Abstract
This paper introduces a Gene Regulatory Neural Cellular Automata (ENIGMA), an innovative extension of the Neural Cellular Automata (NCA) framework aimed at modeling biological development with a greater degree of biological fidelity. Traditional NCAs, while capable of generating complex patterns through neural network-driven update rules, lack mechanisms that closely mimic biological processes such as cell-cell signaling and gene regulatory networks (GRNs). Our ENIGMA model addresses these limitations by incorporating update rules based on a simulated gene regulatory network driven by cell-cell signaling, optimized both through backpropagation and genetic algorithms. We demonstrate the structure and functionality of ENIGMA through various experiments, comparing its performance and properties with those of natural organisms. Our findings reveal that ENIGMA can successfully simulate complex cellular networks and exhibit phenomena such as homeotic transformations, pattern maintenance in variable tissue sizes, and the formation of simple regulatory motifs akin to those observed in developmental biology. The introduction of ENIGMA represents a significant step towards bridging the gap between computational models and the intricacies of biological development, offering a versatile tool for exploring developmental and evolutionary questions with profound implications for understanding gene regulation, pattern formation, and the emergent behavior of complex systems.