Self-organization of developing embryo using scale-invariant approach.

Area of Science:

• Developmental biology
• Systems biology
• Biophysics

Background:

• Self-organization is a fundamental biological process observed across all life scales.
• Embryonic development exhibits complex self-organizing behaviors.
• Quantifying self-organization in embryos is crucial for understanding developmental processes.

Purpose of the Study:

• To introduce and validate a novel scale-invariant power law (SIPL) method for quantifying self-organization in developing embryos.
• To apply the SIPL method to analyze self-organization in early C. elegans embryogenesis.
• To compare the organizational properties of different embryonic cell lineages.

Main Methods:

• Developed a scale-invariant power law (SIPL) method using centro-axial skew symmetrical matrices (CSSM) and basic square matrices (BSM).
• Calculated the SIPL coefficient to estimate the degree of self-organization.
• Validated the SIPL method using fractal dimensions (fd) of geometric shapes (straight line, Koch curve) and diffusion-limited aggregation (DLA).

Main Results:

• The SIPL method demonstrated power-law behavior consistent with fractal dimensions.
• The ABp sublineage exhibited a higher SIPL coefficient compared to the EMS lineage in developing C. elegans.
• Diffusion-limited aggregation analysis indicated higher fractal dimensions in ABp (type 1 cluster) than EMS (type 2 cluster).

Conclusions:

• The SIPL method effectively quantifies self-organization with power-law characteristics.
• The ABp sublineage is demonstrably more organized than the EMS sublineage during early C. elegans embryogenesis.
• Findings provide quantitative insights into differential organization within developing embryos.