A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new Bĕlehdrádek-type model for evaluating the effect of temperature on growth rate

2011 ◽  
Vol 28 (4) ◽  
pp. 770-776 ◽  
Author(s):  
Lihan Huang
2000 ◽  
Vol 63 (2) ◽  
pp. 268-272 ◽  
Author(s):  
DANA M. McELROY ◽  
LEE-ANN JAYKUS ◽  
PEGGY M. FOEGEDING

The growth of psychrotrophic Bacillus cereus 404 from spores in boiled rice was examined experimentally at 15, 20, and 30°C. Using the Gompertz function, observed growth was modeled, and these kinetic values were compared with kinetic values for the growth of mesophilic vegetative cells as predicted by the U.S. Department of Agriculture's Pathogen Modeling Program, version 5.1. An analysis of variance indicated no statistically significant difference between observed and predicted values. A graphical comparison of kinetic values demonstrated that modeled predictions were “fail safe” for generation time and exponential growth rate at all temperatures. The model also was fail safe for lag-phase duration at 20 and 30°C but not at l5°C. Bias factors of 0.55, 0.82, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, indicated that the model generally was fail safe and hence provided a margin of safety in its growth predictions. Accuracy factors of 1.82, 1.60, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, quantitatively demonstrated the degree of difference between predicted and observed values. Although the Pathogen Modeling Program produced reasonably accurate predictions of the growth of psychrotrophic B. cereus from spores in boiled rice, the margin of safety provided by the model may be more conservative than desired for some applications. It is recommended that if microbial growth modeling is to be applied to any food safety or processing situation, it is best to validate the model before use. Once experimental data are gathered, graphical and quantitative methods of analysis can be useful tools for evaluating specific trends in model prediction and identifying important deviations between predicted and observed data.


2017 ◽  
Vol 80 (3) ◽  
pp. 447-453 ◽  
Author(s):  
Ai Kataoka ◽  
Hua Wang ◽  
Philip H. Elliott ◽  
Richard C. Whiting ◽  
Melinda M. Hayman

ABSTRACT The growth characteristics of Listeria monocytogenes inoculated onto frozen foods (corn, green peas, crabmeat, and shrimp) and thawed by being stored at 4, 8, 12, and 20°C were investigated. The growth parameters, lag-phase duration (LPD) and exponential growth rate (EGR), were determined by using a two-phase linear growth model as a primary model and a square root model for EGR and a quadratic model for LPD as secondary models, based on the growth data. The EGR model predictions were compared with growth rates obtained from the USDA Pathogen Modeling Program, calculated with similar pH, salt percentage, and NaNO2 parameters, at all storage temperatures. The results showed that L. monocytogenes grew well in all food types, with the growth rate increasing with storage temperature. Predicted EGRs for all food types demonstrated the significance of storage temperature and similar growth rates among four food types. The predicted EGRs showed slightly slower rate compared with the values from the U.S. Department of Agriculture Pathogen Modeling Program. LPD could not be accurately predicted, possibly because there were not enough sampling points. These data established by using real food samples demonstrated that L. monocytogenes can initiate growth without a prolonged lag phase even at refrigeration temperature (4°C), and the predictive models derived from this study can be useful for developing proper handling guidelines for thawed frozen foods during production and storage.


1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.


2004 ◽  
Vol 70 (5) ◽  
pp. 2928-2934 ◽  
Author(s):  
Maria Lövenklev ◽  
Ingrid Artin ◽  
Oskar Hagberg ◽  
Elisabeth Borch ◽  
Elisabet Holst ◽  
...  

ABSTRACT The effects of carbon dioxide, sodium chloride, and sodium nitrite on type B botulinum neurotoxin (BoNT/B) gene (cntB) expression in nonproteolytic Clostridium botulinum were investigated in a tryptone-peptone-yeast extract (TPY) medium. Various concentrations of these selected food preservatives were studied by using a complete factorial design in order to quantitatively study interaction effects, as well as main effects, on the following responses: lag phase duration (LPD), growth rate, relative cntB expression, and extracellular BoNT/B production. Multiple linear regression was used to set up six statistical models to quantify and predict these responses. All combinations of NaCl and NaNO2 in the growth medium resulted in a prolonged lag phase duration and in a reduction in the specific growth rate. In contrast, the relative BoNT/B gene expression was unchanged, as determined by the cntB-specific quantitative reverse transcription-PCR method. This was confirmed when we measured the extracellular BoNT/B concentration by an enzyme-linked immunosorbent assay. CO2 was found to have a major effect on gene expression when the cntB mRNA levels were monitored in the mid-exponential, late exponential, and late stationary growth phases. The expression of cntB relative to the expression of the 16S rRNA gene was stimulated by an elevated CO2 concentration; the cntB mRNA level was fivefold greater in a 70% CO2 atmosphere than in a 10% CO2 atmosphere. These findings were also confirmed when we analyzed the extracellular BoNT/B concentration; we found that the concentrations were 27 ng · ml−1 · unit of optical density−1 in the 10% CO2 atmosphere and 126 ng · ml−1 · unit of optical density−1 in the 70% CO2 atmosphere.


2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.


2016 ◽  
pp. 77-98
Author(s):  
Nenad Rankovic ◽  
Jelena Nedeljkovic ◽  
Zoran Poduska ◽  
Dragan Nonic

This study examines the influence of some climate elements on the collected quantities of two commercially most significant types of mushrooms in Serbia (porcini and chanterelle). The main objective of the research is to determine the extent of the collected quantity of porcini and chanterelle, which can be expected in different scenarios of climate change (?1Bmin, ?1Bmax, A2min ? A2max), based on forecasts of temperature and rainfall changes. The general (dialectical) and specific (modelling methods) are used in the research, as well as the classical scientific methods of reasoning. The calculation of the average annual exponential growth rate (IS) was carried out by forming exponential regression models of the trend of porcini and chanterelle collected quantities. In the research it was found that, according to the data related to the period up to 2014, one can expect a decrease in the movement of both porcini and chanterelle IS, and thus a decrease in the collected quantities. On the other hand, according to the data related to the period up to 2040, in both cases one can expect some fluctuation (increase and decrease) in the movement of IS. According to the data related to periods after 2041 (especially for the period until 2100), in both cases, one can expect a decrease in the collected quantities, as a result of changes in T and P, caused by the assumed climate change.


2009 ◽  
Vol 27 (No. 6) ◽  
pp. 433-453 ◽  
Author(s):  
A. Medveďová ◽  
Ľ. Valík ◽  
Z. Sirotná ◽  
D. Liptáková

<i>Staphylococcus aureus</i> is a pathogenic bacterium that induces several of human illnesses. The staphylococcal enterotoxin (SE) production as the results of previous growth of toxigenic strains is the most crucial problem which may lead to the staphylococcal food poisoning outbreaks in humans. That is why the growth of three strains of <i>Staphylococcus aureus</i> was characterised in milk and modelled in dependence of temperature. For the lag phase duration of <i>S. aureus</i> 2064, the Davey model was used with the following result: ln(1/lag) = 1.973 – 87.92/<i>T</i> + 285.09/<i>T</i><sup>2</sup> (<i>R</i><sup>2</sup> = 0.962). The dependence of the growth rate on incubation temperature was modelled by the Ratkowsky square root model and Gibson in sub-optimal and whole temperature range, respectively. The validation of both models showed high significance of the growth rate data fitting. The optimal temperature of <i>T</i><sub>opt</sub> = 38.5°C was resulted from Gibson model for the <i>S. aureus</i> 2064 growth in milk. For practical purpose, the time necessary for the increase of <i>S. aureus</i> by 3 log counts was also calculated within the growth temperature range. These data may provide useful information e.g. for the producers using raw milk in their artisanal cheese practice as the specific strains were used in this study.


1994 ◽  
Vol 05 (02) ◽  
pp. 213-218 ◽  
Author(s):  
GABRIEL P. PATERNAIN ◽  
MIGUEL PATERNAIN

Using Yomdin's Theorem [8], we show that for a compact Riemannian manifold M, the geodesic entropy — defined as the exponential growth rate of the average number of geodesic segments between two points — is ≤ the topological entropy of the geodesic flow of M. We also show that if M is simply connected and N ⊂ M is a compact simply connected submanifold, then the exponential growth rate of the sequence given by the Betti numbers of the space of paths starting in N and ending in a fixed point of M, is bounded above by the topological entropy of the geodesic flow on the normal sphere bundle of N.


2017 ◽  
Vol 80 (7) ◽  
pp. 1090-1098 ◽  
Author(s):  
T. Sandoval-Contreras ◽  
S. Marín ◽  
A. Villarruel-López ◽  
A. Gschaedler ◽  
L. Garrido-Sánchez ◽  
...  

ABSTRACT Molds are responsible for postharvest spoilage of citrus fruits. The objective of this study was to evaluate the effect of temperature on growth rate and the time to visible growth of Aspergillus niger strains isolated from citrus fruits. The growth of these strains was studied on agar lime medium (AL) at different temperatures, and growth rate was estimated using the Baranyi and Roberts model (Int. J. Food Microbiol. 23:277–294, 1994). The Rosso et al. cardinal model with inflexion (L. Rosso, J. R. Lobry, S. Bajard, and J. P. Flandrois, J. Theor. Biol. 162:447–463, 1993) was used as a secondary model to describe the effect of temperature on growth rate and the lag phase. We hypothesized that the same model could be used to calculate the time for the mycelium to become visible (tv) by substituting the lag phase (1/λ and 1/λopt) with the time to visible colony (1/tv-opt and 1/tv), respectively, in the Rosso et al. model. High variability was observed at suboptimal conditions. Extremes of temperature of growth for A. niger seem to have a normal variability. For the growth rate and time tv, the model was satisfactorily compared with results of previous studies. An external validation was performed in lime fruits; the bias and accuracy factors were 1.3 and 1.5, respectively, for growth rate and 0.24 and 3.72, respectively, for the appearance time. The discrepancy may be due to the influence of external factors. A. niger grows significantly more slowly on lime fruit than in culture medium, probably because the nutrients are more easily available in medium than in fruits, where the peel consistency may be a physical barrier. These findings will help researchers understand the postharvest behavior of mold on lime fruits, host-pathogen interactions, and environmental conditions infecting fruit and also help them develop guidelines for future work in the field of predictive mycology to improve models for control of postharvest fungi.


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