Load capacity improvements in transcriptional systems using discrete-time L1-adaptive control

DNA-based circuits relying on predictable thermodynamics and kinetics of DNA strand interactions impart flexibility in synthesizing synthetic biological constructs and in coupling these circuits to in vivo processes [1, 2, 6, 7]. Here, we focus on the synthetic Kim-Winfree oscillator network, illustrated in Fig. 1(i), which is a simple but effective coupled oscillator system in which two DNA switches SW1 and SW2 are coupled through activator and inhibitor blocks realized by RNA signals and auxiliary DNA species (see [3]). A typical experimental realization is closed in the sense that once the operation starts, we do not either add any chemicals, especially NTP fuel, externally into the wet-lab apparatus or remove any chemicals, especially waste products, from the apparatus. Within the closed system, the oscillations are bound to die out sooner or later diminishing NTP fuel eventually stops supporting the production of RNA signals and accumulating waste products clog down the toeholds and, as a result, adversely affect the signal propagation. Furthermore, the oxidation effects and the pH variations tend to deactivate the enzymes. Loading poses an additional challenge since it increases the order and the uncertainty of the system indeed, these oscillators have recently been used in [8] to drive conformational changes of a DNA nanomechanical device called DNA tweezers. We show how L1-adaptive control can be used to mitigate these effects