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Keywords = genetic code symmetry

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13 pages, 562 KiB  
Article
Relative Fluctuating Asymmetry and Predictive Metrics of Cast Antler Pairs in White-Tailed Deer (Odocoileus virginianus)
by Brian C. Peterson, Patrick D. Farrell and Casey W. Schoenebeck
Symmetry 2024, 16(10), 1301; https://doi.org/10.3390/sym16101301 - 3 Oct 2024
Viewed by 730
Abstract
Antlers are genetically coded to have bilateral symmetry. However, environmental stressors cause asymmetries between antlers. Previous studies have investigated fluctuating asymmetries on harvested white-tailed deer (Odocoileus virginianus Zimmermann, 1780). Cast antlers provide underutilized metrics that are not available prior to shedding. The [...] Read more.
Antlers are genetically coded to have bilateral symmetry. However, environmental stressors cause asymmetries between antlers. Previous studies have investigated fluctuating asymmetries on harvested white-tailed deer (Odocoileus virginianus Zimmermann, 1780). Cast antlers provide underutilized metrics that are not available prior to shedding. The objectives of this study were to quantify relative fluctuating asymmetry (RFA) between age groups and identify the best age-specific pre- and post-cast antler metrics to confirm an antler pair. We hypothesized lower RFA values for post-cast measurements than pre-cast measurements due to a lessened chance for damage when atop the head. Additionally, younger individuals were hypothesized to have higher RFA values due to greater susceptibility to environmental stressors. Cast antler pairs from 196 white-tailed deer were collected in Nebraska. We measured 14 available antler metrics per cast antler side classified by age group. The most symmetric measurements between antler sides included pedicle seal area, main beam length, and circumference. Antlers of older deer were consistently more symmetric than younger deer. When combining the top metrics and testing against random antler pairs, we found an 81.9–92.3% match rate for 1.5 and ≥2.5-year-olds, respectively. Our findings provided a quantifiable method to assign antler pair classifications more confidently while documenting decreased symmetry in younger individuals. Full article
(This article belongs to the Section Life Sciences)
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22 pages, 4103 KiB  
Article
Maximal Genetic Code Symmetry Is a Physicochemical Purine–Pyrimidine Symmetry Language for Transcription and Translation in the Flow of Genetic Information from DNA to Proteins
by Marija Rosandić and Vladimir Paar
Int. J. Mol. Sci. 2024, 25(17), 9543; https://doi.org/10.3390/ijms25179543 - 2 Sep 2024
Viewed by 876
Abstract
Until now, research has not taken into consideration the physicochemical purine–pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. [...] Read more.
Until now, research has not taken into consideration the physicochemical purine–pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. Its basic structure is a purine–pyrimidine symmetry net with double mirror symmetry. Accordingly, the symmetry of the genetic code directly shows its organisation based on the principle of nucleotide Watson–Crick and codon–anticodon pairing. The maximal purine–pyrimidine symmetries of codons show that each codon has a strictly defined and unchangeable position within the genetic code. We discovered that the physicochemical symmetries of the genetic code play a fundamental role in recognising and differentiating codons from mRNA and the anticodon tRNA and aminoacyl-tRNA synthetases in the transcription and translation processes. These symmetries also support the wobble hypothesis with non-Watson–Crick pairing interactions between the translation process from mRNA to tRNA. The Supersymmetry Genetic Code table shows a specific arrangement of the second base of codons, according to which it is possible that an anticodon from tRNA recognises whether a codon from mRNA belongs to an amino acid with two or four codons, which is very important in the purposeful use of the wobble pairing process. Therefore, we show that canonical and wobble pairings essentially do not lead to misreading and errors during translation, and we point out the role of physicochemical purine–pyrimidine symmetries in decreasing disorder according to error minimisation and preserving the integrity of biological processes during proteinogenesis. Full article
(This article belongs to the Section Molecular Genetics and Genomics)
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13 pages, 2079 KiB  
Article
A Genetic Algorithm for Three-Dimensional Discrete Tomography
by Elena Toscano and Cesare Valenti
Symmetry 2024, 16(7), 923; https://doi.org/10.3390/sym16070923 - 19 Jul 2024
Viewed by 751
Abstract
Discrete tomography is a specific case of computerized tomography that deals with the reconstruction of objects made of a few density values on a discrete lattice of points (integer valued coordinates). In the general case of computerized tomography, several hundreds of projections are [...] Read more.
Discrete tomography is a specific case of computerized tomography that deals with the reconstruction of objects made of a few density values on a discrete lattice of points (integer valued coordinates). In the general case of computerized tomography, several hundreds of projections are required to obtain a single high-resolution slice of the object; in the case of discrete tomography, projections of an object made by just one homogeneous material are sums along very few angles of the pixel values, which can be thought to be 0’s or 1’s without loss of generality. Genetic algorithms are global optimization techniques with an underlying random approach and, therefore, their convergence to a solution is provided in a probabilistic sense. We present here a genetic algorithm able to straightforwardly reconstruct binary objects in the three-dimensional space. To the best of our knowledge, our methodology is the first to require no model of the shape (e.g., periodicity, convexity or symmetry) to reconstruct. Experiments were carried out to test our new approach in terms of computational time and correctness of the solutions. Over the years, discrete tomography has been studied for many interesting applications to computer vision, non-destructive reverse engineering and industrial quality control, electron microscopy, X-rays crystallography, biplane angiography, data coding and compression. Full article
(This article belongs to the Special Issue Feature Papers in Mathematics Section)
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22 pages, 574 KiB  
Article
Fibonacci-like Sequences Reveal the Genetic Code Symmetries, Also When the Amino Acids Are in a Physiological Environment
by Tidjani Négadi
Symmetry 2024, 16(3), 293; https://doi.org/10.3390/sym16030293 - 2 Mar 2024
Cited by 2 | Viewed by 2675
Abstract
In this study, we once again use a set of Fibonacci-like sequences to examine the symmetries within the genetic code. This time, our focus is on the physiological state of the amino acids, considering them as charged, in contrast to our previous work [...] Read more.
In this study, we once again use a set of Fibonacci-like sequences to examine the symmetries within the genetic code. This time, our focus is on the physiological state of the amino acids, considering them as charged, in contrast to our previous work where they were seen as neutral. In a pH environment around 7.4, there are four charged amino acids. We utilize the properties of our sequences to accurately describe the symmetries in the genetic code table. These include Rumer’s symmetry, the third-base symmetry and the “ideal” symmetry, along with the “supersymmetry” classification schemes. We also explore the special chemical structure of the amino acid proline, presenting two perspectives—shCherbak’s view and the Downes–Richardson view—which are included in the description of the above-mentioned symmetries. Our investigation also employs elementary modular arithmetic to precisely describe the chemical structure of proline, connecting the two views seamlessly. Finally, our Fibonacci-like sequences prove instrumental in quickly establishing the multiplet structure of non-standard versions of the genetic code. We illustrate this with an example, showcasing the efficiency of our method in unraveling the complex relationships within the genetic code. Full article
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16 pages, 4084 KiB  
Article
The Supersymmetry Genetic Code Table and Quadruplet Symmetries of DNA Molecules Are Unchangeable and Synchronized with Codon-Free Energy Mapping during Evolution
by Marija Rosandić and Vladimir Paar
Genes 2023, 14(12), 2200; https://doi.org/10.3390/genes14122200 - 12 Dec 2023
Cited by 4 | Viewed by 1431
Abstract
The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the [...] Read more.
The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the form of codons; (3) direct–complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns; (4) A + T-rich and C + G-rich alternate codons in the same row between both columns of the genetic code; (5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axis. The SSyGC table has a unique physicochemical purine–pyrimidine symmetry net which is as the core symmetry common for all, with more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries are present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here, we show that the free energy value of each codon incorporated as fundamentally mapping the “energy code” in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table, the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time, the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine–pyrimidine symmetry net, the quadruplet symmetry of DNA molecule, and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecules, and the energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the “energy code” are unique, unchangeable, and have the power of natural laws. Full article
(This article belongs to the Section Molecular Genetics and Genomics)
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29 pages, 2019 KiB  
Review
Self-Organisation of Prediction Models
by Rainer Feistel
Entropy 2023, 25(12), 1596; https://doi.org/10.3390/e25121596 - 28 Nov 2023
Cited by 1 | Viewed by 2910
Abstract
Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a [...] Read more.
Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a selective advantage from the beneficial use of activity requires a consistent combination of sensual perception, memorised experience, statistical or causal prediction models, and the resulting favourable decisions on actions. This information processing chain originated from mere physical interaction processes prior to life, here denoted as structural information exchange. From there, the self-organised transition to symbolic information processing marks the beginning of life, evolving through the novel purposivity of trial-and-error feedback and the accumulation of symbolic information. The emergence of symbols and prediction models can be described as a ritualisation transition, a symmetry-breaking kinetic phase transition of the second kind previously known from behavioural biology. The related new symmetry is the neutrally stable arbitrariness, conventionality, or code invariance of symbols with respect to their meaning. The meaning of such symbols is given by the structural effect they ultimately unleash, directly or indirectly, by deciding on which actions to take. The early genetic code represents the first symbols. The genetically inherited symbolic information is the first prediction model for activities sufficient for survival under the condition of environmental continuity, sometimes understood as the “final causality” property of the model. Full article
(This article belongs to the Special Issue Information and Self-Organization III)
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24 pages, 3099 KiB  
Article
Groups of Symmetries of the Two Classes of Synthetases in the Four-Dimensional Hypercubes of the Extended Code Type II
by Marco V. José, Eberto R. Morgado and Juan R. Bobadilla
Life 2023, 13(10), 2002; https://doi.org/10.3390/life13102002 - 30 Sep 2023
Cited by 1 | Viewed by 1209
Abstract
Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY [...] Read more.
Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code and the Extended Genetic RNA code type II, which includes codons of the types YNY, YNR, and RNR. Each of the four subsets of codons can be represented in a 4-dimensional hypercube. Altogether, these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group of order 4; YNY: binary group; YNR: amplified octahedral group; and RNR: binary group. We demonstrate that for each hypercube, the group of symmetries in Class 1 is the same as the group of symmetries in Class 2. The biological implications of these findings are discussed. Full article
(This article belongs to the Special Issue The Origins and Evolution of the Genetic Code)
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28 pages, 416 KiB  
Article
Revealing the Genetic Code Symmetries through Computations Involving Fibonacci-like Sequences and Their Properties
by Tidjani Négadi
Computation 2023, 11(8), 154; https://doi.org/10.3390/computation11080154 - 7 Aug 2023
Cited by 6 | Viewed by 6047
Abstract
In this work, we present a new way of studying the mathematical structure of the genetic code. This study relies on the use of mathematical computations involving five Fibonacci-like sequences; a few of their “seeds” or “initial conditions” are chosen according to the [...] Read more.
In this work, we present a new way of studying the mathematical structure of the genetic code. This study relies on the use of mathematical computations involving five Fibonacci-like sequences; a few of their “seeds” or “initial conditions” are chosen according to the chemical and physical data of the three amino acids serine, arginine and leucine, playing a prominent role in a recent symmetry classification scheme of the genetic code. It appears that these mathematical sequences, of the same kind as the famous Fibonacci series, apart from their usual recurrence relations, are highly intertwined by many useful linear relationships. Using these sequences and also various sums or linear combinations of them, we derive several physical and chemical quantities of interest, such as the number of total coding codons, 61, obeying various degeneracy patterns, the detailed number of H/CNOS atoms and the integer molecular mass (or nucleon number), in the side chains of the coded amino acids and also in various degeneracy patterns, in agreement with those described in the literature. We also discover, as a by-product, an accurate description of the very chemical structure of the four ribonucleotides uridine monophosphate (UMP), cytidine monophosphate (CMP), adenosine monophosphate (AMP) and guanosine monophosphate (GMP), the building blocks of RNA whose groupings, in three units, constitute the triplet codons. In summary, we find a full mathematical and chemical connection with the “ideal sextet’s classification scheme”, which we alluded to above, as well as with others—notably, the Findley–Findley–McGlynn and Rumer’s symmetrical classifications. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
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19 pages, 5771 KiB  
Review
The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code
by Marija Rosandić and Vladimir Paar
Int. J. Mol. Sci. 2023, 24(15), 12029; https://doi.org/10.3390/ijms241512029 - 27 Jul 2023
Cited by 3 | Viewed by 2056
Abstract
Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form [...] Read more.
Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson–Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons’ relationship as to how to develop the DNA molecule on the principle of Watson–Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system. Full article
(This article belongs to the Special Issue The Structural and Dynamical Characterization of Biological Processes)
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10 pages, 8012 KiB  
Article
Parametric Multispectral Mappings and Comparative Genomics
by Ivan V. Stepanyan and Michail Y. Lednev
Symmetry 2022, 14(12), 2517; https://doi.org/10.3390/sym14122517 - 29 Nov 2022
Cited by 4 | Viewed by 1626
Abstract
This article describes new algorithms that allow for viewing genetic sequences in the form of their multispectral images. We presented examples of the construction of such mappings with a demonstration of the practical problems of comparative genomics. New DNA visualization tools seem promising, [...] Read more.
This article describes new algorithms that allow for viewing genetic sequences in the form of their multispectral images. We presented examples of the construction of such mappings with a demonstration of the practical problems of comparative genomics. New DNA visualization tools seem promising, thanks to their informativeness and representativeness. The research illustrates how a novel sort of multispectral mapping, based on decomposition in several parametric spaces, can be created for comparative genetics. This appears to be a crucial step in the investigation of the genetic coding phenomenon and in practical activities, such as forensics, genetic testing, genealogical analysis, etc. The article gives examples of multispectral parametric sets for various types of coordinate systems. We build mappings using binary sub-alphabets of purine/pyrimidine and keto/amino. We presented 2D and 3D renderings in different characteristic spaces: structural, integral, cyclic, spherical, and third-order spherical. This research is based on the method previously developed by the author for visualizing genetic information based on new molecular genetic algorithms. One of the types of mappings, namely two-dimensional, is an object of discrete geometry, a symmetrical square matrix of high dimension. The fundamental properties of symmetry, which are traced on these mappings, allow us to speak about the close connection between the phenomenon of genetic coding and symmetry when using the developed mathematical apparatus for representing large volumes of complexly organized molecular genetic information. Full article
(This article belongs to the Section Life Sciences)
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17 pages, 548 KiB  
Article
A Novel Real Coded Genetic Algorithm for Software Mutation Testing
by Deepti Bala Mishra, Biswaranjan Acharya, Dharashree Rath, Vassilis C. Gerogiannis and Andreas Kanavos
Symmetry 2022, 14(8), 1525; https://doi.org/10.3390/sym14081525 - 26 Jul 2022
Cited by 6 | Viewed by 2515
Abstract
Information Technology has rapidly developed in recent years and software systems can play a critical role in the symmetry of the technology. Regarding the field of software testing, white-box unit-level testing constitutes the backbone of all other testing techniques, as testing can be [...] Read more.
Information Technology has rapidly developed in recent years and software systems can play a critical role in the symmetry of the technology. Regarding the field of software testing, white-box unit-level testing constitutes the backbone of all other testing techniques, as testing can be entirely implemented by considering the source code of each System Under Test (SUT). In unit-level white-box testing, mutants can be used; these mutants are artificially generated faults seeded in each SUT that behave similarly to the realistic ones. Executing test cases against mutants results in the adequacy (mutation) score of each test case. Efficient Genetic Algorithm (GA)-based methods have been proposed to address different problems in white-box unit testing and, in particular, issues of mutation testing techniques. In this research paper, a new approach, which integrates the path coverage-based testing method with the novel idea of tracing a Fault Detection Matrix (FDM) to achieve maximum mutation coverage, is proposed. The proposed real coded GA for mutation testing is designed to achieve the highest Mutation Score, and it is thus named RGA-MS. The approach is implemented in two phases: path coverage-based test data are initially generated and stored in an optimized test suite. In the next phase, the test suite is executed to kill the mutants present in the SUT. The proposed method aims to achieve the minimum test dataset, having at the same time the highest Mutation Score by removing duplicate test data covering the same mutants. The proposed approach is implemented on the same SUTs as these have been used for path testing. We proved that the RGA-MS approach can cover maximum mutants with a minimum number of test cases. Furthermore, the proposed method can generate a maximum path coverage-based test suite with minimum test data generation compared to other algorithms. In addition, all mutants in the SUT can be covered by less number of test data with no duplicates. Ultimately, the generated optimal test suite is trained to achieve the highest Mutation Score. GA is used to find the maximum mutation coverage as well as to delete the redundant test cases. Full article
(This article belongs to the Special Issue Recent Advances in Software for Symmetry)
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21 pages, 1316 KiB  
Review
Non-Coding RNAs and Reactive Oxygen Species–Symmetric Players of the Pathogenesis Associated with Bacterial and Viral Infections
by Zaki Milhem, Paul Chiroi, Andreea Nutu, Maximilian Ilea, Mihaela Lupse, Oana Zanoaga and Ioana Berindan-Neagoe
Symmetry 2021, 13(7), 1307; https://doi.org/10.3390/sym13071307 - 20 Jul 2021
Cited by 2 | Viewed by 6390
Abstract
Infections can be triggered by a wide range of pathogens. However, there are few strains of bacteria that cause illness, but some are quite life-threatening. Likewise, viral infections are responsible for many human diseases, usually characterized by high contagiousness. Hence, as bacterial and [...] Read more.
Infections can be triggered by a wide range of pathogens. However, there are few strains of bacteria that cause illness, but some are quite life-threatening. Likewise, viral infections are responsible for many human diseases, usually characterized by high contagiousness. Hence, as bacterial and viral infections can both cause similar symptoms, it can be difficult to determine the exact cause of a specific infection, and this limitation is critical. However, recent scientific advances have geared us up with the proper tools required for better diagnoses. Recent discoveries have confirmed the involvement of non-coding RNAs (ncRNAs) in regulating the pathogenesis of certain bacterial or viral infections. Moreover, the presence of reactive oxygen species (ROS) is also known as a common infection trait that can be used to achieve a more complete description of such pathogen-driven conditions. Thus, this opens further research opportunities, allowing scientists to explore infection-associated genetic patterns and develop better diagnosis and treatment methods. Therefore, the aim of this review is to summarize the current knowledge of the implication of ncRNAs and ROS in bacterial and viral infections, with great emphasis on their symmetry but, also, on their main differences. Full article
(This article belongs to the Special Issue Biochemistry, Gene Symmetry and Molecular Biology)
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17 pages, 1536 KiB  
Article
Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface
by Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Fang Fang and Klee Irwin
Symmetry 2021, 13(7), 1146; https://doi.org/10.3390/sym13071146 - 26 Jun 2021
Cited by 5 | Viewed by 2646
Abstract
Every protein consists of a linear sequence over an alphabet of 20 letters/amino acids. The sequence unfolds in the 3-dimensional space through secondary (local foldings), tertiary (bonds) and quaternary (disjoint multiple) structures. The mere existence of the genetic code for the 20 letters [...] Read more.
Every protein consists of a linear sequence over an alphabet of 20 letters/amino acids. The sequence unfolds in the 3-dimensional space through secondary (local foldings), tertiary (bonds) and quaternary (disjoint multiple) structures. The mere existence of the genetic code for the 20 letters of the linear chain could be predicted with the (informationally complete) irreducible characters of the finite group Gn:=Zn (with n=5 or 7 and 2O the binary octahedral group) in our previous two papers. It turns out that some quaternary structures of protein complexes display n-fold symmetries. We propose an approach of secondary structures based on free group theory. Our results are compared to other approaches of predicting secondary structures of proteins in terms of α helices, β sheets and coils, or more refined techniques. It is shown that the secondary structure of proteins shows similarities to the structure of some hyperbolic 3-manifolds. The hyperbolic 3-manifold of smallest volume—Gieseking manifold—some other 3 manifolds and the oriented hypercartographic group are singled out as tentative models of such secondary structures. For the quaternary structure, there are links to the Kummer surface. Full article
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12 pages, 817 KiB  
Article
Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy
by Michel Planat, David Chester, Raymond Aschheim, Marcelo M. Amaral, Fang Fang and Klee Irwin
Quantum Rep. 2021, 3(1), 68-79; https://doi.org/10.3390/quantum3010005 - 25 Jan 2021
Cited by 6 | Viewed by 3397
Abstract
The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the [...] Read more.
The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)Z52O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)Z62O and G7:=(336,118)Z72O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested. Full article
(This article belongs to the Special Issue Groups, Geometry and Topology for Quantum Computations)
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30 pages, 3393 KiB  
Review
Symmetry Transformations in Metazoan Evolution and Development
by Valeria V. Isaeva and Nickolay V. Kasyanov
Symmetry 2021, 13(2), 160; https://doi.org/10.3390/sym13020160 - 20 Jan 2021
Cited by 7 | Viewed by 8262
Abstract
In this review, we consider transformations of axial symmetry in metazoan evolution and development, the genetic basis, and phenotypic expressions of different axial body plans. In addition to the main symmetry types in metazoan body plans, such as rotation (radial symmetry), reflection (mirror [...] Read more.
In this review, we consider transformations of axial symmetry in metazoan evolution and development, the genetic basis, and phenotypic expressions of different axial body plans. In addition to the main symmetry types in metazoan body plans, such as rotation (radial symmetry), reflection (mirror and glide reflection symmetry), and translation (metamerism), many biological objects show scale (fractal) symmetry as well as some symmetry-type combinations. Some genetic mechanisms of axial pattern establishment, creating a coordinate system of a metazoan body plan, bilaterian segmentation, and left–right symmetry/asymmetry, are analysed. Data on the crucial contribution of coupled functions of the Wnt, BMP, Notch, and Hedgehog signaling pathways (all pathways are designated according to the abbreviated or full names of genes or their protein products; for details, see below) and the axial Hox-code in the formation and maintenance of metazoan body plans are necessary for an understanding of the evolutionary diversification and phenotypic expression of various types of axial symmetry. The lost body plans of some extinct Ediacaran and early Cambrian metazoans are also considered in comparison with axial body plans and posterior growth in living animals. Full article
(This article belongs to the Section Life Sciences)
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