We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the discontinuity of hysteresis. These conditions are formulated in terms of geometry of manifolds defining hysteresis thresholds and the graph of initial data.
Isocitric acid exists in the form of four stereoisomers, of which only the threo-Ds-form (ICA) is a natural active compound, an intermediate of Krebs cycle, and suitable for nutritional and pharmaceutical use. In this paper, we propose a method for ICA production from ethanol by yeast Yarrowia lipolytica. The effects of temperature, pH of the medium, and aeration on the growth of the producer Y. lipolytica VKM Y-2373 and synthesis of ICA were studied. An optimal fermentation regime, which ensures a good growth of the producer and directed synthesis of the target product, was determined. The producer is advised to carry out cultivation at 29°C and various pH of the medium and the oxygen concentration (pH 5 and pO2 20–25% (of saturation) during the growth period and pH 6 and pO2 50–55% (of saturation) during the acid formation) on a nutrient medium containing an increased content of zinc (0.6 mg/L), iron (1.2 mg/L), and 30 mM itaconic acid (inhibitor of isocitrate lyase—the key enzyme of ICA metabolism) should also be introduced into the nutrition medium. Such fermentation production mode provides 90.5 g/L ICA with process selectivity of 80%, mass yield (YICA) of 0.77 g/g, and energy yield (ηICA) of 0.278 g/g.
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