Emergence of structure in mouse embryos: Structural Entropy morphometry applied to digital models of embryonic anatomy.

William Waites,Jamie A Davies

doi:10.1111/joa.13031

Abstract

We apply an information‐theoretic measure to anatomical models of the Edinburgh Mouse Atlas Project. Our goal is to quantify the anatomical complexity of the embryo and to understand how this quantity changes as the organism develops through time. Our measure, Structural Entropy, takes into account the geometrical character of the intermingling of tissue types in the embryo. It does this by a mathematical process that effectively imagines a point‐like explorer that starts at an arbitrary place in the 3D structure of the embryo and takes a random path through the embryo, recording the sequence of tissues through which it passes. Consideration of a large number of such paths yields a probability distribution of paths making connections between specific tissue types, and Structural Entropy is calculated from this (mathematical details are given in the main text). We find that Structural Entropy generally decreases (order increases) almost linearly throughout developmental time (4–18 days). There is one `blip’ of increased Structural Entropy across days 7–8: this corresponds to gastrulation. Our results highlight the potential for mathematical techniques to provide insight into the development of anatomical structure, and also the need for further sources of accurate 3D anatomical data to support analyses of this kind.

Highlights

In his important text on developmental biology (Kauffman, 1993), Kauffman argues that order in living creatures arises from a combination of evolution and self-organisation
We show that Structural Entropy appears reasonably robust to inconsistencies in manual analysis and tagging
We will be concerned with volumes of and adjacency relations between tagged elements, or in other words the sizes of anatomical regions and which are in physical contact with each other

Summary

Introduction

In his important text on developmental biology (Kauffman, 1993), Kauffman argues that order in living creatures arises from a combination of evolution and self-organisation. It is not hard to account for this ambiguity; exactly what should be meant by order, or related words such as structure or complexity as they apply to biological organisms, is not at all obvious. Authors such as Grizzi & Chiriva-Internati (2005) consider the meaning of anatomical structure in detail, making the key point that ‘complexity can reside in the structure of the Accepted for publication 21 May 2019 system,’ and suggest the use of mathematics to quantify this, without explaining precisely how.

Objectives

Methods

Results

Conclusion