Isothermal reactivating Whiplash PCR for locally programmable molecular computation

Whiplash PCR (WPCR; Hagiya et al., in Rubin H, Woods DH (eds) DNA based computers, vol III, pp 55–72. American Mathematical Society, Providence, RI, 1999) is a novel technique for autonomous molecular computation where a state machine is implemented with a single stranded DNA molecule and state transition is driven by polymerase and thermal cycles. The primary difference between WPCR computation and other forms of molecular computing is that the former is based on local, rather than global rules. This allows many (potentially distinct) WPCR machines to run in parallel. However, since each state transition requires a thermal cycle, multi-step WPCR machines are laborious and time-consuming, effectively limiting program execution to only a few steps. To date, no WPCR protocol has been developed which is both autocatalytic (self-executing) and isothermal (with no change in temperature). In this paper, we describe some isothermal and autocatalytic protocols that use a combination of strand displacement and DNA polymerization events. Our designs include (1) a protocol where transition rules cannot be reused in subsequent computing (2) a protocol where rules can be reused using an auxiliary strand displacement event but does not prevent back-hybridization (an event responsible for limiting the program execution to only a few state transitions before the machine stalls), (3) a reusable rule protocol that prevents back-hybridization. Furthermore, we show that the third machine which gets rid of thermal cycles and still prevents back-hybridization, is computationally equivalent to the original WPCR machine. We also compute the state transition likelihood and the corresponding rate in this protocol. Finally we present a DNA sequence design of a 3-state isothermal and reactivating WPCR machine along with an experimental verification plan.