The identity and timing of environmental stimulus play a pivotal role in living organisms in programming their signaling networks and developing specific phenotypes. The ability to unveil history-dependent signals will advance our understanding of temporally regulated biological processes. Here, we have developed a two-input, five-state DNA finite-state machine (FSM) to sense and record the temporally ordered inputs. The spatial organization of the processing units on DNA origami enables facile modulation of the energy landscape of DNA strand displacement reactions, allowing precise control of the reactions along predefined paths for different input orders. The use of spatial constraints brings about a simple, modular design for the FSM with a minimum set of orthogonal components and confers minimized leaky reactions and fast kinetics. The FSM demonstrates the capability of sensing the temporal orders of two microRNAs, highlighting its potential for temporally resolved biosensing and smart therapeutics.

Molecular tessellation research aims to elucidate the underlying principles that govern intricate patterns in nature and to leverage these principles to create precise and ordered structures across multiple scales, thereby facilitating the emergence of novel functionalities. DNA origami nanostructures are excellent building blocks for constructing tessellation patterns. However, the size and complexity of DNA origami tessellation systems are currently limited by several unexplored factors relevant to the accuracy of essential design parameters, the applicability of design strategies, and the compatibility between different tiles. Here, we present a general method for creating DNA origami tiles that grow into tessellation patterns with micrometer-scale order and nanometer-scale precision. Interhelical distance ( D ) was identified as a critical design parameter determining tile conformation and tessellation outcome. Finely tuned D facilitated the accurate geometric design of monomer tiles with minimized curvature and improved tessellation capability, enabling the formation of single-crystalline lattices ranging from tens to hundreds of square micrometers. The general applicability of the design method was demonstrated by 9 tile geometries, 15 unique tile designs, and 12 tessellation patterns covering Platonic, Laves, and Archimedean tilings. Particularly, we took two strategies to increase the complexity of DNA origami tessellation, including reducing the symmetry of monomer tiles and coassembling tiles of different geometries. Both yielded various tiling patterns that rivaled Platonic tilings in size and quality, indicating the robustness of the optimized tessellation system. This study will promote DNA-templated, programmable molecular and material patterning and open up new opportunities for applications in metamaterial engineering, nanoelectronics, and nanolithography.