A Rationale for Mesoscopic Domain Formation in Biomembranes

Abstract

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.

Keywords: clusters; domains; lipid rafts; lipids; membranes; mesophase separation; proteins; vesicles.

Figure 1

(a) Membrane simulation snapshot. The blue lipids are 1,2-dipalmitoylphosphatidylcholine (DPPC), the yellow ones di-C16:2-C18:2 PC (DIPC) and cholesterol appears in green. The pink thick line is the 1D interface delimiting the liquid-ordered (Lo) phase (cholesterol rich, $\varphi \left(\mathbf{r}\right)\simeq 1$ ) and the liquid-disordered (Ld) phase (cholesterol poor, $\varphi \left(\mathbf{r}\right)\simeq 0$ ). This interface has an energy cost per unit length, homogeneous to a force $\lambda$ , named the line tension. Although fluctuating, the membrane is globally planar and parallel to the plane $\left(xOy\right)$ . The height of the membrane above this reference plane $\left(xOy\right)$ is measured by the height function $z=h\left(\mathbf{r}\right)$ . The membrane is taut with surface tension $\sigma$ as illustrated by the four gray arrows parallel to the plane $\left(xOy\right)$ . Adapted from an original membrane image generated by the MARTINI force field, reproduced with the courtesy of Matthieu Chavent. (b) In the cluster-phase scenario, proteins are described as individual objects embedded in a continuous fluctuating 2D lipid mattress, also represented by a height function. They gather because of short-range attractive forces but long-range repulsion between clusters limits their growth. In the present case, each individual protein (in purple) locally imposes a spontaneous curvature to the membrane that is represented as an elastic sheet (in orange). In a taut membrane, an effective long-range repulsion between proteins ensues (see text). The units are arbitrary.

Figure 2

Examples of phase diagrams showing the formation of curvature-induced domains in planar membranes. Each diagram shows 3 phases: the macrophase separation (M), the modulated phase (or mesophase) (O), and the liquid phase which can be simple (L) or structured disordered (SD) with transient domains. (a) Coupling constant between the two leaflets $m_0$ versus $C_1/C_1^{\ast }$ (see text) from the model by Gueguen et al. in which the two leaflets have the same composition but with different averaged area fractions. SD- (resp. SD+) corresponds to curved (resp. flat) transient domains. Here the bending modulus $\kappa$ does not depend on the phase state. Reproduced from [85], with permission of The European Physical Journal (EPJ), Copyright 2014. (b) Temperature versus $C_1/C_1^{\ast }$ from the model by Shlomovitz and Schick in which each leaflet contains a different mixture of two lipids. (SDin) corresponds to curved transient domains in the inner leaflet only, and (SD) in both leaflets. Adapted from [79], with permission from Elsevier, Copyright 2013.

Figure 3

Examples of phase diagram showing the formation of curvature induced domains in vesicles. (a) AT high T or low $C_1$ , the liquid phase is homogeneous; numbered regions correspond to modulated phases with the number of the most stable ℓ-mode ( $\ell =1$ to 5 here; $\ell =1$ corresponds to the macrophase separation). The superscript corresponds to the sign of $C_1$ . The bending modulus $\kappa$ does not depend on the order parameter $\varphi$ in the model. In this case, $C_0=\mathsf{\Delta }p=0$ . Adapted from [104]. (b) Sketch of a quasi-spherical vesicle with two different types of lipids inducing either thicker (with a larger bending modulus ${\kappa }_0+{\kappa }_1$ ) or curved patches with a local spontaneous curvature $C_0+C_1$ . (c) Associated phase diagram in the $(C_{1}R,{\kappa }_1/{\kappa }_0)$ plane. The symbols have the same signification as in Figure 2a. (b) and (c) are reproduced from [85], with permission of The European Physical Journal (EPJ), Copyright 2014.

Figure 4

(a) In the case of plane tensionless membranes, a first approximation consists of considering spherical caps of Lo phase (or $\beta$ phase, in red) of area $A_{\beta }=\pi L^2$ in an otherwise infinite Ld membrane [110]; the spherical cap radius is denoted by R and the radius of the circle delimiting the phase boundary is N. (b) When the line tension $\lambda$ exceeds a critical value ${\lambda }_c$ (Equation (18)), the previously planar domain buckles to a complete sphere in the tensionless case. Owing to the spontaneous symmetry breaking principle, the domain is equally likely to buckle upward or downward (up-down symmetry). (c) In a taut membrane with surface tension $\sigma$ budding is incomplete. Reproduced from [107] with permission from the Proceedings of the National Academy of Sciences USA, Copyright 2009. (d) In the case of giant unilamellar vesicles (GUV), fluorescence microscopy experiments on ternary mixtures of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC)/Sphingomyelin (SM)/cholesterol below the demixing temperature distinguishes the Lo and Ld phases appearing in red and green respectively. Mathematical modeling then enables the extraction of physical parameters such as bending moduli $\kappa$ and line tension $\lambda$ at the Lo/Ld interface. Reproduced from [106], with permission from the American Physical Society, Copyright 2008.

Figure 5

(a) Numerical model of biphasic vesicle with Lo (in white) and Ld (in red) separated phases, sampled by Monte Carlo simulations. The ratio ${\kappa }_{\mathrm{Lo}}/{\kappa }_{\mathrm{Ld}}$ is indicated below each vesicle. Most curvature is accumulated in the more flexible Ld phase. Reproduced from [53], with permission from The Royal Society of Chemistry, Copyright 2011. (b) Another numerical modeling of a biphasic vesicle with various Lo and Ld area fractions (Lo is black and Ld is white), showing patterned morphologies. Panel (a2) is the same simulation snapshot as panel (a1), but displays the mean curvature map instead (curvature units in the color scale on the right are in $\mathsf{\mu }$ m ${}^{-1}$ ), thus illustrating the coupling between the local composition and curvature. The most flexible Ld phase is also the most bent one. Reproduced from reference [123], with permission from the American Physical Society, Copyright 2013. In both panels (a,b), the spontaneous curvature $C_{\mathrm{sp}}$ has been set to 0 for both phases. (c) Fluorescence microscopy images showing a large variety of patterns in the 4-component 1,2-distearoyl-sn-glycero-3-phosphocholine(DSPC)/1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC)/1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/cholesterol vesicles, displaying coexistence of Lo (dark grey) and Ld (light gray) phases below the demixing temperature $T_d$ . The vesicles either appear homogeneous or display roundish domains or labyrinthine phases according to the concentrations of the different lipids. The percentage indicated in each panel is the DOPC to DOPC+POPC molar ratio $\rho$ . Scale bars: 10 $\mathsf{\mu }$ m. Temperature: 23 ${}^{\circ }$ C. Reproduced from [49], with permission from Elsevier, Copyright 2013.

Figure 6

From right to left, the vesicle radius of curvature (written above each snapshot) is increased while the total area of the patch is held fixed. Above a critical curvature, there is a transition from a Lo/Ld mesophase to a macrophase separation. Reproduced from [128], with permission from the American Physical Society, Copyright 2014.

Figure 7

Illustrations of some of the inter-protein forces (denoted by F on this figure) propagated by the lipid membrane. (a) Depletion forces due to the lateral osmotic pressure exerted by lipids (red discs) on the proteins (black). The pressure becomes anisotropic when the distance between proteins is smaller than the lipid size. (b) Hydrophobic mismatch forces resulting from the difference between the thickness of the membrane hydrophobic layer (the hydrocarbon chains) and the height of the protein hydrophobic cores (in gray) (c) Wetting-induced interaction: when the membrane is made of a lipid mixture, a single protein (left panel) nucleates a “halo” of “wetting” lipids (in red). When two proteins get closer (right panel), their halos overlap, which reduces the interfacial energy between lipid species. A force ensues. (d) Mutual interaction felt by two up-down non-symmetric inclusions (in blue) and propagated by the deformable elastic membrane. The asymmetry is schematized by the conical shape of inclusions. It is measured by the cone half-aperture angle $\theta$ . (e) Collective deformation of the membrane by an assembly of up-down non-symmetric inclusions (pink cones). Figures reproduced from [9], with permission from Elsevier, Copyright 2016.

Figure 8

Examples of recycling schemes. (a) In the membrane, domains can undergo scission or fusion, whatever their size. Reproduced from [57], with permission from the American Physical Society, Copyright 2005. (b) In this alternative scheme, clusters can only gain or lose proteins by exchange of monomers with the surrounding membrane (Ostwald ripening) because scission and fusion events are assumed to be rare. Reproduced from [199], with permission from the American Chemical Society, Copyright 2016. In both examples, monomers are injected into the membrane from the cytosol at a rate $j_{\mathrm{on}}$ , either by exocytosis in (a) or by a monomer flux from the cytosol in (b). Multimers are internalized through endocytosis with a rate $j_{\mathrm{off}}$ that is independent of their size.

Figure 9

Examples of steady-state domain-size distributions $p\left(n\right)$ . Here the domains are protein clusters. In these figures, their size is measured as the number n of proteins they contain, proportional to $L^2$ if L is the cluster radius. The units on the vertical axis are arbitrary. (a) Bimodal distributions, where small oligomers coexist with domains of typical size $n^{\ast }$ (vertical dashed line for curve f). When going from curve “a” to curve “f”, the number of monomers in the membrane increases because more and more monomers are injected in the out-of-equilibrium membrane from the cytosol. Above a critical value, multimers nucleate and the distribution becomes bimodal as in curves “d”, “e” and “f”. The limit between monomodal and bimodal distributions is curve “c”. Adapted from [196]. (b) Power-law distributions $p\left(n\right)\propto n^{-3/2}$ with a cut-off $n_{\max }$ (vertical dashed line) above which $p\left(k\right)$ decreases exponentially. Here the coalescence rate between two clusters is independent of their size. Clusters smaller than a size $n_{\mathrm{v}}$ are recycled entirely as a whole, while larger clusters are fragmented and lose an area $n_{\mathrm{v}}$ during a recycling event. The “whole cluster recycling” limit corresponds to $n_{\mathrm{v}}\to \infty$ and the “monomer recycling” limit to $n_{\mathrm{v}}=1$ . Adapted from [201]. For both figures, see the cited references for more details on the recycling dynamics.