Active Surface Flows Accelerate the Coarsening of Lipid Membrane Domains

Phase separation of multicomponent lipid membranes is characterized by the nucleation and coarsening of circular membrane domains that grow slowly in time as $\sim t^{1/3}$, following classical theories of coalescence and Ostwald ripening. In this Letter, we study the coarsening kinetics of phase-separating lipid membranes subjected to nonequilibrium forces and flows transmitted by motor-driven gliding actin filaments. We experimentally observe that the activity-induced surface flows trigger rapid coarsening of noncircular membrane domains that grow as $\sim t^{2/3}$, a $2\mathsf{x}$ acceleration in the growth exponent compared to passive coalescence and Ostwald ripening. We analyze these results by developing analytical theories based on the Smoluchowski coagulation model and the phase field model to predict the domain growth in the presence of active flows. Our Letter demonstrates that active matter forces may be used to control the growth and morphology of membrane domains driven out of equilibrium.

Figure 1

(a) Planar lipid bilayers phase-separate into Lo and liquid-disordered Ld phases. (b) In this Letter, we study the growth of lipid domains of size $a$ under 2D flows generated by internal “active” forcing. (c) Left: in our experiments, actin is bound to the Ld phase, avoiding the Lo phase. Right: actomyosin contraction internally drives lipid membrane flows. (d) Time-lapse images of actin (magenta) contraction with vectors calculated from particle image velocimetry overlaid (top), and Lo lipid domains growing in time (green, bottom). Scale bar is $5\mathrm{\mu }\mathrm{m}$.

Figure 2

Lo lipid domain size $a(t)$ is plotted as a function of time $t$ for experiments (black) and Cahn-Hilliard numerical calculations (green), with growth exponents $\alpha$ presented for each: $a\sim t^{\alpha }$. Closed symbols represent passive domain growth in the absence of flow, with circles and triangles representing three independent passive experiments. Passive domains grow as $\alpha =1/3$ (dashed black line), consistent with classical theories on coalescence and Ostwald ripening. Open symbols represent active domain growth in the presence of 2D flow, either imposed experimentally via actomyosin contraction or incorporated theoretically using particle image velocimetry from experiments [Fig. 1]. Five independent active experiments are presented, along with simulations using three different Péclet numbers (Pe). Each dataset is rescaled by a different factor $a_0$ to capture the power law scaling exponents.

Figure 3

General linear flows modulate the growth and morphology of phase-separating domains. Numerical solution snapshots of phase separation for Eq. (1) in (a) shear flow and (b) rotational flow. Insets: evolution of the domains. (c) Static structure factor for domains under shear flow. (d) Shear flow increases the domain growth rate, whereas rotational flow maintains the same scaling as passive Ostwald ripening, $\approx t^{1/3}$. The parameters shown here correspond to $(M,\kappa ,\dot{\gamma })=(1,0.25,0.04)$, or $\mathrm{Pe}={10}^{-2}$.