Multistep kinetics: choice of models for the growth of bacteria

Saturating relationship between phytoplankton growth rate and nutrient concentration explained by macromolecular allocation

Phytoplankton account for about a half of photosynthesis in the world, making them a key player in the ecological and biogeochemical systems. One of the key traits of phytoplankton is their growth rate because it indicates their productivity and affects their competitive capability. The saturating relationship between phytoplankton growth rate and environmental nutrient concentration has been widely observed yet the mechanisms behind the relationship remain elusive. Here we use a mechanistic model and metadata of phytoplankton to show that the saturating relationship between growth rate and nitrate concentration can be interpreted by intracellular macromolecular allocation. At low nitrate levels, the diffusive nitrate transport linearly increases with the nitrate concentration, while the internal nitrogen requirement increases with the growth rate, leading to a non-linear increase in the growth rate with nitrate. This increased nitrogen requirement is due to the increased allocation to biosynthetic and photosynthetic molecules. The allocation to these molecules reaches a maximum at high nitrate concentration and the growth rate ceases to increase despite high nitrate availability due to carbon limitation. The produced growth rate and nitrate relationships are consistent with the data of phytoplankton across taxa. Our study provides a macromolecular interpretation of the widely observed growth-nutrient relationship and highlights that the key control of the phytoplankton growth exists within the cell.

Accurate and reliable estimation of kinetic parameters for environmental engineering applications: A global, multi objective, Bayesian optimization approach

Accurate and reliable predictions of bacterial growth and metabolism from unstructured kinetic models are critical to the proper operation and design of engineered biological treatment and remediation systems. As such, parameter estimation has progressed into a routine challenge in the field of Environmental Engineering. Among the main issues identified with parameter estimation, the model-data calibration approach is a crucial, yet an often overlooked and difficult optimization problem. Here, a novel and rigorous global, multi objective, and fully Bayesian optimization approach that overcomes challenges associated with multi-variate, sparse and noisy data, as well as highly non-linear model structures commonly encountered in Environmental Engineering practice is presented. This optimization approach allows an improved definition and targeting of the compromise solution space for all multivariate problems, allowing efficient convergence, and a Bayesian component to thoroughly explore parameter and model prediction uncertainty. This global optimization approach outperformed, in terms of parameter accuracy and precision, standard, local non-linear regression routines and overcomes issues associated with premature convergence and addresses overfitting of different variables in the calibration process. •A sequential single, multi-objective, and Bayesian optimization workflow was developed to accurately and reliably estimate unstructured kinetic model parameters.•The global, single objective approach defines the global optimum (the best compromise solution) and "extreme" parameter solutions for each variable, while the global, multi-objective approach confirms the "best" compromise solution space for the Bayesian search to target and convergence is assessed using the single objective results.•The Approximate Bayesian Computational approach fully explores parameter and model prediction uncertainty targeting the compromise solution space previously identified.

Application of unstructured kinetic models to predict microcystin biodegradation: Towards a practical approach for drinking water treatment

Biological drinking water treatment technologies offer a cost-effective and sustainable approach to mitigate microcystin (MC) toxins from harmful algal blooms. To effectively engineer these systems, an improved predictive understanding of the bacteria degrading these toxins is required. This study reports an initial comparison of several unstructured kinetic models to describe MC microbial metabolism by isolated degrading populations. Experimental data was acquired from the literature describing both MC removal and cell growth kinetics when MC was utilized as the primary carbon and energy source. A novel model-data calibration approach melding global single-objective, multi-objective, and Bayesian optimization in addition to a fully Bayesian approach to model selection and hypothesis testing were applied to identify and compare parameter and predictive uncertainties associated with each model structure. The results indicated that models incorporating mechanisms of enzyme-MC saturation, affinity, and cooperative binding interactions of a theoretical single, rate limiting reaction accurately and reliably predicted MC degradation and bacterial growth kinetics. Diverse growth characteristics were observed among MC degraders, including moderate to high maximum specific growth rates, very low to substantial affinities for MC, high yield of new biomass, and varying degrees of cooperative enzyme-MC binding. Model predictions suggest that low specific growth rates and MC removal rates of degraders are expected in practice, as MC concentrations in the environment are well below saturating levels for optimal growth. Overall, this study represents an initial step towards the development of a practical and comprehensive kinetic model to describe MC biodegradation in the environment.

Modeling the Overproduction of Ribosomes when Antibacterial Drugs Act on Cells

Bacteria that are subjected to ribosome-inhibiting antibiotic drugs show an interesting behavior: Although the drug slows down cell growth, it also paradoxically increases the cell’s concentration of ribosomes. We combine our earlier nonlinear model of the energy-biomass balance in undrugged Escherichia coli cells with Michaelis-Menten binding of drugs that inactivate ribosomes. Predictions are in good agreement with experiments on ribosomal concentrations and synthesis rates versus drug concentrations and growth rates. The model indicates that the added drug drives the cell to overproduce ribosomes, keeping roughly constant the level of ribosomes producing ribosomal proteins, an important quantity for cell growth. The model also predicts that ribosomal production rates should increase and then decrease with added drug. This model gives insights into the driving forces in cells and suggests new experiments.

Which games are growing bacterial populations playing?

Microbial communities display complex population dynamics, both in frequency and absolute density. Evolutionary game theory provides a natural approach to analyse and model this complexity by studying the detailed interactions among players, including competition and conflict, cooperation and coexistence. Classic evolutionary game theory models typically assume constant population size, which often does not hold for microbial populations. Here, we explicitly take into account population growth with frequency-dependent growth parameters, as observed in our experimental system. We study the in vitro population dynamics of the two commensal bacteria (Curvibacter sp. (AEP1.3) and Duganella sp. (C1.2)) that synergistically protect the metazoan host Hydra vulgaris (AEP) from fungal infection. The frequency-dependent, nonlinear growth rates observed in our experiments indicate that the interactions among bacteria in co-culture are beyond the simple case of direct competition or, equivalently, pairwise games. This is in agreement with the synergistic effect of anti-fungal activity observed in vivo. Our analysis provides new insight into the minimal degree of complexity needed to appropriately understand and predict coexistence or extinction events in this kind of microbial community dynamics. Our approach extends the understanding of microbial communities and points to novel experiments.

The last generation of bacterial growth in limiting nutrient

Background

Bacterial growth as a function of nutrients has been studied for decades, but is still not fully understood. In particular, the growth laws under dynamically changing environments have been difficult to explore, because of the rapidly changing conditions. Here, we address this challenge by means of a robotic assay and measure bacterial growth rate, promoter activity and substrate level at high temporal resolution across the entire growth curve in batch culture. As a model system, we study E. coli growing under nitrogen or carbon limitation, and explore the dynamics in the last generation of growth where nutrient levels can drop rapidly.

Results

We find that growth stops abruptly under limiting nitrogen or carbon, but slows gradually when nutrients are not limiting. By measuring growth rate at a 3 min time resolution, and inferring the instantaneous substrate level, s, we find that the reduction in growth rate μ under nutrient limitation follows Monod’s law, μ=μ0sks+s. By following promoter activity of different genes we found that the abrupt stop of growth under nitrogen or carbon limitation is accompanied by a pulse-like up-regulation of the expression of genes in the relevant nutrient assimilation pathways. We further find that sharp stop of growth is conditional on the presence of regulatory proteins in the assimilation pathway.

Conclusions

The observed sharp stop of growth accompanied by a pulsed expression of assimilation genes allows bacteria to compensate for the drop in nutrients, suggesting a strategy used by the cells to prolong exponential growth under limiting substrate.

In Silico Modeling in Infectious Disease

Infectious disease has witnessed the emergence of mathematical modeling a tool of synthesizing data of growing complexity now available to clinicians and basic scientists alike. The purpose of this review is to introduce mathematical tools commonly used to model infectious disease. We will illustrate the use of equation-based, agent-based or statistical modeling approaches to a variety of examples pertaining to acute inflammation, bacterial dynamics, viral dynamics, and signaling pathways, focusing of host-pathogen interactions rather than population models. We will discuss the strengths and weaknesses of these approaches and offer future perspectives for this rapidly evolving field.

Trevor Trust – AstraZeneca R&D Boston, 35 Gatehouse Drive, Waltham, MA 02451, USA

Bacterial choices for the consumption of multiple resources for current and future needs

Microorganisms differ in their effectiveness in uptake and selection of substances that they bring in from the environment. They also differ in how they balance the allocation of nutrients for immediate and for delayed use. Moreover, they may not take up resources as fast as they seemingly could, and they may extrude derivatives of substances just pumped in. A good deal of these apparent choices must reside in the uptake systems and the linkage of these with the cell's intermediate metabolism. An important feature is that a resource may vary in concentration from time to time, nutrient to nutrient, and habitat to habitat. This variation must have been critical to the evolution of regulatory processes. Some possibilities for the combined uptake and consumption are considered for substrates serving the same (homologous) and different (heterologous) roles for the bacterium. From the membrane transport processes diagrammed in Fig. 1c and Fig. 2 and corresponding computer program given in Appendix A, the combined effect of uptake processes and cell growth can be studied. The model can be modified for various alternate models to study the possible control of cellular uptake and metabolism for the range of ecological roles of the bacterium.

Dual nutrient limited growth: models, experimental observations, and applications

Dual nutrient limited growth, the control of the cell growth rate (kinetic aspect) or the restriction of the amount of biomass (stoichiometric aspect) by two nutrients at the same time, is a relatively unknown ability of the microorganisms and consequently, still not mentioned in textbooks to date. Nevertheless, multiple nutrient limited or controlled growth has been reported for different systems; e.g. ecosystems, batch, fed-batch, and chemostat cultures. Generally, dual nutrient limited growth has been observed when the microorganism of interest: (a) showed a variation of the cellular composition, (b) was able to accumulate a storage compound, (c) changed the cell metabolism, or (d) excreted metabolic intermediates. Consequently, stoichiometric models have been developed to estimate the growth conditions leading to dual nutrient limited growth. A general problem of the kinetic aspect is the accurate measurement of the growth controlling nutrients in the culture broth (microg l(-1) range), as the cells may consume residual nutrients during sampling. Nevertheless, most models of dual limited growth deal with the kinetic aspect although the control experiments are difficult to carry out. The aim of this survey is to introduce this special growth feature with respect to basic models, experimental data, and potential applications in bioprocesses.

Mutation rates: estimating phase variation rates when fitness differences are present and their impact on population structure

Phase variation is a mechanism of ON-OFF switching that is widely utilized by bacterial pathogens. There is currently no standardization to how the rate of phase variation is determined experimentally, and traditional methods of mutation rate estimation may not be appropriate to this process. Here, the history of mutation rate estimation is reviewed, describing the existing methods available. A new mathematical model that can be applied to this problem is also presented. This model specifically includes the confounding factors of back-mutation and the influence of fitness differences between the alternate phenotypes. These are central features of phase variation but are rarely addressed, with the result that some previously estimated phase variation rates may have been significantly overestimated. It is shown that, conversely, the model can also be used to investigate fitness differences if mutation rates are approximately known. In addition, stochastic simulations of the model are used to explore the impact of 'jackpot cultures' on the mutation rate estimation. Using the model, the impact of realistic rates and selection on population structure is investigated. In the absence of fitness differences it is predicted that there will be phenotypic stability over many generations. The rate of phenotypic change within a population is likely, therefore, to be principally determined by selection. A greater insight into the population dynamics of mutation rate processes can be gained if populations are monitored over successive time points.

Oligotrophs versus copiotrophs

Bacteria can grow rapidly, yet there are some that grow slowly under apparent optimal conditions. These organisms are usually present in environments with low levels of nutrients, and are not found in conditions of more plentiful nutrients. They are known as "oligotrophs"in contrast to "copiotrophs", which are common in environments with greater nutritional opportunities. This essay asks why do the oligotrophs not occupy richer environments, and why are copiotrophs not more prevalent in chronic starvation environments?

Growth kinetics of suspended microbial cells: from single-substrate-controlled growth to mixed-substrate kinetics

Growth kinetics, i.e., the relationship between specific growth rate and the concentration of a substrate, is one of the basic tools in microbiology. However, despite more than half a century of research, many fundamental questions about the validity and application of growth kinetics as observed in the laboratory to environmental growth conditions are still unanswered. For pure cultures growing with single substrates, enormous inconsistencies exist in the growth kinetic data reported. The low quality of experimental data has so far hampered the comparison and validation of the different growth models proposed, and only recently have data collected from nutrient-controlled chemostat cultures allowed us to compare different kinetic models on a statistical basis. The problems are mainly due to (i) the analytical difficulty in measuring substrates at growth-controlling concentrations and (ii) the fact that during a kinetic experiment, particularly in batch systems, microorganisms alter their kinetic properties because of adaptation to the changing environment. For example, for Escherichia coli growing with glucose, a physiological long-term adaptation results in a change in KS for glucose from some 5 mg liter-1 to ca. 30 microg liter-1. The data suggest that a dilemma exists, namely, that either "intrinsic" KS (under substrate-controlled conditions in chemostat culture) or micromax (under substrate-excess conditions in batch culture) can be measured but both cannot be determined at the same time. The above-described conventional growth kinetics derived from single-substrate-controlled laboratory experiments have invariably been used for describing both growth and substrate utilization in ecosystems. However, in nature, microbial cells are exposed to a wide spectrum of potential substrates, many of which they utilize simultaneously (in particular carbon sources). The kinetic data available to date for growth of pure cultures in carbon-controlled continuous culture with defined mixtures of two or more carbon sources (including pollutants) clearly demonstrate that simultaneous utilization results in lowered residual steady-state concentrations of all substrates. This should result in a competitive advantage of a cell capable of mixed-substrate growth because it can grow much faster at low substrate concentrations than one would expect from single-substrate kinetics. Additionally, the relevance of the kinetic principles obtained from defined culture systems with single, mixed, or multicomponent substrates to the kinetics of pollutant degradation as it occurs in the presence of alternative carbon sources in complex environmental systems is discussed. The presented overview indicates that many of the environmentally relevant apects in growth kinetics are still waiting to be discovered, established, and exploited.

Kinetic models for the growth of Escherichia coli with mixtures of sugars under carbon-limited conditions

In natural environments, heterotrophic microorganisms encounter complex mixtures of carbon sources, each of which is present only at very low concentrations. Under such conditions no significant growth could be expected if cells utilized only one of the available carbon compounds as suggested by the principle of diauxic growth. Indeed, there is much evidence that microbial cells utilize many carbon sources simultaneously. In order to predict bacterial growth under such conditions we developed a model describing the specific growth rate as a function of the individual concentrations of several simultaneously utilized carbon substrates. Together with multisubstrate models previously published, this model was evaluated for its ability to describe growth of Escherichia coli during the simultaneous utilization of mixtures of sugars in carbon-limited continuous culture. Using the micromax and Ks constants determined for single substrate growth with six different sugars, the model was able for most experiments to adequately describe the specific growth rate of the culture, i.e., the experimentally set dilution rate, from the measured concentrations of the individual sugars. The model provides an explanation why bacteria can still grow relatively fast under environmental conditions where the concentrations of carbon substrates are usually extremely low.

Biodegradation kinetics of toluene, m-xylene, p-xylene and their intermediates through the upper TOL pathway in Pseudomonas putida (pWWO)

Pseudomonas putida mt-2, harbouring TOL plasmid pWWO, is capable of degrading toluene and a range of di- and tri-alkylbenzenes. In this study, chemostat-grown cells (D = 0.05 h-1, toluene or m-xylene limitation) of this strain were used to assess the kinetics of the degradation of toluene, m-xylene, p-xylene, and a number of their pathway intermediates. The conversion kinetics for the three hydrocarbons showed significant differences: the maximal conversion rates were rather similar [11-14 mmol h-1 (g dry wt)-1] but the specific affinity (the slope of the v vs s curve near the origin) of the cells for toluene [1300 I (g dry wt)-1 h-1] was only 5% and 14% of those found for m-xylene and p-xylene, respectively. Consumption kinetics of mixtures of the hydrocarbons confirmed that xylenes are strongly preferred over toluene at low substrate concentrations. The maximum flux rates of pathway intermediates through the various steps of the TOL pathway as far as ring cleavage were also determined. Supply of 0-5 mM 3-methylbenzyl alcohol or 3-methylbenzaidehyde to fully induced cells led to the transient accumulation of 3-methylbenzoate. Accumulation of the corresponding carboxylic acid (benzoate) was also observed after pulses of benzyl alcohol and benzaldehyde, which are intermediates in toluene catabolism. Analysis of consumption and accumulation rates for the various intermediates showed that the maximal rates at which the initial monooxygenation step and the conversion of the carboxylic acids by toluate 1,2-dioxygenase may occur are two- to threefold lower than those measured for the two intermediate dehydrogenation steps.

Microbial physiology and ecology of slow growth

The uptake capabilities of the cell have evolved to permit growth at very low external nutrient concentrations. How are these capabilities controlled when the substrate concentrations are not extremely low and the uptake systems could import substrate much more rapidly than the metabolic capabilities of the cell might be able to handle? To answer this question, earlier theories for the kinetics of uptake through the cell envelope and steady-state systems of metabolic enzymes are discussed and a computer simulation is presented. The problems to the cell of fluctuating levels of nutrient and too much substrate during continuous culture are discussed. Too much substrate can lead to oligotrophy, substrate-accelerated death, entry into the viable but not culturable state, and lactose killing. The relationship between uptake and growth is considered. Finally, too little substrate may lead to catastrophic attempts at mounting molecular syntheses that cannot be completed.

What size should a bacterium be? A question of scale

There are living prokaryotes (Bacteria and Archaea) that have cell sizes that range from 0.02-400 microns3. Over this tremendous range, various abilities to cope with the environment are needed. This review attempts to formulate some of the problems and some of the solutions. The smallest size for a free-living organism is suggested to be largely set by the catalytic efficiency of enzymes and protein synthetic machinery. Because of fluctuations in the environment, cells must maintain machinery to cope with various catastrophes; these mechanisms increase the minimum size of the cell. On the other hand, the largest cell is reasonably assumed to be limited by the ability of diffusion to bring nutrients to the appropriate part of the cell and to dispose of waste products. To explore the limitation imposed by diffusion, analysis is developed of diffusion processes through stirred and unstirred media, diffusion through media that contains obstacles, and the effect of size and shape.

The growth of Escherichia coli in glucose-limited chemostat cultures: a re-examination of the kinetics

The relationship between specific growth rate (mu) and steady-state glucose concentration was investigated for Escherichia coli ML30 in carbon-limited chemostat culture. This was made possible by the development of a method for measuring reducing sugars in culture media in the microgram.1-1-range. Cells initially cultivated in batch culture at high glucose concentrations required long-term adaptation to nutrient-limited growth conditions in the chemostat (between 100-200 volume changes at D = 0.6 h-1) until steady-state with respect to residual glucose concentration was reached; for adapted cells, however, new steady-state glucose concentrations were usually obtained within less than 10 volume changes. A statistical evaluation of different kinetic models showed that between 0.2 h-1 < D < 0.8 h-1 the three models proposed by Monod (1942), Shehata and Marr (1971), and Westerhoff et al. (1982) described the data equally well and the applicability of the different models is discussed. Depending on the model used, calculated glucose concentrations supporting half maximum growth rate (Ks) were in the range of 40-88 micrograms.1-1. The data strongly suggest that the large differences in Ks constants reported in the literature (ranging from 40 micrograms.1-1 up to 99 mg.1-1) are due to the use of E. coli cells adapted to different degrees to nutrient-limited growth conditions. This indicates that it is probably not possible to describe the kinetic properties of a bacterium with a single set of kinetic 'constants'.

The attractiveness of the Droop equations. II. Generic uptake and growth functions

In a recent paper the authors proved global asymptotic stability of the Droop equations. This system of nonlinear ordinary differential equations describes the growth of a microorganism in a chemostat. In this setting the growth rate of the organism is limited by the availability of a single nutrient. The state variables of the Droop system are biomass density, intracellular nutrient concentration. (I"cell quota" in Droop's terminology), and extracellular nutrient concentration. In the current paper the authors relax Droop's particular choices for the uptake and growth functions. Characterizing these functions in qualitative terms only, they again reach the same conclusion of global asymptotic stability. Their analysis relies on reducing the three-dimensional Droop system to a two-dimensional system via the first integral of Burmaster.

Growth kinetics and competition--some contemporary comments

Results of competition experiments with one growth-limiting factor under idealized experimental conditions have been reported extensively, and usually provide ample support for the conclusion that 'complete competitors cannot coexist'. However, under conditions of multiple substrate limitation and discontinuous or alternating supply of nutrients, coexistence of species is quite common. Since such patterns of nutrient supply may be expected to prevail in many natural environments the mechanisms ruling the survival and growth of bacteria under such conditions need to be understood. However, it appears that surprisingly little is known of the physiological state of individual competing species grown in mixed cultures. Unfortunately, basic information such as the actual concentration of limiting nutrients is lacking in most cases. But perhaps the recent development of new and powerful techniques to explore the physiological properties even of individual cells will further stimulate studies into the mechanisms behind the competitiveness of microbial species.

On the difficulties of fitting the double Michaelis-Menten equation to kinetic data

The double Michaelis-Menten equation describes the reaction kinetics of two independent, saturable uptake mechanisms. The use of this equation to describe drug uptake has been reported several times in the literature, and several methods have been published to fit the equation to data. So far, however, confidence intervals on the fitted kinetic parameters have not been provided. We present a grid-search method for fitting the double Michaelis-Menten equation to kinetic uptake data, and a Monte-Carlo procedure for estimating confidence intervals on the fitted parameters. We show that the fitting problem is extremely ill-conditioned, and that very accurate data are required before any confidence can be placed in the fitted parameters.

The basis of synchronization by repetitive dilution of a growing culture

Cultures of Escherichia coli have been synchronized by periodic dilution with fresh growth medium in the laboratory of Francois Kepes. When diluted by a large factor into complete test medium, the treated cultures undergo up to 12 synchronous divisions. This long term synchrony must result from an adjustment process during the periodic dilution procedure so that all cells have nearly identical biochemical properties. Robert Pritchard (University of Leicester, personal communication) suggested that this phasing would happen if the uptake of a critical nutrient was limited by the surface area of the cell during a portion of the dilution cycle. If his suggestion is valid, a general method for synchronization of almost any organism that grows exponentially and divides by binary fission into equal sized daughters should be achievable. A computer program was devised to simulate the growth of an initially asynchronous culture under periodic dilution with medium containing a single limiting nutrient. Various models of cell shape and growth were tested along with various models for the growth-limiting substrate uptake.

Energetic consequences of multiple K+ uptake systems in Escherichia coli

The energetics of growth of Escherichia coli FRAG 1 under potassium-limited growth conditions and with glucose as sole carbon and energy source were studied in the chemostat and compared with those of a mutant, FRAG 5, defective in the high-affinity potassium uptake system. The steady-state concentration of biomass decreased with increasing growth rate and was the same in both parent and mutant. For each growth rate, the rate of production of ATP was higher in the parent than the mutant strain. Under potassium-limited conditions, FRAG 1 has at least two potassium uptake systems, an inducible high-affinity uptake system and a constitutive low-affinity uptake system (Rhoads, D.B., Waters, F.B. and Epstein, W. (1976) J. Gen. Physiol. 67, 325-341). Apparently, the presence of the high-affinity uptake system in the parent leads to an energy drain. We suggest that this energy drain is due to futile cycling of potassium ions. On the basis of a mosaic non-equilibrium thermodynamic description of bacterial growth, it is concluded that the growth behaviour under potassium limitation corresponds to that expected for a catabolite limitation.

Some reflections on microbial competitiveness among heterotrophic bacteria

The results of a large number of studies on microorganisms subjected to various degrees of substrate limitation have led to the idea that many species are particularly well adapted to growth at a very low rate at extremely low nutrient concentrations. The possible similarity between this type of bacteria and oligotrophic species is discussed. Some attention is paid to the problem of predicting the competitiveness of microbial species. To this end the apparent specific affinity of an organism for a given substrate is discussed in some detail. It is attempted to bring terminology used in describing this parameter in line with that commonly used in microbial physiology and ecology. Using one particular field study as an example the possible usefulness and limitations of this concept in field studies are discussed.

Models for mineralization kinetics with the variables of substrate concentration and population density

The rates of mineralization of [14C]benzoate by an induced population of Pseudomonas sp. were measured at initial substrate concentrations ranging from 10 ng/ml to 100 micrograms/ml. Plots of the radioactivity remaining in the culture were fit by nonlinear regression to six kinetic models derived from the Monod equation. These models incorporate only the variables of substrate concentration and cell density. Plots of the mineralization kinetics in cultures containing low, intermediate, and high initial substrate concentrations were well fit by first-order, integrated Monod, and logarithmic kinetics, respectively. Parameters such as maximum specific growth rate, half-saturation constant, and initial population density divided by yield agreed between cultures to within a factor of 3.4. Benzoate mineralization by microorganisms in acclimated sewage was shown to fit logistic (sigmoidal), Monod, and logarithmic kinetics when the compound was added at initial concentrations of 0.1, 1.0, and 10 micrograms/ml, respectively. The mineralization of 10 micrograms of benzoate per ml in sewage also followed logarithmic kinetics in the absence of protozoa. It is concluded that much of the diversity in shapes of mineralization curves is a result of the interactions of substrate concentration and population density. Nonlinear regression with models incorporating these variables is a valuable means for analysis of microbial mineralization kinetics.

How close to the theoretical diffusion limit do bacterial uptake systems function?

Using a 10 cm flow-through cuvette in a high precision spectrophotometer linked to a mini-computer, the growth rate dependence of Escherichia coli on glucose concentration has been studied. The specific growth rate vs bacterial mass of single cultures consuming small amounts of glucose was followed. The data were analyzed with the computer programs described previously. For neither batch nor chemostat-cultured organisms did growth follow the Monod growth law. Rather, the growth rate vs residual glucose concentration has an almost abrupt change in slope, indicative of a passive diffusion barrier prior to an uptake system possessing hyperbolic dependency. Calculations showed that the diffusion through the outer membrane via the porin channels could quantitatively account for the deviations from hyperbolic dependency. Long term chemostat culture alters the bacteria so that the maximum specific growth rate is reduced, but the initial dependence on glucose concentration is increased approaching more closely the theoretical limit. Therefore there was both a change inthe outer membrane channels and the uptake activity of the cytoplasmic membrane.