Dynamic flow control through active matter programming language

Kinesin purification and microtubule polymerization
Kinesin purification, microtubule polymerization and chamber construction were described in previous work11. In short, we constructed and purified two K401 kinesins with the light-induced hetero-dimer system of iLID or SspB-micro: K401-iLID and K401-micro. For protein expression, we transformed the plasmids into BL21 pLysS cells and induced the cells with IPTG compound. For protein purification, we lysed the cells and used nickel nitrilotriacetic acid (Ni-NTA) agarose resin to pick up His-tagged proteins that were provided by the base plasmids. The maltose-binding protein (MBP) domain was used and subsequently cleaved off in K401-micro expression to ensure the micro domain remains fully functional during expression. Tubulin was polymerized with the non-hydrolysable GTP analogue GMP-CPP. Labelled and unlabelled tubulin were palleted and then incubated at 37 °C to form GMP-CPP-stabilized microtubulues. We then characterized the microtubule length distribution by immobilizing them onto a cover-glass surface using poly-l-lysine. The median microtubule length is 1.0 μm, much smaller than the critical length wc at the scale of 100 μm (Supplementary Fig. 6).
Flow chamber treatment and construction
The chambers were made from microscope slides and cover-slips that were passivated against non-specific protein binding with a hydrophilic acrylamide coating41. In brief, microscope slides and cover-glass were first cleaned by sonication in 2% Hellmanex III solution for 15 min. Excess Hellmanex III was then washed out with double-distilled H2O and then ethanol sonication. The glass was then incubated overnight in 0.1 M HCl to remove any trace metal and finished in 0.1 M KOH sonication. After cleaning and etching, the glass was immersed in a silanizing solution of 98.5% ethanol, 1% acetic acid and 0.5% 3-(trimethoxysilyl)propylmethacrylate for 10–15 min. After rinsing, the glass was baked at 110 °C for 30 min. The glass was than immersed overnight in a degassed 2% acrylamide solution with 0.035% TEMED catalyst and 3 mM ammonium persulfate. The glass was rinsed in double-distilled H2O and air dried just before use. A flow cell made with precut parafilm was used as a seal between the microscope slides and cover-slips, making a channel that was about 70 μm in height. After the addition of reaction mixture, the flow cells were sealed with dental silicone polymer.
Energy mixture and reaction mixture
An energy mix consisting of an energy source (ATP), glycerol (which is crucial for aster formation and microtubule crosslinking in experiments, though the mechanism is not fully understood and may differ from typical macromolecular crowding effects), a surface passivating reagent (pluronic acid), oxygen scavengers (glucose oxidase, glucose, catalase, Trolox and dithiothreitol (DTT)) and ATP-recycling reagents was made on ice prior to combining the motor proteins and microtubules. After equilibrating the energy mix to ambient temperature, K401-micro, K401-iLID and microtubules were combined with the energy mix into a reaction mix. Concentrations for protein monomers for the K401-micro and K401-iLID constructs were 1 μM, and for microtubules, 1.5–2.5 μM. To minimize unintended light activation and non-specific protein binding, the sample was prepared under dark-room conditions with filters to block wavelengths below 580 nm. For all experiments conducted in this study, the reaction mixture consisted of 59.2 mM K-PIPES buffer (pH 6.1), 4.7 mM MgCl2, 3.2 mM potassium chloride, 2.6 mM potassium phosphate, 0.74 mM egtazic acid (EGTA), 1.4 mM Mg ATP (Sigma A9187), 10% glycerol, 0.50 mg ml–1 pluronic F-127 (Sigma P2443), 0.22 mg ml–1 glucose oxidase (Sigma G2133), 3.2 mg ml–1 glucose, 0.038 mg ml–1 catalase (Sigma C40), 5.4 mM DTT, 2.0 mM Trolox (Sigma 238813), 0.026 units μl–1 pyruvate kinase/lactic dehydrogenase (Sigma P0294) and 26.6 mM phosphoenolpyruvic acid. K401-micro and K401-iLID were both diluted with a 1:2 ratio with 2 μl of M2B buffer with pH 6.1 (80 mM K-PIPES (pH 6.1), 1 mM EGTA, 2 mM MgCl2). Microtubules were diluted with a 1:7 ratio with 7 μl DTT M2B with pH 6.1 (45 μl M2B (pH 6.1) with 1 μl of 250 mM DTT and 333.4 mg μl–1 glucose). The reaction mix was then aged in the flow cell for 120–180 min before light activation and data acquisition.
Tracer bead preparation
To visualize the fluid dynamics of our system, we used 1 μm polystyrene beads as tracer particles. The particles were incubated overnight in M2B buffer with pH 6.8 with 50 mg ml–1 pluronic acid. The beads were then washed and palleted at 1,000g for 2 min and resuspended in M2B with pH 6.8 before adding them into the reaction mix.
Fluorescent bead preparation
Fluorescent particles were used to demonstrate the mixing and transport capability of our system. We used 0.5 μm polystyrene beads that are dyed with highly hydrophobic dyes. The particles were incubated in M2B buffer with pH 6.8 with 50 mg ml–1 pluronic acid. The beads were then washed and palleted at 1,000g for 2 min and resuspended in M2B buffer with pH 6.8 before adding them into the reaction mix.
Cell culture
The cells used in the transport study (Jurkat cells, American Type Culture Collection (ATCC) TIB-152 and Raji cells, ATCC CCL-86) were cultured in a medium composed of high-glucose RPMI 1640 (Life Technologies) and 10% foetal bovine serum (qualified; Life Technologies). Jurkat cells were cultured to maintain a cell density between 1 × 105 and 3 × 106 cells ml–1. Before loading the cells in the aster mix, the cells were thoroughly washed with M2B buffer with pH 6.8 (previously described in Methods). Cell cultures were first centrifuged at 300g for 5 min to remove the culture media, then washed twice with M2B of pH 6.8 at 300g for 5 min to remove any remaining culture media and salts. Subsequently, cells suspended in M2B of pH 6.8 were introduced into the microtubule buffer to attain the desired cell density. As an example, for a 5 ml culture with a density of 3 × 106 cells ml–1, the typical protocol would involve suspending the cells in 1 ml of M2B with pH 6.8, of which 10 μl would be used in every 45 μl of the microtubule buffers. Raji cells were used only in Extended Data Fig. 2 because they can form larger clusters. Jurkat cells were used in Figs. 3 and 5.
Cell live/dead staining
Calcein AM (catalogue no. C1430, Life Technologies) and EthD-1 (catalogue no. E1169, Life Technologies) solutions were prepared using DMSO solvent and H2O in a ratio of 1:4 (v/v) for a stock concentration of 1 mM. The 2 μM live/dead stain working concentration was prepared in Dulbecco’s phosphate-buffered saline (DPBS; Life Technologies) by adding 20 μl of each stain to 10 ml of DPBS. Cell cultures were first centrifuged at 300g for 5 min to remove the culture media. The 2 μM live/dead stain was added to the cell pallet. Cells were sufficiently stained after 1 h. Cell cultures were centrifuged at 300g for 5 min again to remove the staining solution. Subsequently, cells were suspended in M2B with pH 6.8 and then added to the active matter mix.
Vesicle preparation
Lipid vesicles were prepared according to a modified version of the method in ref. 42. In a 15 ml glass vial, 0.5 ml chloroform was combined with 15.2 μl of 25 mg ml–1 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC; 850457, Avanti Polar Lipids) and 0.65 μl of 1 mg ml–1 dioleoyl-phosphoethanolamine-lissamine rhodamine B (rhodamine PE; 810158, Avanti Polar Lipids). The chloroform was then evaporated in a fume hood, following all safety guidelines for handling chloroform. The resulting lipid dry film was mixed with 1 ml of mineral oil (M8410, Sigma-Aldrich) to achieve a final concentration of 500 μM in oil solution. This mixture was heated to 50 °C and dissolved by pulse vortexing and sonication for 20 min. The lipid–oil mixture was stored at room temperature under dark conditions and used within two days.
Inner and outer solutions of the lipid vesicles were prepared to match the osmolarity of the active matter mix. Due to the incompatibility of our active matter system with high levels of salts or sugars, and the scarcity of the mixture itself, we increased the inner and outer solution osmolarity by adding KCl to M2B with pH 6.8 to reach 1,820 milliosmoles (mOsm), which is lower than the 2,034 mOsm of the active matter mix but does not disrupt protein functions. To form the vesicles, 300 μl of outer solution was placed in a 1.5 ml tube, and 300 μl of lipid–oil mixture was gently layered onto the outer solution. This was incubated on ice for 60 min to allow the assembly of a lipid monolayer at the interface between the oil and outer solution.
Just before use, 200 μl of lipid–oil mixture was put into a 1.5 ml sample tube and cooled on ice for >15 min. Then, 20 μl of inner solution was added to the lipid–oil mixture and immediately emulsified by first pipetting 20 times and then vortexing at maximum power (Vortex-Genie 2; Scientific Industries) for 10 s. The emulsion was incubated on ice for 5 min to stabilize by the spontaneous alignment of lipid molecules at the interface of the inner buffer and oil. Subsequently, 200 μl of the emulsion was carefully placed on the lipid–oil mixture and the outer solution, and then incubated for 5 min on ice. The 1.5 ml tube was then centrifuged (2,000g, 10 min, 4 °C) to push the emulsion droplets through the interface. After centrifugation, the oil layer and 500 μl of buffer solution were gently drawn off from the top of the tube.
For the final mixture, 1 μl of resuspended vesicles was added to a combination of 8 μl energy mix, 2 μl diluted iLid motor, 2 μl diluted micro motor and 1 μl diluted microtubules.
Design and implementation of different bar patterns
We custom fitted an epi-illuminated pattern projector onto our microscope. The size of the projection field was 800 × 1,280 pixels. Matrices containing coordinates of bars were first computed in Python and then converted to greyscale and eventually saved into the tagged image file format (TIFF). TIFF image sequences were then processed by a custom Micro-Manager script. The scripts can be found at https://github.com/fy26/ActiveMatter.
Data acquisition and projection of patterns
All experiments were performed with an automated wide-field epifluorescence microscope with a custom epi-illuminated projector and gated light-emitting diode (LED) transmitted light, as discussed in our previous work11. All samples were imaged at ×10 magnification. Image sequences were captured using a Nikon TI2 controlled with Micro-Manager. Images of the fluorescent microtubules (Cy5 dye) and tracer particles (bright field) were acquired every 8 s. Bar patterns were projected onto the image plane every 8 s with a brief 200 ms flash of a 2.4 mW mm–2 activation light from a 470 nm LED.
Duration of the activation light
The duration of the light was empirically determined through an iterative process: (1) We started with a short activation time, such as 50 ms, and gradually increased it in 50 ms increments. (2) After each increment, we observed the sample for aster formation. (3) We continued steps 1 and 2 until we observed the formation of a stable aster, defining this as the optimal activation time. (4) A longer pulse duration resulted in contractile activity outside of the intended light pattern, helping establish an upper limit for the activation duration.
Particle image velocimetry
Particle image velocimetry was performed on the images of tracer beads using PIVlab43,44 to extract the solvent flow fields.
Derivation of the general principle for linear superposition
The generalized Stokes equation for the solvent flow is f + μ∇2u − ∇p = 0, where f is the body force applied by external fields or sources; for example, in our system the body force is from the active force generated by the crosslinked microtubules and motors. We now construct a general principle for the linear superposition of flows induced by n different force-generating sources. We denote the force applied on the fluid from the source i, in the absence of other sources, as fi, and the resultant flow and pressure fields as ui and pi, respectively. Similarly, the body force, flow field and pressure field in the presence of all the n sources are denoted by ft, ut and pt, respectively. To establish a linear regime of fluid flows driven by different sources, we require ut = ∑iui and pt = ∑ipi, which can be substituted into the Stokes equation and yields ft = ∑ifi. This result directly comes from the linearity of the Stokes equation in u and p; however, it is not trivial because fi can depend on the flow velocity u, and the formula ft = ∑ifi does not always hold. In our system, the force-generating sources are the microtubule networks, and the force induced by a single network i, in the absence of all other networks, can be expressed as fi = γci(vi − ui), where γ is the drag coefficient of the microtubule and the solvent, and c and v are the density and velocity of the microtubule network, respectively. Therefore, in the presence of n networks, the general principle ft = ∑ifi together with the additional linear relationships, ct = ∑ici and vt = ∑ivi, requires that ∑ici ⋅ ∑jvj = ∑icivi and ∑ici ⋅ ∑juj = ∑iciui. The former requires that civj = 0 when i ≠ j, which is automatically satisfied as long as no networks overlap in the system. The latter requires that ciuj = 0 for any i ≠ j, which is the rule of linear superposition in a multiple-active-agent system.
Numerical simulation
The finite difference method was used in numerical simulations, with the central differencing scheme in space and the method of lines in time. The codes are written in Python and available at https://github.com/fy26/ActiveMatter/tree/main/Simulation.
Calculation of shear modulus
The steady-state value of DF depends on the capillary number \({\mathrm{Ca}}=\mu \frac{\partial {u}_{x}}{\partial x}R/G\) (refs. 45,46,47), where R is the radius of the aster and G is the shear modulus, via a linear relationship DF = ACa. The value of coefficient A is calculated to be 25/6 for elastic capsules45,47, and measured to be around 20 for viscoelastic drops46. Here we choose A = 10 to estimate the shear modulus G of the microtubule aster. Additionally using measurements μ = 0.02 Pa s (ref. 48), ∂ux/∂x = 0.0015 s−1, R = 100 μm, L = 120 μm and B = 70 μm, the shear modulus G of the aster is calculated to be 1 × 10−7 Pa.
Calculation of detachment force on cells in an extensional flow
The flow-induced friction fp on a spherical particle translating in an unbounded fluid with velocity v is fp = −6πμav, which is used to approximate the force on detaching cells. We denote the two attached cells by a and b, and the unperturbed flow velocity at the two cell centres by ua and ub, respectively. Then the cell pair moves at the same velocity (ua + ub)/2. The magnitude of the flow-induced force on each cell is fp = 3πμa∣ua − ub∣ = 3πμa∣∂u/∂x∣Δl. The detachment force on each cell has the same magnitude as fp.
Reporting summary
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