Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Abstract

In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S. A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the observed symmetry and size of MPPNs. Our model suggests how key lipid and protein properties can be modified to produce a range of MPPN symmetries and sizes in experiments. Utilization of MPPNs for high-resolution structural studies requires [4] control over the symmetry and size of MPPNs. In this Letter we develop a physical description of MPPNs which establishes a quantitative link between the shape of MPPNs and key molecular properties of their constituents. We first describe a simple meanfield model of MPPNs inspired by previous work on membrane budding [9-11] and viral capsid self-assembly [12]. Our mean-field model of MPPNs accounts for the lipid bilayer bending deformations induced by MscS [3,5,6] and the MscS packing defects resulting from the spherical topology of MPPNs, and yields the MPPN energy as a function of the number of MscS per MPPN without any free parameters. We confirm some of the key assumptions underlying our mean-field model by carrying out Monte Carlo simulations of a minimal molecular model of MPPN organization, which we formulate following previous work on viral capsid symmetry [13]. Finally, we use our mean-field model of MPPNs to calculate [12,14,15] the MPPN self-assembly phase diagram as a function of protein concentration, bilayer-protein contact angle, and protein size. We show that our model correctly predicts, with all model parameters determined directly from experiments, the observed [4] symmetry and size of MPPNs formed from MscS. Our results suggest that the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects.Mean-field model.-The membrane-spanning region of MscS [5,6] has an approximately conical shape [3,16] with radius ρ i ≈ 3.2 nm in the lipid bilayer midplane and bilayer-protein contact angle α ≈ 0.46-0.54 rad, yielding [3] protein-induced lipid bilayer bending deformations [see Fig. 1(b)]. The preferred MscS arrangement minimizing bilayer bending energy is expected [9-11] to be a uniform hexagonal lattice. Our simple mean-field model of MPPNs therefore considers, on the one hand, contri-

Controlling the shape of membrane protein polyhedra

“…We provide general analytic solutions for the dependence of the MPPN energy on bilayer-protein hydrophobic thickness mismatch and, on this basis, calculate a generalized MPPN self-assembly diagram. Our results suggest that, in addition to the bilayerprotein contact angle [5], the bilayer-protein hydrophobic thickness mismatch is a key molecular control parameter for MPPN shape. In particular, we find that modification of the lipid bilayer composition, or protein hydrophobic thickness, so as to produce pronounced protein-induced lipid bilayer thickness deformations biases the MPPN selfassembly diagram towards highly symmetric and uniform MPPN shapes.…”

“…Realization of MPPNs as a novel method for membrane protein structural analysis, as well as targeted drug delivery, requires [1] control over MPPN symmetry and size. Current experimental approaches, however, yield a distribution of different MPPN shapes [1,5], which limits the …”

“…The transmembrane surface of the protein specifies boundary conditions on h and u at the bilayer-protein interface (see main text). The membrane patch radius ρo = R sin β, where R is the MPPN bilayer midplane radius at ρ = ρo and the membrane patch angle β = arccos[(n − 2)/n] is determined via the relation 4πR 2 = nΩR 2 , in which Ω = 2π(1 − cos β) is the solid angle subtended by each (circular) membrane patch and n is the number of proteins per MPPN [5,7] (see inset). The protein structure shown here corresponds to the closed state of MscS [2,3] used in experiments on MPPNs [1,4], with Protein Data Bank ID 2OAU and different colors indicating different MscS subunits [13].…”

“…Through their well-defined symmetry and characteristic size, MPPNs may [1], in addition to potential applications as novel drug delivery carriers, offer a new route for structure determination of membrane proteins, with the membrane proteins embedded in a lipid bilayer environment and the closed surfaces of MPPNs supporting physiologically relevant transmembrane gradients. We have shown previously [5] that the observed symmetry and size of MPPNs [1] can be understood based on the interplay of protein-induced lipid bilayer curvature deformations [6][7][8] arising [9] from the conical shape of MscS [2,3], topological defects in protein packing necessitated by the spherical shape of MPPNs [10], and thermal fluctuations in MPPN self-assembly [10][11][12].…”

“…Current experimental approaches, however, yield a distribution of different MPPN shapes [1,5], which limits the resolution of MPPN-based structural studies [1] and potential applications of MPPNs as novel drug delivery carriers. To explore strategies for controlling and optimizing MPPN shape, we generalize here our previous model of MPPN self-assembly [5] to account for the effects of a hydrophobic thickness mismatch between membrane protein and the unperturbed lipid bilayer. We provide general analytic solutions for the dependence of the MPPN energy on bilayer-protein hydrophobic thickness mismatch and, on this basis, calculate a generalized MPPN self-assembly diagram.…”