Parallel Implementation and Clique-based Design: Towards an Autonomous Multi-bit DNA Adder with Simultaneous Readout

Abstract

DNA computing involves implementing tuneable chemical reaction networks using synthetic DNA constructs, offering the unique ability to directly compute on medical and environmental samples. However, DNA circuits have yet to achieve the complexity of their in silico equivalents, as the current state of the art is insufficient for synthesising, operating, and reading out molecular circuits at scale. Multi-bit addition exemplifies this gap, having underpinned general-purpose computing in electronic circuits but remaining an elusive benchmark in DNA circuits. This dissertation addresses bottlenecks in both the implementation and design of DNA circuits at scale. First, I present optimisations to a method for high-throughput synthesis and readout using Selective Parallel Amplification and Restriction Enzyme processing (SPARE) of array-synthesised oligonucleotides into nicked double-stranded DNA logic gates, followed by next-generation sequencing. This workflow enables increasingly complex computation, from single and multiplex AND, OR, and NOR logic to multi-bit addition, while reducing operational cost and labour. Second, I introduce a combinatorial approach for improving signal orthogonality in complex DNA circuits, presenting group-level equivalents to historically pairwise sequence design heuristics. I propose a mechanism 'for combinatorial crosstalk', or the simultaneous partial binding of multiple non-target signals. To address this, I present a 'union structure' heuristic for evaluating collective orthogonality, as well as a 'graph-based' design methodology for identifying independent sets of orthogonal signals. I validate this framework across single gates through multi-bit adder circuits, improving performance across circuit breadth and depth. Together, these contributions lay the groundwork for implementing, to my knowledge, the first autonomous molecular 4-bit adder with simultaneous readout.