A minimal scenario for the origin of non-equilibrium order.

Extant life contains numerous non-equilibrium mechanisms to create order not achievable at equilibrium; it is generally assumed that these mechanisms evolved because the resulting order was sufficiently beneficial to overcome associated costs of time and energy. Here, we identify a broad range of conditions under which non-equilibrium order-creating mechanisms will evolve as an inevitable consequence of self-replication, even if the order is not directly functional. We show that models of polymerases, when expanded to include known stalling effects, can evolve kinetic proofreading through selection for fast replication alone, consistent with data from recent mutational screens. Similarly, replication contingent on fast self-assembly can select for non-equilibrium instabilities and result in more ordered structures without any direct selection for order. We abstract these results into a framework that predicts that self-replication intrinsically amplifies dissipative order-enhancing mechanisms if the distribution of replication times is wide enough. Our work suggests the intriguing possibility that non-equilibrium order can arise more easily than assumed, even before that order is directly functional, with consequences impacting mutation rate evolution and kinetic traps in self-assembly to the origin of life.

Physical principles for DNA tile self-assembly.

DNA tiles provide a promising technique for assembling structures with nanoscale resolution through self-assembly by basic interactions rather than top-down assembly of individual structures. Tile systems can be programmed to grow based on logical rules, allowing for a small number of tile types to assemble large, complex assemblies that can retain nanoscale resolution. Such algorithmic systems can even assemble different structures using the same tiles, based on inputs that seed the growth. While programming and theoretical analysis of tile self-assembly often makes use of abstract logical models of growth, experimentally implemented systems are governed by nanoscale physical processes that can lead to very different behavior, more accurately modeled by taking into account the thermodynamics and kinetics of tile attachment and detachment in solution. This review discusses the relationships between more abstract and more physically realistic tile assembly models. A central concern is how consideration of model differences enables the design of tile systems that robustly exhibit the desired abstract behavior in realistic physical models and in experimental implementations. Conversely, we identify situations where self-assembly in abstract models can not be well-approximated by physically realistic models, putting constraints on physical relevance of the abstract models. To facilitate the discussion, we introduce a unified model of tile self-assembly that clarifies the relationships between several well-studied models in the literature. Throughout, we highlight open questions regarding the physical principles for DNA tile self-assembly.

Direct atomic force microscopy observation of DNA tile crystal growth at the single-molecule level.

While the theoretical implications of models of DNA tile self-assembly have been extensively researched and such models have been used to design DNA tile systems for use in experiments, there has been little research testing the fundamental assumptions of those models. In this paper, we use direct observation of individual tile attachments and detachments of two DNA tile systems on a mica surface imaged with an atomic force microscope (AFM) to compile statistics of tile attachments and detachments. We show that these statistics fit the widely used kinetic Tile Assembly Model and demonstrate AFM movies as a viable technique for directly investigating DNA tile systems during growth rather than after assembly.