Related papers: Two-dimensional tile displacement can simulate cel…
A physically-motivated genetic algorithm (GA) and full enumeration for a tile-based model of self-assembly (JaTAM) is implemented using a graphics processing unit (GPU). We observe performance gains with respect to state-of-the-art…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Switchable elements are key components of dynamic technological and biological systems, enabling reversible transitions between well-defined states. Here, we present a DNA origami-based, mechanically bistable snap-through mechanism that can…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding…
We present a modular DNA origami design approach to address the challenges of assembling geometrically complex nanoscale structures, including those with nonuniform Gaussian curvature. This approach features a core structure that completely…
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…
Motor-driven cytoskeletal remodeling in cellular systems can often be accompanied by a diffusive-like effect at local scales, but distinguishing the contributions of the ordering process, such as active contraction of a network, from this…
This paper presents a molecular mechanics study for new nanorobotic structures using molecular dynamics (MD) simulations coupled to virtual reality (VR) techniques. The operator can design and characterize through molecular dynamics…
We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided…
We present a suite of algorithmic techniques for handling substitution tilings by treating a tile's hierarchy of supertiles in a purely combinatorial fashion using finite state automata. The resulting techniques are very convenient for…
We propose a novel theoretical biomolecular design to implement any Boolean circuit using the mechanism of DNA strand displacement. The design is scalable: all species of DNA strands can in principle be mixed and prepared in a single test…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
DNA strand displacement is a key reaction in DNA homologous recombination and DNA mismatch repair and is also heavily utilized in DNA-based computation and locomotion. Despite its ubiquity in science and engineering, sequence-dependent…
DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built…
The distribution and interactions of cellular organelles play a critical role in mediating cellular physiology and pathology. Large-scale electron microscopy enables visualization of organelle distribution and interactions at the tissue…
We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are…
Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…
In living systems, DNA undergoes continuous and rhythmic mechanical remodeling through condensation, looping, and disentangling to regulate gene expression, segregate chromosomes, and guide morphogenesis. Here, we demonstrate a purely…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…