Membrane indentation triggers clathrin lattice reorganization and fluidization

Coat stiffening can explain invagination of clathrin-coated membranes

Clathrin-mediated endocytosis is the main pathway used by eukaryotic cells to take up extracellular material, but the dominant physical mechanisms driving this process are still elusive. Recently, several high-resolution imaging techniques have been used on different cell lines to measure the geometrical properties of clathrin-coated pits over their whole lifetime. Here, we first show that the combination of all datasets with the recently introduced cooperative curvature model defines a consensus pathway, which is characterized by a flat-to-curved transition at finite area, followed by linear growth and subsequent saturation of curvature. We then apply an energetic model for the composite of the plasma membrane and clathrin coat to this consensus pathway to show that the dominant mechanism for invagination could be coat stiffening, which might originate from cooperative interactions between the different clathrin molecules and progressively drives the system toward its intrinsic curvature. Our theory predicts that two length scales determine the invagination pathway, namely the patch size at which the flat-to-curved transition occurs and the final pit radius.

Local changes in protein filament properties drive large-scale membrane transformations involved in endosome tethering and fusion

Large-scale cellular transformations are triggered by subtle physical and structural changes to individual biomacromolecular and membrane components. A prototypical example of such an event is the orchestrated fusion of membranes within an endosome that enables transport of cargo and processing of biochemical moieties. In this work, we demonstrate how protein filaments on the endosomal membrane surface can leverage a rigid-to-flexible transformation to elicit a large-scale change in membrane flexibility to enable membrane fusion. We develop a polymer field-theoretic model that captures molecular alignment arising from nematic interactions with varying surface density and fraction of flexible filaments, which are biologically controlled within the endosomal membrane. We then predict the collective elasticity of the filament brush in response to changes in the filament alignment, predicting a greater than 20-fold increase of the effective membrane elasticity over the bare membrane elasticity that is triggered by filament alignment. These results show that the endosome can modulate the filament properties to orchestrate membrane fluidization that facilitates vesicle fusion, providing an example of how active processes that modulate local molecular properties can result in large-scale transformations that are essential to cellular survival.

Endocytosis gated by emergent properties of membrane-clathrin interactions

Clathrin-mediated endocytosis (CME), the major cellular entry pathway, starts when clathrin assembles on the plasma membrane into clathrin-coated pits (CCPs). Two populations of CCPs are detected within the same cell: 'productive' CCPs that invaginate and pinch off, forming clathrin-coated vesicles (CCVs) [1, 2], and 'abortive' CCPs [3, 4, 5] that prematurely disassemble. The mechanisms of gating between these two populations and their relations to the functions of dozens of early-acting endocytic accessory proteins (EAPs) [5, 6, 7, 8, 9] have remained elusive. Here, we use experimentally-guided modeling to integrate the clathrin machinery and membrane mechanics in a single dynamical system. We show that the split between the two populations is an emergent property of this system, in which a switch between an Open state and a Closed state follows from the competition between the chemical energy of the clathrin basket and the mechanical energy of membrane bending. In silico experiments revealed an abrupt transition between the two states that acutely depends on the strength of the clathrin basket. This critical strength is lowered by membrane-bending EAPs [10, 11, 12]. Thus, CME is poised to be shifted between abortive and productive events by small changes in membrane curvature and/or coat stability. This model clarifies the workings of a putative endocytic checkpoint whose existence was previously proposed based on statistical analyses of the lifetime distributions of CCPs [4, 13]. Overall, a mechanistic framework is established to elucidate the diverse and redundant functions of EAPs in regulating CME progression.

Large self-assembled clathrin lattices spontaneously disassemble without sufficient adaptor proteins

Clathrin-coated structures must assemble on cell membranes to internalize receptors, with the clathrin protein only linked to the membrane via adaptor proteins. These structures can grow surprisingly large, containing over 20 clathrin, yet they often fail to form productive vesicles, instead aborting and disassembling. We show that clathrin structures of this size can both form and disassemble spontaneously when adaptor protein availability is low, despite high abundance of clathrin. Here, we combine recent in vitro kinetic measurements with microscopic reaction-diffusion simulations and theory to differentiate mechanisms of stable vs unstable clathrin assembly on membranes. While in vitro conditions drive assembly of robust, stable lattices, we show that concentrations, geometry, and dimensional reduction in physiologic-like conditions do not support nucleation if only the key adaptor AP-2 is included, due to its insufficient abundance. Nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning additional adaptor types are necessary to form lattices successfully and efficiently. We show that the critical nucleus contains ~25 clathrin, remarkably similar to sizes of the transient and abortive structures observed in vivo. Lastly, we quantify the cost of bending the membrane under our curved clathrin lattices using a continuum membrane model. We find that the cost of bending the membrane could be largely offset by the energetic benefit of forming curved rather than flat structures, with numbers comparable to experiments. Our model predicts how adaptor density can tune clathrin-coated structures from the transient to the stable, showing that active energy consumption is therefore not required for lattice disassembly or remodeling during growth, which is a critical advance towards predicting productive vesicle formation.

Competing pathways for the invagination of clathrin-coated membranes

Clathrin-mediated endocytosis is the major pathway by which eukaryotic cells take up extracellular material, but it is still elusive which physical pathways are being taken during membrane invagination. From a continuum point of view, it can be driven by increases in coat stiffness, preferred curvature or line tension. Here we develop a comprehensive theoretical framework that can be solved analytically and that predicts the consequences of these different scenarios. We find that for the case of increasing stiffness or preferred curvature, curvature will be acquired gradually with growth, while for increasing line tension, the lattice must have grown to a certain size before a flat-to-curved transition can occur. At low membrane tension, the critical value for coat stiffness is 30 kBT, for preferred curvature it is 200 nm, and for line tension it is 6 pN. For high membrane tension, critical coat stiffness is 150 kBT and critical preferred curvature is 70 nm. In the mixed case when a coat with finite rigidity but increasing line tension is considered, a cup-to-sphere transition can occur for a line tension of 6 pN. The flat-to-curved and the cup-to-sphere transitions driven by line tension are both suppressed by high membrane tension.

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.

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.

Gaussian curvature and the budding kinetics of enveloped viruses

The formation of a membrane-enveloped virus starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer develops into a spherical shell (capsid) enveloped by a lipid-rich membrane. In many cases, the budding process stalls prior to the release of the virus. Recently, Brownian dynamics simulations of a coarse-grained model system reproduced protracted pausing and stalling, which suggests that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we propose that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with the neck geometry. A geometrical potential energy barrier develops during the budding that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the capsid. The barrier is generated by a conflict between the positive Gauss curvature of the assembling capsid and the negative Gauss curvature of the neck region. A continuum theory description is proposed and is compared with the Brownian simulations of the budding of enveloped viruses.

Despite intense study, the life-cycle of the HIV-1 virus continues to pose mysteries. One of these is the fact that the assembly of an HIV-1 virus along the plasma membrane (PM) of the host cell—the budding process—stalls prior to release of the virus. Many other important viral pathogens with a surrounding lipid membrane envelope display similar stalling. Combining numerical and analytical methods, we demonstrate that the neck-like shape of the membrane that forms prior to release of the virus creates a barrier that blocks the proteins required for the assembly process from reaching the budding virus. An improved understanding of the physics of the blocking process could enable new strategies to combat enveloped viruses.

Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding

During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.

Membrane bending occurs at all stages of clathrin-coat assembly and defines endocytic dynamics

Clathrin-mediated endocytosis (CME) internalizes plasma membrane by reshaping small regions of the cell surface into spherical vesicles. The key mechanistic question of how coat assembly produces membrane curvature has been studied with molecular and cellular structural biology approaches, without direct visualization of the process in living cells; resulting in two competing models for membrane bending. Here we use polarized total internal reflection fluorescence microscopy (pol-TIRF) combined with electron, atomic force, and super-resolution optical microscopy to measure membrane curvature during CME. Surprisingly, coat assembly accommodates membrane bending concurrent with or after the assembly of the clathrin lattice. Once curvature began, CME proceeded to scission with robust timing. Four color pol-TIRF showed that CALM accumulated at high levels during membrane bending, implicating its auxiliary role in curvature generation. We conclude that clathrin-coat assembly is versatile and that multiple membrane-bending trajectories likely reflect the energetics of coat assembly relative to competing forces.

Two distinct and opposing models for clathrin-mediated endocytosis have been inferred from EM and structural biology data. Here the authors develop an optical method to directly visualize membrane-bending dynamics and show that coat assembly accommodates membrane bending during or after the assembly of the clathrin lattice, which is not predicted by either model.

Self-Assembly of Mesoscale Artificial Clathrin Mimics

Fluidic control and sampling in complex environments is an important process in biotechnology, materials synthesis, and microfluidics. An elegant solution to this problem has evolved in nature through cellular endocytosis, where the dynamic recruitment, self-assembly, and spherical budding of clathrin proteins allows cells to sample their external environment. Yet despite the importance and utility of endocytosis, artificial systems which can replicate this dynamic behavior have not been developed. Guided by clathrin's unusual structure, we created simplified metallic microparticles that capture the three-legged shape, particle curvature, and interfacial attachment characteristics of clathrin. These artificial clathrin mimics successfully recreate biomimetic analogues of clathrin's recruitment, assembly, and budding, ultimately forming extended networks at fluid interfaces and invaginating immiscible phases into spheres under external fields. Particle curvature was discovered to be a critical structural motif, greatly limiting irreversible aggregation and inducing the legs' selective tip-to-tip attraction. This architecture provides a template for a class of active self-assembly units to drive structural and dimensional transformations of liquid-liquid interfaces and microscale fluidic sampling.

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.

Ordered Silicon Pillar Arrays Prepared by Electrochemical Micromachining: Substrates for High-Efficiency Cell Transfection

Ordered arrays of silicon nano- to microscale pillars are used to enable biomolecular trafficking into primary human cells, consistently demonstrating high transfection efficiency can be achieved with broader and taller pillars than reported to date. Cell morphology on the pillar arrays is often strikingly elongated. Investigation of the cellular interaction with the pillar reveals that cells are suspended on pillar tips and do not interact with the substrate between the pillars. Although cells remain suspended on pillar tips, acute local deformation of the cell membrane was noted, allowing pillar tips to penetrate the cell interior, while retaining cell viability.

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.

Shape Effect on Particle-Lipid Bilayer Membrane Association, Cellular Uptake, and Cytotoxicity

Although computer simulation and cell culture experiments have shown that elongated spherical particles can be taken up into cells more efficiently than spherical particles, experimental investigation on effects of these different shapes over the particle-membrane association has never been reported. Therefore, whether the higher cellular uptake of an elongated spherical particles is a result of a better particle-membrane association as suggested by some calculation works or a consequence of its influence on other cellular trans-membrane components involved in particle translocation process, cannot be concluded. Here, we study the effect of particle shape on the particle-membrane interaction by monitoring the association between particles of various shapes and lipid bilayer membrane of artificial cell-sized liposomes. Among the three shaped lanthanide-doped NaYF4 particles, all with high shape purity and uniformity, similar crystal phase, and surface chemistry, the elongated spherical particle shows the highest level of membrane association, followed by the spherical particle with a similar radius, and the hexagonal prism-shaped particle, respectively. The free energy of membrane curvature calculated based on a membrane indentation induced by a particle association indicates that among the three particle shapes, the elongated spherical particle give the most stable membrane curvature. The elongated spherical particles show the highest cellular uptake into cytosol of human melanoma (A-375) and human liver carcinoma (HepG2) cells when observed through a confocal laser scanning fluorescence microscope. Quantitative study using flow cytometry also gives the same result. The elongated spherical particles also possess the highest cytotoxicity in A-375 and normal skin (WI-38) cell lines, comparing to the other two shaped particles.