Collective Construction of 2D Block Structures with Holes

In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures subject to some physical constraints that restrict the order in which the blocks may be attached to the structure. Specifically, we determine a partial ordering on the blocks such that if they are attached in accordance with this ordering, then (i) the structure is a single, connected piece at all intermediate stages of construction, and (ii) no block is attached between two other previously attached blocks, since such a space is too narrow for a robot to maneuver a block into it. Previous work has consider this problem for building 2D structures without holes. Here we extend this work to 2D structures with holes. We accomplish this by modeling the problem as a graph orientation problem and describe an O(n^2) algorithm for solving it. We also describe how this partial ordering may be used in a distributed fashion by the robots to coordinate their actions during the building process.Comment: 13 pages, 3 figure

Autonomously designed free-form 2D DNA origami

Scaffolded DNA origami offers the unique ability to organize molecules in nearly arbitrary spatial patterns at the nanometer scale, with wireframe designs further enabling complex 2D and 3D geometries with irregular boundaries and internal structures. The sequence design of the DNA staple strands needed to fold the long scaffold strand to the target geometry is typically performed manually, limiting the broad application of this materials design paradigm. Here, we present a fully autonomous procedure to design all DNA staple sequences needed to fold any free-form 2D scaffolded DNA origami wireframe object. Our algorithm uses wireframe edges consisting of two parallel DNA duplexes and enables the full autonomy of scaffold routing and staple sequence design with arbitrary network edge lengths and vertex angles. The application of our procedure to geometries with both regular and irregular external boundaries and variable internal structures demonstrates its broad utility for nanoscale materials science and nanotechnology.National Science Foundation (U.S.) (Grant CCF-1564025)National Science Foundation (U.S.) (Grant CMMI-1334109)Office of Naval Research (Grant N000141210621

RNA polyhedrojen algoritminen suunnittelu

The field of bottom-up nanotechnology has been the subject of much research in the recent years. Most of that research has focused on creating nano-scale shapes and structures using multiple strands. DNA origamis and various tile-based schemes are perhaps the most famous examples. No such robust design schemes exist for the design of single stranded RNA structures, however, despite their potential to offer a cheap and sound approach to nanomanufacturing. In this thesis, we study the problem of designing single-stranded RNA polyhedral wireframes, i.e., such RNA strands that fold into the wireframe of a given polyhedron. We introduce a kissing-loop based design scheme, which routes an RNA strand around a spanning tree of a polyhedron, and we show how to do the routing on arbitrary polyhedra while avoiding knots. We also introduce a design tool, Sterna, which is based on these principles. It allows the user to convert a 3D model of a polyhedron into an RNA secondary and tertiary structures, which can be further developed into a primary structure with the additional scripts we have provided. Finally, we design three RNA polyhedra, which are synthesized and imaged in a project related to this master's thesis. The resulting images lend credence to the soundness of Sterna and the underlying design process.Yksi koostavan (engl. bottom-up) nanoteknologian keskeisiä tutkimusalueita viime vuosina on ollut DNA-nanoteknologia, so. nanokokoisten kappaleiden ja rakennelmien tuottaminen biopolymeereistä. Niinsanotut DNA-origamit ja -laatoitukset ovat tämän lähestymistavan tunnetuimpia esimerkkejä. Vastaavaa yleistä menetelmää ei toistaiseksi ole ollut nanorakenteiden tuottamiseen yksisäikeisistä RNA-polymeereistä, vaikka nämä periaatteessa tarjoaisivat edullisen ja skaalautuvan lähtökohdan nanovalmistukselle. Tässä diplomityössä tarkastelemme 3D-monitahokkaiden rautalankamallien laskostamista yksisäikeisistä RNA-polymeereistä. Kehitämme automatisoidun suunnitteluprosessin, joka tuottaa syötteenä annettua monitahokasta vastaavaan muotoon laskostuvan RNA-emästen jonon. Käyttämämme menetelmä perustuu RNA-säikeen reitittämiseen monitahokkaan virittävän puun ympäri ja rakenteen sulkemiseen ns. silmukkapareilla (engl. kissing loop motif). Esitämme myös, miten mielivaltaisen monitahokkaan virittävä puu on mahdollista reitittää tuottamatta topologisia solmuja, jotka estäisivät vastaavan RNA-polymeerin laskostumisen. Toteuttamamme Sterna-suunnitteluohjelman avulla käyttäjä voi tuottaa mistä tahansa 3D-monitahokasmallista sen muotoon laskostuvan RNA-jonon sekundääri- ja tertiäärirakennekuvaukset. Tarjoamme myös ohjelman, jonka avulla nämä voidaan edelleen täydentää emästiedoilla biosynteesiä varten tarvittavaksi RNA-primäärirakenteeksi. Käyttöesimerkkeinä suunnittelemme kolme RNA-monitahokasta, jotka on syntetisoitu ja kuvannettu tämän diplomityön kumppanihankkeissa. Saadut tulokset todentavat suunnittelumenetelmämme ja siihen pohjautuvan Sterna-työkalun oikeellisuutta

Networks, (K)nots, Nucleotides, and Nanostructures

Designing self-assembling DNA nanostructures often requires the identification of a route for a scaffolding strand of DNA through the target structure. When the target structure is modeled as a graph, these scaffolding routes correspond to Eulerian circuits subject to turning restrictions imposed by physical constraints on the strands of DNA. Existence of such Eulerian circuits is an NP-hard problem, which can be approached by adapting solutions to a version of the Traveling Salesperson Problem. However, the author and collaborators have demonstrated that even Eulerian circuits obeying these turning restrictions are not necessarily feasible as scaffolding routes by giving examples of nontrivially knotted circuits which cannot be traced by the unknotted scaffolding strand. Often, targets of DNA nanostructure self-assembly are modeled as graphs embedded on surfaces in space. In this case, Eulerian circuits obeying the turning restrictions correspond to A-trails, circuits which turn immediately left or right at each vertex. In any graph embedded on the sphere, all A-trails are unknotted regardless of the embedding of the sphere in space. We show that this does not hold in general for graphs on the torus. However, we show this property does hold for checkerboard-colorable graphs on the torus, that is, those graphs whose faces can be properly 2-colored, and provide a partial converse to this result. As a consequence, we characterize (with one exceptional family) regular triangulations of the torus containing unknotted A-trails. By developing a theory of sums of A-trails, we lift constructions from the torus to arbitrary n-tori, and by generalizing our work on A-trails to smooth circuit decompositions, we construct all torus links and certain sums of torus links from circuit decompositions of rectangular torus grids. Graphs embedded on surfaces are equivalent to ribbon graphs, which are particularly well-suited to modeling DNA nanostructures, as their boundary components correspond to strands of DNA and their twisted ribbons correspond to double-helices. Every ribbon graph has a corresponding delta-matroid, a combinatorial object encoding the structure of the ribbon-graph\u27s spanning quasi-trees (substructures having exactly one boundary component). We show that interlacement with respect to quasi-trees can be generalized to delta-matroids, and use the resulting structure on delta-matroids to provide feasible-set expansions for a family of delta-matroid polynomials, both recovering well-known expansions of this type (such as the spanning-tree expansion of the Tutte polynnomial) as well as providing several previously unknown expansions. Among these are expansions for the transition polynomial, a version of which has been used to study DNA nanostructure self-assembly, and the interlace polynomial, which solves a problem in DNA recombination

The bracteatus pineapple genome and domestication of clonally propagated crops

Domestication of clonally propagated crops such as pineapple from South America was hypothesized to be a 'one-step operation'. We sequenced the genome of Ananas comosus var. bracteatus CB5 and assembled 513 Mb into 25 chromosomes with 29,412 genes. Comparison of the genomes of CB5, F153 and MD2 elucidated the genomic basis of fiber production, color formation, sugar accumulation and fruit maturation. We also resequenced 89 Ananas genomes. Cultivars 'Smooth Cayenne' and 'Queen' exhibited ancient and recent admixture, while 'Singapore Spanish' supported a one-step operation of domestication. We identified 25 selective sweeps, including a strong sweep containing a pair of tandemly duplicated bromelain inhibitors. Four candidate genes for self-incompatibility were linked in F153, but were not functional in self-compatible CB5. Our findings support the coexistence of sexual recombination and a one-step operation in the domestication of clonally propagated crops. This work guides the exploration of sexual and asexual domestication trajectories in other clonally propagated crops

Understanding Health and Disease with Multidimensional Single-Cell Methods

Current efforts in the biomedical sciences and related interdisciplinary fields are focused on gaining a molecular understanding of health and disease, which is a problem of daunting complexity that spans many orders of magnitude in characteristic length scales, from small molecules that regulate cell function to cell ensembles that form tissues and organs working together as an organism. In order to uncover the molecular nature of the emergent properties of a cell, it is essential to measure multiple cell components simultaneously in the same cell. In turn, cell heterogeneity requires multiple cells to be measured in order to understand health and disease in the organism. This review summarizes current efforts towards a data-driven framework that leverages single-cell technologies to build robust signatures of healthy and diseased phenotypes. While some approaches focus on multicolor flow cytometry data and other methods are designed to analyze high-content image-based screens, we emphasize the so-called Supercell/SVM paradigm (recently developed by the authors of this review and collaborators) as a unified framework that captures mesoscopic-scale emergence to build reliable phenotypes. Beyond their specific contributions to basic and translational biomedical research, these efforts illustrate, from a larger perspective, the powerful synergy that might be achieved from bringing together methods and ideas from statistical physics, data mining, and mathematics to solve the most pressing problems currently facing the life sciences.Comment: 25 pages, 7 figures; revised version with minor changes. To appear in J. Phys.: Cond. Mat

Inference of single-cell phylogenies from lineage tracing data using Cassiopeia.

The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia

GAMIBHEAR: whole-genome haplotype reconstruction from genome architecture mapping data

Motivation: Understanding haplotype-specific regulatory mechanisms becomes increasingly important in genomics and medical research. Investigating differences in allele-specific gene expression, epigenetic changes and their causal variants greatly benefits from haplotype reconstruction or phasing of genetic variants, but direct evidence for the haplotype structure is difficult to obtain from standard short-read sequencing data. Chromatin conformation data obtained from 3C experiments allows inference of haplotypes because inter-chromosomal contacts are more frequent than homologous intra-chromosomal contacts, but these data suffer from technical biases owing to the digestion and ligation process of the 3C technique. Genome Architecture Mapping (GAM) is a novel digestion- and ligation-free method for the inference of chromatin conformation from nuclear cryosections. Due to its high resolution and independence of enzymatic digestion it is well-suited for haplotype reconstruction and for detecting haplotype-specific chromatin contacts. Results: Here, we present GAMIBHEAR, a tool for accurate haplotype reconstruction from GAM data. GAMIBHEAR aggregates allelic co-observation frequencies across multiple nuclear slices and employs a GAM-specific probabilistic model of haplotype capture to optimise phasing accuracy. Using a hybrid mouse embryonic stem cell line with known haplotype structure as a benchmark dataset, we assess correctness and completeness of the reconstructed haplotypes, and demonstrate the power of GAM data and the accuracy of GAMIBHEAR to infer genome-wide haplotypes. Availability: GAMIBHEAR is available as an R package under the open source GPL-2 license at https://bitbucket.org/schwarzlab/gamibhear Maintainer: julia.markowski{at}mdc-berlin.d