A two-stage diffusion-driven morphogenesis model with evolving connectivity
Abstract
Morphogenesis of diatom silica shells involves a sequence of topological transitions: initially separate ribs grow and branch, then merge through bridges, leaving a regular network of pores. Existing models based on diffusion-limited aggregation or reaction-diffusion reproduce either branching or pore formation, but not both within a single framework. Here we propose a two-stage model of diffusion-driven morphogenesis with evolving connectivity. The model is formulated on a fixed finite element mesh with a density field on an active layer. Stage 1 reproduces dendritic growth, where a stimulus based on the local diffusive flux exceeds a threshold. Stage 2 uses an inverted stimulus, where high local flux suppresses precipitation, stabilizing pores between the dendrites. The update rules are analogous to sensitivity in density-based topology optimization and to strain energy density in bone remodeling. The model predicts distinct morphological regimes on each stage, controlled by the respective thresholds. For a reference calculation, the predicted pore network is regular, with approximately uniform spacing, and pores are absent near the domain edges, consistent with observations on diatom valves. The model provides a unified framework for describing both stages of silica morphogenesis and suggests a route for comparing computational predictions with cryo-electron tomography data.
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BibTeX
@misc{safonov2026twostage,
title = {{A two-stage diffusion-driven morphogenesis model with evolving connectivity}},
author = {Alexander Safonov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41798},
eprint = {2610.41798},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41798},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A two-stage diffusion-driven morphogenesis model with evolving connectivity
AU - Alexander Safonov
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41798
UR - https://arxiv.org/abs/2610.41798
AB - Morphogenesis of diatom silica shells involves a sequence of topological transitions: initially separate ribs grow and branch, then merge through bridges, leaving a regular network of pores. Existing models based on diffusion-limited aggregation or reaction-diffusion reproduce either branching or pore formation, but not both within a single framework. Here we propose a two-stage model of diffusion-driven morphogenesis with evolving connectivity. The model is formulated on a fixed finite element mesh with a density field on an active layer. Stage 1 reproduces dendritic growth, where a stimulus based on the local diffusive flux exceeds a threshold. Stage 2 uses an inverted stimulus, where high local flux suppresses precipitation, stabilizing pores between the dendrites. The update rules are analogous to sensitivity in density-based topology optimization and to strain energy density in bone remodeling. The model predicts distinct morphological regimes on each stage, controlled by the respective thresholds. For a reference calculation, the predicted pore network is regular, with approximately uniform spacing, and pores are absent near the domain edges, consistent with observations on diatom valves. The model provides a unified framework for describing both stages of silica morphogenesis and suggests a route for comparing computational predictions with cryo-electron tomography data.
ER -