A Model for Shaping Membrane Sheets by Protein Scaffolds.

Membranes of peripheral endoplasmic reticulum form intricate morphologies consisting of tubules and sheets as basic elements. The physical mechanism of endoplasmic-reticulum shaping has been suggested to originate from the elastic behavior of the sheet edges formed by linear arrays of oligomeric protein scaffolds. The heart of this mechanism, lying in the relationships between the structure of the protein scaffolds and the effective intrinsic shapes and elastic properties of the sheets' edges, has remained hypothetical. Here we provide a detailed computational analysis of these issues. By minimizing the elastic energy of membrane bending, we determine the effects of a rowlike array of semicircular arclike membrane scaffolds on generation of a membrane fold, which shapes the entire membrane surface into a flat double-membrane sheet. We show, quantitatively, that the sheet's edge line tends to adopt a positive or negative curvature depending on the scaffold's geometrical parameters. We compute the effective elastic properties of the sheet edge and analyze the dependence of the equilibrium distance between the scaffolds along the edge line on the scaffold geometry.

Front-to-rear membrane tension gradient in rapidly moving cells.

Membrane tension is becoming recognized as an important mechanical regulator of motile cell behavior. Although membrane-tension measurements have been performed in various cell types, the tension distribution along the plasma membrane of motile cells has been largely unexplored. Here, we present an experimental study of the distribution of tension in the plasma membrane of rapidly moving fish epithelial keratocytes. We find that during steady movement the apparent membrane tension is ∼30% higher at the leading edge than at the trailing edge. Similar tension differences between the front and the rear of the cell are found in keratocyte fragments that lack a cell body. This front-to-rear tension variation likely reflects a tension gradient developed in the plasma membrane along the direction of movement due to viscous friction between the membrane and the cytoskeleton-attached protein anchors embedded in the membrane matrix. Theoretical modeling allows us to estimate the area density of these membrane anchors. Overall, our results indicate that even though membrane tension equilibrates rapidly and mechanically couples local boundary dynamics over cellular scales, steady-state variations in tension can exist in the plasma membranes of moving cells.

Membrane-mediated interaction between strongly anisotropic protein scaffolds.

Specialized proteins serve as scaffolds sculpting strongly curved membranes of intracellular organelles. Effective membrane shaping requires segregation of these proteins into domains and is, therefore, critically dependent on the protein-protein interaction. Interactions mediated by membrane elastic deformations have been extensively analyzed within approximations of large inter-protein distances, small extents of the protein-mediated membrane bending and small deviations of the protein shapes from isotropic spherical segments. At the same time, important classes of the realistic membrane-shaping proteins have strongly elongated shapes with large and highly anisotropic curvature. Here we investigated, computationally, the membrane mediated interaction between proteins or protein oligomers representing membrane scaffolds with strongly anisotropic curvature, and addressed, quantitatively, a specific case of the scaffold geometrical parameters characterizing BAR domains, which are crucial for membrane shaping in endocytosis. In addition to the previously analyzed contributions to the interaction, we considered a repulsive force stemming from the entropy of the scaffold orientation. We computed this interaction to be of the same order of magnitude as the well-known attractive force related to the entropy of membrane undulations. We demonstrated the scaffold shape anisotropy to cause a mutual aligning of the scaffolds and to generate a strong attractive interaction bringing the scaffolds close to each other to equilibrium distances much smaller than the scaffold size. We computed the energy of interaction between scaffolds of a realistic geometry to constitute tens of kBT, which guarantees a robust segregation of the scaffolds into domains.

Theoretical analysis of membrane tension in moving cells.

Lateral tension in cell plasma membranes plays an essential role in regulation of a number of membrane-related intracellular processes and cell motion. Understanding the physical factors generating the lateral tension and quantitative determination of the tension distribution along the cell membrane is an emerging topic of cell biophysics. Although experimental data are accumulating on membrane tension values in several cell types, the tension distribution along the membranes of moving cells remains largely unexplored. Here we suggest and analyze a theoretical model predicting the tension distribution along the membrane of a cell crawling on a flat substrate. We consider the tension to be generated by the force of actin network polymerization against the membrane at the cell leading edge. The three major factors determining the tension distribution are the membrane interaction with anchors connecting the actin network to the lipid bilayer, the membrane interaction with cell adhesions, and the force developing at the rear boundary due to the detachment of the remaining cell adhesion from the substrate in the course of cell crawling. Our model recovers the experimentally measured values of the tension in fish keratocytes and their dependence on the number of adhesions. The model predicts, quantitatively, the tension distribution between the leading and rear membrane edges as a function of the area fractions of the anchors and the adhesions.