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{"CAPTION FIG4.png": "'\\n\\n**Figure supplement 1.** Relationship between endocytic outcome and active Arp2/3 complex surface density or mother filament nucleating protein surface density at the base of the pit.\\n\\n**Figure supplement 2.** A collar of active Arp2/3 complex near the neck the pit does not affect endocytic outcome.\\n\\n**Figure supplement 3.** Internalization as a function of the number of Hip1R molecules and mechanism of self-organization of endocytic actin filaments.\\n\\n**Figure 4-video 1.** Simulations in which the coverage of linker Hip1R around the pit was varied from 1% to 80% of a sphere.\\n\\n**Figure 4.** Spatial distribution of actin/Hip1R attachments strongly affects actin self-organization and pit internalization. **(A)** Schematic of spatial boundary conditions from endocytic actin-binding proteins. Positions of active Arp2/3 complex (blue) and actin/pit attachments via linker proteins such as Hip1R (purple). **(B)** Initial positions of Hip1R around increasingly large pit surface area, from 1% to 80% of a sphere. The top ~20% of the sphere is occluded by the neck. **(C)** Snapshots of a series of simulations for different values of Hip1R coverage showing actin distribution at t = 13 s. **(D-G)** Changes in the endocytic actin network over time as a function of Hip1R coverage (colors). \\\\(n\\\\) = 96 simulations. **(D)** Internalization; **(E)** Number of barbed ends near the base of the pit (within 7.5 nm); **(F)** Number of Arp2/3 complexes bound in the endocytic network; **(G)** Number of actin filaments bound in the endocytic network. Scale bar: 50 nm.\\n\\nThe online version of this article includes the following video and figure supplement(s) for figure 4:\\n\\n**Figure supplement 1.** Relationship between endocytic outcome and active Arp2/3 complex surface density or mother filament nucleating protein surface density at the base of the pit.\\n\\n**Figure supplement 2.** A collar of active Arp2/3 complex near the neck the pit does not affect endocytic outcome.\\n\\n**Figure supplement 3.** Internalization as a function of the number of Hip1R molecules and mechanism of self-organization of endocytic actin filaments.\\n\\n**Figure 4-video 1.** Simulations in which the coverage of linker Hip1R around the pit was varied from 1% to 80% of a sphere.\\n\\n'", "CAPTION FIG5-1.png": "'Figure 5: Bending of endocytic actin filaments stores elastic energy for pit internalization. **(A)** Snapshot of simulation showing filaments bent between the attachment site in the coat and the base of the pit. Also see _Figure_ 1F. Yellow arrowheads point to a bent actin filament. **(B)** Tomographic slice of cryo-electron monogram of an SK-MEL2 cell. Long actin filaments (yellow arrowheads) bend along the clathrin-coated pit between the coat and the base of the pit. **(C)** Snapshot of membrane mechanics simulation under an internalization force with 60 nm internalization. **(D)** Slice of the same nomogram as shown in **B** at a different Z-level (+37 nm) in which the coated plasma membrane (white arrowheads) is visible. Scale bar for A-D: 50 nm. **(E)** Heat map of the bending angle and free filament length of endocytic actin filaments in simulations. Color code is number of filaments (summed for all time points, average of 24 simulations). Lines demarcate the magnitude of energy stored in these filaments, based on the theory of elastic beam rigidity for filaments of persistence length 10 \u03bcm (Materials and methods), in units of k_M_T_ (4.1 pN-nm). Purple lines: filament conformations expected from thermal fluctuations (passive bending): White lines: filament bending greater than from thermal fluctuations (active bending). Magenta lines: lower.\\n\\n'", "CAPTION FIG5-2.png": "'limit for bending energy expected to sever filaments (De La Cruz et al., 2015b). (F) Total elastic energy stored in bent capped (red) or growing (green) endocytic actin filaments during simulation over time compared to mean energy necessary for internalization (black) (n = 96 simulations). (G) Schematic of an in silico experiment to test the mechanical function of bent endocytic actin filaments. At t = 10 s, the membrane tension was reduced to zero, and the filaments were capped. (H) Internalization (green) after spring cut and filament capping, compared to simulation with no change in tension (black, same data as Figure 3D). n = 48 simulations. (I) Bending energy of endocytic actin filaments with barbed ends near base of pit over time. Release of tension and filament capping at t = 10 s (green) compared to no change in tension (black).\\n\\nThe online version of this article includes the following video and figure supplement(s) for figure S:\\n\\n**Figure supplement 1.** Hexagonal and pentagonal lattices in tomogram of clathrin-coated pit.\\n\\n**Figure supplement 2.** Energetics of endocytic actin network.\\n\\n**Figure 5-video 1.** Cryo-electron tomogram of SK-MEL-2 cell grown on holey carbon grid and vitrified, related to Figure 5.\\n\\n**Figure 5-video 2.** Simulation of actin in endocytosis in which, at t = 10 s, filaments were all capped and the membrane tension was reduced to 0 pN/m.\\n\\nhttps://ellfescances.org/articles/49840Wfig5video2'", "CAPTION FIG6.png": "'Figure 6: Irhibiting Arp2/3 complex nucleation activity stalls endocytosis. (**A**) Schematic of the model parameter corresponding to Arp2/3 nucleation activity, and the step inhibited by the small molecule CK_666_. (**B**) Internalization as a function of Arp2/3 complex nucleation rate. Orange region highlights parameter sensitivity, and green region highlights parameter insensitivity. n = 96 simulations. Reducing Arp2/3 nucleation rate reduces internalization as seen in the orange region. (**C**) Histograms of endocytic lifetime in SK-MEL-2 cells endogenously expressing clathrin light chain CLTatagRFP-T and dynamin2-aGFP and treated with CK_666_. \\\\(n\\\\) = 368 tracks from 10 cells. (**D**) Fluorescence intensity over time for endocytic tracks marked by clathrin-RFP and dynamin2-GFP in SK-MEL-2 cells treated with 0.1% DMSO (\\\\(\\\\gtrsim\\\\) mM) or the indicated concentration of CK_666_ for 45 min. Fluorescence events were tracked automatically (Materials and methods). Tracks in which GFP and RFP colocalized are shown. Each track was normalized to its maximum intensity and then all tracks were averaged and aligned to the time of the disappearance of the clathrin-RFP signal. The lifetimes of these events are plotted in **D**. Shaded bars are standard deviations.\\n\\nThe online version of this article includes the following figure supplements(s) for figure 6:'", "CAPTION FIG7.png": "'Figure 7: Adaptation of endocytic actin network to changes in membrane tension. **(A)** Schematic depicting possible adaptation of the actin network to membrane tension via self-organization and bending **(B\u2013D)** Snapshots of simulations from the same time point (14 s) for **(B)** low membrane tension (0.015 pN/nm); **(C)** medium membrane tension (0.15 pN/nm); **(D)** high membrane tension (1 pN/nm). Scale bar is 50 nm. **(E\u2013H)** Changes in the endocytic actin network as a function of membrane tension. **(E)** Internalization; **(F)** Number of barbed ends near base of pH; **(G)** Number of actin filaments in lipid IR-bound network; **(H)** Bending energy for filaments with barbed ends near base of pH. Mean \\\\(\\\\pm\\\\) standard deviation of time points in the last 5 s of simulations. Dashed line in **(E)** is expected internalization based on constant energy usage with 0.01 pN/nm condition as reference (see **Methods**).\\n\\n'", "CAPTION TABNA.png": "'\\n\\n**Figure Captions**\\n\\nFig. 1. The \\\\(\\\\pi^{0}\\\\'", "CAPTION FIG8.png": "'Figure 8: App2/3 complex activity and HipIR/actin attachments are critical for allowing actin filaments to drive endocytic put internalization and adapt to changing tension. **(A)** Schematic of App2/3 complex activity and HipIR coverage along with membrane tension. **(B)** Phase diagram of endocytic internalization as a function of membrane tension and App2/3 complex nucleation rate shown on a log-log plot. Dotted lines are values taken from the literature (**Beltamer and Pollard**, _2008_, **Diz-Munoz et al.**, _2016_, **(C\u2013G)** Changes in the endocytic actin network as a function of HipIR coverage for different values of membrane tension. Low tension = 0.015 pN/nm; medium tension = 0.15 pN/nm; high tension = 1 pN/nm. \\\\(n\\\\) = 288 simulations. **(C)** Internalization; **(D)** Number of barbed ends near base of pit; **(E)** Number of App2/3 complexes bound in network; **(F)** Number of actin filaments bound in network; **(G)** Bending energy of filaments with barbed ends near the base of the pit. Mean + standard deviation of time points in the last 5 s of simulations. **(H)** Summary of load-dependent adaptation of self-organizing endocytic actin network due to spatial segregation of active Arp2/3 complex at the base and HipIR in a broad distribution within the clathrin coat.\\n\\n'", "CAPTION FIG1-1.png": "'Figure 1: Multiscale modeling shows that a minimal branched actin network is sufficient to internalize endocytic pits against physiological membrane tension. (**A**) Schematic of a section of the cell\u2019s plasma membrane being internalized during mammalian endocytosis depicts plasma membrane deformation against membrane tension [purple arrows] countered by the clathrin coat (yellow) and the actin cytoskeleton (red). (**B**) Shape of the membrane and pit internalization from continuum mechanics simulations of the endocytic pit experiencing axial (\\\\(Z\\\\)) forces corresponding to simplified actin forces. To begin with, the plasma membrane (yellow) is deformed by a coat with preferred curvature that expands in area until the pit stalls. A net Figure 1 continued on next page\\n\\n'", "CAPTION FIG2-2.png": "'\\n\\n**Figure supplement 1.** Optimization and validation of fluorescence calibration method.\\n\\n**Figure supplement 2.** Generation of genome-edited human induced pluripotent stem cell lines endogenously expressing AP2-RFP and ArpC3-GFP.\\n\\n**Figure 2-video 1.** Time lapse images of human induced pluripotent stem cells transiently expressing FKBP-60mer-GFP and treated with 0.5 nM AP21967.\\n\\nhttps://elifesciences.org/articles/49840ffig2video1\\n\\n**Figure 2-video 2.** Time-lapse TIRF microscopy image of a human induced pluripotent stem cell endogenously expressing ArpC3-GFP and AP2-RFP.\\n\\nhttps://elifesciences.org/articles/49840ffig2video2'", "CAPTION FIG3.png": "'Figure 3: Self-organization of actin filaments into a radial dendritic network drives endocytic internalization. (**A**) (Left) Schematic depicting actin barbed (plus) or pointed (minus) ends. (Right) Heat maps of the positions of barbed ends (red) or pointed ends (blue) relative to the endocytic pit. Color code represents the relative number of ends. Each graph is averaged across 96 simulations and 1 s of simulation time. (**B**) Simulation output of endocytic actin filaments color-coded for axial (**Z**) orientation. Blue filaments orient toward the base of the pit (+90) and green filaments orient parallel to the base of the pit (**D**). (**C**) Axial orientation of barbed ends. (Left) Schematic of axes. R is radial position of barbed end. (Right) Heat map of axial orientation of barbed ends as a function of R and Z position. Average of 96 simulations. (**D**) Pit internalization over time (\\\\(n\\\\) = 96 simulations). (**E**) Simulation output of endocytic actin filaments color-coded for radial orientation. (**F**) Radially oriented endocytic actin filaments. (Left) Schematic of axes Radial orientation is defined such that +1 = barbed end oriented away from the center of the pit, and -1 = barbed end oriented toward the center of the pit. (Right) Heat map of radial orientation of barbed ends as a function of X and Y position (\\\\(n\\\\) = 96 simulations). Barbed ends radiate outward. (**G**) Radial orientation of barbed ends over time for 96 simulations. Gray curve is negative control of randomly oriented filaments (\\\\(n\\\\) = 50 filaments in one simulation). (**H**) Concentration of barbed ends near the base of the endocytic pit. (Left) Schematic of positions of the neck and base of the pit. (Right) Number of barbed ends near base (green) or neck (blue) of pit, defined as within 7.5 nm of each surface. (**J**) The majority of forces are directed orthogonal to the base of the pit based on positions of barbed ends in simulations. Shaded bars are standard deviations. The online version of this article includes the following video and figure supplements for figure 3:\\n\\nFigure 1: Assembly and self-organization of endocytic actin network. Figure 3\u2014video 1. Simulation of actin in endocytosis with actin filaments color coded for axial orientation.\\n\\n'", "CAPTION FIG1-2.png": "'force (red arrows) is applied downward from the coat and upward into the base of the endocytic pit (red dotted lines). In this simulation, membrane tension was 0.2 pH/nm, and the coated area was rigid (2400 pH nm). (**C**) Force versus pit internalization relationships for different values of membrane tension. Internalization is defined as the pit displacement in \\\\(Z\\\\). Shading delineates linear force-internalization regime (blue); \"transition point\" from U to omega shape (orange); \"omega-shaped\" regime where the neck is narrower than the pit diameter and the force required for internalization is lower than at the transition point (for tensions > 0.1 pN/rem) [yellow]. Color matches the three snapshots in B. Parameters are given in Supplementary files 1 and 2. (**D**) Resistance of pit to internalization versus membrane tension. Resistance (spring constant) is defined as absolute value of slope in C for the \\'U-shaped\\' region. Each curve is calculated for a different value of membrane rigidity (where \\\\(\\\\text{Ix}=320\\\\) pH nm, the rigidity of the uncoated plasma membrane). (**E**) Computational model of branched actin filament polymerization coupled to endocytic pit internalization. An internalizing endocytic pit is modeled as a sphere with a neck attached to a flat surface by a spring. Active Arp2/3 complex (blue) is distributed in a ring around the base of the pit. An actin nucleation protein (pink) generates an actin filament (white), which polymerizes, stalls under load, and is stochastically capped [red]. Arp2/3 complexes bind to the sides of actin filaments and nucleate new filaments at a 77-degree angle, creating new branches. Linker Hip1R (purple) is embedded in the pit and binds to actin filaments. Model parameters are given in Supplementary file 3. (**F**) Graphical output of the simulations from Cytosim (_Nedelec_ and _Foethke_, 2007) at 2 s intervals. Scale bar: 100 rpm. (**G**) Pit internalization over simulated time as a function of the number of available molecules of Arp2/3 complex. Average of 16 simulations per condition. Shaded bars are standard deviations. The online version of this article includes the following video and figure supplement(s) for figure 1:\\n\\n**Figure supplement 1.** Effect of different actin- and simulation-related parameters on pit internalization dynamics.\\n\\n**Figure supplement 2.** Initiation from a pool of diffusing cytoplasmic actin filaments leads to variable timing of internalization.\\n\\n**Figure 1-video 1.** Simulations of continuum membrane mechanics model.\\n\\n**Figure 1-video 2.** Simulation of actin in endocytosis using Cytosim.\\n\\n**Figure 2-video 3.** Simulation of actin in endocytosis using Cytosim.\\n\\n'", "CAPTION FIGSCHEME1.png": "'\\n\\n**Scheme 1.** Flow chart of multiscale modeling and experimental strategy combining membrane mechanics, actin spatiotemporal dynamics, molecule counting, and cryo-electron tomography.\\n\\n'", "CAPTION FIG2-1.png": "'\\nFigure 2: Molecule counting of endogenously GFP-tagged Arp2/3 complex in live human induced pluripotent stem cells. (**A-D**) Development of a calibration curve relating fluorescence intensity to numbers of molecules in live cells. (**A**) Cartoon of intracellular GFP-tagged 60mer nanocage with inducible plasma membrane tether. Each subunit (blue) is tagged with GFP (green) and FKBP (orange). FRB (T2098L) (Purple) is targeted to the plasma membrane by a palmitoylation and myrioylation sequence and dimerizes with FKBP in the presence of rapamycin analog AP21967. Cartoon showing one of 60 tagged subunits is based on PDB structures: Ssp, 2J0a, and 4di. Scale bar 10 nm. (**B**) Inverse contrast fluorescence intensity images of human induced pluripotent stem cells expressing GFP-tagged plasma membrane-bound nanocages. Sum projection of nine 300 nm confocal images. Scale bar: 2 \u03bcm. (**C**) Histograms of fluorescence intensity per spot for the four calibration constructs showing mean \u00b1 standard deviation. Images were corrected for uneven illumination and intensity was background-corrected. Data from 305 spots in 15 cells over three experiments. (**D**) Calibration curve relating fluorescence intensity to numbers of molecules in mammalian cells. Line is a linear fit through zero. Error bars are standard deviations. (**E**) Cartoon drawn to scale of Arp2/3 complex tagged with GFP at the flexible C-terminus of Arp2/3. Known binding and activation sites are distal to this site. Based on PDB 2p9f. (**F**) Montage of CME event marked by AP2-tagRFP-T and ArpC3-tagGFP2 from TIRF imaging. Montage shows 4s intervals from a movie taken at 2 s intervals. (**G**) Relative fluorescence intensity over time of AP2-tagRFP-T and ArpC3-tagGFP2 in endocytic events imaged by TIRF microscopy. Traces were normalized to maximum intensity and averaged 121 traces from 8 cells in four experiments. Shading is \u00b11 s.d. (**H**) Fluorescence micrographs of (left) 60mer-tagGFP2, (left-center) 120mer-tagGFP2, (right-center) ArpC3-tagGFP2, and (right) ArpC3-tagGFP2 and AP2-tagRFP-T. White arrows mark spots in which ArpC3-tagGFP2 and AP2-tagRFP-T colocalize. Scale bar 2 \u03bcm. (**0**) Numbers of molecules of ArpC3 over time.\\n\\n'", "CAPTION FIG5.png": "'* [16] A.\\n\\n'", "CAPTION FIG1.png": "''", "CAPTION FIG2.png": "'\\n\\n[MISSING_PAGE_POST]\\n\\n'"}