Protozoan feeding and bacterial wall growth

A community model of ciliate Tetrahymena and bacteria E coli: Part II. interactions in a batch system

Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of a Tetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions of Tetrahymena pyriformis and E. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation of E. coli sized particles and E. coli toxic metabolites has a stabilizing effect on the system.

Microbial predation in coupled chemostats: a global study of two coupled nonlinear oscillators

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol'd structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.

Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When the chemostat is operated periodically, the interaction of the natural oscillation frequency with the external forcing gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions (local and especially global) between them as the amplitude and frequency of the forcing vary. The transition from low-forcing-amplitude quasiperiodicity to entrainment of the chemostat behavior by strong forcing (involving the concerted closing of resonance horns) is analyzed. We concentrate on certain strong resonance phenomena between the two frequencies and provide an extensive atlas of computed phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of periodically forced chemical oscillators. In particular, the existence and relative succession of several distinct types of global bifurcations resulting in chaotic transients and multistability are studied in detail. The location in the operating diagram of several key codimension 2 local bifurcations of periodic solutions is computed, and their interaction with an interesting feature we name "real-eigenvalues horns" is examined.

Segregated, structured, distributed models and their role in microbial ecology: A case study based on work done on the filter-feeding ciliateTetrahymena pyriformis

Microbial populations are composed of individual organisms each of which, if environmental circumstances are favorable, is undergoing change of its internal state through the operation of the set of processes that we call the cell cycle. The rate of progression through the cycle is subject to internal controls as well as external influences, and exhibits random as well as deterministic features. Microorganisms of the same species in different stages of the cell cycle have different internal states, and thus, the operation of the cell cycle is by itself sufficient to produce a distribution of states among the individual organisms of a population. In turn, the distribution of states produces distributions of the rates at which the cells of a population carry on their activities. Mathematical models of microbial growth that take the operation of the cell cycle and its consequences into account are more complicated than the kinds of models that are often used in microbial ecology. This paper gives some account of the nature, formulation, and uses of complex growth models. The account is illustrated by work done by the author and his collaborators H. M. Tsuchiya and more recently F. Srienc, as well as by others, on the filter-feeding ciliateTetrahymena pyriformis.

Effects of spatial heterogeneity on the dynamics of a microbial feeding interaction

A mathematical model for an ideal chemostat in which one microbial population feeds on another and where Monod's model is used for the specific growth rates of both populations predicts a less stable behavior for the system than the one observed experimentally. Various factors have been proposed as being the reason for the increased stability of such systems. In this work, the effect of spatial heterogeneity on the dynamics of the microbial feeding interaction is studied. It is concluded that spatial heterogeneity has a stabilizing effect on the system. This effect combined with other factors could be the reason for the increased stability observed in systems where a microbial feeding interaction occurs.

Peristance of bacteria in the presence of viable, nonencysting, bacterivorous ciliates

Laboratory studies of the interactions between a bacterial population and a population of bacterivorous ciliates consistently show that the bacteria are able to persist in the presence of viable ciliates. Reproduction of the bacteria, presumably at the expense of substrates produced by death and lysis of the ciliates and/or by their metabolic activity, has been suggested to be a factor involved in the observed bacterial persistence. Rates and extents of growth ofEscherichia coli in broths of mixed cultures of this bacterium and the ciliateTetrahymena pyriformis were determined in order to provide some data necessary to assess the importance of the suggested factor. In addition, an attempt was made to suppress bacterial growth on produced substrates so that feeding of the ciliates could be studied free of this complication. However, the procedure tested-addition of the antibiotic chloramphenicol (CM) at a concentration of 150μg/ml-led to other complications that made it impossible to obtain the desired information about feeding.

Experimental and modeling studies of a four-trophic level predator-prey system

Experimental studies of a microbial food chain involving organic carbon substrates,Enterobacter aerogenes, and ciliate protozoansParamecium primaurelia andDldinium nasutum were conducted in stirred, aerated batch cultures. Quantitative measurements were made of organic carbon levels and of cell numbers, mean cell volumes, and total biovolumes for all three microbial populations. A mathematical model based on Monod kinetics was developed to describe this four-trophic level predator-prey system. The model was formulated in terms of biovolume, which is the product of cell numbers and mean cell size, and includes terms for bio-volume decay. Batch culture data were used to derive parameter values, and model simulations were compared to experimental results. Despite the significance ofParamecium-Didinium studies in ecological literature, the entire food chain has not been previously studied or modeled.