Search Results

Thermodynamically favoured molecular computation offers advantages over more typical out-of-equilibrium computing, including simpler experimental protocols and automatic error correction. But as systems scale to large sizes the number of states increases dramatically, increasing the need for efficiently navigable energy landscapes. We give results in two theoretical models of Scaffolded DNA Computing (SDC), a recently implemented form of thermodynamically favoured DNA computing [Stérin, Eshra et al, bioRχiv 2025]. We show their computational power is characterised by logarithmic space complexity classes, meaning they are expressive at scale. Our first energy landscape result is an exact relation between the probability of target configurations (outputs), temperature and DNA sequence domain length, showing that domain length merely logarithmic in scaffold length is sufficient for the probability of the target configuration to outcompete all off-target structures. We show that even in the presence of imperfect/unequal binding strength scaffold domains we still achieve good kinetics: O(N²) or O(N³) expected completion time, depending on model assumptions, and there are even narrow conditions that yield fast O(N)-time kinetics. Finally, we address a thorny scaling problem: SDC outputs often have repeated compute domains and any binding energy variances get exaggerated under repetition making errors favourable, but we give a construction that reprograms the energy landscape to convert such a non-isoenergetic system into one with almost perfectly isoenergetic energy plateaus. We also show that systems maintain good (polynomial-time) kinetics, even in the face of a poor (uphill) scaffold energy landscape. These results give a roadmap for scaling up the SDC while highlighting the role kinetics and energy landscape programming could play in thermodynamically-favoured computing more generally.