Leak-resilient enzyme-free nucleic acid dynamical systems through shadow cancellation

DNA strand displacement (DSD) emerged as a prominent reaction motif for engineering nucleic acid-based computational devices with programmable behaviors. However, strand displacement circuits are susceptible to background noise that disrupts the circuit behavior, commonly known as leaks. The side effects of leaks are particularly severe in circuits with complex dynamical elements (e.g., feedback loops), as their leaks amplify nonlinearly, disrupting the circuit function. Shadow cancellation is a dynamic leak-elimination strategy originally proposed to control the leak growth in such circuits. However, the kinetic restrictions of the proposed method introduce a significant design overhead, making it less accessible. In this work, we use domain-level DSD simulations to examine the method's capabilities, the inner workings of its components, and, most importantly, robustness to practical deviations in its design requirements. First, we show that the method could stabilize the dynamics of several leak-affected catalytic and autocatalytic dynamical systems of practical importance. Then, through several probing experiments, we show that its design restrictions could be significantly relaxed without impacting the circuit function through simple adjustments to the circuit parameters. Finally, we discuss several ideas to tackle the practical challenges in applying the method to arbitrary DSD circuits, paving the way for future experimental work.