SOAX: a software for quantification of 3D biopolymer networks.

Ridge threshold τ We initialize SOACs on the centerlines of filaments by locating intensity ridge points 23 ( Supplementary Note 1 ). We define a ridge point in axis k to be the image location x where intensity is a local maximum along axis k . A ridge point is detected by searching for a sign change in the k th component of gradient ∂ k I ( x ) where I ( x ) is image intensity. The magnitude of the sign change must be larger than ridge threshold τ. To allow initialization along filaments of different width, there is no restriction on the distance between the positions of the positive and negative intensity gradients ( Supplementary Eq. 6 ). We assume image intensity in the range 0 and 1 (intensity rescaling can be performed within SOAX). Units of τ and other parameters are in rescaled intensity units and pixels. Stretch factor k str The external force exerted on a SOAC is a weighted combination of image force and stretching force, F ext = k img F img + k str F str . We use units in which k img = 1 and vary k str only. The image force is proportional to the magnitude of local image intensity gradient. The stretching force is applied to SOAC tips and is proportional to the local image contrast, 1 − I b / I f , where I f is intensity at SOAC tip and background I b is intensity calculated by sampling uniformly within concentric circles or ellipses from a plane perpendicular to the SOAC tangent vector. The reason we sample the background to the sides of the SOAC is to allow them to extend and form junctions with bright filaments that lie ahead of them 23 . SOAC evolution SOACs evolve according to internal forces representing bending and stretching stiffness and external forces described above (see Supplementary Note 1 ). F-function The F-function evaluates a result based on the SNR of the local neighborhood of a SOAC. The portion of resultant SOACs that lie in regions with local SNR below t are considered uncertain thus penalized from the total length of SOACs in proportion to parameter c ( Supplementary Note 2 and Eq. 8 ). Unlike the Hausdorff distance and vertex error, the F-function does not require ground truth to evaluate the optimal τ and k str, therefore it can also be used for selecting optimal parameters in experimental images that do not have ground truth. However, the soundness of optimal parameters suggested by the F-function depends on the values of t and c . Using synthetic images of varying SNR we find that valid t and c can be found within a fixed small range ( Supplementary Note 2 ). Thus, we vary t and c in a small range to generate a set of “optimal candidates” for the user to choose from. This procedure for guided fine-tuning is necessary, especially for low SNR images where a narrower range of t and c is allowed and these values are sensitive to the precise definition of the local SNR. The small range on the values of t and c we choose are found by synthetic experiments. We construct synthetic images with different SNRs due to either shot noise or Gaussian noise (for the latter see Supplementary Note 2 ). For the shot noise case ( Fig. 2 ) we first assign the background intensity 30 and the foreground intensity 90 to the centerline pixels specified by a set of ground truth SOACs and then convolve it with an anisotropic Gaussian 3D kernel with σ = (1.73, 1.73, 5.0) pixels, which simulates the point spread function. Finally, we scale the image intensity by 0.4 and use the resulting pixel intensity I p to apply a Poisson distributed random variable to each voxel, with average I p . SOAC point density and intensity calculation For the emulsion droplet in Figure 3 we used the following procedure based on the extracted SOAC points. Given that the droplet is a sphere of R pixels centered at p 0 , to calculate the SOAC point density, we counted the number of SOAC points p with with r < || p − p 0 || ≤ r + 1, for all 0 ≤ r ≤ R − 1 (here r is in pixels); this number was then divided by the surface area 4 πr 2 . For the SOAC point intensity we measured the average intensity at the same points p . The image intensity versus r is computed in a similar way by averaging the intensity of voxels with distance to the center in the interval ( r , r + 1]. Filament orientation in 3D Filament orientation in Figures 4 and 5e was quantified by azimuthal angle φ and polar angle θ using a spherical coordinate system. We compute these angles for each SOAC segment denoted by a vector a = [ x, y, z ], which is the line segment between consecutive SOAC points. Since we cannot distinguish the polarity of the filament, we consider the orientation of + a and − a to be the same; thus we define the range of φ and θ to be (−90°, 90°] and [0, 180°), respectively, both with a period of π. To calculate the angles we use φ = atan( y / x ) and θ = acos(z/|| a ||) for positive x . When x < 0, we first invert a before applying these equations. When a is aligned along the z -axis ( x = y = 0) then φ = θ = 0. When a is on the y - z plane but not along z -axis ( x = 0, y ≠ 0), then we invert a when y < 0 and use φ = 90°, θ = acos(z/||a||). In Supplementary Figure 1 we also computed the distribution of the single radial angle γ (0° ≤ γ ≤ 90°), which is the angle between a and the outward radial direction from a pre-defined center. Filament curvature The curvature κ in Figure 5f is defined as the magnitude of the rate of change of unit tangent vector t ( s ) with respect to arc length s , κ = ||d t /ds||. We estimate unit tangent vectors using SOAC points Δ c = 8 pixels apart in arc length, a distance which is large enough to represent the curvature of the filament in the image and is independent of the intrinsic stiffness of the SOAC 33 . Specifically, κ ( s ) = || t ( s + Δ c /2) − t ( s − Δ c /2)||/Δ c , where . To avoid measuring curvature at junction points, we cut the SOACs at all junctions before calculating the curvature distribution.

Actin bundles in emulsion droplets and confocal microscopy

Actin was polymerized in the presence of 1.2 μM fascin and 0.95 μM streptavidin in an actin polymerization buffer (25 mM imidazole-HCl (pH 7.4), 50 mM KCl, 2 mM MgCl 2 , 1 mM DTT, 0.1 mM MgATP, 1.33 mg/mL creatine phosphate, 2.48 mg/mL creatine phosphokinase, 0.1 mg/mL glucose oxidase, 0.1 mg/mL catalase and 280 mM sucrose). The actin concentration was 14 μM, including 34 mole% of AlexaFluor 488-actin and 0.42 mole% of biotinylated actin. An oil-lipid mixture was prepared by dissolving a lipid mixture of DOPC, 40 mole% DOPS and 1 mole% biotinylated lipid (Biotin-x-DHPE) in mineral oil containing 2% (w/w) Span 80 at a total lipid concentration of 0.5 mg/mL. Water-in-oil droplets were prepared using a flow-focusing microfluidic device, obtaining a narrow size distribution, as described elsewhere 39 40 . Droplets were observed at room temperature by an inverted microscope (DMIRB, Leica) equipped with a confocal spinning disc scan head (Yokogawa), a EM-CCD camera (C9100, Hamamatsu Photonics) and a 100x oil immersion objective. The intensity analysis in Figure 3k shows uneven actin encapsulation among droplets.

Hela cells and confocal microscopy

We used HeLa cells stably expressing GFP-tubulin 41 . The culture medium was prepared with MEM medium; Glutamine (200 mM, 6 ml/500 ml media); sodium pyruvate (100 mM, 1 ml/100 ml media); fetal bovine serum (10%); penicillin-streptomycin antibiotic (100X, 1 ml/100 ml media). Cells were cultured in a flask in a NuAire CO 2 incubator (5% CO 2 at 37°C). We used an Olympus FV1000 confocal microscope with an Olympus UPLAN 100X oil immerse objective (NA = 1.3). Image resolution in x-y plane was 62 nm/pixel and z-step size 100 nm.

Fission yeast methods and confocal microscopy

The strain FC1218 ( h − 41nmt1-GFP-CHD (rng2)-leu1 + ade6-M216 leu1-32 ura4-D18 42 ) was cultured at 25°C in the rich media YE5S for 24 h and then washed into the minimal medium without thiamine EMM5S for 24 h at log phase to induce the expression of GFP-CHD. To reduce the interference from actin patches, cells were treated with 100 μM Arp2/3 complex inhibitor CK-666 from a 10-mM stock in DMSO at 25°C for 10 min before imaging. Images were collected using an UltraVIEW ERS spinning-disk confocal microscope (Perkin Elmer, Waltham, MA) with a 100x/1.4 NA Plan-Apo objective lens (Nikon, Melville, NY) as described before 43 . An ORCA-AG CCD camera (Hamamatsu, Bridgewater, NJ) was used without binning. Z stacks spanning 5 μm with a 0.2 μm spacing were collected.

Fission yeast methods and confocal microscopy

The strain FC1218 ( h − 41nmt1-GFP-CHD (rng2)-leu1 + ade6-M216 leu1-32 ura4-D18 42 ) was cultured at 25°C in the rich media YE5S for 24 h and then washed into the minimal medium without thiamine EMM5S for 24 h at log phase to induce the expression of GFP-CHD. To reduce the interference from actin patches, cells were treated with 100 μM Arp2/3 complex inhibitor CK-666 from a 10-mM stock in DMSO at 25°C for 10 min before imaging. Images were collected using an UltraVIEW ERS spinning-disk confocal microscope (Perkin Elmer, Waltham, MA) with a 100x/1.4 NA Plan-Apo objective lens (Nikon, Melville, NY) as described before 43 . An ORCA-AG CCD camera (Hamamatsu, Bridgewater, NJ) was used without binning. Z stacks spanning 5 μm with a 0.2 μm spacing were collected.

Supplementary Material Supplementary Information Supplementary Information Supplementary Information Movie 1 Supplementary Information Movie 2