Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces (original) (raw)

Phase Transitions of the Coupled Membrane-Cytoskeleton Modify Cellular Shape

Biophysical Journal, 2007

Formation of protrusions and protein segregation on the membrane is of a great importance for the functioning of the living cell. This is most evident in recent experiments that show the effects of the mechanical properties of the surrounding substrate on cell morphology. We propose a mechanism for the formation of membrane protrusions and protein phase separation, which may lay behind this effect. In our model, the fluid cell membrane has a mobile but constant population of proteins with a convex spontaneous curvature. Our basic assumption is that these membrane proteins represent small adhesion complexes, and also include proteins that activate actin polymerization. Such a continuum model couples the membrane and protein dynamics, including cell-substrate adhesion and protrusive actin force. Linear stability analysis shows that sufficiently strong adhesion energy and actin polymerization force can bring about phase separation of the membrane protein and the appearance of protrusions. Specifically, this occurs when the spontaneous curvature and aggregation potential alone (passive system) do not cause phase separation. Finite-size patterns may appear in the regime where the spontaneous curvature energy is a strong factor. Different instability characteristics are calculated for the various regimes, and are compared to various types of observed protrusions and phase separations, both in living cells and in artificial model systems. A number of testable predictions are proposed.

The role of spontaneous curvature in the formation of cell membrane necks

Cornell University - arXiv, 2022

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous of neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution is determined by the equilibrium mechanical equations, and, in order to establish the role played by the inhomogeneity, we focus on the catenoid, a surface of zero mean curvature, which can be described in terms of the catenary curve parameterized by arc length. We show that analytic solutions exist for the spontaneous curvature, as well as for both, the surface tension and the radial elastic force. An analytic expression for the constrictive force at the neck, is obtained. From the energetic analysis, it is found that, if we fix the value of the constrictive force at the neck, the set of solutions lies on two branches separated by an energetic barrier. This barrier corresponds to the energy of the maximum catenoid. If instead we fix the axial force, the solution has access to catenoid of any size.

Non-axisymmetric shapes of biological membranes from locally induced curvature

2019

In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved configurations. Previous theoretical and computational studies to understand membrane morphologies resulting from locally induced curvature are often limited to axisymmetric shapes, which severely restricts the physically admissible morphologies. Under the restriction of axisymmetry, past efforts predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction of axisymmetry by employing recent theoretical and numerical advances to understand arbitrarily curved and deforming lipid bilayers. Our non-axisymmetric morphologies reveal membrane morphologies which agree well with axisymmetric studies—however only if the resting tension of the membrane is low. When the resting tension is moderate to high, we show that (i) axisymmetric invaginations are unstable; and (ii) non-axisymme...

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Physics Reports

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein–lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham–Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Mechanisms shaping cell membranes

Current Opinion in Cell Biology, 2014

Membranes of intracellular organelles are characterized by large curvatures with radii of the order of 10-30 nm. While, generally, membrane curvature can be a consequence of any asymmetry between the membrane monolayers, generation of large curvatures requires the action of mechanisms based on specialized proteins. Here we discuss the three most relevant classes of such mechanisms with emphasis on the physical requirements for proteins to be effective in generation of membrane curvature. We provide new quantitative estimates of membrane bending by shallow hydrophobic insertions and compare the efficiency of the insertion mechanism with those of the protein scaffolding and crowding mechanisms.

On the effect of substrate curvature on cell mechanics

Biomaterials, 2009

Cell movement on a substrate or within the extracellular matrix is the phenomenological response to a biochemical signals' cascade transcripted into biophysical processes and viceversa. The process is complex in nature, including different length scales from the whole cell to organelle and protein levels, where substrate/ECM curvature has been shown to play an important role on cell's behavior. From a macroscopic perspective, the cytoskeleton may be modeled as a continuum body unbalanced by internal protein motors. In this work, we propose a cell constitutive model to simulate cell attachment on curved substrates, activated by contractile forces. We first analyze a single fiber bundle composed by microtubules, actin filaments and myosin machinery. Then, the model is macroscopically extended to the cytoskeletal level using homogenization. Substrate curvature has two implications in our model: (i) it forces fibers to work in a curved (bent) position and (ii) it eventually creates a pre-deformation state in the cytoskeleton. Interestingly, the model shows higher contractile force inhibition as curvature increases when implemented over different substrate morphologies, being this consistent with experimental results. The presented model may result useful in many new regenerative medicine techniques, miniaturized experimental tests, or to analyze cell behavior on manufactured nanoscaffolds for tissue engineering.

Use the force: membrane tension as an organizer of cell shape and motility

Trends in Cell Biology, 2013

Many cell phenomena that involve shape changes are affected by the intrinsic deformability of the plasma membrane (PM). Far from being a passive participant, the PM is now known to physically, as well as biochemically, influence cell processes ranging from vesicle trafficking to actin assembly. Here we review current understanding of how changes in PM tension regulate cell shape and movement, as well as how cells sense PM tension.

Shape regulation generates elastic interaction between living cells

New Journal of Physics, 2017

The organization of live cells to tissues is associated with the mechanical interaction between cells, which is mediated through their elastic environment. We model cells as spherical active force dipoles surrounded by an infinite elastic matrix, and analytically evaluate the interaction energy for different scenarios of their regulatory behavior. We obtain attraction for homeostatic (set point) forces and repulsion for homeostatic displacements. When the translational motion of the cells is regulated, the interaction energy decays with distance as d 1 4 , while when it is not regulated the energy decays as d 1 6. This arises from the same reasons as the van der Waals interaction between induced electric dipoles.

Theoretical Model for Cellular Shapes Driven by Protrusive and Adhesive Forces

PLoS Computational Biology, 2011

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix.