# Spatiotemporal patterning of extensile active stresses in microtubule-based
active fluids

Linnea M. Lemma1,2, Minu Varghese1, Tyler D. Ross3,4, Matt Thomson4, Aparna
Baskaran1, and Zvonimir Dogic2,1<EMAIL_ADDRESS>1Department of
Physics, Brandeis University, 2 Department of Physics, University of
California at Santa Barbara, 3 Department of Computing and Mathematical
Sciences, California Institute of Technology, 4 Division of Biology and
Biological Engineering, California Institute of Technology

(September 10, 2022)

###### Abstract

Active stresses, which are collectively generated by the motion of energy-
consuming rod-like constituents, generate chaotic autonomous flows.
Controlling active stresses in space and time is an essential prerequisite for
controlling the intrinsically chaotic dynamics of extensile active fluids. We
design single-headed kinesin molecular motors that exhibit optically enhanced
clustering, and thus enable precise and repeatable spatial and temporal
control of extensile active stresses. Such motors enable rapid, reversible
switching between flowing and quiescent states. In turn, spatio-temporal
patterning of the active stress controls the evolution of the ubiquitous bend-
instability of extensile active fluids and determines its critical length
dependence. Combining optically controlled clusters with conventional kinesin
motors enables one-time switching from contractile to extensile active
stresses. These results open a path towards real-time control of the
autonomous flows generated by active fluids.

##  I Introduction

The shapes of cells, tissues, and organs are determined by the patterns of the
mesoscopic active stresses, which are collectively generated by microscopic
molecular motors [1, 2, 3, 4, 5, 6]. Developing analogous synthetic force-
generating materials is of fundamental interest and is essential for diverse
applications [7], ranging from microfluidics and adaptive optics to soft
robotics. Active matter, which is an assemblage of microscopic force-
generating constituents, provides a promising experimental platform for
realizing these goals [8]. Bulk active materials exhibit diverse dynamical
states [9, 10, 11, 12, 13, 14], which can exhibit chaotic or turbulent-like
flows. However, developing soft active matter systems is only the first step
towards creating life-like synthetic materials; one also needs to harness
their force-generating capabilities to stabilize a targeted dynamical state.
In this vein, previous work demonstrated that immutable geometrical
confinement can stabilize spinning vortices or long-ranged coherent flows [15,
16, 17, 18].

The next challenge is to develop protocols that control transitions between
distinct dynamical states in situ. For inspiration, one can look towards
biological cells, which can sense their environment and adjust force patterns
accordingly [19]. A first step for achieving analogous capabilities in
synthetic materials is to develop active matter whose dynamics are responsive
to external cues. Light patterns have been used to control the motility
induced phase separation and the structure and dynamics of bacterial [12, 13,
20, 21, 22, 23]. Recent advances also demonstrated the optogenetic control of
cytoskeletal active matter, including the control of local contractility and
aster formation, as well as influencing the motion of topological defects [24,
25, 26]. Here we demonstrate robust and repeatable spatial and temporal
control of active stresses in three-dimensional microtubule-based active
fluid.To achieve precise control, we develop single-headed kinesin motors that
exhibit optically induced enhanced clustering. The unique features of this
system enable temporal control of the ubiquitous bend instability of active
fluids, and reveal how this instability depends on the system size.

###  I.1 Optical control of kinesin clustering

Conventional microtubule-based active fluids are powered by clusters of
kinesin-1 molecular motors [9]. Motors within a single cluster bind adjacent
microtubules. Depending on the microtubules’ relative polarity, the motor
clusters induce interfilament sliding and bundle extension [27]. At high
microtubule concentrations, extensile bundles form a percolating network that
is continuously reconfigured by the repeating cycles of motor driven bundles
extending, buckling, fragmenting and re-annealing [11]. Such network dynamics
drive the turbulent-like flows of the background fluid. Coupling energy-
efficient kinesin motors with an ATP regeneration can sustain non-equilibrium
dynamics for hours or even days [28].

The formation of multimotor clusters is essential for generating active
stresses. Isolated motors move along separate filaments, but are unable to
generate interfilament sliding. The biotin-streptavidin interaction used to
assemble conventional clusters is an essentially irreversible non-covalent
bond [29]. Decreasing intra-cluster bond strength, decreased the efficiency of
interfilament sliding, as was revealed by DNA-based clusters, in which the
binding strength can be precisely tuned [30]. Below a minimal bond strength,
the clusters were unable to generate active stresses.

Such considerations suggest that controlling cluster assembly provides a route
towards control of active stresses. Indeed, a recent advance fused optically
responsive dimerizing domains (improved light induced dimers - iLID) to
kinesin motors to establish reversible light control of the assembly of the
kinesin clusters [24, 31]. In the absence of photoactivation, the binding
affinity of the kinesin-iLID to its polypeptide binding partner, which is
attached to another kinesin motor, is low: thus the kinesin motors are largely
isolated. They consume ATP and walk along microtubules, but do not induce
significant interfilament sliding [Fig. 1(a-b)]. When photoactivated, the iLID
domain changes conformation, exposing the binding site and increasing the
affinity for motor pairs to dimerize. The newly formed motor clusters can
crosslink and slide microtubules [Fig. 1(a-b)]. Such opto-kinesin clusters can
induce photoactivated contraction of microtubule asters and generate
programmable fluid flows [24].

Microtubule-based active matter is conventionally powered by the N-terminal
401 amino-acid fragment of _Drosophila_ kinesin-1 motor [9, 11]. Two 401
amino-acid fragments associate to form a two-headed dimeric kinesin motor,
which we refer to as K401. These processive motors are continuously bound to a
microtubule as they take about one hundred 8-nm “hand-over-hand” steps toward
the microtubule plus end, before detaching [32, 33]. The C-terminal of the
K401 motors is labelled with biotin. Adding tetravalent streptavidin induces
assembly of higher-order clusters containing several K401 dimer motors, which
efficiently power active matter dynamics.

Microtubule-based active matter can also be powered by a monomeric N-terminal
365 amino-acid fragment of _Drosophila_ kinesin-1 motor, which we refer to as
K365 [28, 30]. Having a shorter neck linker domain, such fragments do not
dimerize. K365 motors are not processive; they detach from a microtubule after
each step [34, 35]. Similar to K401, K365 kinesin motors are labelled with
biotin and can assemble into higher order clusters with streptavidin. Notably,
the K365 motor clusters are still able to bind multiple filaments and induce
their relative sliding, generating active stresses. The dynamics of an active
fluid driven by clusters of K365 motors exhibit greater temporal stability of
flow speeds and structural length scales, when compared to those driven by
K401 motors [28]. Clustering can transform non-processive motors into
processive ones [36].

##  II Results

###  II.1 Steady-state dynamics of active fluids powered by opto-kinesin
clusters

We first explored the ability of K401-opto clusters to control extensile
dynamics of microtubule-based active fluids [Fig. 1(a)]. In presence of blue
light opto-clusters generated extending bundles that continuously buckled and
annealed [Video 1, Materials and Methods]. Images taken 30 s apart revealed a
continuously reconfiguring microtubule network [Fig. 1(c) bottom]. Upon
deactivation, the microtubule bundles quickly stopped extending and remained
frozen in their paused configuration. Images taken 10 min apart demonstrate
the lack of measurable dynamics in the absence of optical signal [Fig. 1(c)
top]. When exposed to continuous blue light, the photoactivated flows decayed
rapidly, perhaps due to irreversible crosslinking of motors clusters. Pulsed
10 ms photoactivation every 5 s avoided this issue. Additionally, we optimized
the motor concentration to achieve maximal difference between the dark and
photoactivated state [Materials and Methods].

We measured the speed of the microtubule-powered flows through multiple cycles
of photo-activation, using particle image velocimetry (PIV) of the fluorescent
microtubule images [37] [Fig. 1(d), Fig. S1, Materials and Methods]. After
formation of the bundled network, the sample was alternately exposed to dark
and light cycles each lasting 15 minutes and 1 hour respectively. When
illuminated active flows increased 100-fold from $\sim 20$ nm/s in the dark to
$\sim 2$ $\mu$m/s. The difference in speeds persisted over several light
cycles that spanned the active network lifetime.

Quantifying the flow speeds, however, revealed subtle variations of
photoactivated dynamics over time. First, within a single cycle, the maximum
speed was reached within 30 s after photoactivation and then decayed to a
plateau. The decay timescale increased with subsequent photo-activation
cycles. Second, the plateau speed decreased with each successive photo-
activation cycle. Such decay is reminiscent of aging observed in active fluids
driven by the conventional K401 motor clusters [28]. Finally, the background
speed in the dark state increased throughout the sample lifetime [Fig. 1]. The
combination of increased dark flows and decreased photoactivated flows reduced
the contrast between the dark and the illuminated states [Fig. S2]. These
behaviors present a challenge for applications that require repeatable control
of the active stress.

Motivated by the observation that K365 kinesin clusters generate more regular
temporal dynamics [28], we created clusters which fused a monomeric kinesin
fragment (K365) to both iLID domains [Fig. 1(b), Fig. S3]. The K365 opto-
clusters also powered the extensile dynamics upon photo-activation [Video 2].
After formation of the bundled network, the active fluid was exposed to
repeating cycles of photo-activation. In contrast to the K401-opto motors, the
K365-opto constructs exhibited a regular, reversible and reproducible
response. Photoactivated flows immediately plateaued, at 1.2 $\mu$m/s, while
dark state flows were measured $\sim 7$ nm/s. Subsequent photo-activation
cycles generated the same speed, with no significant change over the sample
lifetime. Finally, the dark state flow speeds did not increase over time, and
were effectively zero when compared to enzymatically dead samples [Fig. 1(f),
Fig. S4]. Thus, K365 opto-kinesin clusters allow for robust and repeatable
spatio-temporal control of active stresses.

The steady state dynamics of extensile fluids is uniquely suited to
characterize the temporal response of clusters to optical stimulus, which is
related to the kinetics of the kinesin cluster assembly and disassembly. We
measured the timescale for which the flows reached their maximum speed after
photo-activation. For both K401-opto and K365-opto motor clusters, the
increase in speed was fitted to a bounded exponential function

$\langle|\boldsymbol{v}(t)|\rangle/v_{\textrm{max}}=1-e^{-t/\tau_{\textrm{on}}}.$
(1)

For K401 clusters, $\tau_{\textrm{on}}=14\pm 2.4$ s and for K365 clusters
$\tau_{\textrm{on}}=8\pm 2.7$ s [Fig. 1(g)(h)]. Similarly, we measured the
time scales for the flows to cease after deactivation. We fitted the velocity
decays to a sigmoid function:

$\langle|\boldsymbol{v}(t)|\rangle=\frac{2}{1+e^{-t/\tau_{\textrm{off}}}},$
(2)

from which we extracted $\tau_{\textrm{off}}=33\pm 1.8$ s for K401 clusters
and $\tau_{\textrm{off}}=13\pm 4.0$ s for K365 clusters [Fig. 1(f)(i)].

###  II.2 Controlling the speed of extensile flows

We next aimed to control the speed of active flows. Absorbance assays off
AsLOV proteins, the native protein from which iLID was derived, indicated that
the light intensity controls the fraction of dimerized domains [38]. Thus, we
expect that the light intensity also controls the concentration of bound motor
clusters, which in turn should control the magnitude of the active stress and
the flow speeds. We measured the dependence of the autonomous flow speeds on
the intensity of 488 nm illuminating light at the sample plane [Fig. 2, SI:
Experimental Methods]. With increasing light intensity, the flow speed
increased monotonically until saturating at 0.4 $\mu$W/mm2 for K401-opto
clusters and 1 $\mu$W/mm2 for K365-opto clusters [Fig. 2(a-b)]. Below 0.01
$\mu$W/mm2 the measured flows asymptotically approached the dark state [Fig.
2(a)(b) inset].

###  II.3 Controlling the extensile bend instability

To demonstrate temporal control of active stresses, we used K365 opto-clusters
to probe the bend instability of shear-aligned microtubules, which is a
ubiquitous feature of extensile active fluids [39, 40, 41, 42]. Once aligned
due to shear flow, microtubules remained quiescent in the absence of light
[Fig.3(a)]. When exposed to blue light, the opto-kinesin clusters generated
extensile sliding, which in turn powered the growth of the bend instability.
Upon deactivation, the bend instability stopped [Fig. 3(b), Video 3]. The
individual microtubule bundles within the deactivated network straightened
slightly, but the material only partially relaxed towards its initial
uniformly aligned state. Similar deformation dynamics occurred over multiple
cycles of photo-activation, with motor clusters pushing the microtubules into
an active bend, and the network partially relaxing when deactivated.

To quantify the bend instability, we measured the average filament angle
$\langle\theta\rangle$ away from the initial alignment, by calculating the
local structure tensor from fluorescence images [Fig. 3(b), Fig. S5]. During
the photo-activation, the average angle $\langle\theta\rangle$ grew as the
bend instability developed. Upon deactivation, the average angle decayed, but
after several minutes attained a finite-value plateau. Such dynamics is seen
by overlaying the initial and final images upon photoactivation [Fig. 3(c)]

The decay in the average angle upon deactivation was described by:

$\langle\theta(t)\rangle=M(t)A(t)+R(t).$ (3)

Here, $M(t)$ describes the unbinding kinetics of the motor clusters, $A(t)$
describes the activity-driven angle growth and $R(t)$ describes the relaxation
of the passive microtubule network. The activity drives linear growth such
that $A(t)=\dot{\gamma}t$, where $\dot{\gamma}=0.002$ rad/s is the measured
angular growth rate [Fig. S6]. Upon deactivation, growth slowed due to
unbinding of opto-clusters. To account for this effect, we multiply the growth
rate by the rate at which the clusters fall apart. Studies of unbinding
kinetics of the light activated domain revealed exponential decay,
$M(t)=e^{-t/\tau}$ where $\tau$ = 24 s [Fig. S7, SI.1] [43]. Modeling the
microtubule network as an elastic solid, predicts $R(t)=e^{-t/r}$ where $r$ is
the elastic relaxation time [SI]. Thus:

$\langle\theta\rangle=e^{-t/\tau}\dot{\gamma}t+Ce^{-t/r}$ (4)

where $\tau$ is the characteristic unbinding time for the motors and $C$ is a
scaling fit parameter. To fit the data, we fixed $\dot{\gamma}=0.002$ rad/s,
and left the time scales $\tau$ and $r$ as free parameters [Fig. 4(b) inset,
Fig. S8]. Experimental fits yielded $\tau=17\pm 5.5$ s which is within error
of the previously reported unbinding kinetics of the iLID domain [43]. We also
extracted, the elastic relaxation time $r=17\pm 9.8$ s.

###  II.4 Spatial patterning of active stresses

Theory predicts that the bend instability only develops when the sample size
is larger than a critical length scale, which in turn is determined by the
ratio of the sample elasticity to the activity [39, 44]. Opto-kinesin clusters
enable application of spatially patterned stress, which can elucidate how the
interplay between geometry and activity controls the onset of the bend
instability.

Shear flow associated with chamber loading induced initial alignment of
microtubule bundles. When uniformly illuminated, such samples exhibited the
previously-described bend instability [Fig. 4] [42]. We used a laser scanning
confocal microscope to photoactivate square regions ranging in size from
$50\times 50$ $\mu$m2 to $500\times 500$ $\mu$m2. At a single photoactivation
intensity, the $500\times 500$ $\mu$m2 region exhibited the bend instability,
while the smaller regions remained quiescent, demonstrating a size-dependent
instability [Fig. 4(a-c), Video 4].

To quantify the size-dependent instability, we systematically changed the
photoactivation intensity within a single region. We placed an opaque mask
above the sample with a $400\times 400$ $\mu$m2 square opening. Exposing such
samples to light photoactivated the exposed area, while leaving the rest of
the sample inactive. With sequentially increasing light intensity, we observed
three regimes [Video 5]. At very low intensities, the microtubules inside the
activated region remained stationary [Fig. 4(d)]. Beyond a threshold
intensity, the microtubules started sliding past each other along the
alignment direction, but there was no deformation in the perpendicular
direction [Fig. 4(e)]. Finally, at high intensities, the microtubules buckled
in the direction perpendicular to alignment [Fig. 4(f)]. We refer to these as
the quiescent, sliding, and buckling regimes.

To quantify these observations, we measured the microtubule displacement field
after the region was photoactivated for a defined time [Fig. S9]. The
direction of the initial alignment was the $x$-axis, while $y$-axis was the
perpendicular direction in the image plane. For the purposes of this analysis,
we neglected the out of plane component. We calculated the build up of strain
over time by averaging $\gamma_{xx}$ and $\gamma_{yy}$ over the photoactivated
area [Fig. 4(g-h)]. In the quiescent regime $\gamma_{xx}$ remained zero,
indicating lack of any measurable motor-driven dynamics. Interestingly,
$\gamma_{yy}$ decreased over time [Fig. 4(h)]. This can be attributed to the
depletion induced contraction [45]. Indeed, a flow-aligned sample that was
never photoactivated exhibited a slight contraction, pulling toward the
chamber center [Fig. S10]. In the sliding regime, $\gamma_{xx}$ increased
linearly with time, indicating a constant extension rate. Concurrently,
$\gamma_{yy}$ decreased to the same extent as the quiescent regime, indicating
lack of motor-driven transverse dynamics. In the buckling regime,
$\gamma_{xx}$ grew quickly, increasing by more than 100% in 5 min.
Simultaneously, $\gamma_{yy}$ became positive and grew rapidly, indicating
filament motion perpendicular to the direction of extension.

We estimated the material flux through the boundary of the photoactivated
region, by measuring the change in the average fluorescent intensity of
labeled microtubules within the exposed region [Fig. 4 (i)]. Similar to the
strain analysis results, the fluorescent intensity in the quiescent regime
showed a slight increase of material over time due to the depletion induced
contraction. In the sliding regime, the intensity decreased linearly as
microtubules extended out of the photoactivated region along the $x$-axis. In
the buckling regime, the intensity decreased rapidly as the bend instability
pushed the microtubules out of the photo-activation region. When expelled in
the background, microtubules became stationary and did not return to the
exposed region. Thus, with continued illumination, the photo-activated region
eventually became devoid of microtubules [Video 6].

The combination of the width $W$ and the height $H$ of the microfluidic
channel determines the length scale of the bend instability [42]. We
illuminated aligned samples with rectangular patterns, with length $L$ along
the alignment direction and width $W$ perpendicular to the alignment [Fig.
5(a)]. We systematically increased the light intensity to find the threshold
activity required for the bend instability. The signature of bending is the
growth of $\gamma_{yy}$. We defined a threshold intensity for the bend
instability to be when the strain $\gamma_{yy}$ exceeded 0.5% over a 17 minute
activation [Fig. 5 (b), Fig. S11]. The intensity of light required to generate
buckling in this time depended on the size of the illuminated region. For
example, the intensity required to generate buckling of $L\sim 100$ $\mu$m
region was three times larger than for $L\sim 500$ $\mu$m squares [Fig. 5(c)].

The critical length scale required for instability can be calculated using a
hydrodynamic model [SI: Hydrodynamic Model]. The hydrodynamic theory predicts
that the instability is controlled by a dimensionless activity parameter
$\alpha_{\textrm{eff}}=(\alpha(S_{0}+\xi))/(2\eta D_{R}\kappa)$. For an
aligned nematic channel of dimensions $L$, $W$ and $H$, the threshold for the
onset of the instability is given by:

$\frac{I_{\textrm{threshold}}}{a}=\alpha_{\textrm{eff}}=\left\\{\begin{array}[]{ll}\pi^{2}L^{2}\left(\frac{1}{L^{2}}+\frac{1}{W^{2}}+\frac{1}{H^{2}}\right)^{2},&\hskip
28.45274pt\frac{1}{L^{2}}>\frac{1}{H^{2}}+\frac{1}{W^{2}}\\\
4\pi^{2}\left(\frac{1}{W^{2}}+\frac{1}{H^{2}}\right),&\hskip
28.45274pt\frac{1}{L^{2}}<\frac{1}{H^{2}}+\frac{1}{W^{2}}\end{array}\right\\}$
(5)

where, $S_{0}$ is the magnitude of initial order, $\xi$ is the flow alignment
parameter, $D_{R}$ is the rotational diffusion, $\kappa$ is the elastic
constant, $\eta$ is the viscosity of the active fluid and $L$, $W$ and $H$ are
the dimensions of the activated region [Fig. 5(a)].

If we assume that the active stress is linearly proportional to the intensity
of the optical signal, $I=a\alpha_{\textrm{eff}}$, where $a$ is a fit
parameter, the hydrodynamic model explains the size dependence of the bend
instability [Fig. 5(c)]. The theory further predicts that if the confinement
perpendicular to the direction of alignment is held constant $W=400$ $\mu$m
while the length $L$ of the illuminated region varies, the threshold intensity
will saturate when $1/L^{2}=1/W^{2}+1/H^{2}$ to an effective activity
$4\pi^{2}\left(1/W^{2}+1/H^{2}\right)$. Theoretical predictions agree with the
experiments, where $a=1.1$ nW and $a=0.93$ nW for the respective fits [Eq. 5,
Fig. 5(c)(d)].

###  II.5 Tuning the stress from contractile to extensile

So far, we demonstrated quantitative control of the extensile active stresses
in space and time. In comparison, biological cells are able to control not
only the magnitude but also the sign of the active stress to perform complex
functions. Although both contraction and extension have been observed in a
wide variety of cytoskeletal active matter systems [46, 47, 48], an on-demand
switching between these two regimes has yet to be realized. Motivated by such
reasoning, we explored the dynamics of a multi-motor material composed of K365
opto-kinesin clusters and full length kinesin-14. The latter is a minus-end
directed molecular dimer motor with a passive microtubule-binding domain, a
long neck linker, and a motor domain that steps processively at $\sim 20$ nm/s
[Fig. 6(a)] [49, 50]. Thus, kinesin-14 can simultaneously passively bind one
microtubule and advance towards the minus end of another microtubule, inducing
their relative microtubule sliding [51]. Kinesin-14 powers interfilament
sliding in aligned microtubule networks that is independent of the local
filament polarity [52].

In the presence of a depletion agent, kinesin-14 alone contracted a
microtubule network [Material and Methods]. The active contraction led to the
formation of a single macroscopic bundle aligned with the chamber walls, which
continued contracting for tens of hours [Fig. 6(b), Video 7]. Next, we
combined the kinesin-14 contracting network with K365 opto-kinesin [Fig.
6(c)]. When left in the dark, the material still formed a contracting network,
as it would without the opto-kinesin [Fig. 6(d)]. However, upon illumination,
the opto-kinesin clusters generated their own active stresses [Fig. 6(e),
Video 8]. The system exhibited extension and buckling in the photoactivated
region which suggested extensile active stresses. The extensile behavior was
localized to the activated region, thus the system simultaneously exhibited
spatially distinct regions of extensile and contractile active stress [Fig.
6(f)]. On-demand transition from contractile to extensile stresses opens the
door for new fundamental studies related to the sign of active stress, as well
as engineering applications. However, the transition was not reversible,
highlighting that the microscopic mechanism requires further study.

##  III Discussion

Building on the recent developments, we characterized opto-kinesin clusters of
non-processive K365 motors, showing that they are optimized for controlling
extensile active stresses. These motors add to a growing toolbox of optical
control of active dynamics [22, 24, 25]. The K365 opto-clusters induced up to
a 200-fold increase in the speed of autonomous flows between a dark and a
fully illuminated state. Importantly, gels powered with K365 clusters
displayed greater temporal regularity when compared to K401 clusters, a
finding that parallels the analogous observation of conventional streptavidin-
bound clusters [28].

Kinesin clusters can both generate active stresses and passively cross-link
microtubule bundles [53, 54, 55]. For example, with decreasing ATP
concentration, the motors’ primary role switches from generating active
stresses to cross-linking filaments [53]. Consequently, ATP controls a
transition between a quiescent elastic solid and a spontaneously flowing
active fluid. Opto-kinesin clusters provide a dynamical switch between an
active fluid and a quiescent, passive state. In principle, in the dark state,
the K365 opto-kinesin have a reduced tendency to dimerize. Thus, one might
expect the microtubule network in the dark state to remain fluid-like.
However, we found that upon deactivation, the network froze, and the bundles
retained their structure. Upon re-activation, the flows were almost perfectly
correlated with the flow field measured just before deactivation [Fig. S12].
This behavior suggests, that even in the absence of motor crosslinks, a
microtubule network is an elastic solid that is held together by PEG-induced
depletion.

The properties of opto-kinesin provide insight into the bend instability,
which is a ubiquitous feature of extensile active fluids [39, 41, 42, 40]. In
conventional systems, a uniformly aligned state is unstable to spontaneously
growing bend deformation that increase in time and eventually lead to
turbulent-like dynamics. Opto-kinesin clusters enable one to pause the bend
generation. Once deactivated, we observed only partial relaxation of the
deformed network, wherein the microtubule bundles locally straightened as if
released from tension. In comparison, a deformed conventional liquid crystal,
relaxes to a uniformly aligned state. The partial relaxation again
demonstrates that microtubule-based fluids have complex viscoelastic and
plastic properties, that remain largely unexplored.

Changing the photoactivation intensity of spatially illuminated shear-aligned
sample, revealed a size-dependent lower critical illumination intensity, below
which the bend instability was not observed. This is in agreement with theory,
which predicts a suppression of the bend instability for active nematics that
are confined below a critical length scale [39, 44]. In comparison, the size-
dependent suppression of the instability was not experimentally observed for
shear aligned microtubule fluids confined in microfluidic channels [42]. The
notable difference between the two systems is the nature of the boundaries.
Microfluidic channels aligned the filaments, but compressible isotropic active
fluids could easily separate from the wall, leaving behind regions devoid of
active material. In comparison, partially illuminated aligned gels remained
physically connected to the background elastic network. When a confined region
was activated below the instability threshold for long times, the region did
eventually buckle [Video 9]. However, in this regime microtubules slid against
each other, leading to net outflux of the material, suggesting that the
material properties of the network changed, before the onset of the
instability.

Light intensity controlled the speed of the active flows. Two observations
suggest a complex relationship between measured flow speeds and activity that
warrants further studies. The active fluids exhibited a hysteresis in speeds
[Fig. S13(a)]. Increasing photoactivation intensity from low intensities
increased the speed of the fluid flows. However, after saturating the system
and returning to low intensities, the fluid speed was five times higher than
the original photoactivation at the same intensity. In between photoactivation
events, the dark speed remained constant and near zero, indicating that the
motors returned to their low affinity dark state. There was a noticeable
change in the gel structure between the early and late low-light activation
[Fig. S13(b)]. These data suggest that the material properties of the network,
rather than the motors contribute to the hysteresis. As a possible
explanation, we suggest that the motors are controlling strain rate, which can
lead to different fluid flows depending on the microtubule bundle size and
buckling length. Second, we observed that the intensity for the saturation in
speed of the bulk fluid flow was lower than the intensities which induced
sliding and buckling in the confined system. We attribute this to the
hydrodynamic constraints of the system in which the activity (or intensity)
required for saturation is inversely proportional to the confinement.

Finally, we note that the K401 motors drove extensile active fluids for longer
times and exhibited faster flows than the K365 counterparts. These features
will likely be useful for some applications. In this study, we focused on the
K365 motors, which provide reproducible response to photoactivation and
therefore precise spatio-temporal control over extensile active stress.

Light intensity controlled the speed of the active flows. Two observations
suggest a complex relationship between measured flow speeds and activity that
warrants further studies. The active fluids exhibited a hysteresis in speeds
[Fig. S13(a)]. Increasing photoactivation intensity from low intensities
increased the speed of the fluid flows. However, after saturating the system
and returning to low intensities, the fluid speed was five times higher than
the original photoactivation at the same intensity. In between photoactivation
events, the dark speed remained constant and near zero, indicating that the
motors returned to their low affinity dark state. There was a noticeable
change in the gel structure between the early and late low-light activation
[Fig. S13(b)]. These data suggest that the material properties of the network,
rather than the motors contribute to the hysteresis. As a possible
explanation, we suggest that the motors are controlling strain rate, which can
lead to different fluid flows depending on the microtubule bundle size and
buckling length. Second, we observed that the intensity for the saturation in
speed of the bulk fluid flow was lower than the intensities which induced
sliding and buckling in the confined system. We attribute this to the
hydrodynamic constraints of the system in which the activity (or intensity)
required for saturation is inversely proportional to the confinement.

Finally, we note that the K401 motors drove extensile active fluids for longer
times and exhibited faster flows than the K365 counterparts. These features
will likely be useful for some applications. In this study, we focused on the
K365 motors, which provide reproducible response to photoactivation and
therefore precise spatio-temporal control over extensile active stress.

###  III.1 Acknowledgements

We acknowledge useful discussions with Seth Fraden. We thank Claire E. Walczak
and Stephanie C. Ems-McClung for the gift of kinesin-14 protein. We thank
Bezia Lemma for help with kinesin-14 experiments. We acknowledge the use of a
MRSEC optical and biosynthesis facility supported by NSF-MRSEC-2011846. We
also acknowledge the use of the NRI-MCDB Microscopy Facility and the Resonant
Scanning Confocal at UCSB supported by NSF MRI grant 1625770.

##  IV Figures

Figure 1: Optical switching between active extensile fluid and an inactive
solid. (a) The iLID optogenetic domains are fused to processive kinesin
motors. When the protein is illuminated with blue light, the iLID domain
changes conformation and the complementary constructs bind to each other. The
clustered motors generate interfilament sliding. (b) The iLID domains are
fused to a K365 truncated kinesin motor. The K365 motor clusters also dimerize
and induce interfilament sliding when exposed to blue light. (c) An active
network of labeled microtubules powered by optogenetic kinesin clusters.
Overlaid initial (red) and final frame (cyan) show the network dynamics (red +
cyan = gray). top: In the dark, the microtubule bundles do not move. bottom:
When exposed to blue light, the bundles extend and buckle generating active
flows. Scale bar, 25 $\mu$m. (d) Speed of active flows generated by processive
opto-kinesin clusters. Activation is cycled off (blue) and on (gold). In the
on-state the light is pulsed for 10 ms every 5 s. Inset: the average network
speed in the dark state with subsequent photo-activation cycles. (e) Active
flow speeds with K365 opto-kinesin. Inset: dark speed over time. (f) The decay
of the flow speed upon turning the light off for processive motors. The shaded
region is the standard deviation (n=9). The gray line is a fit to Eq. 2. (g)
For processive motors, the increase in speed upon photoactivation. The gray
line is a fit to Eq. 1. (h) The increase in speed after photoactivation for
K365 (n=7). (i) The decay in the flow speed after deactivation for K365
motors.  Figure 2: Signal intensity controls speed of active flows.  (a)
Autonomous flow speed as a function of the light intensity for processive
motors (n = 2, 2, 2, 2, 2, 1, 1, 1, 4, 1 Intensity = 0 $\rightarrow$ 2
$\mu$W/mm2). (b) Speed of autonomous flows measured through PIV versus the
light intensity for K365 motors (n = 3, 2, 4, 3, 1, 2, 3, 4, 2, 3, 2, 2, 2,
Intensity = 0 $\rightarrow$ 2.5 $\mu$W/mm2). Insets: Log-log scaling of axes.
Error bars represent standard error on multiple samples’ flows. Figure 3:
Controlling the bend instability  (a) Time series of a flow aligned opto-
kinesin microtubule network exposed to alternating dark and light conditions.
Scale bar, 200 $\mu$m. (b) The time-evolution of the average angle for two
photo-activation cycles. Inset: The relaxation dynamics of the bend
instability after deactivation. The average angle as a function of time
elapsed after deactivation. The shaded region is standard deviation (n=5). (c)
Overlays of time points in (a) with early time in red shows relative
microtubule movement across each light cycle. Yellow arrows direct the eye
forward in time.  Figure 4: Instability of confined active fluid (a) White
squares indicate activation regions from 50 $\mu$m2 to 500 $\mu$m2 of aligned
microtubules. (b) Microtubule network after 8 min of constant photoactivation
within the confined regions. (c) The overlay of the initial and final images.
(d-f) The dynamics of the quiescent, sliding and buckling regime is
illustrated by overlaying of initial (red) and final (cyan) state of a flow
aligned network. 400 $\times$ 400 $\mu$m square region was activated. Gray
indicates no movement of filaments (red + cyan = white). (g) $\gamma_{xx}$
within the activated region over time for each activation intensity. (h)
$\gamma_{yy}$ within the activated region over time for the three regimes. (i)
The average fluorescence intensity inside the activated region over time for
the three regimes Figure 5: Length scale of the bend instability (a) A
rectangular region (length $L$ and width $W$) of flow-aligned microtubules is
activated. The system confinement is three-dimensional, with the height $H$
defined as the height of the chamber. (b) $\gamma_{yy}$ plotted over time with
increasing intensity (color). Inset: the strain after 17 min of
photoactivation versus intensity. The bend instability is defined at the
lowest intensity for which $\gamma_{yy}$ increases by more than 0.5% over 17
min, indicated by the red dot. (c) The threshold intensity for instability
plotted versus the $L=W$ of a square activated region in a chamber $H=100$
$\mu$m. Red line is fit to theory Eq. 5 with $a=1.1\leavevmode\nobreak\ $nW-1.
Error bars indicate standard error on multiple activated areas (n = 2, 2, 4,
3, 1, 2, 3, 1 from W = 50 $\mu$m - 500 $\mu$m). (d) The threshold intensity
for instability for $W=400$ $\mu$m plotted versus the length $L$ of the
activated region in a chamber $H=300$ $\mu$m. Error bars indicate standard
erro on multiple activated areas (n = 1, 2, 2, 1, 3, 2, 3 from L = 50 $\mu$m
$\rightarrow$ 600 $\mu$m). Red line is fit to theory Eq. 5 with
$a=0.93\leavevmode\nobreak\ $nW-1.  Figure 6: Optogenetic switch from
contractile to extensile active stress. (a) Kinesin-14 motor has a passive
microtubule binding domain and a motor domain that steps toward the
microtubule minus end (blue arrow). The kinesin drives interfilament sliding
(black arrow). (b) A time series of the kinesin-14-driven microtubule
contractile dynamics of an aligned microtubule gel. (c) Microtubule-based
active matter powered by kinesin-14 and K365 opto-kinesin clusters. In the
dark state, kinesin-14 dominates system dynamics, generating contraction. In
the illuminated state, opto-kinesin clusters generate competing extensile
stresses. (d) A two motor-network with deactivated opto-kinesin clusters
contracts. (e) The contracting network is locally photoactivated with 10
$\mu$W/mm2 at 61 min, and the opto-kinesin induce extension. A time series
shows the transition to extensile, buckling behavior. (f) Entire sample after
photo-activation at t = 156 min. The yellow region has been illuminated.
Outside this region, opto-kinesin remain deactivated.

## References

  * Saadaoui  _et al._ [2020] M. Saadaoui, D. Rocancourt, J. Roussel, F. Corson, and J. Gros, A tensile ring drives tissue flows to shape the gastrulating amniote embryo, Science 367, 453 (2020).
  * Martin  _et al._ [2010] A. C. Martin, M. Gelbart, R. Fernandez-Gonzalez, M. Kaschube, and E. F. Wieschaus, Integration of contractile forces during tissue invagination, Journal of Cell Biology 188, 735 (2010).
  * Behrndt  _et al._ [2012] M. Behrndt, G. Salbreux, P. Campinho, R. Hauschild, F. Oswald, J. Roensch, S. W. Grill, and C.-P. Heisenberg, Forces driving epithelial spreading in zebrafish gastrulation, Science 338, 257 (2012).
  * Etournay  _et al._ [2015] R. Etournay, M. Popović, M. Merkel, A. Nandi, C. Blasse, B. Aigouy, H. Brandl, G. Myers, G. Salbreux, F. Jülicher, _et al._ , Interplay of cell dynamics and epithelial tension during morphogenesis of the drosophila pupal wing, Elife 4, e07090 (2015).
  * Mitchell  _et al._ [2022] N. P. Mitchell, D. J. Cislo, S. Shankar, Y. Lin, B. I. Shraiman, and S. J. Streichan, Visceral organ morphogenesis via calcium-patterned muscle constrictions, eLife 11, e77355 (2022).
  * Nerurkar  _et al._ [2019] N. L. Nerurkar, C. Lee, L. Mahadevan, and C. J. Tabin, Molecular control of macroscopic forces drives formation of the vertebrate hindgut, Nature 565, 480 (2019).
  * Needleman and Dogic [2017] D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nature Reviews Materials 2, 17048 (2017).
  * Marchetti  _et al._ [2013] M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  * Nédélec  _et al._ [1997] F. J. Nédélec, T. Surrey, A. C. Maggs, and S. Leibler, Self-organization of microtubules and motors, Nature 389, 305 (1997).
  * Schaller  _et al._ [2010] V. Schaller, C. Weber, C. Semmrich, E. Frey, and A. R. Bausch, Polar patterns of driven filaments, Nature 467, 73 (2010).
  * Sanchez  _et al._ [2012] T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature 491, 431 EP (2012).
  * Palacci  _et al._ [2013] J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013), https://science.sciencemag.org/content/339/6122/936.full.pdf .
  * Dell’Arciprete  _et al._ [2018] D. Dell’Arciprete, M. L. Blow, A. T. Brown, F. D. C. Farrell, J. S. Lintuvuori, A. F. McVey, D. Marenduzzo, and W. C. K. Poon, A growing bacterial colony in two dimensions as an active nematic, Nature Communications 9, 4190 (2018).
  * Soni  _et al._ [2019] V. Soni, E. S. Bililign, S. Magkiriadou, S. Sacanna, D. Bartolo, M. J. Shelley, and W. T. M. Irvine, The odd free surface flows of a colloidal chiral fluid, Nature Physics 15, 1188 (2019).
  * Wu  _et al._ [2017] K.-T. Wu, J. B. Hishamunda, D. T. Chen, S. J. DeCamp, Y.-W. Chang, A. Fernández-Nieves, S. Fraden, and Z. Dogic, Transition from turbulent to coherent flows in confined three-dimensional active fluids, Science 355 (2017).
  * Guillamat  _et al._ [2016] P. Guillamat, J. Ignés-Mullol, and F. Sagués, Control of active liquid crystals with a magnetic field, Proceedings of the National Academy of Sciences 113, 5498 (2016).
  * Wioland  _et al._ [2013] H. Wioland, F. G. Woodhouse, J. Dunkel, J. O. Kessler, and R. E. Goldstein, Confinement stabilizes a bacterial suspension into a spiral vortex, Physical Review Letters 110, 268102 (2013).
  * Nishiguchi  _et al._ [2018] D. Nishiguchi, I. S. Aranson, A. Snezhko, and A. Sokolov, Engineering bacterial vortex lattice via direct laser lithography, Nature communications 9, 1 (2018).
  * Discher  _et al._ [2005] D. E. Discher, P. Janmey, and Y.-l. Wang, Tissue cells feel and respond to the stiffness of their substrate, Science 310, 1139 (2005).
  * Vizsnyiczai  _et al._ [2017] G. Vizsnyiczai, G. Frangipane, C. Maggi, F. Saglimbeni, S. Bianchi, and R. Di Leonardo, Light controlled 3d micromotors powered by bacteria, Nature Communications 8, 15974 (2017).
  * Frangipane  _et al._ [2018] G. Frangipane, D. Dell’Arciprete, S. Petracchini, C. Maggi, F. Saglimbeni, S. Bianchi, G. Vizsnyiczai, M. L. Bernardini, and R. Di Leonardo, Dynamic density shaping of photokinetic e. coli, eLife 7, e36608 (2018).
  * Arlt  _et al._ [2018] J. Arlt, V. A. Martinez, A. Dawson, T. Pilizota, and W. C. K. Poon, Painting with light-powered bacteria, Nature Communications 9, 768 (2018).
  * Aubret  _et al._ [2018] A. Aubret, M. Youssef, S. Sacanna, and J. Palacci, Targeted assembly and synchronization of self-spinning microgears, Nature Physics 14, 1114 (2018).
  * Ross  _et al._ [2019] T. D. Ross, H. J. Lee, Z. Qu, R. A. Banks, R. Phillips, and M. Thomson, Controlling organization and forces in active matter through optically defined boundaries, Nature 572, 224 (2019).
  * Zhang  _et al._ [2021] R. Zhang, S. A. Redford, P. V. Ruijgrok, N. Kumar, A. Mozaffari, S. Zemsky, A. R. Dinner, V. Vitelli, Z. Bryant, M. L. Gardel, and J. J. de Pablo, Spatiotemporal control of liquid crystal structure and dynamics through activity patterning, Nature Materials 20, 875 (2021).
  * Qu  _et al._ [2021] Z. Qu, J. Jiang, H. J. Lee, R. Phillips, S. Shadkhoo, and M. Thomson, Programming boundary deformation patterns in active networks, arXiv preprint arXiv:2101.08464 (2021).
  * Lemma  _et al._ [2021] L. M. Lemma, M. M. Norton, A. M. Tayar, S. J. DeCamp, S. A. Aghvami, S. Fraden, M. F. Hagan, and Z. Dogic, Multiscale microtubule dynamics in active nematics, Phys. Rev. Lett. 127, 148001 (2021).
  * Chandrakar  _et al._ [2022] P. Chandrakar, J. Berezney, B. Lemma, B. Hishamunda, A. Berry, K.-T. Wu, R. Subramanian, J. Chung, D. J. Needleman, J. Gelles, _et al._ , Engineering stability, longevity, and miscibility of microtubule-based active fluids, Soft Matter 18, 1825 (2022).
  * Sedlak  _et al._ [2020] S. M. Sedlak, L. C. Schendel, H. E. Gaub, and R. C. Bernardi, Streptavidin/biotin: Tethering geometry defines unbinding mechanics, Science advances 6, eaay5999 (2020).
  * Tayar  _et al._ [2021] A. M. Tayar, M. F. Hagan, and Z. Dogic, Active liquid crystals powered by force-sensing dna-motor clusters, Proceedings of the National Academy of Sciences 118, 10.1073/pnas.2102873118 (2021), https://www.pnas.org/content/118/30/e2102873118.full.pdf .
  * Guntas  _et al._ [2015] G. Guntas, R. A. Hallett, S. P. Zimmerman, T. Williams, H. Yumerefendi, J. E. Bear, and B. Kuhlman, Engineering an improved light-induced dimer (ilid) for controlling the localization and activity of signaling proteins, Proceedings of the National Academy of Sciences 112, 112 (2015), https://www.pnas.org/content/112/1/112.full.pdf .
  * Thorn  _et al._ [2000] K. S. Thorn, J. A. Ubersax, and R. D. Vale, Engineering the processive run length of the kinesin motor., J Cell Biol 151, 1093 (2000).
  * Yildiz  _et al._ [2004] A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, Kinesin walks hand-over-hand, Science 303, 676 (2004).
  * Berliner  _et al._ [1995] E. Berliner, E. C. Young, K. Anderson, H. K. Mahtani, and J. Gelles, Failure of a single-headed kinesin to track parallel to microtubule protofilaments, Nature 373, 718 (1995).
  * Hancock and Howard [1998] W. O. Hancock and J. Howard, Processivity of the motor protein kinesin requires two heads, Journal of Cell Biology 140, 1395 (1998), https://rupress.org/jcb/article-pdf/140/6/1395/1278490/32983.pdf .
  * Furuta  _et al._ [2013] K. Furuta, A. Furuta, Y. Y. Toyoshima, M. Amino, K. Oiwa, and H. Kojima, Measuring collective transport by defined numbers of processive and nonprocessive kinesin motors, Proceedings of the National Academy of Sciences 110, 501 (2013).
  * Thielicke and Stamhuis [2014] W. Thielicke and E. Stamhuis, Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab, Journal of open research software 2 (2014).
  * Salomon  _et al._ [2000] M. Salomon, J. M. Christie, E. Knieb, U. Lempert, and W. R. Briggs, Photochemical and mutational analysis of the fmn-binding domains of the plant blue light receptor, phototropin, Biochemistry 39, 9401 (2000).
  * Aditi Simha and Ramaswamy [2002] R. Aditi Simha and S. Ramaswamy, Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles, Phys. Rev. Lett. 89, 058101 (2002).
  * Sokolov  _et al._ [2019] A. Sokolov, A. Mozaffari, R. Zhang, J. J. de Pablo, and A. Snezhko, Emergence of radial tree of bend stripes in active nematics, Phys. Rev. X 9, 031014 (2019).
  * Martínez-Prat  _et al._ [2019] B. Martínez-Prat, J. Ignés-Mullol, J. Casademunt, and F. Sagués, Selection mechanism at the onset of active turbulence, Nature physics 15, 362 (2019).
  * Chandrakar  _et al._ [2020] P. Chandrakar, M. Varghese, S. Aghvami, A. Baskaran, Z. Dogic, and G. Duclos, Confinement controls the bend instability of three-dimensional active liquid crystals, Phys. Rev. Lett. 125, 257801 (2020).
  * Hallett  _et al._ [2016a] R. A. Hallett, S. P. Zimmerman, H. Yumerefendi, J. E. Bear, and B. Kuhlman, Correlating in vitro and in vivo activities of light-inducible dimers: A cellular optogenetics guide,  _ACS Synthetic Biology_ , ACS Synthetic Biology 5, 53 (2016a).
  * Gao  _et al._ [2015] T. Gao, R. Blackwell, M. A. Glaser, M. D. Betterton, and M. J. Shelley, Multiscale polar theory of microtubule and motor-protein assemblies, Phys. Rev. Lett. 114, 048101 (2015).
  * Braun  _et al._ [2016] M. Braun, Z. Lansky, F. Hilitski, Z. Dogic, and S. Diez, Entropic forces drive contraction of cytoskeletal networks, BioEssays 38, 474 (2016).
  * Foster  _et al._ [2015] P. J. Foster, S. Furthauer, M. J. Shelley, and D. J. Needleman, Active contraction of microtubule networks, eLife 4 (2015).
  * Kumar  _et al._ [2018] N. Kumar, R. Zhang, J. J. de Pablo, and M. L. Gardel, Tunable structure and dynamics of active liquid crystals, Science Advances 4 (2018).
  * Mizuno  _et al._ [2007] D. Mizuno, C. Tardin, C. F. Schmidt, and F. C. MacKintosh, Nonequilibrium mechanics of active cytoskeletal networks, Science 315, 370 (2007).
  * Hentrich and Surrey [2010] C. Hentrich and T. Surrey, Microtubule organization by the antagonistic mitotic motors kinesin-5 and kinesin-14, Journal of Cell Biology 189, 465 (2010).
  * Walczak  _et al._ [1997] C. E. Walczak, S. Verma, and T. J. Mitchison, Xctk2: a kinesin-related protein that promotes mitotic spindle assembly in xenopus laevis egg extracts, The Journal of cell biology 136, 859 (1997).
  * Cai  _et al._ [2009] S. Cai, L. N. Weaver, S. C. Ems-McClung, and C. E. Walczak, Kinesin-14 family proteins hset/xctk2 control spindle length by cross-linking and sliding microtubules, Molecular biology of the cell 20, 1348 (2009).
  * Fürthauer  _et al._ [2019] S. Fürthauer, B. Lemma, P. J. Foster, S. C. Ems-McClung, C.-H. Yu, C. E. Walczak, Z. Dogic, D. J. Needleman, and M. J. Shelley, Self-straining of actively crosslinked microtubule networks, Nature Physics (2019).
  * Gagnon  _et al._ [2020] D. A. Gagnon, C. Dessi, J. P. Berezney, R. Boros, D. T.-N. Chen, Z. Dogic, and D. L. Blair, Shear-induced gelation of self-yielding active networks, Phys. Rev. Lett. 125, 178003 (2020).
  * Sarfati  _et al._ [2021] G. Sarfati, A. Maitra, R. Voituriez, J.-C. Galas, and A. Estevez-Torres, Crosslinking and depletion determine spatial instabilities in cytoskeletal active matter, arXiv preprint arXiv:2112.11361 (2021).
  * Najma  _et al._ [2021] B. Najma, M. Varghese, L. Tsidilkovski, L. Lemma, A. Baskaran, and G. Duclos, Dual antagonistic role of motor proteins in fluidizing active networks (2021), arXiv:2112.11364 [cond-mat.soft] .
  * Tayar  _et al._ [2022] A. M. Tayar, L. M. Lemma, and Z. Dogic, Assembling microtubule-based active matter, in  _Microtubules_ (Springer, 2022) pp. 151–183.
  * Lau  _et al._ [2009] A. W. C. Lau, A. Prasad, and Z. Dogic, Condensation of isolated semi-flexible filaments driven by depletion interactions, EPL (Europhysics Letters) 87, 48006 (2009).
  * Püspöki  _et al._ [2016] Z. Püspöki, M. Storath, D. Sage, and M. Unser, Transforms and operators for directional bioimage analysis: A survey, in  _Focus on Bio-Image Informatics_, edited by W. H. De Vos, S. Munck, and J.-P. Timmermans (Springer International Publishing, 2016) pp. 69–93.
  * Blaber  _et al._ [2015] J. Blaber, B. Adair, and A. Antoniou, Ncorr: Open-source 2d digital image correlation matlab software, Experimental Mechanics 55, 1105 (2015).
  * Hallett  _et al._ [2016b] R. A. Hallett, S. P. Zimmerman, H. Yumerefendi, J. E. Bear, and B. Kuhlman, Correlating in vitro and in vivo activities of light-inducible dimers: A cellular optogenetics guide,  _ACS Synthetic Biology_ , ACS Synthetic Biology 5, 53 (2016b).

Spatiotemporal patterning of extensile active stresses in microtubule-based
active fluids
Supplementary Material

Linnea M. Lemma, Minu Varghese, Tyler D. Ross, Matt Thomson, Aparna Baskaran,
and Zvonimir Dogic

##  V Materials and Methods

###  V.1 Protein Preparation

GMPCPP stabilized microtubules with an average length of 1 $\mu$m were
prepared as previously described [56].The plasmids encoding for processive
opto-kinesin K401 (K401-iLID: Addgene 122484 and K401-micro: Addgene 122485;
gifts from Tyler Ross and Matt Thomson) were transformed into BL21 cells.
After culturing for 4 hours in 2XYT media, expression was induced at OD 0.6
with IPTG and grown for 16 hours at 18∘C. Cells were lysed using a Branson tip
sonicator 550 with a 0.25 inch tip for 10 s at 30% power with 50 s recovery
for 6 cycles. Lysate was then clarified by spinning at 100,000 RCF for 30
minutes. Purification was performed using an AKTA Fast Protein Liquid
Chromatography system (GE Healthcare) with a 1 mL Nickel column (HisTrap, GE
Healthcare) [56, 24]. The wash buffer used was 20 mM imidazole, 50 mM Sodium
phosphate, 250 mM NaCl, 4 mM MgCl2, 0.05mM ATP, 5 mM $\beta$mercaptoethanol,
5% w/v glycerol, pH 7.2. The elution buffer was the same as the wash buffer
but with 500 mM imidazole. For the K401-micro construct, the MBP tag was
digested with TEV protease and removed by passing over a Nickel column. The
buffer was exchanged into wash buffer and then diluted to 50% v/v glycerol.
The kinesin motors were aliquoted, flash frozen in liquid nitrogen and stored
at -80∘C.

To construct the K365-iLID and K365-micro plasmids (Addgene 188456, 188457),
we PCR amplified the desired regions [Fig. S3] from the K401-iLID plasmid
(Addgene 122484, gift from Matt Thomson) and the K401-micro plasmid (Addgene
188457, gift from Matt Thomson) with Q5 High-Fidelity DNA polymerase (New
England BioLabs). We then used HiFi DNA assembly kit (New England BioLabs) to
circularize the product. We transformed the plasmids into BL21 cells, and
expressed and purified the protein following the same protocol as the
processive motors described above [24].

The active mixture was prepared without kinesin and microtubules at 1.4 mM ATP
[56]. Briefly, an active mixture was prepared in M2B (80 mM PIPES, 2 mM MgCl2,
1 mM EGTA, pH 6.8) with a depletion agent to induce microtubule bundling, an
ATP regeneration system to maintain activity and oxygen scavenging system to
prevent photobleaching: 0.8% w/v PEG (35 kDa, Sigma Aldrich), 26.6 mM PEP
(Beantown Chemicals product #129745), 1.4 mM ATP (Sigma Aldrich), 6.7 mg/mL
glucose, 0.4 mg/mL glucose catalase, 0.08 mg/mL glucose oxidase, 5 mM MgCl2.
This active mixture was prepared once for all experiments with opto-kinesin.
After mixing, the reagents were flash frozen in liquid nitrogen in 5 $\mu$L
aliquots and stored at -80∘C until the day of experiments.

###  V.2 Chamber Construction

Glass slides were treated with an acrylamide brush to prevent proteins
sticking [57, 56]. The opto-kinesin constructs were especially sensitive to
high coverage surface treatments, when compared to the conventional kinesin-
streptavadin clusters. Parafilm was cut into chambers 1, 2 or 3 mm in width
and sandwiched between two acrylamide slides. Using a hot plate, the parafilm
sandwich was heated to 60∘C. While on the hot plate, we gently pressed down on
the parafilm spacer using the blunt end of an eppendorf 0.5 mL tube until the
parafilm turned translucent. For experiments where the height of the chamber
was altered, multiple parafilm spacers were carefully stacked on top of each
other and the chamber was constructed as above.

###  V.3 Optical Microscopy

Images were taken on Nikon Ti2-Eclipse inverted microscope equipped with
either a Photometrics Prime 95b or an Andor Zyla 5.5 sCMOS camera.
Additionally, we used a Leica Resonant SP8 scanning confocal with Stellaris
white light laser for some confined activation and subsequent imaging.

###  V.4 Sample Preparation

All the samples were prepared in conditions where the sample was only exposed
only to red light from an red LED-equipped desk lamp. Microtubules, active
mixture aliquots and kinesin motors were rapidly thawed. Opto-kinesin motor
constructs were added to 300 nM concentration. This was the minimal
concentration at which we reliably obtained extensile active gels while
photoactivated. Higher concentrations of motors increased the dark state
velocities and decreased the sample lifetime. Components were mixed for final
desired concentrations and immediately loaded into chamber. The chamber was
sealed using a fast setting silicone polymer (Picodent Twinsil Speed).

###  V.5 Sample Preparation of Multimotor Composite

The multimotor composite was prepared in an active mixture at 80 mM PIPES, 5
mM magnesium chloride, 1 mM EGTA, 0.034% pyruvate kinase, 52 mM PEP, 1.4 mM
ATP, 0.5 mg/mL tubulin and 0.1% PEG. An oxygen scavenging system was also
added to prevent photobleaching (6.7 mg/mL glucose, 0.4 mg/mL glucose
catalase, 0.08 mg/mL glucose oxidase). The final concentrations of K365 opto-
kinesin was 450 nM. The final concentration of kinesin-14 was 125 nM. The
sample was photoactivated using Lumencor Sola light engine through a 472 $\pm
30$ nm excitation filter at intensity of 10 $\mu$W/mm2.

###  V.6 Patterning active stress

For bulk activation experiments, the epi-fluorescence arm of the microscope
was used to illuminate the sample with blue light (Lumencor, Sola light engine
white LED, 472 $\pm 30$ nm excitation filter). Initially, the entire chamber
was exposed to 37 mW/mm2 of continuous blue light using a Lumencor Sola light
engine through a $1\times$ 0.04 NA objective (Nikon Instruments, CFI Plan
Achromat 1X) for 10 minutes. This allowed the sample to obtain its isotropic
bundled structure. Subsequent experiments were performed at $4\times$ 0.13 NA
(Nikon Instruments, CFI Plan Fluor 4X) or $4\times$ 0.2 NA (Nikon Instruments,
CFI Plan Apochromat Lambda D 4X) with pulsed blue light.

For spatial patterning of activity, we used a laser scanning confocal (Leica
Microsystems, SP8) to the activate regions of arbitrary shape with a laser
tuned to 488 nm (Leica Microsystems, Stellaris White Light Laser).
Alternatively, an opaque mask was placed above the sample and a white LED
(Nikon Instruments, Dia LED) was used to photoactivate the exposed region from
above. The data in Fig. 5 was taken using opaque masks. For all experiments,
the integrated intensity was calculated by first, measuring the power at the
sample plane with a power meter. The entire sensor was filled by light, so
that the intensity of light
$I_{\textrm{raw}}=\frac{\textrm{power}}{\textrm{area of sensor}}$. To account
for the pulsed activation,

$I_{\textrm{integrated}}=I_{\textrm{raw}}\times\frac{\textrm{exposure
time}}{\textrm{frame interval}}.$ (S1)

This assumption is valid only within the regime where the motors are not
unbinding on the timescales of the frame interval. We found this threshold to
be 30 s from an experiment in which we incrementally increased the time
between photoactivation pulses.

###  V.7 Analysis of Microtubule Flows

Flow fields were obtained through particle image velocimetry (PIVLab MATLAB
plugin) [37]. The PIV analysis parameters were optimized for each data set
[Fig. S1]. Generally, a small window size in pixels resulted in larger average
speeds. Thus, we kept the window size constant across data sets. By
incrementally skipping frames in the analysis, we determined the optimal
sampling of data to suppress noise and maintain temporal and spatial
resolution. The average speed for each frame was calculated within the center
of the chamber.

For Fig. 2, the average speeds were obtained from imaging samples prepared as
described above for 2-6 hours during which they were continuously
photoactivated. The average was taken over the entire imaging time.

###  V.8 Analysis of Network Relaxation

For Fig. 3, the average orientation of the network was found from the
structure tensor of the fluorescent image of the microtubules using the FIJI
Image J plugin OrientationJ with a window size of 8 pixels [58]. The initial
angle was set to zero radians, defined to be along the $x$ axis. The standard
deviation reported in Fig. 3(b) is from the spatially resolved orientation at
a particular time.

###  V.9 Calculation of strain fields

The displacement and strain fields were calculated from the fluorescent images
of the microtubules using NCORR2 in MATLAB [59]. The transition to instability
was defined by the in-plane component of the strain perpendicular to the
network alignment, $\gamma_{yy}$. Over the 17 minute activation for each
intensity, we defined the onset of buckling as when the strain increase beyond
0.5%. Below this threshold, the strain fluctuated around the noise floor [Fig.
S11].

##  VI Relaxation of the bend instability upon deactivation

We measured the average angle of a flow aligned microtubule network driven by
non-processive opto-kinesin. Upon deactivation, the angle partially relaxed
towards a more uniform state. We describe a model that accounts for the
lingering activity of motors that are being deactivated over time and the
elastic decay of the microtubule network.

A function $M(t)$ describes the fraction of unbound motors where $t=0$ is the
last moment of photoactivation. Thus, $M(t=0)=0$ indicates that the bound
motor fraction is completely saturated. In the dark, we will assume that
$M(t\rightarrow\infty)=1$ indicating that the unbound motor fraction is
completely saturated. $M(t)$ should take on a form that is consistent with the
unbinding kinetics of proteins. We define

$M(t)=1-e^{-t/\tau}.$ (S2)

Absorbance assay revealed the thermal reversion kinetics of the iLID domain is
exponential decaying with characteristic time scale $\tau=24$ s assuming
exponential kinetics [Fig. S7] [60] . It follows that the angle relaxation is
described by

$\langle\theta\rangle=(1-M(t))A(t)+R(t)$ (S3)
$\langle\theta\rangle=e^{-t/\tau}A(t)+R(t)$ (S4)

where $A(t)$ is the activity-driven growth of the angle and $R(t)$ is the
elastic relaxation of the network. We measured $A(t)$ during the activation
cycle and found $A(t)=\gamma t$, where $\gamma=0.002$ rad/s [Fig. S6].

We assume that the microtubule network behaves as a Hookean elastic solid such
that its relaxation can be described by an overdamped spring

$\ddot{x}+\beta\dot{x}+\omega_{o}x=0$ (S5)

where the solution is given by the ideal limit conditions

$R(t)=C*e^{-t/r}$ (S6)

where $r=2\left(-\beta-\sqrt{\beta^{2}-4\omega_{o}^{2}}\right)^{-1}$ where
$\beta$ describes the frictional dissipation and $\omega_{o}$ is the angular
frequency of oscillation.

Putting this together, we fitted the measured decay curves to:

$\langle\theta\rangle=e^{-t/\tau}\dot{\gamma}t+e^{-t/r}$ (S7)

where $r$ is a fit parameter describing the characteristic time for the
solid’s relaxation. To compare relaxations at different stages of the bend
instability we normalize the angle
$\langle\theta_{\textrm{norm}}\rangle=\frac{\theta_{\textrm{i}}-\theta_{\textrm{min}}}{\theta_{\textrm{max}}-\theta_{\textrm{min}}}$.

##  VII Hydrodynamic Model of Confined Aligned Microtubule Network

We consider a flow aligned active nematic with spatially patterned active
stresses. In the illuminated region, the extensile active stresses destabilize
orientational order. Let the instantaneous axis of orientational order of the
microtubule bundles at position $\vec{r}$ be denoted $\hat{n}(\vec{r},t)$.
$\hat{x}$ is the axis of initial nematic order, i.e., $\hat{n}(t=0)=\hat{x}$.
Consider a spatially varying perturbation to the orientationally ordered
state, such that $\hat{n}=\hat{x}+\delta\vec{n}_{\perp}(\vec{r})$. Modelling
the illuminated region using the hydrodynamic theory for an active nematic
reveals that the eigenvectors of the dynamics correspond to Fourier transforms
of twist-bend and splay-bend deformations, and that twist-bend modes grow
faster than splay-bend modes [42]. Therefore, the instability seen in the
experiment should correspond to a growing twist-bend deformation. Further, the
dynamics of a twist-bend deformation with wavevector $\vec{k}$ is given by
(see SI of Chandrakar et. al., 2020 [42] for the hydrodynamic model and the
linear stability analysis)

$\displaystyle\partial_{t}[\hat{x}.(\vec{k}\times\delta\tilde{\vec{n}}_{\perp})]=\left(-D_{R}\kappa
k^{2}+\frac{2\alpha}{3\eta}\frac{k_{x}^{2}}{k^{2}}\right)[\hat{x}.(\vec{k}\times\delta\tilde{\vec{n}}_{\perp})]$
(S8)

where $\alpha$ is the “activity” which corresponds to the force dipole
generated by the extending microtubule bundles, $D_{R}$ is the rotational
diffusion constant of the microtubule bundles, $\kappa$ is the nematic
elasticity (assuming that bend, twist, and splay, all have the same energetic
cost), and $\eta$ is the viscosity. Let $H$ be the height of the chamber, $L$
be the size of the illuminated region along $\hat{x}$, and $W$ be the size of
the illuminated region along $\hat{y}$. Then, the components of the wave
vector are quantized by the confinement dimension, and are restricted to be
such that $k_{x}>\pi/L,k_{y}>\pi/W,\ k_{z}>\pi/H$. Based on experimental
observations, we assume $k_{y}=\pi/W$ and $k_{z}=\pi/H$. Then, depending on
the value of $L$, there are two instability regimes:

  1. 1.

At large $L$, the instability sets in as soon as the activity is high enough
for the fastest growing wave mode from equation S8 to be unstable. Taking the
derivative of the growth rate in equation S8 with respect to $k_{x}$ and
equating it to zero, the fastest growing mode satisfies

$\displaystyle\frac{\alpha(S_{0}+\xi)}{2\eta
D_{R}\kappa}=\frac{(k_{x}^{2}+(\pi/W)^{2}+(\pi/H)^{2})^{2}}{(\pi/W)^{2}+(\pi/H)^{2}}$
(S9)

and is unstable (equation S8 with this value of $k_{x}$ is positive) only for

$\displaystyle\frac{\alpha(S_{0}+\xi)}{2\eta
D_{R}\kappa}>4((\pi/W)^{2}+(\pi/H)^{2})$ (S10)

From eqns S9 and S10, the fastest growing mode, if unstable has to satisfy

$\displaystyle k_{x}^{2}>(\pi/W)^{2}+(\pi/H)^{2}$ (S11)

If $L$ is large enough that $(1/L)^{2}<(1/W)^{2}+(1/H^{2})$, equation S11
implies that $k_{x}>\pi/L$, so the fastest growing wave mode is not disallowed
by confinement in the x dimension. Then, the threshold activity for the
instability is given by equation S10. To summarize, for large $L$ (i.e.,
$(1/L)^{2}<(1/W)^{2}+(1/H^{2})$), the activity threshold for the instability
is given by $\frac{\alpha(S_{0}+\xi)}{2\eta
D_{R}\kappa}>4\pi^{2}\left(\frac{1}{W^{2}}+\frac{1}{H^{2}}\right)$

  2. 2.

For small $L$ ($\frac{1}{L^{2}}>\frac{1}{W^{2}}+\frac{1}{H^{2}}$), even when
the activity is high enough for the emergent fastest growing mode given by
equation S9 to be unstable, there is no instability because this emergent mode
is disallowed by the boundaries. Instead, the instability is observed when the
growth rate of the $k_{x}=\frac{\pi}{L}$ mode becomes positive, i.e. (from eq.
S8),

$\displaystyle\frac{\alpha(S_{0}+\xi)}{2\eta
D_{R}\kappa}>\pi^{2}L^{2}\left(\frac{1}{L^{2}}+\frac{1}{W^{2}}+\frac{1}{H^{2}}\right)^{2}$
(S12)

##  VIII Supplementary Figures

Supplementary Fig. 1: PIV flow fields from fluorescence images.

Supplementary Fig. 2: Reduced difference between on and off flows in active
gels driven by processive opto-kinesin upon repeated photoactivation.

Supplementary Fig. 3: Kinesin motor coding regions.

Supplementary Fig. 4: In the dark, the measured microtubule flows for the K365
opto kinesin are zero.

Supplementary Fig. 5: Measuring network angle from microtubule fluorescence
using OrientationJ.

Supplementary Fig. 6: Measuring the angular growth rate from the onset of the
bend instability.

Supplementary Fig 7: Extracting reversion timescale from absorbance recovery
of iLID construct.

Supplementary Fig. 8: Fitting the microtubule network decay to the elastic
model.

Supplementary Fig. 9: Displacement and strain fields of spatially patterned
active stress.

Supplementary Fig. 10: Depletion induced contraction of a flow aligned sample.

Supplementary Fig. 11: Defining threshold intensity for instability.

Supplementary Fig. 12: Flow fields after de-activation are highly correlated
with pre-activation flows.

Supplementary Fig. 13: Hysteresis in intensity-controlled active flow speed.

Figure S1: PIV flow fields from fluorescent microtubule images. (a) Overlay of
two images taken at t=0 (red) and t=5 s (cyan) illustrate the dynamical
microtubule network. (b) Flow field of images in (a) where colormap shows
speed. (c) Average speed versus time for various PIV window sizes. (d) Average
speed versus increasing frame interval. Parameters used for this data set are
represented by bolded curve. (e) The chosen optimal mean speed versus time
curve for this data set.  Figure S2: Aging of active gels powered with K401
opto-kinesin clusters. The ratio of microtubule flow speeds in the illuminated
and dark state as a function of the photoactivation cycle. Figure S3: Kinesin
motor coding regions  Figure S4: Dark-state dynamics of K365 opto-kinesin
active fluids. The velocity of active fluid where the sample is in the dark
(green) and a sample that ran out of ATP (black). Both analyses were done at
30 s/frame and the same PIV settings. Figure S5: Measuring network angle from
microtubule fluorescence using OrientationJ. (a) Fluorescence image of shear-
aligned microtubules undergoing bend instability. (b) Filament orientation
obtained from the structure tensor analysis using OrientationJ with window
size of 8 pixels. Intensity indicates angle. (c) Calculated orientation field
plotted over fluorescence image. Figure S6: Measuring angular growth rate from
the onset of the bend instability. The filament orientation angle versus time
during activation of the bend instability. The line is a fit with the slope
$\gamma=0.002$ rad/s.  Figure S7: Extracting reversion timescale from
absorbance recovery of iLID construct. Modified from [60]. A plot of the
absorbance at 450 nm recovery after activation for the iLID construct where an
absorbance of 1 indicates a full recovery to the dark structure of the iLID
protein. The line indicates a fit to a bounded exponential $A=1-e^{-t/\tau}$
where $\tau=24$ s.  Figure S8: Fitting the microtubule network decay to the
elastic model. (a-e) After de-activation a sample undergoing bend-instability
undergoes partial relaxation. Fits of average angle $\langle\theta\rangle$ to
Equation 1 after de-activation. (f) Data and fits were normalized by the
maximum angle such that
$\langle\theta_{\textrm{norm}}\rangle=\frac{\langle\theta\rangle-\theta_{\textrm{min}}}{\theta_{\textrm{max}}-\theta_{\textrm{min}}}$.
The average is shown in Fig. 3(b). Figure S9: Displacement and strain fields
of spatially patterned active stress. (a-c) Overlay of initial (red) and final
(cyan) of a flow aligned 3-dimensional network of microtubules where the
highlighted region is activated with light. Gray indicates no movement of
filaments (red + cyan = white). Indicated squares are 400 $\times$ 400
$\mu$m2. (a) Quiescent regime: the intensity in the activated region,
indicated by the yellow square, is low 0.11$\mu$W/mm2. (b) Sliding regime: the
intensity in the activated region, indicated by the green square, is 0.28
$\mu$W/mm2. (c) Turbulent regime: the intensity in the activated region,
indicated by the blue square is high 0.64 $\mu$W/mm2. (d-f) Displacement field
of the activated regions in (a-c) respectively. (g-i) Strain field
$\gamma_{xx}$ measured from the displacements in (d-f) respectively.  Figure
S10: Depletion induced contraction of a flow aligned sample. Snapshots of an
aligned microtubule network exhibiting depletion induced contraction. Figure
S11: Defining threshold intensity for instability. (a) The component of strain
perpendicular to alignment $\gamma_{yy}$ as function of time for a 200 $\mu$m2
activated region. Color indicates the intensity of activation light at 488 nm.
b The strain $\gamma_{yy}$ accumulated after 17 min of activation as a
function of activation intensity for a 200 $\mu$m2 activated area. The red
data point indicates the intensity threshold for instability. (c-d) The same
measurements for a 300 $\mu$m2 activation region. The red data point indicates
the threshold intensity for the instability.  Figure S12: Flow fields after
de-activation are highly correlated with pre-activation flows. (a) Flow field
in last frame of of a light cycle PIV. Color indicates flow speed. (b) Re-
activated flow field after 30 min dark cycle. (c) The difference between the
two velocities. The correlation coefficient between the two flow fields is
0.89.  Figure S13: Hysteresis in intensity-controlled active flow speed. (a)
The flow speed plotted as a function of photoactivation intensity. The color
bar indicates forward in time from blue to yellow. (b) Bundle structure at the
same photoactivation intensity for the cycle 1 and cycle 10 respectively.

##  IX Video Captions

Videos are located here.

Video 1: K401 opto-kinesin drive extensile active fluid dynamics when
photoactivated. This video shows fluorescently labeled microtubules in an
active fluid alternately photoactivated by 2.4 $\mu$W/mm2 blue light and
deactivated. Scale bar: 500 $\mu$m.

Video 2: K365 opto-kinesin drive extensile active fluid dynamics. This video
shows fluorescently labeled microtubules in an active fluid alternately
photoactivated by 2.2 $\mu$W/mm2 blue light and deactivated. Scale bar: 500
$\mu$m.

Video 3: Controlling the onset of the bend instability. An initially aligned
microtubule network with 300 nM K365 opto-kinesin was exposed to bursts of
photoactivation which pushed the microtubules into the bend instability.
Subsequent deactivation showed relaxation of the passive microtubule network
as the K365 opto-kinesin un-clustered.

Video 4: Size dependence of bend instability. An initially aligned network of
fluorescently labeled microtubules and K365 opto-kinesin was photoactivated
inside the yellow boxes of various sizes (50 $\mu$m2 \- 500 $\mu$m2). At a
single photoactivation intensity, the largest box (500 $\mu$m2) underwent the
bend instability, the mid-size boxes (250 $\mu$m2, 200 $\mu$m2) mostly
exhibited sliding dynamics and the smaller boxes (100 $\mu$m2 and 50 $\mu$m2)
remained quiescent.

Video 5: Confined flows in aligned microtubule network for quiescent, sliding
and bend instability regimes. An initially aligned network of fluorescently
labeled microtubules was sequentially photoactivated at increasing intensities
within a 400 $\mu$m2 box indicated by the yellow border. Left panel: quiescent
regime at low activation intensity, 0.11 $\mu$W/mm2. Middle panel: sliding
regime at 0.28 $\mu$W/mm2. Right panel: bend instability regime at high
activation intensity, 0.64 $\mu$W/mm2.

Video 6: Depletion of microtubules within activated region. An initially
aligned network of fluorescently labeled microtubules and K365 opto-kinesin
with a photobleached line as a material marker. The region inside the yellow
box was photoactivated with a 488 nm laser. The microtubules undergo
successive bend instabilities and eventually deplete from the activated
region.

Video 7: Kinesin-14 and K365 opto-kinesin without activation contracts for
many hours. An active network of fluorescently labeled microtubules with both
kinesin-14 and K365 opto-kinesin motors. The sample was never photoactivated
so that the K365 opto-kinesin were un-clustered. The network contracts for the
acquisition time, 12 hours.

Video 8: Transition from contractile to extensile active stress in composite
motor system. An active network of fluorescently labeled microtubules with
kinesin-14 motors and K365 opto-kinesin motors. Initially the K365 opto-
kinesin were not activated, so that the network contracted into a dense
aligned bundle driven by kinesin-14 motors. Upon photoactivation, the material
extended and underwent the bend instability.

Video 9: Extended illumination below “threshold” intensity within confined
region eventually leads to the bend instability. An initially aligned
microtubule network is exposed to low intensity photoactivation light within
the indicated 400 $\mu$m2 square. Eventually, the microtubules slide out of
the activated region and the material bends perpendicular to the direction of
alignment.