Abstract
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.
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