Enzyme-free nucleic acid dynamical systems.

INTRODUCTION Embedded controllers enable complex functionality in man-made mechanical and electronic devices. Similarly, intricate regulatory networks within living organisms are at the heart of all cellular processes. However, man-made embedded chemical controllers still cannot be engineered with the ease of their electronic counterparts. Synthetic biology attempts to close the gap by drawing upon billions of years of evolution, borrowing the complex machinery of the central dogma. By contrast, DNA nanotechnology starts with bottom-up understanding of simple molecular components with predictable composition rules. Therefore, it becomes possible—in principle—to recapitulate for molecular systems the hierarchical design strategies that were essential to the development of complex electronic systems. The central concept is to establish a hierarchy of abstractions that permits the programming of high-level dynamical behavior separately from the design of low-level components. RATIONALE Hierarchical molecular programming languages have been previously described, but they have yet to be robustly implemented for molecular dynamical systems. Enzyme-free nucleic acid systems are a promising substrate for molecular design because they obey a predictable class of interactions that arise from just Watson-Crick binding. Beyond static binding, a strand competing with another for the same complement can be displaced (strand displacement), and the displaced strands can, in turn, displace strands in other molecules (cascading). Sequence- and domain-level models (which abstract contiguous sequences that act as a unit) are made possible by predictable thermodynamics and strand displacement rules and are used in easy-to-use tools, such as NUPACK and Visual DSD. At a higher level, formal chemical reaction networks (CRNs)—coupled chemical reaction equations between formal symbols representing different species—have been proposed as a programming language for specifying the dynamics of strand displacement cascades. Extensive theoretical work exploring dynamical systems and algorithms written in the language of CRNs shows the power of reasoning about chemical algorithms independently of the chemical identity of the participating species. RESULTS As a challenging test case for hierarchical design, we set out to implement an oscillator specified by an abstract CRN known as the “rock-paper-scissors” oscillator. This CRN has been proposed and analyzed extensively in theoretical ecology, theoretical physics, theoretical chemistry, and theoretical computer science; yet, until this work, it had no known chemical implementation. To systematically implement each formal chemical reaction, we designed a corresponding set of abstract molecules that mediate the desired interaction pathway according to a domain-level model; subsequent sequence design yielded specific DNA molecules that were expected to satisfy the specifications. Using chemically synthesized oligonucleotides, we experimentally demonstrated a working oscillator after debugging the main sources of design error. We then constructed a mathematical model of individual strand displacement steps and nonidealities that quantitatively captured the observed dynamics. Finally, the critical design principles were codified into a compiler that automates the design process for arbitrary networks. The compiler was tested by successfully designing a new oscillator that worked on the first try. CONCLUSION The programmable nature of base-pairing interactions and the minimal requirements on the chemical environment make DNA a particularly attractive engineering material. Nucleic acids as chemical controllers naturally integrate with the ever-expanding range of molecular structures, machines, and devices developed in DNA nanotechnology and could eventually be embedded within complex synthetic organelles or artificial cells that sense, compute, and respond to their chemical and molecular environment. Besides addressing a technological challenge, we also answer a fundamental scientific question, showing that Watson-Crick base pairing alone suffices for complex temporal dynamics.