Algebraic and Generative Design of DNA Origami via Origami Monoids

AO_SCPLOWBSTRACTC_SCPLOWWe integrate the elegance of monoid structures with the power of deep learning models, specifically Sequential variational autoencoders (SeqVAEs), to explore the vast and stability-dependent structural space of DNA origami. While existing computational tools provide well-established protocols for diverse applications, they lack large-scale datasets that could fully leverage modern computational power. To address this gap, we introduce an encoding framework based on the algebraic properties of Jones monoids. This approach enables both a top-down construction of DNA origami designs and a systematic understanding of how crossover arrangements influence overall shape. This work thus establishes a new framework for the design and analysis of DNA origami, bridging algebraic formalism with generative modeling.