1
|
Lopez-Sauceda J, von Bülow P, Ortega-Laurel C, Perez-Martinez F, Miranda-Perkins K, Carrillo-González JG. Entropy as a Geometrical Source of Information in Biological Organizations. ENTROPY 2022; 24:1390. [PMCID: PMC9601958 DOI: 10.3390/e24101390] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2022] [Accepted: 09/22/2022] [Indexed: 06/17/2023]
Abstract
Considering both biological and non-biological polygonal shape organizations, in this paper we introduce a quantitative method which is able to determine informational entropy as spatial differences between heterogeneity of internal areas from simulation and experimental samples. According to these data (i.e., heterogeneity), we are able to establish levels of informational entropy using statistical insights of spatial orders using discrete and continuous values. Given a particular state of entropy, we establish levels of information as a novel approach which can unveil general principles of biological organization. Thirty-five geometric aggregates are tested (biological, non-biological, and polygonal simulations) in order to obtain the theoretical and experimental results of their spatial heterogeneity. Geometrical aggregates (meshes) include a spectrum of organizations ranging from cell meshes to ecological patterns. Experimental results for discrete entropy using a bin width of 0.5 show that a particular range of informational entropy (0.08 to 0.27 bits) is intrinsically associated with low rates of heterogeneity, which indicates a high degree of uncertainty in finding non-homogeneous configurations. In contrast, differential entropy (continuous) results reflect negative entropy within a particular range (−0.4 to −0.9) for all bin widths. We conclude that the differential entropy of geometrical organizations is an important source of neglected information in biological systems.
Collapse
Affiliation(s)
- Juan Lopez-Sauceda
- Consejo Nacional de Ciencia y Tecnología (CONACYT), Avenida Insurgentes Sur 1582, Colonia Crédito Constructor, Alcaldía Benito Juárez, Mexico City 03940, Mexico
- Departamento de Procesos Productivos, Universidad Autónoma Metropolitana, Avenida de las Garzas No. 10, Colonia El Panteón, Lerma de Villada 52005, Mexico
| | - Philipp von Bülow
- Departamento de Procesos Productivos, Universidad Autónoma Metropolitana, Avenida de las Garzas No. 10, Colonia El Panteón, Lerma de Villada 52005, Mexico
| | - Carlos Ortega-Laurel
- Departamento de Sistemas de Información y Comunicaciones, Universidad Autónoma Metropolitana, Avenida de las Garzas No. 10, Colonia El Panteón, Lerma de Villada 52005, Mexico
| | - Francisco Perez-Martinez
- Departamento de Sistemas de Información y Comunicaciones, Universidad Autónoma Metropolitana, Avenida de las Garzas No. 10, Colonia El Panteón, Lerma de Villada 52005, Mexico
| | - Kalina Miranda-Perkins
- Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT), Avenida Ejército Nacional 223, Colonia Anáhuac, Alcaldía Miguel Hidalgo, Mexico City 11320, Mexico
| | - José Gerardo Carrillo-González
- Consejo Nacional de Ciencia y Tecnología (CONACYT), Avenida Insurgentes Sur 1582, Colonia Crédito Constructor, Alcaldía Benito Juárez, Mexico City 03940, Mexico
- Departamento de Sistemas de Información y Comunicaciones, Universidad Autónoma Metropolitana, Avenida de las Garzas No. 10, Colonia El Panteón, Lerma de Villada 52005, Mexico
| |
Collapse
|
2
|
López-Sauceda J, López-Ortega J, Laguna Sánchez GA, Sandoval Gutiérrez J, Rojas Meza AP, Aragón JL. Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology. ENTROPY (BASEL, SWITZERLAND) 2018; 20:e20090705. [PMID: 33265794 PMCID: PMC7513224 DOI: 10.3390/e20090705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2018] [Revised: 09/06/2018] [Accepted: 09/07/2018] [Indexed: 06/12/2023]
Abstract
A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based on principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (3 to 10-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.
Collapse
Affiliation(s)
- Juan López-Sauceda
- Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico), 03940 Ciudad de Mexico, Mexico
- Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
| | - Jorge López-Ortega
- Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
| | - Gerardo Abel Laguna Sánchez
- Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
| | - Jacobo Sandoval Gutiérrez
- Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
| | - Ana Paola Rojas Meza
- Área de Investigación de Sistemas de Información y Ciencias Computacionales, Universidad Autónoma Metropolitana, Unidad Lerma, 52005 Lerma de Villada, Mexico
| | - José Luis Aragón
- Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, 76230 Queretaro, Mexico
| |
Collapse
|