[Project 1] Heritable state vs. shared environment vs. sister coupling in epithelial cell-cycle lineages (MCF10A) #1013

Rewritten 2026-09-29. The original proposal pointed to Zenodo 10.5281/zenodo.3878526 and 10.5281/zenodo.4179028 as MDCK DeepTree/btrack lineage trees. Both are actually CellMAPtracer TIFF stacks (Ghannoum & Antos, 2020), an unrelated project. The Ulicna et al. 2021 MDCK trees do not appear to be publicly deposited. This version uses Spencer-lab MCF10A movies instead, which were checked directly (see Data check below). The original text is in this issue's edit history.

Question

Is the similarity of cell-cycle duration among relatives caused by a heritable, cell-intrinsic state, by a shared, changing environment (local density / contact inhibition, culture age), or by coupled sister fates?

Kin-correlation studies consistently find that relatives in the same generation are more alike than direct ancestors. Ulicna et al. (Front. Comput. Sci. 2021, MDCK) report mother–daughter r = 0.43, sisters r = 0.65, and first and second cousins above 0.5. The same pattern appears in Sandler et al. (Nature 2015), Chakrabarti et al. (Nat Commun 2018) and Kuchen et al. (eLife 2020). Ulicna et al. suggest the same-generation correlation may be "environmental synchronisation" as cultures become confluent, but correlations alone cannot test that.

Why the current tHMM cannot answer this

• In a first-order Markov tree with sticky states, sister correlation scales roughly as λ² and mother–daughter as λ. The model therefore predicts sisters less alike than mother–daughter, the opposite of the data.
• Sister coupling alone is not enough. A joint sister kernel can make sisters concordant, but first cousins share only a grandmother, so their correlation still falls below mother–daughter. Cousin > mother–daughter needs something shared in time. Environment is the leading candidate.
• Density should enter the emission first. Contact inhibition lengthens the cycle of the cell experiencing it, which is an effect on the emission. If density enters only through transitions, a "slow" hidden state can absorb a pure density effect, and heritability becomes unidentifiable.

Data

Spencer-lab MCF10A live-cell movies (H2B nuclear marker + DHB CDK2 sensor, 12 min/frame). They are EBI BioStudies deposits, and loaders for this format already exist in PR #1017 (palbociclib_loader.py, mitogen_loader.py).

Data check (FigS9, 24 movies, done 2026-09-29)

• tracedata columns (cells × frames × 14): 1–2 = x, y centroid in pixels (range 0–2,040, drift-corrected, so slightly negative values occur); 3 = nuclear area; 4 = integrated nuclear intensity; 11/13 = DHB nuclear/ring medians, as the deposit's Data_organization.docx states. Columns 1–4 were identified from their value ranges, and the lab pipeline follows this convention. Pixel size is not stated in the deposit.

• Every nucleus in the field is tracked. Across the 12 movies profiled, counts run from 138 to 2,835 nuclei per field, and in control wells counts roughly triple over the movie (e.g. 1,044 → 2,835). So local density can be computed from all cells, not just lineage members.

• Density range: the mean number of neighbors within 50 px over a cell's life runs from p5 = 0.6 to p95 = 6.0 among complete cycles. It is not yet clear that the 32 h movies reach contact-inhibited confluence. The 51 h Fig1 movies need checking.

• Lineages: genealogy chains up to 6 cell-cycles deep. Control wells have 38,583 tracks and 5,498 complete cycles (born and divided in-movie).

• Kin correlations of complete cycle durations (control wells):

  • mother–daughter r = 0.12 (n = 1,239)
  • sisters r = 0.56 (n = 1,676)
  • first cousins r = 0.36 (n = 273)

  The MDCK pattern is reproduced: cousins > mother–daughter.

• Warning: window selection bias. Among complete cycles, duration falls with local density (Spearman −0.32; median 14.2 h at low vs 12.0 h at high density), the opposite of contact inhibition. But duration also falls strongly with birth time (Spearman −0.55). Cells born late, when density is high, count as complete only if they finish before the movie ends, so short cycles are overrepresented. The raw correlations above are biased the same way. Any analysis must use a likelihood that handles right-censoring and in-window truncation, not complete-cycle summaries. PR Censored Weibull–Gaussian biosensor emission and palbociclib heritability analysis (#1016) #1017's censored/truncated Weibull emission and root-selection handling are the starting point.

Model

Observations per cell $i$: cycle duration $t_i$ with censoring indicator $\delta_i$ (plus the truncation window from #1017), and a covariate vector $u_i$. Candidate covariates:

• $\bar\rho_i$: local density averaged over the cell's life. Neighbor count within $r$ px, or inverse Voronoi area; stated in pixels until the pixel size is known.
• culture age $a_i$: birth time since plating.

1. Covariate emission (primary). Weibull or Gamma duration with a proportional-hazards / accelerated-failure-time link. For example, Weibull scale $\lambda_{k}(u_i) = \lambda_k \exp(\gamma^\top u_i)$, with $\gamma$ shared across states. Censored cells contribute $S(t_i \mid z_i = k, u_i)$. The hidden state then carries only the heritable part left after accounting for density and culture age.
2. Covariate transitions (alternative). Softmax $T_{kl}(\rho_{p}) \propto \exp(w_{kl}\rho_p + b_{kl})$ with $w_{k1} = b_{k1} = 0$, where $\rho_p$ is the parent's density. Fit as a competing model rather than the default.
3. Symmetric sister kernel. Daughters here have no natural order, so use $P(z_{c_1}=l, z_{c_2}=m \mid z_p=k) = S_{k,lm}$ with $S_{k,lm} = S_{k,ml}$ and $\sum_{l,m} S_{k,lm} = 1$. Nested null: $S_{k,lm} = T_{kl}T_{km}$ (the current model). Report excess concordance $\sum_l S_{k,ll} - \sum_l T_{kl}^2$ relative to that null. Raw off-diagonal mass is positive even for independent sisters.

Model comparison (likelihood ratio / BIC, with lineage bootstrap):

Plus the no-inheritance null (identical rows of $T$, independent_T=True from #1017).

Posterior predictive check (the key test): simulate from each fitted model within the same observation windows and compare predicted mother–daughter, sister and cousin correlations with the observed ones. A model that explains the data must reproduce cousin > mother–daughter.

Implementation notes (current code)

• lineage/HMM/E_step.py: for two-child nodes, get_beta_and_NF replaces the product over children with a sum over sister pairs, $\sum_{l,m} S_{k,lm},\tilde\beta_{c_1}(l),\tilde\beta_{c_2}(m)$, where $\tilde\beta_c = \beta_c/\text{MSD}_c$. $\beta_c$ already includes the child's emission and must not be multiplied by it again. The MSD recursion and get_gamma need the matching joint form. Nodes with other than two children keep the independent path.
• M-step: the joint sister posterior $P(z_{c_1}, z_{c_2} \mid Y)$ gives the expected counts for $S$ in closed form. Symmetrize by averaging the $(l,m)$ and $(m,l)$ counts.
• Emissions live in lineage/states/. Extend CensoredWeibullGaussian from Censored Weibull–Gaussian biosensor emission and palbociclib heritability analysis (#1016) #1017 with a covariate-dependent scale. Its M-step becomes a weighted censored Weibull regression (L-BFGS on $\log\kappa$, $\log\lambda_k$, $\gamma$).
• Covariate transitions: L-BFGS on $(w, b)$ against the expected parent→child counts from the E-step, weighted by parent density.
• Loader: extend the Censored Weibull–Gaussian biosensor emission and palbociclib heritability analysis (#1016) #1017 movie loaders to keep columns 1–2 and compute per-frame neighbor counts / Voronoi areas over all nuclei in the field before reducing to lineages.

Tasks

• Download S-BSST314 Fig1.rar. Repeat the data check on the 51 h no-drug wells: density range, number of complete sister/cousin pairs, and whether confluence is reached.
• Find the pixel size (Min et al. 2020 methods, or ask the Spencer lab). Until then, report density in pixel units.
• Loader: per-cell lifetime-averaged local density and culture age from all tracked nuclei.
• Covariate-dependent censored/truncated Weibull emission, with tests against scipy and a finite-difference gradient check.
• Symmetric sister kernel in the E-step and M-step, with a test that it reduces exactly to the current model when $S_{k,lm} = T_{kl}T_{km}$.
• Covariate softmax transitions (alternative model).
• Simulations: trees with known $\gamma$, $S$ and $T$ under the real observation windows. Check recovery, and check that the model comparison separates environment, coupling and heritability.
• Fit the model grid on Fig1 no-drug wells. Replicate on FigS9 controls and S-BSST167 vehicle.
• Posterior predictive kin-correlation check against the observed mother–daughter / sister / cousin pattern.
• (Stretch) Request the Ulicna/Lowe MDCK trees (8 generations, sparse → confluent) for a second cell type.

References

• Ulicna, Vallardi, Charras & Lowe. Automated deep lineage tree analysis using a Bayesian single cell tracking approach. Front. Comput. Sci. 3:734559 (2021).
• Min, Rong, Tian & Spencer. Temporal integration of mitogen history in mother cells controls proliferation of daughter cells. Science 368 (2020). EBI BioStudies S-BSST314.
• Miller et al. Ki67 is a graded rather than a binary marker of proliferation versus quiescence. Cell Rep 24 (2018). EBI BioStudies S-BSST167.
• Sandler et al. Lineage correlations of single cell division time as a probe of cell-cycle dynamics. Nature 519 (2015).
• Chakrabarti et al. Hidden heterogeneity and circadian-controlled cell fate inferred from single cell lineages. Nat Commun 9 (2018).
• Kuchen et al. Hidden long-range memories of growth and cycle speed correlate cell cycles in lineage trees. eLife 9 (2020).
• Guyon. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann. Appl. Probab. 17 (2007).
• Puliafito et al. Collective and single cell behavior in epithelial contact inhibition. PNAS 109 (2012).
• Streichan et al. Spatial constraints control cell proliferation in tissues. PNAS 111 (2014).