💻 bioinformatics

Biopsy-aware phylogenetic reconstruction from longitudinal single-cell copy number profiles

This paper introduces the Cancer Tree Biopsy Framework (CTBF), a method for reconstructing cancer phylogenies from longitudinal single-cell copy-number profiles that explicitly accounts for temporal sampling order and distinguishes between observed profiles and their ancestral states, demonstrating superior accuracy and genome-scale feasibility compared to existing pooled or topology-only approaches.

Original authors: Paszek, J., Mykowiecka, A., Gogolewski, K.

Published 2026-10-16

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CC BY 4.0

Original authors: Paszek, J., Mykowiecka, A., Gogolewski, K.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Cancer is not a single, static mass of cells; it is a living, evolving ecosystem. Within a single tumor, different groups of cells accumulate unique changes in their genetic blueprints, specifically in the number of copies they carry for various sections of their DNA. These changes, known as copy number alterations, can happen repeatedly and in different orders, creating a complex family tree of cell lineages. Understanding this history is crucial because the order in which these changes occurred often dictates how aggressive a cancer is and how it might respond to treatment. Traditionally, scientists have tried to reconstruct these family trees by taking a single snapshot of a tumor, but this approach misses the most important clue: time. By collecting samples from the same patient at different moments—before treatment, during, and after—researchers can see the tumor's evolution in motion. However, turning these time-stamped snapshots into a coherent family tree is incredibly difficult, especially when the same genetic change appears in different cells at different times, making it hard to tell who is the parent and who is the child.

A team of researchers at the University of Warsaw has developed a new way to solve this puzzle, treating the sequence of biopsies not just as a collection of data points, but as a strict timeline that guides the reconstruction. Their method, called the Cancer Tree Biopsy Framework, acknowledges that a tumor sample taken today is a direct descendant of a sample taken yesterday, even if they look genetically similar. In their work, published as a preprint, the authors describe a system that separates the genetic state of a cell from the specific moment it was collected. This distinction allows the software to recognize that a genetic profile seen in a later biopsy might actually belong to an ancestor of a cell seen in an earlier biopsy, a relationship that older methods would miss or confuse.

To test their approach, the researchers created thousands of simulated cancer histories, complete with known family trees and specific moments when samples were taken. They then fed these simulated samples into their new system and compared the results against the known truth. The simulations showed that by respecting the order in which samples were collected, their method could reconstruct the family tree with significantly higher accuracy than previous techniques that ignored the timeline. Specifically, when they used data from multiple biopsies, their method correctly identified the ancestral relationships between cells far more often than methods that simply pooled all the genetic data together without regard for when it was collected. The study also demonstrated that adding more biopsies to the mix improved the accuracy of the reconstruction, allowing the software to fill in more of the missing branches in the family tree.

The researchers did not stop at simulations. They applied their method to real-world data from a patient with triple-negative breast cancer, a particularly aggressive form of the disease. The patient had provided tumor samples at three distinct times: before chemotherapy, after two cycles of treatment, and after surgery following six cycles. The team processed the DNA from these samples to determine the copy number profiles for hundreds of individual cells. Using their new framework, they successfully built a genome-scale family tree that connected these cells across time. The resulting tree showed how specific genetic profiles appeared, persisted, or disappeared as the treatment progressed, offering a detailed view of the tumor's evolutionary journey. While the researchers could not verify the exact family tree because the true history of the patient's cancer is unknown, the fact that their method produced a coherent, biologically plausible tree from such complex, real-world data proves that the approach is computationally feasible and ready for further study.

One of the most significant aspects of this work is how it handles uncertainty. In many cases, the genetic data alone is not enough to definitively say which cell is the parent of another. Older methods often forced a decision, potentially creating an incorrect family tree. The new framework, however, is designed to defer these difficult decisions. When the data is ambiguous, the system leaves those specific branches of the tree unlabeled rather than guessing. It then uses the timeline of the biopsies to guide the rest of the reconstruction, ensuring that the parts of the tree it does build are consistent with the order of events. This "connect-then-complete" strategy means the method can produce a partial tree that is highly accurate in the areas it is sure about, while honestly admitting where the data is insufficient.

The study also compared their method against other existing tools used in the field. In the simulated tests, their approach consistently outperformed these competitors, particularly when the evolutionary history of the cancer was deep and complex. The researchers found that their method was not only more accurate but also faster and less demanding on computer memory than some of the other advanced tools available. This efficiency is vital, as analyzing the genetic data from thousands of cells across multiple time points requires significant computational power. By streamlining the process, the new framework makes it possible to analyze large datasets that might have been too difficult to process before.

Ultimately, this research offers a more nuanced way to look at cancer evolution. By treating the biopsy samples as a sequence of events rather than a static collection, the researchers have provided a tool that can better capture the dynamic nature of tumors. The ability to distinguish between a genetic state that is merely recurring and one that represents a true ancestral link is a critical step forward. While the method still relies on simulations for its primary validation and the real-world application was an exploratory feasibility study, the results suggest that incorporating the temporal dimension of biopsies can significantly improve our understanding of how cancer develops and changes over time. This clarity could eventually help doctors tailor treatments more effectively, targeting the specific evolutionary paths a tumor is taking rather than just its current state.

Technical Summary: Biopsy-aware phylogenetic reconstruction from longitudinal single-cell copy number profiles

Problem Formulation
The paper addresses the challenge of reconstructing cancer evolutionary histories from longitudinal single-cell DNA sequencing data, specifically focusing on copy-number profiles (CNPs). Traditional phylogenetic methods often treat all observations as terminal leaves, disregarding the temporal order of sample collection. This approach fails to represent sampled ancestors or utilize the constraints imposed by the biopsy collection sequence. Furthermore, the same CNP state can arise from distinct evolutionary histories (non-identifiability), and recurrent states may appear at multiple time points. The authors formulate the problem of reconstructing a tree where nodes represent evolutionary occurrences (time-indexed) rather than just states, allowing the same state to label distinct nodes. They define two output classes:

Partial CNP-trees: Ancestral nodes may remain unlabeled (latent) if their specific CNP state cannot be resolved.
Closed-state CNP-trees: Every node, including ancestors, must be assigned an observed CNP state from the input set.

The input consists of an ordered family of biopsies, where each biopsy contains a set of distinct CNP states observed at a specific time. The reconstruction must respect the temporal constraint: if an occurrence $A$ is an ancestor of $B$ , the biopsy time of $A$ must be less than or equal to that of $B$ .

Methodology: The Cancer Tree Biopsy Framework (CTBF)
The authors introduce the Cancer Tree Biopsy Framework (CTBF), which separates CNP states from biopsy-indexed occurrences. The core reconstruction method follows a "connect-then-complete" strategy:

Biopsy-Guided Bottom Construction:
- The method first constructs a forest of lineages rooted at the earliest biopsy.
- It extends recurrent states across the time intervals between their first and last observations.
- It processes transitions between consecutive biopsies ( $t-1 \to t$ ) using an adaptive/deferred assignment rule. For each occurrence in the current biopsy, it attempts to find a parent in the previous biopsy based on dissimilarity and a "zero-regain" plausibility criterion (preventing impossible copy-number reversals).
- If a unique plausible parent cannot be identified, the assignment is deferred. A "copy-up" operation creates a fresh, unlabeled occurrence at the earlier time point carrying the child's state, allowing the unresolved assignment to be carried forward to the next earlier transition. This mechanism handles cases where a state observed later might have been a founder of an earlier sampled occurrence.
Top Completion:
- Once the bottom forest is established, the method performs a "top completion" to connect the component roots into a single tree.
- Partial Completion: New top nodes remain unlabeled.
- Closed-State Completion: New top nodes are assigned states from the observed set $U$ .
- The authors propose a binary anticentral reduction rule for top completion. This rule selects pairs of component roots to merge based on a score combining pairwise dissimilarity and a centrality metric (inverse mean dissimilarity). It also includes a parent-selection rule to determine the direction of the edge (ancestral state) based on diploid deviation and centrality.
Comparators:
The study evaluates CTBF methods against several baselines:
- Pooled methods (M0, M1, M3, M5): These ignore biopsy order, treating the input as a set of distinct states (collapsing recurrent observations).
- Classical Neighbor Joining (M4): Applied to the biopsy-guided forest but using standard NJ for top completion.
- MEDICC2: A state-of-the-art tool for copy-number phylogenies, used here in a topology-only mode.
- NestedBD-Long: A Bayesian birth-death method using numerical collection times.

Key Contributions

Formalism: The authors define a rigorous framework for longitudinal CNP reconstruction that distinguishes between state identity and occurrence identity, supporting both partial and closed-state outputs.
Algorithm: They develop a biopsy-guided bottom-up construction with a deferred copy-up mechanism to handle ambiguous ancestry, followed by a binary anticentral top completion.
Evaluation: A comprehensive simulation study using 100 independently generated evolutionary histories with controlled sampling schedules (varying biopsy numbers and depths).
Empirical Application: A genome-scale application to three longitudinal biopsies from a triple-negative breast cancer patient (KTN152), demonstrating feasibility on real, patient-derived data.

Results

Simulation Performance:
- Partial Reconstruction: The biopsy-guided partial method (M2) achieved significantly higher mean rooted generalized Robinson–Foulds (GRF) similarity compared to pooled Neighbor Joining (M0), topology-only MEDICC2, and NestedBD-Long (at evaluated depths). The gain was consistent across different evolutionary depths (heights 14, 24, 34).
- Closed-State Reconstruction: Performance was depth-dependent. At shallower depths, biopsy-guided methods (M6, M7) outperformed pooled counterparts. At greater depths, pooled methods sometimes showed higher Ancestor-Descendant F1 (AD-F1) scores, though biopsy-guided methods maintained higher GRF similarity.
- Biopsy Quantity: Increasing the number of biopsies improved ancestry recovery (AD-F1) for biopsy-guided closed-state methods, with gains exceeding those of pooled methods using the same completion rules.
- NestedBD-Long: While NestedBD-Long outperformed pooled NJ, it did not consistently surpass the biopsy-guided partial methods (M2) under a fixed computational budget. Convergence of its Markov Chain Monte Carlo (MCMC) runs was not established within the budget for deeper trees.
Empirical Application (KTN152):
- The framework successfully processed 79 cells across three time points (pre-treatment, mid-treatment, surgery) with 76 distinct CNP states.
- The M2 method produced a partial tree with 148 vertices, including 31 inferred "copy-up" occurrences.
- The pipeline demonstrated computational feasibility, with reconstruction times under 2 seconds per condition and memory usage under 230 MB, significantly lower than MEDICC2.
- The resulting tree illustrated model-inferred ancestry across the three biopsies, linking specific observed occurrences chronologically.

Significance and Claims
The paper claims that distinguishing evolutionary occurrences from copy-number states and utilizing biopsy order are critical for accurate reconstruction of cancer phylogenies from longitudinal data. The biopsy-guided "connect-then-complete" approach effectively leverages temporal constraints to resolve ancestry that pooled methods miss. The authors assert that their method provides a computationally efficient and accurate alternative to existing tools, particularly for partial tree reconstruction where ancestral states are not required to be observed. The empirical application confirms that the method can handle genome-scale, patient-derived data, although the authors note that the lack of a ground-truth topology for the real data limits the assessment to computational feasibility and descriptive properties of the inferred trees. The study highlights that while closed-state reconstruction is possible, its accuracy is sensitive to evolutionary depth and the specific evaluation metric used.

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