Author Correction: Diverse and robust molecular algorithms using reprogrammable DNA self-assembly.

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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 products1 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 processes2,3, and this has been experimentally demonstrated using DNA nanotechnology4 with up to 22 tile types5-11. 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.

Deterministic Function Computation with Chemical Reaction Networks.

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of "eventually periodic" sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕ k → ℕ l by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some "input" species X1, …, Xk , the CRN is guaranteed to converge to having f(x1, …, xk ) molecules of the "output" species Y1, …, Yl . We show that a function f : ℕ k → ℕ l is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕ k × â„• l ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1).

Programming Substrate-Independent Kinetic Barriers With Thermodynamic Binding Networks.

Engineering molecular systems that exhibit complex behavior requires the design of kinetic barriers. For example, an effective catalytic pathway must have a large barrier when the catalyst is absent. While programming such energy barriers seems to require knowledge of the specific molecular substrate, we develop a novel substrate-independent approach. We extend the recently-developed model known as thermodynamic binding networks, demonstrating programmable kinetic barriers that arise solely from the thermodynamic driving forces of bond formation and the configurational entropy of forming separate complexes. Our kinetic model makes relatively weak assumptions, which implies that energy barriers predicted by our model would exist in a wide variety of systems and conditions. We demonstrate that our model is robust by showing that several variations in its definition result in equivalent energy barriers. We apply this model to design catalytic systems with an arbitrarily large energy barrier to uncatalyzed reactions. Our results could yield robust amplifiers using DNA strand displacement, a popular technology for engineering synthetic reaction pathways, and suggest design strategies for preventing undesired kinetic behavior in a variety of molecular systems.

Designing ordered nucleic acid self-assembly processes.

A major goal of self-assembly research is the synthesis of biomolecular structures with diverse, intricate features across multiple length scales. Designing self-assembly processes becomes more difficult as the number of species or target structure size increases. Just as the ordered assembly of a machine or device makes complex manufacturing possible, ordered (or 'algorithmic') biomolecular self-assembly processes could enable the self-assembly of more complex structures. We discuss the design of ordered assembly processes with particular attention to DNA and RNA. The assembly of complexes can be ordered using selective, multivalent interactions or active components that change shape after assembly. The self-assembly of spatial gradients driven by reaction-diffusion can also be ordered. We conclude by considering topics for future research.

An exploratory approach to self-blame and self-derogation by rape victims.

Quantitative and interview data on rape victims' self-evaluation and attributions of personal responsibility were studied to explore the relevance of theories of "defensive attribution" and maintenance of belief in a "just world." Clinical implications of the findings for adjustment of victims, counseling, victim compensation, and the legal system are discussed.

Reproducibility of linear tumor measurements using PACS: comparison of caliper method with edge-tracing method.

The aim of this study was to evaluate inter- and intra-observer reproducibility when making electronic caliper linear tumor measurements on picture archiving and communications systems (PACS) and compare them with linear measurements obtained from circumferential tracing of tumor perimeter. Three radiologists measured 64 masses from 30 patients on body CT scans in two separate settings. Long axis and perpendicular short axis were measured using electronic calipers. The edge of each tumor was traced electronically and the long and short axes were calculated by computer software. The reproducibility of a measurement was evaluated by computing and comparing the absolute value of the mean difference between initial and subsequent measurements. The mean differences +/-95% confidence interval (CI) between two measurements of the long by short axis were 3.8+/-2.6x3.1+/-1.8 mm when the caliper method was used and 3.5+/-2.0x3.2+/-1.5 mm when the tumor tracing method was used. There was no statistically significant difference in individual intra-observer reproducibility of tumor axes measurements. Neither long- nor short-axis single-dimension measurements resulted in significantly greater or lesser intra-observer reproducibility. When comparing caliper and tracing measurements, the overall mean difference (3.42+/-1.8 vs 3.38+/-1.4 mm) was not statistically significant. There was close correlation between the individual measurements made by each observer whether these were made by electronic calipers and when these were calculated from electronic tracings (Pearson correlations between 0.79 and 0.949). Current PACS systems allow reproducible linear, long or short axis, tumor measurements. There is no significant difference in reproducibility of measurements whether these are made directly with electronic calipers or calculated from tumor edge tracings.

Age-related vascular changes in the epiphysis, physis, and metaphysis: normal findings on gadolinium-enhanced MRI of piglets.

OBJECTIVE: We sought to study the normal enhancement patterns seen on MRIs of the epiphysis, physis, and metaphysis and age-related vascular changes in piglets using gadoteridol, a nonionic gadolinium chelate. MATERIALS AND METHODS: We quantitatively and qualitatively analyzed the normal changes on sequential T1-weighted images after the IV administration of gadoteridol. In an investigation approved by the research animal care committee at our hospital, we studied the proximal and distal femurs of 26 piglets 1-6 weeks old and correlated the enhanced images with findings on intermediate-weighted, T2-weighted, and gradient-recalled echo images and at histologic examination. RESULTS: We observed early enhancement of the epiphyseal vascular canals, the main physis, the physis of the secondary ossification center, and a metaphyseal band adjacent to the physis. Enhancement of the epiphyseal and metaphyseal marrow and of the epiphyseal cartilage was slower. In the epiphyseal cartilage, we saw three phases of enhancement: vascular, canalicular, and cartilaginous. As the piglets matured, enhancement of the epiphyseal cartilage decreased, and the epiphyseal vascular canals were less conspicuous. Physeal enhancement was greatest during the first week of life, declined at 3 weeks, and subsequently increased again as the physis came to lie adjacent to a larger segment of the epiphyseal ossification center. CONCLUSION: Gadoteridol-enhanced MRIs showed multiple cartilaginous and vascular structures of the growing skeleton. With maturity and progressive epiphyseal ossification, epiphyseal cartilage enhancement decreased, and physeal cartilage enhancement increased.