Related papers: Are there Unfoldable Proteins in Dimension Three?
We establish the most general form of the discrete elasticity of a 2D triangular lattice embedded in three dimensions, taking into account up to next-nearest neighbour interactions. Besides crystalline system, this is relevant to biological…
The work intends to extend the moir\'e physics to three dimensions. Three-dimensional moir\'e patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a…
A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable.…
A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past…
A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional…
In probability theory, reinforced walks are random walks on a lattice (or more generally a graph) that preferentially revisit neighboring `locations' (sites or bonds) that have been visited before. In this paper, we consider walks with…
Globular proteins are expected to assume folds with fixed secondary structures, alpha-helices and beta-sheets. Fold-switching proteins challenge this expectation by remodeling their secondary and/or tertiary structures in response to…
Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular,…
We use a three dimensional cubic lattice model of proteins to study their properties that determine folding to the native state. The protein chain is modeled as a sequence of $N$ beads. The interactions between beads are taken from a…
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might…
Using a fast tree-searching algorithm and a Pentium cluster, we enumerated all the sequences and compact conformations (structures) for a protein folding model on a cubic lattice of size $4\times3\times3$. We used two types of amino acids…
Proteins experience a wide variety of conformational dynamics that can be crucial for facilitating their diverse functions. How is the intrinsic flexibility required for these motions encoded in their three-dimensional structures? Here, the…
We explore the consequences of very high dimensionality in the dynamical landscape of protein folding. Consideration of both typical range of stabilising interactions, and folding rates themselves, leads to a model of the energy…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
Only about 1,000 qualitatively different protein folds are believed to exist in nature. Here, we review theoretical studies which suggest that some folds are intrinsically more designable than others, {\it i.e.} are lowest energy states of…
On the study of protein folding, our understanding about the protein structures is limited. In this paper we find one way to characterize the compact structures of lattice protein model. A quantity called Partnum is given to each compact…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
Metamorphic proteins like Lymphotactin are a notable exception of the empirical principle that structured natural proteins possess a unique three dimensional structure. In particular, the human chemokine lymphotactin protein (Ltn) exists in…
A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…