scholarly journals n -Nucleotide circular codes in graph theory

2016 ◽  
Vol 374 (2063) ◽  
pp. 20150058 ◽  
Author(s):  
Elena Fimmel ◽  
Christian J. Michel ◽  
Lutz Strüngmann
Keyword(s):  
Graph Theory ◽  
Mathematical Approach ◽  
Code Theory ◽  
Full Generality ◽  
New Approach ◽  
Reading Frame ◽  
Link Type ◽  
Correct Reading ◽  
Circular Codes ◽  
Circular Code

The circular code theory proposes that genes are constituted of two trinucleotide codes: the classical genetic code with 61 trinucleotides for coding the 20 amino acids (except the three stop codons { TAA , TAG , TGA }) and a circular code based on 20 trinucleotides for retrieving, maintaining and synchronizing the reading frame. It relies on two main results: the identification of a maximal C 3 self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses (Michel 2015 J. Theor. Biol. 380, 156–177. ( doi:10.1016/j.jtbi.2015.04.009 ); Arquès & Michel 1996 J. Theor. Biol. 182, 45–58. ( doi:10.1006/jtbi.1996.0142 )) and the finding of X circular code motifs in tRNAs and rRNAs, in particular in the ribosome decoding centre (Michel 2012 Comput. Biol. Chem. 37, 24–37. ( doi:10.1016/j.compbiolchem.2011.10.002 ); El Soufi & Michel 2014 Comput. Biol. Chem. 52, 9–17. ( doi:10.1016/j.compbiolchem.2014.08.001 )). The univerally conserved nucleotides A1492 and A1493 and the conserved nucleotide G530 are included in X circular code motifs. Recently, dinucleotide circular codes were also investigated (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. ( doi:10.1155/2013/538631 ); Fimmel et al. 2015 J. Theor. Biol. 386, 159–165. ( doi:10.1016/j.jtbi.2015.08.034 )). As the genetic motifs of different lengths are ubiquitous in genes and genomes, we introduce a new approach based on graph theory to study in full generality n -nucleotide circular codes X , i.e. of length 2 (dinucleotide), 3 (trinucleotide), 4 (tetranucleotide), etc. Indeed, we prove that an n -nucleotide code X is circular if and only if the corresponding graph is acyclic. Moreover, the maximal length of a path in corresponds to the window of nucleotides in a sequence for detecting the correct reading frame. Finally, the graph theory of tournaments is applied to the study of dinucleotide circular codes. It has full equivalence between the combinatorics theory (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. ( doi:10.1155/2013/538631 )) and the group theory (Fimmel et al. 2015 J. Theor. Biol. 386, 159–165. ( doi:10.1016/j.jtbi.2015.08.034 )) of dinucleotide circular codes while its mathematical approach is simpler.

scholarly journals O-Pair Search with MetaMorpheus for O-glycopeptide Characterization

2020 ◽  
Author(s):  
Lei Lu ◽  
Nicholas M. Riley ◽  
Michael R. Shortreed ◽  
Carolyn R. Bertozzi ◽  
Lloyd M. Smith
Keyword(s):  
Graph Theory ◽  
New Approach ◽  
Confidence Levels ◽  
Link Type ◽  
Processing Software

AbstractWe report O-Pair Search, a new approach to identify O-glycopeptides and localize O-glycosites. Using paired collision- and electron-based dissociation spectra, O-Pair Search identifies O-glycopeptides using an ion-indexed open modification search and localizes O-glycosites using graph theory and probability-based localization. O-Pair Search reduces search times more than 2,000-fold compared to current O-glycopeptide processing software, while defining O-glycosite localization confidence levels and generating more O-glycopeptide identifications. O-Pair Search is freely available: https://github.com/smith-chem-wisc/MetaMorpheus.

scholarly journals Equivalence classes of circular codes induced by permutation groups

2021 ◽  
Vol 140 (1) ◽  
pp. 107-121
Author(s):  
Fariba Fayazi ◽  
Elena Fimmel ◽  
Lutz Strüngmann
Keyword(s):  
Protein A ◽  
Algebraic Approach ◽  
Equivalence Classes ◽  
Finite Alphabet ◽  
Reading Frame ◽  
Biological Reality ◽  
Math Biol ◽  
Circular Codes ◽  
Circular Code ◽  
Translational Process

AbstractIn the 1950s, Crick proposed the concept of so-called comma-free codes as an answer to the frame-shift problem that biologists have encountered when studying the process of translating a sequence of nucleotide bases into a protein. A little later it turned out that this proposal unfortunately does not correspond to biological reality. However, in the mid-90s, a weaker version of comma-free codes, so-called circular codes, was discovered in nature in J Theor Biol 182:45–58, 1996. Circular codes allow to retrieve the reading frame during the translational process in the ribosome and surprisingly the circular code discovered in nature is even circular in all three possible reading-frames ($$C^3$$ C 3 -property). Moreover, it is maximal in the sense that it contains 20 codons and is self-complementary which means that it consists of pairs of codons and corresponding anticodons. In further investigations, it was found that there are exactly 216 codes that have the same strong properties as the originally found code from J Theor Biol 182:45–58. Using an algebraic approach, it was shown in J Math Biol, 2004 that the class of 216 maximal self-complementary $$C^3$$ C 3 -codes can be partitioned into 27 equally sized equivalence classes by the action of a transformation group $$L \subseteq S_4$$ L ⊆ S 4 which is isomorphic to the dihedral group. Here, we extend the above findings to circular codes over a finite alphabet of even cardinality $$|\Sigma |=2n$$ | Σ | = 2 n for $$n \in {\mathbb {N}}$$ n ∈ N . We describe the corresponding group $$L_n$$ L n using matrices and we investigate what classes of circular codes are split into equally sized equivalence classes under the natural equivalence relation induced by $$L_n$$ L n . Surprisingly, this is not always the case. All results and constructions are illustrated by examples.

scholarly journals Circular Tessera Codes in the Evolution of the Genetic Code

2020 ◽  
Vol 82 (4) ◽  
Author(s):  
Elena Fimmel ◽  
Martin Starman ◽  
Lutz Strüngmann
Keyword(s):  
Genetic Code ◽  
Present Form ◽  
The Other ◽  
Translation Process ◽  
Reading Frame ◽  
Other Hand ◽  
Correct Reading ◽  
Circular Codes ◽  
The One ◽  
Mitochondrial Code

Abstract The origin of the modern genetic code and the mechanisms that have contributed to its present form raise many questions. The main goal of this work is to test two hypotheses concerning the development of the genetic code for their compatibility and complementarity and see if they could benefit from each other. On the one hand, Gonzalez, Giannerini and Rosa developed a theory, based on four-based codons, which they called tesserae. This theory can explain the degeneracy of the modern vertebrate mitochondrial code. On the other hand, in the 1990s, so-called circular codes were discovered in nature, which seem to ensure the maintenance of a correct reading-frame during the translation process. It turns out that the two concepts not only do not contradict each other, but on the contrary complement and enrichen each other.

scholarly journals Controllability and Observability of a Large Scale Thermodynamical System via Connectability Approach

2010 ◽  
Author(s):  
Virdiansyah Permana ◽  
Rahmat Shoureshi
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Large Scale ◽  
Point Of View ◽  
Rank Condition ◽  
Computational Point ◽  
New Approach ◽  
Class System ◽  
Necessary And Sufficient ◽  
Controllability And Observability

This study presents a new approach to determine the controllability and observability of a large scale nonlinear dynamic thermal system using graph-theory. The novelty of this method is in adapting graph theory for nonlinear class and establishing a graphic condition that describes the necessary and sufficient terms for a nonlinear class system to be controllable and observable, which equivalents to the analytical method of Lie algebra rank condition. The directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and observability condition are investigated through the structural property of a digraph called connectability. It will be shown that the connectability condition between input and states, as well as output and states of a nonlinear system are equivalent to Lie-algebra rank condition (LARC). This approach has been proven to be easier from a computational point of view and is thus found to be useful when dealing with a large system.

scholarly journals The proteome: structure, function and evolution

2006 ◽  
Vol 361 (1467) ◽  
pp. 441-451 ◽  
Author(s):  
Keiran Fleming ◽  
Lawrence A Kelley ◽  
Suhail A Islam ◽  
Robert M MacCallum ◽  
Arne Muller ◽  
...  
Keyword(s):  
Protein Function ◽  
Sequence Similarity ◽  
Structural Annotation ◽  
New Approach ◽  
Link Type ◽  
University College London ◽  
Automated Pipeline ◽  
3D Genomics ◽  
And Function ◽  
Structural Homologue

This paper reports two studies to model the inter-relationships between protein sequence, structure and function. First, an automated pipeline to provide a structural annotation of proteomes in the major genomes is described. The results are stored in a database at Imperial College, London (3D-GENOMICS) that can be accessed at www.sbg.bio.ic.ac.uk . Analysis of the assignments to structural superfamilies provides evolutionary insights. 3D-GENOMICS is being integrated with related proteome annotation data at University College London and the European Bioinformatics Institute in a project known as e-protein ( http://www.e-protein.org/ ). The second topic is motivated by the developments in structural genomics projects in which the structure of a protein is determined prior to knowledge of its function. We have developed a new approach PHUNCTIONER that uses the gene ontology (GO) classification to supervise the extraction of the sequence signal responsible for protein function from a structure-based sequence alignment. Using GO we can obtain profiles for a range of specificities described in the ontology. In the region of low sequence similarity (around 15%), our method is more accurate than assignment from the closest structural homologue. The method is also able to identify the specific residues associated with the function of the protein family.

scholarly journals A New Technique to Solve the Instant Insanity Problem

2016 ◽  
Vol 11 (10) ◽  
pp. 5766-5773
Author(s):  
Salar Y Alsardary ◽  
Hwee Jung Kim ◽  
Julie George
Keyword(s):  
Graph Theory ◽  
Programming Language ◽  
New Technique ◽  
New Approach ◽  
A New Technique

Instant Insanity [1] consists of four cubes, each of whose six faces are colored with one of the four colors: red, blue, white, and green. The object is to stack the cubes in such a way that each of the four colors appears on each side of the resulting column. See figure 1 below[2]. Traditionally, this could be solved using graph theory.However, in this article, we introduce a new technique to solve the problem without using graph theory. We also used a Perl programming language to implement the new approach for the Instant Insanity.

The 3D graph approach for breakdown voltage calculation in BaTiO3 ceramics

2021 ◽  
pp. 2150103
Author(s):  
Vojislav V. Mitic ◽  
Branislav Randjelovic ◽  
Ivana Ilic ◽  
Srdjan Ribar ◽  
An-Lu Chun ◽  
...  
Keyword(s):  
Graph Theory ◽  
Crystal Structures ◽  
Breakdown Voltage ◽  
Main Idea ◽  
Experimental Results ◽  
Grain Structure ◽  
Mathematical Approach ◽  
Electronic Parameters ◽  
Mathematical Graph

After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

scholarly journals Graph cutting and its application to biological data

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 468-479
Author(s):  
Mária Ždímalová ◽  
Ján Major ◽  
Martin Kopáni
Keyword(s):  
Graph Theory ◽  
Biological Data ◽  
Biomedical Data ◽  
Mathematical Approach ◽  
The Family ◽  
The Brain

Abstract In this paper we introduce the concept of segmentation based on mathematical approach using graph theory algorithms using the family of augmenting paths algorithms. We present a new program, an implementation, algorithms and obtained results devoted to segmentation of biomedical data. We implement our program for handling with segmentation, counting a measure of the existence of the minerals in the biomedical data. As a consequence we prove the existence of minerals in the data obtained from the brain of rabbits.

scholarly journals Single-Frame, Multiple-Frame and Framing Motifs in Genes

Life ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 18 ◽  
Author(s):  
Christian J. Michel
Keyword(s):  
Amino Acids ◽  
Early Life ◽  
Double Helix ◽  
Research Field ◽  
Reading Frame ◽  
Single Frame ◽  
The Origin Of Life ◽  
Multiple Frame ◽  
Dna Double Helix ◽  
Circular Code

We study the distribution of new classes of motifs in genes, a research field that has not been investigated to date. A single-frame motif SF has no trinucleotide in reading frame (frame 0) that occurs in a shifted frame (frame 1 or 2), e.g., the dicodon AAACAA is SF as the trinucleotides AAA and CAA do not occur in a shifted frame. A motif which is not single-frame SF is multiple-frame MF. Several classes of MF motifs are defined and analysed. The distributions of single-frame SF motifs (associated with an unambiguous trinucleotide decoding in the two 5'–3' and 3'–5' directions) and 5′ unambiguous motifs 5'U (associated with an unambiguous trinucleotide decoding in the 5'–3' direction only) are analysed without and with constraints. The constraints studied are: initiation and stop codons, periodic codons AAA,CCC,GGG,TTT, antiparallel complementarity and parallel complementarity. Taken together, these results suggest that the complementarity property involved in the antiparallel (DNA double helix, RNA stem) and parallel sequences could also be fundamental for coding genes with an unambiguous trinucleotide decoding in the two 5'–3' and 3'–5' directions or the 5'–3' direction only. Furthermore, the single-frame motifs SF with a property of trinucleotide decoding and the framing motifs F (also called circular code motifs; first introduced by Michel (2012)) with a property of reading frame decoding may have been involved in the early life genes to build the modern genetic code and the extant genes. They could have been involved in the stage without anticodon-amino acid interactions or in the Implicated Site Nucleotides (ISN) of RNA interacting with the amino acids. Finally, the SF and MF dipeptides associated with the SF and MF dicodons, respectively, are studied and their importance for biology and the origin of life discussed.

Sign in / Sign up

Export Citation Format

Share Document