Active Particles Destabilize Passive Membranes

Abstract

We present a theory for the interaction between active particles and a passive flexible membrane. By explicitly solving for the pressure exerted by the active particles, we show that they reduce the membrane tension and bending modulus and introduce novel non-local contributions to the membrane mechanics. This theory predicts activity-induced instabilities and their morphology are in agreement with recent experimental and simulation data.

Figures (3)

• Figure 1: Theory (left axes): Stability boundaries as functions of $\phi_\infty/\phi_{\rm max}$ and $\alpha$ in $d=3$. Colors denote stable (orange), short-wavelength ($\lambda$) unstable (blue), long $\lambda$ unstable (red), and MIPS (green) regimes. The solid black line is the non-interacting stability boundary at low $\phi_\infty$, replaced by the interacting (WKB) prediction, accurate beyond the red curve, when they cross at higher $\phi_\infty$; the non-interacting line continues dashed. In the hashed region, the WKB approximation is unreliable. Simulations (right axes): Results from Ref. Vutukuri2020 shown versus $\overline{\phi}/\phi_{\rm max}$ and ${\rm Pe}$. Points (outlined for snapshots) colored as in Vutukuri2020: orange ("fluctuating"), blue ("tethering"), and green ("bola"). Two sets of axes allow qualitative comparison, since $\phi_\infty$ and $\overline{\phi}$ are not related directly.
• Figure 2: Critical activity $\alpha_c$ at which $\gamma_{\rm eff}=0$ (red), or $\kappa_{\rm eff}=0$ (blue), plotted versus $g=\gamma V_d(b)/(\Lambda_d k_B T)$ and $k=\kappa V_d(b)/(\Lambda_d^3 k_B T)$ respectively, computed in the non-interacting limit at $\phi_\infty/\phi_{\rm max}=0.05$. Scalings of $\alpha_c$ at large and small $g$ and $k$ are indicated. The yellow star (inset) marks $\alpha_c$, the critical point where increasing activity destabilizes the membrane at low density to the instability type indicated in the main panel. When interactions are included, the short-wavelength unstable region (blue - inset) shrinks as $\gamma$ (red arrow) or $\kappa$ increase (blue arrow).
• Figure 3: Plots of the reduced volume fraction, $\varphi^{*}$ [(a) and (c)], and activity, $\alpha^{*}$ [(b) and (d)], where the interacting solution departs from the non-interacting solution [pink star, inset panel (c)] as functions of reduced bending modulus, $k$ panels (a) and (b), and surface tension, $g$ panels (c) and (d). Approximate scalings with $k$ are indicated. When held fixed, membrane parameters are $g=6$ and $k=154$, consistent with those in Fig. \ref{['fig:Fig']}. These show how the blue region of short wavelength instability shrinks when $\gamma$ or $\kappa$ are increased, as shown by the red and blue arrows in the inset of panel (d).