of DSC and NMR data by partial least squares regression (PLSR) revealed a correlation between denaturation of myosin rods and light chains at 53–58 °C and heat-induced changes in myofibrillar water (T₂ relaxation time 10–60 ms) as well as between actin denaturation at 80–82 °C and expulsion of water from the meat. Accordingly, the present study demonstrates a direct relationship between thermal denaturation of specific proteins/protein structures and heat-induced changes in water mobility during heating of pork.     

Effect of season on color of Hanwoo (Korean native cattle) beef

A total of 1278 head of Hanwoo (Korean native cattle) slaughtered over four seasons were used to evaluate the effect of season on color characteristics of beef longissimus dorsi (LD) muscle. CIE L^*, a^*, b^*, C^* values and hue angle were significantly lower (P<0.05) in cattle slaughtered in the winter season. Meat color was darker in the winter than in the spring and autumn seasons. The L^* values among three average daily temperature (T_a) categories were different (P<0.05) in order of: [5 °CT_a<25 °C] > [T_a25 °C] > [T_a<5 °C], indicating that the meat color of cattle slaughtered at T_a<5 °C was darker. The a^*, b^*, C^* values and hue angle were significantly lower (P<0.05) in cattle slaughtered at T_a<5 °C. Season at slaughter is of great importance for meat color. Namely, meat color of Hanwoo beef was influenced by environmental temperature. Overall, cattle slaughtered in the winter season of T_a<5 °C produced beef with more undesirable meat color properties.     

Bioactivity of the essential oil extracted from Evodia rutaecarpa Hook f. et Thomas against the grain storage insects, Sitophilus zeamais Motsch. and Tribolium castaneum (Herbst)

The toxic, repellent and feeding deterrent activities of the essential oil extracted from Evodia rutaecarpa Hook f. et Thomas, were evaluated against Sitophilus zeamais adults and Tribolium castaneum larvae and adults. Contact toxicity assayed by topical application showed that S. zeamais adults were significantly more susceptible (LD₅₀=0.043 μg/mg body wt) to the essential oil than T. castaneum adults (LD₅₀=0.118 μg/mg body wt) and larvae (LD₅₀=0.093–0.126 μg/mg body wt). However, in the fumigation assays, S. zeamais (LC₅₀=41 μg/L air) was less susceptible to the essential oil than T. castaneum (LC₅₀=11.7 μg/L air). When compared with larvae of various ages, T. castaneum adults were more susceptible to the fumigant toxicity of the essential oil. Also, in the treated filter paper repellency test, the essential oil was more repellent to T. castaneum than to S. zeamais. A flour disk bioassay demonstrated that the essential oil of E. rutaecarpa had a weaker feeding deterrent action against T. castaneum adults than against T. castaneum larvae and S. zeamais adults. The reduction in growth rate of T. castaneum larvae and S. zeamais adults was mainly due to a behavioural (feeding deterrent) action rather than to post-ingestive toxicity of the oil.     

Influence of weak organic acids and salts on the denaturation characteristics of intramuscular connective tissue. A differential scanning calorimetry study

Intramuscular connective tissue obtained from Longissimus dorsi muscle of a 4-year-old beef carcass was treated with NaCl solutions of 2, 4, and 6% (w/v), and CaCl₂ solutions of 50, 100, and 150 mM, and citric and lactic acid solutions of 0.5, 1.0, and 1.5% for three different marinating periods (24, 46, and 72 h). Changes in denaturation characteristics were investigated using differential scanning calorimetry and it was found that the denaturation onset temperature (T_o) and the denaturation peak temperature (T_p) increased as the NaCl concentration increased but decreased as the CaCl₂ concentration increased, irrespective of marinating time. Lactic and citric acid decreased T_o to about 39°C, from over 60°C breaking the structure of fibrils.     

Measurement by MRI of storage changes in commercial chocolate confectionery products

Storage of chocolate confectionery products was monitored non-invasively by Magnetic Resonance Imaging. Using a Carr–Purcell–Meiboom–Gill–(CPMG) sequence, 20 echo images (first echo 5 ms, subsequent echo every 5 ms) were acquired with a 2 s repetition time in a total 8-min scan time. Images were processed to give spatial maps of the proton density (M₀) and the transverse relaxation times (T₂-values) within the samples. In every case the T₂-values were successfully used to follow the migration of lipids from the fillings into the chocolate. The MR images also provided spatial information on the lipid migration.     

Comparing predicting models for heat inactivation of Listeria monocytogenes and Pseudomonas aeruginosa at different pH

Under the same experimental conditions it has been demonstrated that whereas survival curves of Listeria monocytogenes in the range of temperatures from 54 to 62 °C followed a first-order kinetic, those of Pseudomonas aeruginosa in the range of temperatures from 50 to 56 °C were not linear showing a shoulder followed by a linear region. The first order kinetic model did not describe survival curves of P. aeruginosa. A model based on the Weibull distribution (Log₁₀(N_t/N₀)=(1/−2.303)*(t/b)ⁿ)) accurately described the inactivation kinetics of both microorganisms at the three pHs of 4, 5.5, 7.4 investigated. For both microorganisms, the b value depended on the treatment temperature and the pH of the treatment medium. Whereas for L. monocytogenes the n value was independent of the treatment conditions, for P. aeruginosa the n value depended on the pH of the treatment medium.

The model based on the Weibull distribution was capable of accurately predicting the treatment time to inactivate five Log₁₀ cycles of both microorganisms at the three pHs investigated.     

Preliminary investigation of the application of Raman spectroscopy to the prediction of the sensory quality of beef silverside

The potential of Raman spectroscopy for the determination of meat quality attributes has been investigated using data from a set of 52 cooked beef samples, which were rated by trained taste panels. The Raman spectra, shear force and cooking loss were measured and PLS used to correlate the attributes with the Raman data. Good correlations and standard errors of prediction were found when the Raman data were used to predict the panels' rating of acceptability of texture (R²=0.71, Residual Mean Standard Error of Prediction (RMSEP)% of the mean (μ)=15%), degree of tenderness (R²=0.65, RMSEP% of μ=18%), degree of juiciness (R²=0.62, RMSEP% of μ=16%), and overall acceptability (R²=0.67, RMSEP% of μ=11%). In contrast, the mechanically determined shear force was poorly correlated with tenderness (R²=0.15). Tentative interpretation of the plots of the regression coefficients suggests that the -helix to β-sheet ratio of the proteins and the hydrophobicity of the myofibrillar environment are important factors contributing to the shear force, tenderness, texture and overall acceptability of the beef. In summary, this work demonstrates that Raman spectroscopy can be used to predict consumer-perceived beef quality. In part, this overall success is due to the fact that the Raman method predicts texture and tenderness, which are the predominant factors in determining overall acceptability in the Western world. Nonetheless, it is clear that Raman spectroscopy has considerable potential as a method for non-destructive and rapid determination of beef quality parameters.     

Identification of PSE in the Longissimus muscle of pigs stunned by captive-bolt

Meat quality characteristics in the longissimus muscle of 57 pigs slaughtered at approximately 100 kg liveweight were studied. They were slaughtered by captive-bolt stunning and exsanguination. The incidence of pale, soft and exudative (PSE) meat was identified by muscle colour and water holding capacity 24 h post mortem (C₂₄ and WHC₂₄). The muscle pH value 45 min post mortem (pH₁), absorption ratio (R-value) of muscle acid extract, and colour and water holding capacity 1 h post mortem (C₁ and WHC₁) were also determined. The interrelationships among pH₁, R-value, C₁, WHC₁, C₂₄ and WHC₂₄ were studied and the multiple regressions of C₁, C₂₄, WHC₁ and WHC₂₄ with pH₁ and R-value were computed. The results of simple and multiple regression analysis showed that neither muscle pH₁ nor R-value could effectively predict colour or WHC at 24 h post mortem. Combining pH₁ and R-value provided little improvement in the prediction of the ultimate meat colour and WHC.