DOI: 10.6071/m37088
title: Active nematic order and dynamic lane formation of microtubules driven by membrane-bound diffusing motors

description: Dynamic lane formation and long-range active nematic alignment is reported
 using a geometry in which kinesin motors are directly coupled to a lipid
 bilayer, allowing for in-plane motor diffusion during microtubule gliding.
 We use fluorescence microscopy to image protein distributions in and below
 the dense two-dimensional microtubule layer, revealing evidence of
 diffusion-enabled kinesin restructuring within the fluid membrane
 substrate as microtubules collectively glide above. We find that the lipid
 membrane acts to promote filament-filament alignment within the gliding
 layer, enhancing the formation of a globally aligned active nematic state.
 We also report the emergence of an intermediate, locally ordered state in
 which apolar dynamic lanes of nematically-aligned microtubules migrate
 across the substrate. To understand this emergent behavior, we implement a
 continuum model obtained from coarse graining a collection of
 self-propelled rods, with propulsion set by the local motor kinetics.
 Tuning the microtubule and kinesin concentrations as well as active
 propulsion in these simulations reveals that increasing motor activity
 promotes dynamic nematic lane formation. Simulations and experiments show
 that, following fluid bilayer substrate mediated spatial motor
 restructuring, the total motor concentration becomes enriched below the
 microtubule lanes that they drive, with the feedback leading to more
 dynamic lanes. Our results have implications for membrane coupled active
 nematics in vivo as well as for engineering dynamic and reconfigurable
 materials where the structural elements and power sources can dynamically
 co-localize, enabling efficient mechanical work.
description: The data includes 1) Measurements of
 microtubule length.  2) Calculations of order parameter
 in different phases. For experimental imaging we used
 fluorescence microscopy (Leica Microsystems Inc. DM 2500P fluorescence
 Microscope, (Buffalo Grove, IL, USA)) and confocal fluorescence microscopy
 (Zeiss LSM 889 with AiryScan + FAST and a Gallium arsenide phosphide
 (GaAsP) photon counting photodetector.). A QImaging Retigia Exi camera
 (Surrey, BC, Canada) and an ORCA - Flash4.0 LT+ Digital CMOS camera,
 (Hamamatsu, Shizuoka, Japan) were used to record fluorescence movies under
 low light conditions. The images were recorded at 10 second time intervals
 with either 20x, 40x, or 63x objectives. For the phase diagram in Figure
 3a we used a region of interest (ROI) of 500px x 500px (where 2.1 px = 1
 µm) and the following order parameter thresholds to determine the phase
 behavior: Nematic S &gt; 0.25, Coexistence 0.20 &lt; S &lt;
 0.25, Lane formation 0.10 &lt; S &lt; 0.20 and Isotropic 0
 &lt; S &lt; 0.10. In Figure 3 (c-d) we calculated the nematic
 order parameter and the ROI box size was varied to compare local and
 global order parameters. Image analysis was performed using ImageJ
 (http://imagej.nih.gov/ij/) including the ImageJ plugin, OrientationJ to
 calculate angular distributions of microtubules (23). Order parameters in
 each image were calculated with the ImageJ plugin, OrientationJ and a bin
 size of 5° to calculate angular distributions of the microtubules using
 the published method from (23). To calculate microtubule surface density
 on the bilayer, five different regions of area, A are randomly selected
 for each flow cell. The microtubules were counted manually for those
 selected regions and the fraction of fluorescently labeled microtubules
 for each flow cell used to find the total microtubules per unit
 area.