Topological Metric Detects Hidden Order in Disordered Media

Area of Science:

• Biophysics
• Complex Systems
• Microscopy

Background:

• Distinguishing amorphous cellular materials is challenging.
• Microscopy enables single-cell resolution studies of biological systems.
• Understanding dynamics from static snapshots is an open problem.

Purpose of the Study:

• Introduce a novel method to quantify differences between disordered cellular structures.
• Enable reconstruction of system dynamics and phase spaces from static data.
• Apply this method to biological systems like developing tissues and bacterial swarms.

Main Methods:

• Developed a topological earth mover's (TEM) distance metric.
• Analyzed local graph neighborhoods of cell-centroid networks.
• Leveraged neighborhood motif distributions for structural comparison.

Main Results:

• The TEM metric allows interpretable reconstruction of equilibrium and nonequilibrium phase spaces.
• The framework successfully recovers time ordering from static images without prior dynamic knowledge.
• Applied to fly wing development, it reveals a topological optimal transport problem.
• Analysis of bacterial swarms shows a universal neighborhood size distribution consistent with Tracy-Widom statistics.

Conclusions:

• The TEM distance provides a powerful tool for analyzing disordered biophysical systems.
• This method advances our ability to infer dynamics and structure from static microscopy data.
• The findings offer new perspectives on developmental biology and collective bacterial behavior.