Abstract
Genetic circuits have been identified as a promising technology that could revolutionize several areas, including biofuels, biomanufacturing, and medicine. Despite the tremendous potential of this technology, there are significant challenges associated with its development and implementation. One of the major challenges with genetic circuits is the stochastic nature of their behavior. Unlike traditional engineering systems, genetic circuits are inherently probabilistic, which makes it more challenging to design and verify their performance. In particular, genetic circuits can exhibit rare failure states known as glitches, which are difficult to predict and prevent. To address this challenge, multiple stochastic simulation algorithms have been developed that use importance sampling as a variance reduction technique to estimate the probability of glitching behavior. However, these methods are often unreliable and impractical for use in design workflows. As a result, a mathematical analysis of these methods is necessary to identify the reasons why they fail to rapidly estimate low probabilities. To meet this need, we performed a comprehensive mathematical analysis of these methods to determine why they are ineffective in estimating low probabilities and to showcase their strengths and shortcomings. To achieve this end, we developed several case studies highlighting the challenges associated with these methods and their potential applications in genetic circuit design. This analysis provides crucial insights into the development of more effective algorithms for estimating the probability of rare glitching behaviors in genetic circuits. The results of this work will guide the future development of more applicable algorithms that can be used in design workflows to improve the reliability and predictability of genetic circuits. By overcoming the challenges associated with the stochastic nature of genetic circuits, these algorithms will enable the widespread adoption of genetic circuit technology in various fields, including biofuels, biomanufacturing, and medicine.
