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Related Experiment Video

Updated: Dec 13, 2025

Evaluation of Hemisphere Lateralization with Bilateral Local Field Potential Recording in Secondary Motor Cortex of Mice

Evaluation of Hemisphere Lateralization with Bilateral Local Field Potential Recording in Secondary Motor Cortex of Mice

Published on: July 31, 2019

Boolean analysis of lateral inhibition.

Elisa Tonello¹, Heike Siebert²

¹Department of Mathematics and Computer Science, Freie Universität, 14195, Berlin, Germany. elisa.tonello@fu-berlin.de.

Journal of Mathematical Biology

|July 31, 2020

Summary

Boolean networks modeling the Delta-Notch system reveal that all attractors are fixed points. This study characterizes these patterns and their robustness, aiding future research in developmental biology.

Keywords:

Boolean networks Cell signalling Multi-cellular systems Patterns

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Area of Science:

Systems Biology
Computational Biology
Developmental Biology

Background:

The Delta-Notch signaling pathway is crucial for cell-fate decisions in development.
Boolean networks offer a simplified yet powerful framework for modeling biological systems.
Lateral inhibition, mediated by Delta-Notch, generates spatial patterns of cell differentiation.

Purpose of the Study:

To analyze the attractors of spatial Boolean network models of the Delta-Notch system.
To characterize the fixed points, trap spaces, and basins of attraction.
To investigate the robustness of emergent patterns to perturbations.

Main Methods:

Modeling the Delta-Notch system using fully asynchronous Boolean networks on undirected graphs.
Analyzing system dynamics to identify fixed points and their properties.
Characterizing trap spaces and basins of attraction for both full and simplified models.

Main Results:

All attractors in the studied Boolean network models converge to fixed points, irrespective of the neighborhood structure.
These fixed points represent the fine-grained spatial patterns characteristic of lateral inhibition.
A characterization of trap spaces was developed, enabling analysis of pattern robustness.

Conclusions:

The study provides a qualitative analysis of Delta-Notch pattern formation in Boolean networks.
The findings offer insights into the stability and robustness of developmental patterns.
This work can guide simulation-based approaches and the study of more complex biological mechanisms.