A mathematical model for a biphasic DNA amplification reaction

Isothermal DNA amplification reactions are a prevalent tool with many applications, ranging from analyte detection to DNA circuits. Exponential amplification reaction (EXPAR) is a popular isothermal DNA amplification method that exponentially amplifies short DNA oligonucleotides. A recent modification of this technique using an energetically stable looped template with palindromic binding regions demonstrated unexpected biphasic amplification and much higher DNA yield than EXPAR. This ultrasensitive DNA amplification reaction (UDAR) shows high-gain, switch-like DNA output from low concentrations of DNA input. Here we present the first mathematical model of UDAR based on four reaction mechanisms and show the model can reproduce the experimentally observed biphasic behaviour. Furthermore, we show that three of these mechanisms are necessary to reproduce biphasic experimental results. The reaction mechanisms are (i) positively cooperative multistep binding spurred by two trigger binding sites on the template; (ii) gradual template deactivation; (iii) recycling of deactivated templates into active templates; and (iv) polymerase sequestration. These mechanisms can potentially illuminate the behaviour of EXPAR as well as other nucleic acid amplification reactions.