Physics of droplet regulation in biological cells

TL;DR

Biomolecular condensates in cells arise from phase separation but operate under compelling non-ideal conditions: multicomponent composition, crowded and structured environments, and non-equilibrium activity. The paper develops a coherent framework that spans diffuse-interface (Cahn–Hilliard) theory, sharp-interface limits, and active, reaction-diffusion dynamics to explain droplet nucleation, growth, and regulation. Key contributions include (i) a quantitative treatment of interfacial tension and Laplace pressure, (ii) criteria for droplet stability, size selection, and coarsening arrest, and (iii) mechanisms by which cells exploit wetting, elastic meshes, membranes, filaments, and chemical activity to control droplet position, number, and life cycle. Collectively, the work links fundamental soft-matter physics to the regulatory circuits governing condensates, offering insights for both biology and the design of engineered, active emulsions with tunable dynamics and functions.

Abstract

Droplet formation has emerged as an essential concept for the spatiotemporal organisation of biomolecules in cells. However, classical descriptions of droplet dynamics based on passive liquid-liquid phase separation cannot capture the complex situation inside cells. This review discusses three distinct aspects that are crucial in cells: (i) biomolecules are diverse and individually complex, implying that cellular droplets possess complex internal behaviour, e.g., in terms of their material properties; (ii) the cellular environment contains many solid-like structures that droplets can wet; (iii) cells are alive and use fuel to drive processes out of equilibrium. We illustrate how these principles control droplet nucleation, growth, position, and count to unveil possible regulatory mechanisms in biological cells and other applications of phase separation.

Figures (12)

• Figure 1.1: Physical phenomena relevant to intracellular droplets discussed in this review. Droplets inside cells (upper left) display multiple physical phenomena discussed in separate sections of this review. \ref{['sec:basic_LLPS']} introduces the basic physics of phase separation leading to droplet formation. \ref{['sec:internal_complexity']} focuses on the internal complexity of droplets originating from the many different interacting molecules that droplets comprise (upper right). \ref{['sec:complex_environment']} discusses the interaction of droplets with complex environments (lower left). \ref{['sec:chemical_reactions']} introduces driven chemical reactions and their effects on droplets (lower right).
• Figure 2.1: Phase behaviour of a binary liquid. (A) Free energy density $f$ given by equation \ref{['eqn:free_energy_density_binary']} as a function of the fraction $\phi$ (blue line) for $\Omega=1$, $\chi=2.5$, and $w=0.2$. The common-tangent construction (black line) solves equations \ref{['eqn:coexistence']} and thus determines the equilibrium fractions $\phi_\mathrm{out}$ and $\phi_\mathrm{in}$ (black disks) without Laplace pressure $P_\gamma$. Finite $P_\gamma$ requires two parallel tangents offset by $P_\gamma$ (gray lines). The inflection points (orange disks) enclose the spinodal region where $f"(\phi)<0$. (B) Exchange chemical potential $\bar{\mu}$ given by equation \ref{['eqn:chemical_potential_binary']} as a function of $\phi$ corresponding to panel A. The blue regions of equal area indicating a Maxwell construction, equivalent to the common-tangent construction. (C) Osmotic pressure $\Pi=\nu^{-1}\phi\bar{\mu} - f$ as a function of $\phi$ corresponding to panel A. (D) $\Pi$ as a function of $\bar{\mu}$ corresponding to panel A. (E, F) Phase diagrams corresponding to panel A highlighting the equilibrium volume fractions (black binodal line) and the spinodal region (within the orange spinodal line) for a symmetric mixture ($\Omega=1$, panel E) and for large solutes ($\Omega=10$, panel F). The critical point is marked by a star and grey areas denotes the region where bi-continuous structures have lower energy than droplets in two dimensions (obtained by comparing interfacial energies of disks and stripes for equal length scales). (G, H) Grand-canonical phase diagram corresponding to panels E and F. The binodals (black lines) mark the first-order transition between dilute and dense phases. Both phases are linearly stable in the spinodal region (between orange dotted lines).
• Figure 2.2: Interfaces and morphologies in a binary liquid. (A) Interfacial profile $\phi(x)$ that minimises $F$ given by equation \ref{['eqn:free_energy_binary']} in a one-dimensional system (blue dots) compared to a fit of a hyperbolic tangent profile (green line). The slope at the midpoint (grey line) defines the interfacial width $\ell$Cahn1958. (B) Numerical simulations of two-dimensional systems from random initial conditions with $\bar{\phi}=0.3, 0.5, 0.7$ (from left to right), showing droplets, bicontinuous structures, and bubbles, respectively. (A, B) Model parameters are $\Omega=1$ and $\chi=2.5$.
• Figure 2.3: Free energy $\Delta\! F$ of a small droplet of radius $R$ relative to the homogeneous phase in $2$ and $3$ dimensions; see equation \ref{['eqn:energy_nucleation']}. The maximum marks the critical size $R_\mathrm{nucl}$ and the nucleation barrier $\Delta\! F_\mathrm{nucl}$.
• Figure 3.1: Multi-component phase diagrams. Phase diagrams of ${N_\mathrm{c}}=2$ solutes and an inert solvent as a function of the solute fractions $\phi_1$ and $\phi_2$ for two scenarios with different interaction matrices $\chi_{ij}$. A system with an average composition within the blue region can split into two coexisting phases whose compositions follow from the dashed tie lines.