DNA is a useful material for nanoscale construction. Due to highly specific Watson-Crick base pairing, the DNA sequences can be designed to form small tiles or origami. Adjacent helices in such nanostructures are connected via Holliday junction-like crossovers. DNA tiles can have sticky ends which can then be programmed to form large one-dimensional and two-dimensional periodic lattices. Recently, a three-dimensional DNA lattice has also been constructed. Here we report the design and construction of a novel DNA cross tile, called the double-decker tile. Its arms are symmetric and have four double helices each. Using its sticky ends, large two-dimensional square lattices have been constructed which are on the order of tens of micrometers. Furthermore, it is proposed that the sticky ends of the double-decker tile can be programmed to form a three-dimensional periodic lattice with large cavities that could be used as a scaffold for precise positioning of molecules in space.
Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these existing error-resilient tile systems assumed directional growth of the tiling assembly. This is a very strong assumption because experiments show that tile self-assembly does not necessarily behave in such a fashion, since they may also grow in the reverse of the intended direction. The assumption of directional growth of the tiling assembly also underlies the growth model in theoretical assembly models such as the TAM. What is needed is a means for enforce this directionality constraint, which will allow us to reduce assembly errors.In this paper we describe a protection/deprotection strategy to strictly enforce the direction of tiling assembly growth so that the assembly process is robust against errors. Initially, we start with (i) a single "activated" tile with output pads that can bind with other tiles, along with (ii) a set of "deactivated" tiles, meaning that the tile's output pads are protected and cannot bind with other tiles. After other tiles bind to a "deactivated" tile's input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. * This paper is a revised version of the conference proceedings extended abstract: Urmi Majumder, Thomas H. When these are activated in a desired order, we can enforce a directional assembly at the same scale as the original one. Such a system can be built with minimal modifications of existing DNA tile nanostructures. We propose a new type of tiles called activatable tiles and its role in compact proofreading. Activatable tiles can be thought of as a particular case of the more recent Signal Tile Assembly model, where signals transmit binding/unbinding instructions across tiles on binding to one or more input sites.We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree's original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We also perform detailed stepwise simulations using a DNA Tile simulator Xgrow, and show that the activatable tiles mechanism can reduce error rates in self assembly. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as (i) a novel system for concentration of molecules, and (ii) a catalyst in sequentially triggered chemical reactions.
The theoretical basis of computational self-assembly dates back to the idea of Wang tiling models in the early 1960s.1 More recently, it has been recognized that self-assembly is a promising route to nano-scale computation and there have been many experimental demonstrations of self-assembling DNA tiles performing computation. Winfree 2 proposed abstract irreversible (only tile accretion is allowed) models for the self-assembly process that can perform universal computation. Realism, however, requires us to develop models and analysis for reversible tiling models, where tile dissociation is also allowed so that we can measure various thermodynamic properties. To date, however, the stochastic analysis of reversible tiling processes has only been done for one-dimensional assemblies and has not been extended to two or three dimensional assemblies. In this paper we discuss how we can extend prior work in one dimension by Adleman et al. 3 to higher dimensions. We describe how these self-assembly processes can be modeled as rapidly mixing Markov Chains. We characterize chemical equilibrium in the context of self-assembly processes and present a formulation for the equilibrium concentration of various assemblies. Since perfect equilibrium can only be reached in infinite time, we further derive the distribution of error around equilibrium. We present the first known direct derivation of the convergence rates of two and three-dimensional assemblies to equilibrium. Finally we observe that even when errors are allowed in the self-assembly model, the distribution over assemblies converge to uniform distribution with only small number of random association/dissociation events. We conclude with some thoughts on how to relax some of our model constraints.
Whiplash PCR (WPCR; Hagiya et al., in Rubin H, Woods DH (eds) DNA based computers, vol III, pp 55-72. American Mathematical Society, Providence, RI, 1999) is a novel technique for autonomous molecular computation where a state machine is implemented with a single stranded DNA molecule and state transition is driven by polymerase and thermal cycles. The primary difference between WPCR computation and other forms of molecular computing is that the former is based on local, rather than global rules. This allows many (potentially distinct) WPCR machines to run in parallel. However, since each state transition requires a thermal cycle, multi-step WPCR machines are laborious and time-consuming, effectively limiting program execution to only a few steps. To date, no WPCR protocol has been developed which is both autocatalytic (self-executing) and isothermal (with no change in temperature). In this paper, we describe some isothermal and autocatalytic protocols that use a combination of strand displacement and DNA polymerization events. Our designs include (1) a protocol where transition rules cannot be reused in subsequent computing (2) a protocol where rules can be reused using an auxiliary strand displacement event but does not prevent back-hybridization (an event responsible for limiting the program execution to only a few state transitions before the machine stalls), (3) a reusable rule protocol that prevents back-hybridization. Furthermore, we show that the third machine which gets rid of thermal cycles and still prevents back-hybridization, is computationally equivalent to the original WPCR machine. We also compute the state transition likelihood and the corresponding rate in this protocol. Finally we present a DNA sequence design of a 3-state isothermal and reactivating WPCR machine along with an experimental verification plan.
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