Entropy as a Geometrical Source of Information in Biological Organizations

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.

Voronoi Tessellations and the Shannon Entropy of the Pentagonal Tilings

“…Partitioning of an infinite plane into regions based on the distance to a specified discrete set of points (called seeds or nuclei) constructs the Voronoi tessellation. There is a corresponding region for each seed, consisting of all points closer to that seed point (also called generators) than to any other point [17][18][19][20][21][22]. The Voronoi diagram of the addressed Penrose tiling was composed of N polygons.…”

Mathematical Modeling in Systems Biology

“…An information-based approach to quantify geometrical order in biological organizations using varying levels of information is introduced in the article by Juan Lopez-Sauceda et al [2]. The approach employs Shannon entropy to measure the quantity of information in geometrical meshes of biological systems.…”