SIAM Journal on Applied Mathematics, Volume 80, Issue 5, Page 2071-2097, January 2020.
Isothermal DNA amplification schemes have broad applications, from molecular detection to DNA circuits. A newly developed amplification scheme, the ultrasensitive DNA amplification reaction (UDAR), shows a biphasic output with high endpoint product levels that indicates an endogenous switch. We recently developed a mathematical model that reproduces the dynamics displayed by one type of UDAR template. In this contribution, we use dynamical systems theory to analyze a sequence of models that highlight the features differentiating UDAR from previously analyzed DNA amplification models. This approach allows us to explain the biphasic features as the interaction of solution trajectories with equilibria whose stability is controlled by reaction mechanisms unique to UDAR. This analysis can assist rational design of more sensitive and specific amplification assays.

中文翻译：

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双相等温DNA扩增反应动力学分析

SIAM应用数学杂志，第80卷，第5期，第2071-2097页，2020年1月。
等温DNA扩增方案具有广泛的应用，从分子检测到DNA电路。新开发的扩增方案，超敏DNA扩增反应（UDAR），显示出具有高终点产物水平的双相输出，表明内源性转换。我们最近开发了一种数学模型，该模型可再现一种UDAR模板显示的动态。在此贡献中，我们使用动力学系统理论分析了一系列模型，这些模型突出了区别UDAR与先前分析的DNA扩增模型的特征。这种方法使我们能够将双相特征解释为溶液轨迹与平衡的相互作用，平衡的稳定性由UDAR特有的反应机制控制。