Algebraic Nexus of Fibonacci Forms and Two-Simplex Topology in Multicellular Morphogenesis
Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and...
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Published in | Symmetry (Basel) Vol. 16; no. 5; p. 516 |
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Abstract | Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown. Methods: In a multicellular organism, cells adhere to form a macrostructure and to coordinate further replication. We propose and prove simple theorems connecting cell replication and adhesion to Fibonacci forms and simplicial topology. Results: We identify some cellular and molecular properties whereby the contact inhibition of replication by adhered cells may approximate Fibonacci growth patterns. We further identify how a component 2→3 cellular multiplication step may generate a multicellular structure with some properties of a two-simplex. Tracking the homotopy of a two-simplex to a circle and to a tube, we identify some molecular and cellular growth properties consistent with the morphogenesis of tubes. We further find that circular and tubular cellular aggregates may be combinatorially favored in multicellular adhesion over flat shapes. Conclusions: We propose a correspondence between the cellular and molecular mechanisms that generate Fibonacci cell counts and those that enable tubular forms. This implies molecular and cellular arrangements that are candidates for experimental testing and may provide guidance for the synthetic biology of hollow morphologies. |
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AbstractList | Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown. Methods: In a multicellular organism, cells adhere to form a macrostructure and to coordinate further replication. We propose and prove simple theorems connecting cell replication and adhesion to Fibonacci forms and simplicial topology. Results: We identify some cellular and molecular properties whereby the contact inhibition of replication by adhered cells may approximate Fibonacci growth patterns. We further identify how a component 2→3 cellular multiplication step may generate a multicellular structure with some properties of a two-simplex. Tracking the homotopy of a two-simplex to a circle and to a tube, we identify some molecular and cellular growth properties consistent with the morphogenesis of tubes. We further find that circular and tubular cellular aggregates may be combinatorially favored in multicellular adhesion over flat shapes. Conclusions: We propose a correspondence between the cellular and molecular mechanisms that generate Fibonacci cell counts and those that enable tubular forms. This implies molecular and cellular arrangements that are candidates for experimental testing and may provide guidance for the synthetic biology of hollow morphologies. |
Audience | Academic |
Author | Kinane, Thomas Bernard Turcio Cuevas, Luis J. Alcántara, Julio Andrade Loarca, Héctor Lamb, Elizabeth G. Butler Hoyos, William E. Kahle, Kristopher T. Williams, Ziv |
Author_xml | – sequence: 1 givenname: William E. orcidid: 0000-0002-4249-565X surname: Butler Hoyos fullname: Butler Hoyos, William E. – sequence: 2 givenname: Héctor surname: Andrade Loarca fullname: Andrade Loarca, Héctor – sequence: 3 givenname: Kristopher T. surname: Kahle fullname: Kahle, Kristopher T. – sequence: 4 givenname: Ziv surname: Williams fullname: Williams, Ziv – sequence: 5 givenname: Elizabeth G. surname: Lamb fullname: Lamb, Elizabeth G. – sequence: 6 givenname: Julio orcidid: 0000-0001-8122-3991 surname: Alcántara fullname: Alcántara, Julio – sequence: 7 givenname: Thomas Bernard surname: Kinane fullname: Kinane, Thomas Bernard – sequence: 8 givenname: Luis J. surname: Turcio Cuevas fullname: Turcio Cuevas, Luis J. |
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Snippet | Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated... |
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SubjectTerms | Adhesion cell adhesion Cell adhesion & migration Cell cycle Cellular structure Chromosomes Cytoskeleton Eigenvalues epigenomics Extracellular matrix Fibonacci golden ratio Macrostructure Mathematical morphology mitosis Molecular properties Multiplication Organisms Phylogeny Proteins Replication simplex topology Topology Tubes |
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