Growth and remodeling control shape memory in morphogenetic rods

Abstract

Mechanical instabilities provide a general design principle for shaping developing organs and engineering soft materials. However, in slender structures, simple elastic buckling tends to erase rather than preserve shape complexity: structures relax to the simplest possible shape, erasing finer detail. Living systems nonetheless build complex, reproducible morphologies from continually remodeling material, while remaining robust to noise arising across scales. Using analytical theory and numerical simulations of a minimal model of growing visco-elasto-plastic rods, we show that remodeling plays two opposing roles: At low plasticity, patterns coarsen through elastic relaxation, while high plasticity converts fluctuations into geometric disorder. This sets a trade-off between shape complexity and reproducibility with an optimal intermediate plasticity, which protects initial patterns. Growth breaks this trade-off by suppressing both failure modes, enabling complex shapes to be reproducibly generated. Our results identify remodeling and growth rates as two knobs governing whether an encoded pattern is remembered, degraded, or transformed.