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Ordered hexagonal patterns via notch-delta signaling
Eial Teomy1, David A Kessler1, Herbert Levine2,3
1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Biology
|September 21, 2021
Summary
Notch-delta signaling, a cell-to-cell contact mechanism, forms cellular patterns. This study explains hexagonal patterns and reveals novel patterns with low cis-coupling, offering strategies for defect-free pattern generation.
Area of Science:
- Cellular Biology
- Developmental Biology
- Mathematical Biology
Background:
- Notch-delta signaling is crucial for ordered cellular differentiation during development.
- This juxtacrine signaling relies on direct cell-to-cell contact, unlike paracrine signaling.
- Understanding pattern formation in biological systems is key to developmental processes.
Purpose of the Study:
- To provide an exact mathematical treatment of pattern formation driven by notch-delta signaling.
- To analyze the conditions leading to specific cellular patterns, such as hexagonal arrangements.
- To investigate novel patterns arising from variations in signaling parameters and propose methods for defect-free pattern generation.
Main Methods:
- Developed a system of nine coupled ordinary differential equations to model notch-delta signaling.
- Employed co-dimension 2 pitchfork bifurcation analysis to study pattern formation.
- Investigated the effects of varying cis-coupling strengths on pattern outcomes.
Main Results:
- Explained the prevalence of hexagonal patterns with central high delta.
- Identified conditions for anti-hexagonal patterns (central high notch).
- Discovered novel patterns with co-localized high delta and high notch for low cis-coupling.
Conclusions:
- The mathematical model accurately predicts observed hexagonal and anti-hexagonal patterns.
- Low cis-coupling can lead to previously undescribed cellular arrangements.
- The biological system's weak first-order nature necessitates additional mechanisms for defect-free patterns, for which a strategy is proposed.
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