Mechanisms Underlying the Active Self-Assembly of Microtubule

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Mechanisms underlying the active selfassembly of microtubule rings and spools Virginia VanDelinder, Stephanie Brener, and George D. Bachand Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/acs.biomac.5b01684 • Publication Date (Web): 04 Feb 2016 Downloaded from http://pubs.acs.org on February 12, 2016

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Mechanisms underlying the active self-assembly of microtubule rings and spools Virginia VanDelinder, Stephanie Brener, George D. Bachand*

AUTHOR ADDRESS Center for Integrated Nanotechnologies, Sandia National Laboratories, PO Box 5800, MS 1303, Albuquerque, NM 87111 USA. E-mail: [email protected]; Fax: +1 505 284 7778; Tel: +1 505 844 5164.

ABSTRACT

Active self-assembly offer a powerful route for the creation of dynamic multiscale structures that are presently inaccessible with standard microfabrication techniques. One such system uses the translation of microtubule filaments by surface tethered kinesin to actively assemble nanocomposites with bundle, ring and spool morphologies. Attempts to observe mechanisms involved in this active assembly system have been hampered by experimental difficulties with performing observation during buffer exchange and photodamage from fluorescent excitation. In the present work, we used a custom microfluidic device to remove these limitations and directly study ring/spool formation, including the earliest events (nucleation) that drive subsequent

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nanocomposite assembly. Three distinct formation events were observed: pinning, collisions, and induced curvature. Of these three, collisions accounted for the majority of event leading to ring/spool formation, while the rate of pinning was shown to be dependent on the amount of photodamage in the system. We further showed that formation mechanism directly affects the diameter and rotation direction of the resultant rings and spools. Overall the fundamental understanding described in this work provides a foundation by which the properties of motordriven, actively assembled nanocomposites may be tailored toward specific applications.

KEYWORDS Kinesin, microtubule, spool, active-self-assembly

Introduction Bottom-up self-assembly processes may be used to create nano- and microscale structures that are unattainable by standard, top-down fabrication techniques. Self-assembly processes fall in two categories: passive self-assembly, which is driven by thermal energy and produces close-toequilibrium structures; and active self-assembly, which is driven by an applied energy source and produces far-from-equilibrium structures. Biological processes commonly use active selfassembly in which the dissipation of chemical energy in these systems drives emergent behaviors such as adaptive reorganization and self-healing. The power of these behaviors has spurred the ex vivo recapitulation of the associated biological components, such as a minimalistic nanoscale transport system that can actively self-assemble dynamic, multiscale structures.1 Cytoskeletal filaments and their associated motor proteins are one example of a biological active transport system that has been used for the bottom-up, self-assembly of nanostructured,


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composite materials.2 Microtubules (MTs) are one class of cytoskeletal filaments, along with filamentous actin, that provide structural support and scaffolding for vesicular transport inside cells. MTs are hollow, unbranched filaments (25 nm in diameter, 10’s of microns in length) formed by the polymerization of a protein dimer consisting of α and β tubulin subunits. In vivo, MTs possess a lattice of typically thirteen protofilaments and display a distinct polarity with a “plus” (β tubulin terminated) and “minus” (α tubulin terminated) end, which is critical to the bidirectional transport of macromolecules and vesicles by different classes of molecular motors.1 The concerted relationship between MTs and their associated molecular motors plays a crucial role in a number of emergent cellular phenomena such as chromosomal segregation during cell division. Kinesin molecular motors are a superfamily of MT-associated motors that convert chemical energy (i.e., ATP) into the mechanical work needed to transport vesicles through the viscous medium of a cell. Kinesin motors may be tethered to a surface in vitro and work cooperatively to propel MTs across the surface in what is termed the gliding motility geometry. When crosslinkers capable of binding multiple MTs are added to this system, the MTs undergo active self-assembly (Figure 1a), forming bundles, rings, or spools depending upon the specific conditions used for assembly. Following the terminology of Lam et al.,1 a “ring” forms when a single MT is crosslinked to its own tail, while a “spool” forms when a bundle of MTs is crosslinked together in a circular structure. In contrast to the ordered ring and spool structures, in the absence of a driving force (i.e., no kinesin transport) only random, static networks of crosslinked MTs are formed when the MTs, crosslinkers, and motor proteins are combined, which affirms the crucial role of energy dissipation in this active assembly process. MT structures actively self-assembled by kinesin transport have been used for a range of applications


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including use as a template for composite materials,3-8 and use as circular tracks for kinesin carrying cargo.9 Because spools and rings are actively rotated on the surface by the kinesin motors, thus transferring translational motion into rotational motion, these structures may also have potential application as microscale gears for powering large scale systems.

Figure 1. Schematic depiction of (A) the pathway leading to active self-assembly of rings and spools, and (B) the hypothesized mechanisms underlying the assembly process. The red dot indicated the tip of the MT is pinned in place by a dead motor. The blue dots represent places that MTs have been stuck together by crosslinkers. Multiple mechanisms underlying the active self-assembly of rings and spools have been proposed based on direct and indirect evidence, including: pinning, simultaneous sticking, Brownian bending, twist-bend coupling, and tip collisions (Figure 1b).10-12 The first of these mechanisms, pinning, occurs if the tip of a MT encounters an inactive motor, causing it to be “pinned” in place. Continued translation of the MT induces the formation of a loop around the 4 ACS Paragon Plus Environment

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pinned point, allowing the leading and lagging tips to interact and form a closed ring structure.11, 12

Active assembly via simultaneous sticking occurs when three MTs collide with and stick to

one another in a closed triangular geometry. This morphology evolves further as the triplet bundle transitions from translational to rotary motion.11 The third proposed mechanism, Brownian bending, may initiate a spool assembly if the degree of bending due to thermal fluctuation is sufficient to permit the leading end to encounter the lagging end of the MT.11 Based on the rigidity of MTs (1-10mm persistence length),13 active assembly via Brownian bending would result in spools with radii larger than have been observed experimentally, suggesting that it is likely not a dominant mechanism.11 In the twist-bend coupling mechanism, spool assembly is proposed to occur based on the accumulation of mechanical strain as bundles are translated and axially rotated by the kinesin motors.11, 13 Here, the formation of sub-micron, twisted and kinked domains, which were observed by electron microscopy, was hypothesized to induce a curved trajectory of oligomer bundles and drive spool formation when the ends encounter one another. The final mechanism proposed to initiate active assembly, tip collisions, shares similarities with twist-bend coupling: specifically, the interaction between MTs in turn drives the MT bundle in a circular trajectory. In tip collisions, two MT filaments are crosslinked together at the tip and again at a short distance away, resulting in a different arclength between the crosslinked points. As such, more motors are able to bind to the filament section with the longer arclength, leading to a force imbalance at the tip and an induced-circular trajectory.11 Direct observation of these different mechanisms driving the active self-assembly of MT structures has proven problematic due to experimental difficulty in observing the earliest formation events,11 as well as oxidative photodamage to motor proteins exacerbated by fluorescence excitation during observation.14 To date, investigations into which mechanism is


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dominant have primarily been inferred by varying the experimental parameters (i.e. kinesin surface density, MT flexibility, protofilament distribution, etc.) and then observing the effects on the spools that are formed.10, 11, 15-20 Additionally, simulations and calculations have been used to predict the properties of spools that would result from various hypothesized formation mechanisms. In order to fundamentally understand this system, as well as enable assembly of spools with application-specific properties, it is critical to characterize the events that immediately follow the introduction of crosslinkers that drive the active self-assembly of rings and spools. In the present work, we directly observed ring formation starting from the earliest bundling and ring formation events using a customized microfluidic system, and we characterized the properties of the resultant rings. The microfluidic device enabled us to control the delivery of components (e.g., crosslinkers) to initiate ring self-assembly, while visualizing the self-assembly process in situ in real-time without the confounding effects related to photo-oxidative damage.14 The data suggest that at least three mechanisms are responsible for the active self-assembly of rings and spools in this system, and that the resulting spool properties (e.g., diameter) are dictated by the specific mechanism of assembly. Understanding the mechanism underlying the active self-assembly of bundles, rings, and spools establishes a foundation on which we can now begin modulating the properties of these structures toward specific applications. Materials and Methods MT Preparation: Biotinylated and TRITC-labeled MTs were made by polymerizing biotinylated tubulin, TRITC-labeled tubulin, and unlabeled tubulin (30-10-60 molar ratio, 1.31.65mg/mL final concentration; Cytoskeleton, Inc.) in PIPES-DMSO polymerization buffer (5%


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DMSO, 80mM PIPES, 4mM MgCl2, 1mM EGTA, 1 mM GTP; pH adjusted to 6.9 with KOH; Sigma ). After polymerization in 37 ⁰C for 30min, the MTs were stabilized in BRB80T (BRB80: 80mM PIPES, 1mM MgCl2, 1mM EGTA; 10uM taxol; pH adjusted to 6.9 with KOH) at a final concentration of 13-16.5ug/mL. Microfluidic device fabrication and operation: The design and fabrication of the microfluidic device are described in detail in VanDelinder et al.14 The device was initially filled from Inlet 1 with a solution of 60 nM kinesin in BRB80CA (BRB80 buffer with 0.2mg/mL casein and 1mM ATP) with 10 mM CaCl. Then MTs in motility solution (0.2mg/mL casein, 1mM ATP, and 1mM trolox in BRB80T) from inlet 2 was fed into the imaging chamber. Inlet 3 contained 10 nM streptavidin=conjugated quantum dots (sQDs; Life Technologies) in motility solution. After bundling and ring formation events were observed, MTs were removed from the imaging chamber with the solution of Ca2+ from Inlet 1. Formation of MT Rings in Glass Flow Cells: Glass flow cells were made of a glass slide and coverslip connected by two pieces of double-sided sticky tape resulting in a 5 by 20 mm channel. First, 20µL of 60 nM kinesin in BRB80CA was introduced to the flow cell and allowed to incubate for 10min. This solution was followed by 20uL of MT solution, which was 1.3 µg/mL tubulin in motility solution with an oxygen scavenger system (0.2mg/mL casein, 1mM ATP, 0.02mg/mL glucose oxidase, 0.008mg/mL catalase, 20mM D-glucose, 1mM DTT, and 1mM trolox in BRB80T), for 10 min. Finally, 20µL of 10 nM 655 streptavidin-conjugated quantum dots (Life Technologies) in motility solution were added to the flow cell. The glass flow cells were used to look for induced curvature ring formation that are rare events and need larger


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surface areas to search and capture these events. These flow cells were also used to compare the ring formation in the microfluidic device to the conventional glass flow cell setup. Microscopes & data analysis: Spool formation experiments were performed with two different microscopy systems: (1) an Olympus IX71 microscope with a 40X 0.4NA air objective, Orca3CCD camera (Hamamatsu), 25% neutral density (ND) filter, and TRITC filter set; and (2) an Olympus IX81 microscope with a 60X 1.4 NA or 100X 12NA oil immersion objective, 12% ND filter, and sCMOS camera. The microfluidic device was used with system 1, while FLIC experiments were performed with system 2. FLIC experiments: To visualize axial rotation of individual MTs, a solution of 0.1 nM sQDs was used, a concentration we determined to be too low to cause bundling. Here two different color sQDs were used: 10 nM 488 sQDs to bundle the MTs, and 0.1 nM 655 sQDs to image the rotation of bundles using fluorescence interference contrast (FLIC) microscopy.21 Special flow cells were used for FLIC experiments that consisted of a piece of Si wafer sealed to a No. 1 glass coverslip with thin double sided sticky tape, resulting in a flow cell with approximate dimensions 2 mm x 8 mm x 15 µm. A FITC excitation filter, a Cy5 emission filter, and no neutral density filter were used to image the individual sQDs in FLIC. Results and Discussion The microfluidic device described by VanDelinder et al14 and shown in Figure 2 was used in order to observe the earliest ring formation events. During an experiment, solutions from the three inlets were fed sequentially into the device. The entire device was initially filled with a solution of kinesin, followed by motility solution containing biotinylated MTs from inlet 1. The MTs were allowed to adhere to the kinesin surface, and begin motility on the glass surface of the 8 ACS Paragon Plus Environment

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imaging chamber. Next, while imaging, the valves controlling the inlets were actuated to close and stop the flow of the MT solution, and opened to introduce a solution containing streptavidinconjugated quantum dots (sQDs). Here the sQDs served as crosslinkers for the biotinylated MTs, inducing bundling and ring/spool formation, which were observed in situ using fluorescence microscopy. Additional experiments were also performed in glass flow cells, which offered a larger field to search for rare events that occurred at longer time scales, as well as confirm that self-assembly did not differ between different systems (i.e., PDMS and glass cells).

Figure 2. Schematic of the microfluidic device used to characterize the early events of active self-assembly. Insets show cartoon of ring formation process in observation region of device after introduction of solutions containing (1) 10 mM CaCl2 and 60 nM kinesin, (2) biotinylated MTs, and then (3) sQDs. Solutions are successively flowed into the observation region of the device to iterate experiments, with the Ca2+ in Inlet 1 depolymerizing the spools from the previous iteration. Devices measured 0.6 cm x 1.6 cm. Part of this figure was adapted from ref 14. Copyright 2013 American Chemical Society.


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Three distinct mechanisms of ring/spool formation were observed: pinning, collisions, and induced curvature. Time-lapse frames of representative events for each of these formation types are shown in Figure 3. Characterization of the resulting spools suggests that the inner diameter of the spool is dictated by the specific mechanism of formation. Specifically, the inner diameter corresponds to the size at the time of ring formation (nucleation phase), whereas outer diameter is determined by the number of MTs that add to the spool (growth phase). In the present work, all references to diameter are restricted to the inner diameter of spools as this parameter is correlated strongly with the initiation mechanism. The average diameter and histograms of the diameters for each mechanism are provided in Table 1 and Figure 4, respectively.

Figure 3. Time-lapse fluorescence photomicrographs showing the different mechanisms driving spool formation. (A) Pinning: spool formation in which two MTs bundle together and then form a spool when the leading tip becomes pinned. (B) Collisions: a spool is formed via collisions of multiple MTs. (C) Induced curvature: spool formation in which a bundle of MTs travel in a persistent curved trajectory until the end interact to form a closed spool. Frame interval = 10 s, and scale bar = 10 µm.


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Figure 4. Histograms of the diameter and rotational direction ( CW, CCW) of spools formed via pinning (top), collisions (middle), and induced curvature (bottom). Table 1. Properties of spools formed by various mechanisms observed in the microfluidic device and glass flow cell.

Pinning Collisions Induced curvature All rings/spools (microfluidic device) All rings/spools (flow cell)

Diameter (µ µm) 2.7 6.2 32 4.5 3.4

Standard deviation (µm) 1.5 4.8 19 4.0 3.0

Number (N) 23 23 14 46 235

CCW rotation (%) 57 74 54 65 74

The rotation direction of the spools is influenced by the axial rotation of the MT during kinesin transport, which in turn is dictated by its number of protofilaments and consequent supertwist of the tubulin lattice.22 MTs with a CCW supertwist (14 protofilaments) predominately form CCW


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rotating rings, while MTs with a CW supertwist (12 or 15 protofilaments) predominately form CW rotating rings.10, 15, 23 MTs generated in vitro have a distribution with 11-17 protofilaments depending on the polymerization protocol.22, 24 All experiments here were performed with MTs that were made by polymerizing the tubulin for 30 min in a PIPES-DMSO buffer, which has previously been shown to result in predominantly 14-protofilament MTs,19,

22

executing one

CCW axial rotation every ~8 µm of translation. We characterized the distributions of protofilaments in the MTs using FLIC microscopy.21 As measured by this method, ~52% of the MTs had fourteen protofilaments, thus displaying a CCW handedness. Approximately 40% of the MTs possessed 13 protofilaments (no pitch), while the remaining 8% of MTs possessed 15 protofilaments, displaying CW handedness. (Table S1 shows the protofilament distribution we measured versus the distributions measured by other groups following the same polymerization protocol.) Therefore, based on the protofilaments distribution of the MTs, we would expect ~72% of the rings to rotate CCW, assuming that all (52%) of 14-protofilament MTs and half (20%) of 13-protofilament MTs assembled into CCW rings. We characterized the percentage of MTs rotating in CCW direction for each type of spool formation, which is provided in Table 1. Because the initial length distribution of MTs can affect the diameter of the resultant rings,20 we measured the distribution of MT length for both the experiments in the microfluidic device and in the glass flow cell. The average length of MTs used in the microfluidic was 14 ± 12 µm (mean ± standard deviation; N = 666 MTs), while the standard deviation of average MT length across individual experimental iterations (N = 7) was 3.5 µm. Based on the lower variance among iterations, as compared within an experiment, we do not expect that observed differences in the properties of rings/spools was due to differences in the starting MT lengths. Similarly, the average length of MTs in the glass flow cell was 15 ± 27 µm (mean ± standard deviation; N = 12 ACS Paragon Plus Environment

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131 MTs). Although this length distribution is larger, the average length of MTs used in flow cell experiment was not different from those used in the microfluidic device, and thus should not have impacted the mechanism or properties of the rings/spools formed in the different systems. Active self-assembly via pinning We observe pinning both of individual MTs, resulting in rings, as well as pinning of MT bundles, resulting in spools. An example of spool formation via pinning is shown in Figure 3a and Movie S1. Here, an individual MT joins a MT bundle, and the tip of the bundle becomes pinned, causing it to loop around the pinned point and form a spool. Approximately half of the rings formed in the microfluidic device were caused by pinning, resulting in rings with the smallest average diameter (2.7 ± 1.5 µm; mean ± SD), and with a maximum diameter of 8 µm. As shown in Figure 4, the histogram of the diameters of spools formed by pinning displays a relatively narrow distribution. At the lower end, the diameter of rings formed by pinning is constrained by the radius of curvature at which MTs break, ~0.6 µm.25 It was recently proposed by Ziebert et al that, due to rearrangement of the tubulin lattice, MTs can assume a metastable curved conformation with a characteristic radius,26 which may contribute to the uniformity in the diameters arising from this mechanism. Alternatively, the size of rings formed by pinning may be determined by the average spacing between the kinesin that pins the tip of the MT and the next functioning kinesin. The surface density of the kinesin would then control the size of the rings, with on average smaller rings formed at high kinesin density (close kinesin spacing on MT) and larger rings formed at low surface density (larger spacing between kinesin on MT). This relationship (i.e., kinesin density and ring/spool diameter) was previously reported by Lam et al where the properties of spools were characterized after formation was complete.18


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As outlined in Liu et al,10 the amount of elastic energy (U) stored within a typical spool is given by ∑ = ∑ 2⁄( + ), where κ is the flexural rigidity of a MT (2.0 × 10-24 Nm2),27 a is the sum of the sQD and MT diameter (~40 nm), n is the estimated number of coils, and Di is the inner diameter of the spool. During ring formation by pinning, until the first loop is completed and the crosslinker binds the MT to itself, the elastic energy in the ring is = 2⁄ , which is 4.6 aJ (1100 kBT) for a ring with the average diameter (~2.7 µm) of those formed by pinning. A single kinesin motor protein can generate ~5pN of force per 8 nm step without stalling, which corresponds to ~4 x 10-20 J (~10 kBT) of work per step.28 A 2.7-µm diameter ring has a circumference of approximately 8.5 µm, which corresponds to 1,000 kinesin steps and ~4 x 10-17 J (~ 10,000 kBT) of work to take the steps to form such a ring. Given that multiple kinesin are bound to and translating the MT, the collective work performed by the motors is more than sufficient to produce these small diameter rings. Metastable rings formed by pinning were also observed in the absence of crosslinkers, and exemplified by the observed disassembly when the pinned tip becomes freed (see Movie S2 and 3). The addition of crosslinkers, such as the sQDs used in this system, is critical for stabilizing the actively assembled ring and spool structures. The binding constant of biotin-streptavidin is 88kJ/mol (35 kT per bond, or 0.14 aJ), which is one of the highest noncovalent ligand-receptor bonds known in biology.29 Ignoring the contribution of the kinesin motors on stabilizing the ring, the energy required to stabilize a 2.7µm diameter ring would require a minimum of 33 biotin-streptavidin bonds. However, because there are multiple streptavidin molecules on each sQD, rings may potentially be stabilized by fewer sQDs. The majority of rings formed by pinning rotated in the CCW direction (58%), which suggests that the direction of rotation was not completely random, but rather biased by the protofilament 14 ACS Paragon Plus Environment

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distribution, as previously reported.10,

15, 23

This bias in the direction of rotation has been

attributed to the kinesin following the protofilament’s axis of the MT pushing the MT in a biased direction when the leading end encounters an inhibiting point.15 The bias in the rotation direction has also been shown to be dependent on the surface density of kinesin, where the bias in direction decreases close to random at low kinesin surface density.15 This interplay between kinesin density and protofilament distribution likely resulted in the lower than expected bias (72% CCW based on protofilament distribution) observed in the present work. The rate at which MTs encountered a dead motor and self-assemble into a ring based on pinning is a stochastic process. To this point, pinning events were observed over long periods of time in glass flow cell experiments. The frequency of self-assembly via pinning may be increased by amplifying the chances of a MT encountering a dead motor, either by increasing the kinesin surface density or through photodamage or insufficient protection from oxidative damage. For example, in experiments by Lam et al,18 pinning was attributed as the primary mechanism for ring assembly, which is likely as the oxygen scavenging system used in this work is insufficient at preventing oxidative damage to the motors.14 In contrast, the use of either microfluidicdeoxygenating or inert chambers,20, 25, 26 significantly reduces damage to motors, which in turn should reduce the frequency of pinning-induced ring assembly. Active self-assembly via collisions Ring formation via collisions occurred at relatively short timescales following the addition of sQDs, and accounted for approximately half of the spool formation events observed in the microfluidic device. Assembly based on concurrent collisions involving three MTs, previously termed “simultaneous sticking,”11 was observed to form a closed triangular structure, that further


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evolved into a spool as the linear motion was translated into rotary motion (Figure 1B and 3C, Movie S4). Ring assembly induced by such collisions is most frequent when the density of MTs on the surface is high. As such, the frequency may be regulated by reducing the surface density of MTs, which in turn reduces the number of collisions and the active assembly of rings. Simultaneous sticking had been previously observed in experiments, although the fraction of spools formed by this mechanism was unknown due to its occurrence at early time points that are particularly difficult to access.11 Further, the distribution of spool diameter did not match the predictions of the simulations, with more small spools and fewer large ones observed than predicted by the simulations.11 While the formation of rings/spools via the collision of three MTs in a triangular geometry has been observed in prior work,11 a second type of collision was more commonly observed to drive the active assembly of rings and spools. These events involved a MT colliding with and transiently binding to another in such a manner that its trajectory was altered (Movie S5). The change in trajectory, in turn, resulted in interactions with its own tail and the formation of a closed ring. Unlike in a typical gliding assay in which MTs do not bind to one another, the biotinylated MTs carrying sQDs used in the present experiments renders them “sticky” and able to readily assemble upon collision. The force required to rupture a biotin-streptavidin bond is difficult to quantify as it depends on the history of the bond formation and the force loading rate. 30

At a loading rate of 0.2 pN/s, which is typical for many biological systems, 5pN of force is

sufficient to rupture biotin-streptavidin bonds.31 As such, the kinesin motors are able to pull apart MTs with sQDs following collision unless there is a sufficient number of sQDs binding a ring or bundle together.31 This metastable behavior was readily observed experimentally as MTs carrying sQDs would bind and unbind transiently.


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Collisions produced on average slightly larger spools than formed via pinning (6.2 ± 4.8 µm diameter) with a considerably wider distribution (Figure 4). Because rings formed by collisions are slightly larger than those formed by pinning, they require less work to assemble (~2 aJ or ~480 KBT per coil). Rings/spools formed via collisions also displayed a more biased rotation direction (74% CCW) than ones formed via pinning (58%), which was initially unexpected as the collisions and interactions are random. However, we hypothesize that the same impetus underlies the bias in rotation directions for both collisions and pinning. When collisions occur, one MT frequently runs into another and gets temporarily stuck, serving as an inhibiting point similar to pinning. Thus, the kinesin motors continue pushing the stuck MT in a biased direction concurrent with the supertwist of the protofilaments axis, ultimately forming a closed ring or spool. Active self-assembly via induced curvature In addition to spools, we observed curved, but not completely closed bundles that followed circular trajectories (Movie S6). This phenomenon, which we refer to as “induced curvature,” can lead to spool formation. Specifically, when the curved bundles were not long enough for the head to meet the tail and close, the bundle followed a persistent circular trajectory despite not forming a closed spool. If, however, the bundle was long enough with respect to the circular trajectory, the ends would interact to close the structure and form a spool (Movie S7). The formation of spools via induced curvature was problematic to observe directly due to the relative rarity of such events, as well as the longer timescale at which this formation mechanism occurs. Despite these difficulties, fourteen closing events were observed, one of which is shown in Figure 3c. The average diameter of spools formed by induced curvature was 32 ± 19 µm (Figure 4), considerably larger and with the widest distribution. The large diameter spools (>26 µm 17 ACS Paragon Plus Environment

Biomacromolecules

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diameter) were only assembled via induced curvature. The elastic energy stored in a 32-µm spool is ~0.39 aJ (90 KBT) per coil. Of the spools observed to form via induced curvature, 54% rotated CCW, which was a smaller bias than that observed for pinning and collisions, as well as reported in previous work.19 Further considering spool assembly via induced curvature, the question arises as to the source of the strain that induces the curved path of motion. Two mechanisms, twist-bend coupling and tip collisions/frozen-in curvature (see Figure 1), have been proposed and may explain how such strain arises within these bundles. In twist-bend coupling, the supertwist of the individual MTs causes the bundle to rotate about the MT axes as they translate along the surface. As MTs are crosslinked together into bundles, axial rotation of the bundle may lead to the formation of coiled-coil domains; such structures have been observed by scanning transmission electron microscopy.10 Rotation of these domains may result in the formation of strain, similar to twisting of laid rope, which may in turn result in a persistent curvature, enabling head-to-tail closure of a ring structure.10,

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Alternatively, with frozen-in curvature, two MTs may become crosslinked

together in a curved configuration with different arclength between the crosslinking points.11 Luria et al. called this “tip collisions” and assumed that the difference in arclengths between the pinned tip and the next pinned point is due to a mismatch in velocity of the MTs during the collision, which according to their calculations would result in rings with much smaller diameter than were actually observed experimentally.11 The tip collisions mechanism is similar to the one proposed for spool formation of actin filaments driven by surface bound myosin motors and crosslinked together by the protein fascin.32 In that system, Schaller et al. observe that actin bundles that are not fully closed into spools are curved and travel in persistent circular trajectories. They further conclude that these bundles have had the curvature “frozen in” when


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Biomacromolecules

the actin filaments are crosslinked together in a curved configuration, although they do not stipulate that the tip must be one of the pinned points as was hypothesized for the tip collisions mechanism.32 To discern which of these hypotheses is responsible for the induced curvature mechanism, we examined the bundle precursors by characterizing their curvature and rotation. Using FLIC, the axial rotation of individual MTs (Figure S1a) was easily observable, as previously reported.21 If twist-bend coupling was occurring, axial rotation of the bundles, leading to coiling within the bundle, would have been expected. However, while some bundles appeared to rotate axially (

Mechanisms Underlying the Active Self-Assembly of Microtubule

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