Author response: Working strokes produced by curling protofilaments at disassembling microtubule tips can be biochemically tuned and vary with species

Abstract

Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract The disassembly of microtubules can generate force and drive intracellular motility. During mitosis, for example, chromosomes remain persistently attached via kinetochores to the tips of disassembling microtubules, which pull the sister chromatids apart. According to the conformational wave hypothesis, such force generation requires that protofilaments curl outward from the disassembling tips to exert pulling force directly on kinetochores. Rigorously testing this idea will require modifying the mechanical and energetic properties of curling protofilaments, but no way to do so has yet been described. Here, by direct measurement of working strokes generated in vitro by curling protofilaments, we show that their mechanical energy output can be increased by adding magnesium, and that yeast microtubules generate larger and more energetic working strokes than bovine microtubules. Both the magnesium and species-dependent increases in work output can be explained by lengthening the protofilament curls, without any change in their bending stiffness or intrinsic curvature. These observations demonstrate how work output from curling protofilaments can be tuned and suggest evolutionary conservation of the amount of curvature strain energy stored in the microtubule lattice. Editor's evaluation This important and technically sophisticated work advances our understanding of force production by depolymerizing microtubules with implications for the generation of forces that segregate chromosomes during cell division. The authors present compelling evidence for their mechanistic conclusions. This work will be of interest for cell biologists and biophysicists interested in cell division and force production by biopolymers. https://doi.org/10.7554/eLife.83225.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest Dividing cells duplicate their genetic information to create identical pairs of chromosomes, which then need to be equally distributed to the two future daughter cells. In preparation, each chromosome in a pair is pulled towards its final location by hollow tubes of proteins known as microtubules. To create this tugging force, the microtubule acts like a winch: the extremity attached to the chromosome gradually shortens by losing its building blocks. However, it is not clear how the microtubule can keep its grip on the chromosome while also ‘falling apart’ in this way. A possible explanation could stem from the way that microtubules are built, and from how they fall apart. Each tube is composed of rows of building blocks, called ‘protofilaments’. As the microtubule shortens, the protofilaments first curl outwards before crumbling apart; this creates a curling action that could ‘hook’ the chromosome and pull on it as the microtubule shortens. This theory remains difficult to test however, in part because scientists lack ways to alter the properties of curling protofilaments in order to dissect how they work. Murray et al. aimed to fill that gap by using a technique they have previously developed, and which allows them to capture how much force curling protofilaments can apply on their environment. This approach uses an instrument known as laser tweezers to measure the pressure that microtubules exert on attached beads. With this assay, Murray et al. were able to investigate whether microtubule ‘strength’ is linked to protofilament length, a property that varies between species and in response to magnesium. The experiments revealed that adding magnesium not only lengthens protofilament curls but also increases the work generated from curling. In addition, they showed that yeast protofilaments create longer curls with more force compared to bovine microtubules. Together, these findings demonstrate that it is possible to fine-tune the force exerted by protofilaments on their environment by controlling their length. This knowledge could be helpful to scientists investigating the role of microtubules in cell division. Certain cancer drugs already target microtubules in order to stop rogue cells from multiplying. However, serious side-effects often emerge because these compounds also interfere with microtubule-based processes essential for healthy cells. By better understanding how protofilaments ‘pull’ on chromosomes, it may become possible to design targeted approaches to stop cell division but preserve the other fundamental roles that microtubules play in the body. Introduction Microtubules are filamentous polymers central to the active transport of cargoes in cells. While they often serve as passive tracks along which dynein and kinesin motors move, these filaments can also drive motility directly. Dynamic microtubules in the mitotic spindle transport chromosomes during cell division by shortening while their disassembling tips remain coupled via kinetochores to the chromosomes (Desai and Mitchison, 1997; Inoué and Salmon, 1995; McIntosh et al., 2010). Dynamic microtubules also generate force to properly position the mitotic spindle and the nucleus within cells (Carminati and Stearns, 1997; Dogterom et al., 2005; Kozlowski et al., 2007; McIntosh et al., 2010; Nguyen-Ngoc et al., 2007). These microtubule-driven movements are powered by GTP hydrolysis. GTP is incorporated into the assembling polymer tip and then hydrolyzed, depositing energy into the GDP-tubulin lattice. The stored lattice energy is released during disassembly and can be harnessed to generate pulling force. Thus microtubules, like dynein and kinesin motors, convert chemical energy into mechanical work (McIntosh et al., 2010). How they do so remains poorly understood. Two distinct classes of mechanism could explain how disassembling microtubule tips generate pulling force: the biased diffusion and conformational wave mechanisms (Asbury et al., 2011). According to biased diffusion-based models, a tip-coupler such as the kinetochore undergoes a thermally driven random walk along the microtubule surface that is biased at the tip, due to the affinity of the coupler for the microtubule. If the affinity of the coupler for the microtubule is sufficiently high and if its diffusion is sufficiently fast, then the coupler can remain persistently associated with the disassembling tip, where it will experience a thermodynamic force in the direction of disassembly (Hill, 1985). The effect is analogous to capillary action that pulls fluids into narrow channels. Biased diffusion of a key kinetochore element, the Ndc80 complex, has been observed directly on microtubules in vitro (Powers et al., 2009). By contrast, force generation in conformational wave-based models depends on structural changes at disassembling microtubule tips. During disassembly, individual rows of tubulin dimers called protofilaments curl outward from the tip before breaking apart, creating a wave of conformational change that propagates down the long axis of the microtubule (Kirschner et al., 1974; Mandelkow and Mandelkow, 1985). These curling protofilaments are proposed to physically hook the kinetochore and pull against it to drive motility (Koshland et al., 1988). Prior work showed that the amount of mechanical strain energy released by curling protofilaments is more than sufficient to account for kinetochore motility (Driver et al., 2017). However, whether kinetochores specifically harness any of this strain energy remains unclear, owing in part to the lack of methods for modifying mechanical or energetic properties of protofilament curls. Many prior studies have established that added magnesium profoundly affects the dynamics of microtubules in vitro, altering the rates of switching between tip growth and shortening (O’Brien et al., 1990), accelerating tip disassembly (Martin et al., 1987), and lengthening the protofilament curls at disassembling tips (Mandelkow et al., 1991). Binding of magnesium to acidic residues in the disordered C-terminal tail of tubulin is implicated in magnesium-dependent acceleration of disassembly (Fees and Moore, 2018; Sackett et al., 1985; Serrano et al., 1984a; Weisenberg, 1972). Faster disassembly by itself might explain why magnesium also lengthens protofilament curls, because it implies a faster rate of curling (i.e. that GDP-tubulins are losing their lateral bonds and curling outward more quickly; Tran et al., 1997). However, magnesium might also stabilize the longitudinal bonds within protofilament curls, thereby reducing the rate at which the curls break. To disentangle magnesium’s effects on curling and breakage rates, a systematic examination of curl contour length as a function of disassembly speed is required. Previously, we developed an assay for measuring forces and displacements generated by curling protofilaments (Driver et al., 2017) based on earlier pioneering work (Grishchuk et al., 2005). In our ‘wave’ assay, the curling protofilaments push laterally against a microbead tethered to the microtubule wall, thereby generating a brief pulse of bead motion against the force of a feedback-controlled laser trap. We show here that the sizes of these pulses – and the mechanical work energy that can be harnessed from them – are substantially increased by the addition of millimolar levels of magnesium. By measuring wave pulses after proteolytic cleavage of the β-tubulin C-terminal tail, we show that magnesium enlarges the pulses independently of its acceleration of disassembly, indicating that magnesium directly stabilizes the longitudinal bonds within protofilament curls. We also demonstrate that pulses generated by yeast tubulin are larger than those generated by bovine brain tubulin. A simple mechanical model shows that both the magnesium- and species-dependent changes in pulse energy can be explained solely by increasing the contour lengths of protofilament curls, without changing their intrinsic flexural rigidity or curvature. The conservation of protofilament flexural rigidity and stored lattice strain suggest that these biophysical properties are crucial to microtubule function in cells. Results Measuring outward curling of protofilaments from bovine brain microtubules We previously measured the mechanical and energetic properties of protofilaments as they curled outward from recombinant yeast-tubulin microtubules (Driver et al., 2017). In our wave assay, a laser trap applies force against the curling protofilaments, via beads tethered to the microtubule lattice through a single His6 tag on the C-terminus of β-tubulin (Johnson et al., 2011). Linkage through a single β-tubulin C-terminal tail creates a strong, flexible tether approximately 36 nm in length, which probably helps to avoid interference between the tethered bead and the curling protofilaments (Driver et al., 2017). To extend our approach to untagged mammalian brain tubulin, we modified the assay by introducing anti-His beads pre-decorated sparsely with the recombinant His6-tagged yeast tubulin into chambers containing coverslip-anchored microtubules growing from free bovine brain tubulin. The decoration density of yeast tubulin on the beads was kept very low, around one tubulin per bead, by limiting the amount of anti-His antibody on the beads (see Materials and methods). The bead-linked yeast tubulin was incorporated into the assembling bovine microtubules, resulting in beads tethered to the sides of the filaments (Murray et al., 2022; Figure 1a). As in our previous work (Driver et al., 2017), the low density of antibody on the beads ensured that most beads were tethered by a single antibody. Continuous tension, directed toward the plus end, was applied to a microtubule-tethered bead using feedback control. The tension pressed the bead against the microtubule lattice at a secondary contact point and suppressed Brownian motion, which facilitated tracking the bead with high spatiotemporal resolution. The microtubule plus end was then severed with laser scissors to induce disassembly (Franck et al., 2010). As the disassembling tip passed the secondary contact point, protofilament curls pushed laterally on the bead, causing it to rotate about its tether. This rotation produced a brief (100–400 ms) pulse of bead movement against the force of the laser trap, which was followed by bead detachment after further disassembly released the tether (Figure 1b). The pulses were parameterized by their amplitude relative to the baseline bead position (Figure 1—figure supplement 1), which is directly related to the lateral height that the protofilament curls project from the surface of the microtubule lattice (Figure 1—figure supplement 2) (Driver et al., 2017). Figure 1 with 2 supplements see all Download asset Open asset Measuring pulses of movement generated by protofilaments curling outward from the tips of disassembling bovine microtubules. (a) Schematic of the wave assay: a bead is tethered to the microtubule lattice via an engineered tether composed of recombinant His6-tagged yeast tubulin, a biotinylated anti-penta-His antibody, and streptavidin. Tethering by a single anti-penta-His antibody is ensured by keeping the density of antibodies on the beads very low. Using a laser trap, the bead is tensioned toward the (+)-end, pressing it against the microtubule lattice at a secondary contact point. The stabilizing GTP cap is trimmed off the microtubule with laser scissors to initiate disassembly. Curling protofilaments at the disassembling microtubule tip form a conformational wave that pushes laterally on the bead, causing it to rock back about its tether. This rocking action produces a pulse of bead movement against the force of the laser trap. (b) Records of force (black) and bead position (red) versus time for three different bead-microtubule pairs. As the trapping force on the bead was increased, pulse heights decreased, consistent with spring-like behavior of the protofilament curls. At 2 pN of trapping force, 59% of disassembly events yielded measurable pulses, with a mean amplitude of 19.2±2.7 nm. At higher forces, pulse amplitudes became smaller (Figure 1b), consistent with spring-like elasticity of the curling protofilaments, as we previously observed for yeast tubulin protofilament curls (Driver et al., 2017). Pulse amplitudes generated by bovine microtubules were smaller than those we measured previously from yeast microtubules at identical force levels (e.g. 19.2±2.7 vs 51±7 nm on average at 2 pN) (Driver et al., 2017). This observation suggests that bovine protofilament curls might be shorter than yeast curls, consistent with reports that disassembly products released from mammalian brain microtubules are shorter than their yeast-derived counterparts (Howes et al., 2018). Nevertheless, our findings confirm that pulses from bovine microtubules can be reliably measured using our modified wave assay. Adding magnesium enlarges the pulses generated by curling protofilaments Divalent cations have long been known to affect tubulin self-association (Nogales et al., 1995; Olmsted and Borisy, 1975; Weisenberg, 1972) and influence microtubule dynamics (Rosenfeld et al., 1976; Weisenberg, 1972). These effects occur partly through interactions of magnesium ions with the unstructured C-terminal tails of tubulin (Fees and Moore, 2018; Serrano et al., 1984b) and with the exchangeable and non-exchangeable nucleotide binding sites (Lee and Timasheff, 1975). Early cryo-electron microscopy of disassembling microtubules showed that magnesium lengthens protofilament curls at disassembling tips (Mandelkow et al., 1991). Based on these prior observations, we predicted that pulses recorded in our wave assay might become larger and more energetic with added magnesium. As previously observed (Fees and Moore, 2018), we found that adding magnesium accelerated the disassembly of bovine brain tubulin microtubules, increasing their shortening speeds by about threefold, from 380±36 nm∙s–1 at our initial level of 1 mM magnesium to 1200±40 nm∙s–1 at 20 mM magnesium (Figure 2a and b). Consistent with our prediction, adding magnesium also increased the amplitudes of pulses measured in the wave assay (Figure 2c). At 2 pN of trapping force, the mean amplitude increased by 50% from 19.2±2.7 nm at 1 mM magnesium up to 29.1±2.8 nm at 20 mM magnesium (Figure 2d). This magnesium-dependent increase in pulse amplitude might be explained simply by lengthening the protofilament curls, as suggested by early cryo-electron microscopy studies. However, it might also reflect increases in the mechanical stiffness or curvature of the protofilaments, or in the number of protofilaments that push against the bead in the wave assay (as discussed below). Figure 2 Download asset Open asset Added magnesium increases disassembly speed and pulse amplitude. (a) Time-lapse differential interference contrast images of individual microtubules disassembling in the presence of 1 or 12 mM magnesium. Arrowheads (red) indicate locations of disassembling tips. (b) Mean disassembly speed plotted against magnesium concentration. Error bars represent 95% confidence intervals, defined as ± (t∙SEM), where t is drawn from Student’s t-distribution (with ν=N – 1 degrees of freedom and N=34–51 samples per mean). (c) Records of force (black) and bead position (red) versus time for four bead-microtubule pairs, at two different magnesium concentrations. Pulse amplitudes were larger at the higher magnesium level. (d) Mean pulse amplitudes across four different magnesium concentrations, 1, 6, 12, and 20 mM. Error bars represent 95% confidence intervals (defined as in (b), with ν=N – 1 degrees of freedom and N=25–40 samples per mean). Data in (c) and (d) were collected at 2 pN trap force. Figure 2—source data 1 Individual pulse amplitudes and disassembly speeds measured using bovine microtubules across different magnesium levels. These source data are provided in an excel spreadsheet. https://cdn.elifesciences.org/articles/83225/elife-83225-fig2-data1-v1.xlsx Download elife-83225-fig2-data1-v1.xlsx Adding magnesium increases work output from protofilament curls To determine whether adding magnesium affects the mechanochemical work output from curling protofilaments, we measured pulse amplitudes across a variety of trapping forces and magnesium concentrations (Figure 3 and Figure 3—figure supplement 1). Measuring pulse amplitude as a function of force enables estimation of the total capacity for mechanical work output in the assay, which is given by the area under the amplitude vs force curve (Figure 3a; Driver et al., 2017). Based on a line fit to the data, we estimated work output from the bovine brain microtubules in 1 mM magnesium at 107±69 pN·nm (Figure 3b). Adding magnesium increased the work output monotonically, raising it to 177±0.1 pN·nm at 20 mM magnesium (Figure 3b). This magnesium-induced increase was mainly due to enlargement of the pulses measured at low trapping force; extrapolating the line fits to zero force suggested that the unloaded pulse amplitude (i.e. the amplitude that would be measured in the absence of opposing trap force) increased 57% from 23.3±0.9 nm at 1 mM magnesium to 36.6±0.1 nm at 20 mM magnesium (Figure 3c). By contrast, extrapolating the linear fits to higher forces suggested relatively little change in the maximum force at which the pulses were completely suppressed (~9 pN) (Figure 3a). Altogether, these observations show that magnesium increases mechanical work output from curling protofilaments while also increasing the lateral height that they project from the microtubule wall. Figure 3 with 2 supplements see all Download asset Open asset Magnesium increases the mechanical work output harnessed from curling protofilaments. (a) Mean pulse amplitudes (black squares) plotted against trapping force at the four indicated magnesium concentrations. Error bars represent 95% confidence intervals, defined as ± (t∙SEM), where t is drawn from Student’s t-distribution (with ν=N – 1 degrees of freedom and N=9–43 samples per mean). The capacity of protofilament curls to perform mechanical work in the assay was estimated at each magnesium concentration by fitting the amplitude versus force data with a line and then calculating the area under the line (colored triangular areas). To estimate unloaded pulse amplitudes, the line-fits were extrapolated to the y-intercept (open circles). (b) Mechanical work output, based on the colored areas shown in (a), plotted against magnesium concentration. Error bars represent 95% confidence intervals (estimated from the best-fit parameters, as explained in Materials and methods). (c) Unloaded amplitudes, based on extrapolation of the line-fits in (a), plotted versus magnesium concentration. Error bars represent 95% confidence intervals (estimated as explained in Materials and methods). Figure 3—source data 1 Individual pulse amplitudes measured using bovine microtubules across different trapping forces and magnesium levels. These source data are provided in an excel spreadsheet. https://cdn.elifesciences.org/articles/83225/elife-83225-fig3-data1-v1.xlsx Download elife-83225-fig3-data1-v1.xlsx Notably, the mechanical work output from bovine microtubules was about threefold less than we measured previously from microtubules composed entirely of recombinant yeast tubulin under similar conditions (~300 pN·nm at 1 mM magnesium) (Driver et al., 2017). This difference, like magnesium-dependent differences, could reflect altered contour lengths, bending stiffnesses, average curvatures, numbers of curling protofilaments pushing on the beads, or a combination thereof. Curl elongation alone explains the magnesium-dependent increase in work output To develop a deeper understanding of how magnesium increases the mechanical work output from curling protofilaments, we created a simple model of protofilament bending. The model relates structural aspects of protofilament curls, such as their relaxed curvature and the average number of dimers they contain, together with an estimate of their flexural rigidity, to predict the force-deflection behavior of a group of curls projecting radially outward from a microtubule tip. In real protofilaments, elastic bending energy can be distributed throughout the α- and β-tubulin core structures, as well as at both the inter- and intra-dimer interfaces. Rather than modeling this complexity, we placed all the compliance of the model into single bending springs located at the inter-dimer interfaces (Figure 4a). This simplification was important for our analyses, because it allowed data-fitting to provide good constraints on the model parameter values. (A model with more parameters would fit the data just as well or better but would not allow meaningful estimation of parameter values, due to degeneracy.) And while our model cannot address in detail how strain might be distributed across the inter- and intra-dimer interfaces (nor across the α- and β-tubulin core structures), it can describe the overall force-deflection behavior of protofilament curls, and it provides a simple way to estimate stored strain per dimer. In essence, our model convolves all the potential contributions to elastic bending strain together into a single element (an inter-dimer spring) that provides an effective flexural rigidity per dimer. Figure 4 with 5 supplements see all Download asset Open asset Magnesium- and species-dependent increases in work output can be explained solely by a lengthening of protofilament curls. (a) Model for bending of a single protofilament. Tubulin dimers are represented as rigid rods linked by Hookean torsion springs with relaxed angles of 23°. An external force, F, perpendicular to the microtubule long-axis, is applied at the protofilament tip. The balance between F and the torsion at each bending node, τn, is used to calculate the contour shape of the protofilament (i.e. the angles θn). (b) Calculated shapes for a single protofilament at different levels of external force (indicated by the color legend). Model for deflection of multiple protofilaments at a microtubule tip, seen end-on. Single protofilaments, modeled as in (a), are arranged radially according to the geometry of a 13-protofilament microtubule. The bead is modeled as a flat rigid surface, pushed downward onto the protofilaments to predict a force-deflection relationship. Cartoon at right shows distribution of protofilament deflections for an arbitrary bead height. (c) Amplitude versus force curves predicted by the multi-protofilament model, after fitting to measured pulse data (symbols) at indicated magnesium concentrations. Bovine data are recopied from Figure 3a. Yeast data combine new measurements with data previously published in Driver et al., 2017. (d) Two fitted parameters, the mean contour length and bending stiffness (flexural rigidity) of protofilament curls, plotted versus magnesium concentration. The fitted contour length increases with added magnesium and is larger for yeast microtubules, while the apparent flexural rigidity remains unchanged. Figure 4—source data 1 Individual pulse amplitudes measured using yeast and bovine microtubules across different trapping forces and magnesium levels. These source data are provided in an excel spreadsheet. https://cdn.elifesciences.org/articles/83225/elife-83225-fig4-data1-v1.xlsx Download elife-83225-fig4-data1-v1.xlsx Figure 4—source data 2 Table of estimates of protofilament curvature reported in the literature. Each row is colored to reflect the method used to estimate protofilament curvature. https://cdn.elifesciences.org/articles/83225/elife-83225-fig4-data2-v1.docx Download elife-83225-fig4-data2-v1.docx Contour shapes for the individual protofilaments were solved by balancing the external force applied at their tips with the opposing bending spring torques at each inter-dimer node (Figure 4b, left). To model the force-deflection behavior of a group of protofilaments, single protofilaments were arranged radially, according to a 13-protofilament geometry (Figure 4b, right) (Amos and Klug, 1974). The bead was modeled as a rigid, flat surface since its curvature is negligible compared to that of the microtubule tip. Prior cryo-electron tomography studies of disassembling microtubules found almost all the variation in protofilament shape to occur in the radial direction (i.e. within a plane coincident with both the relaxed contour and the long axis of the microtubule) (McIntosh et al., 2018). Therefore, protofilament bending in our model was limited to the radial direction. Given these assumptions, deflection of individual protofilaments varied according to their orientation relative to the bead surface (Figure 4b, right). A detailed analysis of changes in the force-deflection profile that occur with respect to changes in the average curvature, average dimers per curl, and flexural rigidity is shown in the supplemental material (Figure 4—figure supplement 1). To fit the behavior of this multi-protofilament model to the measured pulse amplitude versus force data at each magnesium concentration, we adjusted the average number of dimers in each curl (i.e. the curl contour length) and the stiffness of the bending springs. We kept the relaxed angle per dimer fixed at 23° because, in the absence of microtubule-associated proteins, the curvature of protofilaments at microtubule tips disassembling in vitro is consistently between 20 and 25° per dimer (Figure 4—source data 2), and this curvature does not change appreciably with added magnesium (Figure 4—figure supplement 2; Mandelkow et al., 1991) (nor with added calcium; Müller-Reichert et al., 1998). Because the bead acts as a lever, measured axial displacements of the bead are larger than the lateral deflections of the protofilaments by a leverage factor of approximately twofold (Figure 1—figure supplement 2; Driver et al., 2017). Predicted amplitude vs force curves were roughly linear, but with slight ‘ripples’ that occurred because movement of the bead toward the microtubule gradually engaged more protofilaments (Figure 4c; Figure 4—figure supplement 3; see Materials and methods for details). Optimal fit parameters are plotted as functions of magnesium in Figure 4d. The fitted contour lengths of protofilaments increased monotonically with added magnesium, from 2.3±0.5 dimers at 1 mM magnesium to 3.2±0.2 dimers at 20 mM. However, the fitted bending stiffness per dimer, 176±15 pN∙nm∙rad–1, did not appreciably change with added magnesium (Figure 4d). These results suggest that magnesium increases pulse amplitude and work output by lengthening the protofilament curls, without eliciting any change in their intrinsic stiffness or curvature. Curl elongation alone explains the larger pulses from yeast microtubules To understand why yeast microtubules generated larger, more energetic pulses relative to bovine microtubules, we fit our multi-protofilament model to the amplitude versus force data measured from microtubules composed entirely of recombinant yeast tubulin (Figure 4c). As in our analysis of the bovine microtubule data, we allowed both the curl contour length and the stiffness of the bending springs to vary while keeping the relaxed angle per dimer fixed at 23°, consistent with cryo-electron tomograms of kinetochore microtubules in yeast (McIntosh et al., 2018). The contour length that best fit the yeast data, 4.4±0.5 dimers per curl, was 1.9-fold higher than the contour length inferred at identical magnesium concentration (1 mM) from the bovine data, 2.3±0.5 dimers p