Related papers: The determinism and boundedness of self-assembling…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures.…
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
Amphiphilic molecules spontaneously form self-assembled structures of various shapes depending on their molecular structures, the temperature, and other physical conditions. The functionalities of these structures are dictated by their…
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…
Self-assembly of proteins is a biological phenomenon which gives rise to spontaneous formation of amyloid fibrils or polymers. The starting point of this phase, called nucleation exhibits an important variability among replicated…
Proteins are macromolecules that mediate a significant fraction of the cellular processes that underlie life. An important task in bioengineering is designing proteins with specific 3D structures and chemical properties which enable…
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…
The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling…
Native protein folds often have a high degree of symmetry. We study the relationship between the symmetries of native proteins, and their designabilities -- how many different sequences encode a given native structure. Using a…
A fundamental goal of research in molecular biology is to understand protein structure. Protein crystallography is currently the most successful method for determining the three-dimensional (3D) conformation of a protein, yet it remains…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
Self-assembly of granular particles is of great interest in both applied and basic research. It is commonly observed that when randomly packed into a container, granular particles form disordered structures like glass. As the particles are…
The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress…
We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be…
In the standard DNA brick set-up, distinct 32-nucleotide strands of single-stranded DNA are each designed to bind specifically to four other such molecules. Experimentally, it has been demonstrated that the overall yield is increased if…