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1. Mechanisms of negative membrane curvature sensing and generation by ESCRT III subunit Snf7

   https://doi.org/10.1002/pro.3851  

   Nepal, Binod; Sepehri, Aliasghar; Lazaridis, Themis (March 2020, Protein Science)

   Abstract Certain proteins have the propensity to bind to negatively curved membranes and generate negative membrane curvature. The mechanism of action of these proteins is much less studied and understood than those that sense and generate positive curvature. In this work, we use implicit membrane modeling to explore the mechanism of an important negative curvature sensing and generating protein: the main ESCRT III subunit Snf7. We find that Snf7 monomers alone can sense negative curvature and that curvature sensitivity increases for dimers and trimers. We have observed spontaneous bending of Snf7 oligomers into circular structures with preferred radius of ~20 nm. The preferred curvature of Snf7 filaments is further confirmed by the simulations of preformed spirals on a cylindrical membrane surface. Snf7 filaments cannot bind with the same interface to flat and curved membranes. We find that even when a filament has the preferred radius, it is always less stable on the flat membrane surface than on the interior cylindrical membrane surface. This provides an additional energy for membrane bending which has not been considered in the spiral spring model. Furthermore, the rings on the cylindrical spirals are bridged together by helix 4 and hence are extra stabilized compared to the spirals on the flat membrane surface. 

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2. Transport phenomena in fluid films with curvature elasticity

   https://doi.org/10.1017/jfm.2020.711  

   Mahapatra, Arijit; Saintillan, David; Rangamani, Padmini (December 2020, Journal of Fluid Mechanics)

   null (Ed.)

   Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins and elastic deformation of lipid bilayers. The proteins in the membrane are modelled such that they influence membrane bending by inducing a spontaneous curvature. We formulate the free energy of the membrane with a Helfrich-like curvature elastic energy density function modified to account for the chemical potential energy of proteins. We derive the conservation laws and equations of motion for this system. Finally, we present results from dimensional analysis and numerical simulations and demonstrate the effect of coupled transport processes in governing the dynamics of membrane bending and protein diffusion. 

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3. Elastic properties and shape of the Piezo dome underlying its mechanosensory function

   https://doi.org/10.1073/pnas.2208034119  

   Haselwandter, Christoph A.; Guo, Yusong R.; Fu, Ziao; MacKinnon, Roderick (October 2022, Proceedings of the National Academy of Sciences)

   We show in the companion paper that the free membrane shape of lipid bilayer vesicles containing the mechanosensitive ion channel Piezo can be predicted, with no free parameters, from membrane elasticity theory together with measurements of the protein geometry and vesicle size [C. A. Haselwandter, Y. R. Guo, Z. Fu, R. MacKinnon, Proc. Natl. Acad. Sci. U.S.A. , 10.1073/pnas.2208027119 (2022)]. Here we use these results to determine the force that the Piezo dome exerts on the free membrane and hence, that the free membrane exerts on the Piezo dome, for a range of vesicle sizes. From vesicle shape measurements alone, we thus obtain a force–distortion relationship for the Piezo dome, from which we deduce the Piezo dome’s intrinsic radius of curvature, 42 ± 12 nm, and bending stiffness, 18 ± 2.1   k B T , in freestanding lipid bilayer membranes mimicking cell membranes. Applying these estimates to a spherical cap model of Piezo embedded in a lipid bilayer, we suggest that Piezo’s intrinsic curvature, surrounding membrane footprint, small stiffness, and large area are the key properties of Piezo that give rise to low-threshold, high-sensitivity mechanical gating. 

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4. Curvature-driven feedback on aggregation–diffusion of proteins in lipid bilayers

   https://doi.org/10.1039/d1sm00502b  

   Mahapatra, Arijit; Saintillan, David; Rangamani, Padmini (September 2021, Soft Matter)

   Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein–protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn–Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane–protein interactions. 

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5. A continuum membrane model can predict curvature sensing by helix insertion

   https://doi.org/10.1039/d1sm01333e  

   Fu, Yiben; Zeno, Wade F.; Stachowiak, Jeanne C.; Johnson, Margaret E. (December 2021, Soft Matter)

   Protein domains, such as ENTH (epsin N-terminal homology) and BAR (bin/amphiphysin/rvs), contain amphipathic helices that drive preferential binding to curved membranes. However, predicting how the physical parameters of these domains control this ‘curvature sensing’ behavior is challenging due to the local membrane deformations generated by the nanoscopic helix on the surface of a large sphere. We here use a deformable continuum model that accounts for the physical properties of the membrane and the helix insertion to predict curvature sensing behavior, with direct validation against multiple experimental datasets. We show that the insertion can be modeled as a local change to the membrane's spontaneous curvature, c ins0, producing excellent agreement with the energetics extracted from experiments on ENTH binding to vesicles and cylinders, and of ArfGAP helices to vesicles. For small vesicles with high curvature, the insertion lowers the membrane energy by relieving strain on a membrane that is far from its preferred curvature of zero. For larger vesicles, however, the insertion has the inverse effect, de-stabilizing the membrane by introducing more strain. We formulate here an empirical expression that accurately captures numerically calculated membrane energies as a function of both basic membrane properties (bending modulus κ and radius R ) as well as stresses applied by the inserted helix ( c ins0 and area A ins ). We therefore predict how these physical parameters will alter the energetics of helix binding to curved vesicles, which is an essential step in understanding their localization dynamics during membrane remodeling processes. 

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