A Becker–Döring Type Model for Cell Polarization

We propose a model for cell polarization based on the Becker–Döring equations with the first coagulation coefficient equal to zero. We show convergence to equilibrium for power-law coagulation and fragmentation rates and obtain a loss of mass in the limit t → ∞ depending on the initial mass and the relative strengths of the coagulation and fragmentation processes. In the case of linear rates, we further show that large clusters evolve in a self-similar manner at large times by comparing limits of appropriately rescaled solutions in different spaces.