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Controlling Organization and Forces in Active Matter Through Optically-Defined Boundaries
Tyler D. Ross, Heun Jin Lee, Zijie Qu, Rachel A. Banks, Rob Phillips, Matt Thomson
TL;DR
How can active structures and flows be controlled with light, and what sets their motion and organization? The paper uses optically activated kinesin linkages and models to examine these behaviors, reporting stable 2D flow fields and relationships between light-pattern geometry and observed structures.
Problem
The mechanisms responsible for observed vortex generation remain uncertain, with boundary conditions, microtubule-depleted zones, and non-Newtonian fluid properties among candidate explanations.
Source: §2.23 · p. 39Method
The study uses light-activated kinesin linkages to organize microtubules and models flow using superimposed Stokeslet series representing contracting bundles.
Source: §1.1 · p. 9, §2.23 · p. 39Results
Flow structure and speed did not differ significantly across measured focal planes, supporting a 2D flow-field model for subsequent measurements.
Source: §2.19 · p. 35Takeaways & Limitations
For a “+” light pattern, superimposed single-bar flow fields closely resembled the experimentally observed field, while “L” and “T” cases were roughly similar but had mismatched inflow directions.
Source: §2.23 · p. 40The mechanisms, if any, that cause the observed vortices require further investigation.
Source: §2.23 · p. 39
Abstract
from arXiv · showhide
Living systems are capable of locomotion, reconfiguration, and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, "active" molecules that create and manipulate non-equilibrium structures and force fields that span up to millimeter length scales [1-3]. Experimental active matter systems of biological or synthetic molecules are capable of spontaneously organizing into structures [4,5] and generating global flows [6-9]. However, these experimental systems lack the spatiotemporal control found in cells, limiting their utility for studying non-equilibrium phenomena and bioinspired engineering. Here, we uncover non-equilibrium phenomena and principles by optically controlling structures and fluid flow in an engineered system of active biomolecules. Our engineered system consists of purified microtubules and light-activatable motor proteins that crosslink and organize microtubules into distinct structures upon illumination. We develop basic operations, defined as sets of light patterns, to create, move, and merge microtubule structures. By composing these basic operations, we are able to create microtubule networks that span several hundred microns in length and contract at speeds up to an order of magnitude faster than the speed of an individual motor. We manipulate these contractile networks to generate and sculpt persistent fluid flows. The principles of boundary-mediated control we uncover may be used to study emergent cellular structures and forces and to develop programmable active matter devices.
1 Methods and Materials
The methods combine light-responsive kinesin constructs with microtubules in a prepared flow-cell system, then use microscopy and image processing to study structures and flows.
1.1 Kinesin Chimera Construction and Purification
- K401-iLID and K401-micro chimeras provide the light-responsive motor linkage; the constructs were assembled from kinesin and iLID or SspB-micro coding regions.The MBP domain supports SspB-micro function during expression and can be removed after expression.Source: §1.1 · p. 9
1.2 Microtubule Polymerization and Length Distribution
- Microtubules were polymerized with GMP-CPP, and their measured mean length was 7 ± 0.2 µm, similar to the ≈6 µm exponential-fit mean.The exponential fit is used for comparison even though the full length distribution does not generally follow an exponential decay.Source: §1.2 · p. 10, Figure S2 · p. 11
1.3 Sample Chambers for Aster and Flow Experiments
- Acrylamide-passivated glass slides and coverslips were assembled with 3 mm channel gaskets into flow cells approximately 70 µm high.The glass cleaning and coating protocol is described in detail for aster and flow experiments.Source: §1.3 · p. 11
1.4 Reaction Mixture and Sample Preparation for Aster and Flow Experiments
- Aster and flow reactions used approximately 0.1 µM of each motor type and 1.5–2.5 µM tubulin; motor concentration and motor-to-microtubule ratio affect the resulting structures.Below 0.1 µM motor, light can form bundles or lattices of small asters; above approximately 2 µM, spontaneous bundling and aster formation occur.Source: §1.4 · p. 12
1.5 Sample Preparation for Gliding Assay
- Gliding-assay chambers were prepared by coating glass with antibodies, casein, and motor protein before adding labeled microtubules.The microtubules were supplied in M2B buffer with MgATP and DTT.Source: §1.5 · p. 12
1.6 Preparation of Tracer Particles
- Fluid velocity was measured using 1 µm polystyrene beads passivated with pluronic F-127.The beads were resuspended in buffer containing pluronic at the reaction-mixture concentration.Source: §1.6 · p. 12
1.7 Microscope Instrumentation
- A programmable DLP chip projected 470 nm activation patterns, while a gated 660 nm LED supplied transmitted illumination to limit unintended dimerization.Custom scripts controlled pattern projection and stage movement.Source: §1.7 · p. 13
2 Data Acquisition, Analysis, and Supplemental Discussion
The section describes how asters were imaged and quantified, and discusses how experimental conditions relate to the observed contractile behavior.
2.1 Aster Distribution in 3D
- Z-stack analysis found asters near the sample-plane midpoint, with symmetric intensity profiles in the Y and Z planes.The profiles were fit with Gaussians; the Z-stack projections show asters formed with 100 µm and 300 µm light disks.Source: §2.1 · p. 13, Figure S3 · p. 14, Figure S4 · p. 15
2.2.1 Microtubule Vortices
- Vortices reported in earlier systems were absent here, amid differences in channel spacing, boundary size, microtubule length and stabilization, and surface chemistry.The experiments reporting vortices used 5 µm channel spacing and taxol-stabilized filaments approximately 10–100 µm long; this study used approximately 70 µm spacing and 7 µm GMPCPP-stabilized filaments.Source: §2.2.1 · pp. 15–16
2.2.2 Extensile vs. Contractile
- The system forms contractile networks rather than extensile gels, a distinction the authors associate with filament length and depletion-agent conditions rather than the optically dimerizable motors.The cited comparison describes extensile systems as using high concentrations of depletion agents to preform bundles of short, stiff filaments.Source: §2.2.2 · p. 16
2.3 Microscopy Protocol
- Images for formation, merging, and movement were acquired every 20 s, while flow experiments used 4 s intervals for particle velocimetry.Typically one experiment was run per sample, and imaging was limited to up to one hour to minimize photobleaching, ATP depletion, and global activity; after several hours, dark regions began bundling.Source: §2.3 · p. 16
2.4 Measuring Aster Spatial Distribution with Image Standard Deviation
- Image standard deviation σ measures the width of an intensity-weighted spatial distribution, with pixel intensities interpreted as microtubule density.The analysis normalizes pixel intensity within a region of interest and uses the distribution's center coordinates to calculate variance.Source: §2.4 · pp. 16–17
2.5 Characteristic Size of an Aster
The analysis defines an image-based measure of aster size, specifies preprocessing and regions of interest, and evaluates reversibility and contraction timescales.
2.5.1 Determining Characteristic Size
- Characteristic aster size is the image standard deviation σ after approximately 15 min of activation, summarizing the projected XY distribution.This single measure was chosen because irregular aster arms make detailed segmentation challenging.Source: §2.5.1 · p. 17
2.6.1 Image Preparation
- Image preparation flattens illumination using a smoothed profile from the first frame, then subtracts background estimated from the final formation frame and thresholds negative values to zero.The flattening method depends on a uniform microtubule density in the first frame.Source: §2.6.1 · p. 17
2.6.2 Defining the Regions of Interest
- Formation analysis uses an activation-region disk identified from the final-minus-first-frame void, while decay analysis uses an aster-centered ROI scaled to 1.63 times the aster diameter.The decay ROI reduces contributions from microtubules diffusing in from the boundary.Source: §2.6.2 · p. 18
2.7 Reversibility of Aster Formation and Decay
- A formation–decay–reformation experiment supports reversibility, although the central aster core persists after decay.The time series includes the first and second assembly periods and the intervening decay.Source: §2.7 · p. 18, Figure S5 · p. 19
2.8 Speed and Characteristic Time Scales of Formation and Merging
- Characteristic contraction and merger times were roughly 1–2 min and showed little sensitivity to system size over the measured length range.The fitting used a critically damped harmonic-oscillator model after an empirically determined one-minute lag; it was more robust across excitation scales than an exponential fit.Source: §2.8 · pp. 19–21, Figure S7 · p. 20, Figure S6 · p. 20
2.9 Comparison to Light Activated Actomyosin Networks
The section contrasts localized, free-boundary microtubule networks with globally connected actomyosin networks and notes a shared contraction-scaling pattern.
2.9 Comparison to Light Activated Actomyosin Networks
- Both systems show contraction speed increasing linearly with excitation-region size, while this system's light-activated links create a localized network with a free boundary.Unlike the permanently crosslinked actomyosin network, reversible microtubule links can remodel and resolve after contraction.Source: §2.9 · p. 21
2.10 Analysis of Aster Decay
Aster decay is analyzed as diffusion of unbound microtubules: image variance grows linearly with time, allowing an effective diffusion coefficient to be estimated. Asters decay over tens of minutes, much longer than the tens-of-seconds timescale inferred for individual motor links.
2.10 Analysis of Aster Decay
- Asters appear to decay over tens of minutes, rather than tens of seconds, possibly because the aster center has elevated motor density and decays more slowly than an individual motor link.The authors relate the tens-of-seconds link-reversion timescale to pulsed illumination every 20 seconds and prior characterization of iLID/LOV systems.Source: §2.10 · p. 22
- Linear growth of image variance σ2 with time suggests aster decay is described by diffusion of unbound microtubules, from which an effective diffusion coefficient is estimated by fitting the variance slope.The distributions are not strictly Gaussian; the coefficient is calculated by analogy to the ideal 2D Gaussian case, where variance grows with slope 4D.Source: §2.10 · p. 22
- The effective diffusion coefficient is obtained by linearly fitting σ2 against time after 200 seconds.The time-dependent image variance is used to characterize aster decay.Source: §2.10 · p. 22, Figure S8 · p. 23
2.11 Diffusion Coefficient of a Microtubule
The section estimates a single microtubule’s diffusion coefficient from its drag in liquid media to compare against the effective coefficient measured during aster decay.
2.11 Diffusion Coefficient of a Microtubule
- Using a 7 µm-long, 12.5 nm-radius cylinder model at 298 K, the estimated single-microtubule diffusion coefficients are D∥= 0.3 µm2/s and D⊥= 0.2 µm2/s.The calculation uses previously determined cylinder drag coefficients for motion parallel and perpendicular to the long axis.Source: §2.11 · p. 23
- The authors use D∥, the larger longitudinal diffusion coefficient, as the single-microtubule value for comparison with aster decay.The diffusion coefficient is calculated from thermal energy and drag; the fluid viscosity is estimated as 2×10−3 Pa·s.Source: §2.11 · p. 23
2.12 Scaling Arguments for Aster Size and Comparison to Data
A scaling argument links aster size to the excitation disk size using microtubule abundance and approximate aster geometry. The section also describes image-processing methods for tracking moving asters.
2.12 Scaling Arguments for Aster Size and Comparison to Data
- Microtubule fluorescence scales linearly with light volume, indicating uniform density, and remains constant after initial contraction, indicating constant microtubule number during formation.The excitation region is treated as a cylinder for a disk pattern projected into a channel of approximately 70 µm height.Source: §2.12 · p. 24, Figure S9 · p. 24
- The scaling argument assumes roughly spheroidal asters and estimates their characteristic length from the microtubule number and cylindrical excitation volume.The resulting size-scaling relationship is compared with data using the fixed-exponent fit.Source: §2.12 · pp. 24–25
- A power-law fit with fixed exponent 2/3 is consistent with the scaling argument for aster size versus excitation disk size, although other exponents cannot be ruled out.The fit is applied to the data shown in Fig. 1f.Source: §2.12 · p. 25
2.13 Tracking of Moving Aster
- For moving-aster tracking, z-stacks are summed, illumination is flattened, and aster centers are found by Gaussian fits to one-dimensional intensity profiles.The 2D tracking procedure instead follows frame-to-frame centroid changes after Gaussian filtering and thresholding.Source: §2.13 · p. 25
2.14 Effective Potential of a Moving Aster
A moving aster lags behind a moving light pattern and returns to its center when the pattern stops, behavior modeled using an effective potential. The inferred spring-like force is far stronger than estimated optical-tweezer effects, leading the authors to attribute it to other effects such as microtubule-field remodeling.
2.14 Effective Potential of a Moving Aster
- Modeling the moving aster as a sphere gives a viscous drag force balanced by the pull toward the light pattern, which the authors represent with an effective potential.They first model the behavior with a generic potential without assuming its mechanism.Source: §2.14 · p. 26
- The light pattern’s movement leaves the aster displaced, and the observed linear relation between displacement and pattern speed implies a spring-like pulling force.The aster immediately returns toward the light-pattern center when the pattern stops; Fig. S10 compares return and pattern speeds.Source: §2.14 · pp. 25–26, Figure S10 · p. 26
- At a maximum displacement of approximately 30 µm, the inferred potential stores approximately 300 kBT of energy, equivalent to the work done returning the aster to the pattern center.The estimate uses an aster diameter of approximately 25 µm and a spring constant of approximately 3 × 10−15 N/µm.Source: §2.14 · pp. 26–27
- The estimated optical-tweezer spring constant is roughly a factor of 107 weaker than the observed value, so the authors attribute the potential to other effects such as microtubule-field remodeling.The optical-tweezer estimate is an upper bound based on a generous refractive-sphere assumption.Source: §2.14 · p. 27
2.15 Mechanism and Stability of a Moving Aster
Moving asters are accompanied by bundle streams and simultaneous microtubule loss and incorporation, while structure formation and flow generation require minimum pattern dimensions. The measured single-motor speeds and minimum feature sizes quantify these operating scales.
2.15 Mechanism and Stability of a Moving Aster
- Moving light patterns produce bundle streams that appear to pull aster arms toward a new contractile center, while microtubules are also lost in the wake and incorporated into the aster.Aster intensity begins increasing after a few minutes, indicating incorporation exceeds decay; the authors speculate that incoming linked motors help the aster persist outside the light pattern.Source: §2.15 · pp. 27–28, Figure S11 · p. 28, Figure S12 · p. 29
2.16 Single Motor Velocity Determination from Gliding Assay
- K401-iLID motors have a mean gliding velocity of 230 nm/s (SD 200 nm/s), while K401-micro motors average 300 nm/s (SD 250 nm/s).Source: §2.16 · p. 29, Figure S13 · p. 30
2.17 Minimum Size Limits of Structures
- Flow generation requires an excitation-bar length between 87.5 and 175 µm, corresponding to a microtubule network of approximately 100 × 30 µm.The authors speculate that this limit may relate to the observed bundle buckling length scale.Source: §2.17 · p. 31, Figure S14 · p. 31
- An excitation-bar height of approximately 2 µm is the minimum for generating flow; below it, unstable bundles do not persist long enough to form an ordered structure.The proposed explanation is insufficient active-motor density, potentially related to motor diffusivity and speed.Source: §2.17 · p. 31, Figure S15 · p. 32
- Two overlapping bars retain four distinct inflows and outflows only for angles between π/16 and π/8; shallower angles resemble a single bar.The authors suggest that interaction between orthogonal bundles of approximately 20 µm may pull the networks together and merge them.Source: §2.17 · pp. 32–33, Figure S16 · p. 33
- The minimum disk diameter for forming an aster lies between 6.25 and 12.5 µm; the smallest observed aster arms are approximately 20 µm.Below this limit, transient small bundles remain disordered; the authors hypothesize that the limit may partly reflect microtubule length distribution.Source: §2.17 · p. 33, Figure S17 · p. 34
2.18 Fluid Flow Patterns from Particle Tracking
Particle tracking velocimetry is used to obtain averaged flow fields from tracer-particle displacements. Measurements at separated focal planes show no significant structural or speed differences, supporting single-plane measurements and a 2D model.
2.18 Fluid Flow Patterns from Particle Tracking
- Flow fields are measured by tracking tracer-particle displacements between frames, converting them to velocities, and averaging vectors within spatial windows.The reported field averages vectors in 30-pixel × 30-pixel windows; the figure presents the field for a 350 µm activation bar.Source: §2.18 · p. 34, Figure S18 · p. 35
2.19 2D Flow Field
- Across three focal planes separated by 20 µm in a sample extending approximately 70 µm in z, flow structure and speed show no significant differences, so subsequent measurements use one plane and modeling assumes a 2D pattern.The flow fields were averaged over a 20-minute window.Source: §2.19 · p. 35, Figure S19 · p. 36
2.20 Time Stability of Flow Patterns
Measured flow patterns retain similar structure and maximum speed across the 30-minute experiment. The section also describes how streamlines are generated and how spatial correlation is used to define a flow-pattern length scale.
2.20 Time Stability of Flow Patterns
- Across four successive 7.5-minute windows, the flow-field structure remains similar and its maximum speed stays constant during the 30-minute experiment.The maximum-speed measurements average nine experiments, with standard-deviation error bars.Source: §2.20 · pp. 36–37, Figure S20 · p. 37, Figure S21 · p. 37
2.21 Generation of Streamline Plots
- Streamlines are computed from the velocity field by interpolating trajectories with a second-order Runge–Kutta method and masking regions around existing trajectories to prevent crossings.Source: §2.21 · p. 38
2.22 Correlation Length
- The velocity–velocity correlation coefficient C(R) characterizes the spatial extent of flow patterns; the correlation length is the distance where C(R) reaches zero.At that distance, velocity vectors change to an orthogonal direction; the coefficient is calculated across distances for each bar length.Source: §2.22 · p. 38, Figure S22 · p. 38
2.23 Theoretical Model of the Fluid Flow Field
The authors model induced flow with Stokeslets representing contracting microtubule bundles and test whether simple-pattern flows can reproduce complex-pattern flows. The model captures general flow organization, but misses some experimental features and simple-pattern superposition does not fully match L- and T-shaped cases.
2.23 Theoretical Model of the Fluid Flow Field
- The model represents contracting microtubule bundles as point forces and omits Stokeslets in the bar’s central 120 µm, where contraction appears slower.The two force series each contain seven 2 nN forces spaced 20 µm apart.Source: §2.23 · p. 39
- Possible vortex mechanisms include boundary conditions, microtubule-depleted zones, and non-Newtonian fluid properties, but which, if any, causes the observed vortices remains unresolved.Source: §2.23 · p. 39
- A 14-Stokeslet model recovers the general inflow and outflow pattern for a 350 µm bar, but not the observed vortices or flow-magnitude asymmetries.The model uses two series of seven equal 2 nN point forces, spaced 20 µm apart, and omits the central 120 µm of the bar.Source: §2.23 · p. 39, Figure S23 · p. 40
- Superimposed single-bar flow fields closely match the experimental “+” pattern, while “L” and “T” cases are roughly similar but have mismatched inflow directions.Source: §2.23 · p. 40, Figure S24 · p. 41
2.24 Calculating Fluid Viscosity
The section estimates buffer viscosity from tracer-particle diffusion and compares the engineered motor-linkage system with optically controlled bacteria. It distinguishes their structural organization and resulting flow capabilities.
2.24 Calculating Fluid Viscosity
- The viscosity estimate assumes Newtonian buffer and uses the mean-squared displacement of freely diffusing tracer particles tracked at 4-second intervals.The tracer-particle radius is 0.5 µm.Source: §2.24 · p. 42
- Across nine experiments, estimated buffer viscosity averaged 2 × 10−3 Pa · s.The estimate uses tracer-particle tracking in inactivated regions of the activation-bar experiment.Source: §2.24 · p. 42
2.25 Comparison to Optically Controlled Bacteria
- Localized motor linkages reorganize microtubules into contracting networks that create coherent flows, unlike optically localized bacterial swimmers, which lack structural order.The bacterial system can form arbitrary density patterns corresponding directly to optical projections; the microtubule system's pattern resolution is generally lower than the reported ≈2 µm bacterial resolution.Source: §2.25 · p. 43
- Light defines an effective reaction volume for microtubule reorganization rather than directly patterning the microtubules.Source: §2.25 · p. 43