Curvature-driven positioning of Turing patterns in phase-separating curved membranes

Area of Science:

• Biophysics
• Theoretical Chemistry
• Computational Biology

Background:

• Turing patterns are crucial for biological pattern formation.
• Understanding pattern dynamics on curved, phase-separating membranes like lipid bilayers is complex.
• Existing models often simplify membrane geometry and composition.

Purpose of the Study:

• To introduce a novel finite difference scheme for simulating Turing patterns on curved membranes.
• To investigate the influence of phase-separating binary fluids and membrane curvature on pattern dynamics.
• To explore the coupling between component diffusivity and local membrane composition.

Main Methods:

• Developed a new finite difference numerical scheme.
• Simulated a two-species activator-inhibitor system on a curved membrane.
• Analyzed the effects of membrane composition and local curvature on pattern properties.

Main Results:

• The underlying binary fluid significantly alters Turing pattern dynamics and steady states.
• Membrane curvature can arrest domain coarsening and selectively position patterns.
• A minimal coupling between diffusivity and membrane composition drives observed phenomena.

Conclusions:

• The theoretical framework provides new insights into pattern formation on curved biological membranes.
• This model can be applied to understand intracellular pattern formation involving membrane proteins.
• Geometry and membrane phase separation are critical factors in biological pattern regulation.