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DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
Branched junction molecule assembly of DNA nanostructures, pioneered by Seeman's laboratory in the 1980s, has become increasingly sophisticated, as have the assembly targets. A critical design step is finding minimal sets of branched…
Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into nanostructures through complementary cohesive strand base pairing. The production of DNA nanostructures is valuable in targeted drug delivery and biomolecular…
Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…
We propose a mathematical model of DNA self-assembly using 2D tiles to form 3D nanostructures. This is the first work to combine studies in self-assembly and nanotechnology in 3D, just as Rothemund and Winfree did in the 2D case. Our model…
This project mathematically models the self-assembly of DNA nanostructures in the shape of select Archimedean graphs using the flexible tile model. Under three different sets of restrictions called scenarios, we employ principles of linear…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
The Watson-Crick complementary properties of DNA make DNA a useful tool for the self-assembly of various target complexes. Concepts from graph theory can be used to model the self-assembling process in which the vertices of the graph…
In soft matter science, it is often the goal to design new materials with targeted properties. These materials can be used in many applications, each requiring specific features to be optimized for maximum fitness. The use of self-assembly…
DNA is an ideal candidate to organize matter on the nanoscale, primarily due to the specificity and complexity of DNA based interactions. Recent advances in this direction include the self-assembly of colloidal crystals using DNA grafted…
DNA nanostructures with programmable shape and interactions can be used as building blocks for the self-assembly of crystalline materials with prescribed nanoscale features, holding a vast technological potential. Structural rigidity and…
Molecular electronics and other technologies whose components comprise individual molecules have been pursued for half a century because the molecular scale represents the limit of miniaturisation of objects whose structure is tuneable for…
The field of DNA nanotechnology has made it possible to assemble, with high yields, different structures that have actionable properties. For example, researchers have created components that can be actuated. An exciting next step is to…
We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs directionally-functionalized with DNA. The…
In recent years there have been a number of proposals to utilize the specificity of DNA based interactions for potential applications in nanoscience. One interesting direction is the self-assembly of micro- and nanoparticle clusters using…
Self-assembly is a process found everywhere in the Nature. In particular, it is known that DNA self-assembly is Turing universal. Thus one can do arbitrary computations or build nano-structures using DNA self-assembly. In order to…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
The early promises of DNA computing to deliver a massively parallel architecture well-suited to computationally hard problems have so far been largely unkept. Indeed, it is probably fair to say that only toy problems have been addressed…
DNA self-assembly is a robust and programmable approach for building structures at nanoscale. Researchers around the world have proposed and implemented different techniques to build two dimensional and three dimensional nano structures.…