On Growth and Form showed how physical and mathematical forces affect natural selection.
On Growth and Form Centenary
On 14th April 1917, Nature announced that it had received a new publication entitled “On Growth and Form” by D’arcy Wentworth Thompson. This book was Thompson’s vision of how mathematical and physical principles define the development and final form of biological structures and 100 years later it is a classic text for researchers who cross the traditional disciplinary boundaries between physics, mathematics and biology. Nature celebrates the centenary of the publication of “On Growth and Form” with the publication of some interdisciplinary research and supporting comment pieces reflecting evolving fields in biophysics and applied mathematics. We also present an online collection of research and comment reflecting the diversity of research activity which crosses boundaries between the physical and biological sciences in developing our understanding of morphogenesis in its broadest sense. We hope you enjoy the collection.
Innovative tools are revealing the forces that guide cellular processes such as embryonic development and tumour growth.
Epithelial monolayers remove excess cells by extrusion. Benoit Ladoux and colleagues now report a purely mechanical route to cell extrusion at the site of topological defects within the cell monolayer. By modelling the epithelium as an active nematic liquid crystal, they show that cell extrusion is driven by stresses induced by distortions in cell orientation. Extrusion hotspots were controlled by geometrically inducing defects through microcontact printing of patterned monolayers. The authors also investigated the mechanotransductive effect of stress localization and found that signals related to cell death were induced at these sites of compressive stress. Additionally, tampering with the intercellular adhesion complexes led to a weakening of cell–cell interactions and resulted in an increased number of defects and extrusions. This finding is in line with nematic theory, which predicts that the number of topological defects is inversely related to the orientational elasticity.
Macroscopic patterns in the animal world, such as zebra stripes and leopard spots, can be described by dynamical processes at the level of biological cells acting within the reaction–diffusion framework. Liana Manukyan et al. discover a remarkable mechanism of pattern formation in ocellated lizards. They recorded the changes in skin patterning of several lizards over four years of development and find that their skin colour changes at the level of individual scales. The patterns appear to be produced by a hexagonal cellular automaton, in which the skin scales are the discrete units. Mathematical theory shows that such a discrete system can emerge from the continuous reaction–diffusion framework when taking into account variations in skin thickness. The intriguing conclusion is that cellular automata are not just abstract computational systems, but can directly correspond to processes generated by biological evolution.
Philip Ball celebrates a classic work on the mathematics that shape living structures, from antlers to cells.