Dynamical systems of fate and form in development

Area of Science:

• Developmental biology
• Dynamical systems theory
• Computational biology

Background:

• Cell differentiation and morphogenesis involve complex, high-dimensional gene expression and spatial dynamics.
• Stable developmental outcomes suggest underlying low-dimensional geometric organizing principles.
• Existing research often treats cell fate and morphogenesis separately.

Purpose of the Study:

• To review the application of dynamical systems frameworks in developmental biology.
• To highlight methods for extracting geometric structures from experimental data.
• To promote an integrated understanding of cell fate decisions and morphogenetic movements.

Main Methods:

• Survey of historical and recent advances in dynamical systems approaches.
• Focus on experimental techniques for identifying geometric structures (e.g., attractors, repellers).
• Analysis of interconnections between geometric structures in different spaces.

Main Results:

• Identification of low-dimensional geometric structures (fixed points, manifolds) organizing cell trajectories.
• Demonstration of how these structures govern cell fate decisions and morphogenetic movements.
• Unification of typically distinct domains within developmental biology through a dynamical systems lens.

Conclusions:

• Dynamical systems provide a powerful framework for understanding developmental processes.
• Extracting geometric structures aids in rationalizing complex experimental data.
• This perspective facilitates principled dimensionality reduction and integrated developmental insights.