Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Mechanochemical coupling of lipid organization and protein function through membrane thickness deformations

Cell membranes are composed of a great variety of protein and lipid species with distinct unperturbed hydrophobic thicknesses. To achieve hydrophobic matching, the lipid bilayer tends to deform around membrane proteins so as to match the protein hydrophobic thickness at bilayer-protein interfaces. Such protein-induced distortions of the lipid bilayer hydrophobic thickness incur a substantial energy cost that depends critically on the bilayer-protein hydrophobic mismatch, while distinct conformational states of membrane proteins often show distinct hydrophobic thicknesses. As a result, hydrophobic interactions between membrane proteins and lipids can yield a rich interplay of lipid-protein organization and transitions in protein conformational state. We combine here the membrane elasticity theory of protein-induced lipid bilayer thickness deformations with the Landau-Ginzburg theory of lipid domain formation to systematically explore the coupling between local lipid organization, lipid and protein hydrophobic thickness, and protein-induced lipid bilayer thickness deformations in membranes with heterogeneous lipid composition. We allow for a purely mechanical coupling of lipid and protein composition through the energetics of protein-induced lipid bilayer thickness deformations as well as a chemical coupling driven by preferential interactions between particular lipid and protein species. We find that the resulting lipid-protein organization can endow membrane proteins with diverse and controlled mechanical environments that, via protein-induced lipid bilayer thickness deformations, can strongly influence protein function. The theoretical approach employed here provides a general framework for the quantitative prediction of how membrane thickness deformations influence the joint organization and function of lipids and proteins in cell membranes.

Self-assembly of polyhedral bilayer vesicles from Piezo ion channels

Piezo ion channels underlie many forms of mechanosensation in vertebrates and have been found to bend the membrane into strongly curved dome shapes. We develop a methodology describing the self-assembly of lipids and Piezo proteins into polyhedral bilayer vesicles. We validate this methodology for bilayer vesicles formed from bacterial mechanosensitive channels of small conductance, for which experiments found a polyhedral arrangement of proteins with snub cube symmetry and a well-defined characteristic vesicle size. On this basis, we calculate the self-assembly diagram for polyhedral bilayer vesicles formed from Piezo proteins. We find that the radius of curvature of the Piezo dome provides a critical control parameter for the self-assembly of Piezo vesicles, with high abundances of Piezo vesicles with octahedral, icosahedral, and snub cube symmetry with increasing Piezo dome radius of curvature.

Regulation of membrane proteins through local heterogeneity in lipid bilayer thickness

Cell membranes show an intricate organization of lipids and membrane proteins into domains with distinct composition and hydrophobic thickness. Using mechanosensitive ion channels as a model system, we employ the membrane elasticity theory of lipid-protein interactions together with the Landau-Ginzburg theory of lipid domain formation to quantify protein-induced lipid bilayer thickness deformations in lipid bilayers with heterogeneous hydrophobic thickness. We show that protein-induced lipid bilayer thickness deformations yield, without any assumptions about preferential interactions between particular lipid and protein species, organization of lipids and membrane proteins according to their preferred hydrophobic thickness, and couple the conformational states of membrane proteins to the local membrane composition. Our calculations suggest that protein-induced lipid bilayer thickness deformations endow proteins in cell membranes with diverse and controlled mechanical environments that, in turn, allow targeted regulation of membrane proteins.

Effect of protein steric constraints on the symmetry of membrane protein polyhedra

Experiments have shown that, in an aqueous environment, lipids and membrane proteins can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs are closed, spherical vesicles composed of a lipid bilayer membrane and membrane proteins, with a polyhedral arrangement of membrane proteins. The observed symmetry and size of MPPNs can be understood from the interplay of protein-induced lipid bilayer deformations in MPPNs, topological defects in protein packing necessitated by the spherical shape of MPPNs, and thermal fluctuations in MPPN self-assembly. We explore here the effect of protein steric constraints on MPPN shape. The protein steric constraints considered here may arise from a well-defined shape of protein domains outside the membrane, entropic repulsion between membrane proteins with flexible domains outside the membrane, or binding of other molecules to membrane proteins. Calculating MPPN self-assembly diagrams under protein steric constraints we find that protein steric constraints can strongly affect MPPN self-assembly. Depending on the specific scenario considered, protein steric constraints can leave large portions of the MPPN self-assembly diagrams with no clearly defined MPPN symmetry or substantially expand the regions of MPPN self-assembly diagrams dominated by highly symmetric MPPN states, such as MPPNs with icosahedral or snub cube symmetry. Our results suggest that modification of protein steric constraints may allow the directed self-assembly of MPPNs with specified symmetry, size, and protein composition and may thus facilitate the further utilization of MPPNs for membrane protein structural analysis or targeted drug delivery.

Symmetry of membrane protein polyhedra with heterogeneous protein size

In experiments on membrane protein polyhedral nanoparticles (MPPNs) [Basta et al., Proc. Natl. Acad. Sci. USA 111, 670 (2014)PNASA60027-842410.1073/pnas.1321936111], it has been observed that membrane proteins and lipids can self-assemble into closed lipid bilayer vesicles with a polyhedral arrangement of membrane proteins. In particular, MPPNs formed from the mechanosensitive channel of small conductance (MscS) were found to have the symmetry of the snub cube-a chiral, Archimedean solid-with one MscS protein located at each one of the 24 vertices of the snub cube. It is currently unknown whether MPPNs with heterogeneous protein composition maintain a high degree of symmetry. Inspired by previous work on viral capsid symmetry, we employ here computational modeling to study the symmetry of MPPNs with heterogeneous protein size. We focus on MPPNs formed from MscS proteins, which can exist in closed or open conformational states with distinct sizes. We find that, as an increasing number of closed-state MscS proteins transitions to the open conformational state of MscS, the minimum-energy MscS arrangement in MPPNs follows a strikingly regular pattern, with the dominant MPPN symmetry always being provided by the snub cube. Our results suggest that MPPNs with heterogeneous protein size can be highly symmetric, with a well-defined polyhedral ordering of membrane proteins of different sizes.

Topological Defect-Driven Buckling of Phospholipid Bicelles to Cones for Micromotors with Modulated Heading Pathways

Topological defects are crucial to the shaping of the crystalline membrane systems such as lipid bilayers, virus capsids, and graphene as well as the arrangement of cells in tissues. In a typical case, the introduction of disclination defects elastically buckles the crystalline membranes into conical shapes. However, how planar membranes transform to cones triggered by disclinations is still rarely observed in the experiments. Herein, we experimentally observe the transformation from phospholipid bicelles to cones in response to disclinations. During the transformation process, the wall thickness increases, while the conical generatrix length remains the same with respect to the radius of bicelles. The cones with apex angles of 112.8°, 83.6°, 60°, 39°, and 19.2° are observed when 1, 2, 3, 4, and 5 pentagon defects are introduced, respectively. Monodispersed microcones are obtained by adjusting aging temperature and time. These microcones are then used as templates to form platinum conical micromotors with open tips or closed tips, which display different heading directions in H₂O₂ solution. Our work provides a shape evolution pathway of planar membranes in response to disclinations. The homogeneous microcones can find wide applications in micromotors fabrication, the study of curvature-dependent processes, and the formation of advanced materials.