DOCUMENTATION / ARTIFICIAL LIFE

Rejuvenation Field.

A speculative model of why anthrobots test younger than their source cells.

Speculative: this experiment models one hypothesis. Its results are about versions of a model, not findings about real cells.

What the page shows

The growing anthrobot from Growing Anthrobots, with an extra layer: every cell carries an aging clock that starts at the donor’s age, and a belief about whether it is part of an embryo. Cells that come to believe they are embryonic wind their clocks back. The body is colored by clock age: cyan younger than the donor, red older, gray the same.

Readout: The step, and how much younger the body is on average: for example, a clock of 45 for a 60-year-old donor.
The lineup: Lower on the page: the youngest bodies the research search found under each version of the model.
Where the versions disagree: A map by body shape and size, lighter where the versions disagree more.
Experiments that would tell them apart: Pairs of body types for which two versions predict opposite results.
Healed wounds table: Each version's prediction of whether a healed wound ends up younger than the rest of the body.

How to use it

Restart / Cut in half / Knife: As in Growing Anthrobots: regrow, or cut and watch the wound heal.
Which evidence the cells trust: Six calibrated versions: Balanced, or led by construction, curvature, contact, motion or coherence. The sliders below set custom weights, which are not calibrated.
Sharing: How much cells pass their belief to their neighbors.
Donor age: The age the clocks start at, 20 to 90 years.
View: Clock age, belief (gray adult, cyan embryo), tissue, or one kind of evidence at a time (dark none, yellow strong).
Body shape: Round, elongated or irregular. Restart or cut to see a change.

Try this: grow the same body under Construction-led and Motion-led. They are calibrated to agree on a round body, so compare elongated or irregular ones. Then cut a body and look at the healed region under each version.

Background and theory

The observation

A follow-up study of anthrobots reported that they were about 25% younger, by an epigenetic clock, than the adult cells they were made from. Epigenetic clocks estimate age from patterns of DNA methylation, chemical marks on DNA that change with age.

The hypothesis

One explanation Michael Levin and colleagues have proposed is age evidencing: cells may read signs that they are part of a developing body, such as rapid construction, and partly reset their aging marks in response, as embryonic cells do. Nobody knows which signs cells would trust, if any.

The model

Each step, each cell gathers five kinds of evidence:

Construction: How fast the cell's neighborhood is being built or rebuilt.
Curvature: How curved the body's surface is near the cell.
Contact: How many neighbors the cell has.
Motion: How fast the body is moving.
Coherence: How well a chosen internal signal agrees with the neighbors'.

The weighted evidence nudges the cell’s belief. The belief leaks back toward “adult” over time and is shared with neighbors. Cells whose belief is high wind their clocks back, down to a floor, while all clocks slowly age.

Six versions, one calibration

Because the right weighting is unknown, the model comes in six versions: Balanced trusts all five kinds of evidence equally, and the other five each lead with one. Each version is tuned so the same standard round body ends 25% younger: the reported figure, and the only fit to data. The versions agree on that body by construction. The research question is where they disagree, because that is where an experiment could tell them apart.

The search

A quality-diversity search grew 704 bodies under varied conditions: shape inputs, the size of the starting cluster, how thick the fluid is, and whether, when and where the body is cut. Every body was scored under all six versions at once.

Methods

The aging layer

The model runs on the bodies grown by the Growing Anthrobots rule, one aging step per growth step. Each living cell carries a belief L (the log-odds of “I am in an embryo”) and a clock age a, as a fraction of the donor’s age (1 at the start). Each step it computes five kinds of evidence, each in [0, 1]:

Construction: 1 − exp(−|Δs| / 0.05), from the change in the cell's own 16-channel state over the step. A newborn cell counts fully.
Curvature: Mean curvature of the body surface, (gᵀHg − |g|² ∇²α) / |g|³ from the alpha gradient g and Hessian H (2/r on a sphere), relative to a sphere of radius 3 cells and clipped. Zero away from the surface.
Contact: The fraction of the 26 neighbors alive.
Motion: tanh(body speed / 0.05 cells per step), half-weighted for cells without cilia.
Coherence: exp(−|b − b̄| / 0.1), where b is hidden channel 5 and b̄ the mean over living neighbors.

L \leftarrow L + \sum_{j} w_{j} e_{j} - bias - 0.2 (L - (- 3))

L \leftarrow 0.8 L + 0.2 \cdot mean (L over living neighbors)

p = σ (L) a \leftarrow a + 2 \times 10^{- 4} (1 - p) - 4 \times 10^{- 3} \cdot p \cdot \max (a - 0.4, 0)

So the belief relaxes toward an adult prior of −3, is shared like a gap-junction signal, and the clock ages unless the cell believes it is embryonic, when it winds back toward a floor of 0.4. A newborn cell takes the mean belief and age of its living neighbors; a dead cell’s values are cleared. The aging layer never feeds back into growth or rolling.

Weightings and calibration

Six weightings: balanced (every w = 1), and five that lead with one kind of evidence (1 for the lead, 0.2 for the rest).
For each weighting the bias is found by bisection, so that the standard body ends 25% younger, averaged over four random firing seeds. The standard body is round, grown and rolled for 600 steps. This is the only fit to data. Single bodies on other seeds land at 23–28%.
The page runs an independent implementation of this layer. Against the reference on a run where cells are born and die, beliefs agree within 4.9 × 10⁻⁷ (relative) and ages within 6 × 10⁻⁸ after 24 steps.

The search

Genome (nine genes): the two shape conditions, kept inside the trained triangle; the starting cluster’s radius (0–2.5 cells); a viscosity stand-in for rolling (0.5–4); and a cut (applied when its gene is above 0.4) with its time (steps 150–500), depth (−2 to +3 cells from the center of mass) and direction (two angles).
Map: final size (300–3,000 living cells) × elongation (the square root of the largest over the smallest eigenvalue of the cells’ spread, 1–2.2), 8 × 8 cells.
One run, six clocks: each body is grown once for 600 steps, and all six weightings’ clocks ride along. A body’s youth (1 − mean age) under each weighting is its quality in that weighting’s archive.
Budget: 64 random bodies, then 40 iterations of 16 mutants (Gaussian, 0.1 of each gene’s range), parents drawn from all six archives: 704 bodies. 38 of the 64 map cells were filled.

Analysis

Agreement between versions: Spearman rank correlation of youth across all 704 bodies, for each pair of weightings.
What drives youth: for each weighting, a least-squares fit of standardized youth on standardized genome features and outcomes (size, elongation, viscosity, whether cut and so on). The coefficients are the “standardized effects”.
Disagreement map: in each map cell with at least 3 bodies, every weighting’s mean youth, z-scored per weighting; the cell’s disagreement is the spread of those scores. For each pair of weightings, the two map cells they rank most oppositely give a candidate experiment.
Wound prediction (fixed before the search, from construction evidence): in each of the 451 cut bodies, the mean age near the cut plane (the regrown side plus a 2-cell margin) against the mean age deep inside the kept part. Reported as the share of bodies whose wound is younger, and the mean difference.

Results and what they mean

Each version favors different bodies. The curvature-led and motion-led versions’ rankings of which bodies end youngest are almost unrelated. Curvature-led favors small bodies; motion-led favors anything that keeps moving.
Thick fluid ages bodies in every version, by slowing them down, least in the curvature-led one.
Healed wounds split the versions. Regrowth counts as construction, so the construction-led version sees younger cells where a wound healed (in 80% of 451 cut bodies), and the contact-led version does too (100%). The balanced, curvature, motion and coherence versions mostly predict the opposite: the healed region ends older.

What it means: the experiments that would discriminate between the versions are concrete and doable. Sort anthrobots by size and shape and compare their epigenetic clocks; or wound them and compare the clock in the healed region with the rest. A result in either direction would rule out some versions of the hypothesis.

Preliminary: a quick search (704 bodies, reaching 38 of 64 map squares).

Limits and open questions

Everything except the 25% figure is invented to make the hypothesis concrete: the five kinds of evidence, the belief rule and the clock.
The calibration uses one number, applied to a stylized grown body.
The search is a quick run on one trained growth rule.
The predictions are differences between versions of a model; none is a prediction about real cells until tested.