Symmetry

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9006 KiB

Open AccessArticle

Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata

by Ikuko Tanaka

Symmetry 2015, 7(4), 1768-1779; https://doi.org/10.3390/sym7041768 - 29 Sep 2015

Cited by 3 | Viewed by 5251

Abstract

To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular [...] Read more.

To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular and random initial conditions corresponds to three Wolfram’s classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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23683 KiB

Open AccessArticle

Asymmetry Assessment Using Surface Topography in Healthy Adolescents

by Connie Ho, Eric C. Parent, Elise Watkins, Marc J. Moreau, Douglas Hedden, Marwan El-Rich and Samer Adeeb

Symmetry 2015, 7(3), 1436-1454; https://doi.org/10.3390/sym7031436 - 17 Aug 2015

Cited by 7 | Viewed by 7288

Abstract

The ability to assess geometric asymmetry in the torsos of individuals is important for detecting Adolescent Idiopathic Scoliosis (AIS). A markerless technique using Surface Topography (ST) has been introduced as a non-invasive alternative to standard diagnostic radiographs. The technique has been used to [...] Read more.

The ability to assess geometric asymmetry in the torsos of individuals is important for detecting Adolescent Idiopathic Scoliosis (AIS). A markerless technique using Surface Topography (ST) has been introduced as a non-invasive alternative to standard diagnostic radiographs. The technique has been used to identify asymmetry patterns associated with AIS. However, the presence and nature of asymmetries in the healthy population has not been properly studied. The purpose of this study is therefore to identify asymmetries and potential relationships to development factors such as age, gender, hand dominance and unilateral physical activity in healthy adolescents. Full torso scans of 83 participants were analyzed. Using Geomagic, deviation contour maps (DCMs) were created by reflecting the torso along the best plane of sagittal symmetry with each spectrum normalized. Two classes of asymmetry were observed: twist and thickness each with subgroupings. Averaged interobserver and intraobserver Kappas for twist subgroupings were 0.84 and 0.84, respectively, and for thickness subgroupings were 0.53 and 0.63 respectively. Further significant relationships were observed between specific types of asymmetry and gender such as females displaying predominately twist asymmetry, and males with thickness asymmetry. However, no relationships were found between type of asymmetry and age, hand dominance or unilateral physical activity. Understanding asymmetries in healthy subjects will continue to enhance assessment ability of the markerless ST technique. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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1870 KiB

Open AccessArticle

The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric

by Reijer Lenstra

Symmetry 2015, 7(3), 1211-1260; https://doi.org/10.3390/sym7031211 - 14 Jul 2015

Cited by 4 | Viewed by 12909

Abstract

The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for [...] Read more.

The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon positions: AAA and AAC are at 1-distance; codons are maximally at 3-distance.) The CodonPolytope, a 9-dimensional geometric object, is spanned by 64 vertices that represent the codons and the Euclidian distances between these vertices correspond one-to-one with intercodon Hamming distances. The CodonGraph represents the vertices and edges of the polytope; each edge equals a Hamming 1-distance. The mirror reflection symmetry group of the polytope is isomorphic to the largest permutation symmetry group of the codon set that preserves Hamming distances. These groups contain 82,944 symmetries. Many polytope symmetries coincide with the degeneracy and similarity patterns of the genetic code. These code symmetries are strongly related with the face structure of the polytope with smaller faces displaying stronger code symmetries. Splitting the polytope stepwise into smaller faces models an early evolution of the code that generates this hierarchy of code symmetries. The canonical code represents a class of 41,472 codes with equivalent symmetries; a single class among an astronomical number of symmetry classes comprising all possible codes. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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Review

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Open AccessReview

When and Why Did Brains Break Symmetry?

by Lesley J. Rogers and Giorgio Vallortigara

Symmetry 2015, 7(4), 2181-2194; https://doi.org/10.3390/sym7042181 - 2 Dec 2015

Cited by 89 | Viewed by 15112

Abstract

Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the allocation of different functions [...] Read more.

Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the allocation of different functions to the left and right sides. This paper discusses the differing functions of the left and right sides of the brain, including the roles of the left and right antennae of bees (several species) in both short- and long-term recall of olfactory memories and in social behaviour. It considers the likely advantages of functional asymmetry in small and large brains and whether functional asymmetry in vertebrates and invertebrates is analogous or homologous. Neural or cognitive capacity can be enhanced both by the evolution of a larger brain and by lateralization of brain function: a possible reason why both processes occur side-by-side is offered. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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49674 KiB

Open AccessReview

Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development

by Christian Pohl

Symmetry 2015, 7(4), 2062-2107; https://doi.org/10.3390/sym7042062 - 11 Nov 2015

Cited by 18 | Viewed by 13456

Abstract

Animal development relies on repeated symmetry breaking, e.g., during axial specification, gastrulation, nervous system lateralization, lumen formation, or organ coiling. It is crucial that asymmetry increases during these processes, since this will generate higher morphological and functional specialization. On one hand, cue-dependent symmetry [...] Read more.

Animal development relies on repeated symmetry breaking, e.g., during axial specification, gastrulation, nervous system lateralization, lumen formation, or organ coiling. It is crucial that asymmetry increases during these processes, since this will generate higher morphological and functional specialization. On one hand, cue-dependent symmetry breaking is used during these processes which is the consequence of developmental signaling. On the other hand, cells isolated from developing animals also undergo symmetry breaking in the absence of signaling cues. These spontaneously arising asymmetries are not well understood. However, an ever growing body of evidence suggests that these asymmetries can originate from spontaneous symmetry breaking and self-organization of molecular assemblies into polarized entities on mesoscopic scales. Recent discoveries will be highlighted and it will be discussed how actomyosin and microtubule networks serve as common biomechanical systems with inherent abilities to drive spontaneous symmetry breaking. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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7151 KiB

Open AccessReview

Concise Review: Asymmetric Cell Divisions in Stem Cell Biology

by Florian Murke, Symone Vitorianoda Conceição Castro, Bernd Giebel and André Görgens

Symmetry 2015, 7(4), 2025-2037; https://doi.org/10.3390/sym7042025 - 5 Nov 2015

Cited by 16 | Viewed by 22514

Abstract

Somatic stem cells are rare cells with unique properties residing in many organs and tissues. They are undifferentiated cells responsible for tissue regeneration and homeostasis, and contain both the capacity to self-renew in order to maintain their stem cell potential and to differentiate [...] Read more.

Somatic stem cells are rare cells with unique properties residing in many organs and tissues. They are undifferentiated cells responsible for tissue regeneration and homeostasis, and contain both the capacity to self-renew in order to maintain their stem cell potential and to differentiate towards tissue-specific, specialized cells. However, the knowledge about the mechanisms controlling somatic stem cell fate decisions remains sparse. One mechanism which has been described to control daughter cell fates in selected somatic stem cell systems is the process of asymmetric cell division (ACD). ACD is a tightly regulated and evolutionary conserved process allowing a single stem or progenitor cell to produce two differently specified daughter cells. In this concise review, we will summarize and discuss current concepts about the process of ACD as well as different ACD modes. Finally, we will recapitulate the current knowledge and our recent findings about ACD in human hematopoiesis. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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3127 KiB

Open AccessReview

Physics of the Chemical Asymmetry of the Cell Membrane: Implications in Gene Regulation and Pharmacology

by Ziad Omran, Paula Williams and Cyril Rauch

Symmetry 2015, 7(4), 1780-1787; https://doi.org/10.3390/sym7041780 - 30 Sep 2015

Cited by 1 | Viewed by 6297

Abstract

Signalling proteins are key regulators of basic cell physiology and tissues morphogenesis. Whilst signalling proteins are paramount for the cell to function optimally, their down regulation or inhibition is also central to tune the cell and its environment. One process involved in this [...] Read more.

Signalling proteins are key regulators of basic cell physiology and tissues morphogenesis. Whilst signalling proteins are paramount for the cell to function optimally, their down regulation or inhibition is also central to tune the cell and its environment. One process involved in this tuning mechanism is membrane budding, otherwise known as endocytosis. The origin of the physical force driving the budding process and endocytosis has been the subject of much controversy. After two decades the budding process is now well described and it is acknowledged that fundamental principles from soft matter physics are at play. This opens a new window for understanding gene regulations, pharmacokinetic and multi drug resistance in cancer. This review recalls the first steps that have led to a better understanding of cell biology through the use of physics and; how the use of physics has shed light in areas of cell biology, cancer and pharmacology. It is, therefore, not a review of the many enzymes involved in membrane vesiculation and membrane curvature; it is more of an historical account. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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10554 KiB

Open AccessReview

Symmetry Breaking and Establishment of Dorsal/Ventral Polarity in the Early Sea Urchin Embryo

by Vincenzo Cavalieri and Giovanni Spinelli

Symmetry 2015, 7(4), 1721-1733; https://doi.org/10.3390/sym7041721 - 28 Sep 2015

Cited by 7 | Viewed by 11644

Abstract

The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of [...] Read more.

The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of nodal on the future ventral side, in apparent contrast with other metazoan embryos, where nodal is expressed dorsally. A subtle maternally-inherited redox anisotropy, plus some maternal factors such as SoxB1, Univin, and p38-MAPK have been identified as inputs driving the spatially asymmetric transcription of nodal. However, all the mentioned factors are broadly distributed in the embryo as early as nodal transcription occurs, suggesting that repression of the gene in non-ventral territories depends upon negative regulators. Among these, the Hbox12 homeodomain-containing repressor is expressed by prospective dorsal cells, where it acts as a dorsal-specific negative modulator of the p38-MAPK activity. This review provides an overview of the molecular mechanisms governing the establishment of DV polarity in sea urchins, focusing on events taking place in the early embryo. Altogether, these findings provide a framework for future studies aimed to unravel the inceptive mechanisms involved in the DV symmetry breaking. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)

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