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Interfacial Permeability, Reflectivity and Preferential Internal Mixing of Phase-Separated Condensates

Oihan Joyot, Zoé Ferrand, Fernando Muzzopappa, Pierre Weiss, Fabian Erdel

Abstract

Biomolecular condensates organize biochemical processes by spatially concentrating molecules while allowing for dynamic exchange with their surroundings. However, transport across their interface can be strongly attenuated, leading to enhanced retention and preferential internal mixing. Two key mechanisms have been proposed to describe this behavior: biased interfacial reflectivity, which compares how strongly particles are reflected at the interface when attempting to enter or leave the condensate, and interfacial resistance, which sets the kinetic rate at which particles can cross the interface. Quantifying these parameters experimentally has remained challenging. Here, we present a theoretical and experimental framework to address this issue, extending our previously developed half-FRAP approach. We solve the spherical diffusion problem with a semipermeable interface by spectral decomposition. By evaluating the information content of the integrated recovery curves, we show that they encode sufficient information to recover interfacial parameters over extended regions of parameter space. Applying our framework to tunable coacervates composed of poly-lysine and hyaluronic acid, we find that their interfaces exhibit strongly biased reflectivity and substantial resistance, both driving preferential internal mixing. These parameters depend on salt concentration, linking interfacial transport to intermolecular interaction strength and position in the phase diagram. Our results establish a quantitative connection between interfacial properties and condensate dynamics, revealing how their interplay gives rise to distinct transport regimes.

Interfacial Permeability, Reflectivity and Preferential Internal Mixing of Phase-Separated Condensates

Abstract

Biomolecular condensates organize biochemical processes by spatially concentrating molecules while allowing for dynamic exchange with their surroundings. However, transport across their interface can be strongly attenuated, leading to enhanced retention and preferential internal mixing. Two key mechanisms have been proposed to describe this behavior: biased interfacial reflectivity, which compares how strongly particles are reflected at the interface when attempting to enter or leave the condensate, and interfacial resistance, which sets the kinetic rate at which particles can cross the interface. Quantifying these parameters experimentally has remained challenging. Here, we present a theoretical and experimental framework to address this issue, extending our previously developed half-FRAP approach. We solve the spherical diffusion problem with a semipermeable interface by spectral decomposition. By evaluating the information content of the integrated recovery curves, we show that they encode sufficient information to recover interfacial parameters over extended regions of parameter space. Applying our framework to tunable coacervates composed of poly-lysine and hyaluronic acid, we find that their interfaces exhibit strongly biased reflectivity and substantial resistance, both driving preferential internal mixing. These parameters depend on salt concentration, linking interfacial transport to intermolecular interaction strength and position in the phase diagram. Our results establish a quantitative connection between interfacial properties and condensate dynamics, revealing how their interplay gives rise to distinct transport regimes.

Paper Structure

This paper contains 50 sections, 4 theorems, 132 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Results
  3. Diffusion of particles in a semipermeable sphere
  4. Mathematical model
  5. Solution via spectral decomposition
  6. Reparametrization
  7. Preferential internal mixing
  8. Limiting case I: Fast diffusion in an unbounded outer domain
  9. Limiting case II: Vanishing interfacial resistance
  10. FRAP curves for a semipermeable sphere
  11. Integrated half-FRAP curves
  12. Integrated full-FRAP curve
  13. Dip depth in half-FRAP
  14. Influence of interfacial properties and diffusion coefficients on half-FRAP curves
  15. Information content of integrated curves
  16. ...and 35 more sections

Key Result

Lemma A.2

The spaces $V$ and $H$ satisfy the dense and continuous inclusions:

Figures (11)

  • Figure 1: Schematic representation of the diffusion problem and link between reflective bias of the interface and equilibrium partitioning.
  • Figure 2: Spatial distributions of bleached particles at different times after half-bleaching.
  • Figure 3: Integrated half-FRAP curves for different parameter combinations.
  • Figure 4: Dip depth and normalized dip time.
  • Figure 5: Link between dip depth and internal mixing.
  • ...and 6 more figures

Theorems & Definitions (9)

  • Definition A.1: Hilbert Spaces and Inner Products
  • Lemma A.2: Gelfand Triple
  • proof
  • Lemma A.3: Properties of the Bilinear Form
  • proof
  • Theorem A.4: Existence and Uniqueness
  • proof
  • Theorem A.5: Spectral Decomposition
  • proof