Optimal self-assembly of finite shapes at temperature 1 in 3D

Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for an arbitrary finite, connected shape $X \subset \mathbb{Z}^2$, there is a tile set that uniquely self-assembles into a 3D representation of a scaled-up version of $X$ at temperature 1 in 3D with optimal program-size complexity (the "program-size complexity", also known as "tile complexity", of a shape is the minimum number of tile types required to uniquely self-assemble it). Moreover, our construction is "just barely" 3D in the sense that it only places tiles in the $z = 0$ and $z = 1$ planes. Our result is essentially a just-barely 3D temperature 1 simulation of a similar 2D temperature 2 result by Soloveichik and Winfree (SICOMP 2007)

A population-based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events

Self-assembly, modularity and physical complexity

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures.Comment: 9 pages, submitted for publicatio

Low-cost, bottom-up fabrication of large-scale single-molecule nanoarrays by DNA origami placement

Large-scale nanoarrays of single biomolecules enable high-throughput assays while unmasking the underlying heterogeneity within ensemble populations. Until recently, creating such grids which combine the unique advantages of microarrays and single-molecule experiments (SMEs) has been particularly challenging due to the mismatch between the size of these molecules and the resolution of top-down fabrication techniques. DNA Origami Placement (DOP) combines two powerful techniques to address this issue: (i) DNA origami, which provides a 100-nm self-assembled template for single-molecule organization with 5 nm resolution, and (ii) top-down lithography, which patterns these DNA nanostructures, transforming them into functional nanodevices via large-scale integration with arbitrary substrates. Presently, this technique relies on state-of-the-art infrastructure and highly-trained personnel, making it prohibitively expensive for researchers. Here, we introduce a bench-top technique to create meso-to-macro-scale DNA origami nanoarrays using self-assembled colloidal nanoparticles, thereby circumventing the need for top-down fabrication. We report a maximum yield of 74%, two-fold higher than the statistical limit of 37% imposed on non-specific molecular loading alternatives. Furthermore, we provide a proof-of-principle for the ability of this nanoarray platform to transform traditionally low-throughput, stochastic, single-molecule assays into high-throughput, deterministic ones, without compromising data quality. Our approach has the potential to democratize single-molecule nanoarrays and demonstrates their utility as a tool for biophysical assays and diagnostics

Self-replication and evolution of DNA crystals

Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required

Stretchable, Transparent, Ionic Conductors

Existing stretchable, transparent conductors are mostly electronic conductors. They limit the performance of interconnects, sensors, and actuators as components of stretchable electronics and soft machines. We describe a class of devices enabled by ionic conductors that are highly stretchable, fully transparent to light of all colors, and capable of operation at frequencies beyond 10 kilohertz and voltages above 10 kilovolts. We demonstrate a transparent actuator that can generate large strains and a transparent loudspeaker that produces sound over the entire audible range. The electromechanical transduction is achieved without electrochemical reaction. The ionic conductors have higher resistivity than many electronic conductors; however, when large stretchability and high transmittance are required, the ionic conductors have lower sheet resistance than all existing electronic conductors.Chemistry and Chemical BiologyEngineering and Applied SciencesOther Research Uni

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

Towards New Robust Zn(II) Complexes for the Ring-Opening Polymerization of Lactide Under Industrially Relevant Conditions

The synthesis of bio-based and biodegradable plastics is a hot topic in research due to growing environmental problems caused by omnipresent plastics. As a result, polylactide, which has been known for years, has seen a tremendous increase in industrial production. Nevertheless, the manufacturing process using the toxic catalyst Sn(Oct)2 is very critical. As an alternative, five zinc acetate complexes have been synthesized with Schiff base-like ligands that exhibit high activity in the ring-opening polymerization of non-purified lactide. The systems bear different side arms in the ligand scaffold. The influence of these substituents has been analyzed. For a detailed description of the catalytic activities, the rate constants kapp and kp were determined using in-situ Raman spectroscopy at a temperature of 150 °C. The polymers produced have molar masses of up to 71 000 g mol−1 and are therefore suitable for a variety of applications. Toxicity measurements carried out for these complexes proved the nontoxicity of the systems. © 2019 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA

Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions

The field of algorithmic self-assembly is concerned with the design and analysis of self-assembly systems from a computational perspective, that is, from the perspective of mathematical problems whose study may give insight into the natural processes through which elementary objects self-assemble into more complex ones. One of the main problems of algorithmic self-assembly is the minimum tile set problem (MTSP), which asks for a collection of types of elementary objects (called tiles) to be found for the self-assembly of an object having a pre-established shape. Such a collection is to be as concise as possible, thus minimizing supply diversity, while satisfying a set of stringent constraints having to do with the termination and other properties of the self-assembly process from its tile types. We present a study of what we think is the first practical approach to MTSP. Our study starts with the introduction of an evolutionary heuristic to tackle MTSP and includes results from extensive experimentation with the heuristic on the self-assembly of simple objects in two and three dimensions. The heuristic we introduce combines classic elements from the field of evolutionary computation with a problem-specific variant of Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte

On Applying Molecular Computation to the Data Encryption Standard

Recently, Boneh, Dunworth, and Lipton (1996) described the potential use of molecular computation in attacking the United States Data Encryption Standard (DES), Here, we provide a description of such an attack using the sticker model of molecular computation. Our analysis suggests that such an attack might be mounted on a tabletop machine using approximately a gram of DNA and might succeed even in the presence of a large number of errors