Growth and Adhesion of Pseudomonas fluorescens in a Batch Culture: A Kinetic Analysis of the Action of Extracellular Antiadhesins

This work tests 6 hypothetical models simulating the growth, respiration, and adhesion of cells to the walls of the cultivation flask. All the models postulate the synthesis of antiadhesins (AAs), i.e., extracellular metabolites decreasing the degree of cell adhesion. The models have the following distinguishing features: (model 1) the blocking of sorption centers on the glass walls by antiadhesins (the competitive inhibition of adhesion); (model 2) the noncompetitive inhibition of adhesion; (model 3) the accelerated release of bound cells; (model 4) a combination of models 1 and 3; (model 5) a combination of models 1 and 3 with a delay; (model 6) a combined action of two AAs, one of which, AA₁, inhibits cell adhesion, and the other, AA₂ (its synthesis is induced when the concentration of AA₁ reaches a threshold level), stimulates the detachment of bound cells. Model 6 fits the relevant experimental data best. The delay effect is relatively small. The sigmoid character of the curve showing cell adhesion as a function of the antiadhesin concentration implies the existence of a strong cooperative effect in the adhesion inhibition. The models proposed satisfactorily simulate the growth, respiration, and adhesion of cells and AA synthesis in a batch bacterial culture grown either in a fresh nutrient medium or in the medium supplemented with the filtrate of a mature culture of the same species.     

Mathematical models of bacterial growth,inhibition and death under combined stress conditions

Summary In this report we review the history of growth theories. We show how classical growth models may be derived as special cases of a generic growth rate equation. We show how growth models may be modified to represent survival data. We use linear combinations of growth and survival models to represent complex growth/survival curves and give practical examples utilizing nonlinear regression analysis. We show that traditional methods of estimating D values are inappropriate for complex, multiphasic growth/survival data. We show how such data may be modeled mathematically and illustrate methods for estimating true D values from such data.     

Evaluation of different approaches for modelling individual tree seedling height growth

We compared different approaches for modelling height growth of individual beech seedlings in a controlled factorial experiment as well as in field data from naturally regenerated beech seedlings under the canopy of overstorey mature beech trees. Several competition indices, a model of overstorey fine root density, relative photosynthetically active radiation (PAR) values, and soil water values were used in these approaches. In the factorial experiment relative PAR and soil water content were measured and used for the prediction of seedlings height growth. In the field experiment this was done by using relative PAR and estimated fine root biomass as a surrogate for below ground resource availability. The latter approach was compared with a model where we used various competition indices representing the impact of overstorey trees on beech seedlings. Our results suggested that (1) models which combine resource based growth functions are suitable for the prediction of individual height growth of beech seedlings. Resource based models offer the opportunity to investigate on the independent multiplicative effect of irradiance and water supply and their interactions on tree seedlings. It was (2) shown that a combined model could be used not only to predict individual height growth of beech seedlings in a controlled experiment but also in the field. The model parameters of a pure light response function for the controlled factorial experiment are comparable to those obtained in the field study. The results showed (3) that the precision of predicting beech seedlings height growth is comparable between the model types tested within this study. Approximately half of the observed variation in seedlings relative height growth rate could be explained. However, the simple competition index approach provides no information on the environmental factors constraining tree seedlings growth; whereas the multiplicative combined models can be used to get a better understanding of growth dynamics in the field.     

Growth kinetics for shelf-life prediction: Theory and practice

Summary Predictive microbiology can be used to determine and predict the shelf-life of perishable foods under commercial distribution conditions based on microbial growth kinetics. This paper presents general microbial growth kinetics with the Monod model and the Gompertz function. Additional models are given to describe effects of food composition (e. g.a _w) and environmental conditions (e.g. temperature, gas atmosphere) as well as their interaction on the growth kinetic parameters (lag time and specific growth rate). These models can be used to predict the time to reach a critical level under any constant conditions within the range tested. A combination of microbial kinetics with an engineering accumulation approach can be used to predict the final microbial level in a food, or the loss of shelf-life, for any known time-temperature sequence, if there is no history effect or the history effect is negligible. A time-temperature indicator, could be used for predicting the remaining shelf-life of perishable foods under any distribution condition based on microbial growth kinetics.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.     

Modeling of growth and sporulation of <Emphasis Type="Italic">Bacillus thuringiensis</Emphasis> in an intermittent fed batch culture with total cell retention

An extended dynamical model for growth and sporulation of Bacillus thuringiensis subsp. kurstaki in an intermittent fed-batch culture with total cell retention is proposed. This model differs from reported models, by including dynamics for natural death of cells and substrate consumption for cell maintenance. The proposed model uses sigmoid functions to describe these kinetic parameters. Equations for time evolution of substrate, vegetative, sporulated and total cell concentration were taken from previous works. Model parameters were determined from batch experimental data obtained in pilot plant. Parameter identification was developed in two stages: (1) coarse identification using a multivariable optimization with constraints algorithm, (2) fine identification by heuristic fit of model parameters looking for a minimal model error. The proposed model estimates adequate time evolution of the process variables with a mean error of 2.6% on substrate concentration and 6.7% on biomass concentration.     

The relationship between kinetics of substrate-limited transitions and steady-state growth in continuous cultures ofAquaspirillum autotrophicum limited by pyruvate

Heterotrophic growth at steady state and during transient states caused by the sudden change of the concentration of the limiting factor in the feed medium was investigated experimentally for continuous cultures ofAquaspirillum autotrophicum limited by pyruvate. A model for describing the growth at steady state was selected from three unstructured models after statistical tests of the data. This model postulates that the growth yield increases linearly with the growth rate. Growth during transitions where the substrate remained limiting at all times was fitted with first-order kinetics. Theoretical predictions of these kinetics were derived from the unstructured models used to describe steady state. The predicted rate coefficients of the transients were compared to the experimental coefficients. It appeared that the model which best described steady-state growth also provided the best predictions for growth during the transient state. It is a widespread opinion that unstructured models are adequate to describe growth under steady-state conditions but not to predict transitions in continuous culture. However, for the particular case studied here, no higher degree of complexity was required to describe transitions, provided the growth of the culture was always limited by the substrate.     

A size-structured model of bacterial growth and reproduction

We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.     

Energy allocation in the cladoceran Daphnia magna Straus,under starvation and refeeding

Summary Models incorporating the energetics of individual daphnids (Cladocera) have been developed to predict the effect of environmental variables, particularly food availability, on population dynamics. One of them, that of Kooijman (1986), assumes that all assimilated energy enters a storage compartment prior to use in production and metabolism, and that under starvation the stores are used to support maintenance, reproduction and somatic growth, in that order of priority. This predicts that, under starvation, reproduction and growth will continue for a time, and that after they cease death will be immediate. Another model, that of McCauley et al. (1990), assumes that assimilated energy is used directly for maintenance and production, and that stores are accumulated to support maintenance metabolism under starvation. This predicts that growth and reproduction should cease immediately upon starvation and that death will not be immediate. We have carried out laboratory experiments, manipulating starvation time, on Daphnia magna to distinguish between these two models. The results support features of both models in that reproduction, but not growth, ceases upon starvation. We therefore developed a third model in which both maintenance and growth are supported from stores under starvation, with maintenance taking priority over growth under these conditions.     

Biomass and lutein productivity of <Emphasis Type="Italic">Scenedesmus almeriensis</Emphasis>: influence of irradiance,dilution rate and temperature

In this paper, the biomass and lutein productivity of the lutein-rich new strain Scenedesmus almeriensis is modelled versus irradiance and temperature. The results demonstrate that S. almeriensis is a mesophile microorganism with an optimal growth temperature of 35 degrees C, and capable of withstanding up to 48 degrees C, which caused culture death. This strain is also tolerant to high irradiances, showing no signs of photoinhibition even at the maximum irradiance essayed of 1625 microE m(-2) s(-1) accumulating up to 0.55% dry weight (d.wt.) of lutein. The optimal conditions that maximise the biomass productivity also favour the lutein productivity, lutein being a primary metabolite. Maximal biomass and lutein productivities of 0.87 g l(-1) day(-1) and 4.77 mg l(-1) day(-1), respectively, were measured. The analysis of light availability inside the cultures, quantified as average irradiance, demonstrates that the cultures were mainly photo-limited, although photosaturation also took place at high external irradiances. The effect of temperature was also investigated finding that the specific maximal growth rate is modified by the temperature according to the Arrhenius equation. The influence of both light availability and temperature was included in an overall growth model, which showed, as a result, capable of fitting the whole set of experimental data. An overall lutein accumulation rate model was also proposed and used in a regression analysis. Simulations performed using the proposed models show that under outdoor conditions a biomass productivity of 0.95 g l(-1) day(-1) can be expected, with a lutein productivity up to 5.31 mg l(-1) day(-1). These models may be useful to assist the design and operation optimisation of outdoor cultures of this strain.     

A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms

This paper advances a unified approach to the modeling of sigmoid organismal growth. There are numerous studies on growth, and there have been several proposals and applications of candidate models. Still, a lack of interpretation of the parameter values persists and, consequently, differences in growth patterns have riddled this field. A candidate regression model as a tool should be able to assess and compare growth-curve shapes, systematically and precisely. The Richards models constitute a useful family of growth models that amongst a multitude of parameterizations, re-parameterizations and special cases, include familiar models such as the negative exponential, the logistic, the Bertalanffy and the Gompertz. We have reviewed and systemized this family of models. We demonstrate that two specific parameterizations (or re-parameterizations) of the Richards model are able to substitute, and thus to unify all other forms and models. This unified-Richards model (with its two forms) constitutes a powerful tool for an interpretation of important characteristics of observed growth patterns, namely, [I] maximum (relative) growth rate (i.e., slope at inflection), [II] age at maximum growth rate (i.e., time at inflection), [III] relative mass or length at maximum growth rate (i.e., relative value at an inflection), [IV] value at age zero (i.e., birth, hatching or germination), and [V] asymptotic value (i.e., adult weight or length). These five parameters can characterize uniquely any sigmoid-growth data. To date most studies only compare what is referred to as the “growth-rate constant” or simply “growth rate” (k). This parameter can be interpreted as neither relative nor actual growth rate, but only as a parameter that affects the slope at inflection. We fitted the unified-Richards and five other candidate models to six artificial data sets, generated from the same models, and made a comparison based on the corrected Akaike’s Information Criterion (AICc). The outcome may in part be the result of the random generation of data points. Still, in conclusion, the unified-Richards model performed consistently well for all data sets, despite the penalty imposed by the AICc.     

Somatic gene targeting in the developing and adult mouse retina

Retinogenesis is a developmental process that is tightly regulated both temporally and spatially and is therefore an excellent model system for studying the molecular and cellular mechanisms of neurogenesis in the central nervous system. Understanding of these events in vivo is greatly facilitated by the availability of mouse mutant models, including those with natural or targeted mutations and those with conditional knockout or forced expression of genes. This article reviews these genetic modifications and their contribution to the study of retinogenesis in mammals, with special emphasis on conditional gene targeting approaches.     

Minimum recruitment frequency in plants with episodic recruitment

There is concern about the lack of recruitment of Acacia trees in the Negev desert of Israel. We have developed three models to estimate the frequency of recruitment necessary for long-term population survival (i.e. positive average population growth for 1,000 years and <10% probability of extinction). Two models assume purely episodic recruitment based on the general notion that recruitment in arid environments is highly episodic. They differ in that the deterministic model investigates average dynamics while the stochastic model does not. Studies indicating that recruitment episodes in arid environments have been overemphasized motivated the development of the third model. This semi-stochastic model simulates a mixture of continuous and episodic recruitment. Model analysis was done analytically for the deterministic model and via running model simulations for the stochastic and semi-stochastic models. The deterministic and stochastic models predict that, on average, 2.2 and 3.7 recruitment events per century, respectively, are necessary to sustain the population. According to the semi-stochastic model, 1.6 large recruitment events per century and an annual probability of 50% that a small recruitment event occurs are needed. A consequence of purely episodic recruitment is that all recruitment episodes produce extremely large numbers of recruits (i.e. at odds with field observations), an evaluation that holds even when considering that rare events must be large. Thus, the semi-stochastic model appears to be the most realistic model. Comparing the prediction of the semi-stochastic model to field observations in the Negev desert shows that the absence of observations of extremely large recruitment events is no reason for concern. However, the almost complete absence of small recruitment events is a serious reason for concern. The lack of recruitment may be due to decreased densities of large mammalian herbivores and might be further exacerbated by possible changes in climate, both in terms of average precipitation and the temporal distribution of rain.     

A structured approach for selection among candidate metabolic network models and estimation of unknown stoichiometric coefficients

A metabolic network model is one of the cornerstones of the emerging Metabolic Engineering methodology. In this article, special attention is therefore, given to the phase of model building. A five-stage structured approach to metabolic network modeling is introduced. The basic steps are: (1) to collect a priori knowledge on the reaction network and to build candidate network models, (2) to perform an a priori check of the model, (3) to estimate the unknown parameters in the model, (4) to check the identified model for acceptability from a biological and thermodynamic point of view, and (5) to validate the model with new data. The approach is illustrated with a growth system involving baker's yeast growing on mixtures of substrates. Special attention is given to the central uncertainties in metabolic network modeling, i.e., estimation of energetic parameters in the network and the choice of the source of anabolic reducing equivalents NADPH.     

Functional analysis of mutations in the human carnitine/acylcarnitine translocase in Aspergillus nidulans

Deficiency of the carnitine/acylcarnitine translocase (CACT), the most severe disorder of fatty acid beta-oxidation, is usually lethal in both humans and animals, precluding the development of animal models of the disease. In contrast, CACT deficiency is conditionally lethal in the fungus Aspergillus nidulans, since loss-of-function mutations in acuH, the translocase structural gene, do not prevent growth on carbon sources other than ketogenic compounds, such as fatty acids. Here, we describe the molecular characterization of extant acuH alleles and the development of a fungal model for CACT deficiency based on the ability of human CACT to fully complement, when expressed at physiological levels, the growth defect of an A. nidulans DeltaacuH strain on acetate and long-chain fatty acids. By using growth tests and in vitro assays this model enabled us to carry out a functional characterization of human CACT mutations showing that it may be useful for distinguishing potentially pathogenic human CACT missense mutations from neutral, single residue substitution-causing polymorphisms.     

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

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

Conductance measurements for data generation in predictive modeling

Summary The electrical resistance of a growth medium inoculated with bacteria may be automatically recorded throughout an incubation period without the necessity for sampling. The rate of change in conductance is dependent on the bacteria studied, the medium composition and the prevailing growth conditions.The effect of growth medium composition, growth conditions and inoculum level on the conductance response was studied forYersinia enterocolitica O:3. A large number of combinations of factors affecting the growth/activity of the bacteria could be studied simultaneously due to the large instrumental capacity of the Malthus 2000. A polynomial model based on conductance measurements was developed forY. enterocolitica describing the effect of temperature, pH andl-lactate level on conductance response curve parameters. The model was used for predicting growth rates. Growth rates calculated from bacterial counts ofY. enterocolitica growing in minced pork corresponded to growth rates predicted using the polynomial conductance models.     

A prototype model structure for mixed microbial populations in homogeneous food products

An important factor which has not been included in many models in the field of predictive microbiology is the influence of a background of microflora in a food product. It is however generally known that the growth of a microorganism as a pure culture can be substantially different from its growth in a mixed culture, due to microbial interactions. Because of the importance of these interactions and the lack of suitable modeling techniques in the field of predictive microbiology to describe them, the potential of models in other research fields-namely ecology-to deal with interactions is explored in previous work of the authors. However, a model structure for microbial growth in food products cannot simply be copied from those elaborated in ecology. The structure of a predictive growth model is indeed typical, primarily due to the explicit modeling of a lag phase. The current paper proposes a prototype model structure for growth of mixed microbial populations in homogeneous food products. The model is able to describe a lag phase and reduces to a classical predictive growth model in the special case of single-species growth.     

不同施肥方法对马来沉香和土沉香苗期根系生长的影响

以珍贵树种马来沉香、土沉香1年生播种苗木为材料进行试验,研究指数施肥、平均施肥对2种沉香苗期根系生长动态及对N的响应特征。结果表明,经氮素处理的马来沉香、土沉香的根系生物量、根系长度、根系表面积、根系平均直径、根体积等指标均显著高于对照处理(P<0.05)。经指数施肥处理的苗木根系生长及各形态指标均高于平均施肥处理。同一时期在相同施肥处理方式下,马来沉香苗根系生长及根系形态指标值均高于土沉香。洛伦兹模型对不同施肥方法处理下马来沉香、土沉香苗木生长指标与根系生物量进行拟合,具有较高的R²(0.95-0.99)和较低的RSMD(0.538-2.352);抛物面模型对不同施肥方法处理下马来沉香、土沉香苗木生长指标与比根长进行拟合,具有较高的R²(0.92-0.99)和较低的RSMD(3.218-6.692)。     

Kinetic Modeling of cometabolic degradation of ethanethiol and phenol by Ralstonia eutropha

Cometabolism, as a complex phenomenon in microbial world, is a special mechanism for transformation of many compounds of environmental and toxicological significance. Several models have been proposed to describe the cometabolic transformations of non-growth substrates in the absence or presence of growth substrates. In this study, a model was proposed to simulate the degradation kinetics of phenol and ethanethiol (ET) by a pure culture of Ralstonia eutropha, including the effects of cell growth, endogenous cell decay, loss of transformation activity, competitive inhibition between growth and non-growth substrates, and self-inhibition of non-growth substrate. The model parameters were determined independently and were then used for evaluating the applicability of the model by comparing experimental data with model predictions. The model successfully predicted ET transformation and phenol utilization for a wide range of concentrations of ET (0 ～ 40 mg/L) and phenol (0 ～ 100 mg/L).