Figure 3.

Anatomical morphospace and its navigation by cellular collective intelligence. (A) Example of morphospace—the space of possible shapes—for coiled shells (taken with permission from [87]). Three parameters (rate of increase in the size of the generated shell cross section per revolution, the distance between the cross section and the coiling axis, and the rate of translation of the cross section along the axis per revolution) define a space within which many taxa can be found. (B) Space of possible planarian heads defined by possible values of three morphogen values in a computational model (taken with permission from [88]). (C,D) The idea of morphospace and different species of animals as mathematical transformations of coordinates in those spaces was originally proposed by D’Arcy Thompson (panels taken with permission from [89]). Traversals of morphospace can be seen in regeneration, such as for the salamander limb, which will continue to grow when amputated at any position (brought to a new region of morphospace for the limb) until the system reaches the correct state (the shape of a normal limb), at which point it stops ((E) panel by Jeremy Guay of Peregrine Creative), or in the ability of both normal and scrambled tadpole faces to rearrange until a correct frog craniofacial morphology is reached ((F,G) taken from [90]). (H) Remodeling, de novo embryogenesis, and regeneration are all examples of biological systems’ abilities to navigate from starting positions in morphospace “s1”–“s4” and reach the target morphology goal state “G” while avoiding the local maxima “LM”. Morphospace plasticity (I) includes the ability of higher-level constraints to activate diverse underlying molecular mechanisms as needed. For example, (I) tubulogenesis in the amphibian kidney normally works via cell–cell communication, but when the cells are forced to be very large (by induced polyploidy), this reduces the number of cells and eventually leads to switching to using cytoskeletal bending to form the same diameter of tube from just one cell bending around itself (panel by Jeremy Guay from [91,92]).