Fast growing E. coli cells, in glucose-aerobic conditions, excrete fermentation by-products such as acetate. This phenomenon is known as overflow metabolism and has been observed in a diverse range of microorganisms. In this paper, we study a chemostat model subject to overflow metabolism: if the substrate uptake rate (or the specific growth rate) is above a threshold rate (different from zero), then secretion of a by-product happens. We assume that the presence of the by-product has an inhibitory effect on the growth of the microorganism. The model is described by a non-smooth differential system of dimension three. We prove the existence of at most one equilibrium (or steady-state) with presence of microorganism, which is globally stable. We use these results to discuss the performance of chemostat-type systems to produce biomass or recombinant proteins.

快速生长的大肠杆菌在葡萄糖需氧条件下，细胞分泌发酵副产物，如醋酸盐。这种现象被称为溢出代谢，并已在多种微生物中观察到。在本文中，我们研究了一个受溢出代谢影响的恒化器模型：如果底物吸收率（或特定生长率）高于阈值率（不同于零），则会发生副产物的分泌。我们假设副产物的存在对微生物的生长有抑制作用。该模型由维度为 3 的非光滑微分系统描述。我们证明了在微生物的存在下至多存在一个平衡（或稳态），这是全局稳定的。我们使用这些结果来讨论恒化器型系统生产生物质或重组蛋白的性能。