On Growth and Form, and Function: Reusable Regulatory Handles Control Phenotypic Variation

2026-09-24

AI Summary

This study addresses how large-scale phenotypic morphological transformations can be realized through low-dimensional variations in underlying regulatory dynamics. To investigate this, the authors employ Neural Cellular Automata (NCA) to simulate developmental processes and utilize Low-Rank Adaptation (LoRA) to encode morphological transformations as low-rank modulations of a fixed regulatory scaffold, thereby uncovering reusable system-level scaling directions within the latent space. The work presents a computational instantiation of D'Arcy Thompson's grid transformations, demonstrating that phenotypic variation can be effectively encoded, composed, and controlled via low-dimensional directions within a two-dimensional NCA weight space. Furthermore, the discovered scaling directions enable adaptive zero-shot transfer from a single phenotype to structurally and semantically distinct phenotypes while preserving their intrinsic characteristics.

Abstract

How phenotypic transformations are implemented by changes in underlying regulatory dynamics remains a central question in developmental biology. Inspired by D'Arcy Thompson's 1917 "On Growth and Form", we ask whether coherent large-scale transformations of morphology can be encoded as low-dimensional modulations of a self-organizing developmental system. We use neural cellular automata (NCAs) as bio-inspired models of distributed development, in which a shared local regulatory network grows target morphologies from a single cell. We apply low-rank adaptation (LoRA) to pretrained NCAs, representing each adapted developmental program as a low-rank modulation of a fixed regulatory scaffold. Horizontal and vertical scaling of a fully grown 2D emoji phenotype can each be implemented by rank-one adaptations. Their linear combinations parametrically control phenotype size, generalize beyond the training distribution, and compose with target-specific adapters. Strikingly, adaptations learned for one phenotype transfer zero-shot across structurally and semantically diverse phenotypes sharing the same reference scaffold, while largely preserving internal features. This suggests reusable system-level hyper-directions of scale rather than morphology-specific transformations. From approximately 25,000 independently trained phenotype-specific NCA adapters with a shared scaffold, we further identify latent low-dimensional directions that functionally control phenotypic variation including scaling, style, and symmetrical fission. Together, our results provide a computational realization of D'Arcy Thompson's remarkable grid transformations in a 2D NCA---a minimal cybernetic tissue in which variations of fully grown emoji phenotypes can be encoded, combined, and controlled through low-dimensional directions in regulatory weight space.

Problem

• phenotypic variation
• regulatory dynamics
• developmental biology
• morphological transformation
• neural cellular automata

Innovation

• Neural Cellular Automata
• Low-Rank Adaptation
• Zero-Shot Transfer
• Phenotypic Variation
• Morphogenesis