A kinetic model for microbial growth on liquid hydrocarbons

A kinetic model is presented to explain microbial growth using liquid n-alkanes as substrate. The model is based on the assumption that growth occurs on the soluble alkane and that the metabolite produced by the growing cells helps the dissolution of liquid alkanes in the aqueous medium. Growth curves based on that model fit well with growth data for batch and continuous culture reported by various authors. The model also explains the differences between the relative length of exponential and linear phases of growth reported earlier.     

A model for noninhibitory microbial growth

A model for noninhibitory microbial growth has been developed which is superior to the Monod model in that it can predict the decline in steady-state growth yields at both the slow and the fast specific growth rates. The model parameters are evaluated from data obtained for steady-state, phenol-limited Pseudomonas putida growth using a conventional 1-dm(3) cheniostat. The model also has been successfully applied to Mor and Fiechter's data for cheniostat yeast cultures.     

A kinetic model for product formation of microbial and mammalian cells

Growth of microbial and mammalian cells can be classified into substrate-limited and substrate-sufficient growth according to the relative availability of the substrate (carbon and energy source) and other nutrients. It has been observed for a number of microbial and mammalian cells that the consumption rate of substrate and energy (ATP) is generally higher under substratesufficient conditions than under substrate limitation. Accordingly, the product formation under substrate excess often exhibits different patterns from those under substrate limitation. The extent of increase or decrease in product formation may depend not only on the nature of limitation and cell growth rate but also on the residual substrate concentration in a relatively wide range. The product formation kinetic models existing in literature cannot describe these effects. In this study, the Luedeking-Piret kinetic is extended to include a term describing the effect of residual substrate concentration. The extended model has a similar structure to the kinetic model for substrate and energy consumption rate recently proposed by Zeng and Deckwer. The applicability of the extended model is demonstrated with three microbial cultures for the production of primary metabolites and three hybridoma cell cultures for the production of ammonia and lactic acid over a wide range of substrate concentration. The model describes the product formation in all these cultures satisfactorily. Using this model, the range of residual substrate concentration, in which the product formation is affected, can be quantitatively assessed. (c) 1995 John Wiley & Sons, Inc.     

Mechanistic model for microbial growth on hydrocarbons

Based on available information describing the transport and consumption of insoluble alkanes, a mechanistic model is proposed for microbial growth on hydrocarbons. The model describes the atypical growth kinetics observed, and has implications in the design of large scale equipment for single cell protein (SCP) manufacture from hydrocarbons. The model presents a framework for comparison of the previously published experimental kinetic data.     

A generalized diffusion model for growth and dispersal in a population

A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.Part of this work was done while at the Mathematical Institute, Oxford University as a Senior Visiting Fellow supported by the Science Research Council of Great Britain under grant GR/B31378     

A kinetic study of the growth of fatty acid vesicles

Membrane vesicles composed of fatty acids can be made to grow and divide under laboratory conditions, and thus provide a model system relevant to the emergence of cellular life. Fatty acid vesicles grow spontaneously when alkaline micelles are added to buffered vesicles. To investigate the mechanism of this process, we used stopped-flow kinetics to analyze the dilution of non-exchanging FRET probes incorporated into preformed vesicles during growth. Oleate vesicle growth occurs in two phases (fast and slow), indicating two pathways for the incorporation of fatty acid into preformed vesicles. We propose that the fast phase, which is stoichiometrically limited by the preformed vesicles, results from the formation of a "shell" of fatty acid around a vesicle, followed by rapid transfer of this fatty acid into the preformed vesicle. The slower phase may result from incorporation of fatty acid which had been trapped in an intermediate state. We provide independent evidence for the rapid transformation of micelles into an aggregated intermediate form after transfer from high to low pH. Our results show that the most efficient incorporation of added oleate into oleic acid/oleate vesicles occurs under conditions that avoid a large transient increase in the micelle/vesicle ratio.     

A mathematical model for microbial growth under limitation by conservative substrates

A mathematical model is suggested for growth of microorganisms under limitation by “conservative” substrates such as inorganic ions or vitamins that are not broken down after uptake into the cells, but that wholely or partly remain available for production of biomass. The specific growth rate is expressed here as a function of the intracellular “concentration” of the limiting substrate, defined as the amount of substrate within the cells per unit of cell dry weight. In the model, the intracellular substrate is divided into two parts. One part is a “structural” substrate not available for further growth. The other part is an “excess” or “functional” substrate that is used for biomass production and is assumed to be converted into structural substrate proportionally to growth. The rate of growth is believed to be controlled by the intracellular concentration of excess substrate.     

A predictive model for combined temperature and water activity on microbial growth during the growth phase

An empirical and generalized model is presented, based on a modified Arrhenius equation, for predicting the combined effect of temperature and water activity on the growth rate of bacteria. When it was applied to seven separate sets of wide ranging published results, spanning some 50 years and including a spore-former and a silage micro-organism, predictions explained between 92.9 and 99.0% of the variation in the results with an overall mean of 96.6%. Advantages over existing models are that it is relatively easy to fit to data using least squares regression and requires only five coefficients. These, together with its simplicity and demonstrated wide application, will facilitate its practical use.     

A predictive model for combined temperature and water activity on microbial growth during the growth phase

An empirical and generalized model is presented, based on a modified Arrhenius equation, for predicting the combined effect of temperature and water activity on the growth rate of bacteria. When it was applied to seven separate sets of wide ranging published results, spanning some 50 years and including a spore-former and a silage micro-organism, predictions explained between 92.9 and 99.0% of the variation in the results with an overall mean of 96.6%. Advantages over existing models are that it is relatively easy to fit to data using least squares regression and requires only five coefficients. These, together with its simplicity and demonstrated wide application, will facilitate its practical use.     

A kinetic model for suspended and attached growth of a defined mixed culture

Kinetic experiments were carried out in a semicontinuous wastewater treatment process called self-cycling fermentation (SCF) using a defined mixed culture and various concentrations of synthetic brewery wastewater. The same consortium, which had been previously identified as Acinetobacter sp., Enterobacter sp., and Candida sp., were used in these experiments. The overall rate of substrate removal was attributable to both suspended microbes and the biofilm that formed during the treatment process. A rate expression was developed for the SCF system for a range of synthetic wastewaters containing glucose and various initial concentrations of ethanol and maltose. The data indicated that substrate removal by the suspended cells was directly related to the biomass concentration. However, substrate removal by the biofilm was apparently not affected by the biofilm thickness and was a function of substrate concentration only.     

A model for oscillatory kinetic systems

A kinetic model is proposed for oscillatory kinetic phenomena. The exact analytic solution is exhibited and shown to account for several features exhibited by oscillatory chemical and biological systems.     

A kinetic model for glutamate dehydrogenase

A model for the glutamate dehydrogenase reaction has been obtained that contains the reported intermediates suggested by binding and equilibrium isotope exchange methods. Calculated steady state-initial velocity rates using this model are quantitatively consistent with a wide range of nonlinear experimental data in both directions.     

A kinetic model for calcium distribution

Models for the distribution of minerals in the body are of interest as they allow researchers to trace the effect of a dose on mineral levels in plasma, storage and other compartments. Limited models are available in the literature for tracing the distribution of a calcium dose through a short time period. We propose a more general kinetic model which includes both limited absorption through the gut and loss of calcium via excretion. This new method has the advantages of giving reasonable results over moderate time periods, and allowing the extrapolation of calcium levels in extracellular fluid and storage. We fit the model to published data in order to obtain typical parameter values. These values are then used to analyze the implications of the model regarding the effect of calcium dose on calcium levels in various compartments.     

A kinetic model for plasmid curing

A simple mathematical model of drug-induced plasmid elimination (curing) considering density-dependent growth rates and plasmid transfers is presented. It describes nonlinear population dynamics of conjugative plasmids during in vitro curing experiments in batch culture. The model was tested on kinetics of acridine orange curing of F'lac plasmid. Effects of density dependence, plasmid elimination, selection for plasmidless segregants, conjugation, initial and maximal population density, and postsegregational killing on curing kinetics are simulated and discussed.     

A kinetic model for cell agglutination

A model of concanavalin A (ConA) mediated cell agglutination kinetics is proposed, in which the binding of the lectin, the agglutination of cells and the disintegration of cell clumps are discussed. This resulted in a differential equation, which is solved in terms of the average number of cells per cell clump as a function of time.     

A kinetic model for the quantitative analysis of complement

A simple model has been developed which accurately predicts the time course of complement mediated lysis of sensitized red cells. The model assumes that the one hit theory of immune hemolysis is applicable and that the rate of lysis is directly proportional to the concentration of a complement component present in rate limiting amounts. It also assumes that the rate of lysis is dependent on the fraction of cells lysed. The model can be related to the classical von Krogh equation for end point complement analyses and can be used to estimate the rate constant for the critical step in hemolysis, as well as the efficiency of the critical complement component in the rate limiting step. Parameters derived from the model can be quantitatively related to complement concentration and can be used as the basis for a quantitative assay of complement activity. The model can also be used to calculate, for a particular sample, the concentration at which complement activity becomes undectable, the complement activity of the pure, undiluted sample, and the time required for the sample to produce complete lysis of the available cells.