Nondeterministic self-assembly with asymmetric interactions

Genotype-phenotype mapping with polyominos made from DNA origami tiles

The correlation between genetic information and characteristics of a living cell-its genotype and its phenotype-constitutes the basis of genetics. Here, we experimentally realize a primitive form of genotype-phenotype mapping with DNA origami. The DNA origami can polymerize into two-dimensional lattices (phenotype) via blunt-end stacking facilitated by edge staples at the seam of the planar DNA origami. There are 80 binding positions for edge staples, which allow us to translate an 80-bit long binary code (genotype) onto the DNA origami. The presence of an edge staple thus corresponds to a "1" and its absence to a "0." The interactions of our DNA-based system can be reproduced by a polyomino model. Polyomino growth simulations qualitatively reproduce our experimental results. We show that not only the absolute number of base stacks but also their sequence position determine the cluster size and correlation length of the orientation of single DNA origami within the cluster. Importantly, the mutation of a few bits can result in major morphology changes of the DNA origami cluster, while more often, major sequence changes have no impact. Our experimental realization of a correlation between binary information ("genotype") and cluster morphology ("phenotype") thus reproduces key properties of genotype-phenotype maps known from living systems.

DNA Nanotechnology for Building Sensors, Nanopores and Ion-Channels

DNA nanotechnology has revolutionised the capabilities to shape and control three-dimensional structures at the nanometre scale. Designer sensors, nanopores and ion-channels built from DNA have great potential for both cross-disciplinary research and applications. Here, we introduce the concept of structural DNA nanotechnology, including DNA origami, and give an overview of the work flow from design to assembly, characterisation and application of DNA-based functional systems. Chemical functionalisation of DNA has opened up pathways to transform static DNA structures into dynamic nanomechanical sensors. We further introduce nanopore sensing as a powerful label-free single-molecule technique and discuss how it can benefit from DNA nanotechnology. Especially exciting is the possibility to create membrane-inserted DNA nanochannels that mimic their protein-based natural counterparts in form and function. In this chapter we review the status quo of DNA sensors, nanopores and ion channels, highlighting opportunities and challenges for their future development.

Determinism and boundedness of self-assembling structures

Self-assembly processes are widespread in nature and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems.

Hidden geometries in networks arising from cooperative self-assembly

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors. Therefore, a comprehensive understanding of these processes is essential for the design of assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with the simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity of the system to accept excess particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, we characterize the emergent structures by metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometric factors and that it can be efficiently modulated by changing the chemical potential and the polydispersity of the binding simplexes.