Energetics and dynamics of global integrals modeling interaction between stiff filaments

Area of Science:

• Biophysics
• Soft Matter Physics
• Computational Biology

Background:

• Filamentous structures, like actin filaments, interact via cross-linkers (e.g., myosin).
• Understanding these interactions is crucial for cellular processes and material science.
• Previous models often simplify the complex dynamics of filament alignment.

Purpose of the Study:

• To model the attractive and spacing interactions between pairs of filaments using global integral kernels.
• To investigate the stability of different filament alignment states (parallel, anti-parallel, orthogonal).
• To analyze the effects of stochastic perturbations on filament dynamics and simulate myosin-mediated sliding.

Main Methods:

• Developed a simplified 2D model for stiff, long rods interacting via cross-linkers.
• Utilized negative gradient flow differential equations to analyze energy functionals.
• Incorporated stochastic perturbations (Gaussian noise) to model cross-link binding variability.
• Performed explicit calculations for forces and torques, and conducted stochastic simulations.

Main Results:

• Identified parallel and anti-parallel alignments as 'super-stable' equilibria.
• Demonstrated that stochastic noise leads to generalized (bimodal Gaussian) stationary distributions.
• Observed characteristic sliding behavior in simulations, consistent with myosin-actin interactions.
• Extended analysis to finite-length filaments, showing similar phenomena.

Conclusions:

• The model accurately captures the 'super-stable' nature of parallel/anti-parallel filament alignments.
• Stochastic effects are essential for understanding realistic filament dynamics and observed sliding behaviors.
• The findings provide insights into the self-organization principles of filamentous biological systems.