Related papers: A modular Fibonacci sequence in proteins
The remarkable structural diversity of modern proteins reflects millions of years of evolution, during which sequence space has expanded while many structural features remain conserved. This conservation is evident not only among homologous…
Protein one-dimensional (1D) structures such as secondary structure and contact number provide intuitive pictures to understand how the native three-dimensional (3D) structure of a protein is encoded in the amino acid sequence. However, it…
Most amino acids are encoded by multiple synonymous codons. For an amino acid, some of its synonymous codons are used much more rarely than others. Analyses of positions of such rare codons in protein sequences revealed that rare codons can…
The Fibonacci sequence $\mathbb{F}$ is the fixed point beginning with $a$ of morphism $\sigma(a,b)=(ab,a)$. Since $\mathbb{F}$ is uniformly recurrent, each factor $\omega$ appears infinite many times in the sequence which is arranged as…
In the protein sequence space, natural proteins form clusters of families which are characterized by their unique native folds whereas the great majority of random polypeptides are neither clustered nor foldable to unique structures. Since…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length…
A method based on mapping a symbolic sequence into a set of patterns (strings resulting from the sequence parsing) is proposed as a tool for the reconstruction of ancestral sequences. The set union of patterns comprises all the patterns…
One of the most puzzling and unsolved challenges in molecular biology is understanding how proteins fold. Despite having advanced predictive tools that can accurately estimate the native structures of proteins, we still lack a comprehensive…
This paper presents, for the first time, four diversity types of protein amino acids. The first type includes two amino acids (G, P), both without standard hydrocarbon side chains; the second one four amino acids, as two pairs [(A, L), (V,…
The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also…
The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end…
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict distinction in Genetic Code Table (GCT) into some different quantums: 20, 23, 61 amino acid molecules. These molecules…
This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA…
The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical sequences $a(n)$ defined by Fibonacci-like recursions: the…
The Fibonacci sequence $\mathbb{F}$ is the fixed point beginning with $a$ of morphism $\sigma(a,b)=(ab,a)$. In this paper, we get the explicit expressions of all squares and cubes, then we determine the number of distinct squares and cubes…
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…
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…
Motivation: 3D structures of proteins provide rich information for understanding their biochemical roles. Identifying the representative protein structures for protein sequences is essential for analysis of proteins at proteome scale.…
A $K$-Fibonacci sequence is a binary recurrence sequence where $F_0=0$, $F_1=1$, and $F_n=K\cdot F_{n-1}+F_{n-2}$. These sequences are known to be periodic modulo every positive integer greater than $1$. If the length of one shortest period…