Embryonic lateral inhibition as optical modes: An analytical framework for mesoscopic pattern formation

Area of Science:

• Developmental biology
• Biophysics
• Solid-state physics analogies

Background:

• Cellular checkerboard patterns are crucial in embryonic development.
• Lateral inhibition is a key mechanism governing cell fate decisions.
• Understanding pattern formation requires considering discrete cellular arrangements.

Purpose of the Study:

• To analyze cellular checkerboard patterns using a tractable model of lateral inhibition.
• To explore the relationship between lattice structures and pattern selection.
• To provide new predictions for experimental validation.

Main Methods:

• Analytical modeling of lateral inhibition in linear and hexagonal lattices.
• Analogy to solid-state physics concepts like phonons and crystal lattices.
• Redefinition of lattice bases based on interaction symmetries.

Main Results:

• Steady states of lateral inhibition are analogous to optical phonons at the Γ point (k=0).
• Lattice bases were redefined for linear (2-cell basis) and hexagonal (3-cell basis) arrangements.
• Hexagonal lattices can exhibit three distinct pattern states, including coexisting periodic checkerboards.

Conclusions:

• The granularity of cellular patterns necessitates a solid-state physics approach for pattern selection.
• Redefined lattice bases provide insights into the symmetries of cellular interactions.
• The model predicts distinct emergent patterns in hexagonal lattices, guiding future experiments.