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Homarus Americanus Stomatogastric Nervous System Dissection

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A discrete-time continuous-space neural model for shell patterns in mollusks.

Rahnuma Islam¹, Bard Ermentrout¹, Sabrina Streipert¹

¹Department of Mathematics, University of Pittsburgh, Thackeray Hall, Pittsburgh, 15213, PA, USA.

Journal of Theoretical Biology

|December 20, 2025

Summary

This summary is machine-generated.

A new neural model generates diverse mollusk shell and pigmentation patterns using excitation and inhibition. This biologically inspired model reveals how parameters control pattern formation in aquatic organisms.

Keywords:

Bifurcation analysis Molluscan pigmentation Neural excitation-inhibition model Shell pattern formation Spatio-temporal dynamics

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Area of Science:

Computational Biology
Developmental Biology
Biophysics

Background:

Aquatic mollusks exhibit complex shell structures and pigmentation patterns.
Previous neural models for shell patterns had limitations, such as requiring a "refractory" substance.

Purpose of the Study:

To introduce a novel discrete-time, continuous-space neural model for generating diverse molluskan shell and pigmentation patterns.
To improve upon existing models by separating neural inhibition into its own population.

Main Methods:

Development of a discrete-time, continuous-space neural model incorporating separate neural excitation and inhibition populations.
Analysis of local stability around equilibria and bifurcation analysis to understand parameter roles.
Simulation of secretory activity to replicate natural patterns.

Main Results:

The model successfully produces a wide variety of molluskan pigmentation patterns.
The incorporation of a separate inhibition population eliminates the need for a "refractory" substance.
Parameter analysis demonstrates their critical role in governing spatial, temporal, and spatio-temporal pattern emergence.

Conclusions:

The developed neural model effectively replicates diverse natural shell and pigmentation patterns in aquatic mollusks.
The model provides insights into the mechanisms underlying pattern formation through neural excitation and inhibition.
Bifurcation analysis highlights the significant influence of system parameters on pattern complexity and dynamics.