Role of the density (bundling) instability in the motor–filament continuum model

Determine the role of the density (bundling) instability in the microtubule–motor continuum model defined by Eqs. (m) and (der), specifically when the passive-to-active ratio α is small enough that the effective diffusivity becomes negative and a bilaplacian regularization term is required in the microtubule density equation. Ascertain how this density instability affects the stability, pattern formation, and phase behavior of the system compared to the regimes analyzed here with sufficiently large α where the instability is not present.

Background

In the linear stability analysis of the isotropic state, the authors identify an ordering instability of the polarization field and note a separate density (bundling) instability occurring at high microtubule density. This density instability requires a higher-order regularization term (a bilaplacian in the density equation) to control short-wavelength behavior.

Throughout the main analysis, the paper focuses on parameter regimes (specifically sufficiently large passive-to-active ratio α) where the density instability does not arise, allowing the authors to avoid introducing and analyzing the bilaplacian term. The explicit impact of the density instability on the model’s dynamics and phases is therefore left unresolved and deferred for future investigation.