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Phase-separated lipid vesicles: continuum modeling, simulation, and validation

Maxim Olshanskii, Annalisa Quaini

TL;DR

The paper addresses modeling, simulation, and validation of phase separation and surface hydrodynamics in lipid membranes by formulating a surface NSCH system on a curved membrane Γ that couples incompressible surface flow with Cahn–Hilliard phase dynamics and membrane elasticity. It implements a TraceFEM-based computational framework with a decoupled, semi-implicit time-stepping scheme to solve the coupled equations and validates predictions against in vitro measurements for DOPC/DPPC/Chol compositions and DOTAP-containing liposomes. Key contributions include a stable numerical strategy, parameter guidance for densities, viscosities, and interfacial properties, and demonstration that NSCH more accurately reproduces domain evolution than CH alone. The work provides a predictive, physics-grounded tool for understanding membrane heterogeneity, vesicle fusion mechanisms, and the design of phase-separated liposomes with tailored fusogenicity.

Abstract

The paper presents a complete research cycle comprising continuum-based modeling, computational framework development, and validation setup to predict phase separation and surface hydrodynamics in lipid bilayer membranes. We starting with an overview of the key physical characteristics of lipid bilayers, including their composition, mechanical properties, and thermodynamics, and then discuss continuum models of multi-component bilayers. The most complex model is a Navier--Stokes--Cahn--Hilliard (NSCH) type system, describing the coupling of incompressible surface fluid dynamics with phase-field dynamics on arbitrarily curved geometries. It is discretized using trace finite element methods, which offer geometric flexibility and stability in representing surface PDEs. Numerical studies are conducted to examine physical features such as coarsening rates and interfacial dynamics. The computational results obtained from the NSCH model are compared against experimental data for membrane compositions with distinct phase behaviors, demonstrating that including both phase-field models and surface hydrodynamics is essential to accurately reproduce domain evolution observed in epi-fluorescence microscopy. Lastly, we extend the model to incorporate external forces that enable the simulation of vesicles containing cationic lipids, used to enhance membrane fusion.

Phase-separated lipid vesicles: continuum modeling, simulation, and validation

TL;DR

The paper addresses modeling, simulation, and validation of phase separation and surface hydrodynamics in lipid membranes by formulating a surface NSCH system on a curved membrane Γ that couples incompressible surface flow with Cahn–Hilliard phase dynamics and membrane elasticity. It implements a TraceFEM-based computational framework with a decoupled, semi-implicit time-stepping scheme to solve the coupled equations and validates predictions against in vitro measurements for DOPC/DPPC/Chol compositions and DOTAP-containing liposomes. Key contributions include a stable numerical strategy, parameter guidance for densities, viscosities, and interfacial properties, and demonstration that NSCH more accurately reproduces domain evolution than CH alone. The work provides a predictive, physics-grounded tool for understanding membrane heterogeneity, vesicle fusion mechanisms, and the design of phase-separated liposomes with tailored fusogenicity.

Abstract

The paper presents a complete research cycle comprising continuum-based modeling, computational framework development, and validation setup to predict phase separation and surface hydrodynamics in lipid bilayer membranes. We starting with an overview of the key physical characteristics of lipid bilayers, including their composition, mechanical properties, and thermodynamics, and then discuss continuum models of multi-component bilayers. The most complex model is a Navier--Stokes--Cahn--Hilliard (NSCH) type system, describing the coupling of incompressible surface fluid dynamics with phase-field dynamics on arbitrarily curved geometries. It is discretized using trace finite element methods, which offer geometric flexibility and stability in representing surface PDEs. Numerical studies are conducted to examine physical features such as coarsening rates and interfacial dynamics. The computational results obtained from the NSCH model are compared against experimental data for membrane compositions with distinct phase behaviors, demonstrating that including both phase-field models and surface hydrodynamics is essential to accurately reproduce domain evolution observed in epi-fluorescence microscopy. Lastly, we extend the model to incorporate external forces that enable the simulation of vesicles containing cationic lipids, used to enhance membrane fusion.

Paper Structure

This paper contains 15 sections, 1 theorem, 50 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Lipid bilayer composition, mechanics, and thermodynamics
  3. Continuum models of multi-component bilayers
  4. Surface model for fluid flow
  5. Surface model for phase separation
  6. Coupled surface model for fluid flow and phase separation
  7. Surface models for elasticity
  8. Estimation of modeling parameters
  9. External forces
  10. Computational methods
  11. Validation against experimental data
  12. NSCH model
  13. NSCH model with an external force
  14. Future perspectives
  15. Conclusions

Key Result

Theorem 1

Assume $h$ and $\Delta t$ satisfy $\Delta t \le c |\ln h|^{-1} \epsilon$ and for some sufficiently small $c>0$, independent of $h$, $\Delta t$, $\epsilon$ and position of $\Gamma$ in the background mesh. Then, the solution to eq:CH_FE1--NSEh2 satisfies for all $N=1,2,\dots$, with $K=\int_\Gamma\left(\rho^{0}|\mathbf u^{0}_h|^2 +\frac{\sigma_\gamma}{\epsilon}f_0(c^{0}_h)\right) ds + a_c(c^{0}_h,c

Figures (9)

  • Figure 1: Two layers of phospholipids with hydrophilic “heads” in yellow and hydrophobic “tails” in cyan.
  • Figure 2: Schematic phase diagram qualitatively corresponding to one of the cases analyzed inveatch2007critical.
  • Figure 3: Simulation set-up: GUV, represented as a plane, and a phase-separated SUV. The $L_o$ phase in the phase-separated SUV is colored in red, while the $L_d$ phase is blue.
  • Figure 4: Qualitative comparison for 1:2:25% (top two rows) and 1:1:15% (bottom two rows): epi-fluorescence microscopy images (with black background) and numerical results (with white background) at four different times.
  • Figure 5: Total lipid domain perimeter $p_{\text{ld}}$ in µm over time for composition 1:2:25% (left) and 1:1:15% (right): numerical results average (solid line) and experimental data (markers). Different markers correspond to different GUVs analyzed experimentally.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1