Structure and dynamics of motor-driven microtubule bundles

Connecting the large-scale emergent behaviors of active cytoskeletal materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems. We approach this problem by studying the impact of depletion attraction on bundles of microtubules and kinesin-14 molecular motors. For all depletant concentrations, kinesin-14 bundles generate comparable extensile dynamics. However, this invariable mesoscopic behavior masks the transition in the microscopic motion of microtubules. Specifically, with increasing attraction, we observe a transition from bi-directional sliding with extension to pure extension with no sliding. Small-angle X-ray scattering shows that the transition in microtubule dynamics is concurrent with a structural rearrangement of microtubules from an open hexagonal to a compressed rectangular lattice. These results demonstrate that bundles of microtubules and molecular motors can display the same mesoscopic extensile behaviors despite having different internal structures and microscopic dynamics. They provide essential information for developing multiscale models of active matter.

Connecting the large-scale emergent behaviors of active materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems.We approach this problem by studying the impact of polyethylene glycol, a crowding agent, on bundles of microtubules and kinesin-14 molecular motors.Bundles assembled in the presence of either low or high concentrations of polyethylene glycol generate similar net extensile behaviors.However, as polyethylene glycol concentration is increased, the motion of microtubules in the bundles transition from bi-directional sliding with extension to pure extension with no sliding.Small-angle X-ray scattering shows that the transition in microtubule dynamics is concomitant with a rearrangement of microtubules in the bundles from an open hexagonal to a compressed rectangular lattice.These results demonstrate that bundles of microtubules and molecular motors can display similar mesoscopic extensile behaviors despite having very different internal structures and dynamics.
Experiments measuring the relative speed between two microtubules within a single bundle or a nematic domain have revealed two distinct types of microscopic dynamics.Two-dimensional active nematics driven by kinesin-1 clusters displayed a broad unimodal distribution of relative velocities.These microtubule velocities were significantly slower than those of unloaded motors [21].In comparison, bundles of aligned microtubules driven by kinesin-14 displayed a bi-modal sharply peaked distribution of velocities, with antiparallel populations of microtubules sliding apart at the speed of the unloaded molecular motor [17].
Intriguingly, both systems can produce extensile stresses, generating turbulent-like flows.In addition to * These authors contributed equally being powered by different kinesin motors, the two systems differ by the presence of polyethylene glycol (PEG) in kinesin-1 active-nematics and its absence in kinesin-14 bundles.PEG is a crowding/depletion agent that induces an effective attraction between microtubules and can even alter their structure [22][23][24].
To gain insight into the microscale dynamics of active bundles, we studied how PEG concentration influences the internal dynamics and microscopic structure of extensile microtubule bundles powered by kinesin-14.We found that increasing the concentration of PEG induces a transition in the motions of microtubules inside the bundles.Small-Angle X-ray Scattering (SAXS) of microtubule bundles demonstrates that the dynamical transition in the microscopic filament motion is correlated with a structural transition from open hexagonal to tight rectangular packing.
We studied the dynamics of microtubule sliding in bundles driven by kinesin-14 (XCTK2).Kinesin-14 is a minus-end directed dimeric molecular motor that contains a C-terminus motor domain and a passive microtubule-binding N-terminus [25,26].Kinesin-14 crosslinks microtubules and induces their relative sliding [27,28].When we combined kinesin-14 (200 nM) with GMPcPP stabilized microtubules (16 µM), the microtubules coarsened into bundles [Fig.1(a-c  ever, these other systems contained bundling agents in addition to molecular motors.In contrast, kinesin-14 can yield microtubule bundles without a supplemental bundling agent. To visualize the motion of individual filaments, we created bundles with kinesin-14 (and no PEG) in which 1 in 10,000 microtubules were labeled [Fig.1(d-e)].Within a bundle, individual microtubules exhibited pronounced and sustained motion along the bundle's long axis.Furthermore, individual filaments hardly ever changed direction, and the bundle exhibited net extensile motion [Fig.1(e), Vid.2].We next made kinesin-14 bundles with the addition of 1% w/w PEG and found a similar net bundle extension [Fig.1(g), Vid.1].However, in the presence of PEG, individual microtubules exhibited markedly different dynamics with reduced speeds and a stuttering motion in which microtubules changed direction [Fig.1(f-i), Vid.2].Thus, while both systems produced similar net bundle extension, the microscopic filament dynamics were quite distinct, with and without PEG.
To quantify the dynamics of these two regimes, we photo-bleached two stripes several microns apart and perpendicular to the bundle's long axis [Fig.2(a-b), Vid.3].In a sample with 0% PEG, each bleached region split into two lines that moved in opposite directions along the bundle's long axis [Fig.2(c-d)].These data are consistent with the observation of sparsely labeled microtubules sliding continuously without changing direction [Fig.1].In contrast, the two bleached regions in 1% PEG bundles slowly moved apart from each other without splitting [Fig.2(e-f)].
We next analyzed space-time plots (i.e.kymographs) to quantify the dynamics of the bleach patterns [Fig.2(cf)].We defined L split as the distance between the two peaks which evolve from each bleach mark, while L cen is the distance between the center of masses of the two different bleach marks [Fig.2(g)].In the cases where the bleach marks split, we calculated the center of mass by weighing the two splitting marks I 1 and I 2 by their intensity such that L cen = I1L1+I2L2 I1+I2 .On the timescales probed, both L split and L cen increased linearly in time [Fig.2(h), top].Thus, we calculated V split , which is the speed at which microtubules in one marked region slide relative to their neighbors, and V cen , which is the extension speed of the bundle between the two marked regions for a given lateral spacing [Fig. 2

(h), bottom].
To quantify the transition between the splitting and blurring regimes, we made samples with a range of PEG concentrations.For all samples, we measured L cen , and where possible, L split .The average extensile speed of the system V cen gradually decreased from ∼8.8 nm/s at 0% PEG to ∼4.5 nm/s at 1% PEG [Fig.2(i)].The splitting speed V split ranged between ∼45 nm/s at 0% PEG and ∼30 nm/s at 0.3% PEG [Fig.2(j)].Between 0.15% and 0.4% PEG, only a fraction of microtubule bundles within a sample displayed splitting of the bleached lines.At 0.3% PEG, roughly 2/3 of bundles had splitting dynamics, while at 0.4% PEG, only 1/5 of bundles had splitting dynamics [Fig.2(j), inset].At these intermediate PEG concentrations, some bleach lines partially split while leaving behind a third fainter line, suggesting a coexistence of the two dynamic regimes [Vid. 3].
Bleaching experiments demonstrate the existence of two dynamical regimes with changing PEG concentration.To gain further insight into the differences between these regimes, we next used Small Angle X-ray Scattering (SAXS) to measure the structure of the bundles.The SAXS scattering curves of samples with and without PEG were notably different, suggesting that the introduction of PEG changed the organization of microtubules in the bundles [Fig.3(a)].To understand the change of the SAXS curves, we modeled the scattering amplitude of various microtubule bundle packing configurations using a numerical solver that computes X-ray scattering curves of basic filamentous structures distributed in random orientations [30].We generated several microtubule packing configurations with variable spacing and microtubule number (SI).At PEG, in the of kinesin-14, we found that models of hexagonal lattices with a center-to-center spacing of L h = ± 5 nm closely match the experimental scattering curve [Fig.3(b)].In comparison, at 1% PEG, in the presence of kinesin-14, the scattering curves are consistent with a model of microtubules with an ellipti-cal cross-section close packing in a rectangular lattice (L a = 13.6 nm, L b = 10.1 [Fig.3(d)].The SAXS curves between the 0% PEG and 1% PEG concentrations can be modeled as a coexistence of the hexagonal and rectangular lattice patterns [Fig.3(c)].The anisotropic compression of the microtubule and the formation of a rectangular lattice have been observed previously in passive bundles [31].The matching model uses a small number (< 10) of microtubules in both rectangular and hexagonal phases.The broad shape of the peaks and the correspondingly small number of microtubules in the lattice models suggest that the filament packing has short-range order at both concentrations.
In this work, we showed that motor-driven microtubule bundles can exhibit similar large-scale extension despite having very different internal structures and dynamics.Our experiments also highlight the difference between filament sliding and bundle extension.Hypothetically, it is possible to have a bundle in which filaments slide apart from each other without generating any material extension within the bundle.In such a bundle, half the filaments move leftward (velocity −V ) and the other half rightward (velocity +V ).As a consequence the two bleach lines would each split in two (with V split = 2V ) but their centers of mass would remain constant (V CoM = 0) [Fig.4(a)].In contrast, bleaching two lines in a purely extending bundle, which had no additional filament sliding, would result in the relative motion of the center of masses of the marked regions (V CoM = 0) with no line splitting [Fig.4(b)].The velocities of filaments in such a bundle would be telescoping exponentially outwards from all locations.
Without PEG, the microtubule bundles display both sliding and extending dynamics.This regime has a local hexagonal packing structure with significant space in between the microtubules that are roughly comparable to the kinesin size [Fig.4(c)].Above a threshold PEG concentration, the packing structure becomes rectangular with no significant space between the microtubules.The system exhibits extensile dynamics but with no further sliding [Fig.4(d)].This exstensile dynamics, with no additional sliding, is reminiscent of observations in dense 2D active nematics driven by streptavidin-kinesin-1 clusters [21].These 2D active nematics experiments explicitly showed that the extension velocity increases exponentially along the director.A similar exponential extension presumably exists in the kinesin-14 bundles studied here even though the dynamics appeared linear [Fig.2(h)], likely because an exponential measured over a short time is well approximated as being linear.
Understanding the large-scale dynamics of cytoskeletal active matter has emerged as an important and extensively studied research theme.In comparison, relatively little is known about the microscopic structure of basic units that power these large-scale non-equilibrium behaviors.Our work provides structural insight into extensile microtubule bundles, which drive diverse forms of microtubule-based active matter.However, this work is only the first step, as the microscopic arrangement of kinesin-14 within a microtubule bundle remains unknown.The tight rectangular lattice suggests a lack of space for the kinesin motors between microtubules.One possibility is that kinesin is excluded from the bundle interior and can only bind to and power the motion of surface-bound microtubules.Alternatively, kinesin binding within the bundle interior would require the formation of highly localized filament deformations.These questions, which require alternative experimental methods such as electron microscopy, must be addressed before a complete multiscale understanding of microtubulebased active matter emerges.

FIG. 1 .
FIG. 1. PEG alters the microtubule motions within extensile bundles formed with kinesin-14.(a-b) Microtubule bundles powered by kinesin-14, without PEG, in a thin chamber.A cyan arrow indicates kinesin motion, and a grey arrow indicates microtubule motion.(c) A time sequence of a PEG-free kinesin-14/microtubule bundle extending and buckling.(d) Time sequence of an extending bundle with yellow tracer microtubules.The initial frame is in red, and the final frame is in blue.The overlay shows the net movement of the microtubules over 90 s.(e) Microscale dynamics of tracer microtubules within a bundle without PEG display a smooth sliding motion with distinct populations of downward moving (yellow) and upward moving microtubules (cyan).(f ) Microtubule bundles with kinesin-14 and PEG.PEG induces attractive forces between microtubules.(g) Time sequence of extensile bundles with 1% PEG and microtubule tracers (yellow).(h) Time sequence of an extending bundle with yellow tracer microtubules.(i) Microscale dynamics of tracer microtubules within a bundle in the presence of 1% PEG exhibit a stuttering motion.

FIG. 2 .
FIG. 2. PEG induces a transition from splitting to non-splitting dynamics regions.(a) A laser (orange) bleaches two lines of Alexa-647 labeled microtubules while Azide-DBCO-488 labeled tracer microtubules remain fluorescent.(b) A microtubule bundle with tracer microtubules and photobleached lines.(c) A time sequence of a PEG-free sample in which both bleached regions split into two lines that moved in opposite directions.(d) Top: Initial bleach lines.Middle: A space-time image showing the temporal evolution of the bleached lines.Bottom: Bleached patterns at t = 90 s. (e,f ) A time sequence and space-time image of bleach patterns in the presence of 1% PEG.(g) A schematic space-time diagram of splitting bleach lines.The black lines indicate the bleach mark trajectories.Dotted blue lines represent the center of mass of a bleach mark.Lcen is the distance between the center of masses.L split is the average distance between splitting marks.If the lines do not split L split = 0. (h) Experimental data of Lcen and L split at 0% PEG, from which Vcen and V split are calculated.(i) Vcen as a function of PEG.Faded dots are the results from individual samples; error bars indicate standard error.(j) Dark black dots show the average V split , bars show standard error, and faded dots represent individual samples.Inset: The fraction of bundles that display splitting behavior as a function of % PEG.

FIG. 3 .
FIG. 3. PEG induces a structural transition in the microtubule bundles.(a) Radially averaged SAXS curves of microtubule bundles in the presence of kinesin-14 with increasing PEG concentrations.(b) At 0% PEG, the SAXS curve is consistent with a hexagonal lattice of microtubules with a spacing of L h = 45.8 nm (cyan).Data is shifted along the Y-axis for clarity.(c) Models of a combination of the hexagonal lattice and the rectangular lattice fit SAXS curves at 0.25% PEG.(d) SAXS curves at 1% PEG match a model (cyan) of microtubules with an ellipsoidal cross-section arranged in a rectangular lattice with La = 10.1 nm and L b = 13.6 nm.

FIG. 4 .
FIG. 4. The transition between splitting and extending microtubule bundles corresponds to a transition from hexagonal to rectangular bundle structure (a) An idealized model of pure sliding, in which half the microtubules move with velocity V and half with velocity −V .Bleached lines split into two and move at constant velocities, but the center of mass of the two bleached regions remains at a fixed distance.(b) An idealized model of pure extension generated by a telescoping elongation of the bundle, which leads to a thinning in the lateral direction.Bleached lines do not split, but their separation increases over time.(c) In bundles with kinesin-14 and low (or no) PEG, microtubules form a loosely packed hexagonal lattice and exhibit both sliding and extension.(d) In bundles with kinesin-14 and high PEG, microtubules form a tightly packed rectangular lattice and exhibit extension with no additional sliding.