Comparing Nonsynergistic Gamma Models with Interaction Models To Predict Growth of Emetic Bacillus cereus when Using Combinations of pH and Individual Undissociated Acids as Growth-Limiting Factors

A combination of multiple hurdles to limit microbial growth is frequently applied in foods to achieve an overall level of protection. Quantification of hurdle technology aims at identifying synergistic or multiplicative effects and is still being developed. The gamma hypothesis states that inhibitory environmental factors aiming at limiting microbial growth rates combine in a multiplicative manner rather than synergistically. Its validity was tested here with respect to the use of pH and various concentrations of undissociated acids, i.e., acetic, lactic, propionic, and formic acids, to control growth of Bacillus cereus in brain heart infusion broth. The key growth parameter considered was the maximum specific growth rate, μ_max, as observed by determination of optical density. A variety of models from the literature describing the effects of various pH values and undissociated acid concentrations on μ_max were fitted to experimental data sets and compared based on a predefined set of selection criteria, and the best models were selected. The cardinal model developed by Rosso (for pH dependency) and the model developed by Luong (for undissociated acid) were found to provide the best fit and were combined in a gamma model with good predictive performance. The introduction of synergy factors into the models was not able to improve the quality of the prediction. On the contrary, inclusion of synergy factors led to an overestimation of the growth boundary, with the inherent possibility of leading to underestimation of the risk under the conditions tested in this research.Consumers expect safe and sufficiently stable food within the given shelf life of a food product or component. Several growth-limiting factors, collectively referred to as hurdles, can be used to ensure food stability and safety. Examples of such hurdles are low pH, low water activity, or low temperature (12). Combining hurdles to achieve food stability and safety, known as hurdle technology, can be used to achieve an overall level of protection in food while minimizing impacts on food quality (20). When a combination of hurdles is used, generally the intensity of the hurdles may be lower, to exert a comparable preservative effect, than the intensity of those hurdles when used individually (20). Three classes of interaction can be defined when applying hurdle technology: “no interaction,” in which the effect of a combination is as expected from the response of the separate factors; “synergy,” in which the effect is greater than expected; and “antagonism,” in which the effect is less than expected (6).Though the concept of hurdle technology is rather well established, the quantification of the combined impact of hurdles on growth of microorganisms is still being developed. One significant problem is that there are two opposite views of how antimicrobial factors combine. One view states that there are interactive effects between hurdles; when they are applied together, they give a protection significantly greater than that expected on the basis of the application of the individual hurdles (synergy). The alternative view considers that the combined effect may be complex but that there are no interactive effects culminating in synergy. The latter view is called the gamma hypothesis (41) and states that inhibitory environmental factors combine in a multiplicative manner to produce the observed overall microbial inhibition. A major benefit of models based on the gamma hypothesis is a reduction in experimental work, since growth rates and, as a result, growth boundaries can be estimated upon evaluating single hurdles rather than their various combinations. This benefit can only be realized, however, when the gamma hypothesis is valid for the combination of hurdles considered. If the hypothesis is not valid and interactive effects are present, growth boundaries are estimated wrongly, which might result in fail-safe predictions.Over the years, the gamma hypothesis has been confirmed by several studies (16, 17, 26, 34, 38) that concluded that the combined effect of hurdles on growth rates is multiplicative rather than synergistic. Contrarily, Rödel and Scheuer (30) concluded that interaction occurs when various hurdles are combined, stressing the occurrence of synergy. Both Le Marc et al. (21) and Augustin and Carlier (5) developed a synergy model to take account of synergy occurring when hurdles are combined. It is prudent to conclude that the effect of combinations of hurdles is best evaluated on a case-by-case basis in order to ensure appropriate utility of hurdle technology approaches in establishing food designs that are stable and safe.This research aimed to validate or falsify the gamma hypothesis for two closely related hurdles often used in the food industry: the pH level and the undissociated acid concentration ([HA]). The approach chosen was to establish an overview of models for pH and undissociated acid from the literature. Based on predefined criteria, models were then selected to construct a new gamma model without synergy factors for the various hurdle combinations. The criteria were meant to enable evaluation of the fitting performance of all individual models to select the best-performing models for inclusion in the new gamma models. Finally, the validity of the gamma hypothesis was judged by comparing the predictive performance of the newly constructed gamma models with two gamma models, including a synergy factor reported in the literature. Bacillus cereus F4810/72, relevant for both food spoilage and poisoning (14, 19), was used as the model microorganism. Maximum specific growth rates were determined by optical density measurements combined with time to detection. This method was selected after thorough investigation of three different methods to obtain parameters for growth, as recently published (8).     

Gamma study of pH, nitrite, and salt inhibition of Aeromonas hydrophila

The gamma hypothesis states that there are no interactions between antimicrobial environmental factors. The time to growth of Aeromonas hydrophila challenged with pH, NaNO(2), and salt combinations at 30 degrees C was investigated. Data were examined using a model based on the gamma hypothesis (the gamma model), which takes into account variance-stabilizing transformations and which gives biologically relevant parameters. At high concentrations of NaNO(2) and at pHs of >6.0, the antimicrobial action of the nitrite ion has a strong influence (MIC = 2,033 mg liter(-1)), whereas at pHs of <6, nitrous acid is dominant (MIC = 1.5 mg liter(-1)). This change is not due to a "synergy" between pH and the nitrite ion but is due to the shift in the equilibrium concentrations of nitrous acid and nitrite in solution caused by pH. In combination with salt, the parameters found for the action of Na nitrite were identical to those found when it was examined in isolation. Therefore, pH, NaNO(2), and salt act independently on the growth of A. hydrophila. By expanding the gamma model with a cardinal temperature model, the results of fitting the model of Palumbo et al. (J. Food Prot. 54:429-435, 1994) to randomly produced environmental conditions could be reproduced, suggesting that temperature also has an independent effect.     

Modelling the combined effect of temperature,pH and aw on the growth rate of Monascus ruber,a heat-resistant fungus isolated from green table olives

AIMS: Growth modes predicting the effect of pH (3.5-5.0), NaCl (2-10%), i.e. aw (0.937-0.970) and temperature (20-40 degrees C) on the colony growth rate of Monascus ruber, a fungus isolated from thermally-processed olives of the Conservolea variety, were developed on a solid culture medium. METHODS AND RESULTS: Fungal growth was measured as colony diameter on a daily basis. The primary predictive model of Baranyi was used to fit the growth data and estimate the maximum specific growth rates. Combined secondary predictive models were developed and comparatively evaluated based on polynomial, Davey, gamma concept and Rosso equations. The data-set was fitted successfully in all models. However, models with biological interpretable parameters (gamma concept and Rosso equation) were highly rated compared with the polynomial equation and Davey model and gave realistic cardinal pHs, temperatures and aw. CONCLUSIONS: The combined effect of temperature, pH and aw on growth responses of M. ruber could be satisfactorily predicted under the current experimental conditions, and the models examined could serve as tools for this purpose. SIGNIFICANCE AND IMPACT OF THE STUDY: The results can be successfully employed by the industry to predict the extent of fungal growth on table olives.     

Rheological investigation of synergistic interactions between galactomannans and non-pectic polysaccharide fraction from water soluble yellow mustard mucilage

Synergistic interactions between galactomannans (GMs) and non-pectic polysaccharides (NPP) from yellow mustard mucilage were investigated in the present study. Structural analysis revealed that NPP was mainly composed of β-1,4-d glucosidic linkage. Four types of GMs, namely fenugreek gum (FG), guar gum (GG), tara gum (TG) and locust bean gum (LBG) with mannose to galactose ratios (M/G) of 1.2, 1.7, 3.0 and 3.7, respectively, were blended with NPP at various ratios. The viscoelastic properties of the mixtures were measured in order to evaluate the effects of GM/NPP blending ratio, M/G ratio, total polysaccharide concentration and pH on the synergistic interactions. Results revealed that at a total polysaccharide concentration of 0.5% (w/w), the highest synergism occurred at the GM/NPP blending ratio of 3/7 for all four types of GMs. The interaction between TG and NPP showed the highest synergy, followed by LBG/NPP, FG/NPP and GG/NPP. At a higher total polysaccharide concentration (1.0% w/w), the mixture of TG and NPP still exhibited the highest synergy, however, the order of synergy between NPP and other GMs was changed as FG/NPP, LBG/NPP and GG/NPP. At the total polysaccharide concentration of 0.5% and GM/NPP blending ratio of 3/7, neutral pH (pH 6.5) showed the strongest synergy compared to that at pH 2.0 and pH 12.0. The mechanism of the synergistic effects could be explained by a combination of segregative association model and junction zone model.     

Procedure for testing kinetic models of the photocycle of bacteriorhodopsin.

Given some simple kinetic models of the photocycle of bacteriorhodopsin (bR) and data taken at many wavelengths and under conditions that avoid photoselection and steady-state cycling complications, it is shown how to extract the apparent rate constants and the spectra of the intermediates. Special consideration was given to establishing the range of error of these results. There are many criteria, which we explicitly discuss, that the spectra should satisfy in order that the kinetic model be acceptable. New data for the photocycle of purple membrane fragments in dilute buffer at pH 7.0 has been obtained at 15 measuring wavelengths and four temperatures. The procedure, which can be generalized to more complex models, has been applied to these data to test two kinds of kinetic models: the unidirectional unbranched model and the undirectional model with simple branching straight back to bR from any intermediate. In these models the spectrum of the O intermediate is highly temperature sensitive, even with branching, and/or has two broad maxima. Moreover, the spectrum of the M intermediate has a secondary maximum and two M-like states appear to be required. Thus, neither model satisfies the physical criteria.     

Convenient Model To Describe the Combined Effects of Temperature and pH on Microbial Growth

A new model in which the maximum microbial specific growth rate ((mu)(infmax)) is described as a function of pH and temperature is presented. The seven parameters of this model are the three cardinal pH parameters (the pH below which no growth occurs, the pH above which no growth occurs, and the pH at which the (mu)(infmax) is optimal), the three cardinal temperature parameters (the temperature below which no growth occurs, the temperature above which no growth occurs, and the temperature at which the (mu)(infmax) is optimal), and the specific growth rate at the optimum temperature and optimum pH. The model is a combination of the cardinal temperature model with inflection and the cardinal pH model (CPM). The CPM was compared with the models of Wijtzes et al. and Zwietering et al. by using previously published data sets. The models were compared on the basis of the usual criteria (simplicity, biological significance and minimum number of parameters, applicability, quality of fit, minimum structural correlations, and ease of initial parameter estimation), and our results justified the choice of the CPM. Our combined model was constructed by using the hypothesis that the temperature and pH effects on the (mu)(infmax) are independent. An analysis of this new model with an Escherichia coli O157:H7 data set showed that there was a good correspondence between observed and calculated (mu)(infmax) values. The potential and convenience of the model are discussed.     

Development and validation of experimental protocols for use of cardinal models for prediction of microorganism growth in food products

An experimental protocol to validate secondary-model application to foods was suggested. Escherichia coli, Listeria monocytogenes, Bacillus cereus, Clostridium perfringens, and Salmonella were observed in various food categories, such as meat, dairy, egg, or seafood products. The secondary model validated in this study was based on the gamma concept, in which the environmental factors temperature, pH, and water activity (aw) were introduced as individual terms with microbe-dependent parameters, and the effect of foodstuffs on the growth rates of these species was described with a food- and microbe-dependent parameter. This food-oriented approach was carried out by challenge testing, generally at 15 and 10 degrees C for L. monocytogenes, E. coli, B. cereus, and Salmonella and at 25 and 20 degrees C for C. perfringens. About 222 kinetics in foods were generated. The results were compared to simulations generated by existing software, such as PMP. The bias factor was also calculated. The methodology to obtain a food-dependent parameter (fitting step) and therefore to compare results given by models with new independent data (validation step) is discussed in regard to its food safety application. The proposed methods were used within the French national program of predictive microbiology, Sym'Previus, to include challenge test results in the database and to obtain predictive models designed for microbial growth in food products.     

Cadmium adsorption by an organic soil: a comparison of some humic – metal complexation models

Abstract

The retention of Cd by an organic soil was investigated as a function of pH and ionic strength. The adsorption of Cd at pH values from 2 to 11 at two ionic strengths (0.053 M and 0.017 M LiNO₃) were found to be a function of both pH and ionic strength. Four Cd-humic complexation models were evaluated in order to test the applicability of these models to fit data from batch adsorption experiments. The models varied greatly in their complexity and implicit assumptions. Three were discrete functional group models – a simple diprotic acid model, a two diprotic acid model and the Windermere Humic Aqueous Acid (WHAM) model, and a continuous functional group model - the non-ideal competitive adsorption (NICA) model. The concentration of proton binding sites in the soil was found to be 4.51 mol kg^-1. The NICA and WHAM models were more successful than either a simple diprotic acid model or a two diprotic acid model at modeling Cd complexation by the organic soil, although both underestimated adsorption at very high pH values.     

In vitro biofilm models to study dental caries: a systematic review

The aim of this systematic review is to characterize and discuss key methodological aspects of in vitro biofilm models for caries-related research and to verify the reproducibility and dose-response of models considering the response to anti-caries and/or antimicrobial substances. Inclusion criteria were divided into Part I (PI): an in vitro biofilm model that produces a cariogenic biofilm and/or caries-like lesions and allows pH fluctuations; and Part II (PII): models showing an effect of anti-caries and/or antimicrobial substances. Within PI, 72.9% consisted of dynamic biofilm models, while 27.1% consisted of batch models. Within PII, 75.5% corresponded to dynamic models, whereas 24.5% corresponded to batch models. Respectively, 20.4 and 14.3% of the studies reported dose-response validations and reproducibility, and 32.7% were classified as having a high risk of bias. Several in vitro biofilm models are available for caries-related research; however, most models lack validation by dose-response and reproducibility experiments for each proposed protocol.     

Linear-Arrhenius models for bacterial growth and death and vitamin denaturations

Summary The development of the quantitative, linear-Arrhenius model of Davey for predicting bacterial growth and death (inactivation) is reviewed. The applicability of the model to published data from independent researchers for both the growth phase and lag phase, involving combined environmental factors (T, a _w) is illustrated. Also illustrated is its applicability to thermal inactivation kinetics and vitamin denaturation (with combinedT, pH). Integration of the model to produce complex models describing the thermal sterilization of liquid is demonstrated. Advantages of the model, including its simplicity and the fact that the coefficients to build the model can be obtained easily by relatively unsophisticated users, are highlighted in a comparison with other models.Mention of brand or firm names does not constitute an endorsement by the US Department of Agriculture over others of a similar nature not mentioned.     

Growth in solid heterogeneous human colon adenocarcinomas: comparison of simple logistical models

Abstract. Three models of simple logistical growth were used to describe volumetric growth in heterogeneous tumours. Two clonal subpopulations (designated as clone A and clone D) originally obtained from a human colon adenocarcinoma were used to produce solid xenograft tumours in nude mice. Volumetric growth of tumours produced from pure cells alone was compared to that produced from 50% A:50% D, 88% A:12% D, and 9% A:91% D admixtures. Gompertzian analysis of the in vivo growth data indicated significant differences in both the initial growth rates and final asymptotic limiting volumes of the pure versus the admixed tumours. Verhulstian and modified Verhulstian models were also used to derive regression curves from the same data. The fit of the curves was compared with each other using standard (Akaike, 1974; Schwartz, 1978) information criteria. In four of the five tumour populations the Gompertz equation fitted best. Only in the 88% A:12% D tumours did the modified Verhulst model fit best. The deviations from the regression curves, the residuals, for all three models were systematically distributed. These systematic errors are likely to be the result of using simplified logistical models to describe the growth kinetics of interacting populations in heterogeneous tumours.     

Combined blockade of EGFR and glutamine metabolism in preclinical models of colorectal cancer

Improving response to epidermal growth factor receptor (EGFR)-targeted therapies in patients with advanced wild-type (WT) RAS colorectal cancer (CRC) remains an unmet need. In this preclinical work, we evaluated a new therapeutic combination aimed at enhancing efficacy by targeting cancer cell metabolism in concert with EGFR. We hypothesized that combined blockade of glutamine metabolism and EGFR represents a promising treatment approach by targeting both the “fuel” and “signaling” components that these tumors need to survive. To explore this hypothesis, we combined CB-839, an inhibitor of glutaminase 1 (GLS1), the mitochondrial enzyme responsible for catalyzing conversion of glutamine to glutamate, with cetuximab, an EGFR-targeted monoclonal antibody in preclinical models of CRC. 2D and 3D in vitro assays were executed following treatment with either single agent or combination therapy. The combination of cetuximab with CB-839 resulted in reduced cell viability and demonstrated synergism in several cell lines. In vivo efficacy experiments were performed in cell-line xenograft models propagated in athymic nude mice. Tumor volumes were measured followed by immunohistochemical (IHC) analysis of proliferation (Ki67), mechanistic target of rapamycin (mTOR) signaling (pS6), and multiple mechanisms of cell death to annotate molecular determinants of response. In vivo, a significant reduction in tumor growth and reduced Ki67 and pS6 IHC staining were observed with combination therapy, which was accompanied by increased apoptosis and/or necrosis. The combination showed efficacy in cetuximab-sensitive as well as resistant models. In conclusion, this therapeutic combination represents a promising new precision medicine approach for patients with refractory metastatic WT RAS CRC.     

Growth in solid heterogeneous human colon adenocarcinomas: comparison of simple logistical models

Three models of simple logistical growth were used to describe volumetric growth in heterogeneous tumours. Two clonal subpopulations (designated as clone A and clone D) originally obtained from a human colon adenocarcinoma were used to produce solid xenograft tumours in nude mice. Volumetric growth of tumours produced from pure cells alone was compared to that produced from 50% A:50% D, 88% A:12% D, and 9% A:91% D admixtures. Gompertzian analysis of the in vivo growth data indicated significant differences in both the initial growth rates and final asymptotic limiting volumes of the pure versus the admixed tumours. Verhulstian and modified Verhulstian models were also used to derive regression curves from the same data. The fit of the curves was compared with each other using standard (Akaike, 1974; Schwartz, 1978) information criteria. In four of the five tumour populations the Gompertz equation fitted best. Only in the 88% A:12% D tumours did the modified Verhulst model fit best. The deviations from the regression curves, the residuals, for all three models were systematically distributed. These systematic errors are likely to be the result of using simplified logistical models to describe the growth kinetics of interacting populations in heterogeneous tumours.     

Gamma Study of pH, Nitrite, and Salt Inhibition of Aeromonas hydrophila

The gamma hypothesis states that there are no interactions between antimicrobial environmental factors. The time to growth of Aeromonas hydrophila challenged with pH, NaNO₂, and salt combinations at 30°C was investigated. Data were examined using a model based on the gamma hypothesis (the gamma model), which takes into account variance-stabilizing transformations and which gives biologically relevant parameters. At high concentrations of NaNO₂ and at pHs of >6.0, the antimicrobial action of the nitrite ion has a strong influence (MIC = 2,033 mg liter⁻¹), whereas at pHs of <6, nitrous acid is dominant (MIC = 1.5 mg liter⁻¹). This change is not due to a “synergy” between pH and the nitrite ion but is due to the shift in the equilibrium concentrations of nitrous acid and nitrite in solution caused by pH. In combination with salt, the parameters found for the action of Na nitrite were identical to those found when it was examined in isolation. Therefore, pH, NaNO₂, and salt act independently on the growth of A. hydrophila. By expanding the gamma model with a cardinal temperature model, the results of fitting the model of Palumbo et al. (J. Food Prot. 54:429-435, 1994) to randomly produced environmental conditions could be reproduced, suggesting that temperature also has an independent effect.     

Dissociation of dimers of human hemoglobins A and F into monomers

Dissociation of alpha beta and alpha gamma dimers of human hemoglobins (Hb) A and F into monomers was studied by alpha chain exchange (Shaeffer, J. R., McDonald, M. J., Turci, S. M., Dinda, D. M., and Bunn, H. F. (1984) J. Biol. Chem. 259, 14544-14547). Unlabeled carbonmonoxy-Hb A was incubated with trace amounts of preparatively purified, native, 3H-alpha subunits in 10 mM sodium phosphate, pH 7.0, at 25 degrees C. At appropriate times, free alpha monomers were separated from Hb A tetramers by anion exchange high performance liquid chromatography. Transfer of radioactivity from the alpha chain pool into Hb A was measured, yielding a first order dimer dissociation rate constant, k2 = (3.2 +/- 0.3) X 10(-3) h-1. The Arrhenius plot of k2 was linear between 7 and 37 degrees C, yielding an enthalpy of activation of 23 kcal/alpha beta dimer. As the chloride concentration was raised from 0 to 0.2 M, the dissociation rate increased 3-fold; with higher salt concentrations, however, the rate gradually returned to baseline. This rate was not altered by raising the pH from 6.5 to 7.2, but as pH was further raised to 8.4, kappa 2 increased about 3-fold. Hb F, which has an increased stability at alkaline pH, dissociated into alpha and gamma monomers 3 times more slowly than Hb A. Moreover, the dimer-monomer dissociation of Hb F was characterized by a significantly reduced pH dependence. These results demonstrate that both alpha beta and alpha gamma dimers of Hb A and Hb F dissociate reversibly into monomers under physiologic conditions. The differential pH dependence for dimer dissociation between Hb A and Hb F suggests that specific amino acid replacement at the alpha 1 gamma 1 interface confers increased resistance to alkaline denaturation.     

Effects of excluded volume and polydispersity on solution properties of lentinan in 0.1 M NaOH solution

Seven lentinan fractions of various weight-average molecular weights (M(w)), ranging from 1.45 x 10(5) to 1.13 x 10(6) g mol(-1) were investigated by static light scattering and viscometry in 0.1M NaOH solution at 25 degrees C. The intrinsic viscosity [eta] - M(w) and radius of gyration s(2)(z) (1/2) - M(w) relationships for lentinan in 0.1M NaOH solution were found to be represented by [eta] = 5.1 x 10(-3)M(w) (0.81) cm(3) g(-1) and s(2)(z) (1/2) = 2.3 x 10(-1)M(w) (0.58) nm, respectively. Focusing on the effects of the M(w) polydispersity with the Schulz-Zimm distribution function, the data of M(w), s(2)(z) (1/2), and [eta] was analyzed on the basis of the Yoshizaki-Nitta-Yamakawa theory for the unperturbed helical wormlike chain combined with the quasi-two-parameter (QTP) theory for excluded-volume effects. The persistence length, molecular weight per unit contour length, and the excluded-volume strength were determined roughly to be 6.2 nm, 980 nm(-1), and 0.1, respectively. Compared with the theoretical value calculated by the Monte Carlo model, the persistence length is longer than that of the single (1 --> 3)-beta-(D)-glucan chain. The results revealed that lentinan exists as single-stranded flexible chains in 0.1M NaOH solution with a certain degree of expansion due to the electrostatic repulsion from the interaction between the OH(-) anions and lentinan molecules.     

Synergy between chemotherapeutic agents and CTLA-4 blockade in preclinical tumor models

Ipilimumab, a cytotoxic T-lymphocyte antigen-4 (CTLA-4) binding agent, has proven to be an effective monotherapy for metastatic melanoma and has shown antitumor activity in trials when administered with other therapeutic agents. We hypothesized that the combination of ipilimumab with chemotherapeutic agents, such as ixabepilone, paclitaxel, etoposide, and gemcitabine, may produce therapeutic synergy based on distinct but complementary mechanisms of action for each drug and unique cellular targets. This concept was investigated using a mouse homolog of ipilimumab in preclinical murine tumor models, including SA1N fibrosarcoma, EMT-6 mammary carcinoma, M109 lung carcinoma, and CT-26 colon carcinoma. Results of CTLA-4 blockade in combination with one of various chemotherapeutic agents demonstrate that synergy occurs in settings where either agent alone was not effective in inducing tumor regression. Furthermore, when combined with CTLA-4 blockade, ixabepilone, etoposide, and gemcitabine elicited prolonged antitumor effects in some murine models with induction of a memory immune response. Future investigations are warranted to determine which specific chemo-immunotherapy combinations, if any, will produce synergistic antitumor effects in the clinical setting.