Protein-Induced Membrane Curvature Alters Local Membrane Tension

Abstract

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks

“…While our model assumes an idealized catenoid shape for membrane necks, it is possible that necks may not remain as exact catenoids and the dynamics of the neck formation process, including biochemical reactions, heterogeneity in membrane composition and moduli 35 , forces exerted by proteins and cytoskeleton molecules, and in-plane diffusion of lipids and proteins 34,39,41,42 play an important role during fission and fusion. Despite these shortcomings, we have identified some fundamental features of the interaction between Gaussian curvature and spontaneous curvature in catenoids.…”

“…(Additional details are provided in the Supplementary Material). This approach, initally developed in 34,38,39 , results in an equivalent model to the one obtained by variational considerations 31,33,40 , but accounts for local inhomogenities on the membrane 38 .…”

“…As a result, one can use this framework to ask, given a spontaneous curvature field, what is the resulting shape of the membrane? Such efforts have been used successfully in 20,[32][33][34][35] among others, leading to a good understanding of the role of the mean curvature and spontaneous curvature. However, the role of the Gaussian curvature on membrane physics is trickier to grasp.…”

Design principles for robust vesiculation in clathrin-mediated endocytosis

“…We use a modified version of the Helfrich energy that includes spatially varying spontaneous curvature C (θ α ) bending modulus κ(θ α ) and Gaussian modulus κG (θ α ) (42,48,50,52),…”

Paradoxical signaling regulates structural plasticity in dendritic spines

“…Spatial compartmentalization of signaling and shape can affect the dynamics of the activity of different signaling molecules in cell motility (30,(62)(63)(64). Membrane mechanics studies have shown that protein interaction with the membrane cannot only induce a curvature but also, change membrane properties (65). The role of these factors in spine dynamics is as yet unknown.…”