Estimating non-isothermal bacterial growth in foods from isothermal experimental data

Mechanism of Synergistic Photoinactivation Utilizing Curcumin and Lauric Arginate Ethyl Ester against Escherichia coli and Listeria innocua

This study investigated the mechanism of how lauric arginate ethyl ester (LAE) improves the photoinactivation of bacteria by curcumin after diluting the 100 µmol/L stock curcumin-LAE micelle solution to the concentration used during the treatment based on the curcumin concentration. The photoinactivation of bacteria was conducted by irradiating the 1 µmol/L curcumin-LAE solution containing cocktails of Escherichia coli and Listeria innocua strains (7 log CFU/mL) for 5 min with UV-A light (λ = 365 nm). The changes in solution turbidity, curcumin stability, and bacterial morphology, viability, and recovery were observed using SEM, TEM, and live/dead cell assays. The study found that LAE enhances the photoinactivation of bacteria by increasing the permeability of cell membranes which could promote the interaction of reactive oxygen species produced by photosensitized curcumin with the cell components. The combination of curcumin and LAE was demonstrated to be more effective in inhibiting bacterial recovery at pH 3.5 for E. coli, while LAE alone was more effective at pH 7.0 for L. innocua.

Engineering modeling frameworks for microbial food safety at various scales

The landscape of mathematical model-based understanding of microbial food safety is wide and deep, covering interdisciplinary fields of food science, microbiology, physics, and engineering. With rapidly growing interest in such model-based approaches that increasingly include more fundamental mechanisms of microbial processes, there is a need to build a general framework that steers this evolutionary process by synthesizing literature spread over many disciplines. The framework proposed here shows four interconnected, complementary levels of microbial food processes covering sub-cellular scale, microbial population scale, food scale, and human population scale (risk). A continuum of completely mechanistic to completely empirical models, widely-used and emerging, are integrated into the framework; well-known predictive microbiology modeling being a part of this spectrum. The framework emphasizes fundamentals-based approaches that should get enriched over time, such as the basic building blocks of microbial population scale processes (attachment, migration, growth, death/inactivation and communication) and of food processes (e.g., heat and moisture transfer). A spectrum of models are included, for example, microbial population modeling covers traditional predictive microbiology models to individual-based models and cellular automata. The models are shown in sufficient quantitative detail to make obvious their coupling, or their integration over various levels. Guidelines to combine sub-processes over various spatial and time scales into a complete interdisciplinary and multiphysics model (i.e., a system) are provided, covering microbial growth/inactivation/transport and physical processes such as fluid flow and heat transfer. As food safety becomes increasingly predictive at various scales, this synthesis should provide its roadmap. This big picture and framework should be futuristic in driving novel research and educational approaches.

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.

Shelf Life of Food Products: From Open Labeling to Real-Time Measurements

The labels currently used on food and beverage products only provide consumers with a rough guide to their expected shelf lives because they assume that a product only experiences a limited range of predefined handling and storage conditions. These static labels do not take into consideration conditions that might shorten a product's shelf life (such as temperature abuse), which can lead to problems associated with food safety and waste. Advances in shelf-life estimation have the potential to improve the safety, reliability, and sustainability of the food supply. Selection of appropriate kinetic models and data-analysis techniques is essential to predict shelf life, to account for variability in environmental conditions, and to allow real-time monitoring. Novel analytical tools to determine safety and quality attributes in situ coupled with modern tracking technologies and appropriate predictive tools have the potential to provide accurate estimations of the remaining shelf life of a food product in real time. This review summarizes the necessary steps to attain a transition from open labeling to real-time shelf-life measurements.

Growth and Modeling of Staphylococcus aureus in Flour Products under Isothermal and Nonisothermal Conditions

This study was conducted to investigate the growth of Staphylococcus aureus in traditional Chinese flour products under isothermal (10, 15, 20, 25, 30, and 37°C) and nonisothermal (10 to 20, 20 to 30, and 25 to 37°C) conditions. Then, models for the growth of S. aureus in flour products as a function of storage temperature, pH, and water activity (a_w) were developed, and the goodness of fit of models was evaluated using the determination coefficient (R²), root mean square error (RMSE), bias factor (B_f), and accuracy factor (A_f). Based on the above information, S. aureus growth in steamed bread under nonisothermal conditions was predicted from experiments performed under isothermal conditions. It was shown that different combinations of temperature and a_w in flour products have a strong influence on the growth of S. aureus . The modified Gompertz model was found to be more suitable for describing the growth data of S. aureus in flour products, with an R² of >0.99 and an RMSE of <0.37. The newly developed secondary models were validated, and for the specific growth rate and the lag time, the R² values were 0.96 and 0.97, A_f was 1.12 and 1.06, and B_f was 1.13 and 1.05, respectively. The predicted nonisothermal growth curves of S. aureus were in agreement with the reported experimental ones, with RMSE <0.29, A_f value 1.02 to 1.09, and B_f value 0.92 to 0.99. These results indicated that the predictive models provided useful information for the establishment of safety standards and a risk assessment for S. aureus in flour products.

Methodology for modeling the microbial contamination of air filters

In this paper, we propose a theoretical model to simulate microbial growth on contaminated air filters and entrainment of bioaerosols from the filters to an indoor environment. Air filter filtration and antimicrobial efficiencies, and effects of dust particles on these efficiencies, were evaluated. The number of bioaerosols downstream of the filter could be characterized according to three phases: initial, transitional, and stationary. In the initial phase, the number was determined by filtration efficiency, the concentration of dust particles entering the filter, and the flow rate. During the transitional phase, the number of bioaerosols gradually increased up to the stationary phase, at which point no further increase was observed. The antimicrobial efficiency and flow rate were the dominant parameters affecting the number of bioaerosols downstream of the filter in the transitional and stationary phase, respectively. It was found that the nutrient fraction of dust particles entering the filter caused a significant change in the number of bioaerosols in both the transitional and stationary phases. The proposed model would be a solution for predicting the air filter life cycle in terms of microbiological activity by simulating the microbial contamination of the filter.

Compartmental models for apical efflux by P-glycoprotein--part 1: evaluation of model complexity

PURPOSE

With the goal of quantifying P-gp transport kinetics, Part 1 of these manuscripts evaluates different compartmental models and Part 2 applies these models to kinetic data.

METHODS

Models were developed to simulate the effect of apical efflux transporters on intracellular concentrations of six drugs. The effect of experimental variability on model predictions was evaluated. Several models were evaluated, and characteristics including membrane configuration, lipid content, and apical surface area (asa) were varied.

RESULTS

Passive permeabilities from MDCK-MDR1 cells in the presence of cyclosporine gave lower model errors than from MDCK control cells. Consistent with the results in Part 2, model configuration had little impact on calculated model errors. The 5-compartment model was the simplest model that reproduced experimental lag times. Lipid content and asa had minimal effect on model errors, predicted lag times, and intracellular concentrations. Including endogenous basolateral uptake activity can decrease model errors. Models with and without explicit membrane barriers differed markedly in their predicted intracellular concentrations for basolateral drug exposure. Single point data resulted in clearances similar to time course data.

CONCLUSIONS

Compartmental models are useful to evaluate the impact of efflux transporters on intracellular concentrations. Whereas a 3-compartment model may be sufficient to predict the impact of transporters that efflux drugs from the cell, a 5-compartment model with explicit membranes may be required to predict intracellular concentrations when efflux occurs from the membrane. More complex models including additional compartments may be unnecessary.

Isothermal and non-isothermal kinetic models of chemical processes in foods governed by competing mechanisms

A process or reaction that peaks at high temperatures but not at low ones indicates competition between synthesis and degradation. A proposed phenomenological model composed of a decay factor superimposed on a growth term can describe both. Temperature elevation shortens the two subprocesses' characteristic times and increases their rates. The degradation's characteristic time relative to the experiment's determines whether a peak is observed. All of the parameters determine the peak's height and shape as can be seen in two interactive Wolfram demonstrations on the Web. Detailed knowledge of the underlying mechanisms is unnecessary for the model's construction, and uniqueness is not a prerequisite either. However, different expressions might be needed for ongoing processes and ones initially undetectable. The model's applicability is demonstrated with published results on very different reactions in foods. In principle, it can be converted into a dynamic rate equation for simulating a process's evolution under non-isothermal conditions.

Model on the microbial quality change of seasoned soybean sprouts for on-line shelf life prediction

The growth of aerobic bacteria on Korean seasoned soybean sprouts was modelled as a function of temperature to estimate microbial spoilage and shelf life on a real-time basis under dynamic storage conditions. Counts of aerobic bacteria on seasoned soybean sprouts stored at constant temperatures between 0 degrees C and 15 degrees C were recorded. The bootstrapping method was applied to generate many resampled data sets of mean microbial plate counts that were then used to estimate the parameters of the microbial growth model of Baranyi and Roberts. The distributions of the model parameters were quantified, and their temperature dependencies were expressed as mathematical functions. When the temperature functions of the parameters were incorporated into differential equations describing microbial growth, predictions of microbial growth under fluctuating temperature conditions were similar to observed microbial growth.

Estimating microbial growth parameters from non-isothermal data: A case study with Clostridium perfringens

Microbial growth parameters are usually calculated from the fit of a growth model to a set of isothermal growth data gathered at several temperatures. In principle at least, it is also possible to derive them from non-isothermal ('dynamic') growth data. This requires the numerical solution of a rate model whose coefficients are nested terms that include the temperature profile. The methodology is demonstrated with simulated non-isothermal growth data on which random noise had been superimposed to emulate the scatter found in experimental microbial counts. The procedure has been validated by successful retrieval of the known generation parameters from the simulated growth curves. The method was then applied to experimental non-isothermal growth data of C. perfringens cells in cooled ground beef. The growth data collected under one cooling regime were used to predict the organism's growth patterns under different temperature histories. The practicality of the method is currently limited because of the relatively large scatter found in experimental microbial growth data and the relatively low frequency at which they are collected. But if and when the scatter could be reduced and the counts taken at short time intervals, the method could be used to determine the growth model in situ thus enabling to translate the changing temperature during processing, transportation or storage into a corresponding growth curve of the organism in question.

Linear and non-linear kinetics in the synthesis and degradation of acrylamide in foods and model systems

Isothermal acrylamide formation in foods and asparagine-glucose model systems has ubiquitous features. On a time scale of about 60 min, at temperatures in the approximate range of 120-160 degrees C, the acrylamide concentration-time curve has a characteristic sigmoid shape whose asymptotic level and steepness increases with temperature while the time that corresponds to the inflection point decreases. In the approximate range of 160-200 degrees C, the curve has a clear peak, whose onset, height, width and degree of asymmetry depend on the system's composition and temperature. The synthesis-degradation of acrylamide in model systems has been recently described by traditional kinetic models. They account for the intermediate stages of the process and the fate of reactants involved at different levels of scrutiny. The resulting models have 2-6 rate constants, accounting for both the generation and elimination of the acrylamide. Their temperature dependence has been assumed to obey the Arrhenius equation, i.e., each step in the reaction was considered as having a fixed energy of activation. A proposed alternative is constructing the concentration curve by superimposing a Fermian decay term on a logistic growth function. The resulting model, which is not unique, has five parameters: a hypothetical uninterrupted generation-level, two steepness parameters; of the concentration climbs and fall and two time characteristics; of the acrylamide synthesis and elimination. According to this model, peak concentration is observed only when the two time constants are comparable. The peak's shape and height are determined by the gap between the two time constants and the relative magnitudes of the two "rate" parameters. The concept can be extended to create models of non-isothermal acrylamide formation. The basic assumption, which is yet to be verified experimentally, is that the momentary rate of the acrylamide synthesis or degradation is the isothermal rate at the momentary temperature, at a time that corresponds to its momentary concentration. The theoretical capabilities of a model of this kind are demonstrated with computer simulations. If the described model is correct, then by controlling temperature history, it is possible to reduce the acrylamide while still accomplishing much of the desirable effects of a heat process.

Validation of a tertiary model for predicting variation of Salmonella typhimurium DT104 (ATCC 700408) growth from a low initial density on ground chicken breast meat with a competitive microflora

Growth of a multiple antibiotic-resistant strain (ATCC 700408) of Salmonella Typhimurium definitive phage type 104 (DT104) from a low initial density (10(0.6) most probable number [MPN] or CFU/g) on ground chicken breast meat with a competitive microflora was investigated and modeled as a function of time and temperature (10 to 40 degrees C). MPN and viable counts (CFU) on a selective medium with four antibiotics enumerated the pathogen. Data from five replicate challenge studies per temperature were combined and fit to a primary model to determine maximum specific growth rate (micro), maximum population density (Nmax), and the 95% prediction interval (PI). Nonlinear regression was used to obtain secondary models as a function of temperature for micro, Nmax, and PI, which ranged from 0.04 to 0.4 h(-1), 1.6 to 9.4 log MPN or CFU/g, and 1.4 to 2.4 log MPN or CFU/g, respectively. Secondary models were combined with the primary model to create a tertiary model for predicting variation (95% PI) of pathogen growth among batches of ground chicken breast meat with a competitive microflora. The criterion for acceptable model performance was that 90% of observed MPN or CFU data had to be in the 95% PI predicted by the tertiary model. For data (n=344) used in model development, 93% of observed MPN and CFU data were in the 95% PI predicted by the tertiary model, whereas for data (n=236) not used in model development but collected using the same methods, 94% of observed MPN and CFU data were in the 95% PI predicted by the tertiary model. Thus, the tertiary model was successfully verified against dependent data and validated against independent data for predicting variation of Salmonella Typhimurium DT104 growth among batches of ground chicken breast meat with a competitive microflora and from a low initial density.

Effect of trabecular bone loss on cortical strain rate during impact in an in vitro model of avian femur

Background

Osteoporotic hip fractures occur due to loss of cortical and trabecular bone mass and consequent degradation in whole bone strength. The direct cause of most fractures is a fall, and hence, characterizing the mechanical behavior of a whole osteopenic bone under impact is important. However, very little is known about the mechanical interactions between cortical and trabecular bone during impact, and it is specifically unclear to what extent epiphyseal trabecular bone contributes to impact resistance of whole bones. We hypothesized that trabecular bone serves as a structural support to the cortex during impact, and hence, loss of a critical mass of trabecular bone reduces internal constraining of the cortex, and, thereby, decreases the impact tolerance of the whole bone.

Methods

To test this hypothesis, we conducted cortical strain rate measurements in adult chicken's proximal femora subjected to a Charpy impact test, after removing different trabecular bone core masses to simulate different osteopenic severities.

Results

We found that removal of core trabecular bone decreased by ~10-fold the cortical strain rate at the side opposite to impact (p < 0.01), i.e. from 359,815 ± 1799 μm/m per second (mean ± standard error) for an intact (control) specimen down to 35,997 ± 180 μm/m per second where 67% of the total trabecular bone mass (~0.7 grams in adult chicken) were removed. After normalizing the strain rate by the initial weight of bone specimens, a sigmoid relation emerged between normalized strain rate and removed mass of trabecular bone, showing very little effect on the cortex strain rate if below 10% of the trabecular mass is removed, but most of the effect was already apparent for less than 30% trabecular bone loss. An analytical model of the experiments supported this behavior.

Conclusion

We conclude that in our in vitro avian model, loss of over 10% of core trabecular bone substantially altered the deformation response of whole bone to impact, which supports the above hypothesis and indicates that integrity of trabecular bone is critical for resisting impact loads.

Modeling and predicting non-isothermal microbial growth using general purpose software

Published experimental isothermal growth curves of Clostridium perfringens cells in ground ham were fitted with a modified three-parameter version of the logistic equation as a primary model and the temperature dependence of the three parameters by ad hoc empirical secondary models. These were used to predict the organism's non-isothermal growth curves under three different cooling regimes. The assumption has been that the organism's instantaneous (or momentary) non-isothermal growth rate is the isothermal rate at the given temperature at a time that corresponds to its instantaneous population size. This could be translated into a differential rate model equation, whose coefficients are constructed from terms that reflect the changing growth parameters with temperature and hence with time. The continuous rate equation, however, can be solved incrementally by a numerical procedure that can be implemented in similar purpose software like Microsoft Excel(R). In all three cases, there was good agreement between the growth curves predicted by the model and those found experimentally. This demonstrated that the procedure can be used to generate growth curves under complicated thermal histories that may include regular and irregular temperature oscillations.

On modeling and simulating transitions between microbial growth and inactivation or vice versa

Resumed growth of the survivors of a heat or chemical treatment after cooling or a disinfectant dissipation is not an uncommon phenomenon. Similarly, the inverse, the onset of mortality in a growing microbial population as a result of exposure to increasing temperature or concentration of an antimicrobial agent, is also a familiar scenario. Provided that in either regime, the organism has no time to adapt biologically, the continuous transition from growth to inactivation or vice versa can be simulated with conventional growth and inactivation models, whose rate constant is allowed to change sign. Where both the growth and inactivation follow first-order kinetics, the sign change has no effect on the model equation's solutions. The same applies when the growth and inactivation patterns are described by a rate model, like the differential logistic equation or its various variants. However, determination of such models' coefficients from experimental isothermal growth and inactivation data can be difficult for technical reasons, unless the model can be integrated analytically. If not, or when the model itself is unknown a priori, then the rate equation would have to be derived from the fit of empirical models like the Weibull, modified versions of the logistic function and the like. But this may create a new kind of problem as a result of that the log and certain power operations cannot be used for negative numbers. For certain models at least, the problem can be solved through modification of the procedure by which the rate equation is solved numerically. This is demonstrated in simulated transitions between growth and inactivation and between inactivation and growth based on the log linear and Weibullian-power law models and three logistic patterns based on a shifted logistic function, the Baranyi-Roberts model and a shifted arctan model.

Pressure–time cell death threshold for albino rat skeletal muscles as related to pressure sore biomechanics

Deep pressure sores (DPS) are associated with inadequate soft tissue perfusion and excessive tissue deformation over critical time durations, as well as with ischemia-reperfusion cycles and deficiency of the lymphatic system. Muscle tissue shows the lowest tolerance to pressure injuries, compared with more superficial tissues. In this communication, we present new histopathology data for muscle tissue of albino (Sprague-Dawley) rats exposed to pressures for 15 or 30 min. These data are superimposed with an extensive literature review of all previous histopathology reported for albino rat skeletal muscles subjected to pressure. The pooled data enabled a new mathematical characterization of the pressure-time threshold for cell death in striated muscle of rats, in the form of a sigmoid pressure-time relation, which extends the previous pressure-time relation to the shorter exposure periods. We found that for pressure exposures shorter than 1 h, the magnitude of pressure is the important factor for causing cell death and the exposure time has little or no effect: even relatively short exposures (15 min - 1 h) to pressures greater than 32 kPa (240 mmHg) cause cell death in rat muscle tissue. For exposures of 2 h or over, again the magnitude of pressure is the important factor for causing cell death: pressures greater than 9 kPa (67 mmHg) applied for over 2 h consistently cause muscle cell death. For the intermediate exposures (between 1 and 2 h), the magnitude of cell-death-causing pressure strongly depends on the time of exposure, i.e., critical pressure levels drop from 32 to 9 kPa. The present sigmoidal pressure-time cell death threshold is useful for design of studies in albino rat models of DPS, and may also be helpful in numerical simulations of DPS development, where there is often a need to extrapolate from tissue pressures to biological damage.