Conception-calibrated male pediatric tumor mitotic clocks

Abstract

Molecular clocks can reconstruct tumorigenesis, but their calibration is limited by uncertainty in cancer ages. Pediatric cancers simplify this problem because age ranges are narrowly bounded by conception and a minimum of ~30 divisions. We developed mitotic clocks from rapidly fluctuating CpG (fCpG) DNA methylation on the X chromosome in male cancers, applying a two-state Markov model to estimate mitotic age and epimutation rates. Across acute lymphoblastic leukemia, acute myeloid leukemia, neuroblastoma, and embryonal brain tumors, modeled and observed methylation data were highly concordant, yielding epimutation rates of ~10^-3 per division and tumor mitotic ages between 30 and several hundred divisions. The clocks also resolved remission dynamics, inferring relapses seeded by small numbers of variably dormant residual cancer cells. By exploiting the unique age constraints of male pediatric tumors, calibrated fCpG clocks provide a quantitative framework to reveal otherwise hidden features of human tumor evolution.

Pediatric cancers provide naturally bounded timeframes that calibrate fast-ticking fluctuating CpG methylation clocks, revealing similar mitotic ages regardless of patient age and suggesting relapse from dormant residual lineages.

Introduction

Many aspects of human tumorigenesis cannot be directly observed, but past events can be inferred by analyzing somatic alterations that accumulate in the final tumor^1,2. A challenge for molecular clock methods is that their conclusions are inferential, and few cancers have natural histories that allow for robust validation. Relative to adult cancers, pediatric cancers provide a simpler modeling framework because their development timelines are more tightly constrained, particularly for tumors resected in infancy. In such cases, maximum tumor age is limited by conception, and a minimum of ~30 cell divisions to reach detectable size.

A limitation of pediatric clocks is that few somatic alterations are detected in these tumors³. To overcome this, we measured rapidly fluctuating methylation at CpG sites (fCpGs), which undergo balanced cycles of methylation and demethylation³. This approach is orders of magnitude more informative than mutation-based clocks, with epimutation rates of ~10⁻³ per division compared to ~10⁻⁹ for mutations. fCpG sites can resolve even short intervals, as their methylation is polymorphic in tumors resected during the first months of life. The clock is further simplified with monoallelic X chromosome fCpGs in male cancers. In this setting, methylation is initiated at either 0% or 100% in the progenitor cell, and elapsed time can be inferred from the extent of drift toward ~50% average methylation in the final tumor population (Fig. 1A).

Fig. 1. fCpG molecular clock.

A Schematic of the clock. At the start of growth, each fCpG site on the X-chromosome in males can only be methylated or unmethylated in the progenitor cell. With cell division and growth, fCpG sites largely retain the pattern of the progenitor cell but average population values (measured with arrays) drift towards 50% from stochastic epimutations. With more divisions and oscillating epimutations (balanced methylation and demethylation), fCpG average methylation drifts from bimodal “U” shaped distributions in younger cancers to more unimodal distributions in older cancers. B Cancer-specific clocks for ALL, AML, and ETMR comprising 416, 754, and 242 fCpG sites, respectively. Overlap between clocks was minimal; no site was shared by all four. (not illustrated, NB with 183 fCpG sites; NB:ALL 12 sites, NB:AML 13 sites, NB:ETMR 14 sites overlap). C Representative methylation distributions from “younger” (bimodal) and “older” (unimodal) tumors. Bottom row: tumors detected in the first months of life with unimodal fCpG distributions, illustrating that cancers detected very early in life are not typically very mitotically young cancers. D Conversion of the methylation drift metric to mitotic ages or numbers of inferred divisions, using epimutation rates estimated under a symmetric two-state (binary) Markov model. Older cancers have lower drift values. E: Inferred epimutation rates for individual clock fCpGs. Rates varied across the sites, but mean values closely matched those inferred from pooled tumor data (Fig. 1D), consistent with largely independent two-state dynamics at fCpGs. Average ETMR fCpG site epimutation rate was 0.0029 versus 0.0029 from pooled data, 0.0038 versus 0.0037 from pooled ALL data, 0.0077 versus 0.0076 from pooled NB data, and 0.0044 versus 0.0043 from pooled AML data. Sample sizes: n = 137, 344, 61, and 76 tumors for ALL, AML, ETMR, and NB, respectively (C, D); n = 416, 754, 242, and 183 fCpG sites, respectively (B, E).

We developed fCpG molecular clocks for pediatric acute lymphoblastic leukemia (ALL), acute myeloid leukemia (AML), neuroblastoma (NB), and embryonal brain tumors (ETMR). These clocks reconstructed tumorigenesis, remission, and relapse, with simulations that closely matched experimental data. More broadly, pediatric cancer datasets provide a bounded temporal framework to train and validate clock methods that may extend to older children and adults.

Results

fCpG mitotic clock development

fCpG clocks were developed using pediatric ALL, AML, ETMR and NB methylation array data^4–8. Methylation in male progenitor cells starts at either 0 or 100% on X-chromosome fCpG sites. With rapid and balanced fCpG methylation and demethylation, average methylation will drift towards 50% as the tumor grows (Fig. 1A). Conceptually, fCpG sites in mitotically younger cancers are synchronized by the pattern in their progenitor cells, with more sites near 0 or 100% methylation. Older cancer populations are more polymorphic with average fCpG methylation near 50%. fCpG sites, with average methylation between 40 and 60% in their cancers, had little overlap between the cancer specific clocks, and no fCpG site was shared by all four clocks (Fig. 1B).

Mitotic age was quantified using a “drift” metric—the mean deviation of all fCpG sites from 50% methylation—where low drift values indicate mitotically older cancers. Variation in drift across tumors was modeled using a two-state (binary) Markov process to infer relative ages, which were then converted to numerical mitotic age estimates. No tumor was allowed to begin growth before conception or to be younger than 30 cell divisions. To reflect the rarity of each diagnosis before birth, onset boundaries were set at −2 months for ALL, −4 months for AML, -4 months for NB, and 4 months of age for ETMR (see Methods).

Average fCpG methylation distributions differed across individual cancers (Fig. 1C). Mitotically younger cancers had bimodal “U” shaped distributions, likely reflecting synchronization between cells by the binary states (methylated or unmethylated) in their progenitor cells (Fig. 1A). Older cancers had more unimodal distributions, likely reflecting more divisions and stochastic fluctuating methylation and demethylation between cells. Cancers removed from the youngest infants generally had more unimodal distributions, indicating that cancers detected shortly after birth are not necessarily more rapidly growing.

Mitotic ages (divisions from growth onset and resection) spanned ~30 to several hundred divisions (Fig. 1D). As an internal check, per-site epimutation rates were estimated from single tumor values. Consistent with an overall binary error process, epimutation rates varied between fCpG sites but, on average, closely matched estimates from pooled tumor values (Fig. 1E). Using cancer-derived mitotic ages, these epimutation rates were converted to per-division methylation flip rates for each fCpG, ranging from 0.0016 to 0.011 per division per site.

Patient ages at the start of tumor growth were inferred from cancer mitotic ages, assuming one division per day (Fig. 2). No cancers were inferred to start growth before conception, albeit inferred starts would be earlier or later if tumor cells respectively divide slower or faster than once per day. Average mitotic ages were respectively 103, 101,158 and 57 divisions for ALL, AML, ETMR and NB. Cancer mitotic ages were similar across patient ages (Fig. 2), indicating growth dynamics are not markedly different between infants and older children.

Fig. 2. Ages at the start of growth for ETMR, ALL, AML and NB were estimated by subtracting mitotic age from the age at diagnosis, assuming one division per day.

A ETMR, ALL and AML. Each horizontal bar represents an individual tumor and spans the interval between its inferred start of growth (left end) to diagnosis (right end). No cancer started before conception, and none had less than 30 divisions. The inset shows mitotic age vs. calendar age at diagnosis, indicating little dependence of mitotic age on patient age at diagnosis. B Neuroblastoma (NB) tumors. NBs that tend to progress (Stage 4, red bars; MYCN amplified “+”) all started to grow after one year of age and would have been missed by screening during infancy. Sample sizes: n = 61, 137, 344, and 76 tumors for ETMR, ALL, AML, and NB, respectively.

The NB clock is testable with orthogonal data because population screening and surgical resection of NBs during the first year of life did not reduce mortality⁹. Consistent with this failure, all high-risk NBs were inferred to begin growth after one year of age and thus could not have been intercepted by infancy screening (Fig. 2B). The NB clock indicates that tumors growing during the first year of life were those that tend to regress spontaneously¹⁰, with many initiating growth before birth. Taken together, the clocks infer when pediatric cancers begin to grow, show that growth dynamics are similar across ages, and align with the findings from large-scale NB infancy screening studies.

Extension to adult AML

The pediatric AML clock was used to infer adult AML mitotic ages¹¹, with ages that overlapped the pediatric ranges (Fig. 3A). Although composed of heterogenous cell types, normal cord¹² and adult blood¹³ “mitotic” age averages were greater than the AML samples, with narrower ranges than AML. Methylation variations between fCpG sites in normal blood was much lower than AML, even in cord blood obtained at birth. The low variances between fCpG site in normal blood are consistent with fluctuating methylation and demethylation driving methylation towards equilibrium values in polyclonal populations.

Fig. 3. fCpG clock with adult samples.

A Adult AML exhibited mitotic age ranges comparable to pediatric AML. Normal cord and adult peripheral blood generally display higher inferred “mitotic” ages, with narrower ranges. B fCpG site methylation across adult AML samples is highly variable, whereas normal blood samples are highly similar, consistent with fluctuating methylation reaching near equilibrium in polyclonal populations, even by the time of birth in cord blood. Note that applying the AML clock to normal blood is an out of context use (see Fig. 1B) and is only shown here to illustrate high fCpG methylation variability between new clonal expansions (AML) versus loss of variability between older, polyclonal human cell populations. C Serial AML samples collected during decitabine treatment showed mitotic age variability but a significant increase in inferred mitotic age over calendar time (one-sided Wilcoxon signed-rank test, p < 0.001; n = 17 paired samples). Despite exposure to a hypomethylating agent, fCpG methylation profiles remained highly correlated within patients (red bars) and poorly correlated between patients (black bars). This pattern with strong within-patient similarity along progressive age increases is consistent with a clock in which methylation states are largely copied while stochastic epimutations accumulate through time. D Mitotic ages of paired diagnosis-relapse pediatric AML samples were variable through time and fCpG methylation was often discordant. In contrast to the monotonic age increases of serial adult AML samples without remission (Fig. 3C), mitotic ages at relapse were typically much lower than the elapsed calendar time between diagnosis and relapse, consistent with dormancy during remission. Sample sizes: n = 142, 244, and 423 samples for adult AML, cord blood, and adult blood, respectively (A, B); n = 17 paired samples (C); n = 73 diagnosis-relapse pairs (D).

Reproducibility and progression of the AML clock were assessed using serial adult AML samples¹⁴ collected during treatment (Fig. 3C). Although age estimates over the few weeks varied, there were significant increases in mitotic age over time. Within patient fCpG methylation patterns were more similar across time points than between patients. The serial data support a molecular clock model in which fCpG methylation is typically copied between divisions while stochastic epimutations accumulate through time.

Pediatric AML diagnosis-relapse pairs⁶ exhibited more divergent trajectories over time, with many showing discordant fCpG methylation, consistent with continued epimutations during remission (Fig. 3D). In most cases, relapse mitotic ages were much lower than their remission intervals, suggesting dormancy during remission rather than the monotonic mitotic age increases seen in cancers without remission (Fig. 3C). Remission dynamics can be potentially reconstructed by comparing fCpG methylation between diagnosis and relapse (see below).

Cancer simulations with fCpG clocks

Calibration of hundreds of fCpG sites with empirically derived error rates enables a novel test: whether simulations initiated from a single progenitor cell can reproduce the methylation patterns observed in hundreds of real cancers. For each cancer type, simulations used the same fCpG sites and error rates, with mitotic age as the cancer-specific variable. Simulated final-stage methylation for ALL, AML, ETMR, and NB cancers closely matched experimental data, both in overall drift (Fig. 4A) and in Pearson correlations across fCpG sites (Fig. 4B). The ability to recapitulate tumorigenesis using inferred mitotic ages and calibrated site-specific epimutation rates supports the adequacy of Markov-model parameterization.

Fig. 4. Tumor simulations from inferred parameters.

A For each tumor, we simulated its final bulk methylation starting from a single progenitor cell by evolving each fCpG under a symmetric two-state Markov process using per-site flip rates and the tumor-specific mitotic age. Simulated final-stage drift closely matched observed values; five independent simulation replicates were performed per tumor. B Simulated per-site methylation profiles also closely recapitulated the observed profiles for each tumor. Sample sizes: n = 61, 137, 344, and 76 tumors for ETMR, ALL, AML, and NB, respectively; five simulation replicates were performed per tumor.

Inference of progression between diagnosis and relapse

fCpG clocks were used to reconstruct remission (Fig. 5A). Differences between diagnosis and relapse patterns reflect the numbers and dormancy of residual cancer cells responsible for relapse. To simulate remission, we used approximate Bayesian computation (ABC¹⁵) and methylation profiles at diagnosis and relapse, along with the number of intervening days, to infer three parameters: (i) number of relapse-initiating cells (1–32), (ii) latency fraction (0–0.995; proportion of divisions without net growth), and (iii) mitotic quiescence (0.001–1; proportion of mitotic activity per calendar day). Simulations were accepted if both drift and Pearson correlation between simulated and observed relapse methylation approximated experimental values. In simulations, ABC recovered the latency interval and divisions during latency more reliably than mitotic quiescence or the number of relapse-initiating cells (Fig. S1).

Fig. 5. ABC inference of dormancy during remission.

A Remission schematic. Relapse results from a small number of cells present at diagnosis that survive remission, which is modeled as two phases: latency (no net growth; cell numbers constant) and regrowth (net expansion). During latency, cells may be quiescent, with less than one division per day. During regrowth, cell division rates return to once per day. B Inferred numbers of relapse-initiating cancer cells responsible for relapse. Residual cancer cells were low in ALL and NB (often one), and heterogeneous and higher in AML and ETMR. Y axis indicates the remission interval in days. C Latency is the proportion of remission time before regrowth starts. Latency was high for ALL and NB, and heterogeneous in AML and ETMR. D Quiescence is the relative mitotic rate during latency, with a value of 1 indicating one division per day. Quiescence was low (low mitotic rate) for ALL and NB, and variable in AML and ETMR. E Latency divisions were minimal for ALL and NB, and heterogeneous in AML and ETMR. F ETMR (WGS) and NB (WES) sequencing data were available for some diagnosis-relapse pairs and document mutations gained during remission. Female mutation data (green circles) are also shown. ETMR relapse-specific mutations scale with both remission days and inferred numbers of latency divisions, consistent with ongoing divisions during remission. By contrast, NB relapse-specific mutations do not increase with remission days or with the small number of inferred latency divisions, consistent with quiescent, non-cycling persister cells during remission. Sample sizes: n = 73 diagnosis–relapse pairs (B–E); n = 4 ETMR (2 male, 2 female) and 16 NB (8 male, 8 female) diagnosis–relapse pairs with sequencing data (F).

Acceptable parameter combinations were recovered for all ALL¹⁶, ETMR⁷ and NB¹⁷ pairs, but not for 8 of 73 AML⁶ pairs. The AML pairs that failed ABC had shorter remissions (117 days versus 402 days for successful ABC), suggesting scenarios outside the small-residual-cell-latency remission model. There was a diversity of possible residual cancer cell, latency, and quiescent combinations that reproduced the experimental data (Fig. 5). Relapse occurred with one or more residual cancer cells (Fig. 5B), and all cancers showed evidence of dormancy with different degrees of latency and mitotic quiescence (Fig. 5 C,D). Across cancer types, ALL and NB generally exhibited higher latency and quiescence, with fewer residual relapsing cells (often one), and fewer divisions during latency. AML and ETMR showed heterogeneity with examples with less latency and quiescence, and more residual relapsing cells.

fCpG clock remission inferences are orthogonally testable with remission dynamics inferred by mutation differences between the same paired diagnosis and relapse samples. ETMR relapse samples harbor many more mutations than diagnostic samples, with clear chemotherapy-associated mutational signatures, consistent with substantial mitotic activity during remission⁷. By contrast, NB relapse samples also contain more mutations than at diagnosis, but many of these variants are detectable at low frequency in the diagnostic sample, indicating that relatively few new mutations are acquired during remission¹⁷. Supporting this dormancy, NB cells sampled during remission often display non-cycling persister cell signatures¹⁸. Consistent with these findings, the fCpG clocks inferred very few cell divisions during NB remission compared with ETMR (Fig. 5E). ETMR mutations gained during remission scale with both remission duration and the numbers of inferred latency divisions (Fig. 5F), whereas in NB, mutations gained do not increase with remission time or with the few inferred remission divisions. Overall, fCpG clocks parameterized on primary cancers can also resolve remission dynamics, capturing features of latency and mitotic quiescence.

Discussion

This study demonstrates that pediatric cancers can be natural calibrators for tumor molecular clocks. Because the maximum possible age of any pediatric tumor is bounded by conception, these cancers provide a rare setting where molecular time can be anchored to narrow calendar intervals. We exploited this setting to calibrate mitotic clocks based on fCpG sites on the X chromosome in male cancers. A key strength of this approach is that the clock records epimutations that oscillate over short time scales. Many existing cancer molecular clocks are based on cumulative, essentially irreversible mutational processes (e.g., base substitutions), which lack high temporal resolution in pediatric cancers with low mutation burdens¹⁹. Other epigenetic clocks can infer aspects of human tumorigenesis²⁰, but our clock³ resets to the pattern of the progenitor cell at start of growth, and balanced methylation and demethylation at fCpG sites provide a high-frequency ( ~ 10^-3 per division) “tick” suitable for measuring divisions over months to years. Consistent with high epimutation rates, cancers detected in the first few months of life had polymorphic fCpG methylation (Fig. 1C). Calibrating this epimutation rate in cancers with narrowly bounded ages enables inferences about tumor initiation and progression that have been difficult to obtain with other molecular markers.

The Markov-model calibration revealed that site-specific epimutation rates were consistent with rates inferred from tumor-averaged data, supporting the assumption that these CpG sites function as largely independent two-state systems governed by similar per-division flip processes. Using these rates and the estimated mitotic age for each cancer, simulations reproduced both the drift distributions and site–site correlation structures observed in hundreds of tumors across ALL, AML, NB, and ETMR. This concordance, together with orthogonal data^7,9,17,18, strongly supports the validity of the inferred parameters and the binary-drift model.

Applying this clock to paired diagnosis–relapse samples extends its utility to one of the least accessible phases of cancer biology: remission and dormancy, when growth is limited and cells divide more slowly for multiple possible reasons^21–24. Small numbers of leukemic stem cells are thought to persist during remission²⁵, leading to relapses that often carry new secondary genetic alterations and frequently originate from minor subclones at diagnosis^26,27. Direct observation of residual cancer cell dynamics is rarely possible, yet these dynamics likely affect relapse risk. Using ABC, we inferred three biologically interpretable parameters for each diagnosis-relapse pair: the number of relapse-initiating cells, latency fraction, and the degree of mitotic quiescence. Relapses were consistently inferred to arise from small numbers of residual cancer cells that exhibited at least some dormancy, recapitulating the non-cycling persister phenotype observed in NB remission^17,18 and the higher mitotic activity characteristic of ETMR remissions⁷. Concordance with orthogonal sequencing data strengthens clock validation, while higher clock epimutation rates enable more granular insights into the numbers and dormancy of remission cells that eventually drive relapse.

Reconstructing remission dynamics may help clarify mechanisms of relapse. In ALL, higher latency and quiescence with typically a single residual leukemic stem cell may reflect selection for dormancy under maintenance therapy^28,29. The greater heterogeneity inferred for AML and ETMR, with larger numbers of residual cancer cells, may underlie their higher relapse frequencies and the limited efficacy of AML maintenance³⁰.

This analysis has limitations inherent to molecular clocks. It assumes that epimutation rates remain constant during tumor growth and across ages, although age-related stabilization of lineage-tracing methylation has been reported³¹, and rates during progression, therapy, and aging remain to be better defined. In particular, epimutation rates inferred from primary tumors may be variable during treatment, dormancy or after relapse. The ground-truth boundary anchored to birth or conception was based on relatively few tumors resected in infancy, and ETMR ages were recorded only in years. Additional cases sampled shortly after birth could more precisely define how many epimutations or other alterations accumulate during the earliest months of tumor growth. Restricting the analysis to X-linked fCpGs in male cancers simplifies interpretation and allows application of the relatively simple two-state Markov model, but limits general applicability. Analogous, tissue-specific fCpG clocks have been developed for autosomal sites with different methods in normal tissues³, clonal hematopoiesis in twins³², breast cancers³³, and chronic lymphoid leukemia³⁴.

Pediatric cancers, with their more defined timelines, provide unique opportunities to validate and calibrate somatic evolutionary reconstruction methods applicable across all ages. Fast-ticking clocks better match the pace of tumorigenesis, enabling reconstructions over clinically relevant weeks-to-months timescales. Understanding how individual tumors respond to therapy could lead to improved treatments specifically directed towards their resistance mechanisms.

Methods

Cohorts and samples

Methylation array data (Illumina 450 K/EPIC) were obtained from X-chromosome CpG sites and male individuals (Table S1). Methylation beta values were used as provided or obtained from available idat files using minfi³⁵ at standard setting. For the TARGET NB data, purity estimates were provided in the dataset, and samples with less than 40% tumor cells were excluded. Empirically, tumor purity did not confound NB mitotic age estimates, as there was no correlation (R = 0.005) between estimated mitotic ages and tumor purity (Fig. S2).

fCpG clock site identification

For each cancer type, we selected X-chromosome fCpGs using three criteria: 1) Mean methylation between 0.40–0.60 (0.37-0.63 for NB) across tumors of the same type, 2) High variability between individual cancers with CpG site variances between 0.03 and 0.1, and 3) Lack of age-related changes in methylation (Pearson between methylation and age at diagnosis between 0.1 and -0.1). This process produced cancer-specific panels of [416] (ALL, from 137 samples), [754] (AML, from 344 samples), [183] (NB from 76 samples), and [242] (ETMR from 61 samples) sites (Fig. 1B). Overlap across panels was minimal (see Fig. 1B) and no site was shared by all four clocks.

Estimation of mitotic ages

We estimated tumor mitotic ages using a symmetric two-state (“flip”) Markov model of fCpG methylation, chosen because it matches the biology of male X-linked CpGs and requires minimal assumptions. At each fCpG in a single cell the state is either methylated (1) or unmethylated (0); with each cell division, the state can flip with a per-division epimutation rate (ε). In bulk, array β values are the population average of these binary states and, under the model, relax toward 0.50 at a rate determined by ε. The model therefore has only two unknowns—the flip rate ε and the sample’s mitotic age t—without needing to assume a specific growth curve or site-specific selection. The approach works directly on standard methylation array data. We summarized distance from equilibrium with a “drift” metric defined per tumor as the mean absolute deviation of β from 0.50 across the fCpG panel (i.e., average of |β − 0.50 | ).

We implemented a Python workflow (Program 1) of a symmetric two-state Markov process that takes as input the age at diagnosis of each cancer and its average drift value. The program evaluates 500 linearly spaced candidate epimutation (flip) rates ε on [0.001, 0.01] (step ≈ 1.8×10⁻⁵) and selects the ε that minimizes the mean squared error (MSE) between the observed drift and the model-predicted drift computed with t = diagnosis age (assuming one division per day). Estimates are constrained so that no tumor has t < 30 divisions ( < 35 divisions for NB, which typically present as large tumors), and no start occurs earlier than disease-specific bounds (ALL: −2 months; AML: −4 months; NB: - 4 months; ETMR: +4 months relative to birth). The selected ε, the MSE, and the equations used to compute mitotic ages for each cancer type are provided in Table S2.

To obtain epimutation rates for individual fCpG sites, we used a second Python workflow (Program 2) that takes as input (i) tumor-specific mitotic ages and (ii) per-site drift values across tumors. For each fCpG site, the program fits a symmetric two-state Markov (“flip”) model by grid-searching epimutation rates over 0.0001–0.01 (step 0.0001) and minimizing the mean squared error between observed drift and the model expectation across tumors (sites with <3 evaluable tumors are skipped). The best-fitting epimutation rate and its MSE are written to a results file and summarized in Supplemental Data 2.

The two methods for estimating epimutation rates—using pooled drift (Program 1) and per-site data (Program 2)—provide an internal cross-check of the two-state Markov model assumptions, as they are expected to yield similar rates. Although epimutation rates varied across individual fCpG sites (Fig. 1E), the averages were similar to the values estimated from pooled data (Fig. 1D).

Tumor simulations

Tumors were simulated from single founder cells carrying the cancer-specific fCpG panel (Program 3). Founder states were initialized from the observed target tumor methylation: 0% if <40%, 100% if >60%, and random if 40–60%. Cells divided forward under a symmetric two-state “flip” model, copying the parental pattern and applying site specific epimutation rates from Program 2 at each division. Population growth followed a simple branching scheme (one or two surviving daughters per division) and continued until ~10⁵ cells were reached, with total divisions tuned to the inferred mitotic age of the target tumor. We then computed bulk per-site methylation values and sample-level summaries (drift; cross-site Pearson correlation) and compared simulations with data (Fig. 4). Five replicates were run per tumor.

Approximate Bayesian computation

For each diagnosis–relapse pair, we initialized the simulation (Program 4) with the case-specific primary-tumor fCpG profile (from Program 3) and evaluated a discrete parameter grid spanning: N (number of relapse-initiating cells; integers 1–32), L (latency fraction; 0–1, which partitions the remission interval R days into a latency phase L·R with no net growth and a regrowth phase (1 − L)·R), and M (quiescence; 0.005–1, the relative division rate during latency so that lower M indicates greater dormancy). During latency, cell numbers were held constant while fCpGs flipped at the per-site rates inferred in Program 2; during regrowth, we simulated net expansion at 1 division/day until the population reached ~3×10^4 cells. For each grid point (N,L,M)(N,L,M)(N,L,M), we generated a simulated relapse methylation profile and computed two summaries—drift and the cross-site Pearson correlation with the observed relapse profile. Parameter settings were accepted if both summaries met preset tolerances; N, L, M sets with greatest acceptances are reported in Supplemental Data 3 and Fig. 5. Across synthetic datasets (remission intervals 100, 200, 400, 600 and 1000 days and grids of N, L, M), ABC more readily recovered L and latency-division counts than M or N (Fig. S1).

The robustness of our ABC inference was evaluated by calculating 95% confidence intervals (CIs) for each diagnosis-relapse pair (Fig. S3, and Supplemental Data 4). In accordance with synthetic data simulations, parameters associated with the timing of regrowth (Latency (L)) exhibited higher precision than those describing relapsing cell number (N) or mitotic quiescence (M) during dormancy. ALL and NB samples generally yielded the most constrained parameter estimates, while AML and ETMR displayed higher inter-patient variability in both point estimates and uncertainty ranges.

Statistics and reproducibility

All statistical analyses and modeling were performed using custom Python workflows as described in the Methods. Comparisons of paired measurements in serial AML samples (Fig. 3C) were conducted using a one-sided Wilcoxon signed-rank test; p-values are reported as indicated.

Methylation-based comparisons throughout the study relied primarily on summary metrics rather than formal hypothesis testing. These included the “drift” metric, defined as the mean absolute deviation of CpG methylation (β values) from 0.50 across selected fCpG sites, and Pearson correlation coefficients, which were used as descriptive measures of similarity between methylation profiles (e.g., within-patient vs. between-patient comparisons, and simulated vs. observed data). Pearson correlation was also used as part of the acceptance criteria in ABC analyses.

Model parameters, including epimutation (flip) rates (ε), were estimated by minimizing mean squared error (MSE) between observed and model-predicted drift values using grid search over predefined parameter ranges. Per-site epimutation rates were similarly inferred using MSE minimization across tumors. For ABC inference of remission dynamics, parameter combinations (number of relapse-initiating cells, latency fraction, and mitotic quiescence) were evaluated over discrete grids and accepted if simulated data matched observed drift and Pearson correlation within predefined tolerances (see Methods).

Tumor simulations were performed using a stochastic two-state Markov model with site-specific epimutation rates. For each tumor, five independent simulation replicates were generated to assess reproducibility of inferred methylation patterns. Input data were filtered using predefined criteria, including restriction to X-chromosome CpG sites in male samples, selection of fCpGs based on methylation range and variance thresholds, exclusion of samples with tumor purity below 40%, and omission of CpG sites with fewer than three evaluable tumors.

Uncertainty in ABC parameter estimates was assessed using 95% confidence intervals derived from accepted parameter distributions. All parameter ranges, constraints, and implementation details are specified in the corresponding Methods sections to ensure reproducibility.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

D.S. and J.V.J. conceived the study, performed the primary analyses and writing of the manuscript.

Peer review

Peer review information

Communications Biology thanks Hayan Lee and the other anonymous reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Laura Rodriguez Perez.

Funding

This work was supported by the National Institutes of Health (P01CA196569). Jeremiah John was supported by the CHLA/USC Summer Oncology Research Fellowship (CA225513).

Data availability

All methylation array datasets analyzed in this study are publicly available through the Gene Expression Omnibus (GEO) under accession numbers GSE38235, GSE76585, GSE190931, GSE122038, GSE159907, GSE154915, GSE87571, GSE175758, GSE49031, and GSE65306, and through the TARGET Neuroblastoma dataset available from the Genomic Data Commons (https://portal.gdc.cancer.gov/projects/TARGET-NBL). Processed data generated during the current study and source data underlying the graphs are provided in the Supplementary Material and Supplemental Data 1. All other relevant data are available from the corresponding author upon reasonable request.

Code availability

Custom Python scripts used for fCpG clock calibration, tumor simulations, and Approximate Bayesian Computation (ABC) remission inference analyses are publicly available through Zenodo³⁶ at https://doi.org/10.5281/zenodo.20240964 and GitHub at https://github.com/darrylshibata/fcpg-pediatric-tumor-clocks. The deposited repository corresponds to the version of the code used in this study. Analyses were performed using Python 3 together with standard scientific computing libraries including NumPy, SciPy, pandas, and matplotlib.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s42003-026-10480-w.