Banks
et al
. eLife 2023;12:e79402. DOI: https://doi.org/10.7554/eLife.79402
1 of 30
Motor processivity and speed determine
structure and dynamics of microtubule-
motor assemblies
Rachel A Banks
1
, Vahe Galstyan
1
, Heun Jin Lee
2
, Soichi Hirokawa
2
,
Athena Ierokomos
3
, Tyler D Ross
4
, Zev Bryant
5
, Matt Thomson
1
, Rob Phillips
1,2,6
*
1
Division of Biology and Biological Engineering, California Institute of Technology,
Pasadena, United States;
2
Department of Applied Physics, California Institute of
Technology, Pasadena, United States;
3
Biophysics Program, Stanford University,
Stanford, United States;
4
Department of Computing and Mathematical Science,
California Institute of Technology, Pasadena, United States;
5
Department of
Bioengineering, Stanford University, Stanford, United States;
6
Department of Physics,
California Institute of Technology, Pasadena, United States
Abstract
Active matter systems can generate highly ordered structures, avoiding equilibrium
through the consumption of energy by individual constituents. How the microscopic parameters that
characterize the active agents are translated to the observed mesoscopic properties of the assembly
has remained an open question. These active systems are prevalent in living matter; for example,
in cells, the cytoskeleton is organized into structures such as the mitotic spindle through the coor
-
dinated activity of many motor proteins walking along microtubules. Here, we investigate how the
microscopic motor-
microtubule interactions affect the coherent structures formed in a reconstituted
motor-
microtubule system. This question is of deeper evolutionary significance as we suspect motor
and microtubule type contribute to the shape and size of resulting structures. We explore key
parameters experimentally and theoretically, using a variety of motors with different speeds, proces-
sivities, and directionalities. We demonstrate that aster size depends on the motor used to create
the aster, and develop a model for the distribution of motors and microtubules in steady-
state asters
that depends on parameters related to motor speed and processivity. Further, we show that network
contraction rates scale linearly with the single-
motor speed in quasi-
one-
dimensional contraction
experiments. In all, this theoretical and experimental work helps elucidate how microscopic motor
properties are translated to the much larger scale of collective motor-
microtubule assemblies.
Editor's evaluation
Banks et al. demonstrate that the organization and dynamics of microtubule/kinesin asters depend
upon the speed and processivity of motors. By combining in vitro reconstitutions with theory, they
are able to extract parameters that relate to the dynamics of the motors. This study is of interest to
readers working on microtubules, motors, and in the active matter physics field.
Introduction
A signature feature of living organisms is their ability to create beautiful, complex patterns of activity,
as exemplified in settings as diverse as the famed flocks of starlings in Rome or the symmetrical and
dazzling microtubule arrays that separate chromosomes in dividing cells (
Popkin, 2016
). While such
organization in nature has long captured the attention of artists and scientists alike, many questions
RESEARCH ARTICLE
*For correspondence:
phillips@pboc.caltech.edu
Competing interest:
The authors
declare that no competing
interests exist.
Funding:
See page 13
Preprinted:
23 October 2021
Received:
11 April 2022
Accepted:
07 February 2023
Published:
08 February 2023
Reviewing Editor:
Karsten
Kruse, University of Geneva,
Switzerland
Copyright Banks
et al
. This
article is distributed under the
terms of the Creative Commons
Attribution License, which
permits unrestricted use and
redistribution provided that the
original author and source are
credited.
Research article
Physics of Living Systems
Banks
et al
. eLife 2023;12:e79402. DOI: https://doi.org/10.7554/eLife.79402
2 of 30
remain about how the patterns and structures created by living organisms arise. In active systems
such as bird flocks or microtubule-
motor arrays, energy is consumed at the local level of the individual
actors, and constituents move based on interactions with their neighbors. These local actions create
patterns at scales hundreds to thousands of times larger than the individual constituent. How the
specific microscopic activity of each individual leads to the final large-
scale assembly formed remains
an open question in these systems from the molecular to organismal level.
The motor-
microtubule system is an excellent system in which to test this question, as many motor
proteins with a variety of properties, such as speeds, stall and detachment forces, processivities, and
directionalities, exist in nature. These motors play a variety of roles in cells; some transport cargo
while others localize to distinct regions of the mitotic spindle (
Wickstead and Gull, 2006
;
Mann and
Wadsworth, 2019
;
Endow et al., 1994
;
Pavin and Toli
ć
, 2021
;
Anjur-
Dietrich et al., 2021
). Studies
have investigated how the microscopic properties of these motors makes them uniquely suited to
their cellular role. For example, kinesin-
1s high speed and processivity make it excellent at trans-
porting cargo (
Grover et al., 2016
;
Hirokawa et al., 1991
). However, in in vitro systems, kinesin-
1
tetramers are able to form asters, extensile networks, and contractile networks (
Surrey et al., 2001
;
Sanchez et al., 2012
;
DeCamp et al., 2015
;
Ross et al., 2019
). Ncd (kinesin-
14) and Kif11 (kinesin-
5)
have similarly been shown to form asters in vitro, yet it remains unclear how the properties of these
motors affect the structure and dynamics of the assemblies created (
Surrey et al., 2001
;
Sanchez
et al., 2012
;
DeCamp et al., 2015
;
Ross et al., 2019
;
Roostalu et al., 2018
).
In this work, we create motor-
microtubule structures with a variety of motors and develop theo-
retical models to connect the motor properties to the organization and dynamics of the assemblies.
Our recently developed optogenetic in vitro motor-
microtubule system demonstrated the formation
of asters and other contractile networks with kinesin-
1 (K401) upon light activation (
Ross et al., 2019
).
Briefly, we fused K401 motors to an optogenetic pair of light-
dimerizable proteins, such that in the
presence of light the optogenetic pair bind, acting as a crosslink between microtubules that the motor
heads are walking along. Previously, we showed that this scheme enabled us to form microtubule
structures with spatiotemporal control by illuminating regions of the sample at will. We now show
how this system can be re-
purposed to ask a new set of questions with kinesin-
5 (Kif11) and kinesin-
14
(Ncd), and form asters of varying sizes with each motor, demonstrating light-
controlled aster forma-
tion with these motors for the first time. Our controlled structure formation with these various motors
enabled us to develop a theoretical model connecting the distribution of motors and microtubules in
asters that depends on microscopic motor properties. We find that calculated motor distributions in
an aster depend on the motor properties and fit with our experimental data. Further, by using motors
with different speeds, we find that contraction rates in quasi-
one-
dimensional microtubule networks
directly depend on the single-
motor velocity. This theoretical and experimental work sheds light on
the ways that microscopic motor properties are reflected in the 1000-
fold larger length scale of motor-
microtubule assemblies.
Results
Aster size depends on motor used
We build on the foundational work that demonstrated the ability to control motor-
microtubule systems
with light (
Ross et al., 2019
) to consider a new set of motors with different fundamental properties.
In brief, kinesin motors are fused to the light-
dimerizable pair iLid and micro. In the absence of light,
motor dimers walk along microtubules but do not organize them; upon activation with light, the motor
dimers couple together to form tetramers, crosslinking the microtubules they are walking along as
shown in
Figure 1A
. The optogenetic bond lasts for about 20 s before reverting to the undimerized
state, thus in our experiments, we repeatedly illuminate the sample every 20 s (
Guntas et al., 2015
).
As demonstrated by Ross et al., projecting a cylinder of light on the sample results in the formation of
an aster, and different structures can be formed and manipulated by illumination with different light
patterns. For the purposes of this study, we were careful to remain in a regime of motor and microtu-
bule concentrations that produced a single aster upon illumination. However, by varying concentra-
tions of the motors and microtubules, it is possible to form multiple smaller asters within the region, a
few examples of which are shown in
Figure 1—figure supplement 1
. How varying the composition of
the reaction mixture impacts the resulting structures warrants further investigation.
Research article
Physics of Living Systems
Banks
et al
. eLife 2023;12:e79402. DOI: https://doi.org/10.7554/eLife.79402
3 of 30
+
+
+
+
~1 μm
h
ν
+
-
+
+
+
-
-
-
microtubules
motors
crosslinked
microtubules
dimerized
motors
(A)
K401
Kif1
1N
cd236
600 μm
50 μm
(C)
20 μm
ASTERS FORMED BY VARIOUS MOTORS
ASTER SIZE DEPENDS ON MOTOR
(D)
MEASUREMENT OF ASTER SIZE
LIGHT ACTIVATION DIMERIZES MOTORS
(B)
20 μm
radial distance (μm)
0
10
20
30
40
0
40
80
120
tubulin (μM)
tubulin threshold
r outer
aster radius (μm)
excitation diameter (μm)
Figure 1.
Aster size depends on motor used. (
A
) Motor heads are fused to optogenetic proteins such that activation with light causes the formation
of motor tetramers (dimer of dimers). Motors are shown walking toward the microtubule plus-
end. K401 and Kif11 walk in this direction, however Ncd
is minus-
end directed. (
B
) Images of the microtubule fluorescence for asters formed with each of the motors excited with a disk either 50 or 600 μm in
diameter. (
C
) Image of the microtubule fluorescence from an aster with the measured size represented with the outer black circle. The plot on the right
shows the radial microtubule concentration as revealed by fluorescence intensity; the threshold concentration used to determine the aster size is shown
as a black horizontal line. (
D
) Mean aster size (
n
≈ 5 asters for each condition) for the three motors and different excitation diameters; the error bars
represent the standard deviation.
The online version of this article includes the following figure supplement(s) for figure 1:
Figure supplement 1.
Examples of multiple asters formed.
Figure supplement 2.
Example images of microtubule fluorescence of asters made with each motor used and each excitation diameter.
Research article
Physics of Living Systems
Banks
et al
. eLife 2023;12:e79402. DOI: https://doi.org/10.7554/eLife.79402
4 of 30
In this work, we aim to determine how the properties of the motor affect the resulting structures.
While experiments with this system were previously performed with
Drosophila melanogaster
kine-
sin-
1 motors (K401) (
Ross et al., 2019
), in the present work, we investigate if other kinesin motor
species with different intrinsic properties such as speed and processivity would lead to light-
inducded
microtubule organization. Toward this end, we use the same light-
dimerizable scheme to form micro-
tubule structures with two other motors: Ncd (
D. melanogaster
kinesin-
14) and Kif11 (
Homo sapiens
kinesin-
5). The single-
molecule properties of all three motors we use are summarized in
Table 1
. We
measure the speed of each motor species by gliding assays (SI section ‘Gliding assay’); the proces-
sivities are based on literature values. Further, we fluorescently label the motors using mVenus or
mCherry to visualize the motors and microtubules in separate imaging channels within the same assay
(see
Supplementary file 1
).
As seen in
Figure 1B
and
Figure 1—figure supplement 2
, each of these motors is able to form
asters of varying sizes in our system. It was previously unclear whether there were limits to speed,
processivity, or stall force that might prevent any of these motors from forming asters in our light-
controlled system, although Ncd has previously been shown to form asters as constitutive oligomers
(
Belmonte et al., 2017
;
Hentrich and Surrey, 2010
). We found that all were able to form asters upon
illumination by various excitation diameters ranging from 50 to 600 μm. Interestingly, the dynamics of
aster formation by these motors seemed to roughly scale with the motor speeds – K401 formed asters
the quickest, followed by Ncd236, and Kif11 took the most time to form an aster.
We sought to determine if there are discernible differences between the asters formed with the
various motors. First, we measured the size of the asters using the distribution of fluorescently labeled
microtubules, which peaks in the center of the aster and generally decreases moving outward, as
shown in
Figure 1C
. We tend to observe a shoulder in the microtubule distribution (around 20 in
the example in
Figure 1C
). This is around the size of the disordered aster core, which is discussed
in SI section ‘Disordered aster core’. We defined the outer radius of the aster as the radius at which
the microtubule fluorescence is twice the background microtubule concentration (see
Figure 1C
for
an example aster outer radius determination). We found that this method agreed well with a visual
inspection of the asters (
Figure 1—figure supplement 2
).
We found that aster size increases with excitation diameter, as shown in
Figure 1B, D
, consistent
with what was shown by Ross et al. for K401 (
Ross et al., 2019
). In Ross et al., it was determined that
the aster size roughly scaled with the volume of the excitation area, suggesting that the number of
microtubules limits the size of the aster. This hints that there may be a density limit to the microtubules
in an aster. Interestingly, we find that the size of the asters also depends on the motor used. For each
excitation diameter, except for the 50 μm case, K401 formed the largest asters and Ncd formed the
smallest, with Kif11 producing asters of intermediate size (
Figure 1D
). What is it about the different
motors that confers these different structural outcomes? We found that this trend correlates with
motor processivity; K401 is the most processive, followed by Kif11, and then Ncd. This is similar to the
findings in
Surrey et al., 2001
, in which intensity of aster formation was related to motor processivity.
Other factors could also be contributing to aster size such as the ratio of microtubules to motors as
was suggested by
Surrey et al., 2001
, but not investigated in the present work, or the motor stall
force.
Table 1.
Properties of motor proteins used in this study.
Speeds were measured by us by gliding assay, the processivity and directionality are literature
values.
Motor
Speed
Processivity
Direction
K401
≈ 600 nm/s
≈100 steps (
Belmonte et al.,
2017
)
Plus (
Hirokawa et al., 1991
)
Ncd236
≈115 nm/s
Not processive (
Hentrich and
Surrey, 2010
,
Nédélec et al.,
2001
,
Lee and Kardar, 2001
)
Minus (
Sankararaman et al.,
2004
)
Kif11(513)
≈70 nm/s
≈10 steps (
Aranson and
Tsimring, 2006
)
Plus (
Aranson and Tsimring,
2006
)
Research article
Physics of Living Systems
Banks
et al
. eLife 2023;12:e79402. DOI: https://doi.org/10.7554/eLife.79402
5 of 30
Spatial distribution of motors in asters
The nonuniform distribution of filaments and motors in an aster is a key feature of its organization
and has been the subject of previous studies. In these studies, continuum models were developed
for motor-
filament mixtures which predicted the radial profile of motors in confined two-
dimensional
systems (
Nédélec et al., 2001
;
Lee and Kardar, 2001
;
Sankararaman et al., 2004
;
Aranson and Tsim-
ring, 2006
). A notable example is the power-
law decay prediction by Ndlec et al., who obtained it for
a prescribed organization of microtubules obeying a
1/
r
decay law (
Nédélec et al., 2001
). Measuring
the motor profiles in asters formed in a quasi-
two-
dimensional geometry (with the
z
- dimension of the
sample being only a few microns deep) and fitting them to a power-
law decay, the authors found a
reasonable yet noisy match between the predicted and measured trends in the decay exponent.
In our work, we also develop and test a minimal model that predicts the motor profile from the
microtubule distribution and the microscopic properties of the motor. Our well-
defined asters of
various sizes shown above, created with varying motor properties yields an opportunity for us to test
how our model and assess how the microscopic motor properties are translated to the aster scale.
Additionally, in contrast to the earlier study (
Nédélec et al., 2001
), asters formed in our experiments
are three-
dimensional due to the much larger depth of the flow cells (roughly 100 μm), and are thus
more similar to the structures observed in cells. While the largest asters we form are likely partially
compressed in the
z
- direction, we assume that this effect does not significantly alter the protein
distributions in the central
z
- slice. For modeling purposes, then, we consider our asters to be radially
symmetric outside the central disordered region (which we refer to as the aster core, as depicted sche-
matically in
Figure 2A
). The core has a typical radius of
≈
15
μm, beyond which microtubules have a
predominantly polar organization (see SI section ‘Disordered aster core’ for the discussion of the two
aster regions and an example Pol-
Scope image that demonstrates their distinction).
Similar to the treatment in earlier works (
Nédélec et al., 2001
;
Sankararaman et al., 2004
;
Aranson
and Tsimring, 2006
), we introduce two states of the motor – an unbound state where the motor can
freely diffuse with a diffusion constant
D
and a bound state where the motor walks toward the aster
center with a speed
v
, depicted in
Figure 2B
. In the steady state of the system, which we assume our
asters have reached at the end of the experiment, microtubules on average have no radial movement
and hence, do not contribute to motor speed. To assess the validity of this assumption, we performed
fluorescence recovery after photobleaching (FRAP) experiments of steady-
state asters, and observe
little radial flux of the microtubules, an example is shown in
Appendix 1—figure 4
. They are still
dynamic, as can be seen by the angular motion that leads to the recovery of fluorescence in the photo-
bleached areas. We denote the rates of motor binding and unbinding by
k
on
and
k
off
, respectively.
When defining the first-
order rate of motor binding, namely,
k
on
ρ
MT
(
r
)
, we explicitly account for the
local microtubule concentration
ρ
MT
(
r
)
extracted from fluorescence images. This is unlike the previous
models which imposed specific functional forms on the microtubule distribution (e.g., a constant value
[
Lee and Kardar, 2001
;
Sankararaman et al., 2004
] or a power-
law decay [
Nédélec et al., 2001
]),
rendering them unable to capture the specific features often seen in our measured microtubule
profiles, such as the presence of an inflection point (see
Figure 1C
for an example).
From these assumptions, the governing equations for the bound (
m
b
) and free (
m
f
) motor concen-
trations are shown in
Figure 2C
. They involve binding and unbinding terms, as well as a separate flux
divergence term for each population. Solving these equations at steady state, we arrive at an equa-
tion for the total local concentration of motors defined as
m
tot
(
r
)=
m
b
(
r
)+
m
f
(
r
)
. The derivation of this
result can be found in SI section ‘Model formulation’. As seen in the equation for
m
tot
(
r
)
(
Figure 2C
),
knowing the microtubule distribution
ρ
MT
(
r
)
along with two effective microscopic parameters, namely,
the effective dissociation constant
K
d
=
k
off
/
k
on
and the length scale
λ
0
=
D
/
v
, we can obtain the motor
distribution up to a multiplicative constant (
C
in the equation). Note that in the special case where the
motors do not move (
v
→
0
or
λ
0
→∞
), the exponential term becomes 1 and an equilibrium relation
between the motor and microtubule distributions dependent only on
K
d
is recovered, as we would
expect for an equilibrium system.
To test this model, we extract the average radial distributions of microtubule and motor concen-
trations for each aster. Then, using the microtubule profile as an input, we fit our model to the motor
data and infer the effective parameters
K
d
and
λ
0
(see SI sections ‘Extraction of concentration profiles
from raw images’ and ‘Model fitting’ for details). A demonstration of this procedure on an example
Kif11 aster is shown in
Figure 2D
where a good fit to the average motor data can be observed. As