Steering Active Matter

The result

We compared seven light patterns in a simulated loop channel, each tested from 32 turbulent starting states it was never designed on, under the conditions it was designed for and eight shifted ones. The test, its measures and its decision rules were written down before any of these runs.

Optimized patterns pump; the obvious designs don’t. Uniform light gives no net flow, as symmetry requires. A sawtooth “ratchet” of light and triangles copied from a pump made of posts push weakly, not clearly more than uniform light. The best patterns found by optimization drive a steady clockwise flow of about 0.033–0.036, around 14% of the turbulence’s typical speed, three to four times the ratchet’s.

Gradients weren’t needed. The simulation is differentiable, so a pattern can be improved by following the gradient of the flow through thousands of time steps. That worked, but a search that only tries patterns and keeps what helps, with 17 pattern settings, did as well at about the same cost. With 33 settings the same search did much worse. Trained three times each, the gradient’s designs ranged from 0.012 to 0.033 and the search’s from 0.022 to 0.035: the training run matters more than the method, and every run found a pattern that pumps.

Designing for the wrong model is cheap to guard against. A design optimized over a range of conditions (activity and elasticity each 25% either way, and random jostling) gave up nothing under the conditions it was made for, and kept more of its flow than the design made for one exact model under seven of eight shifts, including activity 40% stronger. The exception is the strongest dimming, 40% weaker, outside its training, where it kept less. Most designs also kept most of their flow in a shorter channel they never saw, though one training run kept only a quarter.

One simplified model at one resolution, in 2D; designs are fixed in time and limited to coarse patterns a projector could show. Random jostling during the run raised every design’s flow, uniform light’s included; that wasn’t a question of the test and is noted only.

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Conclusion

A self-driven fluid that churns with no net flow can be made to pump one way round a loop by a single fixed pattern of light, coarse enough for a projector. The obvious designs, a sawtooth ratchet and light-made copies of a pump built from posts, barely do it; patterns found by optimization drive a steady clockwise flow of about 14% of the turbulence’s typical speed, three to four times the ratchet’s. Gradients through the simulation were not needed to find them: a simple search with fewer pattern settings did as well, and which training run you get matters more than which method. Designing over a range of conditions, rather than for one exact model, cost nothing and kept more of the flow when the conditions shifted, except under the strongest dimming. For an experiment, that points to a practical recipe: search over coarse patterns, design for the uncertainty in the parameters, and expect the result to survive modest errors in the model. All of this is in a simplified 2D model; whether such a pattern pumps a real microtubule layer is the test that would settle it.

The science

An active nematic is a dense layer of rod-like units that push on their surroundings: microtubules driven by kinesin motors, actin and myosin, or bacteria. Like the molecules in a liquid crystal display, the rods tend to line up, but each one also pushes along its length. Above a threshold of activity, alignment breaks up into self-driven turbulence, with defects, points where the rods can’t agree on a direction, constantly forming, swimming and annihilating. Confined in a narrow ring, the same fluid can circulate on its own, but in either direction, and at high activity not at all.

With light-activated motors, light sets the activity point by point, so a projector can shape the flow. Earlier work used optimal control with patterns that change in space and time to steer defects and draw channel flows, but found no stable channel flow above the turbulence threshold, and didn’t test what happens when the model is wrong. Physical posts shaped like triangles pump an active nematic; here the triangles are made of light instead, as a baseline.

The model is the standard continuum one: an orientation field relaxing toward alignment, carried and turned by the flow, and a flow driven by the rods’ push and resisted by viscosity and friction with the floor (no inertia, as at the scale of cells). The walls are regions of very high friction. Each step solves for the flow, then advances the orientation. Light patterns are built from 17 or 33 smooth shapes around and across the loop, so no pattern is finer than a projector could show.