Fluctuations and symmetries in two-dimensional active gels

Area of Science:

• Soft Matter Physics
• Biophysics
• Non-equilibrium Systems

Background:

• Biological active matter, such as cytoskeletal dynamics in eukaryotic cells, exhibits unique physical properties.
• Understanding the collective behavior of active gels is crucial for comprehending cellular processes.

Purpose of the Study:

• To derive effective two-dimensional (2D) coarse-grained hydrodynamic equations for thin active gels.
• To investigate the influence of polar or nematic symmetries and boundary conditions on the constitutive relations.
• To analyze linear instabilities, correlation functions, and particle diffusion in these active gel systems.

Main Methods:

• Utilizing established three-dimensional (3D) descriptions of active gels confined between parallel plates.
• Deriving effective 2D constitutive relations for small deviations from thermodynamic equilibrium.
• Applying these relations to study system dynamics under varying symmetries and boundary conditions.

Main Results:

• Demonstrated how spatial symmetries and boundary conditions dictate the structure of constitutive relations in active gels.
• Analyzed linear instabilities and calculated correlation functions.
• Quantified the diffusion constant of a tagged particle, linking it to the system's activity or non-equilibrium drive.

Conclusions:

• The derived 2D hydrodynamic equations provide a simplified yet accurate model for active gel dynamics.
• The study elucidates the critical role of symmetry and confinement in shaping the macroscopic behavior of active matter.
• Results offer a foundation for further research into active matter systems and their biological relevance.