Related papers: The difficulty of folding self-folding origami
We review theoretical approaches, experiments and numerical simulations that have been recently proposed to investigate the folding problem in single-domain proteins. From a theoretical point of view, we emphasize the energy landscape…
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way,…
The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the…
The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to…
An edge tessellation is a tiling of the plane generated by reflecting a polygon in its edges. We prove that a polygon generating an edge tessellation is one the following eight types: a rectangle; an equilateral, 60-right, isosceles right,…
The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation,…
The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…
A common metaphor for describing development is a rugged "epigenetic landscape" where cell fates are represented as attracting valleys resulting from a complex regulatory network. Here, we introduce a framework for explicitly constructing…
Nucleation is the rate-determining step in the kinetics of many self-assembly processes. However, the importance of nucleation in the kinetics of DNA-origami self-assembly, which involves both the binding of staple strands and the folding…
Using a mathematical model for self-foldability of rigid origami, we determine which monohedral quadrilateral tilings of the plane are uniquely self-foldable. In particular, the Miura-ori and Chicken Wire patterns are not self-foldable…
Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or…
Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and…
Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities…
In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers…
The study of origami-based mechanical metamaterials usually focuses on the kinematics of deployable structures made of an assembly of rigid flat plates connected by hinges. When the elastic response of each panel is taken into account,…
Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First,…
Origami, which transforms flat sheets into three-dimensional shapes through folding patterns, has inspired the emergence of deployable systems in architecture and civil realms. Most existing origami-inspired deployable systems are based on…
Understanding the principles of protein folding is a cornerstone of computational biology, with implications for drug design, bioengineering, and the understanding of fundamental biological processes. Lattice protein folding models offer a…