Self-assembly of a filament by curvature-inducing proteins

- We introduce a model for the attachment of curvature-inducing proteins on a membrane.
- The stability of the filament shape is characterized by the protein recruitment parameters.
- The dynamics of protein aggregation leads to the formation of regions of high and low curvatures.
- Phase-coarsening eventually leads to a filament with uniform curvature.

We explore a simplified macroscopic model of membrane shaping by means of curvature-sensing BAR proteins. Equations describing the interplay between the shape of a freely floating filament in a fluid and the adhesion kinetics of proteins are derived from mechanical principles. The constant curvature solutions that arise from this system are studied using weakly nonlinear analysis. We show that the stability of the filament's shape is completely characterized by the parameters associated with protein recruitment and establish that in the bistable regime, proteins aggregate on the filament forming regions of high and low curvatures. This pattern formation is then followed by phase-coarsening that resolves on a time-scale dependent on protein diffusion and drift across the filament, which contend to smooth and maintain the pattern respectively. The model is generalized for multiple species of BAR proteins and we show that the stability of the assembled shape is determined by a competition between proteins attaching on opposing sides.