Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces

Abstract

Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.

Cell confinement reveals a branched-actin independent circuit for neutrophil polarity

“…However, in microenvironments where neutrophils experience compression forces, a second hidden bleb-based program can maintain polarity even if the branched actin-dependent program is broken. By decoupling changes in membrane tension from changes in cell volume, we further show that polarity-regulating mechanosensors are unlikely to respond directly to tension changes but may instead distinguish changes in membrane morphology, such as local curvature (Gov, 2018). Going forward, leveraging such well-defined environmental perturbations will be helpful in deconvolving the pleiotropic effects arising when disrupting components with multiple cellular functions.…”

Self-organization: the fundament of cell biology

“…They review the self-organization of actin polymerization and acto-myosin contractility in the context of migration, where membrane tension is an important player. Similar to the contributions by Gov [11] and Yang & Wu [10], introduced above, the relation between forces and membrane deformation is discussed, although here the focus lies in the direct link to cell polarity and cell migration. The known connection between actin polymerization and acto-myosin contractility is the starting point to discuss the regulation of experimentally observed contractile pulses.…”

Modeling membrane nanotube morphology: the role of heterogeneity in composition and material properties

“…-We assume that the total energy of the system includes the membrane bending energy and a contribution from membrane-protein aggregation in a dilute regime. Thus, the membrane is modeled using an augmented version of Helfrich energy for elastic manifolds including the membrane-protein interaction contributions [48,[60][61][62][63]. The aggregation energy of the proteins, which is proportional to the gradient of the protein density, is modeled in our system by a constitutively prescribed hyperbolic tangent function.…”

“…Also, we assume the lateral phase separation of the proteins is complete, and hence neglect the entropic energy associated with the membrane -protein interactions [64]. A detailed discussion of the full energy can be found in [48,63,65]. -We do not explicitly model the diffusion of proteins on the surface and the dynamics of domain formation in this study; rather we assume that diffusion has run its course and we are left with a protein heterogeneity on the surface (see above comment on a hyperbolic tangent).…”

“…The interaction energy of transmembrane proteins with the lipid bilayer is written as a constitutive function of the protein density σ (number per unit area). While the exact form of this energy is yet to be experimentally verified, based on thermodynamic arguments, a quadratic dependence of the energy on the local protein density has been proposed as [48,60,63,[70][71][72],…”