Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models

Maximum specific growth rate (mu(max)) and lag time (lambda) were estimated from viable count and absorbance data and compared for different microorganisms, incubation systems and growth conditions. Data from 176 growth curves and 120 absorbance detection times of serially diluted cultures were evaluated using different mathematical growth models. Accurate estimates of mu(max) and lambda were obtained from individual absorbance growth curves by using the Richard model, with values of the parameter m fixed to 0.5, 1.0 or 2.0 to describing different degrees of growth dampening, as well as from absorbance detection times of serially diluted cultures. It is suggested to apply the two techniques complementarily for accurate, rapid and inexpensive estimation of microbial growth parameter values from absorbance data. In contrast, considerable limitations were demonstrated for the ability of the Exponential, the Gompertz and the Logistic models to estimate mu(max) and lambda values accurately from absorbance data. Limitations of these models were revealed due the wide range of growth conditions studies.     

Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes

AIMS: The effect of temperature (2-30 degrees C), pH (4.8-7.4) and water activity (0.946-0.995) on the relationship between optical density (OD) at 600 nm and the plate count (CFU ml(-1)) was investigated for Listeria monocytogenes. METHODS AND RESULTS: Calibration curves, relating OD with plate counts, were collected by measuring the OD of consecutive one-half dilution series, before determining the cell density by classic plate count methods. The calibration curves were observed to be shifting in a parallel way, with increasing stress levels. Especially pH influenced the curve in a great extent, while the other variables were showing more synergetic effects. The reason for the shift was investigated by a microscopic viability test, showing a viability decrease with increasing stress levels, causing the shift of the calibration curve. In a last step a model was made describing the effect of environmental factors on the calibration curve, with different data transformations being tested. A polynomial equation was fitted to the data, taking into account a set of constraints to incorporate microbiological knowledge in the black box model. Hence, illogical interpolation results and overfitting of the data could be avoided. CONCLUSIONS: Different stress factors are affecting the relationship between the OD and the cell count of L. monocytogenes by lowering the cell viability. These effects could be modelled using a constrained polynomial model. SIGNIFICANCE AND IMPACT OF THE STUDY: The observed phenomena are important when calculating growth parameters, like growth rate and lag phase, based on OD data.     

Estimation of temperature dependent growth rate and lag time of Listeria monocytogenes by optical density measurements.

An automated turbidimetric system, Bioscreen C, was used to monitor growth of ten strains of Listeria monocytogenes at different temperatures. Several methods for estimation of maximum specific growth rate (mu(max)) and lag time (lag) from turbidimetric data were compared to values estimated from viable count data. By using a calibration factor, reliable estimations of mu(max) could be obtained from turbidimetric measurements. On the other hand, accurate estimations of lag required some viable count data.     

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.     

Modelling the work to be done by Escherichia coli to adapt to sudden temperature upshifts

AIMS: This paper studies and models the effect of the amplitude of a sudden temperature upshift DeltaT on the adaptation period of Escherichia coli, in terms of the work to be done by the cells during the subsequent lag phase (i.e., the product of growth rate mumax and lag phase duration lambda). METHODS AND RESULTS: Experimental data are obtained from bioreactor experiments with E. coli K12 MG1655. At a predetermined time instant during the exponential growth phase, a sudden temperature upshift is applied (no other environmental changes take place). The length of the (possibly) induced lag phase and the specific growth rate after the shift are quantified with the growth model of Baranyi and Roberts (Int J Food Microbiol 23, 1994, 277). Different models to describe the evolution of the product lambda x mumax as a function of the amplitude of the temperature shift are statistically compared. CONCLUSIONS: The evolution of lambda x mumax is influenced by the amplitude of the temperature shift DeltaT and by the normal physiological temperature range. As some cut-off is observed, the linear model with translation is preferred to describe this evolution. SIGNIFICANCE AND IMPACT OF THE STUDY: This work contributes to the characterization of microbial lag phenomena, in this case for E. coli K12 MG1655, in view of accurate predictive model building.     

Use of a D-optimal design with constrains to quantify the effects of the mixture of sodium,potassium, calcium and magnesium chloride salts on the growth parameters of <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis>

The combined effect of NaCl, KCl, CaCl(2), and MgCl(2) on the water activity (a (w)) and the growth parameters of Saccharomyces cerevisiae was studied by means of a D-optimal mixture design with constrains (total salt concentrations < or = 9.0%, w/v). The a (w) was linearly related to the concentrations of the diverse salts; its decrease, by similar concentrations of salts, followed the order NaCl > CaCl(2) > KCl > MgCl(2), regardless of the reference concentrations used (total absence of salts or 5% NaCl). The equations that expressed the maximum specific growth (mu (max)), lag phase duration (lambda), and maximum population reached (N (max)) showed that the values of these parameters depended on linear effects and two-way interactions of the studied chloride salts. The mu (max) decreased as NaCl and CaCl(2) increased (regardless of the presence or not of previous NaCl); however, in the presence of a 5% NaCl, a further addition of KCl and MgCl(2) markedly increased mu (max). The lambda was mainly affected by MgCl(2) and the interactions NaCl x CaCl(2) and CaCl(2) x MgCl(2). The further addition of NaCl and CaCl(2) to a 5% NaCl medium increased the lag phase while KCl and MgCl(2) had negligible or slightly negative effect, respectively. N (max) was mainly affected by MgCl(2) and its interactions with NaCl, KCl, and CaCl(2); MgCl(2) stimulated N (max) in the presence of 5% NaCl while KCl, NaCl, and CaCl(2) had a progressive decreasing effect. These results can be of interest for the fermentation and preservation of vegetable products, and foods in general, in which this yeast could be present.     

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.     

检测大肠杆菌群体生长动力学过程4种方法的比较

用浊度测定、菌落形成数计数（CFU）、流式细胞计数（FCT）,以及MTT还原测脱氢酶活力4种检测方法,测定了E．coliCVCC249群体的生长量,并通过Logistic模型、Sigmoid模型,以及正态分布方程拟合由上述生物量所表征的群体生长动力学过程曲线．结果表明,对浊度和流式检测数据,Logistic和Sigmoid方程可给出较好的拟合度,而对CFU法和脱氢酶活力检测法,仅有正态分布方程能呈现更好的拟合．通过应用有限时域向前差分的方法,消除不能增殖的休止细胞对浊度生长过程曲线的影响,以模拟菌群增殖的过程曲线．在此基础上,求得菌群生长的即时速度（advancingvelocity,Vad。）和即时速度的瞬变率,以此为据将E．coliCVCC249生长过程划分为线性增长期、指数增长期、指数减速期、线性减速期,以及衰亡期5个阶段．此外,对新的划分生长阶段的方法与经典方法的不同,以及R。（拟合决定系数）能否作为确定模型是否拟合的唯一判据,进行了讨论．     

The effect of sodium chloride and temperature on the rate and extent of growth of Clostridium botulinum type A in pasteurized pork slurry

A selective medium was used to enumerate Clostridium botulinum growing in the presence of natural spoilage organisms in a model cured pork slurry. The growth responses of a mixed spore inoculum of six strains of Cl. botulinum type A were studied at 15 degrees, 20 degrees and 27 degrees C with 1.5, 2.5, 3.5 or 4.5% (w/v) salt added (aw range 0.961-0.990). Gompertz and logistic curves, which have a sigmoid shape, were fitted to the data and lag times, growth rates, generation times and time to maximum growth rates were derived. Variation in germination rates of the spores occasionally gave a falsely extended lag time resulting in an exceptionally high estimate for growth rate. Products containing 4.5% (w/v) NaCl would be capable of supporting growth of proteolytic strains of Cl. botulinum, even at 15 degrees C, although the lag period would be extended. In products where absence of Cl. botulinum cannot be assured additional preservative measures are essential. The information obtained provides a framework to investigate the effects of a wider range of additives or variables on the growth responses of Cl. botulinum.     

The effect of sodium chloride and temperature on the rate and extent of growth of Clostridium botulinum type A in pasteurized pork slurry

A selective medium was used to enumerate Clostridium botulinum growing in the presence of natural spoilage organisms in a model cured pork slurry. The growth responses of a mixed spore inoculum of six strains of Cl. botulinum type A were studied at 15°, 20° and 27°C with 1˙5, 2˙5, 3˙5 or 4˙5% (w/v) salt added (a_w range 0961–0990). Gompertz and logistic curves, which have a sigmoid shape, were fitted to the data and lag times, growth rates, generation times and time to maximum growth rates were derived. Variation in germination rates of the spores occasionally gave a falsely extended lag time resulting in an exceptionally high estimate for growth rate. Products containing 4˙5% (w/v) NaCl would be capable of supporting growth of proteolytic strains of Cl. botulinum , even at 15°C, although the lag period would be extended. In products where absence of Cl. botulinum cannot be assured additional preservative measures are essential. The information obtained provides a framework to investigate the effects of a wider range of additives or variables on the growth responses of Cl. botulinum .     

Growth studies of plasmid bearing and plasmid cured Yersinia enterocolitica GER O:3 in the presence of cefsulodin, irgasan and novobiocin at 25 and 37 degrees C

AIM: In this study, the growth characteristics of Yersinia enterocolitica biotype 4, GER O:3 plasmid bearing (P+) and plasmid cured (P-) strain types were evaluated in brain heart infusion broth supplemented with cefsulodin, irgasan, and novobiocin alone or in combination. METHODS AND RESULTS: Growth curves were obtained for the two strain types in broth supplemented with selective agents at 25 or 37 degrees C for 32 h to obtain data on the lag phase durations and growth rates of the strains. Generally, the lag times and growth rates of the P+ and P- strains were similar for cultures incubated at 25 degrees C regardless of the selective agent added and where plasmid replication and expression were not under any significant burden. However, where the lag times and growth rates of the strains were examined at 37 degrees C, significant differences were observed in the lag phase durations of the plasmid bearing strain type compared the plasmid cured strain, an effect that was due to the burden of the plasmid and the influence of selective agents. Generally, when two or more agents were present, lag phase durations were longer for the plasmid bearing strain. Some exceptions noted where in the presence of irgasan or full selective agent (CIN) the opposite case was observed. When growth rates were compared, the plasmidless strain type was typically faster than the plasmid bearing strain in the presence of most selective agents at 37 degrees C and the growth rates of both strain types at 25 degrees C were similar where the temperature appeared to negate the effects of plasmid. CONCLUSIONS: The data obtained in these studies suggest that selective agents (in particular irgasan) and incubation temperature play a significant role in influencing the growth characteristics of plasmid bearing and plasmid cured strains of Y. enterocolitica. SIGNIFICANCE AND IMPACT OF THE STUDY: This data presented in this study has significant implications for enrichment methods used in the detection or recovery of plasmid bearing Y. enterocolitica strains from food, environmental or clinical samples.     

Molecular analysis of the rstR and orfU genes of the CTX prophages integrated in the small chromosomes of environmental Vibrio cholerae non-O1, non-O139 strains

The ctxAB genes encoding cholera toxin, reside in the genome of a filamentous bacteriophage CTXphi. The presence of CTX prophage in non-epidemic environmental Vibrio cholerae strains is rare. The CTX prophage, the lysogenic form of CTXphi in V. cholerae, is comprised of the 'RS2' and the 'Core'. Analysis of the rstR gene present in the RS2 region of the CTX prophage revealed the presence of new alleles of the prophages in four environmental non-O1, non-O139 strains VCE22 (O36), VCE228 (O27), VCE232 (O4) and VCE233 (O27), and the CTX prophages are located in the small chromosomes. Phylogenetic analysis based on the nucleotide sequences of the rstR and orfU (present in the core) genes of these prophages placed them in a single unique cluster, which is distally located compared with that of epidemic V. cholerae O1 strains. Further analysis indicated that the genome of the prophage present in the strain VCE22 is devoid of the ctxAB genes, called pre-CTX prophage and the strain also possess the toxin-coregulated pilus protein coding gene tcpA of classical type, another important pathogenicity determining locus of the epidemic V. cholerae strains. Comparative analysis of the nucleotide sequences of the rstR and orfU genes indicated that the pre-CTX prophage of VCE22 might be the progenitor of new alleles of the CTX prophages present in these environmental strains.     

Postnatal growth pattern of F1 hybrids of a cross between two strains of large and small musk shrews, Suncus murinus

In our previous comparison of the postnatal growth of two laboratory strains of the musk shrew (Suncus murinus), the large shrews originating in Bangladesh (BAN strain) and the small shrews from Nagasaki, Japan (NAG strain), we found that differences in the 120-day adult body weight of the two strains (BAN: males 135.3g and females 82.0g; NAG: 52.9 and 34.2g, respectively) reflect both an approximately 2.5 times longer linear growth phase and an approximately 1.5 times higher growth rate during this phase in the BAN strain. We examined the postnatal growth (from 5 to 120 days after birth) of the F1 hybrids of a cross between the two strains and compared our findings with the above-mentioned growth data for the parent strains. A growth equation composed of linear and monomolecular functions was fitted to the growth data for the shrews. The growth trajectories of both sexes of the F1 hybrids were situated roughly midway between those of the two parent strains throughout the entire growth process. The adult body weight of the F1 shrews at 120 days of age averaged 86.0g in the males and 51.7g in the females. The growth phase lasted approximately 60 days in the males and approximately 40 days in the females of both the F1 shrews and the parent strains. The duration of the linear growth phase of the F1 hybrids (29.8 days in the males and 19.0 days in the females), however, was approximately intermediate between the parent strains (BAN: males 33.4 days and females 26.1 days; NAG: 18.8 and 13.9 days, respectively).(ABSTRACT TRUNCATED AT 250 WORDS)     

The quantitative genetics of maximal and basal rates of oxygen consumption in mice

A positive genetic correlation between basal metabolic rate (BMR) and maximal (VO(2)max) rate of oxygen consumption is a key assumption of the aerobic capacity model for the evolution of endothermy. We estimated the genetic (V(A), additive, and V(D), dominance), prenatal (V(N)), and postnatal common environmental (V(C)) contributions to individual differences in metabolic rates and body mass for a genetically heterogeneous laboratory strain of house mice (Mus domesticus). Our breeding design did not allow the simultaneous estimation of V(D) and V(N). Regardless of whether V(D) or V(N) was assumed, estimates of V(A) were negative under the full models. Hence, we fitted reduced models (e.g., V(A) + V(N) + V(E) or V(A) + V(E)) and obtained new variance estimates. For reduced models, narrow-sense heritability (h(2)(N)) for BMR was <0.1, but estimates of h(2)(N) for VO(2)max were higher. When estimated with the V(A) + V(E) model, the additive genetic covariance between VO(2)max and BMR was positive and statistically different from zero. This result offers tentative support for the aerobic capacity model for the evolution of vertebrate energetics. However, constraints imposed on the genetic model may cause our estimates of additive variance and covariance to be biased, so our results should be interpreted with caution and tested via selection experiments.     

Comparison of definitions of the lag phase and the exponential phase in bacterial growth.

Different definitions for the lag time and of the duration of the exponential phase can be used to calculate these quantities from growth models. The conventional definitions were compared with newly proposed definitions. It appeared to be possible to derive values for the lag time and the duration of the exponential phase from the growth models and differences between the various definitions could be quantified. All the different values can be calculated from the growth parameters microm, lambda and alpha. Therefore, it appeared to be unnecessary to use complicated mathematical equations; simple equations were adequate. For the Gompertz model the conventional definition of the lag time did not differ appreciably from the newly proposed definition. The end-point of the exponential phase and thus the duration of the exponential phase differed considerably for the two definitions. For the logistic model the two definitions lead to considerable differences for all quantities. It is recommended that the conventional definition is used for calculating the lag time. For the duration of the exponential phase it is recommended that the new definition is used. The value can be calculated, however, directly from the conventional growth parameters.     

Aerobic degradation of 2,4,6-trichlorophenol by a microbial consortium - selection and characterization of microbial consortium

A microbial consortium that efficiently degrades 2,4,6-TCP (2,4,6-trichlorophenol), as the sole source of carbon and energy under aerobic conditions was selected from municipal activated sludge. Six bacterial strains, designated S(1), S(2), S(3), S(4), S(5) and S(6), were isolated from the selected consortium and five were identified as Sphingomonas paucimobilis (S(2), S(3)), Burkholderia cepacia(S(4)), Chryseomonas luteola (S(5)) and Vibrio metschnikovii (S(6)). After prolonged cultivation followed by successive transfers, the consortium's degradation ability was improved and reached a specific degradation rate of 34 mg 2,4,6-TCP g(-1) dry weight h(-1) (about 51 mg 2,4,6-TCP g(-1) cell protein h(-1)). The soluble chemical oxygen demand, chloride and oxygen uptake balance data clearly indicate the complete dechlorination and mineralization of 2,4,6-TCP. The consortium's activity was not inhibited by 2,4,6-TCP concentrations 相似文献   

Kinetic comparison of seven strains of 2,4-dichlorophenoxyacetic acid-degrading bacteria.

Seven strains of 2,4-dichlorophenoxyacetic acid-degrading bacteria, including Pseudomonas, Alcaligenes, and Bordetella spp., were compared on the basis of growth kinetics. Estimates of maximum growth rate (mu max, k1) and half-saturation growth constant (Ks, k3) were obtained by fitting substrate depletion curves to a four-parameter version of the integrated Monod equation. Estimates of Ks ranged from 2.2 micrograms/ml (10 microM) to 33.8 micrograms/ml (154 microM), and estimates of mu max ranged from 0.20 h-1 (Td = 3.5 h) to 0.32 h-1 (Td = 2.2 h). Estimates of mu max, but not Ks, were affected by changes in initial inoculum density. Maximum growth rates (mu max) were also estimated from turbidity measurements. They ranged from 0.10 h-1 (Td = 6.9 h) to 1.0 h-1 (Td = 0.7 h). There was no correlation between estimates of mu max derived from substrate depletion curves and those derived from turbidity measurements (P = 0.20).     

Kinetic comparison of seven strains of 2,4-dichlorophenoxyacetic acid-degrading bacteria.

Seven strains of 2,4-dichlorophenoxyacetic acid-degrading bacteria, including Pseudomonas, Alcaligenes, and Bordetella spp., were compared on the basis of growth kinetics. Estimates of maximum growth rate (mu max, k1) and half-saturation growth constant (Ks, k3) were obtained by fitting substrate depletion curves to a four-parameter version of the integrated Monod equation. Estimates of Ks ranged from 2.2 micrograms/ml (10 microM) to 33.8 micrograms/ml (154 microM), and estimates of mu max ranged from 0.20 h-1 (Td = 3.5 h) to 0.32 h-1 (Td = 2.2 h). Estimates of mu max, but not Ks, were affected by changes in initial inoculum density. Maximum growth rates (mu max) were also estimated from turbidity measurements. They ranged from 0.10 h-1 (Td = 6.9 h) to 1.0 h-1 (Td = 0.7 h). There was no correlation between estimates of mu max derived from substrate depletion curves and those derived from turbidity measurements (P = 0.20).