Endocytic proteins drive vesicle growth via instability in high membrane tension environment

Applying Spatiotemporal Modeling of Cell Dynamics to Accelerate Drug Development

Cells act as physical computational programs that utilize input signals to orchestrate molecule-level protein-protein interactions (PPIs), generating and responding to forces, ultimately shaping all of the physiological and pathophysiological behaviors. Genome editing and molecule drugs targeting PPIs hold great promise for the treatments of diseases. Linking genes and molecular drugs with protein-performed cellular behaviors is a key yet challenging issue due to the wide range of spatial and temporal scales involved. Building predictive spatiotemporal modeling systems that can describe the dynamic behaviors of cells intervened by genome editing and molecular drugs at the intersection of biology, chemistry, physics, and computer science will greatly accelerate pharmaceutical advances. Here, we review the mechanical roles of cytoskeletal proteins in orchestrating cellular behaviors alongside significant advancements in biophysical modeling while also addressing the limitations in these models. Then, by integrating generative artificial intelligence (AI) with spatiotemporal multiscale biophysical modeling, we propose a computational pipeline for developing virtual cells, which can simulate and evaluate the therapeutic effects of drugs and genome editing technologies on various cell dynamic behaviors and could have broad biomedical applications. Such virtual cell modeling systems might revolutionize modern biomedical engineering by moving most of the painstaking wet-laboratory effort to computer simulations, substantially saving time and alleviating the financial burden for pharmaceutical industries.

Vesiculation pathways in clathrin-mediated endocytosis

During clathrin-mediated endocytosis, a patch of flat plasma membrane is internalized to form a vesicle. In mammalian cells, how the clathrin coat deforms the membrane into a vesicle remains unclear and two main hypotheses have been debated. The "constant area" hypothesis assumes that clathrin molecules initially form a flat lattice on the membrane and deform the membrane by changing its intrinsic curvature while keeping the coating area constant. The alternative "constant curvature" hypothesis assumes that the intrinsic curvature of the clathrin lattice remains constant during the formation of a vesicle while the surface area it covers increases. Previous experimental studies were unable to unambiguously determine which hypothesis is correct. In this paper, we show that these two hypotheses are only two extreme cases of a continuum of vesiculation pathways if we account for the free energies associated with clathrin assembly and curvature generation. By tracing the negative gradient of the free energy, we define vesiculation pathways in the phase space of the coating area and the intrinsic curvature of clathrin coat. Our results show that, overall, the differences in measurable membrane morphology between the different models are not as big as expected, and the main differences are most salient at the early stage of endocytosis. Furthermore, the best fitting pathway to experimental data is not compatible with the constant-curvature model and resembles a constant-area-like pathway where the coating area initially expands with minor changes in the intrinsic curvature, later followed by a dramatic increase in the intrinsic curvature and minor change in the coating area. Our results also suggest that experimental measurement of the tip radius and the projected area of the clathrin coat will be the key to distinguish between models.

Inferring biophysical properties of membranes during endocytosis using machine learning

Endocytosis is a fundamental cellular process in eukaryotic cells that facilitates the transport of molecules into the cell. With the help of fluorescence microscopy and electron tomography, researchers have accumulated extensive geometric data of membrane shapes during endocytosis. These data contain rich information about the mechanical properties of membranes, which are hard to access via experiments due to the small dimensions of the endocytic patch. In this study, we propose an approach that combines machine learning with the Helfrich theory of membranes to infer the mechanical properties of membranes during endocytosis from a dataset of membrane shapes extracted from electron tomography. Our results demonstrate that machine learning can output solutions that both match the experimental profile and satisfy the membrane shape equations derived from Helfrich theory. The learning results show that during the early stage of endocytosis, the inferred membrane tension is negative, indicating the presence of strong compressive forces at the boundary of the endocytic invagination. Our method presents a generic framework for extracting membrane information from super-resolution imaging.

Cristae formation is a mechanical buckling event controlled by the inner mitochondrial membrane lipidome

Cristae are high-curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous lipid-based mechanisms have yet to be elucidated. Here, we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the inner mitochondrial membrane against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. This model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that cardiolipin is essential in low-oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of cardiolipin is dependent on the surrounding lipid and protein components of the IMM.

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

Cristae are high curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous mechanisms for lipids have yet to be elucidated. Here we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the IMM against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. The model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that CL is essential in low oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of CL is dependent on the surrounding lipid and protein components of the IMM.

Influenza A Virus Infections Sense Host Membrane Tension to Dynamically Tune Assembly

Enveloped viruses often exhibit a pleomorphic morphology, ranging in size from 100nm spheres to tens-of-micron long filaments. For influenza A virus (IAV), spheres enable rapid replication and minimize metabolic cost, while filaments resist effects of antibodies or other cell-entry pressures. The current paradigm is that virion shape changes require genetic adaptation; however, a virus evolved to alter its shape phenotypically would outperform one that relies on genetic selection. Using a novel quantitative flow virometry assay to characterize virion shape dynamics we find that IAV rapidly tunes its shape distribution to favor spheres under optimal, and filaments under attenuating conditions including the presence of antibodies. We identify membrane tension as a key cue sensed by IAV determining shape distributions. This phenotypic shift outpaces genetic change and serves to enable additional life cycles under pressure. Our work expands knowledge of the complex host-virus interplay to include viral responses to the local environment by optimizing its structure to maximize replication and ultimately host-host transmission.

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. These tubes can be formed due to localized forces acting on the membrane or by the curvature induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.

A Review of Continuum Mechanics for Mechanical Deformation of Lipid Membranes

Mechanical deformation of lipid membranes plays important roles in various cellular tasks. Curvature deformation and lateral stretching are two major energy contributions to the mechanical deformation of lipid membranes. In this paper, continuum theories for these two major membrane deformation events were reviewed. Theories based on curvature elasticity and lateral surface tension were introduced. Numerical methods as well as biological applications of the theories were discussed.

The endocytic protein machinery as an actin-driven membrane-remodeling machine

In clathrin-mediated endocytosis, a principal membrane trafficking route of all eukaryotic cells, forces are applied to invaginate the plasma membrane and form endocytic vesicles. These forces are provided by specific endocytic proteins and the polymerizing actin cytoskeleton. One of the best-studied endocytic systems is endocytosis in yeast, known for its simplicity, experimental amenability, and overall similarity to human endocytosis. Importantly, the yeast endocytic protein machinery generates and transmits tremendous force to bend the plasma membrane, making this system beneficial for mechanistic studies of cellular force-driven membrane reshaping. This review summarizes important protein players, molecular functions, applied forces, and open questions and perspectives of this robust, actin-powered membrane-remodeling protein machine.

Compression-induced buckling of a semiflexible filament in two and three dimensions

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show the theory is highly sensitive to fluctuations in length in two dimensions, and that the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.

The many faces of membrane tension: Challenges across systems and scales

Our understanding of the role of membrane tension in the field of membrane biophysics is rapidly evolving from a passive construct to an active player in a variety of cellular phenomena. Membrane tension has been shown to be a key regulator of many cellular processes ranging including trafficking, ion channel activation, and the invasion of red blood cells by malaria parasites. Recent experimental advances in cells, including the development of a fluorescent tension reporter, have shown that membrane tension is heterogeneous. In this mini-review, I summarize the recent advances in membrane tension measurements and discuss the contributions from different cellular constituents such as the cortical cytoskeleton. Then, I will explore how these different complexities can be considered in biophysical models of different scales. Finally, I will elaborate on the need for iterations between models and experiments as technologies in both fields advance to enable us to obtain critical insights into the physiological role of membrane tension as a critical component of mechanotransduction.

Molecular mechanics underlying flat-to-round membrane budding in live secretory cells

Membrane budding entails forces to transform flat membrane into vesicles essential for cell survival. Accumulated studies have identified coat-proteins (e.g., clathrin) as potential budding factors. However, forces mediating many non-coated membrane buddings remain unclear. By visualizing proteins in mediating endocytic budding in live neuroendocrine cells, performing in vitro protein reconstitution and physical modeling, we discovered how non-coated-membrane budding is mediated: actin filaments and dynamin generate a pulling force transforming flat membrane into Λ-shape; subsequently, dynamin helices surround and constrict Λ-profile's base, transforming Λ- to Ω-profile, and then constrict Ω-profile's pore, converting Ω-profiles to vesicles. These mechanisms control budding speed, vesicle size and number, generating diverse endocytic modes differing in these parameters. Their impact is widespread beyond secretory cells, as the unexpectedly powerful functions of dynamin and actin, previously thought to mediate fission and overcome tension, respectively, may contribute to many dynamin/actin-dependent non-coated-membrane buddings, coated-membrane buddings, and other membrane remodeling processes.

The morphological role of ligand inhibitors in blocking receptor- and clathrin-mediated endocytosis

Cells often internalize particles through endocytic pathways that involve the binding between cell receptors and particle ligands, which drives the cell membrane to wrap the particle into a delivery vesicle. Previous findings showed that receptor-mediated endocytosis is impossible for spherical particles smaller than a minimum size because of the energy barrier created by membrane bending. In this study, we investigate the morphological role of ligand inhibitors in blocking endocytosis, inspired by antibodies that inhibit virus ligands to prevent infection. While ligand inhibitors have the obvious effect of reducing the driving force due to adhesion, they also have a nontrivial (morphological) impact on the entropic and elastic energy of the system. We determine the necessary conditions for endocytosis by considering the additional energy barrier due to the membrane bending to wrap the inhibiting protrusions. We find that inhibitors increase the minimum radius previously reported, depending on their density and size. In addition, we extend this result to the case of clathrin-mediated endocytosis, which is the most common pathway for virus entry. The assembly of a clathrin coat with a spontaneous curvature increases the energy barrier and sets a maximum particle size (in agreement with experimental observations on spherical particles). Our investigation suggests that morphological considerations can inform the optimal design of neutralizing viral antibodies and new strategies for targeted nanomedicine.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.

On the Role of Electrostatic Repulsion in Topological Defect-Driven Membrane Fission

Within a modified Langevin Poisson–Boltzmann model of electric double layers, we derived an analytical expression for osmotic pressure between two charged surfaces. The orientational ordering of the water dipoles as well as the space dependencies of electric potentials, electric fields, and osmotic pressure between two charged spheres were taken into account in the model. Thus, we were able to capture the interaction between the parent cell and connected daughter vesicle or the interactions between neighbouring beads in necklace-like membrane protrusions. The predicted repulsion between them can facilitate the topological antidefect-driven fission of membrane daughter vesicles and the fission of beads of undulated membrane protrusions.

Actin-generated force applied during endocytosis measured by Sla2-based FRET tension sensors

Mechanical forces are integral to many cellular processes, including clathrin-mediated endocytosis, a principal membrane trafficking route into the cell. During endocytosis, forces provided by endocytic proteins and the polymerizing actin cytoskeleton reshape the plasma membrane into a vesicle. Assessing force requirements of endocytic membrane remodeling is essential for understanding endocytosis. Here, we determined actin-generated force applied during endocytosis using FRET-based tension sensors inserted into the major force-transmitting protein Sla2 in yeast. We measured at least 8 pN force transmitted over Sla2 molecule, hence possibly more than 300-880 pN applied during endocytic vesicle formation. Importantly, decreasing cell turgor pressure and plasma membrane tension reduced force transmitted over the Sla2. The measurements in hypotonic conditions and mutants lacking BAR-domain membrane scaffolds then showed the limits of the endocytic force-transmitting machinery. Our study provides force values and force profiles critical for understanding the mechanics of endocytosis and potentially other key cellular membrane-remodeling processes.

Dynamic interplay between cell membrane tension and clathrin-mediated endocytosis

Deformability of the plasma membrane, the outermost surface of metazoan cells, allows cells to be dynamic, mobile and flexible. Factors that affect this deformability, such as tension on the membrane, can regulate a myriad of cellular functions, including membrane resealing, cell motility, polarisation, shape maintenance, membrane area control and endocytic vesicle trafficking. This review focuses on mechanoregulation of clathrin-mediated endocytosis (CME). We first delineate the origins of cell membrane tension and the factors that yield to its spatial and temporal fluctuations within cells. We then review the recent literature demonstrating that tension on the membrane is a fast-acting and reversible regulator of CME. Finally, we discuss tension-based regulation of endocytic clathrin coat formation during physiological processes.

Nanodissected elastically loaded clathrin lattices relax to increased curvature

Clathrin-mediated endocytosis (CME) is the major endocytosis pathway for the specific internalization of large compounds, growth factors, and receptors. Formation of internalized vesicles from the flat plasma membrane is accompanied by maturation of cytoplasmic clathrin coats. How clathrin coats mature and the mechanistic role of clathrin coats are still largely unknown. Maturation models proposed clathrin coats to mature at constant radius or constant area, driven by molecular actions or elastic energy. Here, combining high-speed atomic force microscopy (HS-AFM) imaging, HS-AFM nanodissection, and elasticity theory, we show that clathrin lattices deviating from the intrinsic curvature of clathrin form elastically loaded assemblies. Upon nanodissection of the clathrin network, the stored elastic energy in these lattices drives lattice relaxation to accommodate an ideal area-curvature ratio toward the formation of closed clathrin-coated vesicles. Our work supports that the release of elastic energy stored in curvature-frustrated clathrin lattices could play a major role in CME.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces’ nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO₂ nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO₂ nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

Mechanical Principles Governing the Shapes of Dendritic Spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

Value of models for membrane budding

The budding of membranes and curvature generation is common to many forms of trafficking in cells. Clathrin-mediated endocytosis, as a prototypical example of trafficking, has been studied in great detail using a variety of experimental systems and methods. Recently, advances in experimental methods have led to great strides in insights on the molecular mechanisms and the spatiotemporal dynamics of the protein machinery associated with membrane curvature generation. These advances have been ably supported by computational models, which have given us insights into the underlying mechanical principles of clathrin-mediated endocytosis. On the other hand, targeted experimental perturbation of membranes has lagged behind that of proteins in cells. In this area, modeling is especially critical to interpret experimental measurements in a mechanistic context. Here, we discuss the contributions made by these models to our understanding of endocytosis and identify opportunities to strengthen the connections between models and experiments.

Endocytosis against high turgor pressure is made easier by partial coating and freely rotating base

During clathrin-mediated endocytosis, a patch of flat plasma membrane is deformed into a vesicle. In walled cells, such as plants and fungi, the turgor pressure is high and pushes the membrane against the cell wall, thus hindering membrane internalization. In this work, we study how a patch of membrane is deformed against turgor pressure by force and by curvature-generating proteins. We show that a large amount of force is needed to merely start deforming the membrane and an even larger force is needed to pull a membrane tube. The magnitude of these forces strongly depends on how the base of the membrane is constrained and how the membrane is coated with curvature-generating proteins. In particular, these forces can be reduced by partially, but not fully, coating the membrane patch with curvature-generating proteins. Our theoretical results show excellent agreement with experimental data.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Complimentary action of structured and unstructured domains of epsin supports clathrin-mediated endocytosis at high tension

Membrane tension plays an inhibitory role in clathrin-mediated endocytosis (CME) by impeding the transition of flat plasma membrane to hemispherical clathrin-coated structures (CCSs). Membrane tension also impedes the transition of hemispherical domes to omega-shaped CCSs. However, CME is not completely halted in cells under high tension conditions. Here we find that epsin, a membrane bending protein which inserts its N-terminus H0 helix into lipid bilayer, supports flat-to-dome transition of a CCS and stabilizes its curvature at high tension. This discovery is supported by molecular dynamic simulation of the epsin N-terminal homology (ENTH) domain that becomes more structured when embedded in a lipid bilayer. In addition, epsin has an intrinsically disordered protein (IDP) C-terminus domain which induces membrane curvature via steric repulsion. Insertion of H0 helix into lipid bilayer is not sufficient for stable epsin recruitment. Epsin's binding to adaptor protein 2 and clathrin is critical for epsin's association with CCSs under high tension conditions, supporting the importance of multivalent interactions in CCSs. Together, our results support a model where the ENTH and unstructured IDP region of epsin have complementary roles to ensure CME initiation and CCS maturation are unimpeded under high tension environments.

Nonaxisymmetric Shapes of Biological Membranes from Locally Induced Curvature

In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes-an indeed unphysical constraint. Past studies 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 to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane's ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.

Mechanobiology predicts raft formations triggered by ligand-receptor activity across the cell membrane

Clustering of ligand-binding receptors of different types on thickened isles of the cell membrane, namely lipid rafts, is an experimentally observed phenomenon. Although its influence on cell's response is deeply investigated, the role of the coupling between mechanical processes and multiphysics involving the active receptors and the surrounding lipid membrane during ligand-binding has not yet been understood. Specifically, the focus of this work is on G-protein-coupled receptors (GPCRs), the widest group of transmembrane proteins in animals, which regulate specific cell processes through chemical signalling pathways involving a synergistic balance between the cyclic Adenosine Monophosphate (cAMP) produced by active GPCRs in the intracellular environment and its efflux, mediated by the Multidrug Resistance Proteins (MRPs) transporters. This paper develops a multiphysics approach based on the interplay among energetics, multiscale geometrical changes and mass balance of species, i.e. active GPCRs and MRPs, including diffusion and kinetics of binding and unbinding. Because the obtained energy depends upon both the kinematics and the changes of species densities, balance of mass and of linear momentum are coupled and govern the space-time evolution of the cell membrane. The mechanobiology involving remodelling and change of lipid ordering of the cell membrane allows to predict dynamics of transporters and active receptors -in full agreement with experimentally observed cAMP levels- and how the latter trigger rafts formation and cluster on such sites. Within the current scientific debate on Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) and on the basis of the ascertained fact that lipid rafts often serve as an entry port for viruses, it is felt that approaches accounting for strong coupling among mechanobiological aspects could even turn helpful in better understanding membrane-mediated phenomena such as COVID-19 virus-cell interaction.

Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

The biconcave disk shape of the mammalian red blood cell (RBC) is unique to the RBC and is vital for its circulatory function. Due to the absence of a transcellular cytoskeleton, RBC shape is determined by the membrane skeleton, a network of actin filaments cross-linked by spectrin and attached to membrane proteins. While the physical properties of a uniformly distributed actin network interacting with the lipid bilayer membrane have been assumed to control RBC shape, recent experiments reveal that RBC biconcave shape also depends on the contractile activity of nonmuscle myosin IIA (NMIIA) motor proteins. Here, we use the classical Helfrich-Canham model for the RBC membrane to test the role of heterogeneous force distributions along the membrane and mimic the contractile activity of sparsely distributed NMIIA filaments. By incorporating this additional contribution to the Helfrich-Canham energy, we find that the RBC biconcave shape depends on the ratio of forces per unit volume in the dimple and rim regions of the RBC. Experimental measurements of NMIIA densities at the dimple and rim validate our prediction that (a) membrane forces must be non-uniform along the RBC membrane and (b) the force density must be larger in the dimple than the rim to produce the observed membrane curvatures. Furthermore, we predict that RBC membrane tension and the orientation of the applied forces play important roles in regulating this force-shape landscape. Our findings of heterogeneous force distributions on the plasma membrane for RBC shape maintenance may also have implications for shape maintenance in different cell types.

The spectrin-actin network of the membrane skeleton plays an important role in controlling specialized cell membrane morphology. In the paradigmatic red blood cell (RBC), where actin filaments are present exclusively in the membrane skeleton, recent experiments reveal that nonmuscle myosin IIA (NMIIA) motor contractility maintains the RBC biconcave disk shape. In this study, we have identified criteria for micron-scale distributions of NMIIA forces at the membrane required to maintain the biconcave disk shape of an RBC in the resting condition. Supported by experimental measurements of RBC NMIIA distribution, we showed that a heterogeneous force distribution with a larger force density at the dimple is able to capture the experimentally observed biconcave morphology of an RBC with better accuracy compared to previous models that did not consider the heterogeneity in the force distribution. Furthermore, we showed that the biconcave geometry of the RBC is closely regulated by the effective membrane tension and the direction of applied forces on the membrane. These findings can be generalized to any force-mediated membrane shape, providing insight into the role of actomyosin forces in prescribing and maintaining the morphology of different cell types.

Nanoparticle elasticity regulates phagocytosis and cancer cell uptake

The ability of cells to sense external mechanical cues is essential for their adaptation to the surrounding microenvironment. However, how nanoparticle mechanical properties affect cell-nanoparticle interactions remains largely unknown. Here, we synthesized a library of silica nanocapsules (SNCs) with a wide range of elasticity (Young's modulus ranging from 560 kPa to 1.18 GPa), demonstrating the impact of SNC elasticity on SNC interactions with cells. Transmission electron microscopy revealed that the stiff SNCs remained spherical during cellular uptake. The soft SNCs, however, were deformed by forces originating from the specific ligand-receptor interaction and membrane wrapping, which reduced their cellular binding and endocytosis rate. This work demonstrates the crucial role of the elasticity of nanoparticles in modulating their macrophage uptake and receptor-mediated cancer cell uptake, which may shed light on the design of drug delivery vectors with higher efficiency.

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

Membrane nanotubes are dynamic structures that may connect cells over long distances. Nanotubes are typically thin cylindrical tubes, but they may occasionally have a beaded architecture along the tube. In this paper, we study the role of membrane mechanics in governing the architecture of these tubes and show that the formation of bead-like structures along the nanotubes can result from local heterogeneities in the membrane either due to protein aggregation or due to membrane composition. We present numerical results that predict how membrane properties, protein density, and local tension compete to create a phase space that governs the morphology of a nanotube. We also find that there exists a discontinuity in the energy that impedes two beads from fusing. These results suggest that the membrane-protein interaction, membrane composition, and membrane tension closely govern the tube radius, number of beads, and the bead morphology.

A mechanical model reveals that non-axisymmetric buckling lowers the energy barrier associated with membrane neck constriction

Membrane neck formation is essential for scission, which, as recent experiments on tubules have demonstrated, can be location dependent. The diversity of biological machinery that can constrict a neck such as dynamin, actin, ESCRTs and BAR proteins, and the range of forces and deflection over which they operate, suggest that the constriction process is functionally mechanical and robust to changes in biological environment. In this study, we used a mechanical model of the lipid bilayer to systematically investigate the influence of location, symmetry constraints, and helical forces on membrane neck constriction. Simulations from our model demonstrated that the energy barriers associated with constriction of a membrane neck are location-dependent. Importantly, if symmetry restrictions are relaxed, then the energy barrier for constriction is dramatically lowered and the membrane buckles at lower values of forcing parameters. Our simulations also show that constriction due to helical proteins further reduces the energy barrier for neck formation when compared to cylindrical proteins. These studies establish that despite different molecular mechanisms of neck formation in cells, the mechanics of constriction naturally leads to a loss of symmetry that can lower the energy barrier to constriction.

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here, we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit vs implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through, e.g., a protein-protein interaction), which can greatly increase the stability of multiprotein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics.

Role of Nanoparticle Mechanical Properties in Cancer Drug Delivery

The physicochemical properties of nanoparticles play critical roles in regulating nano-bio interactions. Whereas the effects of the size, shape, and surface charge of nanoparticles on their biological performances have been extensively investigated, the roles of nanoparticle mechanical properties in drug delivery, which have only been recognized recently, remain the least explored. This review article provides an overview of the impacts of nanoparticle mechanical properties on cancer drug delivery, including (1) basic terminologies of the mechanical properties of nanoparticles and techniques for characterizing these properties; (2) current methods for fabricating nanoparticles with tunable mechanical properties; (3) in vitro and in vivo studies that highlight key biological performances of stiff and soft nanoparticles, including blood circulation, tumor or tissue targeting, tumor penetration, and cancer cell internalization, with a special emphasis on the underlying mechanisms that control those complicated nano-bio interactions at the cellular, tissue, and organ levels. The interesting research and findings discussed in this review article will offer the research community a better understanding of how this research field evolved during the past years and provide some general guidance on how to design and explore the effects of nanoparticle mechanical properties on nano-bio interactions. These fundamental understandings, will in turn, improve our ability to design better nanoparticles for enhanced drug delivery.

Molecular mechanisms of force production in clathrin-mediated endocytosis

During clathrin-mediated endocytosis (CME), a flat patch of membrane is invaginated and pinched off to release a vesicle into the cytoplasm. In yeast CME, over 60 proteins-including a dynamic actin meshwork-self-assemble to deform the plasma membrane. Several models have been proposed for how actin and other molecules produce the forces necessary to overcome the mechanical barriers of membrane tension and turgor pressure, but the precise mechanisms and a full picture of their interplay are still not clear. In this review, we discuss the evidence for these force production models from a quantitative perspective and propose future directions for experimental and theoretical work that could clarify their various contributions.

Geometric instability catalyzes mitochondrial fission

The mitochondrial membrane undergoes extreme remodeling during fission. While a few membrane-squeezing proteins are recognized as the key drivers of fission, there is a growing body of evidence that strongly suggests that conical lipids play a critical role in regulating mitochondrial morphology and fission. However, the mechanisms by which proteins and lipids cooperate to execute fission have not been quantitatively investigated. Here, we computationally model the squeezing of the largely tubular mitochondrion and show that proteins and conical lipids can act synergistically to trigger buckling instability and achieve extreme constriction. More remarkably, the study reveals that the conical lipids can act with different fission proteins to induce hierarchical instabilities and create increasingly narrow and stable constrictions. We reason that this geometric plasticity imparts significant robustness to the fission reaction by arresting the elastic tendency of the membrane to rebound during protein polymerization and depolymerization cycles. Our in vitro study validates protein–lipid cooperativity in constricting membrane tubules. Overall, our work presents a general mechanism for achieving drastic topological remodeling in cellular membranes.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

The role of traction in membrane curvature generation

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.

Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation

Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially ordered recruitment according to function. WASP family proteins form a circular nanoscale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template optimizes force generation for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.

Sensing Exocytosis and Triggering Endocytosis at Synapses: Synaptic Vesicle Exocytosis-Endocytosis Coupling

The intact synaptic structure is critical for information processing in neural circuits. During synaptic transmission, rapid vesicle exocytosis increases the size of never terminals and endocytosis counteracts the increase. Accumulating evidence suggests that SV exocytosis and endocytosis are tightly connected in time and space during SV recycling, and this process is essential for synaptic function and structural stability. Research in the past has illustrated the molecular details of synaptic vesicle (SV) exocytosis and endocytosis; however, the mechanisms that timely connect these two fundamental events are poorly understood at central synapses. Here we discuss recent progress in SV recycling and summarize several emerging mechanisms by which synapses can “sense” the occurrence of exocytosis and timely initiate compensatory endocytosis. They include Ca²⁺ sensing, SV proteins sensing, and local membrane stress sensing. In addition, the spatial organization of endocytic zones adjacent to active zones provides a structural basis for efficient coupling between SV exocytosis and endocytosis. Through linking different endocytosis pathways with SV fusion, these mechanisms ensure necessary plasticity and robustness of nerve terminals to meet diverse physiological needs.

Membrane bending by actin polymerization

Actin polymerization provides driving force to aid several types of processes that involve pulling the plasma membrane into the cell, including phagocytosis, cellular entry of large viruses, and endocytosis. In endocytosis, actin polymerization is especially important under conditions of high membrane tension or high turgor pressure. Recent modeling efforts have shown how actin polymerization can give rise to a distribution of forces around the endocytic site, and explored how these forces affect the shape dynamics; experiments have revealed the structure of the endocytic machinery in increasing detail, and demonstrated key feedback interactions between actin assembly and membrane curvature. Here we provide a perspective on these findings and suggest avenues for future research.

Irreversible thermodynamics of curved lipid membranes

The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intramembrane lipid flow, intramembrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.

Actin growth profile in clathrin-mediated endocytosis

Clathrin-mediated endocytosis in yeast is driven by a protein patch containing close to 100 different types of proteins. Among the proteins are 5000-10000 copies of polymerized actin, and successful endocytosis requires growth of the actin network. Since it is not known exactly how actin network growth drives endocytosis, we calculate the spatial distribution of actin growth required to generate the force that drives the process. First, we establish the force distribution that must be supplied by actin growth, by combining membrane-bending profiles obtained via electron microscopy with established theories of membrane mechanics. Next, we determine the profile of actin growth, using a continuum mechanics approach and an iterative procedure starting with an actin growth profile obtained from a linear analysis. The profile has fairly constant growth outside a central hole of radius 45-50 nm, but very little growth in this hole. This growth profile can reproduce the required forces if the actin shear modulus exceeds 80 kPa, and the growing filaments can exert very large polymerization forces. The growth profile prediction could be tested via electron-microscopy or super-resolution experiments in which the turgor pressure is suddenly turned off.

Clathrin polymerization exhibits high mechano-geometric sensitivity

How tension modulates cellular transport has become a topic of interest in the recent past. However, the effect of tension on clathrin assembly and vesicle growth remains less understood. Here, we use the classical Helfrich theory to predict the energetic cost that clathrin is required to pay to remodel the membrane at different stages of vesicle formation. Our study reveals that this energetic cost is highly sensitive to not only the tension in the membrane but also to the instantaneous geometry of the membrane during shape evolution. Our study predicts a sharp reduction in clathrin coat size in the intermediate tension regime (0.01-0.1 mN m-1). Remarkably, the natural propensity of the membrane to undergo bending beyond the Ω shape causes a significant decrease in the energy needed from clathrin to drive vesicle growth. Our studies in mammalian cells confirm a reduction in clathrin coat size in an increased tension environment. In addition, our findings suggest that the two apparently distinct clathrin assembly modes, namely coated pits and coated plaques, observed in experimental investigations might be a consequence of varied tensions in the plasma membrane. Overall, the mechano-geometric sensitivity revealed in this study might also be at play during the polymerization of other membrane remodeling proteins.

Design principles for robust vesiculation in clathrin-mediated endocytosis

A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions.

Ultradonut topology of the nuclear envelope

The nuclear envelope is a unique topological structure formed by lipid membranes in eukaryotic cells. Unlike other membrane structures, the nuclear envelope comprises two concentric membrane shells fused at numerous sites with toroid-shaped pores that impart a "geometric" genus on the order of thousands. Despite the intriguing architecture and vital biological functions of the nuclear membranes, how they achieve and maintain such a unique arrangement remains unknown. Here, we used the theory of elasticity and differential geometry to analyze the equilibrium shape and stability of this structure. Our results show that modest in- and out-of-plane stresses present in the membranes not only can define the pore geometry, but also provide a mechanism for destabilizing membranes beyond a critical size and set the stage for the formation of new pores. Our results suggest a mechanism wherein nanoscale buckling instabilities can define the global topology of a nuclear envelope-like structure.

Kinetics of cellular uptake of viruses and nanoparticles via clathrin-mediated endocytosis

Several viruses exploit clathrin-mediated endocytosis to gain entry into host cells. This process is also used extensively in biomedical applications to deliver nanoparticles (NPs) to diseased cells. The internalization of these nano-objects is controlled by the assembly of a clathrin-containing protein coat on the cytoplasmic side of the plasma membrane, which drives the invagination of the membrane and the formation of a cargo-containing endocytic vesicle. Current theoretical models of receptor-mediated endocytosis of viruses and NPs do not explicitly take coat assembly into consideration. In this paper we study cellular uptake of viruses and NPs with a focus on coat assembly. We characterize the internalization process by the mean time between the binding of a particle to the membrane and its entry into the cell. Using a coarse-grained model which maps the stochastic dynamics of coat formation onto a one-dimensional random walk, we derive an analytical formula for this quantity. A study of the dependence of the mean internalization time on NP size shows that there is an upper bound above which this time becomes extremely large, and an optimal size at which it attains a minimum. Our estimates of these sizes compare well with experimental data. We also study the sensitivity of the obtained results on coat parameters to identify factors which significantly affect the internalization kinetics.

Fractional hereditariness of lipid membranes: Instabilities and linearized evolution

In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response.

Membrane Mechanics of Endocytosis in Cells with Turgor

Endocytosis is an essential process by which cells internalize a piece of plasma membrane and material from the outside. In cells with turgor, pressure opposes membrane deformations, and increases the amount of force that has to be generated by the endocytic machinery. To determine this force, and calculate the shape of the membrane, we used physical theory to model an elastic surface under pressure. Accurate fits of experimental profiles are obtained assuming that the coated membrane is highly rigid and preferentially curved at the endocytic site. The forces required from the actin machinery peaks at the onset of deformation, indicating that once invagination has been initiated, endocytosis is unlikely to stall before completion. Coat proteins do not lower the initiation force but may affect the process by the curvature they induce. In the presence of isotropic curvature inducers, pulling the tip of the invagination can trigger the formation of a neck at the base of the invagination. Hence direct neck constriction by actin may not be required, while its pulling role is essential. Finally, the theory shows that anisotropic curvature effectors stabilize membrane invaginations, and the loss of crescent-shaped BAR domain proteins such as Rvs167 could therefore trigger membrane scission.

Cells use endocytosis to intake molecules and to recycle components of their membrane. Even in its simplest form, endocytosis involves a large number of proteins with often redundant functions that are organized into a microscopic force-producing “machine”. Knowing how much force is needed to induce a membrane invagination is essential to understand how this endocytic machine may operate. We show that experimental membrane shapes are well described theoretically by a thin sheet elastic model including a difference of pressure across the membrane due to turgor. This allows us to integrate the different contributions that shape the membrane, and to compute the forces opposing membrane deformation. This calculation provides an estimate of the pulling force that must be generated by the actin machinery in yeast. We also identify a membrane instability that could lead to vesicle budding.

Cell spreading area regulates clathrin-coated pit dynamics on micropatterned substrate

Clathrin-mediated endocytosis (CME) is the most characterized pathway for the endocytic entry of proteins and lipids at the plasma membrane of eukaryotic cells. Numerous studies have probed the roles of different endocytic accessory proteins in regulating the dynamics of clathrin-coated pit (CCP) assembly. However, it is not completely clear how physical cues regulate CCP dynamics. Here we employ microcontact printing to control cell shape and examine CCP dynamics as a function of cell spreading area for three differently sized cells. Cells with a large spreading area had more short-lived CCPs but a higher CCP initiation rate. Interestingly, we found that fluorescence intensity of CCPs decreased with increasing cell spreading area in a manner that was dependent on the cortical actin network. Our results point to another facet of the regulation of CCP dynamics, suggesting that CME may be modulated while cells change their mechanical state and remodel their actin cytoskeleton during various processes.