Phase Separation on Bicontinuous Cubic Membranes: Symmetry Breaking, Reentrant, and Domain Faceting

Cubic Membranes Formation in Synchronized Human Hepatocellular Carcinoma Cells Reveals a Possible Role as a Structural Antioxidant Defense System in Cell Cycle Progression

Cubic membranes (CMs) represent unique biological membrane structures with highly curved three-dimensional periodic minimal surfaces, which have been observed in a wide range of cell types and organelles under various stress conditions (e. g., starvation, virus-infection, and oxidation). However, there are few reports on the biological roles of CMs, especially their roles in cell cycle. Hence, we established a stable cell population of human hepatocellular carcinoma cells (HepG2) of 100% S phase by thymidine treatment, and determined certain parameters in G2 phase released from S phase. Then we found a close relationship between CMs formation and cell cycle, and an increase in reactive oxygen species (ROS) and mitochondrial function. After the synchronization of HepG2 cells were induced, CMs were observed through transmission electron microscope in G2 phase but not in G1, S and M phase. Moreover, the increased ATP production, mitochondrial and intracellular ROS levels were also present in G2 phase, which demonstrated a positive correlation with CMs formation by Pearson correlation analysis. This study suggests that CMs may act as an antioxidant structure in response to mitochondria-derived ROS during G2 phase and thus participate in cell cycle progression.

Phase transitions on non-uniformly curved surfaces: coupling between phase and location

For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range of behaviours can emerge. Using a combination of bespoke Monte Carlo, molecular dynamics and basin-hopping methods, we show that the stable states of attractive colloids confined to non-uniformly curved surfaces are distinguished not only by the phase of matter but also by their location on the surface. Consequently, the transitions between these states involve cooperative migration of the entire colloidal assembly. We demonstrate these phenomena on toroidal and sinusoidal surfaces for model colloids with different ranges of interactions as described by the Morse potential. In all cases, the behaviour can be rationalised in terms of three universal considerations: cluster perimeter, stress, and the packing of next-nearest neighbours.

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

We develop and implement a finite difference lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. The standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focusing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of the torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our finite difference lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

Thermodynamic equilibrium of binary mixtures on curved surfaces

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.

Protein-Eye View of the in Meso Crystallization Mechanism

For evolving biological and biomedical applications of hybrid protein?lipid materials, understanding the behavior of the protein within the lipid mesophase is crucial. After more than two decades since the invention of the in meso crystallization method, a protein-eye view of its mechanism is still lacking. Numerous structural studies have suggested that integral membrane proteins preferentially partition at localized flat points on the bilayer surface of the cubic phase with crystal growth occurring from a local fluid lamellar L_? phase conduit. However, studies to date have, by necessity, focused on structural transitions occurring in the lipid mesophase. Here, we demonstrate using small-angle neutron scattering that the lipid bilayer of monoolein (the most commonly used lipid for in meso crystallization) can be contrast-matched using deuteration, allowing us to isolate scattering from encapsulated peptides during the crystal growth process for the first time. During in meso crystallization, a clear decrease in form factor scattering intensity of the peptides was observed and directly correlated with crystal growth. A transient fluid lamellar L_? phase was observed, providing direct evidence for the proposed mechanism for this technique. This suggests that the peptide passes through a transition from the cubic Q_II phase, via an L_? phase to the lamellar crystalline L_c phase with similar layered spacing. When high protein loading was possible, the lamellar crystalline L_c phase of the peptide in the single crystals was observed. These findings show the mechanism of in meso crystallization for the first time from the perspective of integral membrane proteins.