Related papers: Statistical Properties of Contact Maps

The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue…

The possibility of deriving the contact potentials between amino acids from their frequencies of occurence in proteins is discussed in evolutionary terms. This approach allows the use of traditional thermodynamics to describe such…

We present an efficient algorithm to recover the three dimensional structure of a protein from its contact map representation. First we show that when a physically realizable map is used as target, our method generates a structure whose…

Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…

Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…

Various subsets of self-avoiding walks naturally appear when investigating existing methods designed to predict the 3D conformation of a protein of interest. Two such subsets, namely the folded and the unfoldable self-avoiding walks, are…

We present a statistical approach to protein structure by introducing a representation of protein folds based on simple observables defined as frequencies of oriented cycles in contact graphs. Motivated by the idea that these cycles may…

The classical approach to protein folding inspired by statistical mechanics avoids the high dimensional structure of the conformation space by using effective coordinates. Here we introduce a network approach to capture the statistical…

We study a number of combinatorial and algebraic structures arising from walks on the two-dimensional integer lattice. To a given step set $X\subseteq\mathbb Z^2$, there are two naturally associated monoids: $\mathscr F_X$, the monoid of…

Motivation. Protein contact map describes the pairwise spatial and functional relationship of residues in a protein and contains key information for protein 3D structure prediction. Although studied extensively, it remains very challenging…

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have…

Walks in a directed graph can be given a partially ordered structure that extends to possibly unconnected objects, called hikes. Studying the incidence algebra on this poset reveals unsuspected relations between walks and self-avoiding…

By means of contact-density chain-growth simulations, we investigate a simple lattice model of a flexible polymer interacting with an attractive substrate. The contact density is a function of the numbers of monomer-substrate and…

The $k$-th power of the adjacency matrix of a simple undirected graph represents the number of walks with length $k$ between pairs of nodes. As a walk where no node repeats, a path is a walk where each node is only visited once. The set of…

In protein folding the term plasticity refers to the number of alternative folding pathways encountered in response to free energy perturbations such as those induced by mutation. Here we explore the relation between folding plasticity and…

Physical mechanisms underlying the empirical correlation between relative contact order (CO) and folding rate among naturally-occurring small single-domain proteins are investigated by evaluating postulated interaction schemes for a set of…

The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a…

Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of…

We present a review of a series of contact maps for the determination of native interactions in proteins and nucleic acids based on a distance-threshold. Such contact maps are mostly based on physical and chemical construction, and yet they…