Rigidity of triskelion arms and clathrin nets

De novo endocytic clathrin coats develop curvature at early stages of their formation

Sculpting a flat patch of membrane into an endocytic vesicle requires curvature generation on the cell surface, which is the primary function of the endocytosis machinery. Using super-resolved live cell fluorescence imaging, we demonstrate that curvature generation by individual clathrin-coated pits can be detected in real time within cultured cells and tissues of developing organisms. Our analyses demonstrate that the footprint of clathrin coats increases monotonically during the formation of pits at different levels of plasma membrane tension. These findings are only compatible with models that predict curvature generation at the early stages of endocytic clathrin pit formation. We also found that CALM adaptors associated with clathrin plaques form clusters, whereas AP2 distribution is more homogenous. Considering the curvature sensing and driving roles of CALM, we propose that CALM clusters may increase the strain on clathrin lattices locally, eventually giving rise to rupture and subsequent pit completion at the edges of plaques.

Label-retention expansion microscopy

Expansion microscopy (ExM) increases the effective resolving power of any microscope by expanding the sample with swellable hydrogel. Since its invention, ExM has been successfully applied to a wide range of cell, tissue, and animal samples. Still, fluorescence signal loss during polymerization and digestion limits molecular-scale imaging using ExM. Here, we report the development of label-retention ExM (LR-ExM) with a set of trifunctional anchors that not only prevent signal loss but also enable high-efficiency labeling using SNAP and CLIP tags. We have demonstrated multicolor LR-ExM for a variety of subcellular structures. Combining LR-ExM with superresolution stochastic optical reconstruction microscopy (STORM), we have achieved molecular resolution in the visualization of polyhedral lattice of clathrin-coated pits in situ.

Clathrin: the molecular shape shifter

Clathrin is best known for its contribution to clathrin-mediated endocytosis yet it also participates to a diverse range of cellular functions. Key to this is clathrin's ability to assemble into polyhedral lattices that include curved football or basket shapes, flat lattices or even tubular structures. In this review, we discuss clathrin structure and coated vesicle formation, how clathrin is utilised within different cellular processes including synaptic vesicle recycling, hormone desensitisation, spermiogenesis, cell migration and mitosis, and how clathrin's remarkable 'shapeshifting' ability to form diverse lattice structures might contribute to its multiple cellular functions.

The AP2 adaptor enhances clathrin coat stiffness

Deformation of the plasma membrane into clathrin-coated vesicles is a critical step in clathrin-mediated endocytosis and requires the orchestrated assembly of clathrin and endocytic adaptors into a membrane-associated protein coat. The individual role of these membrane-bending and curvature-stabilizing factors is subject to current debate. As such, it is unclear whether the clathrin coat itself is stiff enough to impose curvature and if so, whether this could be effectively transferred to the membrane by the linking adaptor proteins. We have recently demonstrated that clathrin alone is sufficient to form membrane buds in vitro. Here, we use atomic force microscopy to assess the contributions of clathrin and its membrane adaptor protein 2 (AP2) to clathrin coat stiffness, which determines the mechanics of vesicle formation. We found that clathrin coats are less than 10-fold stiffer than the membrane they enclose, suggesting a delicate balance between the forces harnessed from clathrin coat formation and those required for membrane bending. We observed that clathrin adaptor protein AP2 increased the stiffness of coats formed from native clathrin, but did not affect less-flexible coats formed from clathrin lacking the light chain subunits. We thus propose that clathrin light chains are important for clathrin coat flexibility and that AP2 facilitates efficient cargo sequestration during coated vesicle formation by modulating clathrin coat stiffness.

Structure and Assembly of Clathrin Cages

The unusual structure of clathrin, combined with its ability to assemble and disassemble rapidly in cells provides a model system for us to learn about the ways in which proteins can contribute mechanically to a functioning cell. In this article, we discuss the structural properties of clathrin cages and the triskelions which assemble to form them. The function of clathrin depends on the structure of these triskelions and the interactions they make both with each other during assembly and with the adaptor protein network that drives coated vesicle formation. The atomic resolution structure of clathrin domains has been revealed by X-ray crystallography while scattering studies have enabled the shape of a triskelion in solution to be deduced. Cryo-electron microscopy maps have shown the secondary structure of entire cages, how individual triskelion legs are arranged to form a cage and enabled some bound adaptor proteins to be located. Cage formation itself is energetically finely balanced and requires specific interactions between triskelion legs to be productive, as biochemical studies and in silico modeling have shown. Theoretical, structural and cell biological investigations over many years have contributed to our knowledge of clathrin structure and assembly. It now remains to determine the precise nature of the interactions which occur between clathrin triskelions, light chain and heavy chain and the adaptor protein network.

Mechanotransduction in tumor progression: The dark side of the force

Broders-Bondon et al. review the pathological mechanical properties of tumor tissues and how abnormal mechanical signals result in oncogenic biochemical signals during tumor progression.

Cancer has been characterized as a genetic disease, associated with mutations that cause pathological alterations of the cell cycle, adhesion, or invasive motility. Recently, the importance of the anomalous mechanical properties of tumor tissues, which activate tumorigenic biochemical pathways, has become apparent. This mechanical induction in tumors appears to consist of the destabilization of adult tissue homeostasis as a result of the reactivation of embryonic developmental mechanosensitive pathways in response to pathological mechanical strains. These strains occur in many forms, for example, hypervascularization in late tumors leads to high static hydrodynamic pressure that can promote malignant progression through hypoxia or anomalous interstitial liquid and blood flow. The high stiffness of tumors directly induces the mechanical activation of biochemical pathways enhancing the cell cycle, epithelial–mesenchymal transition, and cell motility. Furthermore, increases in solid-stress pressure associated with cell hyperproliferation activate tumorigenic pathways in the healthy epithelial cells compressed by the neighboring tumor. The underlying molecular mechanisms of the translation of a mechanical signal into a tumor inducing biochemical signal are based on mechanically induced protein conformational changes that activate classical tumorigenic signaling pathways. Understanding these mechanisms will be important for the development of innovative treatments to target such mechanical anomalies in cancer.

Utilizing clathrin triskelions as carriers for spatially controlled multi-protein display

The simultaneous and spatially controlled display of different proteins on nanocarriers is a desirable property not often achieved in practice. Here, we report the use of clathrin triskelions as a versatile platform for functional protein display. We hypothesized that site-specific molecular epitope recognition would allow for effective and ordered protein attachment to clathrin triskelions. Clathrin binding peptides (CBPs) were genetically fused to mCherry and green fluorescent protein (GFP), expressed, and loaded onto clathrin triskelions by site-specific binding. Attachment was confirmed by surface plasmon resonance. mCherry fusion proteins modified with various CBPs displayed binding affinities between 470 nM and 287 μM for the clathrin triskelions. Simultaneous attachment of GFP-Wbox and mCherry-Cbox fusion constructs to the clathrin terminal domain was verified by Förster resonance energy transfer. The circulating half-lives, area under the curve, and the terminal half-lives of GFP and mCherry were significantly increased when attached to clathrin triskelions. Clathrin triskelion technology is useful for the development of versatile and multifunctional carriers for spatially controlled protein or peptide display with tremendous potential in nanotechnology, drug delivery, vaccine development, and targeted therapeutic applications.

Forty Years of Clathrin-coated Vesicles

The purification of coated vesicles and the discovery of clathrin by Barbara Pearse in 1975 was a landmark in cell biology. Over the past 40 years, work from many labs has uncovered the molecular details of clathrin and its associated proteins, including how they assemble into a coated vesicle and how they select cargo. Unexpected connections have been found with signalling, development, neuronal transmission, infection, immunity and genetic disorders. But there are still a number of unanswered questions, including how clathrin-mediated trafficking is regulated and how the machinery evolved.

Membrane indentation triggers clathrin lattice reorganization and fluidization

Clathrin-mediated endocytosis involves the coordinated assembly of clathrin cages around membrane indentations, necessitating fluid-like reorganization followed by solid-like stabilization. This apparent duality in clathrin's in vivo behavior provides some indication that the physical interactions between clathrin triskelia and the membrane effect a local response that triggers fluid-solid transformations within the clathrin lattice. We develop a computational model to study the response of clathrin protein lattices to spherical deformations of the underlying flexible membrane. These deformations are similar to the shapes assumed during intracellular trafficking of nanoparticles. Through Monte Carlo simulations of clathrin-on-membrane systems, we observe that these membrane indentations give rise to a greater than normal defect density within the overlaid clathrin lattice. In many cases, the bulk surrounding lattice remains in a crystalline phase, and the extra defects are localized to the regions of large curvature. This can be explained by the fact that the in-plane elastic stress in the clathrin lattice are reduced by coupling defects to highly curved regions. The presence of defects brought about by indentation can result in the fluidization of a lattice that would otherwise be crystalline, resulting in an indentation-driven, defect-mediated phase transition. Altering subunit elasticity or membrane properties is shown to drive a similar transition, and we present phase diagrams that map out the combined effects of these parameters on clathrin lattice properties.

Membrane fluctuations destabilize clathrin protein lattice order

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.

Kinetics of loop formation in worm-like chain polymers

A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.

Micellization model for the polymerization of clathrin baskets

A thermodynamic model is used to investigate the conditions under which clathrin triskelions form polyhedral baskets. The analysis, which is similar to classical methods used to study micelle formation, relates clathrin basket energetics to system parameters linked to triskelial rigidity, the natural curvature of an isolated triskelion, and interactions between triskelial legs in the assembled polyhedra. Mathematical theory predicts that a minimal ("critical") clathrin concentration, C(C), needs to be surpassed in order for basket polymerization to occur, and indicates how C(C), and the amount of polymerized material, depend on the chosen parameters. Analytical expressions are obtained to indicate how changes in the parameters affect the sizes of the polyhedra which arise when the total clathrin concentration exceeds C(C). A continuum analytic approximation then is used to produce numerical results that illustrate the derived dependences.

Unraveling protein-protein interactions in clathrin assemblies via atomic force spectroscopy

Atomic force microscopy (AFM), single molecule force spectroscopy (SMFS), and single particle force spectroscopy (SPFS) are used to characterize intermolecular interactions and domain structures of clathrin triskelia and clathrin-coated vesicles (CCVs). The latter are involved in receptor-mediated endocytosis (RME) and other trafficking pathways. Here, we subject individual triskelia, bovine-brain CCVs, and reconstituted clathrin-AP180 coats to AFM-SMFS and AFM-SPFS pulling experiments and apply novel analytics to extract force-extension relations from very large data sets. The spectroscopic fingerprints of these samples differ markedly, providing important new information about the mechanism of CCV uncoating. For individual triskelia, SMFS reveals a series of events associated with heavy chain alpha-helix hairpin unfolding, as well as cooperative unraveling of several hairpin domains. SPFS of clathrin assemblies exposes weaker clathrin-clathrin interactions that are indicative of inter-leg association essential for RME and intracellular trafficking. Clathrin-AP180 coats are energetically easier to unravel than the coats of CCVs, with a non-trivial dependence on force-loading rate.

Fishing for clathrin-coated pit nucleators

The membrane-curvature-inducing protein Fcho was proposed to be part of a ubiquitous nucleation mechanism for clathrin-coated pits. However, studies in developing zebrafish embryos now indicate a role for Fcho as a receptor-specific adaptor in bone morphogenetic protein (BMP) signalling, rather than a global coated-pit nucleator.

The generation of curved clathrin coats from flat plaques

Flat clathrin lattices or 'plaques' are commonly believed to be the precursors to clathrin-coated buds and vesicles. The sequence of steps carrying the flat hexagonal lattice into a highly curved polyhedral cage with exactly 12 pentagons remains elusive, however, and the large numbers of disrupted interclathrin connections in previously proposed conversion pathways make these scenarios rather unlikely. The recent notion that clathrin can make controlled small conformational transitions opens new avenues. Simulations with a self-assembling clathrin model suggest that localized conformational changes in a plaque can create sufficiently strong stresses for a dome-like fragment to break apart. The released fragment, which is strongly curved but still hexagonal, may subsequently grow into a cage by recruiting free triskelia from the cytoplasm, thus building all 12 pentagonal faces without recourse to complex topological changes. The critical assembly concentration in a slightly acidic in vitro solution is used to estimate the binding energy of a cage at 25-40 k(B) T/clathrin.

A TACC3/ch-TOG/clathrin complex stabilises kinetochore fibres by inter-microtubule bridging

Kinetochore fibres (K-fibres) of the spindle apparatus move chromosomes during mitosis. These fibres are discrete bundles of parallel microtubules (MTs) that are crosslinked by inter-MT 'bridges' that are thought to improve fibre stability during chromosomal movement. The identity of these bridges is unknown. Clathrin is a multimeric protein that has been shown to stabilise K-fibres during early mitosis by a mechanism independent of its role in membrane trafficking. In this study, we show that clathrin at the mitotic spindle is in a transforming acidic colied-coil protein 3 (TACC3)/colonic, hepatic tumour overexpressed gene (ch-TOG)/clathrin complex. The complex is anchored to the spindle by TACC3 and ch-TOG. Ultrastructural analysis of clathrin-depleted K-fibres revealed a selective loss of a population of short inter-MT bridges and a general loss of MTs. A similar loss of short inter-MT bridges was observed in TACC3-depleted K-fibres. Finally, immunogold labelling confirmed that inter-MT bridges in K-fibres contain clathrin. Our results suggest that the TACC3/ch-TOG/clathrin complex is an inter-MT bridge that stabilises K-fibres by physical crosslinking and by reducing rates of MT catastrophe.

AFM visualization of clathrin triskelia under fluid and in air

Atomic force microscopy (AFM) is used to characterize the structure and interactions of clathrin triskelia. Time sequence images of individual, wet triskelia resting on mica surfaces clearly demonstrate conformational fluctuations of the triskelia. AFM of dried samples yields images having nanometric resolution comparable to that obtainable by electron microscopy of shadowed samples. Increased numbers of triskelion dimers and assembly intermediates, as well as structures having dimensions similar to those of clathrin cages, are observed when the triskelia were immersed in a low salt, low pH buffer. These entities have been quantified by AFM protein volume computation.

Clathrin triskelia show evidence of molecular flexibility

The clathrin triskelion, which is a three-legged pinwheel-shaped heteropolymer, is a major component in the protein coats of certain post-Golgi and endocytic vesicles. At low pH, or at physiological pH in the presence of assembly proteins, triskelia will self-assemble to form a closed clathrin cage, or "basket". Recent static light scattering and dynamic light scattering studies of triskelia in solution showed that an individual triskelion has an intrinsic pucker similar to, but differing from, that inferred from a high resolution cryoEM structure of a triskelion in a clathrin basket. We extend the earlier solution studies by performing small-angle neutron scattering (SANS) experiments on isolated triskelia, allowing us to examine a higher q range than that probed by static light scattering. Results of the SANS measurements are consistent with the light scattering measurements, but show a shoulder in the scattering function at intermediate q values (0.016 A(-1)), just beyond the Guinier regime. This feature can be accounted for by Brownian dynamics simulations based on flexible bead-spring models of a triskelion, which generate time-averaged scattering functions. Calculated scattering profiles are in good agreement with the experimental SANS profiles when the persistence length of the assumed semiflexible triskelion is close to that previously estimated from the analysis of electron micrographs.

Conformation of a clathrin triskelion in solution

A principal component in the protein coats of certain post-golgi and endocytic vesicles is clathrin, which appears as a three-legged heteropolymer (known as a triskelion) that assembles into polyhedral cages principally made up of pentagonal and hexagonal faces. In vitro, this assembly depends upon the pH, with cages forming more readily at low pH and less readily at high pH. We have developed procedures, on the basis of static and dynamic light scattering, to determine the radius of gyration, R(g), and hydrodynamic radius, R(H), of isolated triskelia, under conditions where cage assembly occurs. Calculations based on rigid molecular bead models of a triskelion show that the measured values can be accounted for by bending the legs and a puckering at the vertex. We also show that the values of R(g) and R(H) measured for clathrin triskelia in solution are qualitatively consistent with the conformation of a triskelion in a "D6 barrel" cage assembly measured by cryoelectron microscopy.

Anisotropy in Sickle Hemoglobin Fibers from Variations in Bending and Twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.

Measuring the elasticity of clathrin-coated vesicles via atomic force microscopy

Using a new scheme based on atomic force microscopy (AFM), we investigate mechanical properties of clathrin-coated vesicles (CCVs). CCVs are multicomponent protein and lipid complexes of approximately 100 nm diameter that are implicated in many essential cell-trafficking processes. Our AFM imaging resolves clathrin lattice polygons and provides height deformation in quantitative response to AFM-substrate compression force. We model CCVs as multilayered elastic spherical shells and, from AFM measurements, estimate their bending rigidity to be 285 +/- 30 k(B)T, i.e., approximately 20 times that of either the outer clathrin cage or inner vesicle membrane. Further analysis reveals a flexible coupling between the clathrin coat and the membrane, a structural property whose modulation may affect vesicle biogenesis and cellular function.

Clathrin self-assembly involves coordinated weak interactions favorable for cellular regulation

The clathrin triskelion self-assembles into a polyhedral coat surrounding membrane vesicles that sort receptor cargo to the endocytic pathway. A triskelion comprises three clathrin heavy chains joined at their C-termini, extending into proximal and distal leg segments ending in a globular N-terminal domain. In the clathrin coat, leg segments entwine into parallel and anti-parallel interactions. Here we define the contributions of segmental interactions to the clathrin assembly reaction and measure the strength of their interactions. Proximal and distal leg segments were found to lack sufficient affinity to form stable homo- or heterodimers under assembly conditions. However, chimeric constructs of proximal or distal leg segments, trimerized by replacement of the clathrin trimerization domain with that of the invariant chain protein, were able to self-assemble in reversible reactions. Thus clathrin assembly occurs because weak leg segment affinities are coordinated through trimerization, sharing a dependence on multiple weak interactions with other biopolymers. Such polymerization is sensitive to small environmental changes and is therefore compatible with cellular regulation of assembly, disassembly and curvature during formation of clathrin-coated vesicles.

Atomic force microscopy of nanometric liposome adsorption and nanoscopic membrane domain formation

Scanning probe microscopy studies of membrane fusion and nanoscopic structures were performed using hydrated single lipids and lipid mixtures. Extruded vesicles of DMPC and mixtures at various concentrations of DLPC, DPPC and cholesterol were deposited on freshly cleaved mica and studied in a fluid environment by AFM. The nanostructures formed by these extruded liposomes ranged from isolated unilamellar vesicles to flat sheet membranes and were marked influenced by thermodynamic phase behavior. For DMPC membrane, intact bilayers exhibited a phase transition process in agreement with large bilayer patches. In the DLPC, DPPC and cholesterol mixtures, nanoscopic domain diameters ranged from approximately 25 to 48nm with height differences of approximately 1.4nm; all values were lipid composition-dependent. Our data support and extend previous studies of microscopic domains and phase boundaries of the same mixtures in giant unilamellar vesicles determined by confocal light microscopy. Our approach for preparing and utilizing supported membrane structures is potentially relevant to studies of native cell membranes.

Micromechanics of isolated sickle cell hemoglobin fibers: bending moduli and persistence lengths

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.

Clathrin-dependent and clathrin-independent endocytosis are differentially sensitive to insertion of poly (ethylene glycol)-derivatized cholesterol in the plasma membrane

We examined the effect of a cholesterol derivative, poly (ethylene glycol) cholesteryl ether on the structure/function of clathrin-coated pits and caveolae. Addition of the compound to cultured cells induced progressive smoothening of the surface. Markedly, when the incorporated amount exceeded 10% equivalent of the surface area, fluid pinocytosis, but not endocytosis of transferrin, became inhibited in K562 cells. In A431 cells, both clathrin-independent fluid phase uptake and the internalization of fluorescent cholera-toxin B through caveolae were inhibited with concomitant flattening of caveolae. In contrast, clathrin-mediated internalization of transferrin was not affected until the incorporated poly (ethylene glycol) cholesteryl ether exceeded 20% equivalent of the plasma membrane surface area, at which point opened clathrin-coated pits accumulated. The cells were ruptured upon further addition of poly (ethylene glycol) cholesteryl ether. We propose that the primary reason for the differential effect of poly (ethylene glycol) cholesteryl ether is that the bulk membrane phase and caveolae are both more elastic than the rigid clathrin-coated pits. We analyzed the results with the current mechanical model (Rauch and Farge, Biophys J 2000;78:3036-3047) and suggest here that the functional clathrin-lattice is much stiffer than typical phospholipid bilayers.

Energetics of clathrin basket assembly

A minimal thermodynamic model is used to study the in vitro equilibrium assembly of reconstituted clathrin baskets. The model contains parameters accounting for i) the combined bending and flexing rigidities of triskelion legs and hubs, ii) the intrinsic curvature of an isolated triskelion, and iii) the free energy changes associated with interactions between legs of neighboring triskelions. Analytical expressions for basket size distributions are derived, and published size distribution data (Zaremba S, Keen JH. J Cell Biol 1983;97: 1339-1347) are then used to provide estimates for net total basket assembly energies. Results suggest that energies involved in adding triskelions to partially formed clathrin lattices are small (of the order of kBT), in accord with the notion that lattice remodeling during basket formation occurs as a result of thermodynamic fluctuations. In addition, analysis of data showing the effects of assembly proteins (APs) on basket size indicates that the binding of APs increases the intrinsic curvature of an elemental triskelial subunit, the stabilizing energy of leg interactions, and the effective leg/hub rigidity. Values of effective triskelial rigidity determined in this investigation are similar to those estimated by previous analysis of shape fluctuations of isolated triskelia.