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Preparation of Hydroxy-PAAm Hydrogels for Decoupling the Effects of Mechanotransduction Cues

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Geometry-induced patterns through mechanochemical coupling.

Laeschkir Würthner¹, Andriy Goychuk¹, Erwin Frey^1,2

¹Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany.

Physical Review. E

|August 16, 2023

Summary

This summary is machine-generated.

Cell shape dynamics influence intracellular protein patterns, creating feedback loops. Geometric changes in cell membranes can regionally induce or suppress these patterns, controlling cell behavior.

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Area of Science:

Biophysics
Computational Biology
Cell Biology

Background:

Intracellular protein patterns regulate essential cell processes like division and motility.
Cell shape dynamics and protein pattern formation are intricately linked through feedback mechanisms.
The precise mechanisms governing this cell shape-chemical dynamics feedback are not fully understood.

Purpose of the Study:

To elucidate the mechanisms underlying the feedback loop between cell shape and intracellular protein dynamics.
To explore a conceptual model of cell polarity on a dynamic manifold.
To investigate how geometric changes in cell membranes affect reaction-diffusion systems.

Main Methods:

Developed a conceptual model for cell polarity on a dynamic one-dimensional manifold.
Utilized differential geometry to derive equations for mass-conserving reaction-diffusion systems on evolving manifolds.
Applied and generalized the local equilibria theory for reaction-diffusion systems.

Main Results:

Demonstrated that dynamic membrane shape changes can induce regional pattern-forming instabilities.
Showed that geometric deformations can suppress pattern formation and shift existing patterns.
Derived a criterion for geometry-induced pattern-forming instabilities linked to system phase space.

Conclusions:

Local membrane geometry acts as a critical dynamical control parameter for pattern formation.
The interplay between membrane shape and reaction-diffusion dynamics generates diverse patterns like oscillations and waves.
Findings reveal how dynamic geometry influences cell polarity and behavior.