Biochemical limits to microbial growth yields: An analysis of mixed substrate utilization

A theoretical analysis has been made of carbon conversion efficiency during heterotrophic microbial growth. The expectation was that the maximal growth yield occurs when all the substrate is assimilated and the net flow of carbon through dissimilation is zero. This, however, is not identical to a 100% carbon conversion, since assimilatory pathways lead to a net production of CO(2). It can be shown that the amount of CO(2) produced by way of assimilatory processes is dependent upon the nature of the carbon source, but independent of its degree of reduction and varies between 12 and 29% of the substrate carbon. An analysis of published yield data reveals that nearly complete assimilation can occur during growth on substrates with a high energy content. This holds for substrates with a heat of combustion of ca. 550 kJ/mol C, or a degree of reduction higher than 5 (e.g. ethane, ethanol, and methanol). Complete assimilation can also be achieved on substrates with a lower energy content, provided that an auxiliary energy source is present that cannot be used as a carbon source. This is evident from the cell yields reported for Candida utilis grown on glucose plus formate and for Thiobacillus versutus grown on acetate plus thiosulfate. This evaluation of the carbon conversion efficiency during assimilation also made it possible to compare the energy content of the auxiliary energy substrate added with the quantity of the carbon source it had replaced. It will be shown that utilization of the auxiliary energy source may lead to extreme changes in the efficiency of dissimilatory processes.     

Modeling substrate inhibition of microbial growth

This article presents a general equation for substrate inhibition of microbial growth using a statistical thermodynamic approach. Existing empirical models adapted from enzyme kinetics, for example, the Haldane-Andrews equation, often criticized for not being physically based for microbial growth, are shown to derive from the general equation in this article, and their empirical parameters are shown to be well defined physically. Three sets of experimental data from the literature are used to test the modeling abilities of the general equation to represent experimental data. The results are compared with those obtained by fitting the same data set to a widely used empirical model existing in the literature. The general equation is found to represent all three experimental data sets better than the alternative model tested. In addition, a graphical method existing in enzyme kinetics is successfully adapted and further developed to determine the number of inhibition sites of a basic functional unit of a bacterial cell. (c) 1996 John Wiley & Sons, Inc.     

Linear growth in microbial cultures limited by accumulated substrate

Summary The linear growth phase in cultures limited by intracellular (conservative) substrate is represented by a flat exponential curve. Within the range of experimental errors, the presented model fits well the data from both batch and continuous cultures ofEscherichia coli, whose growth is limited in that way.List of symbols D dilution rate, h^–1 - K_S saturation constant, g.L^–1 - S concentration of the limiting substrate, g.L^–1 - S_i concentration of the limiting substrate accumulated in the cells, g.g^–1 - S_o initial concentration of the limiting substrate, g.L^–1 - t time of cultivation, h - t₁ time of exhaustion of the limiting substrate from medium, h - t_o beginning of exponential phase, h - X biomass concentration, g.L^–1 - X₁ biomass concentration at the time of exhaustion of the limiting substrate from the medium, g.L^–1 - X_o biomass concn. at the beginning of exponential phase, g.L^–1 - biomass concn. at steady-state, g.L^–1 - Y growth yield coefficient (biomass/substrate) - specific growth rate, h^–1 - _m maximum specific growth rate, h^–1     

Modelling of microbial growth for sequential utilization in a multisubstrate environment

Microbial growth in multisubstrate environments is posed as a problem of multivariable constraint optimization. The optimization aims at maximizing the instantaneous growth rate of cells. The model developed for microbial growth using this hypothesis involves simple representation of complex cell structure as an optimization function which regulates the interplay of cellular machinery. The model parameters are estimated using single substrate growth data. Model simulation fits very well with earlier published experimental data of bacterial growth of Klensiella oxytoca on a variety of sugar mixtures involving glucose, fructose, lactose, and xylose. Moreover, the model is also able to predict the diauxic growth of Saccharomyces cerevisiae on glucose and galactose. One of the interesting outcomes of the above representation is the ability to prove analytically that the growth on the mixture of two sugars will be diauxic if one of the substrates has a very low K_s value and a high μ_m value.     

Macrokinetic basis for the model of microbial growth in a limited volume under constant conditions with a single leading substrate

Within the framework of the macrokinetic approach and continuum and chemical/biochemical gross reaction conceptions, an equation describing the complete dynamics of microbial growth and decline as function of a variable concentration of the leading substrate was deduced. This equation allows us to distinguish quantitatively and qualitatively the stages of microbial growth and the intervals of microbial tolerance to the initial concentration of the leading substrate. Adequacy of the model was confirmed by comparison with experimental dynamics of aerobic microorganisms in the samples of groundwater collected from a region polluted with uranium.     

Bioflocculation as a microbial response to substrate limitations

Previous theories of nutrient supply to microbial floes assumed that transport within the flocs was by molecular diffusion, and they predict that overall nutrient uptake is reduced in floes compared to dispersed cells. Calculations, supported by recent advances in understanding fluid flow through suspended aggregates, however, have shown that substantial fluid flow may occur through highly permeable bacterial floes. Since bioflocculation of microorganisms in bioreactors is known to occur under conditions of low substrate availability, the rate of substrate uptake is assumed to be mass transfer limited. The hydrodynamic environment of a cell then determines cellular uptake rates. Through development of a relative uptake factor, the overall uptake by cells in flocs in sheared fluids and floes attached to bubbles are compared with the uptake by an identical quantity of dispersed cells. Bioflocculation is found to increase the rate of substrate transport to cells in permeable floes compared to dispersed cells, particularly for large-molecular-weight substrates and when bubbles are present.     

An epidemic model in a patchy environment

An epidemic model is proposed to describe the dynamics of disease spread among patches due to population dispersal. We establish a threshold above which the disease is uniformly persistent and below which disease-free equilibrium is locally attractive, and globally attractive when both susceptible and infective individuals in each patch have the same dispersal rate. Two examples are given to illustrate that the population dispersal plays an important role for the disease spread. The first one shows that the population dispersal can intensify the disease spread if the reproduction number for one patch is large, and can reduce the disease spread if the reproduction numbers for all patches are suitable and the population dispersal rate is strong. The second example indicates that a population dispersal results in the spread of the disease in all patches, even though the disease can not spread in each isolated patch.     

Beyond host-pathogen interactions: microbial defense strategy in the host environment

Many extracellular pathogenic bacteria colonize human or animal bodies through evasion of the host immune system, a process called host-pathogen interaction. What happens when other intruders try to invade the same host and try to establish themselves in the same niche is largely unknown. In one well-studied case, Pseudomonas aeruginosa is known to secrete the protein azurin as a weapon against such invaders as cancers, parasites and viruses. The production of such weapons by pathogenic bacteria could provide important insights into how a pathogen responds in the post-colonization state to impede other intruders for its own survival. Moreover, these molecules might find use in the pharmaceutical industry as next-generation therapeutics.     

Long-term dynamics of catabolic plasmids introduced to a microbial community in a polluted environment: a mathematical model

The long-term dynamics of mobile plasmids in natural environments are unclear. This is the first study of the long-term dynamics of introduced plasmids with xenobiotic degradation abilities using a mathematical model that describes the horizontal gene transfer (HGT) of plasmids into indigenous bacteria via conjugation. We focussed on negative feedback between the spread of plasmids and their selective advantage, i.e. the severe competition between plasmid-bearing and plasmid-free bacteria resulting from a decrease in xenobiotic concentration caused by the gene expression of plasmids, favoring plasmid-free bacteria. Two types of HGT enhanced the persistence of plasmids and the degradation of the xenobiotic in different conditions: a relatively low rate of 'intergeneric HGT' from introduced to indigenous bacteria and a high rate of 'intraindigenous HGT' from indigenous to indigenous bacteria. In addition, when the indigenous resource supply rate was high and when the cost of bearing plasmids was low, both types of HGT made large contributions to xenobiotic degradation compared to the contribution of vertical transfer via plasmid replication within the introduced host population. Initial conditions were also important; a higher initial density of introduced plasmid-bearing bacteria led to a lower degradation rate over a long time scale.     

Modeling of microbial substrate conversion,growth and product formation in a recycling fermentor

Paracoccus denitrificans and Bacillus licheniformis were grown in a carbon- and energy source-limited recycling fermentor with 100% biomass feedback. Experimental data for biomass accumulation and product formation as well as rates of carbon dioxide evolution and oxygen consumption were used in a parameter optimization procedure. This procedure was applied on a model which describes biomass growth as a linear function of the substrate consumption rate and the rate of product formation as a linear function of the biomass growth rate. The fitting procedure yielded two growth domains for P. denitrificans. In the first domain the values for the maximal growth yield and the maintenance coefficient were identical to those found in a series of chemostat experiments. The second domain could be described best with linear biomass increase, which is equal to a constant growth yield. Experimental data of a protease producing B. licheniformis also yielded two growth domains via the fitting procedure. Again, in the first domain, maximal growth yield and maintenance requirements were not significantly different from those derived from a series of chemostat experiments. Domain 2 behaviour was different from that observed with P. denitrificans. Product formation halts and more glucose becomes available for biomass formation, and consequently the specific growth rate increases in the shift from domain 1 to 2. It is concluded that for many industrial production processes, it is important to select organisms on the basis of a low maintenance coefficient and a high basic production of the desired product. It seems less important that the maximal production becomes optimized, which is the basis of most selection procedures.     

Kinetic model for microbial uptake of insoluble solid-state substrate

A kinetic model for anaerobic digestion of insoluble solid-state substrates was developed. Rate equations for cell growth and substrate consumption were derived based on the assumption that the microorganisms assimilate the substrate mainly at the point of contact where they grow. The model emphasizes effects of substrate particle size, organic loading, and cell concentration on the rates of cell growth and substrate utilization. Batch digestion of a stearic acid emulsion with a mean particle size of 2.0 mum and a biological sludge was conducted at 30 and 37 degrees C to verify the proposed model. Agreement between the experimental and calculated results indicated the validity of the model for describing the microbial degradation of insoluble solid-state substrates. Further examinationof the model revealed that with low cell substrate affinity or at low cell concentration, it coincided with a Michaelis-Menten type kinetics in which the effect of particle size was taken into consideration.     

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.     

Cybernetic modeling of microbial growth on multiple substrates

The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as a manifestation of an invariant strategy to optimize some goal of the cells. A goal-seeking or cybernetic model is proposed here, with the optimization obased on a short-term perspective of response to the environment. The model parameters are determined from the growth data on single substrates. The model predicts the entire range of microbial growth behavior on multiple substrates from simultaneous utilization of all sugars to sequential utilization with pronounced diauxic lags. It is shown to predict the many variations of the diauxic phenomenon in different growth conditions. The transients in continuous culture growth on mixed substrates caused by varying the feed strategies are easily simulated by this model. The framework of this model can be applied to batch or continuous culture growth of many bacteria on different combinations of substrates.     

Determination of the Monod substrate saturation constant for microbial growth

Abstract Methods used to determine the Monod substrate saturation constant for microbial growth are surveyed. The preferred and most accurate method is to assay the concentrations of growth rate-limiting nutrients in steady-state continuous cultures. But, this is not always possible due to the lack of sufficiently sensitive assay methods or due to high nutrient fluxes in rapidly growing cultures. It is suggested that an acceptable and simple alternative method for aerobic microorganisms is to measure initial oxygen uptake rates during growth in the presence of different initial concentrations of growth rate-limiting nutrient. It is important in this method that the microbial cells are taken from rapidly growing cultures and are suspended in a medium permitting growth.     

Improvement of growth ofRhizopus oligosporus on a model solid substrate

Summary Metal ions and cassava extracts stimulated growth ofRhizopus oligosporus on a model solid substrate. A large improvement in protein content was obtained by simultaneously increasing the nitrogen content and decreasing the particle size of the substrate. No improvement occurred when these conditions were applied to cassava, however, because of the sticky consistency of the cassava after gelatinization.     

An optimal pooling strategy applied to high-throughput screening for rare marker-free transformants

An optimal pooling system, called Accurate and Fast Target Screening, has been developed for high-throughput identifying the rare marker-free transformants. This system can identify targets between 10- and 100-fold more efficiently than analysis of individual samples. By calculating the efficiency for different proportions of targets and the optimal group size in a worst case scenario, we are able to estimate an upper limit for the number of tests that are required. The application of this system to determine the transgene in an artificially constructed population of transgenic and non-transgenic wheat lines successfully identified the 10 positive samples located randomly with 990 negative samples using only 92 PCR reactions. The same approach was also applied to determine transgene expression by SDS-PAGE of seed proteins. This system gives unambiguous positive or negative results and should facilitate marker-free transformation.These authors contributed equally to this work.