Microbial populations, modeling

P. R. Darrah, Models of the rhizosphere. I. Microbial population dynamics around the root releasing. soluble and in.soluble carbon. Plant Soil 733 187 (1991). 

III. MODELING THE DYNAMICS OF MICROBIAL POPULATIONS AROUND THE ROOT... 

The rates of each of the environmentally important chemical processes are influenced by numerous parameters, but most processes are described mathematically by only one or two variables. For example, the rate of biodegradation varies for each chemical with time, microbial population characteristics, temperature, pH, and other reactants. In modeling efforts, however, this rate can be approximated by a first-order rate constant (in units of time). 

Nonetheless, if the microbial population is steady and geochemical conditions such as pH are controlled, an enzymatic model can be appropriate. Bekins et al. (1998), for example, considered how the mineralization of phenol,... 

In the next chapter (Chapter 27) we show calculations of this type can be integrated into mass transport models to produce models of weathering in soils and sediments open to groundwater flow. In later chapters, we consider redox kinetics in geochemical systems in which a mineral surface or enzyme acts as a catalyst (Chapter 28), and those in which the reactions are catalyzed by microbial populations (Chapter 33). 

We take two cases in which mineral surfaces catalyze oxidation or reduction, and one in which a consortium of microbes, modeled as if it were a simple enzyme, promotes a redox reaction. In Chapter 33, we treat the question of modeling the interaction of microbial populations with geochemical systems in a more general way. 

Parametric uncertainty A great number of bacterial species carry out the transformations of organic load and nutrients in wastewater treatment processes without direct or easily comprehensible relationships between the microbial populations and viability. The role of each bacterial species is fuzzy [30], and aspects such as cellular physiology and its modeling are not easily understood from external measurements [18], [68]. As a first consequence, the kinetics of these transformations is often poorly or inadequately known [66]. Extensive efforts to model the kinetics have been undertaken, but these have not been successful to elucidate how yield coefficients, kinetic parameters and the bacterial population distribution change as a function of both, the influent composition and the operating conditions. 

An application well-suited for IMS is the decommissioning and cleanup of sites where extensive manufacturing of explosives has taken place in the last century and where widespread contamination of soils and waters has occurred [74]. Decontamination of model metal scrap artificially contaminated with TNT and of decommissioned mortar rounds stiU containing explosives residue was followed by sampling surfaces with analysis by a portable mobility spectrometer. Mixed anaerobic microbial populations of bioslurries were employed in decontamination of scrap and the mortar rounds, and the IMS analyzer was seen as a sensitive field... 

By now, it has not been made possible to determine the levels of antimicrobials that can cause an increase of primarily resistant Enterobacteriaceae in the gut of the consumer. As a result, measuring the microbial significance of antimicrobial residues continues to be the subject of considerable discussion. Much of the discussion involves the development of model systems that will reflect the effects of residue levels of antimicrobials on human intestinal microbial populations. The consensus of opinion at a recent symposium is that no such single system is available (64). The human intestine is a very complex microbial ecosystem, about which little is known of the effects of antimicrobial residues on the population dynamics and biochenoical responses (65). 

Box 17.1 Monod-Limiting-Substrate Models of Microbial Population Growth... 

The conceptual model expressed by Eq. 17-61 implies that no other substance is simultaneously limiting microbial population growth. This assumption may be invalid for example, an electron acceptor like 02 may be simultaneously needed for the degradation of the organic chemical of interest. Such dual-limiting substrate cases require modifying Eq. 17-61 to reflect the impacts of both chemicals (see Case... 

Box 17.1 Monod Limiting-Substrate Models of Microbial Population Growth Case 1 Single limiting substrate, i (Monod, 1949) ... 

O. G. Berg. A model for the statistical fluctuations of protein numbers in a microbial population. J. Theoret. Biol., 71 587-603, 1978. 

In the previous chapter the gradostat was introduced as a model of competition along a nutrient gradient. The case of two competitors and two vessels with Michaelis-Menten uptake functions was explored in considerable detail. In this chapter the restriction to two vessels and to Michaelis-Menten uptake will be removed, and a much more general version of the gradostat will be introduced. The results in the previous chapter were obtained by a mixture of dynamical systems techniques and specific computations that established the uniqueness and stability of the coexistence rest point. When the number of vessels is increased and the restriction to Michaelis-Menten uptake functions is relaxed, these computations are inconclusive. It turns out that unstable positive rest points are possible and that non-uniqueness of the coexistence rest point cannot be excluded. The main result of this chapter is that coexistence of two microbial populations in a gradostat is possible in the sense that the concentration of each population in each vessel approaches a positive equilibrium value. The main difference with the previous chapter is that we cannot exclude the possibility of more than one coexistence rest point. 

While some models of sulfide mineral leaching in natural or heap situations have considerable utility for the management of metal recovery operations (Harris, 1969), the complexity of such situations has so far defied efforts to construct models which accommodate all the observed phenomena, and there is a need for intensification of multi-disciplinary approaches to the overall problem. Considerably greater understanding of the interactions between microbial populations and mineral arrays in the dynamic patterns of the field context is needed before this task can be accomplished. 

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