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.     

A spin label study of immobilized enzyme spectral subpopulations

Electron spin resonance (ESR) spin label studies have been carried out to examine the active site conformation of alpha-chymotrypsin before and after immobilization on two types of organic polymer supports: Amberlite XAD-8 and XAD-2. alpha-Chymotryspin was first chemically modified by reaction with methyl-4-phenylbutyrimidate and then inhibited by the active site spin label 4-(2,2,6,6-tetramethyl-piperdine-1-oxyl)-m-flurosulfonylbenzamide. In general, the ESR spectra of the active site lable revealed no significant changes in conformation for most of the enzyme before or after derivatization. On the other hand, two spectral subpopulations (A and B) of spin-labeled enzyme were characterized on the basis of their ESR spectra after immobilization on Amberlite XAD-8. Spectral subpopulation A (distinguished by a highly restrained spectrum) appeared to retain its active site structure and conformation and represented a large majority of the labeled chymotrypsin on the beads. Its presence correlated with the high activity and stability of phenylbutyramidinated chymotryspin on the Amberlite XAD-8 beads. Spectral subpopulation B (distinguished by a very weakly constrained spectrum) appeared to reflect loosely bound or denatured enzyme which was removable upon washing with 40% (v/v) ethylene glycol. Two methods for examining solvent accessibility to the active site lable of the kinetics of ascorbate reduction suggested that both spectral subpopulations had identical accessibilities to the bulk solvent. Paramagnetic broadening of the signal by K(3)Fe(CN)(6) revealed differences in the spin-spin broadening of the A and B components but is deemed and inappropriate indicator of solvent accessibility.     

Strategies for reducing solvent toxicity in extractive fermentations

The toxicity of an Alamine 336/oleyl-alcohol extraction system on Lactobacillus delbrueckii was investigated. It was shown that the solvent affected the cells through the water-soluble portion and the immiscible portion of the solvent. While immobilization significantly protected the cells from the immiscible solvent phase, the water-soluble part of the solvent still caused toxicity to the microorganisms due to diffusion of the solvent into the matrix. Adding soybean oil to the kappa-carrageenan matrix could trap the diffusing solvent molecules, and therefore reduce the toxic effect from the water soluble portion of the solvent. The protective ability of soybean oil was quantified through mathematical modeling and experimentation.     

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.