Related papers: Are there Unfoldable Proteins in Dimension Three?
The folding kinetics of three-dimensional lattice Go models with side chains is studied using two different Monte Carlo move sets. A flexible move set based on single, double and triple backbone moves is found to be far superior compared to…
Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is…
Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein's linear sequence of amino acids folds into its specific three dimensional structure.This structure is…
A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the…
We study the high-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular…
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
Intricate comparison between two given tertiary structures of proteins is as important as the comparison of their functions. Several algorithms have been devised to compute the similarity and dissimilarity among protein structures. But,…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant $\mathbb{N}^3$. For the $35548$ non-trivial models with at most six steps, they found that many models associated to a group of order at…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the…
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
Recent advances in coarse-grained lattice and off-lattice protein models are reviewed. The sequence dependence of thermodynamical folding properties are investigated and evidence for non-randomness of the binary sequences of good folders…
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of…
When interacting electrons are confined to low-dimensions, the electron-electron correlation effect is enhanced dramatically, which often drives the system into exhibiting behaviors that are otherwise highly improbable. Superconductivity…