Related papers: Are there Unfoldable Proteins in Dimension Three?
E. Gutkin found a remarkable class of convex billiard tables in the plane which have a constant angle invariant curve. In this paper we prove that in dimension 3 only round sphere has such a property. For dimension greater than 3 it must be…
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…
We study the space of all compact structures on a two-dimensional square lattice of size $N=6\times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the…
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last…
Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding…
In order to extend the results obtained with minimal lattice models to more realistic systems, we study a model where proteins are described as a chain of 20 kinds of structureless amino acids moving in a continuum space and interacting…
Mechanical metamaterials have continued to offer unprecedented tunability in mechanical properties, but most designs to date have prioritized attaining high stiffness and strength while sacrificing deformability. The emergence of woven…
In this paper we construct a new family of lattice packings for superballs in three dimensions (unit balls for the $l^p_3$ norm) with $p \in (1, 1.58]$. We conjecture that the family also exists for $p \in (1.58, \log_2 3 =…
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
The primary building block of the body is collagen, which is found in the extracellular matrix and in many stress-bearing tissues such as tendon and cartilage. It provides elasticity and support to cells and tissues while influencing…
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
Evolutionally conserved quantity that specifies folding nuclei is pursued by a case study for a small protein (PDB code: 1ten). First it is demonstrated that the sequences of amino acids at folding nuclei are not conserved. Then 3D…
In this paper we study the dynamics of the constrained $n$--dimensional rigid body (the Suslov problem). We give a review of known integrable cases in three dimensions and present their higher dimensional generalizations.
Recent single-molecule force measurements on single-domain proteins have highlighted a three-state folding mechanism where a stabilized intermediate state (I) is observed on the folding trajectory between the stretched state and the native…
We identify three dimeric proteins whose mechanostability is anisotropic and should exceed 1 nN along some directions. They come with distinct mechanical clamps: shear-based, involving a cystine slipknot, and due to dragging of a cystine…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
See chem-ph/9505003.
Using an off-lattice model, we fully enumerate folded conformations of polypeptide chains of up to N = 19 monomers. Structures are found to differ markedly in designability, defined as the number of sequences with that structure as a unique…
By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…
Many types of peripheral and transmembrane proteins can sense and generate membrane curvature. Laterally isotropic proteins and crescent proteins with twofold rotational symmetry, such as Bin/Amphiphysin/Rvs superfamily proteins, have been…