Field closure, ice neurons, and when a dendrite is a motif
Abstract
Dendritic silhouettes are cheap. Pond ice neurons, diffusion-limited aggregates, wiring-minimizing arbors, and biological neurons can share a branching statistic because they share a growth instability, not because they are functionally similar. We take that observation as a modeling constraint. The ice neuron only structurally resembles a biological neuron. A biological neuron carries an internal state and a field that it helps generate, letting geometry, dynamics, and field co-sculpt one another. In our construction, the ice neuron is the zero-gain limit of an interfacial system in which a FitzHugh--Nagumo state lives on the moving front and writes back into the field that drives it, with dimensionless gain γ. At γ=0, morphology and internal dynamics decouple into a Mullins--Sekerka growth band and a damped oscillator. Finite γ deforms the spectrum, shifts the selected instability, and opens an oscillatory region below the isolated Hopf threshold. On a dendrite grown at γ=0 and then frozen, field closure increases distal persistence without changing the geometry; its first-order effect remains positive across repeated realizations of the same growth rule and localizes to a small set of non-cable field shortcuts. Nonlinear dynamics remain finite beyond the linear instability: below threshold, closure is almost the transmission; at spike amplitude, it is a correction to a regenerative cable event. A dendritic tree therefore is not intrinsically a structural spandrel. Shape alone is morphology without an internal state or a source term. That is the dendritic silhouette of the ice neuron. Excitability adds an active cable. Field closure is the biophysical mélange in which the neuron helps write the field that acts back on it, sculpting its dynamics and, during growth, its structure. That is a biological neuron.
Related
- Ligand-binding/transcriptional repressor domain-deficient REV-ERBβ inhibits dendrite and spine formation of newborn adult hippocampal neurons
- Clustered inputs engage dendritic nonlinearities and calcium signaling to support efficient place-field formation in CA1 pyramidal neurons
- Opposing Roles for the Spectraplakin Short Stop in Stable and Dynamic Dendrites Reveal Divergent DLK Signaling and a Role in Dendrite Regeneration
- RTK signaling and epidermis remodeling instruct dendrite regrowth after pruning in the Drosophila PNS
- Why bother with controlled-environment phenotyping when field phenomics is already up and running?
BibTeX
@misc{dehghani2026field,
title = {{Field closure, ice neurons, and when a dendrite is a motif}},
author = {Nima Dehghani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00184},
eprint = {2610.00184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Field closure, ice neurons, and when a dendrite is a motif
AU - Nima Dehghani
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00184
UR - https://arxiv.org/abs/2610.00184
AB - Dendritic silhouettes are cheap. Pond ice neurons, diffusion-limited aggregates, wiring-minimizing arbors, and biological neurons can share a branching statistic because they share a growth instability, not because they are functionally similar. We take that observation as a modeling constraint. The ice neuron only structurally resembles a biological neuron. A biological neuron carries an internal state and a field that it helps generate, letting geometry, dynamics, and field co-sculpt one another. In our construction, the ice neuron is the zero-gain limit of an interfacial system in which a FitzHugh--Nagumo state lives on the moving front and writes back into the field that drives it, with dimensionless gain γ. At γ=0, morphology and internal dynamics decouple into a Mullins--Sekerka growth band and a damped oscillator. Finite γ deforms the spectrum, shifts the selected instability, and opens an oscillatory region below the isolated Hopf threshold. On a dendrite grown at γ=0 and then frozen, field closure increases distal persistence without changing the geometry; its first-order effect remains positive across repeated realizations of the same growth rule and localizes to a small set of non-cable field shortcuts. Nonlinear dynamics remain finite beyond the linear instability: below threshold, closure is almost the transmission; at spike amplitude, it is a correction to a regenerative cable event. A dendritic tree therefore is not intrinsically a structural spandrel. Shape alone is morphology without an internal state or a source term. That is the dendritic silhouette of the ice neuron. Excitability adds an active cable. Field closure is the biophysical mélange in which the neuron helps write the field that acts back on it, sculpting its dynamics and, during growth, its structure. That is a biological neuron.
ER -