The Growing Canvas of Biological Development: Multiscale Pattern Generation on an Expanding Lattice of Gene Regulatory Nets

The spontaneous generation of an entire organism from a single cell is the epitome of a self-organizing, decentralized complex system. How do nonspatial gene interactions extend in 3-D space? In this work I present a simple model that simulates some biological developmental principles using an expanding lattice of cells. Each cell contains a genetic regulatory network (GRN), modeled as a feedforward hierarchy of switches that can settle in various on/off expression states. Local morphogen gradients provide positional information in input, which is integrated by each GRN to produce differential expression of identity genes in output. Similarly to striping in the Drosophila embryo, the lattice becomes segmented into spatial domains of homogeneous genetic expression that resemble stained glass motifs. Meanwhile, it also expands by cell proliferation, creating new local gradients of positional information within former single-identity domains. Analogous to a “growing canvas” painting itself, the alternation of growth and patterning results in the creation of a form. This preliminary study attempts to reproduce pattern formation through a multiscale, recursive and modular process. It explores the elusive relationship between nonspatial GRN weights (genotype) and spatial patterns (phenotype). Abstracting from biology in the same spirit as neural networks or swarm optimization, I hope to be contributing to a novel engineering paradigm of system construction that could complement or replace omniscient architects with decentralized collectivities of agents.