Actin-Regulator Feedback Interactions during Endocytosis

Both Las17-binding sites on Arp2/3 complex are important for branching nucleation and assembly of functional endocytic actin networks in S. cerevisiae

Arp2/3 complex nucleates branched actin filaments that drive membrane invagination during endocytosis and leading-edge protrusion in lamellipodia. Arp2/3 complex is maximally activated in vitro by binding of a WASP family protein to two sites-one on the Arp3 subunit and one spanning Arp2 and ARPC1-but the importance of each site in the regulation of force-producing actin networks is unclear. Here, we identify mutations in budding yeast Arp2/3 complex that decrease or block engagement of Las17, the budding yeast WASP, at each site. As in the mammalian system, both sites are required for maximal activation in vitro. Dimerization of Las17 partially restores activity of mutations at both CA-binding sites. Arp2/3 complexes defective at either site assemble force-producing actin networks in a bead motility assay, but their reduced activity hinders motility by decreasing actin assembly near the bead surface and by failing to suppress actin filament bundling within the networks. While even the most defective Las17-binding site mutants assembled actin filaments at endocytic sites, they showed significant internalization defects, potentially because they lack the proper architecture to drive plasma membrane remodeling. Together, our data indicate that both Las17-binding sites are important to assemble functional endocytic actin networks in budding yeast, but Arp2/3 complex retains some activity in vitro and in vivo even with a severe defect at either Las17-binding site.

A condensate dynamic instability orchestrates actomyosin cortex activation

A key event at the onset of development is the activation of a contractile actomyosin cortex during the oocyte-to-embryo transition^1-3. Here we report on the discovery that, in Caenorhabditis elegans oocytes, actomyosin cortex activation is supported by the emergence of thousands of short-lived protein condensates rich in F-actin, N-WASP and the ARP2/3 complex^4-8 that form an active micro-emulsion. A phase portrait analysis of the dynamics of individual cortical condensates reveals that condensates initially grow and then transition to disassembly before dissolving completely. We find that, in contrast to condensate growth through diffusion⁹, the growth dynamics of cortical condensates are chemically driven. Notably, the associated chemical reactions obey mass action kinetics that govern both composition and size. We suggest that the resultant condensate dynamic instability¹⁰ suppresses coarsening of the active micro-emulsion¹¹, ensures reaction kinetics that are independent of condensate size and prevents runaway F-actin nucleation during the formation of the first cortical actin meshwork.

Modeling the dynamic growth and branching of actin filaments

As an essential component of the cytoskeleton, actin filaments play a key role in a variety of cellular physiological activities. To better understand the function of actin filaments, which are a special kind of polymer chain, researchers have started to focus on the Brownian dynamics of polymers. Currently, to study the dynamics of polymers, classical explicit bead-spring models and finite-element methods (FEMs) have both been broadly used. However, compared to bead-spring models, FEMs can address the mechanical properties of actin filaments and actin networks with more detail and better accuracy. However, current FEMs do not consider the dynamic assembly of actin into an actin filament network. Here, we extend the traditional FEM and present a new framework of the FEM based on the co-rotational grid method, which allows us to simulate the dynamic growth and branching of actin filaments. Several examples are studied. The proposed numerical model is capable of capturing the dynamic assembly of actin filaments.

Non-linear elastic properties of actin patches to partially rescue yeast endocytosis efficiency in the absence of the cross-linker Sac6

Clathrin mediated endocytosis is an essential and complex cellular process involving more than 60 proteins. In yeast, successful endocytosis requires counteracting a large turgor pressure. To this end, yeasts assemble actin patches, which accumulate elastic energy during their assembly. We investigated the material properties of reconstituted actin patches from a wild-type (WT) strain and a mutant strain lacking the cross-linker Sac6 (sac6Δ), which has reduced endocytosis efficiency in live cells. We hypothesized that a change in the viscous properties of the actin patches, which would dissipate more mechanical energy, could explain this reduced efficiency. There was however no significant difference in the viscosity of both types of patches. However, we discovered a significantly different non-linear elastic response. While WT patches had a constant elastic modulus at different stress values, sac6Δ patches had a lower elastic modulus at low stress, before stiffening at higher ones, up to values similar to those of WT patches. To understand the consequences of this discovery, we performed, in vivo, a precise analysis of actin patch dynamics. Our analysis reveals that a small fraction of actin patches successfully complete endocytosis in sac6Δ cells, provided that those assemble an excess of actin at the membrane compared to WT. This observation indicates that the non-linear elastic properties of actin networks in sac6Δ cells contribute to rescue endocytosis, requiring nevertheless more actin material to build-up the necessary stored elastic energy.

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.

Thermodynamically consistent treatment of the growth of a biopolymer in the presence of a smooth obstacle interaction potential

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force, as previous work has often done, is thermodynamically inconsistent and can overestimate the stall force, sometimes by more than a factor of two. We perform simulations and analytic calculations of the force-velocity relation satisfying the thermodynamic relationship. The force-velocity relation can deviate strongly from the Brownian-Ratchet predictions. For shallow potential wells of depth ∼5k_{B}T, which might correspond to transient filament-membrane attachments, the velocity drops more rapidly than predicted by the Brownian-Ratchet model, in some cases by as much as a factor of 50 at an opposing force of only 1 pN. On the other hand, the zero-force velocity is much less affected than would be expected from naive use of the Boltzmann factor. Furthermore, the growth velocity has a surprisingly strong dependence on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing but only if the attractive well is relatively flat over a region comparable to or greater than the monomer size. For double-well potentials, which have such a flat region, the slowing of polymerization by external pushing force is almost linear up to the stall force in some parameter ranges.

Principles of self-organization and load adaptation by the actin cytoskeleton during clathrin-mediated endocytosis

Force generation by actin assembly shapes cellular membranes. An experimentally constrained multiscale model shows that a minimal branched actin network is sufficient to internalize endocytic pits against membrane tension. Around 200 activated Arp2/3 complexes are required for robust internalization. A newly developed molecule-counting method determined that ~200 Arp2/3 complexes assemble at sites of clathrin-mediated endocytosis in human cells. Simulations predict that actin self-organizes into a radial branched array with growing ends oriented toward the base of the pit. Long actin filaments bend between attachment sites in the coat and the base of the pit. Elastic energy stored in bent filaments, whose presence was confirmed by cryo-electron tomography, contributes to endocytic internalization. Elevated membrane tension directs more growing filaments toward the base of the pit, increasing actin nucleation and bending for increased force production. Thus, spatially constrained actin filament assembly utilizes an adaptive mechanism enabling endocytosis under varying physical constraints.

The outer membrane of a cell is a tight but elastic barrier that controls what enters or leaves the cell. Large molecules typically cannot cross this membrane unaided. Instead, to enter the cell, they must be packaged into a pocket of the membrane that is then pulled inside. This process, called endocytosis, shuttles material into a cell hundreds of times a minute.

Endocytosis relies on molecular machines that assemble and disassemble at the membrane as required. One component, a protein called actin, self-assembles near the membrane into long filaments with many repeated subunits. These filaments grow against the membrane, pulling it inwards. But it was not clear how actin filaments organize in such a way that allows them to pull on the membrane with enough force – and without a template to follow.

Akamatsu et al. set about identifying how actin operates during endocytosis by using computer simulations that were informed by measurements made in living cells. The simulations included information about the location of actin and other essential molecules, along with the details of how these molecules work individually and together. Akamatsu et al. also developed a method to count the numbers of molecules of a key protein at individual sites of endocytosis. High-resolution imaging was then used to create 3D pictures of actin and endocytosis in action in human cells grown in the laboratory.

The analysis showed the way actin filaments arrange themselves depends on the starting positions of a few key molecules that connect to actin. Imaging confirmed that, like a pole-vaulting pole, the flexible actin filaments bend to store energy and then release it to pull the membrane inwards during endocytosis. Finally, the simulations predicted that the collection of filaments adapts its shape and size in response to the resistance of the elastic membrane. This makes the system opportunistic and adaptable to the unpredictable environment within cells.

Pulling-force generation by ensembles of polymerizing actin filaments

The process by which actin polymerization generates pulling forces in cellular processes such as endocytosis is less well understood than pushing-force generation. To clarify the basic mechanisms of pulling-force generation, we perform stochastic polymerization simulations for a square array of polymerizing semiflexible actin filaments, having different interactions with the membrane. The filaments near the array center have a strong attractive component. Filament bending and actin-network elasticity are treated explicitly. We find that the outer filaments push on the membrane and the inner filaments pull, with a net balance of forces. The total calculated pulling force is maximized when the central filaments have a very deep potential well, and the outer filaments have no well. The steady-state force is unaffected by the gel rigidity, but equilibration takes longer for softer gels. The force distributions are flat over the pulling and pushing regions. Actin polymerization is enhanced by softening the gel or reducing the filament binding to the membrane. Filament-membrane detachment can occur for softer gels, even if the total binding energy of the filaments to the membrane is 100 [Formula: see text] or more. It propagates via a stress-concentration mechanism similar to that of a brittle crack in a solid, and the breaking stress is determined by a criterion similar to that of the 'Griffith' theory of crack propagation.

Crosslinking actin networks produces compressive force

Actin has been shown to be essential for clathrin-mediated endocytosis in yeast. However, actin polymerization alone is likely insufficient to produce enough force to deform the membrane against the huge turgor pressure of yeast cells. In this paper, we used Brownian dynamics simulations to demonstrate that crosslinking of a meshwork of nonpolymerizing actin filaments is able to produce compressive forces. We show that the force can be up to several thousand pico-Newtons if the crosslinker has a high stiffness. The force decays over time as a result of crosslinker turnover, and is a result of converting chemical binding energy into elastic energy.

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

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'.

Type I myosins anchor actin assembly to the plasma membrane during clathrin-mediated endocytosis

Actin assembly and type I myosins are both required for clathrin-mediated endocytosis. Here Pedersen and Drubin show that type I myosins anchor actin assembly factors to the plasma membrane at sites of clathrin-mediated endocytosis, facilitating force generation by actin assembly.

The actin cytoskeleton generates forces on membranes for a wide range of cellular and subcellular morphogenic events, from cell migration to cytokinesis and membrane trafficking. For each of these processes, filamentous actin (F-actin) interacts with membranes and exerts force through its assembly, its associated myosin motors, or both. These two modes of force generation are well studied in isolation, but how they are coordinated in cells is mysterious. During clathrin-mediated endocytosis, F-actin assembly initiated by the Arp2/3 complex and several proteins that compose the WASP/myosin complex generates the force necessary to deform the plasma membrane into a pit. Here we present evidence that type I myosin is the key membrane anchor for endocytic actin assembly factors in budding yeast. By mooring actin assembly factors to the plasma membrane, this myosin organizes endocytic actin networks and couples actin-generated forces to the plasma membrane to drive invagination and scission. Through this unexpected mechanism, myosin facilitates force generation independent of its motor activity.

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.

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.

Local actin polymerization during endocytic carrier formation

Extracellular macromolecules, pathogens and cell surface proteins rely on endocytosis to enter cells. Key steps of endocytic carrier formation are cargo molecule selection, plasma membrane folding and detachment from the cell surface. While dedicated proteins mediate each step, the actin cytoskeleton contributes to all. However, its role can be indirect to the actual molecular events driving endocytosis. Here, we review our understanding of the molecular steps mediating local actin polymerization during the formation of endocytic carriers. Clathrin-mediated endocytosis is the least reliant on local actin polymerization, as it is only engaged to counter forces induced by membrane tension or cytoplasmic pressure. Two opposite situations are coated pit formation in yeast and at the basolateral surface of polarized mammalian cells which are, respectively, dependent and independent on actin polymerization. Conversely, clathrin-independent endocytosis forming both nanometer [CLIC (clathrin-independent carriers)/GEEC (glycosylphosphatidylinositol (GPI)-anchored protein enriched endocytic compartments), caveolae, FEME (fast endophilin-mediated endocytosis) and IL-2β (interleukin-2β) uptake] and micrometer carriers (macropinocytosis) are dependent on actin polymerization to power local membrane deformation and carrier budding. A variety of endocytic adaptors can recruit and activate the Cdc42/N-WASP or Rac1/WAVE complexes, which, in turn, engage the Arp2/3 complex, thereby mediating local actin polymerization at the membrane. However, the molecular steps for RhoA and formin-mediated actin bundling during endocytic pit formation remain unclear.

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.

A master equation approach to actin polymerization applied to endocytosis in yeast

We present a Master Equation approach to calculating polymerization dynamics and force generation by branched actin networks at membranes. The method treats the time evolution of the F-actin distribution in three dimensions, with branching included as a directional spreading term. It is validated by comparison with stochastic simulations of force generation by actin polymerization at obstacles coated with actin “nucleation promoting factors” (NPFs). The method is then used to treat the dynamics of actin polymerization and force generation during endocytosis in yeast, using a model in which NPFs form a ring around the endocytic site, centered by a spot of molecules attaching the actin network strongly to the membrane. We find that a spontaneous actin filament nucleation mechanism is required for adequate forces to drive the process, that partial inhibition of branching and polymerization lead to different characteristic responses, and that a limited range of polymerization-rate values provide effective invagination and obtain correct predictions for the effects of mutations in the active regions of the NPFs.

Endocytosis is a dynamic process by which cells internalize substances from outside the cell. Especially in yeast, endocytosis is mechanically demanding due to the high pressure difference across the cell membrane, or turgor pressure. Polymerization of a branched actin network is the major process providing the mechanical force to overcome the turgor pressure. Understanding the kinetics of the actin network, and the mechanical interaction between the actin network and the cell membrane, is thus crucial for the study of endocytosis. We develop an efficient mathematical framework for actin dynamics that can realistically incorporate these two features, thus providing a practical method for quantitatively modeling actin dynamics during endocytosis. The resulting model mechanistically reveals that spontaneous nucleation at the center of the endocytic site is required for successful endocytosis, distinguishes the roles of branching and polymerization, and predicts several other experimentally testable outcomes. The accuracy and efficiency of the method, in describing both mechanics and chemistry, render it applicable to a broad field of membrane-bending processes.

A Distinct Endocytic Mechanism of Functionalized-Silica Nanoparticles in Breast Cancer Stem Cells

Nanoparticles provide new fields for life medical science application, including targeted-drug delivery and cancer treatment. To maximize the delivery efficiency of nanoparticle, one must understand the uptake mechanism of nanoparticle in cells, which may determine their ultimate fate and localization in cells. Recently, the proposed-cancer stem cell (CSC) theory has been attracted great attention and regarded as new targets for the new nanodrug developmet and cancer therapies. The interaction between nanoparticles and cancer cells has been extensively studied, but the uptake mechanism of nanoparticles in CSCs has received little attention. Here, we use the pharmacological inhibitors of major endocytic pathways to study the silica nanoparticle (SiNP) uptake mechanisms in the human breast adenocarcinoma cell line (MCF-7) and MCF-7-derived breast cancer stem cells (BCSCs). The results demonstrate that the uptake of SiNPs, particularly amino-functionalized SiNPs, in MCF-7 cells is strongly affected by the actin depolymerization, whereas BCSCs more strongly inhibit the amino-functionalized SiNP uptake after the scavenger receptor disruption. These findings indicate a distinct endocytic mechanism of functionalized SiNPs in BCSCs, which is significant for designing ideal nanosized drug delivery systems and improving the selectivity for CSC-targeted therapy.

Matrix Stiffness Differentially Regulates Cellular Uptake Behavior of Nanoparticles in Two Breast Cancer Cell Lines

Matrix stiffness regulates cell behavior in various biological contexts. In breast tumors, the deposition of extracellular matrix correlates with increasing matrix stiffness and poor survival. Nanoparticulate carriers represent a promising therapeutic vehicle for disease diagnosis and efficient anticancer drug delivery. However, how matrix stiffness influences cellular uptake of nanoparticles remains largely unexplored. Here, we selected photopolymerized polyacrylamide gels with varying stiffnesses as model substrates and studied the impact of matrix stiffness on cell morphology and nanoparticle uptake efficiency in two representative breast cancer cell lines with varying invasiveness, that is, MCF-7 with low invasiveness and MDA-MB-231 with high invasiveness. In our study, both cell lines showed similar morphological changes with changing stiffness. MCF-7 cells adhered on compliant substrates (1 kPa) showed a roundlike morphology with the lowest cell uptake efficiency among four stiffnesses under investigation at each given time point, whereas for MDA-MB-231 cells, the uptake efficiency showed no significant differences across varying stiffnesses. The percentages of MCF-7 cell proliferation on a 1 kPa substrate were significantly decreased at 48 and 72 h as compared to those on stiff substrates and coverslips. When treated with pluronic/d-α-tocopheryl polyethylene glycol 1000 succinate mixed micelle-loaded paclitaxel, cells on stiff substrates of 7, 20, and 25 kPa showed higher cell apoptosis rates as compared to those of cells on 1 kPa substrates. To sum up, our work presents an example of how physical cues impact specific cellular behavior and function, which may further contribute to engineering nanoparticulate delivery systems for more efficient delivery in vivo.

Local Turgor Pressure Reduction via Channel Clustering

The primary drivers of yeast endocytosis are actin polymerization and curvature-generating proteins, such as clathrin and BAR domain proteins. Previous work has indicated that these factors may not be capable of generating the forces necessary to overcome turgor pressure. Thus local reduction of the turgor pressure, via localized accumulation or activation of solute channels, might facilitate endocytosis. The possible reduction in turgor pressure was calculated numerically, by solving the diffusion equation through a Legendre polynomial expansion. It was found that for a region of increased permeability having radius 45 nm, as few as 60 channels with a spacing of 10 nm could locally decrease the turgor pressure by 50%. We identified a key dimensionless parameter, p = P₁a/D, where P₁ is the increased permeability, a is the radius of the permeable region, and D is the solute diffusion coefficient. When p > 0.44, the turgor pressure is locally reduced by >50%. An approximate analytic theory was used to generate explicit formulas for the turgor pressure reduction in terms of key parameters. These findings may also be relevant to plants, where the mechanisms that allow endocytosis to proceed despite high turgor pressure are largely unknown.

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.