Title: Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles Show Chinese title

Title: 尿素-脲酶反应在巨型脂质囊泡中pH振荡的精确简化模型

Abstract: This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms. Show Chinese abstract

Abstract: 这项理论研究涉及基于尿素-脲酶反应的pH振荡器，该反应被限制在巨脂质囊泡中。 在适当的条件下，尿素和氢离子通过单层囊泡膜的差异运输会周期性地重置pH钟，使系统在酸性到碱性之间切换，从而产生自持续的振荡。 我们分析了相流和极限环的结构，这些结构控制着巨囊泡的动力学，并主导了亚微米大小小囊泡中显著的随机振荡。 为此，我们推导了简化的模型，这些模型易于进行解析处理，并通过数值解进行补充，得到了振荡的周期和振幅以及振荡行为持续的参数范围。 我们表明，这些预测的准确性对所采用的简化方案非常敏感。 特别是，我们提出了一种准确的两变量模型，并展示了它与一个三变量模型的等价性，该模型可以解释为化学反应网络。 对单个pH振荡器的精确建模对于合理化实验和理解囊泡的通信以及节奏的同步至关重要。