We build on the foundational work that demonstrated the ability to control motor-microtubule systems with light (Ross et al., 2019) to consider a new set of motors with different fundamental properties. In brief, kinesin motors are fused to the light-dimerizable pair iLid and micro. In the absence of light, motor dimers walk along microtubules but do not organize them; upon activation with light, the motor dimers couple together to form tetramers, crosslinking the microtubules they are walking along as shown in Figure 1A. The optogenetic bond lasts for about 20 s before reverting to the undimerized state, thus in our experiments, we repeatedly illuminate the sample every 20 s (Guntas et al., 2015). As demonstrated by Ross et al., projecting a cylinder of light on the sample results in the formation of an aster, and different structures can be formed and manipulated by illumination with different light patterns. For the purposes of this study, we were careful to remain in a regime of motor and microtubule concentrations that produced a single aster upon illumination. However, by varying concentrations of the motors and microtubules, it is possible to form multiple smaller asters within the region, a few examples of which are shown in Figure 1—figure supplement 1. How varying the composition of the reaction mixture impacts the resulting structures warrants further investigation.

In this work, we aim to determine how the properties of the motor affect the resulting structures. While experiments with this system were previously performed with Drosophila melanogaster kinesin-1 motors (K401) (Ross et al., 2019), in the present work, we investigate if other kinesin motor species with different intrinsic properties such as speed and processivity would lead to light-inducded microtubule organization. Toward this end, we use the same light-dimerizable scheme to form microtubule structures with two other motors: Ncd (D. melanogaster kinesin-14) and Kif11 (Homo sapiens kinesin-5). The single-molecule properties of all three motors we use are summarized in Table 1. We measure the speed of each motor species by gliding assays (SI section ‘Gliding assay’); the processivities are based on literature values. Further, we fluorescently label the motors using mVenus or mCherry to visualize the motors and microtubules in separate imaging channels within the same assay (see Supplementary file 1).

As seen in Figure 1B and Figure 1—figure supplement 2, each of these motors is able to form asters of varying sizes in our system. It was previously unclear whether there were limits to speed, processivity, or stall force that might prevent any of these motors from forming asters in our light-controlled system, although Ncd has previously been shown to form asters as constitutive oligomers (Belmonte et al., 2017; Hentrich and Surrey, 2010). We found that all were able to form asters upon illumination by various excitation diameters ranging from 50 to 600 μm. Interestingly, the dynamics of aster formation by these motors seemed to roughly scale with the motor speeds – K401 formed asters the quickest, followed by Ncd236, and Kif11 took the most time to form an aster.

We sought to determine if there are discernible differences between the asters formed with the various motors. First, we measured the size of the asters using the distribution of fluorescently labeled microtubules, which peaks in the center of the aster and generally decreases moving outward, as shown in Figure 1C. We tend to observe a shoulder in the microtubule distribution (around 20 in the example in Figure 1C). This is around the size of the disordered aster core, which is discussed in SI section ‘Disordered aster core’. We defined the outer radius of the aster as the radius at which the microtubule fluorescence is twice the background microtubule concentration (see Figure 1C for an example aster outer radius determination). We found that this method agreed well with a visual inspection of the asters (Figure 1—figure supplement 2).

We found that aster size increases with excitation diameter, as shown in Figure 1B, D, consistent with what was shown by Ross et al. for K401 (Ross et al., 2019). In Ross et al., it was determined that the aster size roughly scaled with the volume of the excitation area, suggesting that the number of microtubules limits the size of the aster. This hints that there may be a density limit to the microtubules in an aster. Interestingly, we find that the size of the asters also depends on the motor used. For each excitation diameter, except for the 50 μm case, K401 formed the largest asters and Ncd formed the smallest, with Kif11 producing asters of intermediate size (Figure 1D). What is it about the different motors that confers these different structural outcomes? We found that this trend correlates with motor processivity; K401 is the most processive, followed by Kif11, and then Ncd. This is similar to the findings in Surrey et al., 2001, in which intensity of aster formation was related to motor processivity. Other factors could also be contributing to aster size such as the ratio of microtubules to motors as was suggested by Surrey et al., 2001, but not investigated in the present work, or the motor stall force.

The nonuniform distribution of filaments and motors in an aster is a key feature of its organization and has been the subject of previous studies. In these studies, continuum models were developed for motor-filament mixtures which predicted the radial profile of motors in confined two-dimensional systems (Nédélec et al., 2001; Lee and Kardar, 2001; Sankararaman et al., 2004; Aranson and Tsimring, 2006). A notable example is the power-law decay prediction by Ndlec et al., who obtained it for a prescribed organization of microtubules obeying a 1/r decay law (Nédélec et al., 2001). Measuring the motor profiles in asters formed in a quasi-two-dimensional geometry (with the z-dimension of the sample being only a few microns deep) and fitting them to a power-law decay, the authors found a reasonable yet noisy match between the predicted and measured trends in the decay exponent.

In our work, we also develop and test a minimal model that predicts the motor profile from the microtubule distribution and the microscopic properties of the motor. Our well-defined asters of various sizes shown above, created with varying motor properties yields an opportunity for us to test how our model and assess how the microscopic motor properties are translated to the aster scale. Additionally, in contrast to the earlier study (Nédélec et al., 2001), asters formed in our experiments are three-dimensional due to the much larger depth of the flow cells (roughly 100 μm), and are thus more similar to the structures observed in cells. While the largest asters we form are likely partially compressed in the z-direction, we assume that this effect does not significantly alter the protein distributions in the central z-slice. For modeling purposes, then, we consider our asters to be radially symmetric outside the central disordered region (which we refer to as the aster core, as depicted schematically in Figure 2A). The core has a typical radius of ≈15 μm, beyond which microtubules have a predominantly polar organization (see SI section ‘Disordered aster core’ for the discussion of the two aster regions and an example Pol-Scope image that demonstrates their distinction).

Similar to the treatment in earlier works (Nédélec et al., 2001; Sankararaman et al., 2004; Aranson and Tsimring, 2006), we introduce two states of the motor – an unbound state where the motor can freely diffuse with a diffusion constant D and a bound state where the motor walks toward the aster center with a speed v, depicted in Figure 2B. In the steady state of the system, which we assume our asters have reached at the end of the experiment, microtubules on average have no radial movement and hence, do not contribute to motor speed. To assess the validity of this assumption, we performed fluorescence recovery after photobleaching (FRAP) experiments of steady-state asters, and observe little radial flux of the microtubules, an example is shown in Appendix 1—figure 4. They are still dynamic, as can be seen by the angular motion that leads to the recovery of fluorescence in the photobleached areas. We denote the rates of motor binding and unbinding by kon and koff, respectively. When defining the first-order rate of motor binding, namely, kon⁢ρMT⁢(r), we explicitly account for the local microtubule concentration ρMT⁢(r) extracted from fluorescence images. This is unlike the previous models which imposed specific functional forms on the microtubule distribution (e.g., a constant value [Lee and Kardar, 2001; Sankararaman et al., 2004] or a power-law decay [Nédélec et al., 2001]), rendering them unable to capture the specific features often seen in our measured microtubule profiles, such as the presence of an inflection point (see Figure 1C for an example).

From these assumptions, the governing equations for the bound (mb) and free (mf) motor concentrations are shown in Figure 2C. They involve binding and unbinding terms, as well as a separate flux divergence term for each population. Solving these equations at steady state, we arrive at an equation for the total local concentration of motors defined as mtot⁢(r)=mb⁢(r)+mf⁢(r). The derivation of this result can be found in SI section ‘Model formulation’. As seen in the equation for mtot⁢(r) (Figure 2C), knowing the microtubule distribution ρMT⁢(r) along with two effective microscopic parameters, namely, the effective dissociation constant Kd=koff/kon and the length scale λ0=D/v, we can obtain the motor distribution up to a multiplicative constant (C in the equation). Note that in the special case where the motors do not move (v→0 or λ0→∞), the exponential term becomes 1 and an equilibrium relation between the motor and microtubule distributions dependent only on Kd is recovered, as we would expect for an equilibrium system.

To test this model, we extract the average radial distributions of microtubule and motor concentrations for each aster. Then, using the microtubule profile as an input, we fit our model to the motor data and infer the effective parameters Kd and λ0 (see SI sections ‘Extraction of concentration profiles from raw images’ and ‘Model fitting’ for details). A demonstration of this procedure on an example Kif11 aster is shown in Figure 2D where a good fit to the average motor data can be observed. As a validation of our inference method, we additionally extract the radial concentration profiles inside separate wedges of the aster and show that they can be accurately captured by only choosing an appropriate multiplicative constant C for each wedge, while keeping the pair (Kd,λ0) inferred from average profile fixed. Fits to 5 out of 16 different wedge profiles are shown in Figure 2D for clarity. The fitting error for other asters is similarly low (Figure 2E, see Figure 2—figure supplement 1 for the collection of fitted profiles).

Plotting the inferred parameters Kd and λ0 from all fits, shown in Figure 2F, we find that they are clustered around single values for each motor type and vary between the motors. Based on the single-molecule motor properties in Table 1 and the reported motor binding rates (Valentine and Gilbert, 2007), our expectation was that the Kd values for Kif11 and K401 would have a ratio of ≈4.6:1 (see SI section ‘Expected ratio of K_d values for K401 and Kif11 motors’), while Kd for Ncd would be the highest due to its non-processivity. The ratio of median inferred Kd values for Kif11 and K401 is ≈5.6:1 – close to our expectation. However, the inferred Kd values for Ncd are low and comparable to those for K401.

One possible resolution of this discrepancy comes from the finding of an in vitro study suggesting a substantial increase in the processivity of Ncd motors that act collectively (Furuta et al., 2013). Specifically, a pair of Ncd motors coupled through a DNA scaffold was shown to have a processivity reaching 1 μm (or, ≈100 steps) – a value close to that reported for K401 motors. A highly processive movement was similarly observed for clusters of HSET (human kinesin-14) (Norris et al., 2018) and plant kinesin-14 motors (Jonsson et al., 2015).

This collective effect, likely realized for Ncd tetramers clustered on microtubules in highly concentrated aster structures, is therefore a possible cause for the low inferred values of their effective Kd. We also note that while a similar collective effect on processivity was observed for K401 motors (Furuta et al., 2013), it is far less dramatic since their single-motor processivity is already about the length of our microtubules, and therefore would have a small effect on the effective Kd.

Next, looking at the inference results for the λ0 parameter (Figure 2F), we can see that Kif11 and Ncd motors have an average λ0 value of ≈10-20 μm, while the average value for K401 motors is ≈40 μm. From the measured diffusion coefficient of D≈1 μm²/s for tagged kinesin motors (Grover et al., 2016) and the single-molecule motor speeds reported in Table 1, our rough estimate for the λ0 parameter for Kif11 and Ncd motors was ≈10-15 μm, and ≈2 μm for K401. While the inferred values for the two slower motors are well within the order-of-magnitude of our guess, the inferred λ0 for the faster K401 motor is much higher than what we anticipated. This suggests a significant reduction in the effective speed. One contributor to this reduction is the stalling of motors upon reaching the microtubule ends. Recall that in our model formulation (Figure 2B) we assumed an unobstructed walk for bound motors. Since the median length of microtubules (≈1.6 μm) is comparable to the processivity of K401 motors (≈1 μm), stalling events at microtubule ends will be common, leading to a reduction of their effective speed in the bound state by a factor of ≈1.5 (see SI section ‘Accounting for finite MT lengths’ for details). This correction alone, however, is not sufficient to capture the factor of ≈25 discrepancy between our inference and the estimate of λ0. We hypothesize that an additional contribution may come from the jamming of K401 motors in dense aster regions. This is motivated by the experiments which showed that K401 motors would pause when encountering obstructions during their walk (Ferro et al., 2019; Schneider et al., 2015). In contrast, for motors like Ncd and Kif11 which take fewer steps before unbinding and have a larger effective K_d, jamming would have a lesser effect on their effective speed as they would unbind more readily upon encountering an obstacle. Overall, our study shows that the minimal model of motor distributions proposed in Figure 2 is able to capture the distinctions in aster structure through motor-specific effective parameters, although more work needs to be done to explain the emergence of higher-order effects such as motor clustering and jamming, and their contribution to these effective parameters.

Our model also provides insights on the observation that the distribution of microtubules is generally broader than that of the motors. This feature can be observed by comparing the two example profiles in Figure 2D, and it also holds for the profiles extracted from other asters (Figure 2—figure supplement 1). In SI section ‘Broader spread of the tubulin profile’, we use our model to demonstrate this feature in a special analytically tractable case, and discuss its generality across asters in greater detail. We found that the relative width of the motor distribution compared to the microtubule distribution is fairly constant among asters, with their difference being the largest for Ncd motors, consistent with our model predictions. This relationship between the shapes of the distributions may be an important factor in the spatial organization of end-directed motors in the spindle where their localization to the spindle pole is of physiological importance.

Besides the steady-state structure of motor-microtubule assemblies, it is also of great interest to understand their dynamics. Ross et al. demonstrated the formation of quasi-one-dimensional contractile networks by creating two asters that are initially separated by a given distance, then activating a thin rectangular region between them to form a network connecting the asters that pulls them together (Ross et al., 2019). Example images of microtubule fluorescence during one of these experiments are shown in Figure 3a. In these experiments, an increase in maximum aster merger speed with greater initial separation was observed. We aimed to confirm this behavior with our various motors and to test the relationship between aster merger speed and single-motor speed.

First, we tested the relationship between distance and speed in our experiments. Using optical flow to measure the contraction speed throughout the network, we observe a linear increase in contractile speed with distance from the center of the network, as shown in Figure 3b. This relationship suggests that the contractile network can be thought of as a series of connected contractile units. These findings are in agreement with results from several studies of contractile rates in actomyosin networks, that suggested telescoping models of contraction, and suggest that this may be a common mechanism across cytosketetal networks (Thoresen et al., 2011; Linsmeier et al., 2016; Schuppler et al., 2016). Independent contraction of each unit would generate the observed linear increase in speed because more contractile units are added with distance from the center of the network.

Next, we investigated how contractile speeds vary by motor in aster merger experiments. We repeated aster merger experiments with each motor and with various initial separations between the asters. Figure 3c shows the results, where each point represents the maximum aster speed measured in a single experiment by tracking the aster, and the lines are linear fits to the data for each motor (see SI section ‘Merger analysis’ for details on measuring the aster speeds). Interestingly, the ratios of the slopes of these lines match the ratios of motor speeds from Table 1. For example, the slope of the best fit line for Ncd is ≈0.0023⁢s-1 and the best fit slope for Kif11 is ≈0.0013⁢s-1. The ratio of these (Ncd/Kif11) is ≈1.8, which closely matches the ratio of their single-motor speeds (≈1.6). Similar calculations can be done with these two motors and K401, with the same result. Thus, we conclude that the rate of contraction in the network is set by the motor speed and the increase of network speed with distance is due to adding more connected contractile units (Figure 3—figure supplement 1). It is important to note that we only measure the initial contraction rate in these experiments, over the first ≈100 s. On this time scale, we think of the network as an elastic material, since the time for motor unbinding and rearrangement should be longer than this. The time scale for the optogenetic pair to unbind is about 20 s (Guntas et al., 2015); since binding events are independent then the average time for two to unbind is about 400 s. There are likely several motors bound between any two microtubules within the network, thus the relaxation time, or the time to observe the viscous properties of the system, will be the time for multiple motors to unbind or optogenetic links to rearrange. Therefore, to account for the change in contraction rate throughout the process, one would likely need to account for these viscous effects.

Human kinesin-5 (Kif11/Eg5) 5–513 was PCR amplified from mCherry-Kinesin11-N-18 plasmid (gift from Michael Davidson, Addgene # 55067). This fragment was previously shown to form functional dimers (Valentine et al., 2006). Kinesin 1 1–401 (K401) was PCR amplified from pWC2 plasmid (Addgene # 15960). Ncd 236–701 was PCR amplified from a plasmid gifted by Andrea Serra-Marques.

The optogenetic proteins, iLid, and Micro were PCR amplified from pQE-80L iLid (Addgene # 60408, gift from Brian Kuhlman) and pQE-80L MBP-SspB Micro (Addgene # 60410). mCherry was PCR amplified from mCherry-Kinesin11-N-18 and mVenus was PCR amplified from mVenus plasmid (Addgene # 27793).

Constructs were assembled by Gibson assembly of the desired motor protein, optogenetic protein, and fluorophore in order to make the plasmids listed in Supplementary file 1.

Protein expression and purification was done in SF9 cells. Cells were seeded at a density of 1,000,000 cells per mL in a 15 mL volume and transiently transfected with the desired plasmid using Escort IV transfection reagent, then incubated for 72 hr before purification. Cells were collected for purification by centrifugation at 500 × g for 12 min, and the pellet was resuspended in lysis buffer (200 mM NaCl, 4 mM MgCl₂, 0.5 mM EDTA, 1.0 mM EGTA 0.5% Igepal, 7% sucrose by weight, 20 mM imidazole pH 7.5, 10 g/mL aprotinin, 10 g/mL leupeptin, 2 mM ATP, 5 mM DTT, 1 mM PMSF) and incubated on ice for 30 min. The lysate was then clarified by centrifugation at 200,000 × g for 30 min at 4°C. Clarified supernatant was incubated with 40 L anti-FLAG M2 affinity gel (Sigma-Aldrich A2220) for 3 hr at 4°C. To wash out unbound protein, the resin (with bound protein) was collected by centrifugation at 2000 × g for 1 min, the supernatant was removed and the resin was washed with wash buffer (for Ncd and Kif11: 150 mM KCl, 5 mM MgCl₂, 1 mM EDTA, 1 mM EGTA, 20 mM imidazole pH 7.5, 10 g/mL aprotinin, 10 g/mL leupeptin, 3 mM DTT, 3 mM ATP; for K401: M2B with 10 g/mL aprotinin, 10 g/mL leupeptin, 3 mM DTT, 3 mM ATP). This was repeated two more times with decreasing ATP concentration (0.3 and 0.03 mM ATP) for a total of three washes. After the third wash, about 100 L supernatant was left and the bound protein was eluted by incubation with 10 L FLAG peptide (Sigma-Aldrich F3290) at 4°C for 3 hr. The resin was then spun down by centrifugation at 2000 × g for 1 min and the supernatant containing the purified protein was collected. Purified protein was then concentrated to a volume of 10–20 L by centrifugation in mini spin filters (Millipore 50 kDa molecular weight cut-off). Protein was kept at 4°C and used the same day as purification or stored in 50% glycerol at –20°C for longer storage. Protein concentration was determined with QuBit Protein Assay Kit (Thermo Fisher Q33212).

Microtubules were polymerized as reported previously (Ross et al., 2019) and originally from the Mitchison lab website (Georgoulia, 2012). In brief, 75 μM unlabeled tubulin (Cytoskeleton) and 5 μM tubulin-Alexa Fluor 647 (Cytoskeleton) were combined with 1 mM DTT and 0.6 mM GMP-CPP in M2B buffer and incubated spun at 300,000 × g to remove aggregates, then the supernatant was incubated at 37°C for 1 hr to form GMP-CPP stabilized microtubules.

The GMP-CPP stabilized microtubules were imaged with TIRF microscopy to determine their length. A flow chamber was made using a KOH cleaned slide, KOH cleaned coverslip (optionally coated with polyacrylamide), and parafilm cut into chambers. The flow cell was incubated with poly-L-lysine for 10 min, washed with M2B, then microtubules were flown in. The chamber was sealed with Picodent and imaged with TIRF microscopy.

Microtubules were segmented using home-written Python code and histogrammed to determine the distribution of microtubule lengths (Appendix 1—figure 1).

Slides and coverslips were cleaned with Helmanex, ethanol, and KOH, silanized, and coated with polyacrylamide as in Ross et al., 2019. Just before use, slides and coverslips were rinsed with MilliQ water and dried with compressed air. Flow chambers (3 mm wide) were cut out of Parafilm M and melted using a hotplate at 65°C to seal the slide and coverglass together, forming chambers that are ≈70-100 μm in height and contain ≈7 μL.

The reaction mixture consisted of kinesin motors (∼250⁢nM), microtubules (∼1 μM tubulin), and energy mix that contained ATP, an ATP recycling system, a system to reduce photobleaching, F-127 pluronic to reduce interactions with the glass surfaces, and glycerol (Ross et al., 2019). To prevent pre-activation of the optogenetic proteins and photobleaching of the fluorophores, the motors and microtubules were always handled in a dark room where wavelengths of light below 520 nm were blocked with a filter or a red light was used to illuminate. The reaction mixture was prepared right before loading into the flow cell and then sealed with Picodent Speed.

We performed the experiments with an automated widefield epifluorescence microscope (Nikon TE2000). We custom modified the scope to provide two additional modes of imaging: epi-illuminated pattern projection and LED gated transmitted light. We imaged light patterns from a programmable DLP chip (EKB TEchnologies DLP LightCrafter E4500 MKIITM Fiber Couple) onto the sample through a user-modified epi-illumination attachment (Nikon T-FL). The DLP chip was illuminated by a fiber coupled 470 nm LED (ThorLabs M470L3). The epi-illumination attachment had two light-path entry ports, one for the projected pattern light path and the other for a standard widefield epi-fluorescence light path. The two light paths were overlapped with a dichroic mirror (Semrock BLP01-488R-25). The magnification of the epi-illuminating system was designed so that the imaging sensor of the camera (FliR BFLY-U3-23S6M-C) was fully illuminated when the entire DLP chip was on. Experiments were run with Micro-Manager (Edelstein et al., 2010), running custom scripts to controlled pattern projection and stage movement.

For the experiments in which we make asters with excitation disks of different sizes, we use five positions within the same flow cell simultaneously in order to control for variation within flow cells and over time. Each position is illuminated with a different sized excitation region: 50, 100, 200, 400, or 600 μm diameter cylinder. Each position was illuminated with the activation light for ∼50-200 ms and both the microtubules (Cy5 labeled) and motors (mVenus labeled) were imaged at ×10 magnification every 15 s. After an hour of activation, a z-stack of the microtubule and motor fluorescence throughout the depth of the flow chamber was taken at 5 μm increments in each position. Typically, one experiment was run per flow chamber. We placed the time limitations on the sample viewing to minimize effects related to cumulative photobleaching, ATP depletion, and global activity of the light-dimerizable proteins. After several hours, inactivated dark regions of the sample begin to show bundling of microtubules.

For the aster merger experiments, two 50 μm disks are illuminated at different distances apart. Again, five positions within the same flow cell are chosen, and the separation between the two disks varies for each position: 200, 400, 600, 800, or 1000 μm apart. For K401 and Ncd experiments, the disks are illuminated for 30 frames, for Kif11 experiments, the disks are illuminated for 60 frames (frames are every 15 s). Then, a bar ≈5 μm wide connecting the disks is illuminated to merge the asters.

Motor speeds were determined by gliding assay. Glass slides and coverslips were Helmanex, ethanol, and KOH cleaned. Flow cells with ≈10 L volume were created with double sided sticky tape, and rinsed with M2B buffer. Then, anti-GFP antibody was applied and incubated for 10 min. The flow cell was then rinsed with M2B and then mVenus labeled motor proteins (at ∼5 nM in M2B) were flowed in and incubated for 10 min. The flow cell was rinsed with M2B to remove unbound motors and microtubules (in M2B with 3 mM ATP and 1 mM DTT) were flowed in. Microtubules were then imaged using total internal reflection fluorescence (TIRF) microscopy at a rate of one frame per second. Individual microtubules were tracked using custom-written Python code to determine their speed. The mean microtubule speed (excluding those that were not moving) was determined as the motor speed. Appendix 1—figure 2 shows the histogram of speeds obtained for K401 motors purified from SF9 cells.

The experiments for this study were performed in a regime in which we obtained a single aster, in order to measure properties of the structure and compare between various motors. However, by varying concentrations of components within the system such as motor and microtubule concentration, it is possible to obtain different results. Some examples include mini asters everywhere in the sample before activation, a few asters within the activation region, or many small asters within the activation region. Example images of these cases are shown in Figure 1—figure supplement 1. The various possible resulting structures, and the perturbations to the system to obtain them, warrant further study in the future.

We observe that the asters we create have centers that are very dense with motors and microtubules. By fluorescence microscopy, we do not observe organized aster arms in this region and hypothesized that the microtubules are disordered in this region. To assess the extent of microtubule organization in our asters, we imaged asters with a polarized light microscope (Pol-Scope). This microscope utilizes polarized white light to image birefringent substances. Microtubules are birefringent due to their aspect ratio; they interact differently with light polarized parallel to their long axes compared to light polarized perpendicular to their long axes. Thus, the Pol-Scope allows determination of the alignment of microtubules, but not their plus/minus end polarity (Oldenbourg and Mei, 1995). When imaged with a Pol-Scope, the arms of our asters are bright, indicating high alignment, and their azimuthal angle confirms that they are radially symmetric around the center (Appendix 1—figure 3). The center of the aster is dark, which we interpret to mean that this region is disordered. It is possible that the microtubules in the center could be aligned pointing in the z-direction, which could also result in the center being dark. A disordered center may be a result from steric hindrance due to a high density of microtubules in that region, which prevents the motors from aligning the microtubules. Due to the disorder in the aster center, we exclude this region from our theoretical analysis.

When we measure aster size and the distributions of motors and microtubules, we do so once the aster has reached a dynamic steady state. To assess this notion, we performed FRAP experiments. We photobleached the microtubules in a fully formed aster in a grid pattern and took images of the recovery, shown in Appendix 1—figure 4. From these images, it is clear that there is little to no net radial movement of the microtubules, and slow angular motion. Therefore, at this point, the aster is no longer contracting, but the microtubules are still dynamic. We attempted similar experiments with the motors, but they recover very quickly.

We formed asters of various sizes using cylindrical illumination regions, ranging in diameter from 50 to 600 μm. Figure 1—figure supplement 2 shows representative images of the microtubule fluorescence of asters formed with each motor and each excitation diameter. The yellow circles are by-hand determination of the outer boundary of the aster. It can be seen in these images that for the smallest asters, the aster size can be larger than the illumination region. We believe this is due to diffusion of dimerized motors outside of the activation region, where they can bind microtubules in the background region and incorporate them into the asters. For larger excitation diameters, the microtubules in the activated region get concentrated in the aster, leaving a region depleted of microtubules between the aster and the background region. In order to measure the size of asters in a more systematic way, we used the measured microtubule distribution, as shown in Figure 1C. Outside of the central core region of the aster, microtubule fluorescence decreases monotonically before rising again to the background level outside of the activation region. We chose to define the outer radius of the aster as the radius at which the median microtubule fluorescence is twice the background fluorescence. This metric agrees well with a visual inspection of the asters.