A generalized diffusion model for growth and dispersal in a population

A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.Part of this work was done while at the Mathematical Institute, Oxford University as a Senior Visiting Fellow supported by the Science Research Council of Great Britain under grant GR/B31378     

Epidemics in competition

When two or more epidemic agents are simultaneously present in a population, they may interact to increase or decrease each other's effectiveness. One form of interaction is competition where each agent confers immunity to the others. Such competition occurs, for example, between different strains of myxomatosis in rabbit populations. We consider some consequences of introducing competition into mathematical epidemic models. Both deterministic and stochastic simple epidemic models are examined. In either case the conclusions are similar: the faster spreading epidemic has a considerable advantage.     

Effect of oxygen on steady-state product distribution in Bacillus polymyxa fermentations

Bacillus polymyxa ferments glucose to 1-2,3 butanediol, acetoin, ethanol, acetic acid, lactic acid, and formic acid. This research investigates product formation as a function of oxygen availability. A predictive model that simulates product distribution at known oxygen transfer rates is developed on the hypothesis that, in an energy-limited environment, B. polymyxa utilizes glucose and oxygen in the most efficient manner. The efficiency of utilization of glucose and oxygen is measured in terms of the ATP yields of each oxidative pathway. The identity of the products constituting the profile at the given oxygen transfer rate is determined by comparing the ATP production and consumption rates. While the ATP generated is calculated from a knowledge of the oxygen transfer rate and ATP yields of the oxidative pathways, the ATP consumption is estimated by the Pirt expression in terms of growth- and nongrowth-associated components. The product formation rates are obtained by solving ATP and NAD balance equations. They equate the production and consumption rates of these intermediates and are derived from the pseudo-steady-state hypothesis. The model is applied to continuous culture systems that are both open and closed with respect to biomass. At a given oxygen transfer rate, dilution rate, and inlet glucose concentration, the model predicts steady-state concentrations of two dominant fermentation endproducts with the help of four parameters that can be determined from independent experiments. In contrast with earlier approaches, the experimental studies are carried out in continuous culture. Product profiles are obtained at various oxygen transfer rates, fer rates, inlet glucose concentrations, and dilution rates. The effect of pH on the relative distribution of products is also demonstrated. Results indicate that the model is fairly successful in predicting product profiles as a function of oxygen availability. (c) 1992 John Wiley & Sons, Inc.     

Effect of hydrogen sulfide on growth of sulfate reducing bacteria

A culture of sulfate reducing bacteria (SRB) growing on lactate and sulfate was incubated at different pH values in the range of 5.8-7.0. The effect of pH on growth rate was determined in this pH range; the highest growth rate was observed at pH 6.7. Hydrogen sulfide produced from sulfate reduction was found to have a direct and reversible toxicity effect on the SRB. A hydrogen sulfide Concentration of 547 mg/L (16.1 mM) completely inhibited the culture growth. Comparison between acetic acid and hydrogen sulfide inhibition is presented and the concomitant inhibition kinetics are mathematically described. (c) 1992 John Wiley & Sons, Inc.     

A model for light-limited continuous cultures: growth, shading, and maintenance

Light-limited growth in continuous cultures of phototrophic organisms is modeled. It is assumed that light energy up-take rate depends hyperbolically on light intensity and that the maintenance costs are proportional to biomass. Modeling the light distribution caused by shading within the vessel is necessary to explain the existence of steady state in light-limited chemostats. The model fits well to experimental data from literature on light-limited chemostats and turbidostats. Attention is given to the implications of the model for the estimation of the specific maintenance rate constant in light-limited continuous cultures.     

Active site conformation in myoglobin as determined by X-ray absorption spectroscopy

X-ray absorption fine structure experiments were performed to study structural and dynamic aspects of the active site of various forms of myoglobin. The structures determined for deoxyMb, MbCO, and MbO2 are consistent with the structure established by X-ray absorption fine structure experiment and X-ray crystallography. The first shell of ferrous MbNO determined contains 5 nitrogens located at 2.02 A and a short NO bond length of 1.76 A. This study focuses on the change of the XAFS Debye-Waller factor with temperature, which is a measure of thermal and static disorder. It was found that the changes of Debye-Waller factor with temperature for the Mb proteins, except deoxyMb, are consistent with a simple Einstein model, in which a single frequency was assumed for the bond stretching modes. In contrast, the temperature dependence of deoxyMb cannot be fitted to the Einstein model and a large disorder was found at low temperatures, which indicates the existence of conformational substates of the active site.