Diverse and robust molecular algorithms using reprogrammable DNA self-assembly

Molecular biology provides an inspiring proof-of-principle that chemical systems can store and process information to direct molecular activities such as the fabrication of complex structures from molecular components. To develop information-based chemistry as a technology for programming matter to function in ways not seen in biological systems, it is necessary to understand how molecular interactions can encode and execute algorithms. The self-assembly of relatively simple units into complex products is particularly well suited for such investigations. Theory that combines mathematical tiling and statistical–mechanical models of molecular crystallization has shown that algorithmic behaviour can be embedded within molecular self-assembly processes, and this has been experimentally demonstrated using DNA nanotechnology with up to 22 tile types. However, many information technologies exhibit a complexity threshold—such as the minimum transistor count needed for a general-purpose computer—beyond which the power of a reprogrammable system increases qualitatively, and it has been unclear whether the biophysics of DNA self-assembly allows that threshold to be exceeded. Here we report the design and experimental validation of a DNA tile set that contains 355 single-stranded tiles and can, through simple tile selection, be reprogrammed to implement a wide variety of 6-bit algorithms. We use this set to construct 21 circuits that execute algorithms including copying, sorting, recognizing palindromes and multiples of 3, random walking, obtaining an unbiased choice from a biased random source, electing a leader, simulating cellular automata, generating deterministic and randomized patterns, and counting to 63, with an overall per-tile error rate of less than 1 in 3,000. These findings suggest that molecular self-assembly could be a reliable algorithmic component within programmable chemical systems. The development of molecular machines that are reprogrammable—at a high level of abstraction and thus without requiring knowledge of the underlying physics—will establish a creative space in which molecular programmers can flourish

Digital Sensing and Molecular Computation by an Enzyme-Free DNA Circuit.

DNA circuits form the basis of programmable molecular systems capable of signal transduction and algorithmic computation. Some classes of molecular programs, such as catalyzed hairpin assembly, enable isothermal, enzyme-free signal amplification. However, current detection limits in DNA amplification circuits are modest, as sensitivity is inhibited by signal leakage resulting from noncatalyzed background reactions inherent to the noncovalent system. Here, we overcome this challenge by optimizing a catalyzed hairpin assembly for single-molecule sensing in a digital droplet assay. Furthermore, we demonstrate digital reporting of DNA computation at the single-molecule level by employing ddCHA as a signal transducer for simple DNA logic gates. By facilitating signal transduction of molecular computation at pM concentration, our approach can improve processing density by a factor of 104 relative to conventional DNA logic gates. More broadly, we believe that digital molecular computing will broaden the scope and efficacy of isothermal amplification circuits within DNA computing, biosensing, and signal amplification in general

Verification in Generalizations of the 2-Handed Assembly Model

Algorithmic Self Assembly is a well studied field in theoretical computer science motivated by the analogous real world phenomenon of DNA self assembly, as well as the emergence of nanoscale technology. Abstract mathematical models of self assembly such as the Two Handed Assembly model (2HAM) allow us to formally study the computational capabilities of self assembly. The 2HAM is one of the most thoroughly studied models of self assembly, and thus in this paper we study generalizations of this model. The Staged Tile Assembly model captures the behavior of being able to separate assembly processes and combine their outputs at a later time. The k-Handed Assembly Model relaxes the restriction of the 2HAM that only two assemblies can combine in one assembly step. The 2HAM with prebuilt assemblies considers the idea that you can start your assembly process with some prebuilt structures. These generalizations relax some rules of the 2HAM, in ways which reflect real world self assembly mechanics and capabilities. We investigate the complexity of verification problems in these new models, such as the problem of verifying whether a system produces a specified assembly (Producibility), and verifying whether a system uniquely assembles a specified assembly (Unique Assembly Verification). We show that these generalizations introduce a high amount of intractability to these verification problems

Computational Complexity in Tile Self-Assembly

One of the most fundamental and well-studied problems in Tile Self-Assembly is the Unique Assembly Verification (UAV) problem. This algorithmic problem asks whether a given tile system uniquely assembles a specific assembly. The complexity of this problem in the 2-Handed Assembly Model (2HAM) at a constant temperature is a long-standing open problem since the model was introduced. Previously, only membership in the class coNP was known and that the problem is in P if the temperature is one (τ = 1). The problem is known to be hard for many generalizations of the model, such as allowing one step into the third dimension or allowing the temperature of the system to be a variable, but the most fundamental version has remained open. In this Thesis I will cover verification problems in different models of self-assembly leading to the proof that the UAV problem in the 2HAM is hard even with a small constant temperature (τ = 2), and finally answer the complexity of this problem (open since 2013). Further, this result proves that UAV in the staged self-assembly model is coNP-complete with a single bin and stage (open since 2007), and that UAV in the q-tile model is also coNP-complete (open since 2004). We reduce from Monotone Planar 3-SAT with Neighboring Variable Pairs, a special case of 3SAT recently proven to be NP-hard

Purification of DNA Origami Nanostructures Using Capillary Electrophoresis

DNA origami are nanostructures designed based on Watson-Crick base-pairing that fold a scaffold into non-arbitrary morphologies using an excess of linear single-stranded DNA staples . As an engineered nanomaterial (ENM) with great customizability, DNA origami also enjoys the benefit of naturally encoded and well-studied structural and functional properties. The flexibility of different folding patterns allows for construction of a wide variety of shapes and sizes of DNA origami, showing potential applications in fields such as medicine, biocomputing, biomedical engineering , and measurement science. Despite the successes as a functional nanomaterial, a major barrier to the applicability of DNA origami rests in the lack of pure, well-folded structures. As such, the development of different purification techniques is essential to support the rapid development of the material toward a vast scope of applications. Current techniques to purify DNA origami from excess precursors (staples), misfolded structures and other impurities have shown low yields, low scalability, tendency for aggregated samples, and lack optimization for automation. Capillary electrophoresis (CE) has previously shown effective separation of single-stranded DNA based on differences of size and charge in a manner similar to gel electrophoresis, but with the added benefit of automation and more substantial control and detection throughout the separation. The development of CE as a purification technique for DNA origami is investigated in this study, where a highly reproducible separation between folded DNA origami from excess DNA staples was achieved by manipulating and understanding the effect of buffer conditions , capillary specifications , and injection parameters on the electropherogram profile. Specifically , CE was investigated under both capillary zone electrophoresis (CZE) and capillary transient isotachophoresis (ctITP) modes, and optimization of both systems yielded baseline resolved separations of DNA origami from the staple strands. The ctITP system demonstrated superior performance in terms of decreasing band broadening, improving resolution, and improving the Gaussian character of migration peaks. Further, the optimized ctITP separation was used in a fraction collection procedure, where the resulting fractions were imaged by atomic force microscopy (AFM) for offline validation of purified structures. However, issues with the intercalating dye and origami aggregation were suspected to impede the imaging process. The reproducibility of the fraction collection procedure was validated to show a highly linear relationship between the peak area of a reinjection of pooled sample and the number of pooled fractions. An approach to calculating the percent yield of CE-based purification was attempt ed but requires further validation. Continued exploration and analysis of CE for the purification of DNA origami could thus lead to a novel , promising, and efficient tool to advance the field as a whole