www.sciencemag.org/cgi/content/full/1151086/DC1

Supporting Online Material for

Assembly Mechanism of the Contractile Ring for Cytokinesis by Fission Yeast

Dimitrios Vavylonis, Jian-Qiu Wu, Steven Hao,

Ben O’Shaughnessy, Thomas D. Pollard*

*To whom correspondence should be addressed. E-mail: thomas.pollard@yale.edu

Published 13 December 2007 on Science Express

DOI: 10.1126/science.1151086

This PDF file includes:

Materials and Methods Figs. S1 to S18 Table S1 References

Other Supporting Online Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/1151086/DC1)

Movies S1 to S19

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Assembly Mechanism of the Contractile Ring for Cytokinesis by Fission Yeast

Dimitrios Vavylonis, Jian-Qiu Wu, Steven Hao, Ben O’Shaughnessy, Thomas D. Pollard

Supporting Online Material Contents Materials and Methods Table S1 Figs. S1 to S18 Supplementary References and Notes Movies and Animations Materials and Methods Strains construction and functionalities Table S1 lists the S. pombe strains used in this study. We constructed strains rlc1-mEGFP (JW948), rlc1-mRFP1 (JW1086), sad1-mRFP1 (JW1099), rlc1-3GFP (JW1258), and rlc1-tdTomato (JW1341) in wild-type strains JW81 or JW729 by a PCR-based gene targeting method (S1) using pFA6a-mEGFP-kanMX6 (S2), pFA6a-mRFP1-kanMX6 (S3, S4), pFA6a-3GFP-kanMX6 (S5, S6), and pFA6a-tdTomato-natMX6 (S7) as templates. The strains expressed fusion proteins under the control of their native promoters and from their normal chromosomal loci. Tagged strains were functional by several criteria. First, all strains resembled wild-type cells in morphology and formed normal colonies during growth on plates at temperatures from 18 to 36°C. Second, their growth rates in liquid YE5S culture at 25°C were the same (doubling time ~4 h) as the wild-type strain JW729. Third, although the double mutant rlc1Δ clp1Δ is synthetically lethal (S8), strains rlc1-mEGFP clp1Δ (JW1274) and rlc1-3GFP clp1Δ (JW1275) were viable and resembled clp1Δ at temperatures from 25 to 36°C. Other strains were constructed using standard genetic methods (S9). All cells for microscopy were grown in YE5S liquid medium at 25°C (S6). Cells in cdc25-22 background were then arrested at 35.5ºC for 4 h then released to 23ºC before imaging. Cells expressing GFP-CHD were grown in YE5S medium for ~24 h and then switched to EMM5S medium to induce the expression of GFP-CHD. Microscopy We observed cells in growth chambers (S2) at 23°C except where noted with an inverted microscope (IX-71; Olympus) equipped with a 100X/1.4 NA objective (Plan-Apo) and a spinning-disc confocal system (UltraView RS; Perkin Elmer) with excitation by 488-nm and 568-nm argon ion lasers. We acquired all images using cooled CCD camera (ORCA-

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ER, Hamamatsu). The fluorescence intensity of rlc1-3GFP (JW1258) cells was 1.5-3 times higher than rlc1-mEGFP (JW948). Data Analysis Photobleaching correction and image averaging. Before analysis, we corrected some images for photobleaching by fitting the average intensity of a region of order the size of one cell, I, to an exponential, I(n) = A + B e-λn, where n is the frame number. The intensity of a pixel in the transformed image was b = (b0-A) eλn, where b0

is the original

intensity of the pixel. To increase the signal to noise, we smoothed certain images by averaging the intensity values over a box of 3 x 3 pixels in the x and y directions. In certain cases we also averaged over 2 to 6 consecutive images (depending on the exposure times and experiments) so that each frame shown is the average of successive frames of the original movie (for example, if 6 frames were averaged, frame 1 is the average of original frames 1-6, frame 2 the average of 2-7, etc). Measurement of the width of broad bands. Since the average intensity distribution along the long axis of the cell is approximately Gaussian, we define the half-width of the broad band to be the standard deviation of the corresponding Gaussian. Therefore our width includes two thirds of the nodes. Measurement of node turnover. In the experiments of Fig. 2A and 2B we observed the majority of newly formed stationary nodes continuously for more than 100 s. We thus estimate the rate of node disappearance during the stationary stage to be <0.002 s-1

. Once a broad band of nodes forms, new nodes appear at a low rate (<15% of existing nodes over ~ 100 s). Analysis of node intensity distributions (Fig. S1C). The ~63 nodes in a broad band of a single cell are too few to get a clear distribution of intensities. Differences in the microscope’s point spread function at different locations in the cell and photobleaching complicate the comparison of node intensities at the top and bottom of cells. Comparing different cells is also involved, since the precise intensity value of each node varies between the position of the cell on the slide, the stage of node assembly, and the extent of photobleaching. In Fig. S1C we compared intensities of nodes at the top of cells with uncondensed broad bands by normalizing intensity values, I, with the width of intensity distribution per cell, σ, after background subtraction. We imaged the top region of cells with 14 z-sections separated by 0.1 μm and subtracted the cytoplasmic background separately for each section. We screened for cells with uncondensed broad bands by selecting cells with 13 or more nodes whose intensity maxima were located within the imaged region and rejected nodes whose maxima were located within the 2 top/bottom z-sections. We averaged intensity values over a box of 3 x 3 pixels in the x and y directions and 3 sections along the z-axis. We located the centers of boxes that were local maxima of the averaged intensity and assigned I to be the corresponding averaged intensity value after a visual check to eliminate maxima that do not correspond to nodes. This procedure for measuring I helped increase the signal to noise ratio. Analysis of mean square displacement (MSD). We measured node MSDs in Fig. 2E using three approaches: (1) tracking the position of the pixel in each node that had the

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maximum intensity; (2) using the commercial program Imaris (Bitplane Inc., Saint Paul, MN) to track the centers of nodes; and (3) using the freely available SpotTracker2D plug-in (S10) for ImageJ software (National Institutes of Health; http://rsb.info.nih.gov/ij/). All 3 methods gave similar results for the slope vs. time (and thus D values). We selected 1-5 nodes per cell that did not exhibit any observable directed motion and whose intensity field did not overlap with neighbors. We could track each node reliably for 100 or more frames (100 s). We calculated the MSD for a given interval t by averaging all time intervals within a given trajectory that were separated by t. Thus the MSD is more accurate for smaller t values, while the values of the MSD for t > 50 s are correlated and were not included in the calculation of the D values from the slope. Note that MSD(0) is determined by extrapolation, since the data point with the shortest time interval is MSD(Δt), where Δt is the time interval between frames. The value of MSD(0) represents the mean square error upon re-sampling in the absence of any motion. Analysis of node motions (Fig. 2F and 2G of main text). We measured the distribution of node speeds, duration of motion, and angles in Fig. 2F and 2G using ImageJ by visually identifying the positions of nodes and the times that these nodes started and stopped moving in cells with condensing broad bands of nodes. Dynamics of linear actin elements. The high density of dynamic actin filaments and bundles in the forming contractile ring and the great difficulty of imaging single actin filaments in live cells prevented us from systematically measuring the turnover of the vast majority of the filaments. We measured the lifetimes of a few favorable filaments growing on the lateral margins of the ring to be ≥ 16.4 s (n=9). We estimate filament lifetimes are <20 s from their growth rate of about 0.2 µm/s and the fact that the zone of filaments on the margins of contractile rings is about ~4 μm wide (Fig. 3, A and B). Description of Model and Numerical Simulation Methods We used a Monte Carlo method to simulate the condensation of a broad band of nodes. Simulations were performed in 2 dimensions that represent the cylindrical surface of the cell. One axis is oriented along the long axis of the cell while the other represents arc length. Periodic boundary conditions with period 2πR [where R = 1.73 μm is cell radius (S11)] were imposed along the direction normal to the long axis. We did not impose any constraint on the length of the long axis of the cell, since actin filaments rarely elongated over distances comparable to the distance between the center of the cell and cell tips. We limit our description to 2 dimensions since (i) experimentally, the vast majority of actin filaments marked by GFP-CHD and nodes marked by Rlc1p localize near the plasma membrane through unknown mechanisms (Movie S9), (ii) actin filaments growing towards the center of the cell will fail to connect with nodes bound to the plasma membrane so such filaments can be effectively neglected, and (iii) the cell nucleus positioned within the broad band region prevents excursions of actin filaments towards the cell interior.

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Time step. We used time steps dt = 0.05 s or 0.1 s. We checked that our results are independent of the value of dt when 0.01 s < dt < 0.2 s. For example, for the parameter values in Fig. 1J, the average time required for the broad band to condense to 1/2 its initial width was 390 ± 136 s using dt = 0.01 s and 382 ± 128 s using dt = 0.2 s, where the averages and standard deviations were calculated over 50 realizations. Initial conditions. We generated the initial node distributions by placing the nodes along the long axis of the cell at positions whose coordinate was picked from a Gaussian distribution centered at zero and standard deviation (or “half-width”) σ = 0.8 μm as in experiment (fig. S1A), unless otherwise indicated. The initial coordinates of nodes along the arc length were generated from a uniform distribution, since all of our experimental observations were consistent with cylindrical symmetry. Filament elongation (“search”). Since nodes contain on average 2 formin dimers (S11), we assumed that 2 pointed ends grow out of each node with speed vpol, unless otherwise indicated. The initial direction of growth was random but subsequently remained fixed throughout the growing phase of the filament. Fixed filament orientation is consistent with the expected reduced orientational diffusion coefficient of long tethered filaments and experimental observations of linear filament growth (Fig. 3C). In the simulation the growing filaments were represented as elongating lines whose lengths grew by vpol dt every time interval dt. Capture. When a pointed end grew within the capture radius rc of a neighboring node we associated the pointed end with the neighbor (“capture”), up to the time of connection breakage (i.e. we assume that when a pointed end is in contact with a node, the probability of association is unity). We neglected connections from nodes that contact the sides of actin filaments. This simplifying approximation is valid during the early stages of node condensation, when nodes are widely spaced and the probability of an encounter between a node and the sides of a filament in the simulations is small. We did not place a limit on the number of connections that a node can make with incoming actin filaments. Traction. We assume each connection generates an attractive force F due to myosin pulling along the connecting actin filament. In each time step we calculate the total force exerted on each node, Ftot and move the node by a distance Ftot/ζ dt along the direction of Ftot. The positions of barbed ends and connected pointed ends associated with moving nodes are updated accordingly. We assume F is independent of v, which is consistent with myosin motors operating near stall, as explained in the main text. We do not account for rotational rigidity of connections since, for realistic parameter values, nodes move over short distances during a connection episode and thus the change in filament angles during node motions is small. We choose the magnitude of the speed of single filament connections, |F|/ζ, to be 20 nm/s such that the distribution of node speeds 100 s after the onset of condensation has an average of ~30 nm/s as in experiment (see Fig. 2F and fig. S6A). Turnover. We assume that connected and unconnected filaments are broken with probability dt/τbreak, and dt/τturn, in each time step, respectively, to simulate actin turnover as observed experimentally. New filaments were immediately initiated, growing along a random direction.

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Effect of tension on elongation rates. Connected filaments are assumed to be under tension due to myosin pulling towards the barbed end of the initiating node. The effect of tension on formin-mediated polymerization rates has not been experimentally measured. In the main text and all the figures, we make the simple, physically motivated assumption that tension switches off polymerization. This assumption is suggested by the architecture of formins and our understanding of the mechanism of processive actin filament elongation by Cdc12p and other formins (S12). Formin Cdc12p elongates actin filaments exclusively by transferring profilin-actin from binding sites on unstructured FH1 domains to the barbed end of the filament associated with the FH2 domains. Thus myosin-induced extensional tension may stretch FH1 domains away from the barbed end and slow down transfer of profilin-actin from the FH1 domain to the barbed end. We tested the importance of the assumption that tension switches off polymerization by performing simulations of a model in which tension has no effect on elongation. In this model growing actin filaments were allowed to polymerize past connected nodes and establish connections involving more than two nodes. We assumed that the myosin in each captured node generates an attractive force F towards the node of the nucleating formin dimer. Each such force was balanced by a force exerted on the nucleating node in the opposite direction. When a filament broke, all associated connections were broken. We neglected the small effect of node movement on the direction of the forces by assuming that forces between the nucleating node and each captured node remain along a straight line connecting each pair (i.e. we did not include forces due to actin filament bending). We found that using the same parameters as Fig. 1J, the average time required for the broad band to condense to 1/2 its initial width was reduced from 390 ± 136 s in Fig. 1J to 193 ± 80 s (averages and standard deviations were calculated over 50 realizations). More significantly, in this modified model, clumping was pronounced: the largest circumferential gap between nodes 500 s after the onset of condensation (see Fig. 4B) increased to 2.6 ± 2.6 μm from 1.3 ± 0.6 μm. Increased clumping is due to the fact that nodes nucleating filaments towards clumps are attracted to them by a strong force due to connections with multiple nodes within the clumps. This increases the instability towards aggregate formation. We conclude that tension switching off polymerization may be important in suppressing instabilities. Short range repulsion. Since nodes are large (> 22,000 kDa) multi-protein membrane-associated complexes, we assume that there is a short-range excluded volume repulsion. The repulsive force is zero for internode separations exceeding minr and has a constant value repf for separations less than minr , with the force acting radially. We used minr = 150 nm and repf = 10 pN, except for fig. S12 where the effect of changing repf was explored. For most of the simulations the force is so large that nodes interact approximately as hard spheres (fig. S12). Dependence of results on distribution of node friction coefficients. The spread in observed node diffusion coefficients seen in fig. S2A may reflect intrinsic variability in node friction coefficients ζ. We checked that variability in the values of ζ does not influence the main results. We found that if, instead of a single ζ value, we assign values for ζ to nodes from a uniform distribution whose minimum is <ζ>/2 and maximum

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3<ζ>/2 (where <ζ> is the average value), then the average time required for the broad band to condense to 1/2 its initial width only changed from 390 ± 136 s to 392 ± 126 s. Model with permanent node connections (Fig. 1I). In the simple model of Fig. 1I we placed nodes in a broad band as described above in the paragraph “initial conditions”. Since a node contains on average 2 formin dimers that may nucleate two filaments (S6), permanent node connections were established by scanning through all the nodes and establishing connections between each node and its first and second nearest neighbors. Thus each node initiates at least two filament connections but can receive more than two connections from its neighbors. Node positions were then evolved as described in paragraph “traction” above. We selected a value |F|/ζ = 1.6 nm/s such that the broad band condenses within ~ 500 sec. Simulated images. Simulated 2D images were generated by broadening nodes and actin filaments to optical resolution by convoluting their coordinates with a 2D Gaussian distribution with standard deviation σ = 0.1 μm.

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Table S1. S. pombe strains used in this study. Strain Genotype Source/Reference

DMY821 h+ clp1Δ::ura4+ ade6-M216 leu1-32 ura4-D18 (S13) DMY822 h- clp1Δ::ura4+ ade6-M216 leu1-32 ura4-D18 Dan McCollum FC1218 h- nmt41-GFP-CHD (rng2)-leu1+ ade6-M216 ura4-

D18 leu1-32 (S14)

JW81 h- ade6-M210 leu1-32 ura4-D18 (S2) JW729 h+ ade6-M210 leu1-32 ura4-D18 (S2) JW948 h- rlc1-mEGFP-kanMX6 ade6-M210 leu1-32 ura4-D18 This study JW1086 h- rlc1-mRFP1-kanMX6 ade6-M210 leu1-32 ura4-D18 This study JW1099 h+ sad1-mRFP1-kanMX6 ade6-M210 leu1-32 ura4-

D18 This study

JW1258 h+ rlc1-3GFP-kanMX6 ade6-M210 leu1-32 ura4-D18 This study JW1274 rlc1-mEGFP-kanMX6 clp1Δ::ura4+ ade6 leu1-32

ura4-D18 This study

JW1275 rlc1-3GFP-kanMX6 clp1Δ::ura4+ ade6 leu1-32 ura4-D18

This study

JW1311 h- cdc25-22 nmt41-GFP-CHD (rng2)-leu1+ ade6 leu1-32 ura4-D18

This study

JW1312 h- for3Δ::kanMX6 nmt41-GFP-CHD (rng2)-leu1+ ade6 leu1-32 ura4-D18

This study

JW1329 cdc25-22 nmt41-GFP-CHD (rng2)-leu1+ sad1-mRFP1-kanMX6 ade6 leu1-32 ura4-D18

This study

JW1332-1 h+ nmt41-GFP-CHD (rng2)-leu1+ rlc1-mRFP1-kanMX6 ade6-M210 leu1-32 ura4-D18

This study

JW1336-1 cdc25-22 nmt41-GFP-CHD (rng2)-leu1+ rlc1-mRFP1-kanMX6 ade6-M210 leu1-32 ura4-D18

This study

JW1341 h- rlc1-tdTomato-natMX6 ade6-M210 leu1-32 ura4-D18

This study

JW1349 h+ nmt41-GFP-CHD (rng2)-leu1+ rlc1-tdTomato-natMX6 ade6-M210 leu1-32 ura4-D18

This study

JW1351 nmt41-GFP-CHD (rng2)-leu1+ rlc1-tdTomato-natMX6 ade6-M210 leu1-32 ura4-D18 cdc25-22

This study

JW1353 nmt41-GFP-CHD (rng2)-leu1+ rlc1-tdTomato-natMX6 ade6 leu1-32 ura4-D18 for3Δ::kanMX6

This study

JW1375 cdc25-22 rlc1-3GFP ade6-M210 leu1-32 ura4-D18 This study

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Fig. S1. Quantitative analysis of Rlc1p-3GFP nodes. (A) Average intensity of Rlc1p-3GFP fluorescence along the long axes of four cells with fully formed but uncondensed broad bands. (B) Time course of Rlc1p-3GFP fluorescence intensities during node formation as in Fig. 2A, after background subtraction and correction for photobleaching in a box of size of order of the diffraction limit. Black curve: box center located at a node present at t = 0. Colored curves: boxes located at sites where a node appeared. Mean time of formation = 65 ± 50 s (n = 11). (C) Distribution of node intensities in 23 cells with fully formed but uncondensed broad bands. Intensity values are normalized with the standard deviation of node intensities per cell, σ. Black and white columns show the intensity distribution of nodes in two individual cells. The variation was reproducible by immediate re-sampling and is thus not due to noise. The smaller, high intensity peak probably represents pairs of unresolved nodes.

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Fig. S2. Distributions of node diffusive coefficients of newly formed Rlc1p-3GFP nodes and evidence for independence of diffusive node motions. (A) Distribution of node diffusion coefficients from the slope of absolute MSDs as in Fig. 2E. (B and C) Histograms showing that the diffusive node motions during the stationary node stage (Fig. 2E) are uncorrelated by comparing the absolute MSDs to the mean square displacement of the distance between the centroids of pairs of nodes. (B) Distribution of ratio between the sum of absolute diffusivities of pairs of nodes in the same cell and their relative diffusivity, Drel. The ratio peaks at unity, consistent with uncorrelated node diffusion. (C) Distribution of the ratio of the sum of the t = 0 value of the absolute MSDs of pairs of nodes in the same cell and the t = 0 value of their relative MSD. The ratio peaks at unity, consistent with uncorrelated node diffusion. (D) Same as panel A, but for cells treated with Lat A to depolymerize actin filaments. The cells were imaged on bare slides (no gelatin pad) to allow delivery of Latrunculin A (Lat A). The diffusion coefficients are similar, though somewhat smaller than those of untreated cells. (E) Same as panel B, for cells treated with Lat A. The relative node motions are somewhat correlated (ratio > 1), most likely due to whole cell motion due to the absence of the stabilizing gelatin pad. (F) Same as panel C, for cells treated with Lat A. The ratio peaks at unity. (G) Control experiment: same as panel D but with addition of DMSO instead of Lat A and no gelatin pad. The diffusion coefficients are similar to those of Lat A cells. (H) Same as panel E, for cells treated with DMSO. (I) Same as panel F, for cells treated with DMSO. The ratio peaks at unity.

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Fig. S5. Examples of actin-filament dynamics in cells expressing GFP-CHD. Time in seconds. (A) Frames at 8s intervals of a GFP-CHD cell (strain FC1218) at late stages of broad band condensation. Images are maximum intensity projections of 2 z-sections spaced at 0.3 μm tangential to the cell membrane. The transient bright spots are actin patches. (B-D) Frames at 0.8 s intervals from the cell of panel (A) showing linear elements growing at speeds ~0.2 μm/s (arrows point to initial and final points). (E) Image of cell expressing GFP-CHD (green) and Rlc1p-rdTomato (red) (strain JW1349). Single confocal section tangential to cell membrane. (F-I) Frames at 0.3 s intervals from the cell of panel (E) showing linear elements marked with GFP-CHD associating with Rlc1p nodes at a single focal plane (Movie S10). The Rlc1p signal (red) is the same in all images and is the average of the Rlc1p signal in the first 6 sec (the Rlc1p signal per frame is otherwise very weak). The GFP-CHD signal (green) is a moving average over 3 successive frames. Time increases from left to right, top to bottom. (F) Linear structure marked with GFP-CHD associated with a node (arrow) breaks and subsequently a new actin containing structure appears to grow from the node. (G) A linear structure marked with GFP-CHD appears to grow from a node and then disappears. The transient bright spot is an actin patch. (H) A linear structure marked with GFP-CHD whose end is associated with a node (arrow) breaks. (I) A linear structure marked with GFP-CHD growing out of the top right node appears to establish a connection with a neighboring node and then disappears. (J) Distribution of the orientation of linear elements marked by GFP-CHD whose ends are associated with Rlc1p nodes in cells with uncondensed broad bands. Clear examples are rare, so we combined data from experiments with strains JW1329, JW1332-1, JW1336-1, JW1349 and JW1351. Angle was measured with respect to the long axis of the cell. Bars, 0.5 μm.

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Fig. S6. Simulations of the distribution of node speeds and directions and comparison to experiment. (A) Histograms showing the distribution of node speeds 100 s after the onset of condensation (parameters same as Fig. 1J) as a function of the value of the node speed of a singly connected node, F/ζ, where F is the magnitude of the attractive force per connection. Each histogram includes results from 10 cells. The value F/ζ = 20 nm/s produces a distribution which is close to experiment (Fig. 2F). (B) Histograms showing the distribution of angles of node movement with respect to the long axis of the cell 100 s after the onset of condensation (10 cells). The distribution is broad, similarly to experiment (Fig. 2G inset). (C) Test of correlation between node speed and direction of motion with respect to the long axis of the cell. Black symbols: simulation results testing the correlation 100 s after the onset of condensation. Red symbols: experimental measurements from Fig. 2F and 2G. Simulation results show little correlation, in agreement with experiment.

A B C

D E F

G H I

Fig. S7. Model results: condensation kinetics as a function of the velocity of actin polymerization, vpol. Each column shows simulated images of condensing broad bands as a function of time (seconds) for a given value of vpol. The x-axis in each simulated image is arc length around the cylindrical body of a cell of radius R. Nodes in red and actin filaments in green are broadened to optical resolution for comparison with microscopic images. Graphs in this and following figures quantify the results of the simulations in terms of 4 parameters: (i) Time (τconv) for the band of nodes to condense to 50% of its initial width vs. modified parameter. (ii) Half-width 500 s after the onset of condensation vs. modified parameter. (iii) Largest circumferential gap between nodes 500 s after the onset of condensation vs. modified parameter. (iv) Fraction of arc length which is node-free (circumferential “porosity”) vs. modified parameter value, assuming a node radius of 100 nm. Each point is an average of 50 simulations ± SD. These simulations show that a value vpol > 0.1 μm/s is required for reliable ring formation. Small vpol values lead to formation of disconnected aggregates. In this and following figures the reference parameter values are as follows: 63 nodes, 2 active formin dimers per node, vpol = 0.2 μm/s, F/ζ = 20 nm/s, turnτ =

breakτ = 20 s, and rc = 100 nm. The half-width of the broad band is w = 0.8 μm and the short-range repulsive force has a magnitude of 10 pN when nodes are closer than 150 nm.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4vpol (μm/s)

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Fig. S8. Model results: condensation kinetics as a function of the value of the half-width of the broad band, w. Values smaller than 1.4 μm lead to a more or less continuous ring. If w > 1.4 μm condensation is slower than experiment and disconnected aggregates form. See Fig. S7 for other parameter values.

A B C

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Fig. S9. Model results: condensation kinetics as a function of the number of nodes. Broad bands with fewer than 60 nodes condense into discontinuous aggregates. Broad bands with >80 nodes condense into more uniform rings. See Fig. S7 for other parameter values.

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Fig. S10. Model results: condensation kinetics as a function of the lifetime of disconnected actin filaments, turnτ . Condensation into structures similar to contractile rings requires turnτ >10 s. Lifetimes 5 s < turnτ < 10 s promote connections between nearest neighbors and lead to formation of clumps of nodes. Lifetimes < 5 s lead to very slow condensation kinetics. See Fig. S7 for other parameter values.

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Fig. S11. Model results: condensation kinetics as a function of the lifetime of connected actin filaments, breakτ . For values of breakτ >45 s the broad band condenses into disconnected aggregates of nodes. Lifetimes < 10 s do not lead to excessive clump formation but slow condensation. See Fig. S7 for other parameter values.

A B C

D E F

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Fig. S12. Model results: condensation kinetics as a function of the magnitude of the short-range repulsive force. The results are insensitive to the precise value of the repulsive force, provided it exceeds a value of order 5 pN. Smaller repulsive forces cannot counteract the forces due to node connections. This leads to the formation of clumps consisting of nodes that constantly connect to one another and thus do not extend actin filaments beyond the clump. See Fig. S7 for other parameter values.

A B C

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Fig. S13. Model results: condensation kinetics as a function of the number of active formin dimers per node. When the number of formin dimers exceeds 4, condensation is much faster than experiment due to the large number of connections. In this case, the magnitude of forces due to node connections exceeds the magnitude of the short-range repulsive forces, leading to clump formation at long times. Actin filaments do not escape out of the clumps due to the high density of nodesSee Fig. S7 for other parameter values.

A B C

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fraction of nodes with 2 formin dimers

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Fig. S14. Model results: condensation kinetics as a function of the fraction of nodes containing 2 formin dimers, f. Each node is assumed to nucleate either 2 or 0 actin filaments. A value f > 0.5 is required for fast condensation as in experiment. See Fig. S7 for other parameter values.

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capture radius (μm)

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Fig. S15. Model results: condensation kinetics as a function of the capture radius of node-actin filament association. Radii in the range 50 nm < rc < 150 nm produce similar results. For rc < 50 nm condensation is slower that experiment. When rc approaches 200 nm, actin filaments cannot escape away from their nearest neighbors and condensation is halted. See Fig. S7 for other parameter values.

A B C

D E F

G H I

Fig. S16. Model results: condensation kinetics as a function of the value of F/ζ. For F/ζ < 5 nm/s condensation is slower than experiment while values larger than 30 nm/s lead to disconnected aggregates with high probability. See Fig. S7 for other parameter values.

0 10 20 30 40 50 60 70 80 90 100F/ζ (nm/s)

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Fig. S17. Simulation of the condensation of the broad band of a cdc25-22 cell released from arrest (same parameters as Fig. 4E). Top: Simulated images as a function of time. Bottom: graphs quantifying the success of condensation as a function of broad band half-width in terms of 4 parameters as in Fig. S7. Black curves: 2 formin dimers per node. Red curves: 4 formin dimers per node to simulate possible excessive accumulation of Cdc12p in nodes in cdc25-22 cells. The results are qualitatively similar for both black and red curves.

A B C

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Fig. S18. Simulations of attraction between contractile rings (70 nodes each) as a function of their initial separation and time (S15). Rings separated by 4 μm fuse within 20 min or less but rings separated by more than 8 μm fail to converge, similarly to experiment (S15). See Fig. S7 for other parameter values.

28

Supplementary References and Notes

S1. J. Bähler et al., Yeast 14, 943 (1998). S2. J.-Q. Wu, J. R. Kuhn, D. R. Kovar, T. D. Pollard, Dev. Cell 5, 723 (2003). S3. R. E. Campbell et al., Proc. Natl. Acad. Sci. U.S.A. 99, 7877 (2002). S4. W. K. Huh et al., Nature 425, 686 (2003). S5. W.-L. Lee, J. R. Oberle, J. A. Cooper, J. Cell Biol. 160, 355 (2003). S6. J.-Q. Wu et al., J. Cell Biol. 174, 391 (2006). S7. H. A. Snaith, I Samejima, K. E. Sawin, EMBO J. 24, 3690 (2005) S8. M. Mishra et al., J. Cell Sci. 117, 3897 (2004). S9. S. Moreno, A. Klar, P. Nurse, Methods Enzymol. 194, 795 (1991). S10. D. Sage, F. R. Neumann, F. Hediger, S. M. Gasser, M. Unser, IEEE Trans. Image

Process 14, 1372 (2005). S11. J.-Q. Wu, T. D. Pollard, Science 310, 310 (2005). S12. D. Vavylonis, D. R. Kovar, B. O'Shaughnessy, T. D. Pollard, Mol. Cell 21, 455 (2006). S13. S. Trautmann, S. Rajagopalan, D. McCollum, Dev. Cell 7, 755 (2004). S14. S. G. Martin, F. Chang, Curr. Biol. 16, 1161 (2006). S15. R. R. Daga, F. Chang, Proc. Natl. Acad. Sci. U.S.A. 102, 8228 (2005).

29

Movies and Animations Movie S1. Rotated 3D reconstruction of 81 z-sections of 0.1 μm of the broad band of a cell expressing Rlc1p-3GFP (strain JW1258) showing the distribution of nodes near the plasma membrane.

Movie S2. Time-lapse series of a cell expressing Rlc1p-3GFP showing the condensation of nodes into a ring through stochastic node motions. Movie shows a single focal plane at the top of a cell. The time interval between frames is 1 s (display rate: 8X) and the movie is corrected for photobleaching. The long axis of the cell runs from left to right. To increase the signal to noise ratio at the expense of time resolution, each frame shown is the average of six frames of the original movie (frame 1 is the average of original frames 1-6, frame 2 the average of 2-7, etc).

Movie S3. Movie showing the results of a simulation. The time interval between frames is 1 s. Display rate: 8X. The parameter values are the same as those of Fig. 1J of the main text. Nodes in red, actin filaments in green (broadened to optical resolution).

Movie S4. Enlarged region of a portion of Movie S3. Right part shows nodes in red and actin in green. Left part shows only the nodes, whose motions are similar to those in experiment (Movie S2). Display rate: 8X.

Movie S5. Time-lapse series of a cell expressing Rlc1p-3GFP showing the appearance of nodes at a single focal plane at the top of a cell. The time interval between frames is 1 s (display rate: 8X) and the movie is corrected for photobleaching. The long axis of the cell runs from top left to bottom right. To increase the signal to noise ratio at the expense of time resolution, each frame shown is the average of six frames of the original movie, as for Movie S2. Note that a few nodes at the top of the movie apparently form by a splitting event of a node already present at t = 0. This particular event could have been triggered by movement of material within the cell unrelated to node formation.

Movie S6. Time-lapse series of a cell expressing Rlc1p-3GFP showing stationary nodes at a single focal plane at top of cells. Nodes transition to a mobile phase near frame 300 and start to condense into a contractile ring. The time interval between frames is 1 s (display rate: 8X) and the movie was corrected for photobleaching. The long axis of the cell runs from top to bottom. Each frame shown is the average of six frames of the original movie, as for Movie S2.

Movie S7. A time-lapse series of two representative cdc25-22 cells (strain JW1329) expressing GFP-CHD (green) and Sad1p-mRFP1 (red) showing the timing of actin filament accumulation at the division site relative to the duplication and separation of the spindle pole body labeled with Sad1p-mRFP1. The time zero is the start of imaging. The real time is shown as h:min:s.

Movie S8. A time-lapse series of a cell expressing GFP-CHD showing that the contractile actin ring assembles from a meshwork of actin filaments. A stack of 12 z-sections spaced

30

at 0.6 µm was collected every minute for 41 minutes and projected into a 2D image using maximum intensity projection. The bright spots are actin patches. Display rate: 190 X. Movie S9. Movie showing that actin filaments connect nodes together to form a network in cdc25-22 cells expressing GFP-CHD and Rlc1p-mRFP1. Stacks of 24 z-sections of 0.3 µm were collected. 3D projections of the middle portions of cells b to d in Fig. 3G are shown. Note: The Fig. 3B shows the maximum intensity projections of the bottom half of the cells a to f. Movie S10. Time series showing dynamic actin network associating with Rlc1p nodes. The movie shows a single focal plane at the top of a cell expressing GFP-CHD and Rlc1p-tdTomato (strain JW1349). Time interval between frames is 0.3 s. The Rlc1p signal (red) is static and is the average of all the Rlc1p frames from the first 6 sec (the Rlc1p signal per frame is otherwise very weak). The GFP-CHD signal (green) is a moving average over 3 successive frames. The transient bright spots are actin patches. Display rate: 3.6X. Movie S11. Time series of an actin filament associating with a node before the condensation of nodes into a contractile ring, consistent with a search and capture mechanism. The movie shows a single focal plane at the top of cdc25-22 cells expressing GFP-CHD to mark actin filaments and Rlc1p-tdTomato to mark nodes (strain JW1351). The long axis of the cell is vertical. An actin filament/bundle (green) starts at a node, moves laterally by ~ 0.2 μm and becomes captured by a neighboring node (marked by an arrowhead). The filament/bundle appears to break 10 s after capture. Time interval between frames is 0.2 s. Display rate: 2X. Movie S12. Time series showing actin filaments dynamically associated with nodes as they condense into a contractile ring in for3Δ cells expressing GFP-CHD and Rlc1p-tdTomato (strain JW1353). The long axis of the cell is vertical. Two nodes near the ring (arrowheads) move closer to one another, then split and move in separate paths. The nodes move after associating with linear elements marked by GFP-CHD, consistent with a search, capture, pull and release mechanism. A filament/bundle appears between the nodes as they merge, while a new filament/bundle originates from the center of the forming ring and seems to pull the nodes apart and towards the contractile ring. A stack of two z-sections spaced at 0.1 µm were collected with an exposure time of 0.2 s for each section in each channel and projected into a 2D image using average intensity projection. The transient bright spots are actin patches. Time interval between frames is 1.8 s. Display rate: 16X. Movie S13. Time series showing actin filaments marked by GFP-CHD growing from a node, associating with other actin structures and causing the node to move towards the contractile ring. The movie shows a single focal plane at the top of for3Δ cells expressing GFP-CHD and Rlc1p-tdTomato (strain JW1353). The long axis of the cell is vertical. An actin filament/bundle elongates from a lagging node (marked by arrowhead). The

31

filaments/bundles appear to move laterally as they connect to other filaments before the movement of the node towards the contractile ring. Time interval between frames is 0.8 s. The transient bright spots are actin patches. Display rate: 4X. Movie S14. Evidence for search, capture, pull and release mechanism. A time series shows actin filaments associating with a lagging node as it moves towards the contractile ring during the late stages of condensation of nodes into a contractile ring in cells expressing GFP-CHD and Rlc1p-tdTomato (strain JW1349). The long axis of the cell is vertical. The movie is consistent with actin filaments (green) growing to capture a lagging node (marked by an arrowhead), and pulling it towards the contractile ring until the filaments break (sudden decrease in local GFP-CHD intensity marked by an arrow). Some actin filaments associated with the node at the beginning of the movie are lost before new filaments establish connections with the node. A stack of two z-sections spaced at 0.2 µm were collected with an exposure time of 0.3 s for each section in each channel and projected into a 2D image using average intensity projection. Fig. 3D shows a montage and kymograph of the cell from a region below the contractile ring. Time interval between frames is 2.5 s. The transient bright spots are actin patches. Display rate: 12.5X.

Movie S15. Time series showing actin filaments associated with and growing from Rlc1p nodes. The movie shows actin filaments transiently connecting two nodes and regrowing from one of these nodes. Single focal plane at the top of a cell expressing GFP-CHD and Rlc1p-tdTomato (strain JW1349). Time interval between frames is 0.3 s. The Rlc1p signal (red) is static and is the average of all the Rlc1p frames from the first 6 sec (the Rlc1p signal per frame is otherwise very weak). The GFP-CHD signal (green) is a moving average over 3 successive frames. The transient bright spots are actin patches. Display rate: 2.1X.

Movie S16. Time series showing actin filaments growing and turning over on the lateral margins of a fully formed contractile ring. The movie shows a single focal plane at the top of for3Δ cells expressing GFP-CHD and Rlc1p-tdTomato (strain JW1353). The long axis of the cell is vertical. GFP-CHD: left panel and green in the merged panel. Rlc1- tdTomato: middle panel and red in the merged panel. An actin filament/bundle (marked by arrowhead) elongates from the contractile ring. Some filaments (marked by ∧) detach (i.e. turnover) from the contractile ring. Time interval between frames is 0.8 s. The bright spots are actin patches. Display rate: 5X. Movie S17. Movie showing a linear actin element buckling in the broad band. Average of two z slices spaced at 0.3 µm at the top of a cdc25-22 cell expressing GFP-CHD (strain JW1311). The transient bright spots are actin patches. Time interval between frames is 0.8 s. Display rate: 8X.

Movie S18. Times series showing a linear actin filament/bundle breaking at the division site. Movie shows a single focal plane at the top of a cell expressing GFP-CHD (strain FC1218). Only the left side of the cell is shown. Time interval between frames is 0.4 s.

32

The transient bright spots are actin patches. A linear actin filament/bundle (marked with a green arrowhead) grows from the middle portion of the contractile ring to the left. It then detaches from the ring and moves rapidly towards the left side of the cell. Each frame shown is the average of three frames of the original movie (frame 1 is the average of original frames 1-3, frame 2 the average of 2-4, etc). Display rate: 2X.

Movie S19. Time-lapse series of cells expressing Rlc1p-3GFP showing the transient alignment of nodes into linear structures during the late stages of contractile ring formation. The movie shows a single focal plane at the top of a cell. The time interval between frames is 1 s (display rate: 8X). The long axis of the cell runs from top left to bottom right. To increase the signal to noise ratio at the expense of time resolution, each frame shown is the average of six frames of the original movie.