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 μg liter−1. The data suggest that a dilemma exists, namely, that either “intrinsic” KS (under substrate-controlled conditions in chemostat culture) or μmax (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.

Growth Kinetics of Suspended Microbial Cells: From Single-Substrate-Controlled Growth to Mixed-Substrate Kinetics

Chaos is usually regarded as a distinct alternative to random effects such as environmental fluctuations or external disturbances. We argue that strict separation between chaotic and stochastic dynamics in ecological systems is unnecessary and misleading, and we present a more comprehensive approach for systems subject to stochastic perturbations. The defining property of chaos is sensitive dependence on initial conditions. Chaotic systems are "noise amplifiers" that magnify perturbations; nonchaotic systems are "noise mufflers" that dampen perturbations. We also present statistical methods for detecting chaos in time-series data, based on using nonlinear time-series modeling to estimate the Lyapunov exponent λ, which gives the average rate at which perturbation effects grow (λ > 0) or decay (λ < 0). These methods allow for dynamic noise and can detect low-dimensional chaos with realistic amounts of data. Results for natural and laboratory populations span the entire range from noise-dominated and strongl...

Chaos in a noisy world: new methods and evidence from time-series analysis

Summary 1. Dynamic energy budget (DEB) models describe how individuals acquire and utilize energy, and can serve as a link between diAerent levels of biological organization. 2. We describe the formulation and testing of DEB models, and show how the dynamics of individual organisms link to molecular processes, to population dynamics, and (more tenuously) to ecosystem dynamics. 3. DEB models oAer mechanistic explanations of body-size scaling relationships. 4. DEB models constitute powerful tools for applications in toxicology and bio

http://eaton.math.rpi.edu/CSUMS/Papers/EcoEnergy/nisbetdynamicenergy.pdf

From molecules to ecosystems through dynamic energy budget models.

Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of interacting populations. We studied the dynamical behavior of a two-species aquatic laboratory community encompassing the interactions between a demographically structured herbivore population, a primary producer, and a mineral resource, yet still amenable to description and parameterization using a mathematical model. The qualitative dynamical behavior of our experimental system, that is, cycles, equilibria, and extinction, is highly predictable by a simple nonlinear model.

https://science.sciencemag.org/content/sci/290/5495/1358.full.pdf

Crossing the Hopf Bifurcation in a Live Predator-Prey System

The previous chapters have shown that the rumen harbours a large number of different species of bacteria, phycomycete fungi and protozoa. Metabolic interactions between these different populations are essential for sustaining the microbial community and its collective activities. Products of the metabolism of some species of microorganisms are sources of energy for other species. Similarly, products of vitamin synthesis and nitrogen metabolism of some species become the sources of the vitamins and nitrogen compounds required by other microorganisms. The kinds and extents of these microbial interactions regulate the concentrations and activities of individual species and the qualitative and quantitative nature of the products of the fermentation of dietary substrates. Products that are used by, and are essential for, the ruminant include acetate, propionate and butyrate and the constituents of microbial cells. The amounts of CH4 and CO2 produced by the fermentation are determined by the same microbial interactions. The purpose of this chapter is to describe the major metabolic interactions that define the nature of the microbial community and its contributions to the host. Some of these interactions have, of necessity, been mentioned in connection with the topics of other chapters in the book.

Microbe-microbe interactions

A study was made of the food web formed from a protozoon, two bacteria, and a glucose minimal medium in chemostat culture. The system was also divided into simpler parts, first by omitting the protozoon to obtain a competition system, and then by omitting one or the other of the bacteria to obtain two food chains. In the competition studies, one bacterium was displaced by the other at all holding times used. In the food chain studies, sustained oscillations of the population densities of predator and prey developed at short holding times, and then changed to damped oscillations at longer holding times. In addition, the level of residual glucose remained high at long holding times. A new model of microbial growth is necessary to explain these results. In the food web studies, predation of the protozoon on the two bacteria stabilized the competition between the latter and allowed their coexistence in the same habitat. Thus, Gause9s principle was circumvented.

Interactions of Tetrahymena pyriformis, Escherichia coli, Azotobacter vinelandii, and Glucose in a Minimal Medium

Saccharomyces cerevisiae and a riboflavin assay strain of Lactobacillus casei have been propagated anaerobically in mixed culture. Both batch and continuous culture techniques were used. By varying...

Studies in intermicrobial symbiosis. Saccharomyces cerevisiae and Lactobacillus casei.

Dictyostelium discoideum and Escherichia coli were aerobically propagated in mixed continuous culture in a predator-prey relationship, and the effects of temperature and holding times were examined. Oscillations developed in the concentration of glucose, the limiting substrate for E. coli, and in the densities of the two populations, but eventually steady-state populations were reached. The experimental data were analyzed according to the Lotka-Volterra model for prey-predator relationships and by the Monod model for saturation kinetics. A comparison of the adequacy of the two models in describing predation is given.

J. F. Drake

Papers

Interactions of Tetrahymena pyriformis, Escherichia coli, Azotobacter vinelandii, and Glucose in a Minimal Medium

Studies in intermicrobial symbiosis. Saccharomyces cerevisiae and Lactobacillus casei.

Predator-Prey Interactions of Dictyostelium discoideum and Escherichia coli in Continuous Culture

Microbial food chains and food webs

The Food Chain