Reconstitution of contractile actomyosin rings in vesicles

One of the grand challenges of bottom-up synthetic biology is the development of minimal machineries for cell division. The mechanical transformation of large-scale compartments, such as Giant Unilamellar Vesicles (GUVs), requires the geometry-specific coordination of active elements, several orders of magnitude larger than the molecular scale. Of all cytoskeletal structures, large-scale actomyosin rings appear to be the most promising cellular elements to accomplish this task. Here, we have adopted advanced encapsulation methods to study bundled actin filaments in GUVs and compare our results with theoretical modeling. By changing few key parameters, actin polymerization can be differentiated to resemble various types of networks in living cells. Importantly, we find membrane binding to be crucial for the robust condensation into a single actin ring in spherical vesicles, as predicted by theoretical considerations. Upon force generation by ATP-driven myosin motors, these ring-like actin structures contract and locally constrict the vesicle, forming furrow-like deformations. On the other hand, cortex-like actin networks are shown to induce and stabilize deformations from spherical shapes.


Details regarding theoretical modeling
Simulations are based on the Brownian dynamics model of Adeli- Koudehi et al. 1 , as summarized below.
Filament representation Filaments are represented as series of beads separated by ! = 0.1 , representing 37 actin subunits, connected by springs. Bead motion is governed by forces from the spring and bending forces, rigid confining boundary, crosslinking and stochastic forces. The 3D positions, " of the i bead is evolved in time according to: where ( = 0.108 pN s/µm is an effective drag coefficient, which corresponds to a viscosity 350 times higher than water (lower viscosity values become computationally costly to simulate). The spring, bending and stochastic forces are as follows: where is the number of beads per filament, 2 = 5 234 − 2 7 6 234 − 2 6 E is the local unit tangent vector, = < $ is the flexural rigidity, < is Boltzmann's constant, is temperature, $ is the persistence length of the filament, k = 100 pN/µm is the spring constant between filament beads (stiff enough to prevent significant filament extension or compression) and C 9; is the second-order unit tensor ( and labeling the x, y or z directions).
Attraction force between actin filaments Crosslinking between filaments is due to a short-range, isotropic attractive potential between filament beads. If bead i is within the distance 0+% to bead j, then the force on bead i due to bead j is: where the spring constant is 0+% and the crosslink equilibrium length is ! = 0.012 µm. The parameters 0+% and 0+% characterize the effective stiffness and range of interaction between filament beads due to cross-linking. For the simulations in this study we used 0+% = 0.06 µm, a value that allows bundle formation without significant filament sliding along the bundle. (1) Boundary conditions and interactions Filaments are in a spherical confinement with a repulsive hard wall, which was represented by a constant force of magnitude 1 pN normal to the cell boundary exerted on every bead crossing it. In simulations where filaments were attracted to the boundary, a short-range attraction near the spherical hard wall was implemented by the following short-range surface force to each bead: where #%> = 3 pN/µm is the corresponding spring constant and #%> = 0.06 µm is the distance from the confinement surface where beads can feel the force. Here -,&> points to the confining sphere boundary in the direction of " .

Simulation of polymerization
We start with a fixed number of filament nuclei which elongate over time by addition of beads at one end of the filament. The elongation rate is proportional to the concentration of the remaining bulk monomers, ( ) and the barbed end polymerization rate, 3 = 10 µM/s . For a fixed filament concentration ( ) decays according to: where ! is the initial filament nuclei concentration and 0-+"& is the initial bulk actin monomer concentration. In these simulations, all filaments are the same length and we tuned ! to get the desired final filament length, taking into consideration that the higher spontaneous nucleation rate of higher actin concentrations leads to shorter filaments, as in Adeli-Koudehi et al.  Supplementary Fig. 11b, c, Supplementary Fig. 12c), we see formations that are close to what could be considered a ring, but have some imperfections such as forking small bundles that stick out of the main ring. Such structures are not as frequently observed in experiments. We anticipate that simulations with longer run-times that also allow filament breakage for filaments with high curvature at intersection points would allow a clean single ring to eventually form. We thus labeled such structures as RL. In the simulations with short filaments for c = 2 µM and final filament length L = 1.2 µm (Fig. 3, Supplementary Fig. 11a), we also labeled as RL structures with small gaps (less the 20% of the circumference) that could also be filled by

Implementation of the simulation
diffusion of bundle segments to the main ring over longer simulation times. Explicit examples are shown in Supplementary Fig. 11.

Details regarding experimental analysis
Image processing and analysis of the Z-stack confocal datasets of actin-labelled vesicles was mostly performed using the software ImageJ/Fiji 2,3 , complemented with the plugins Image Stabilizer 4 and Squassh 5 (from the MOSAIC ToolSuite update site). The organization of the actin networks in vesicles under the different experimental conditions was characterized using ImageJ/Fiji in combination with SOAX 6,7 . Specifically, the workflow to derive a skeleton model from the confocal volumes was implemented as a combination of a series of ImageJ scripts, each one performing a processing step on all the images acquired. Some parts of analysis required manual intervention, as below outlined. After making the images conform to its input specifications, the software SOAX was launched and controlled through Fiji to determine a model of the filaments in batch mode. When characterizing actin bundle morphologies, we analyzed vesicles regardless of their content with exception of clear outliers, such as deformed vesicles and vesicles that did not contain any discernable actin bundles.
Image processing for 3D analysis (Fig. 1d and for Fig. 2b) The confocal z-stacks were deconvolved using the software Huygens Essential (Scientific Volume Imaging), by means of the Classic Maximum Likelihood Estimation algorithm with a theoretical Point Spread Function. In some stacks a drift between planes of either the actin network within the vesicles or the vesicles themselves was compensated with the Image Stabilizer plugin 4 . All the vesicles in each stack were manually selected and then cropped to generate subvolumes, each containing only one vesicle. The subvolumes were filtered and the filaments segmented from them with the Squassh algorithm as implemented in Fiji 5 . The structures were detected using the following options: background removal with a window of 1 µm size; regularization parameter: 0.075; removal of background intensity with threshold determined by the Triangle method; removal of segmented regions smaller than 1 µm linear size; automatic local intensity estimation; Poisson noise model; soft mask applied to final segmentation. Finally the subvolumes were scaled along the z axis to make the voxels isotropic, as required by SOAX, and a mild 3D Gaussian Blur filter (1 pixel sigma) was applied to reduce any artefact from the scaling procedure.
Generation of 3D actin filament network models ( Fig. 1d and for Fig. 2b) A model for the filament network in each vesicle was determined using the software SOAX 7 on the subvolumes of the segmented filaments. The software implements a Stretching Open Active Contours method to compute a centerline (called 'snake' in the software) from each filament, which can be used for quantitative analysis. The batch processing procedure to extract the centerlines was launched from Fiji, after setting the parameters that controls the algorithm (see SOAX documentation for their definitions) as follows: Intensity Scaling: 0; Gaussian std: 1. Curvature Analysis (Fig. 2b) The filament models generated by batch processing were then analyzed from the SOAX GUI, using the Filament Curvature Analysis option. This tool divides the models into equally sized segments and then determines a curvature value for each of the segments. The curvature values (in µm -1 ) from each vesicle were then normalized with respect to the curvature of the respective vesicle membranes, and the values from all the vesicles under the same experimental condition were finally aggregated to generate the bundle curvature distribution. Curvature values less than 1 corresponds to regions where the filaments are flatter than the membrane, and vice versa.
Membrane Proximity Analysis (Fig. 3c, d) The quantification of the distribution of the actin networks inside the vesicles was performed on the radial intensity profile. The center and the radius of the vesicle was determined semi automatically, starting from two opposite points on the membrane marked manually in Fiji on a maximum intensity projection of the volume (script provided at https://doi.org/10.5281/zenodo.4555840). The radial profile was used to compute the membrane proximity metric, defined as the weighted average of the radii, with the weights given by the intensity at each radius, and the average normalized by the vesicle radius. Values close to one indicate that most of the intensity is found close to the membrane, while a uniform distribution of the intensity within the vesicle gives a membrane proximity value of 0. Smaller values indicate that the intensity is condensed at the vesicle center. Supplementary Fig. 1: GUV with labelled membrane containing actin bundles bundled by αactinin. Vesicle is made from POPC with 0.015% DOPE-ATTO655. Images in this paper are taken as z-stacks of confocal slices. a Center z-slice of a data set with 62 confocal slices. b Projection of all confocal slices. c Side-view of a 3D reconstruction of the vesicles.  Fig. 3a. With increasing amounts of fascin, actin bundles get thicker, while the amount of unbundled actin filaments in the vesicle decreases. By plotting the ratio of the fluorescence intensity of the bundles to the intensity of the lumen, we visualize this shift of actin from the bulk phase into bundles. For each condition we analyzed two vesicles. We did 4 measurements per vesicles by plotting the spatial intensity along 4 straight lines (0°,45°, 90°, 135°) and calculated the ratio between highest and lowest intensity within the vesicles. Hollow squares: averages for vesicles. Solid squares: averages for conditions.