Applicability of an Arrhenius Model for the Combined Effect of Temperature and CO2 Packaging on the Spoilage Microflora of Fish

The temperature behavior of the natural microflora on the Mediterranean fish red mullet (Mullus barbatus) was examined as a case study. The growth of the spoilage bacteria Pseudomonas spp., Shewanella putrefaciens, Brochothrix thermosphacta, and lactic acid bacteria was modeled as a function of temperature and the concentration of carbon dioxide in modified atmosphere packaging. Combined models were developed and comparatively assessed based on polynomial, Belehradek, and Arrhenius equations. The activation energy parameter of the Arrhenius model, E_A, was independent of the packaging atmosphere and ranged from 75 to 85 kJ/mol for the different bacteria, whereas the preexponential constant decreased exponentially with the packaging CO₂ concentration. We evaluated the applicability of the models developed by using experimental bacterial growth rates obtained from 42 independent experiments performed with three Mediterranean fish species and growth rates predicted from the models under the same temperature and packaging conditions. The accuracy factor and bias factor were used as statistical tools for evaluation, and the developed Arrhenius model and the Belehradek model were judged satisfactory overall.     

Predictive modeling of the shelf life of fish under nonisothermal conditions

The behavior of the natural microflora of Mediterannean gilt-head seabream (Sparus aurata) was monitored during aerobic storage at different isothermal conditions from 0 to 15 degrees C. The growth data of pseudomonads, established as the specific spoilage organisms of aerobically stored gilt-head seabream, combined with data from previously published experiments, were used to model the effect of temperature on pseudomonad growth using a Belehradek type model. The nominal minimum temperature parameters of the Belehradek model (T(min)) for the maximum specific growth rate (micro(max)) and the lag phase (t(Lag)) were determined to be -11.8 and -12.8 degrees C, respectively. The applicability of the model in predicting pseudomonad growth on fish at fluctuating temperatures was evaluated by comparing predictions with observed growth in experiments under dynamic conditions. Temperature scenarios designed in the laboratory and simulation of real temperature profiles observed in the fish chill chain were used. Bias and accuracy factors were used as comparison indices and ranged from 0.91 to 1.17 and from 1.11 to 1.17, respectively. The average percent difference between shelf life predicted based on pseudomonad growth and shelf life experimentally determined by sensory analysis for all temperature profiles tested was 5.8%, indicating that the model is able to predict accurately fish quality in real-world conditions.     

Predictive Modeling of the Shelf Life of Fish under Nonisothermal Conditions

The behavior of the natural microflora of Mediterannean gilt-head seabream (Sparus aurata) was monitored during aerobic storage at different isothermal conditions from 0 to 15°C. The growth data of pseudomonads, established as the specific spoilage organisms of aerobically stored gilt-head seabream, combined with data from previously published experiments, were used to model the effect of temperature on pseudomonad growth using a Belehradek type model. The nominal minimum temperature parameters of the Belehradek model (T_min) for the maximum specific growth rate (μ_max) and the lag phase (t_Lag) were determined to be −11.8 and −12.8°C, respectively. The applicability of the model in predicting pseudomonad growth on fish at fluctuating temperatures was evaluated by comparing predictions with observed growth in experiments under dynamic conditions. Temperature scenarios designed in the laboratory and simulation of real temperature profiles observed in the fish chill chain were used. Bias and accuracy factors were used as comparison indices and ranged from 0.91 to 1.17 and from 1.11 to 1.17, respectively. The average percent difference between shelf life predicted based on pseudomonad growth and shelf life experimentally determined by sensory analysis for all temperature profiles tested was 5.8%, indicating that the model is able to predict accurately fish quality in real-world conditions.     

Determination of the shelf life of sliced cooked ham based on the growth of lactic acid bacteria in different steps of the chain

Aims: Development of a predictive model for the determination of the shelf life of modified atmosphere‐packed (MAP) cooked sliced ham in each step of the cold chain. Methods and Results: The growth of lactic acid bacteria (LAB), as well as the development of the total viable count and changes of sensory and pH value parameters in MAP cooked sliced ham, stored under different constant temperature conditions from 2 to 15°C was investigated. As a result of the measurements, the end of the shelf life could be considered as the time when LAB reach more than 7 log₁₀ CFU g^?1. Different primary and secondary models were tested and analysed to find the best way to calculate the shelf life. For primary modelling, the modified Gompertz Function and the modified Logistic Function were compared. There was no substantial difference between either model. The effect of temperature on the growth rate was modelled by using the Arrhenius and the Square root model, whereas the Arrhenius equation gave a better result. A combination of the primary and secondary model was used for shelf‐life prediction under dynamic conditions. This combination showed the best prediction of microbial counts using the modified Logistic model and the Arrhenius equation. Conclusions: With the developed model, it is possible to predict the shelf life of MAP cooked sliced ham based on the growth of LAB under different temperature conditions. Significance and Impact of the Study: The developed model can be used to calculate the remaining shelf life in different steps of the chain. Thus, it can deliver an important contribution to improve food quality by optimizing the storage management.     

Factors influencing nitrogen and phosphorus excretion rates of fish in a shallow lake

Summary 1. Fish excretion can be an important source of nutrients in aquatic ecosystems. Nitrogen (N) and phosphorus (P) excretion rates are influenced by many factors, including fish diet, fish growth rate and fish size. However, the relative influence of these and other factors on community‐level excretion rates of fish is unknown. 2. We used bioenergetics modeling to estimate excretion rates of eight fish species in a shallow, Minnesota (U.S.A.) lake over four months in both 2004 and 2005. Excretion rates of each species were summed for community‐level N and P excretion rates, as well as the N : P ratio of excretion. We then used a model‐selection approach to assess ability of independent variables to predict excretion rates, and to identify the most parsimonious model for predicting N : P excretion ratios and P and N excretion rates at the community scale. Predictive models were comprised of the independent variables water temperature and average fish density, fish size, fish growth rate, nutrient content of fish and nutrient content of fish diets at the community scale. 3. Fish density and nutrient content of fish diets (either N or P) were the most parsimonious models for predicting both N and P excretion rates, and explained 96% and 92% of the variance in N and P excretion, respectively. Moreover, fish density and nutrient models had 1400‐fold more support for predicting N and 21‐fold more support for predicting P excretion relative to models based on fish density only. Water temperature, fish size, fish growth rates and nutrient content of fish showed little influence on excretion rates, and none of our independent variables showed a strong relationship with N : P ratios of excretion. 4. Past work has focused on the importance of fish density as a driver of fish excretion rates on a volumetric basis. However, our results indicate that volumetric excretion rates at the community scale will also change substantially in response to changes in relative abundance of fish prey or shifts in relative dominance of planktivores, benthivores, or piscivores. Changes in community‐scale excretion rates will have subsequent influences on algal abundance, water clarity, and other ecosystem characteristics.     

Effect of temperature on Brettanomyces bruxellensis: metabolic and kinetic aspects

The effect of temperatures ranging from 15 to 35 degrees C on a culture of Brettanomyces bruxellensis was investigated in regards to thermodynamics, metabolism, and kinetics. In this temperature range, we observed an increase in growth and production rates. The growth behavior was well represented using the Arrhenius model, and an apparent activation energy of 16.61 kcal/mol was estimated. A stuck fermentation was observed at 35 degrees C as represented by high cell death. The carbon balance established that temperature had no effect on repartition of the glucose consumption between biomass and products. Hence, the same biomass concentration was obtained for all temperatures, except at 35 degrees C. Moreover, using logistic and Luedeking-Piret models, we demonstrated that production rates of ethanol and acetic acid were partially growth associated. Parameters associated with growth (alpha eth and alpha aa) remained constant with changing temperature, whereas, parameters associated with the population (beta eth and beta aa) varied. Optimal values were obtained at 32 degrees C for ethanol and at 25 degrees C for acetic acid.     

Development of a microbial model for the combined effect of temperature and pH on spoilage of ground meat, and validation of the model under dynamic temperature conditions

The changes in microbial flora and sensory characteristics of fresh ground meat (beef and pork) with pH values ranging from 5.34 to 6.13 were monitored at different isothermal storage temperatures (0 to 20 degrees C) under aerobic conditions. At all conditions tested, pseudomonads were the predominant bacteria, followed by Brochothrix thermosphacta, while the other members of the microbial association (e.g., lactic acid bacteria and Enterobacteriaceae) remained at lower levels. The results from microbiological and sensory analysis showed that changes in pseudomonad populations followed closely sensory changes during storage and could be used as a good index for spoilage of aerobically stored ground meat. The kinetic parameters (maximum specific growth rate [mu(max)] and the duration of lag phase [lambda]) of the spoilage bacteria were modeled by using a modified Arrhenius equation for the combined effect of temperature and pH. Meat pH affected growth of all spoilage bacteria except that of lactic acid bacteria. The "adaptation work," characterized by the product of mu(max) and lambda(mu(max) x lambda) was found to be unaffected by temperature for all tested bacteria but was affected by pH for pseudomonads and B. thermosphacta. For the latter bacteria, a negative linear correlation between ln(mu(max) x lambda) and meat pH was observed. The developed models were further validated under dynamic temperature conditions using different fluctuating temperatures. Graphical comparison between predicted and observed growth and the examination of the relative errors of predictions showed that the model predicted satisfactorily growth under dynamic conditions. Predicted shelf life based on pseudomonads growth was slightly shorter than shelf life observed by sensory analysis with a mean difference of 13.1%. The present study provides a "ready-to-use," well-validated model for predicting spoilage of aerobically stored ground meat. The use of the model by the meat industry can lead to effective management systems for the optimization of meat quality.     

Effect of time and temperature of fermentation on the microflora of grape pomace

The effects of fermentation time and temperature of grape pomace on the number of bacteria and yeasts were assessed using ANOVA of experimentally generated data, as well as analysis of models derived from first principles and fitted by non-linear regression to such data. Specific rates of death of yeasts and bacteria were experimentally obtained at different fermentation times (pilot scale), and at different fermentation times and different temperatures (laboratory scale) for pomace of Alvarinho and Loureiro grape varieties obtained after vinification at two different locations. Viable numbers of yeasts and bacteria in grape pomace were high, especially in the first 3 week of fermentation; for bacteria, there was an increase of their levels during the first 3 week, followed by a significant decrease towards 9 week; for yeasts there was a monotonic decrease throughout such whole period. The numbers of viable microorganisms were mathematically correlated with time and temperature for both wineries using mechanistic models and following a methodology of increasing model complexity. After having checked the validity of underlying assumptions of normal distribution and constant variance of residuals of the experimental data, determination of the best nested model was based on an F-test; such model considered that the behavior of the microbial population is well described by a constant specific growth rate and an increasing specific death rate, both of which vary with temperature following Arrhenius relationships. Activation energies for the specific death rates of yeasts and bacteria were (1.469-1.560)᎒⁴ and (2.584-4.152)᎒⁴ cal/mol, respectively, for the temperature range 20-35 ^:C. Prediction of the time profile of viable numbers of the major families in the adventitious microflora of grape pomace, as a function of fermentation parameters that are easily manipulated is important in attempts to eventually standardize this solid-state, ill-defined fermentation and so eventually optimize the manufacture of marcs obtained by steam distillation of such fermented pomaces.     

Characterization of Pseudomonas spp. associated with spoilage of gilt-head sea bream stored under various conditions.

The population dynamics of pseudomonads in gilt-head sea bream Mediterranean fish (Sparus aurata) stored under different conditions were studied. Phenotypic analysis and sodium dodecyl sulfate-polyacrylamide gel electrophoresis of whole-cell proteins were performed to identify a total of 106 Pseudomonas strains isolated from S. aurata stored under different temperatures (at 0, 10, and 20 degrees C) and packaging conditions (air and a modified atmosphere of 40% CO(2)-30% N(2)-30% O(2)). Pseudomonas lundensis was the predominant species, followed by Pseudomonas fluorescens, while Pseudomonas fragi and Pseudomonas putida were detected less frequently. Fluorescent Pseudomonas strains dominated under air conditions, while proteolytic and less lipolytic strains dominated under modified-atmosphere packaging. Different storage conditions appear to govern the selection of pseudomonads in gilt-head sea bream fish.     

Model for combined effect of temperature and salt concentration/water activity on the growth rate of Staphylococcus xylosus

The combined effect of temperature and NaCl concentration/water activity on the growth rate of a strain of halotolerant Staphylococcus is described by the square-root models which had been used previously to model temperature dependence only. The model square root r = b(T-T min) is shown to be a special case of the B?lehrádek temperature function which is given by r = a(T-alpha)d. The constant alpha is the socalled 'biological zero' and equivalent to T min in the square-root models. This and the exponent d = 2 were unaffected by changing NaCl concentration/water activity. The B?lehrádek-type equations are preferable to the Arrhenius equation in that their parameters do not change with temperature. The constancy of T min allows derivation of a simple expression relating growth rate of strain CM21/3 to temperature and salt concentration/water activity within the range of linear response to temperature predicted by the square-root model.     

Application of some growth models to the black scallop,Chlamys varia (L.) from lanveoc,bay of brest

Linear day degree models were constructed, separately for each age group of the black scallop, Chlamys varia (L.) from Lanveoc, Bay of Brest and were found to be capable of predicting growth in terms of increase in shell height. Instantaneous growth rates, computed for evry month of the year, decreased with increase in age and showed minimal values in winter months. Q₁₀ values, calculated from instantaneous growth rates, demonstrated that growth did not depend upon temperature alone. Empirical models developed using temperature, food, and gonad index as independent variables, showed that both temperature and food together formed decisive factors for growth rates. The growth of the dry body tissue of the black scallop was also calculated for each age group and showed an obvious seasonal fluctuation.     

Energetics of Bacillus stearothermophilus growth: molar growth yield and temperature effects on growth efficiency.

The major growth yield of a prototrophic strain of Bacillus stearothermophilus under aerobic conditions on salts medium containing ammonium nitrate as the nitrogen source and glucose or succinate as the carbon source was maximal at the lowest growth temperature employed and decreased steadily as the temperature was raised. The temperature optima for growth yield and for growth rate were thus different. The molar growth yield values of the thermophile, especially at the lower growth temperatures, were similar to those reported for aerobically grown mesophilic bacteria, both on glucose and on succinate. At the higher growth temperatures, a lower proportion of glucose carbon was incorporated into cells and a correspondingly greater proportion was left incompletely utilized in the medium, mostly as acetate. This suggests a greater inefficiency in the coordination of the nonoxidative and oxidative phases of glucose metabolism at the gigher temperatures. Another factor causing a decreased cell yield at higher temperatures was possibly an uncoupling of energy production from respiration. The rates of respiration by intact cells of the thermophile on glucose and on succinate followed the Arrhenius relationship from 55 C to 20 C, which is some 20 C below the minimal growth temperature of the organism. The Arrhenius constant was 17.1 kcal/mol for glucose oxidation and 13.5 kcal/mol for succinate oxidation. These results are comparable to those reported for some mesophiles, and they suggest that the inability of the thermophile to grow at temperatures below about 41 C is not due to an abnormally high temperature coefficient for the uptake and oxidation of the carbon source.     

Comparison of temperature effects on soil respiration and bacterial and fungal growth rates

Temperature is an important factor regulating microbial activity and shaping the soil microbial community. Little is known, however, on how temperature affects the most important groups of the soil microorganisms, the bacteria and the fungi, in situ. We have therefore measured the instantaneous total activity (respiration rate), bacterial activity (growth rate as thymidine incorporation rate) and fungal activity (growth rate as acetate-in-ergosterol incorporation rate) in soil at different temperatures (0-45 degrees C). Two soils were compared: one was an agricultural soil low in organic matter and with high pH, and the other was a forest humus soil with high organic matter content and low pH. Fungal and bacterial growth rates had optimum temperatures around 25-30 degrees C, while at higher temperatures lower values were found. This decrease was more drastic for fungi than for bacteria, resulting in an increase in the ratio of bacterial to fungal growth rate at higher temperatures. A tendency towards the opposite effect was observed at low temperatures, indicating that fungi were more adapted to low-temperature conditions than bacteria. The temperature dependence of all three activities was well modelled by the square root (Ratkowsky) model below the optimum temperature for fungal and bacterial growth. The respiration rate increased over almost the whole temperature range, showing the highest value at around 45 degrees C. Thus, at temperatures above 30 degrees C there was an uncoupling between the instantaneous respiration rate and bacterial and fungal activity. At these high temperatures, the respiration rate closely followed the Arrhenius temperature relationship.     

Model for combined effect of temperature and salt concentration/water activity on the growth rate of Staphylococcus xylosus

The combined effect of temperature and NaCl concentration/water activity on the growth rate of a strain of halotolerant Staphylococcus is described by the squareroot models which had been used previously to model temperature dependence only. The model r = b ( T - T _min) is shown to be a special case of the BélehraAdek temperature function which is given by r = a ( T - aL)^d. The constant aL is the so-called 'biological zero' and equivalent to T _min in the square-root models. This and the exponent d = 2 were unaffected by changing NaCl concentration/water activity. The Bélehradek-type equations are preferable to the Arrhenius equation in that their parameters do not change with temperature. The constancy of T _min allows derivation of a simple expression relating growth rate of strain CM21/3 to temperature and salt concentration/water activity within the range of linear response to temperature predicted by the square-root model.     

Modelling and predicting the effect of temperature,water activity and pH on growth of Streptococcus iniae in Tilapia

Aims: To evaluate and model the growth of Streptococcus iniae affect by temperatures (10–45°C), water activity (A_w; 0·995–0·957), and pH (5–8). Methods and Results: Temperatures, A_w, and pH were adjusted. The behaviour of S. iniae was studied and modelled. Growth curves were fitted by using logistic, Gompertz, and Baranyi models. The maximum growth rates obtained from the primary model were then modelled as a function of temperature, A_w, and pH using the Belehradek‐type models for secondary model. The optimum values for growth were found to be in the range of 35–40°C, A_w 0.995–1, and pH 6–7. The statistical characteristics of the models were validated by r², mean square error, bias, and accuracy factors. The results of validation indicated that Baranyi model performed the best. Conclusions: The effect of temperature, A_w/NaCl, pH control of S. iniae in tilapia could be satisfactorily predicted under current experimental conditions, and the proposed models could serve as a tool for this purpose. Significance and Impact of the Study: The suggested predictive model can be used for risk assessment concerning S. iniae in tilapia.     

Development of a bioenergetics model for fish embryos and larvae during the yolk feeding period

A mechanistic model of an energy budget in fish embryos and yolk-sac larvae was developed using data for five freshwater fish species: rainbow trout Oncorhynchus mykiss , nase Chondrostoma nasus , carp Cyprinus carpio , tench Tinca tinca and African catfish Clarias gariepinus , based on the existing models for adult and juvenile fishes. The model simulates changes in the components of the budget under various conditions. Besides the effects of body mass and temperature on consumption and metabolic rate, the dependence of ration size on amount of available yolk and initial egg size was implemented in the model. The model parameters were found through optimization. A sensitivity analysis of the model was conducted by varying its parameters and observing changes in the output. A comparative analysis showed that the values generated by the model closely approximated independent empirical observations. Simulations of energy budgets demonstrated that the overall pattern of energy partitioning was the same for different species, irrespective of egg size and temperature preferences. Most energy was allocated to body growth. Clarias gariepinus showed the fastest growth and had the highest yolk conversion efficiency.     

Modeling of the enzymatic kinetic synthesis of cephalexin--influence of substrate concentration and temperature

During enzymatic kinetic synthesis of cephalexin, an activated phenylglycine derivative (phenylglycine amide or phenylglycine methyl ester) is coupled to the nucleus 7-aminodeacetoxycephalosporanic acid (7-ADCA). Simultaneously, hydrolysis of phenylglycine amide and hydrolysis of cephalexin take place. This results in a temporary high-product concentration that is subsequently consumed by the enzyme. To optimize productivity, it is necessary to develop models that predict the course of the reaction. Such models are known from literature but these are only applicable for a limited range of experimental conditions. In this article a model is presented that is valid for a wide range of substrate concentrations (0-490 mM for phenylglycine amide and 0-300 mM for 7-ADCA) and temperatures (273-298 K). The model was built in a systematic way with parameters that were, for an important part, calculated from independent experiments. With the constants used in the model not only the synthesis reaction but also phenylglycine amide hydrolysis and cephalexin hydrolysis could be described accurately. In contrast to the models described in literature, only a limited number (five) of constants was required to describe the reaction at a certain temperature. For the temperature dependency of the constants, the Arrhenius equation was applied, with the constants at 293 K as references. Again, independent experiments were used, which resulted in a model with high statistic reliability for the entire temperature range. Low temperatures were found beneficial for the process because more cephalexin and less phenylglycine is formed. The model was used to optimize the reaction conditions using criteria such as the yield on 7-ADCA or on activated phenylglycine. Depending on the weight of the criteria, either a high initial phenylglycine amide concentration (yield on 7-ADCA) or a high initial 7-ADCA concentration (yield on phenylglycine amide) is beneficial.     

Using matrix models to explore the influence of temperature on population growth of arthropod pests

1 Population growth of four arthropod pests on agricultural crops, the pea aphid, the bird‐cherry oat aphid, the Mediterranean fruit fly, and the two‐spotted spider mite, was modelled using stage matrix models. 2 Temperature was included as a variable in the model, affecting fecundity, mortality and growth rate. Linear temperature dependence was used to describe fecundity and individual growth rate in the matrix model. Life table data collected at various constant experimental temperatures were used to parameterize the model. 3 Sensitivity analysis identified the most influential demographic parameters determining the growth rate of the population at different temperature regimes. Mortality of young adults and immature stages were found to be the most important parameters in determining population growth for all species presented. However, high temperatures increased the relative impact of individual growth rates and fecundity on the growth of the population.     

Effect of temperature and arsenic on Aeromonas hydrophila growth,a modelling approach

Aeromonas hydrophila is frequently reported from arsenic affected areas. Present study was aimed to determine the effect of arsenic and temperature on growth of A. hydrophila. The bacteria were isolated from naturally infected fish from a water body in Birbhum, West-Bengal, India, which is reported to be an arsenic-free area. Arsenic concentration in natural aquatic reservoirs (e.g., pond, lake or river) varies from 0–6 mg/L. No significant change in bacterial growth was observed within this range of arsenic exposure. However, variation in temperature impacted the growth of A. hydrophila. A single dimension model was constructed using simple logistic equation. Rate parameters of the model were derived from the experimental observations. Comparison of model results and laboratory observations gives a good conformity regarding the effect of variation of arsenic concentration and temperature change on growth of this bacterium. From the analysis of this model we further get the idea that the maximum growth of A. hydrophila is supposed to be at 31.4°C in absence of arsenic, whereas at 477 mg/L arsenic concentration, the growth of the bacteria totally stops at 30°C.