Morphogenesis

How do spatial patterns and bodies develop, maintain form and regenerate? Chemical pattern formation, computational constructions and biological interventions provide different kinds of evidence.

Physical form and positional information

  • Physical and geometric form - Connects organismal form to scale, growth and physical forces. Coordinate transformations compare related shapes; these geometric correspondences describe variation without identifying the developmental process that produced it. Thompson 1917.
  • Positional information - Cells interpret position relative to reference points using their genome and developmental history. Reaction-diffusion can generate signals that this interpretation uses; signal formation and positional interpretation can act together. Wolpert 1969, Green and Sharpe 2015.

Chemical pattern formation

  • Turing patterns - Reaction and diffusion can destabilize a homogeneous chemical state and amplify small disturbances into spatial patterns. A mechanism for symmetry breaking, analyzed in idealized tissues. Turing 1952.
  • Belousov-Zhabotinsky waves - Breaking a chemical wavefront creates rotating spiral waves in Winfree’s experiments. Persistent wave sources organize reaction activity; visible form results from an excitable chemical medium. Winfree 1972.
  • Gray-Scott patterns - Numerical reaction-diffusion experiments produce spots that grow and divide, and overcrowded regions that collapse. The reported patterns arise from finite-amplitude perturbations. Pearson 1993.
  • Angelfish stripe dynamics - Stripes rearrange as marine angelfish grow, unlike a fixed pattern stretched with the skin. Reaction-diffusion simulations predict later arrangements, supporting a dynamic patterning mechanism without identifying its molecular components. Kondo and Asai 1995.

Growth and repair

  • L-systems - Parallel rewriting rules model cell division and branching growth. Symbols encode developmental states; geometric interpretation turns their expansion into plant forms. The rules specify a developmental model, not just a final shape. Lindenmayer 1968, Prusinkiewicz and Lindenmayer 1990.
  • Bioelectric pattern memory - Briefly perturbing gap-junction signaling changes later planarian regeneration, including in normal-looking worms amputated again in water. Manipulating resting potential can reset the altered head-pattern outcome. Durant et al. 2017.
  • synNotch morphogenesis - Engineered contact signals change cell adhesion, which rearranges neighbors and alters later signals. Mouse fibroblasts form layered or asymmetric assemblies, and cut layered structures regenerate their organization. Toda et al. 2018.
  • Growing neural cellular automata - Train a shared local neural rule to grow a target image. Reusing intermediate states improves persistence; exposing the model to damage strengthens repair. Local execution follows global optimization through time. Mordvintsev et al. 2020; code, demo.

Open questions

  • Which perturbations distinguish changes in a spatial signal from changes in how cells interpret that signal?
  • Which repair mechanisms generalize beyond damage encountered during development, selection or training?
  • Which persistent cellular states determine regenerated form, and how do targeted perturbations change the outcome?