Identification of approximate symmetries in biological development

Abstract

Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular organisms, exhibit a property referred to as symmetry. However, precise measures of symmetry are often difficult to formulate and apply in a meaningful way to biological systems, where symmetries and asymmetries can be dynamic and transient, or be visually apparent but not reliably quantifiable using standard measures from mathematics and physics. Here, we present and illustrate a novel measure that draws on concepts from information theory to quantify the degree of symmetry, enabling the identification of approximate symmetries that may be present in a pattern or a biological image. We apply the measure to rotation, reflection and translation symmetries in patterns produced by a Turing model, as well as natural objects (algae, flowers and leaves). This method of symmetry quantification is unbiased and rigorous, and requires minimal manual processing compared to alternative measures. The proposed method is therefore a useful tool for comparison and identification of symmetries in biological systems, with potential future applications to symmetries that arise during development, as observed in vivo or as produced by mathematical models. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Inferring local molecular dynamics from the global actin network structure: a case study of 2D synthetic branching actin networks

“…To test the hypothesis that only geometric properties of the actin networks may be important for accurate classification, we use a novel and robust measure of symmetry that is grounded in concepts of entropy and information theory called transformation information (Gandhi et al, 2021, Vstovsky, 1997). We apply this method to quantify asymmetries of actin density plots under image transformations parameterized by the rotation angle θ as outlined in Section 2.2.3 (Figure 3).…”

“…To identify geometric properties of simulated actin networks, we calculate the transformation information (TI) associated with each network density plot as outlined in Gandhi et al (2021). The TI function quantifies the amount of information lost by approximating the original image by the transformed image.…”

“…TI) associated with each network density plot as outlined inGandhi et al (2021). The TI function quantifies the amount of information lost by approximating the original image by the transformed image.…”

Fundamental Cause of Bio-Chirality - Space-Time Symmetry: Concept Review

“…All forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular "organisms, exhibit a property referred to as symmetry" [Gandhi, et al 2021].…”

Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’

“…They conjecture a universality in the bifurcation regimes found, and give important arguments as to how such information can be valuable in modelling natural phenomena. Whereas Al Saadi and Champneys start with particular classes of models in mind, Gandhi et al [ 9 ] take the opposite viewpoint and consider the problem of identifying and quantifying symmetry in natural systems in the absence of an underlying mechanistic model. Based on information-theoretic considerations from condensed-matter physics, they propose a suite of measures of symmetry with the aim of providing a universal quantitative operationalization of the term across a range of biological scenarios.…”