💻 bioinformatics

LeafRank: A phylodynamic framework for inferring relative fitness from single-cell phylogenies in chromosomally unstable tumors

LeafRank is a novel phylodynamic framework that leverages single-cell DNA-seq phylogenies and a multi-type branching process model to infer the relative fitness of individual cells in chromosomally unstable tumors, successfully quantifying growth heterogeneity and revealing that fitness in whole-genome duplication lineages is acquired through subsequent alterations rather than immediate advantages.

Original authors: Wu, C., Leder, K., Wang, Z., Sun, R.

Published 2026-07-09

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Wu, C., Leder, K., Wang, Z., Sun, R.

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 ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed.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

The Big Picture: The "Family Tree" Detective

Imagine a tumor not as a messy lump of cells, but as a giant, sprawling family tree. Every cancer cell is a descendant of a single "founder" cell. Over time, these cells divide, mutate, and branch out. Some branches grow huge and fast (like a family with many children), while others stay small or die out.

The problem is that in many aggressive cancers (specifically those with Chromosomal Instability or CIN), the family tree gets distorted. Sometimes, a cell accidentally copies its entire genome (a Whole-Genome Duplication or WGD). This is like a cell suddenly doubling its library of instruction manuals. Because it has twice as many manuals, it starts making mistakes (mutations) twice as fast.

If you try to measure how "fit" or "strong" a cell is just by looking at how many mutations it has, you get tricked. The fast-mutating cells look like they've been around longer or are evolving faster, but they might just be the ones with the doubled library.

LeafRank is a new mathematical tool designed to cut through this confusion. It looks at the shape of the family tree to figure out which cells are actually the "super-athletes" of the tumor and which are just average runners, even when the mutation rates are chaotic.

How LeafRank Works: The "Branching Race"

The authors built a model based on a Multi-type Branching Process. Think of this as a race where runners (cells) have different speeds.

The Input: LeafRank takes a reconstructed family tree of cancer cells (built from single-cell DNA data).
The Logic: It asks, "If I see this specific shape of branches, how likely is it that this cell is a fast runner versus a slow runner?"
- Fast runners tend to create "late but rapid" branches. They might appear later in the tree's history, but they explode in number quickly, creating a dense cluster of leaves at the end.
- Slow runners might start early but only produce a few leaves, or they might die out.
The Algorithm: LeafRank uses a clever "message-passing" system. Imagine sending a note up the tree from the leaves to the root, and another note down from the root to the leaves. These notes carry information about the "fitness" (growth speed) of the cells. By combining these notes, the system calculates the probability that any specific cell is a high-fitness or low-fitness type.

The Special Trick: Fixing the "Speed Bump" (WGD)

The paper highlights a major hurdle: Whole-Genome Duplication (WGD).

The Analogy: Imagine two cars on a highway. Car A is a standard sedan. Car B is a truck that suddenly doubled its engine size. Car B now accelerates much faster and covers more ground in the same amount of time.
The Problem: If you look at a map and see Car B has traveled 100 miles while Car A has traveled 50, you might think Car B has been driving for twice as long. But actually, they started at the same time; Car B just has a faster engine (higher mutation rate).
The Solution: LeafRank includes a "tree-rescaling" strategy. It recognizes when a branch has undergone WGD (the "engine upgrade"). It mathematically slows down the timeline for that specific branch so that the distance on the map represents time, not just distance. This allows the tool to compare the "fitness" of the WGD cells fairly against the non-WGD cells.

What They Found: Testing the Tool

The researchers tested LeafRank in two ways:

Virtual Simulations: They created fake tumors in a computer where they knew the "true" fitness of every cell.
- Result: LeafRank was very accurate. It could correctly identify the "super-athletes" (high-fitness cells) just by looking at the tree shape.
- Robustness: Even if they messed up the input settings (like guessing the wrong mutation rate), the ranking of the cells (who is #1, #2, #3) stayed mostly the same. It was very hard to fool the tool.
- Spatial Bias: They even simulated tumors where cells are packed tight in 3D space (like a real tumor). LeafRank still worked well, proving it can handle real-world messiness.
Real Patient Data (Ovarian Cancer): They applied LeafRank to data from patients with High-Grade Serous Ovarian Cancer (HGSOC), a type of cancer known for having these genome-doubling events.
- Directional Selection: In some patients, they saw a clear path where cells kept getting "fitter" over time, jumping to higher fitness levels like stepping up a ladder.
- Parallel Selection: In other patients, different branches of the tree independently found their own ways to become "fitter," like two different teams solving the same puzzle in different ways.
- The WGD Surprise: A key finding was that Whole-Genome Duplication (WGD) itself did not immediately make cells stronger.
  - Analogy: Getting a bigger engine (WGD) didn't instantly make the car win the race. The cells that had WGD didn't automatically beat the cells without it.
  - The Real Winner: The cells that became "super-fit" were the ones that, after the WGD event, picked up specific other mutations (like losing a specific gene called PTEN). The WGD just gave them the potential to evolve faster; they still had to find the right "winning moves" to actually win.

Summary of Limitations

The paper is honest about where the tool might struggle:

Neutral Evolution: If a tumor is growing completely randomly without any "super-athletes" (no selection), the tree looks like a boring, uniform bush. LeafRank can't find a ranking there because there isn't one to find.
Stalled Tumors: The tool assumes the tumor is still growing. If the tumor has stopped growing and reached a "carrying capacity" (like a crowded room where no one can enter), the tree loses the "expansion signal" LeafRank needs to work.
Tree Quality: If the initial family tree is built poorly (bad data), the results will be off. The tool relies on the quality of the input map.

The Takeaway

LeafRank is like a high-tech detective that looks at the family tree of a cancer tumor to figure out which cells are the most dangerous and aggressive. It solves the tricky problem of "genome doubling" by adjusting its internal clock, ensuring it doesn't get fooled by fast-mutating cells. It reveals that in ovarian cancer, doubling the genome is just the start of the story; the real danger comes from the specific mutations that happen after that doubling.

Technical Summary: LeafRank – A Phylodynamic Framework for Inferring Relative Fitness from Single-Cell Phylogenies

Problem Statement
Tumors exhibit significant heterogeneity in cellular fitness, driven by somatic variants such as single-nucleotide variants (SNVs) and copy-number alterations (CNAs). While characterizing this fitness diversity is critical for understanding cancer evolution, treatment resistance, and adaptive potential, quantifying it remains challenging, particularly in tumors with chromosomal instability (CIN) and whole-genome duplication (WGD). Existing methods for inferring subclonal fitness often rely on bulk sequencing (which confounds variant allele frequencies in CIN contexts) or focus on predefined subclones with uniform fitness assumptions. Furthermore, standard phylogenetic inference often assumes a constant molecular clock, an assumption violated in CIN tumors where WGD accelerates genomic aberration rates, distorting branch lengths and obscuring true evolutionary time. There is a need for a framework that can infer the relative fitness of individual cells from single-cell DNA sequencing (scDNA-seq) phylogenies while accounting for the complex, non-linear dynamics of chromosomal instability.

Methodology
The authors present LeafRank, a probabilistic framework designed to infer the relative fitness ranking of sampled single cells from phylogenetic trees reconstructed from scDNA-seq data.

Model Foundation: LeafRank utilizes a multi-type branching process model. It assumes a discrete set of $V$ fitness types, each characterized by specific birth ( $b$ ) and death ( $d$ ) rates. The model incorporates driver aberration events (rate $\nu$ ) that transition cells to higher fitness states and passenger aberrations (rate $\mu$ ) that accumulate neutrally.
Algorithmic Core: Unlike previous approaches that rely on continuous diffusion approximations or deterministic ordinary differential equations, LeafRank employs an exact decomposition of the phylogenetic probability density into branch propagators and bifurcation propagators. This formulation enables the use of a message-passing algorithm (belief propagation). The algorithm performs a bidirectional pass:
- Up-message (Rootward): Recursively collects conditional probabilities of the descending subtree from each node.
- Down-message (Leafward): Updates the marginal probability of fitness types for each node, conditioned on the observed phylogeny "above" the node (ancestral and sibling lineages).
  This approach efficiently computes the marginal fitness distribution for every leaf cell without enumerating all possible latent state configurations.
Handling Chromosomal Instability (WGD): To address the violation of the molecular clock assumption caused by WGD (which doubles the DNA substrate and accelerates aberration rates), LeafRank integrates a tree-rescaling strategy. Using a modified chronos algorithm, the framework converts distance-matrix (DM) based trees (where branch lengths represent genomic divergence) into ultrametric trees (where branch lengths represent evolutionary time). This is achieved under a state-dependent molecular clock model that assigns distinct aberration rates to WGD-negative and WGD-positive branches, effectively normalizing the tempo of evolution across lineages.
Parameter Robustness: The framework includes a quality control workflow to detect "ranking instability" (excessive sensitivity to noise) and "boundary saturation" (compression of fitness estimates to extremes), guiding users to tune input parameters (e.g., time-scale $\tau$ , number of fitness states $V$ ) for informative rankings.

Key Contributions

Cell-Level Resolution: Unlike methods that estimate fitness for predefined subclones, LeafRank ranks all sampled cells, enabling the detection of fitness heterogeneity within lineages and the identification of "late but rapid" branching patterns indicative of high fitness.
Robustness to CIN: The introduction of the WGD-adjusted tree rescaling allows for accurate fitness inference in tumors with chromosomal instability, correcting the spurious fitness inflation often observed in WGD-negative lineages when using unadjusted distance matrices.
Parameter Resilience: The method demonstrates that while absolute fitness values may vary with parameter choices, the relative fitness ranking of cells remains robust across a wide range of biologically plausible parameter perturbations.
Diagnostic Framework: The authors provide a diagnostic approach using subsampling variance as a proxy for inference accuracy, allowing users to assess the reliability of results in the absence of ground truth.

Results

Simulation Validation: In non-spatial and 3D spatial virtual tumor simulations, LeafRank achieved high correlation (Spearman $r_s > 0.7$ in 35/50 cases) between inferred and ground-truth fitness rankings using true-time (TT) trees. When applied to noisy, reconstructed trees, the WGD-adjusted ultrametric trees significantly outperformed unadjusted distance-matrix trees, recovering rankings close to the TT benchmark and correcting biases in fitness estimation.
Clinical Application (HGSOC): Applied to single-cell data from high-grade serous ovarian cancer (HGSOC) patients:
- Truncal WGD Tumors: LeafRank revealed directional selection in several patients, where fitness increased through discrete jumps (e.g., from type 0 to 6, then 9, then 10) rather than neutral expansion. It also identified parallel selection events where distinct lineages independently acquired high fitness.
- Genomic Drivers: By correlating fitness rankings with copy-number profiles, the framework identified recurrent SCNAs associated with high fitness. Notably, loss of Chromosome 10q (containing the tumor suppressor PTEN) was recurrently associated with high fitness across six patients. Other recurrent events included KRAS-containing Chr12p gains and Chr6q losses (linked to chemoresistance).
- Subclonal WGD: In tumors containing both WGD+ and WGD- lineages, LeafRank found that WGD+ cells did not exhibit an immediate, uniform fitness advantage over their WGD- counterparts at the time of sampling. Instead, fitness advantages were acquired through subsequent alterations, suggesting WGD provides long-term evolvability rather than an instantaneous growth boost.

Significance and Claims
The paper claims that LeafRank provides a generalizable tool for translating the structural information of single-cell phylogenies into relative fitness rankings, offering a high-resolution view of cancer clonal expansion. The authors emphasize that their approach does not assume uniform fitness within subclones, allowing for the resolution of selection within lineages. By decoupling aberration rates from evolutionary time through tree rescaling, LeafRank addresses a critical limitation in analyzing CIN tumors. The study concludes that while WGD is a recurrent event in HGSOC, it does not necessarily confer an immediate fitness benefit; rather, its prevalence may be driven by enhanced long-term evolvability. The framework enables the identification of specific aneuploidy patterns driving clonal expansion that might remain hidden in standard bulk genomic analyses. The authors note limitations, particularly regarding tumors evolving under strict neutrality or those that have reached carrying capacity (population stasis), where the expansion signal required for inference may be absent.