Numerical investigations of the dynamics of two-component vesicles

Cell-size space effects on phase separation of binary polymer blends

Within living cells, a diverse array of biomolecules is present at high concentrations. To better understand how molecular behavior differs under such conditions (collectively described as macromolecular crowding), the crowding environment has been reproduced inside artificial cells. We have previously shown that the combination of macromolecular crowding and microscale geometries imposed by the artificial cells can alter the molecular behaviors induced by macromolecular crowding in bulk solutions. We have named the effect that makes such a difference the cell-size space effect (CSE). Here, we review the underlying biophysics of CSE for phase separation of binary polymer blends. We discuss how the cell-size space can initiate phase separation, unlike nano-sized spaces, which are known to hinder nucleation and phase separation. Additionally, we discuss how the dimensions of the artificial cell and its membrane characteristics can significantly impact phase separation dynamics and equilibrium composition. Although these findings are, of themselves, very interesting, their real significance may lie in helping to clarify the functions of the cell membrane and space size in the regulation of intracellular phase separation.

Pattern formation in reaction-diffusion system on membrane with mechanochemical feedback

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

A Rationale for Mesoscopic Domain Formation in Biomembranes

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also be observed in vitro on model systems such as supported membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and liquid-disordered phases below a demixing temperature play a pivotal role in this context. Protein-protein and protein-lipid interactions also contribute to membrane shaping by promoting small domains or clusters. Such phase separations displaying characteristic length-scales falling in-between the nanoscopic, molecular scale on the one hand and the macroscopic scale on the other hand, are named mesophases in soft condensed matter physics. In this review, we propose a classification of the diverse mechanisms leading to mesophase separation in biomembranes. We distinguish between mechanisms relying upon equilibrium thermodynamics and those involving out-of-equilibrium mechanisms, notably active membrane recycling. In equilibrium, we especially focus on the many mechanisms that dwell on an up-down symmetry breaking between the upper and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in condensed matter physics at the heart of several important phenomena. In the present case, it can be either spontaneous (domain buckling) or explicit, i.e., due to an external cause (global or local vesicle bending properties). Whenever possible, theoretical predictions and simulation results are confronted to experiments on model systems or living cells, which enables us to identify the most realistic mechanisms from a biological perspective.

Growth kinetics of circular liquid domains on vesicles by diffusion-controlled coalescence

Motivated by recent experiments on multicomponent membranes, the growth kinetics of domains on vesicles are theoretically studied. It is known that the steady-state rate of coalescence cannot be obtained by taking the long-time limit of the coalescence rate when the membrane is regarded as an infinite two-dimensional (2D) system. The steady-state rate of coalescence is obtained by explicitly taking into account the spherical vesicle shape. Using the expression for the 2D diffusion coefficient obtained in the limit of small domain size, an analytical expression for domain growth kinetics is obtained when a circular shape is always maintained. For large domains, the growth kinetics are discussed by investigating the size dependence of the coalescence rate, using the expression for the diffusion coefficient of arbitrary domain size.

Multiple membrane interactions and versatile vesicle deformations elicited by melittin

Melittin induces various reactions in membranes and has been widely studied as a model for membrane-interacting peptide; however, the mechanism whereby melittin elicits its effects remains unclear. Here, we observed melittin-induced changes in individual giant liposomes using direct real-time imaging by dark-field optical microscopy, and the mechanisms involved were correlated with results obtained using circular dichroism, cosedimentation, fluorescence quenching of tryptophan residues, and electron microscopy. Depending on the concentration of negatively charged phospholipids in the membrane and the molecular ratio between lipid and melittin, melittin induced the “increasing membrane area”, “phased shrinkage”, or “solubilization” of liposomes. In phased shrinkage, liposomes formed small particles on their surface and rapidly decreased in size. Under conditions in which the increasing membrane area, phased shrinkage, or solubilization were mainly observed, the secondary structure of melittin was primarily estimated as an α-helix, β-like, or disordered structure, respectively. When the increasing membrane area or phased shrinkage occurred, almost all melittin was bound to the membranes and reached more hydrophobic regions of the membranes than when solubilization occurred. These results indicate that the various effects of melittin result from its ability to adopt various structures and membrane-binding states depending on the conditions.

Dynamic sorting of lipids and proteins in multicomponent membranes

Dynamic sorting of lipids and proteins in cellular membranes plays a critical role in establishing and maintaining distinct compositions in various organelles. Recent experiments found that the lipid sorting in a membrane tube highly depends on the pulling speed at the tip. However, the mechanism of this velocity dependence has not yet been revealed. In this Letter, we found that when a membrane is deformed rapidly, the lipid flow induced by fast membrane shape change will significantly affect the sorting results. The competition between the curvature-driven lipid sorting and the pulling-induced lipid flow leads to novel behaviors. When a membrane tube is pulled out from a liquid ordered (L(o)) domain at a constant speed, slow pulling leads to the formation of a liquid disordered (L(d)) tube, while fast pulling results in a L(o) tube. Interestingly, in a membrane tube pulled at an intermediate speed, alternate L(d) and L(o) domains appear in the tube. The sorting dynamics and the corresponding pulling force were systematically studied. The results of this study could lead to a better understanding of the dynamic sorting and traffic of lipids and proteins in living cells.

Two-dimensional lattice liquid models

A family of models of liquid on a two-dimensional lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on some honeycomb lattices of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability and peculiar anomalous diffusions in their time-averaged mean-square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.