Related papers: Simplified amino acid alphabets based on deviation…
The primitive data for deducing the Miyazawa-Jernigan contact energy or BLOSUM score metrix are the pair frequency counts. Each amino acid corresponds to a distribution. Taking the Kullback-Leibler distance of two probability distributions…
Based on the concept of energy landscape a picture of the mismatch between the reduced interaction matrix of residues and the matrix of statistical contact potentials is presented. For the Miyazawa and Jernigan (MJ) matrix, rational…
By using a mixture model for the density distribution of the three pseudobond angles formed by $C_\alpha$ atoms of four consecutive residues, the local structural states are discretized as 17 conformational letters of a protein structural…
In a statistical approach to protein structure analysis, Miyazawa and Jernigan (MJ) derived a $20\times 20$ matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we…
Methods for alignment of protein sequences typically measure similarity by using substitution matrix with scores for all possible exchanges of one amino acid with another. Although widely used, the matrices derived from homologous sequence…
We have considered the problem of protein design based on a model where the contact energy between amino acid residues is fitted phenomenologically using the Miyazawa--Jernigan matrix. Due to the simple form of the contact energy function,…
What are proteins made from, as the working parts of the living cells protein machines? To answer this question, we need a technology to disassemble proteins onto elementary func-tional details and to prepare lumped description of such…
We develop a simple optimization procedure for assigning binary values to the amino acids. The binary values are determined by a maximization of the degree of pattern conservation in groups of closely related protein sequences. The…
In this work it is shown that three pairs of the factors appear to be the key, i.e. main factors of a natural classification of protein (canonical) amino acids within the amino acid (genetic) code. First pair: the factors of the habit of an…
The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same…
All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…
Evolutionary models measure the probability of amino acid substitutions occurring over different evolutionary distances. We examine various evolutionary models based on empirically derived amino acid substitution matrices. The models are…
We investigated the error-minimization properties of putative primordial codes that consisted of 16 supercodons, with the third base being completely redundant, using a previously derived cost function and the error minimization percentage…
We study the designability of all compact 3x3x3 and 6x6 lattice-protein structures using the Miyazawa-Jernigan (MJ) matrix. The designability of a structure is the number of sequences that design the structure, i.e. sequences that have that…
Window profiles of amino acids in protein sequences are taken as a description of the amino acid environment. The relative entropy or Kullback-Leibler distance derived from profiles is used as a measure of dissimilarity for comparison of…
This paper studies the nonterminal complexity of weakly conditional grammars, and it proves that every recursively enumerable language can be generated by a weak conditional grammar with no more than \textit{seven} nonterminals. Moreover,…
Using the crystal basis model of the genetic code, a set of relations between the physical-chemical properties of the amino acids are derived and compared with the experimental data. A prevision for the not yet measured thermodynamical…
We attempt to set a mathematical foundation of immunology and amino acid chains. To measure the similarities of these chains, a kernel on strings is defined using only the sequence of the chains and a good amino acid substitution matrix…
The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the…
Motivation: Protein sequence world is discrete as 20 amino acids (AA) while its structure world is continuous, though can be discretized into structural alphabets (SA). In order to reveal the relationship between sequence and structure, it…