Dobramysl U , Jarsch IK , Inoue Y , Shimo H , Richier B , Gadsby JR , Mason J , Szałapak A , Ioannou PS , Correia GP , Walrant A , Butler R , Hannezo E , Simons BD , Gallop JL .

Wellcome Trust , WT095829AIA Wellcome Trust ,  219482/Z/19/Z Wellcome Trust , 098357 Wellcome Trust , 092096 Wellcome Trust , C6946/A14492 Cancer Research UK, 105602/Z/14/Z Wellcome Trust , 281971 European Research Council, MC_PC_17230 Medical Research Council , P 31639 Austrian Science Fund FWF, 219482/Z/19/Z Wellcome Trust

             filopodium assembly

	Still from Video 1. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of enaGFP, en-Gal4;UAS-cd8mCherry embryos, late stage 14. Representative video of a total of 12 videos from seven embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Ena is in cyan, membrane in magenta.
	Still from Video 3. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of Scar/WAVENeonGreen en-Gal4;UAS-cd8mCherry embryos, late stage 14. Representative video of a total of 13 videos from eight embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Scar/WAVE is in cyan, membrane in magenta.
	Still from Video 3. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of enaGFP, btl-Gal4;UAS-cd8mCherry embryos, late stage 14. Representative video of of a total of 24 videos from 20 embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Ena is in cyan, membrane in magenta.
	Figure 5. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of Scar/WAVENeonGreen;btl-Gal4 UAS-CAAXCherry embryos, stage 15. Representative video of a total of nine videos from six embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Scar/WAVE is in cyan, membrane in magenta.
	Still from video 5. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of enaGFP, mef2-Gal4 UAS-CAAXCherry embryos, stage 15. Representative video of a total of 15 videos from 12 embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Ena is in cyan, membrane in magenta.
	Still from Video 6. Maximum-intensity projection of laser scanning confocal time-lapse z-stacks of Scar/WAVENeonGreen;mef2-Gal4 UAS-CAAXCherry embryos, stage 15. Representative video of a total of 12 videos from eight embryos. Scale bar represents 10 µm. Images were captured at 15-s intervals and are replayed at 10 frames per second. Scar/WAVE is in cyan, membrane in magenta
	Figure 1. Heterogeneity in Ena and Scar at filopodium tips accompanies exponentially distributed filopodium lengths in vivo. (A–C) Varying intensities of Ena (cyan) at the tips of filopodia (membrane marker expressed using the Gal4 system shown in magenta) in leading edge cells in dorsal closure (A), myotubes (B), and tracheal cells (C) in the Drosophila embryo. Pictures are maximum-intensity projections of the cell marker together with the filopodium tip z-slice of the Ena channel. Scale bars = 2 μm. (D) Time-lapse montages every 15 s of filopodia in leading edge cells in dorsal closure in the Drosophila embryo with fluorescent Ena. Yellow and white arrowheads indicate filopodium tips with and without protein, respectively. Scale bar = 1 µm. (E–H) Similarly, Scar in dorsal closure (E), Ena in myotubes (F), Scar in myotubes (G), Ena in tracheal cells (H), and Scar in tracheal cells (I). (J–L) Scatter plot of maximal (Max.) Ena and Scar intensities at filopodium tips versus maximal end-to-end (straight) filopodia length, respectively, in dorsal closure (n = 53 and 58), tracheal cells (n = 42 and 51), and myotubes (n = 10 and 12). Spearman correlation coefficients and associated P values are shown. (M) Log plots of filopodium lengths from control (n = 150), GFP-Ena (n = 343), and mNeonGreen-Scar/WAVE (n = 213) knock-in homozygous flies are exponentially distributed and largely similar.
	Figure 2. FLS growth and segmentation of actin bundles and tip complex assembly. (A) Images from HILO and confocal or wide-field illumination on the same fields of view. Individual FLSs are segmented based on the actin fluorescence from the z-stack. Red arrows indicate straight tip-to-end distance. A mask on the actin channel is used as an overlay on any other channel, measuring intensities inside the tip complex area defined at the membrane with background correction (at the base slice), and along the shaft. Output includes protein intensity information and shape parameters of the bundle. (B) Single example of bundle growth in time, together with its 3D reconstruction (blue mesh). Actin structures are shown by setting each voxel’s transparency according to its measured intensity (darker indicates higher intensity). The 3D reconstruction overlay uses the output of FLS Ace rendered using Blender software. Black scale tripods indicate 1 μm along each axis. (C) Time-lapse montages of six example FLS tip complexes showing the intensity increase of actin, TOCA-1, and another tip complex protein (scale bars = 5 µm). Protein concentrations labeled/unlabeled were Actin 210/14,000; TOCA-1 10/3; VASP 20/16; N-WASP 20/1; GBD 2/0; Fascin 300/416; Diaph3: 20/10; and Ena: 40/40 in nanomolars.
	Figure S1. Purified protein gels and quantitative Western blots. (A) Coomassie staining of purified protein size separated via SDS-PAGE. (B) Quantification of three or four independent measurements for endogenous actin regulators within the HSS extracts. Black horizontal lines indicate the measurement mean. (C–G) Example blots of purified protein and X. laevis egg HSS extracts used to calculate concentration of proteins via quantitative Western blotting, probed as TOCA-1 (C), N-WASP (D), Ena (E), VASP (F; where we combined the bands suspecting they represented different phosphorylation states), and Fascin (G). (H) Purified IRSp53. (I) Time course showing that Alexa488-SNAP-IRSp53 foci do not localize to FLS actin bundles, whereas control N-WASP does (both added at 50 nM). Scale bars = 1 μm. (J) Alexa488-SNAP-IRSp53 binds the supported lipid bilayer. Scale bars = 10 μm. HSS, high-speed supernatant. TIRFM, total internal reflection fluorescence microscopy.
	Figure 3. Actin regulatory proteins assemble cooperatively to polymerize actin bundles. (A) Mean intensity of accumulation in actin regulators over time as FLSs form combined from the experiments listed in Table 1: Actin n = 19,974; Fascin n = 2,898; TOCA-1 n = 19,893; Diaph3 n = 3,811; N-WASP = 1,743; Cdc42•GTP n = 7,839; Ena n = 1,828; and VASP n = 1,857. (B) Shaded area is the standard deviation of protein accumulation data from A. (C) LatB treatment reduces TOCA-1, Ena, and N-WASP foci on the membrane and inhibits recruitment of fascin and VASP, with partial inhibition of Cdc42•GTP localization. Scale bars = 10 µm. (D) Quantification of number of local maxima computed by protein fluorescence intensities plus and minus LatB. Error bars are the SEM. FLSs are from 8–15 fields of view of more than three independent experiments, and a normal distribution was assumed. (E). The fraction of local maxima when LatB was added normalized to the control. P values are from two-sided Welch’s t test. Error bars represent SEM.
	Figure 4. Actin regulators are heterogeneous, display redundancy, and exhibit preferred subcomplexes. (A) Complexes of diverse composition generate FLSs in vitro. Example of three different actin regulatory proteins (TOCA-1, Cdc42•GTP, and Ena) at the membrane together with a 3D reconstruction of the z-stack of the FLSs growing from a supported bilayer. Note the diversity of regulatory protein combinations observed under the FLSs (colored image in the top right, FLSs highlighted with circles throughout the panel). Grid spacing and scale bars = 10 µm. Volume-rendered FLSs are shown by setting each voxel’s transparency according to its measured intensity (lighter indicates higher intensity). Numbered squares indicate the positions of the example areas displayed in G. (B) Matrix showing Spearman protein–protein intensity correlation and morphology–protein intensity correlation values calculated separately per field of view and averaged. See Fig. S3 for FLS n numbers and Table 1 and Table 2 for numbers of experiments. Gray boxes mean exact correspondence (Diaph3 and Fascin are both enhanced GFP tagged). (C) Correlations of protein immunostaining intensity with actin intensity, FLS tip complex area, FLS straightness, and length are similar to the correlations from tagged protein experiments in Fig. 2 B. FLS numbers: Ena, n = 1,176; N-WASP, n = 1,971; VASP, n = 698; and Fascin, n = 877. (D) FLS lengths are approximately exponentially distributed. The dashed line is a guide for the eye and indicates an exponential with characteristic length L* = 7.6 µm. FLS count, n = 117,365. (E) FLS base areas are approximately exponentially distributed. The dashed line indicates an exponential with characteristic area A* = 1.07 µm2. FLS count, n = 117,365. (F) Relative change in FLS length for enriched FLS with zero, one, two, or three observed proteins compared with the total population length mean, calculated for each field of view and subsequently averaged. Error bars indicate the 95% confidence interval of the mean. Data were pooled from all the different combinations of proteins. Zero, n = 579; one, n = 577; two, n = 566; three, n = 376. (G) Closeups of individual tip complexes (from the numbered examples in A) showing cases where one, two, or all three proteins are enriched in an experiment containing labeled TOCA-1, Cdc42, and Ena. Scale bars = 1 µm.
	Figure S3. Positive correlations between actin regulators. (A) The correlation value matrix from Fig. 2 B with numbers of FLSs (lower right, in thousands). (B) Correlations between pairs of actin regulatory proteins for FLS tip complexes with an effective diameter below 1 μm. The color scale is the same as in Fig. 4 B. (C) Same as above for tip complexes with a diameter above 1 μm. The pattern of weak and stronger correlations is the same for both larger and smaller FLSs.
	Figure S4. The FLS shaft intensity is similar in all compositions. (A) Actin intensity along the shaft perpendicular to the x-y plane and relative to the intensity at the FLS tip complex for FLS cohorts (n = 1,818). The FLSs are categorized according to their lengths in 1-μm cohorts. (B) The same as in A for the fascin intensity along the shaft. (C) Median actin intensity along the shaft perpendicular to the x-y plane and relative to the intensity at the FLS tip complex from assays with the given proteins labeled (n numbers given in the legend). (D) Median actin intensity exponential decay length along the FLS shaft from fitting an exponential decay for a given protein enriched (high) or absent (low) compared with the whole set (all). Diaph3/all, n = 1,846; Cdc42·GTP/all, n = 2,312; VASP/all, n = 4,321; VASP/high, n = 1,297; VASP/low, n = 1,297; Ena/all, n = 15,921; Ena/high, n = 4,797; Ena/low, n = 4,793; Fascin/all, n = 8,181; Fascin/high, n = 2,463; Fascin/low, n = 2,461; TOCA-1/all, n = 32,581; TOCA-1/high, n = 9,813; and TOCA-1 low, n = 9,806. Error bars represent the 66% confidence interval obtained via resampled residuals bootstrap. Missing bars are due to fitting failures resulting from too small n numbers. (E) Median cross-sectional FLS area along the shaft from assays with different proteins labeled (n numbers given in C). (F) Median negative slope of actin width from linear decay fits for a given protein enriched (high, above 70th percentile) or absent (low, below 30th percentile) compared with the whole set (all). N numbers given for D. Error bars represent the 66% confidence interval obtained via resampled residuals bootstrap.
	Figure S5. FLS lengths for different double combinations of proteins. Cumulative frequency plots (empirical cumulative distribution function, ECDF) of FLS length for all double combinations of regulatory proteins for the specific cohort (blue lines), both proteins enriched above a 70% intensity threshold (orange lines), and both proteins below the enrichment threshold (green lines). N values are given in the panel legends. All combinations enriched in Diaph3 and Ena are longer, together with some others. FLSs enriched in Fascin are usually no longer than those without, except when TOCA-1 is also enriched (compare green and orange lines). The triple combination of Diaph3/N-WASP/Cdc42•GTP shows similar effects (bottom right, black outline). Overall, length arises from multiple small, interacting effects.
	Figure 5. Mathematical framework for FLS growth captures experimental FLS length distribution and growth dynamics. (A) Four smoothed, different example experimental FLS length trajectories (top) and their instantaneous growth velocities (bottom) in different colors. (B) Histogram of measured FLS growth velocities (n = 114,816) from tracked FLS trajectories with maximum likelihood estimation fit of a bi-exponential Laplace distribution. (C) Four randomly selected smoothed example trajectories (top) generated from our sum-product framework with their instantaneous velocities (bottom). We started simulations at random initiation points at 0–20 min. (D) FLS length distribution (blue circles; n = 3,193 observations) and corresponding data from simulating 10,000 trajectories (solid orange line; shaded area is the 95% confidence interval of the histogram bin means). The simulation data histogram was scaled by the ratio between the median FLS lengths larger than 5 µm and the median simulated FLS lengths larger than 5 µm to visualize agreement between theory and experiment. (E) Predicted persistence time distribution (top row, blue solid lines) and length distributions (bottom row, blue solid lines) agree with the experimental distributions (black dots) for the different values of M and N in Fig. 3 E. Values for θ are given in min−1. Persistence time distribution n = 20,679. (F) Comparison of the experimental normalized growth velocity distributions to the simulations for different combinations of number of sum terms M and number of product factors N, using the Kolmogorov-Smirnov goodness-of-fit statistic. Darker blue indicates a better fit. The best fit N for any given M is highlighted by a red dot and follows an approximate square root dependence. Colored squares correspond to the data shown in G. (G) Force/velocity distributions (vel. distrib.) for the five combinations highlighted by colored squares in F. The dashed line is the normalized experimental growth velocity. The inset shows an enlargement of the peak of the distributions indicated by the dashed rectangle. The data used to generate the graphs is available in the Supplemental data.
	Still from Video 7. Time-lapse z-stack spinning disk confocal video of actin visualized with GFP-utrophin CH domain probe at 20–30 min. The video shows individual FLSs oscillating between growth and shrinkage phase. Scale bar represents 10 µm. Images were captured at 10-s intervals and are replayed at 6 frames per second.
	Figure 6. The FLS tip complex actin regulatory protein is semidynamic. (A) Time course recovery of AF488 actin (n = 65), GFP-Fascin (n = 40), AF488 TOCA-1(n = 51), GFP-Diaph3 (n = 34), AF488 N-WASP (n = 39), pmKate-GBD (n = 39), AF488 Ena (n = 36), and AF568 VASP (n = 51) after photobleaching in tips of FLSs at steady state grown for at least 30 min. Solid lines show the median, and the shaded area is the 95% confidence interval. (B) The half-time and percentage recovery from fitted exponential curves for each protein. Error bars represent the 95% confidence interval of the mean. (C) Actin regulatory protein localization to FLS and fluorescence recovery after photobleaching at FLS tips (green: protein of interest, magenta: AF647 actin). Protein concentrations unlabeled/labeled: Actin 210/4,000; TOCA-1 10/4; VASP 45/24; N-WASP 18/18; GBD 2.46/0; fascin 650/625; Diaph3 16/15; and Ena 60/60 in nanomolars. Scale bars = 2 µm (main images) or 1 µm (insets). (D) Time series cross-correlation of the absolute values of the FLS growth velocity and background-corrected N-WASP (n = 780), Ena (n = 2,003), and VASP (n = 2,783) intensities at FLS tip complexes, averaged over all measured FLS trajectories. The graph shows the cross-correlation coefficient at the given time shift (negative time shifts mean that intensity changes precede velocity changes). Shaded areas are 95% confidence interval of the mean.
	Figure 7. Heterogeneous levels of fascin and corresponding length distributions in vivo. (A) Time-lapse montages of maximum-intensity projections every 15 s of filopodia in leading edge cells in dorsal closure in the Drosophila embryo. Endogenous fluorescent Fascin is in cyan and membrane marker in magenta. Yellow and white arrowheads indicate filopodia with and without fascin. Scale bars = 1 µm. (B) Histogram of Fascin fluorescence intensity normalized to local background in filopodia, set to 1 (n = 3,432). (C) Histogram of Fascin fluorescence intensity normalized to local background in FLS shafts (n = 1,515). Most filopodia and FLSs only show background levels of fluorescence, with few at higher intensities. (D) Scatterplot of fascin intensity in filopodia shafts versus maximal filopodia length in leading edge cells in dorsal closure (n = 519). (E) Cumulative frequency plot (empirical cumulative distribution function, ECDF) of filopodia lengths with mutant (n = 47), wild-type (n = 48), knock-in GFP-Fascin (n = 53), and overexpressed (overexpr.) GFP-Fascin (n = 57) in dorsal closure leading edge filopodia. P values compared with control with two-sample Kolmogorov-Smirnov test: labeled Fascin, P = 0.765; mutant Fascin, P = 0.996; and Fascin overexpression, P = 0.047. (F) Q:Q plots show that control, labeled (knock-in) fascin, and mutant fascin filopodial lengths are consistent with an exponential distribution, but Fascin overexpression is not. (G) Lateral transverse myotube filopodial growth velocity distribution in stage 15 (early, n = 191) and stage 16 (late, n = 121). Crosses indicate experimentally derived data, and solid lines show maximum likelihood fits of a Laplace distribution. (H) Laplace distribution variances shown as crosses. Error bars indicate the 95% confidence intervals. The distributions for early and late stages are significantly different (***P = 0.00028, two-sample Kolmogorov-Smirnov test). Data are from four time-lapse movies each. Colors are the same as in G.
	Still from Video 8. https://www.dropbox.com/s/t6dcg0mly0ve24i/Screen%20Shot%202021-10-22%20at%202.10.37%20PM.jpg?dl=0

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