Microbial symbioses based on nutrient exchange and interdependence are ubiquitous in nature and biotechnologically promising; however, an in-depth mathematical description of their exact underlying dynamics from first principles is still missing. Hence, in this paper a novel mechanistic mathematical model of such a relationship in a continuous chemostat culture is derived. In contrast to preceding works on the topic, only parameters which can be directly measured and understood from biological first principles are used, allowing for a higher degree of mechanistic understanding of the underlying processes compared to previous approaches. The predictive power of the model is validated by demonstrating that it accurately recapitulates both the temporal dynamics as well as the final state of a previously published cross-feeding experiment. The model is then used to examine the influence of the biological traits of the involved organisms on the position and stability of the equilibrium states of the system using bifurcation analyses. It is additionally demonstrated how manipulating the external metabolite concentrations of the system can shift the species interaction on a continuous spectrum ranging from mutualism over commensalism to parasitism. This further reinforces the idea of a continuous spectrum of symbiotic interactions as opposed to static and discrete categories. Finally, the practical implications of the results for the biotechnological application of such microbial consortia are discussed.

中文翻译：

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微生物代谢共生的机制模型概括了实验数据并确定了共生相互作用的连续体。

基于营养交换和相互依赖的微生物共生在自然界中无处不在，在生物技术上很有前景；然而，仍然缺少从第一原理对它们的确切潜在动力学进行深入的数学描述。因此，在本文中，推导出了连续恒化器培养中这种关系的新型机械数学模型。与之前关于该主题的工作相比，仅使用可以从生物学第一原理直接测量和理解的参数，与以前的方法相比，允许对潜在过程有更高程度的机械理解。该模型的预测能力通过证明它准确地概括了先前发布的交叉喂养实验的时间动态和最终状态来验证。然后使用该模型通过分叉分析来检查所涉及生物的生物学特性对系统平衡状态的位置和稳定性的影响。此外还证明了操纵系统的外部代谢物浓度如何在从共生共生到寄生的连续谱上改变物种相互作用。这进一步强化了共生相互作用的连续谱的想法，而不是静态和离散的类别。最后，讨论了该结果对此类微生物聚生体的生物技术应用的实际意义。此外还证明了操纵系统的外部代谢物浓度如何在从共生共生到寄生的连续谱上改变物种相互作用。这进一步强化了共生相互作用的连续谱的想法，而不是静态和离散的类别。最后，讨论了该结果对此类微生物聚生体的生物技术应用的实际意义。此外还证明了操纵系统的外部代谢物浓度如何在从共生共生到寄生的连续谱上改变物种相互作用。这进一步强化了共生相互作用的连续谱的想法，而不是静态和离散的类别。最后，讨论了该结果对此类微生物聚生体的生物技术应用的实际意义。