Self-Organization and Cyclic Positioning of Active Condensates

Abstract

Active transport of biomolecular condensates and cell migration in collectives are fundamental to development, homeostasis, and processes such as cancer progression, wound healing, and infection response. Yet how these assemblies are positioned, regulated, and driven through cycles of dissolution and reassembly is not fully understood. We address this using a model of attractive active Brownian particles (ABPs). Using Brownian dynamics simulations, we show that these particles undergo liquid-gas phase separation, and spatially varying activity fields induce striking emergent dynamics. Droplets migrate up activity gradients, and above a critical activity, they fragment into a gas phase. The gas then migrates down the gradient, and droplets reassemble, yielding robust positioning cycles. This emergent condensate cycle arises without biochemical feedback loops and relies only on the interplay of attractions, motility, and gradients. In binary mixtures of active-passive particles, differential cohesion leads to self-sorting of particles, where strongly-cohesive ABPs compact into dense cores surrounded by peripheries enriched with weakly-cohesive passive particles. The passive particles stabilize the dynamic clusters of ABPs, and they migrate toward high-activity regions. Our findings suggest a generic mechanism for spatial control and turnover of condensates in biology.

Figures (5)

• Figure 1: (a) A snapshot of the simulation box for ${\rm Pe}=10$ and $\epsilon=4$. The system exhibits phase coexistence, with a dense liquid-like slab at the center surrounded by a dilute vapor phase. (b) Phase diagrams as a function of attraction strength $\epsilon$. Circles indicate simulation points, solid lines are fits to Eq. (S1) of SM, and dashed lines are the approximate $\epsilon$ values beyond which the system transitions to a solid-like phase. Star symbols indicate the estimated critical points ($\rho^*$, $\epsilon^*$). (c) Profile of the average propulsion direction along $z$-axis, $\langle e_z(z) \rangle$, for various ${\rm Pe}$ at fixed $\epsilon/\epsilon^* = 1.7$. Legends of (b) also apply to (c). (d-f) Velocity streamlines at the interfaces of the condensed phase $z=\pm7$ and at the center of condensate $z=0$. Here, Pe$=10$ and $\epsilon=4$.
• Figure 2: (a) Initial configuration at time $t=0$, showing a dense droplet with $\epsilon=5$ placed on the left side of the box ($z < -20$), where activity is lowest. The activity field is given by $f_{\rm a}(z) = 20(1 - |z|/25)$, creating a linear gradient symmetric about $z=0$. (b) Steady-state normalized density profiles $\rho(z)/\rho_0$ for varying $\epsilon$. (c) Steady-state profiles of the ABP propulsion direction projected along the $z$-axis, $\langle e_z(z) \rangle$.
• Figure 3: (a) Steady-state density profile of ABPs along the z axis. The activity field is given by $f_{\rm a}(z) = f_{\rm a}^*(z + 25)/50$, with $f_{\rm a}^*=20$. The system along the z-axis is non-periodic. (b) $\langle e_{r}\rangle=\langle\Sigma_{i\in r} \boldsymbol{e^i}\cdot\boldsymbol{\hat{r}}\rangle_t$ for the largest cluster as a function of $r$ from the cluster center-of-mass, averaged over time. (c)-(g) Transition matrix $P(N_1 \vert N_0, \Delta t)$ for varying $\epsilon$. Results for $f_{\rm a}^*\in\{10,40,80\}$ are presented in Figs. S3 and S4 of SM.
• Figure 4: Steady-state density profiles ($\rho/\rho_0$, green, left axis) and $\langle e_z\rangle$, purple, right axis) for: (a) A passive condensate in a thermal gradient. (b) An attractive active condensate in an activity gradient. (c) A MIPS cluster in an activity gradient. Animations of simulations are presented in Movie 1 of SM.
• Figure 5: Binary mixtures of passive particles and APBs. A fraction $1-\chi$ of ABPs are $\alpha$-type with $\epsilon^{\alpha\alpha}=4$ and a fraction $\chi$ are passive $\beta$-type with $\epsilon^{\beta\beta}=2$. (e) Steady–state density $\rho(z)$. (f–h) $g^{ij}(r)$ with (e-g) corresponding snapshots, respectively. ABPs are in blue and passive particles in orange.