Neurobot Motion.

A lab for one behavior score. A simulated cilia-driven bot swims in a well for 30 minutes; its tracked path is replayed beside the power spectra of its x and y positions, the peaks the complexity index counts, and four readings of its minimum speed. Below the lab: examples where one track scores differently under two settings, simulated studies of the paper’s size for seventeen explanations, the findings, and an analyzer for your own tracks.

Dish

The tracked center over 30 minutes at 60×, the last two minutes bright; the body is drawn to scale with its ciliated cells on the rim.

Complexity index

The number of distinct spectral peaks above the threshold, x and y together, a peak at the same frequency in both counted once.

Spectra

Power of x (solid) and y (dashed) by frequency, log scale, with the threshold dotted and counted peaks marked.

Minimum speed

Four readings of the same track: the slowest 10 s and 60 s from 1 s speeds, the 1st percentile, and the slowest single frame.

Study panel

Pass rates of the paper's four criteria over 1,000 simulated studies, a dot per study for 200 of them, and studies you run.

Presets

Eight bots, each showing something the score responds to: steady and irregular circlers, a drifting ring, a looper, a straight swimmer, a staller, a sitter and a spinner.

The bot

Top speed, handedness (how hard the cilia turn the body), polarity (how hard they push it forward), beat noise, and a neural effect with its strength. New run draws fresh noise.

The measurement

Frame rate, tracking error, a 0.13 mm pixel grid, the spectral window, the overlap (as written in the paper, or the usual half window), the threshold, and when x and y peaks count as one.

Share

A link that restores the bot and the measurement.

Run one study

46 neurobots and 48 biobots simulated and tested in your browser, about a second on a laptop.

Analyzer

A CSV of t, x, y; nothing leaves your browser.

Try this: pick the looper and set the threshold to ×¼, then ×4. Then pick the straight swimmer, set 30 fps and the pixel grid, and compare its slowest 10 s with its slowest frame.

Neurobots

Xenobots are clumps of frog embryo skin that swim with cilia. Neurobots add a clump of neural precursor cells when the xenobot forms; the cells become neurons, grow processes toward the surface and fire. Fotowat and colleagues compared 46 neurobots with 48 plain biobots over 30 minutes and reported two behavioral differences: a higher complexity index and a higher minimum speed, with distance, mean speed, acceleration and area covered unchanged. Neurobots were also larger, longer and had fewer ciliated cells per area. The question here is what those measures can tell apart.

The complexity index

The power spectral density of x(t) and of y(t) is estimated by Welch’s method: 400 s windows, each windowed and Fourier-transformed, the squared amplitudes averaged. A local maximum above 10 px²/Hz (about 0.17 mm²/Hz) is a peak; the index is the number of distinct peaks across x and y. A circle gives one peak at its orbit frequency in both, so an index of 1. Anything that adds power at another frequency adds a peak: a second rhythm, but also noise, harmonics of a non-circular path, a frequency that drifts across windows, or slow wandering in the lowest bin.

Cilia-driven bodies

A ciliated cell at site k on the rim pushes the body along a beat direction p shared by all cells and, with a handedness χ, along the rim’s tangent t_k. Summed over the rim, the push gives a velocity and the off-center pushes a spin; at low Reynolds number both stop the moment beating stops. A uniform rim with both components swims in a circle of radius about 4a / 3χ for a body of radius a. An uneven rim adds force and torque of its own, which is how fewer or rearranged cells change the orbit (Growing Anthrobots uses the same idea in 3D).

The body

A rigid ellipse with the area of a 0.4 mm circle and 64 rim sites, each a ciliated cell or not. Cell k at rate b_k pushes with

and the summed force and torque give velocity and spin through a sphere’s Stokes drag. Beat rate is b_k = (1 + η_k)(1 + G)·M_k·A: slow noise per cell, a slow shared state, stops, and the neural effects M_k on the cells within reach of the implant. The well (9.4 × 10.7 mm) reflects the body.

Biobots

Populations were calibrated by random search to the paper’s published biobot distributions: the complexity index histogram, the number that don’t move, minimum speed and mean speed. Three versions: “stallers”, whose low minimum speed comes from stopping now and then; “sitters”, a share that never moves and the rest moving steadily, as the paper’s supplementary video shows; and sitters with minimum speed read as the slowest single frame.

Explanations

• Fewer cilia: fewer cells, a gap near the implant, a longer body (development only). Sham: a weaker version.
• Neural bursts that speed nearby cells; bursts that stop them; a tonic modulator that speeds them and cuts stops (the serotonin route); fewer cilia plus the tonic modulator.
• Exploratory, added later: a slow neural rhythm, the rhythm plus the tonic modulator, fewer sitters, and sharper tracking of neurobots (4 or 3 µm of error against 5).
• Exploratory, a 2.5D body: every bot rolls about its long axis, and its tracked center wobbles sideways by 0.2 mm per unit of elongation (times its size) once per turn, while its cilia beat. Neurobots differ only in shape (longer and bigger), alone, with fewer sitters, and with sharper tracking. These studies score criterion 3 with the paper’s signed acceleration.
• Exploratory, batch effects: no neurons and no designed difference; biobots and neurobots each come from their own batch, every body parameter multiplied by its own random factor (about 10% or 20%).

Studies and criteria

A study draws 46 neurobots (one setting from an explanation’s range) and 48 biobots, tests each measure with a Kruskal–Wallis test, and checks the paper’s four results: (1) complexity index higher, p < 0.05; (2) minimum speed higher, p < 0.05; (3) distance, mean speed, acceleration and area each p ≥ 0.05; (4) the numbers of bots that score 0 inside the 95% intervals of the paper’s 6 of 48 and 1 of 47. Each explanation ran 1,000 studies; the 10 settings closest to the paper were re-run 40 times each.

Pre-registered and exploratory

The stallers comparison, its explanations, ranges, criteria and predictions were written down before any neural change was simulated. Everything after it (the rhythm, the sitters, the minimum-speed reconstruction and the tracking explanation) is exploratory and labelled so on the page.

Minimum speed

The paper doesn’t define it. 120 candidate readings (frame rate, tracking error, a pixel grid, smoothing) were applied to simulated bots and scored against the paper’s biobot minimum and mean speeds together. Only the slowest unsmoothed frame-to-frame speed, with tracking error about one frame’s movement, fits.

Checks

The browser’s measures match the research code exactly on 19 golden tracks under 8 readings (the index exact, everything else within 10⁻¹⁴), and its Kruskal–Wallis p-values to 3 × 10⁻¹⁴; its bot populations match the research populations by distribution. Both are checked on the parity page.

• The index counts more than rhythms. The same track scores 2 or 5 with the threshold at the paper’s value or a quarter of it, and 7 or 16 with a 400 or 800 s window.
• A flat body can’t reproduce both results. With stallers, the index and minimum speed pull against each other; with sitters, they rise together but distance and mean speed rise with them. All four criteria held in under 1% of studies for every flat-body explanation.
• A rolling body comes closest, without neurons. With the 2.5D wobble, neurobots that differ only in shape score about one point higher in two-thirds of studies; with fewer sitters and sharper tracking, all four criteria hold in 1.6% of studies, the most of any explanation.
• Minimum speed depends on tracking. Read as the slowest frame, it reflects how precisely a bot is tracked as well as how it moves.
• A reading without neurons, as a hypothesis. The paper’s sham bots had a complexity index like the neurobots’ (short of significance at n = 22), and an implanted clump off center would make the tracked center of mass wobble as a bot rolls, in shams and neurobots alike; tracking identical bots with 4 µm of error instead of 5 µm reproduces the minimum-speed medians with everything else unchanged. Each part rests on an unmeasured assumption.
• Batch differences mimic half the result. With 20% differences between batches and nothing else, the index and minimum speed are both higher in 11% of studies, more than most neural explanations, though never with all four criteria.
• At the paper’s size, explanations look alike. Settings of different explanations that produce similar medians were told apart in 5–60% of 46-against-46 studies, and in most at 500 against 500.

• The body is 2D and rigid; real bots are 3D, change shape and roll. The 2.5D wobble stands in for rolling with one sinusoid; a full 3D body could give other shapes of motion.
• Neural effects are guessed routes, not measured ones; other routes (other cell types, mucus) aren’t modelled.
• Calibration used distributions read off published plots; the raw tracks would replace most of the guesswork.
• The minimum-speed reading and the tracking-error difference are inferred, not known.
• Findings about the measures (what the index counts, how readings move it) apply to the paper’s real tracks; findings about mechanisms apply to this model. The physical experiment also had batches, recording sessions, a particular tracker and camera, light, temperature and handling, of which only batches, tracking error and a wobble are simulated.
• Open: re-analyze the raw tracks for stops and speed variability; measure tracking error by bot size; a serotonin-receptor knockdown; an optogenetic pulse with flow measured near and far from the neurons.