Longitudinal Phylogenetic Inference of Copy Number Alterations and Single Nucleotide Variants from Single-Cell Sequencing

This paper introduces LoPhy, a novel sequential tree-building algorithm that reconstructs biologically and temporally consistent longitudinal phylogenies of single nucleotide variants and copy number alterations from single-cell sequencing data, thereby elucidating how these genetic changes jointly drive cancer evolution and treatment resistance.

The Gist

Imagine cancer not as a single, static monster, but as a rapidly evolving city. In this city, different neighborhoods (called clones) are constantly being built, destroyed, and remodeled. Some neighborhoods have new, dangerous buildings (mutations) that help them survive attacks from the police (chemotherapy).

For a long time, scientists could only take a blurry, high-level photo of this city (bulk sequencing) or look at individual bricks one by one without knowing how they fit together (early single-cell sequencing). They struggled to see two critical things happening at once:

1. Tiny typos in the blueprint (Single Nucleotide Variants or SNVs).
2. Whole sections of the city being added or demolished (Copy Number Alterations or CNAs).

Until now, no one had a good map to track how these typos and construction projects happened together over time as the city changed.

Enter LoPhy: The Time-Traveling Cartographer

The paper introduces LoPhy, a new computer algorithm that acts like a time-traveling cartographer. Its job is to draw a family tree of cancer cells that shows exactly how the city evolved from the first diagnosis, through treatment, to relapse.

Here is how LoPhy works, using some everyday analogies:

1. The "Time-Travel" Rule

Imagine you are watching a movie of a city being built. You can't see a skyscraper appear in the final scene if it wasn't there in the first scene.

• Old methods often looked at all the photos from the beginning, middle, and end of the movie and mixed them up. They might accidentally say a building existed at the start just because it was huge at the end.
• LoPhy respects the timeline. It builds the map step-by-step. It says, "Okay, at Time 1, we see these specific typos. At Time 2, we see a new construction project on top of those typos." It ensures the history makes sense chronologically.

2. The "Noisy Construction Site" Problem

Single-cell sequencing is like trying to count bricks in a building while standing in a heavy fog. Sometimes you miss a brick (a "dropout"), and sometimes the light hits a wall in a way that makes it look like there are more bricks than there really are (coverage variation).

• LoPhy is smart about the fog. It knows that different samples (different days of observation) might have different levels of fog. It adjusts its counting based on the specific conditions of that day, rather than assuming the fog is the same everywhere. This prevents it from inventing fake construction projects just because the light looked weird.

3. The "Family Tree" of Cancer

LoPhy builds a tree where the trunk is the original healthy cell. As it moves up the branches, it adds the mutations.

• The Big Discovery: When the researchers applied LoPhy to patients with Acute Myeloid Leukemia (AML), they found something surprising. The "super-villain" clones that survived the chemotherapy weren't just the ones with a few typos. They were the ones that had both typos and massive construction projects (like gaining or losing whole chromosomes).
• Think of it like a criminal gang. Some members just learned a new trick (a typo). But the ones who actually took over the city after the police raid were the ones who had both learned the trick and bought a private army (a copy number change).

Why This Matters

Before LoPhy, scientists were trying to solve a puzzle with half the pieces missing. They might see the typos but miss the construction, or vice versa.

• The Result: LoPhy showed that to understand why cancer comes back (relapse) or why it stops listening to medicine (resistance), you have to look at the typos and the construction projects together.
• The Proof: When they tested LoPhy on real patient data, the maps it drew matched what the doctors saw in the clinic. It correctly predicted which cells would survive treatment and why.

The Bottom Line

LoPhy is a new tool that lets us watch cancer evolve in real-time, with high definition. It tells us that cancer isn't just about small mistakes in the DNA code; it's often about big, structural changes to the genome happening at the same time. By understanding this full picture, doctors might be better able to predict how a patient's cancer will behave and design treatments that stop the "super-villain" clones before they take over the city.

Technical Summary

1. Problem Statement

Cancer evolution is driven by the accumulation of somatic mutations, primarily Single Nucleotide Variants (SNVs) and Copy Number Alterations (CNAs). Understanding how these mutations jointly evolve over time is critical for deciphering disease progression and therapeutic resistance.

While longitudinal single-cell DNA sequencing (sampling the same tumor at multiple time points) has emerged as a powerful tool, existing computational methods face significant limitations:

• Lack of Joint Modeling: Most existing tools model either SNVs or CNAs, but not both simultaneously from single-cell data.
• Lack of Longitudinal Integration: Methods that do model both (e.g., COMPASS, BiTSC2) are designed for cross-sectional data. Applying them to longitudinal data requires either pooling all time points (ignoring temporal structure and technical variation) or reconstructing trees independently for each time point (yielding disjoint, incoherent evolutionary histories).
• Technical Noise: Single-cell amplicon sequencing data suffers from non-uniform coverage, allele-specific dropout, and varying sequencing depths across samples, which complicates the inference of copy number states.

There is a critical gap for an algorithm that can reconstruct longitudinally consistent phylogenies of both SNVs and CNAs from noisy single-cell amplicon data.

2. Methodology: LoPhy

The authors introduce LoPhy, a novel algorithm designed to infer clone trees from longitudinal single-cell amplicon sequencing data.

A. Input Data

LoPhy processes data from targeted single-cell amplicon sequencing (e.g., Tapestri platform), which provides:

• Total read counts ($D$) and alternative allele read counts ($A$) for specific genomic loci.
• Sample metadata indicating the time point of collection for each cell.

B. Evolutionary Model

LoPhy models four types of somatic events:

1. SNV acquisition: Modeled using the k-Dollo model (acquired once, lost at most once per lineage due to deletion).
2. Copy Number Gains.
3. Copy Number Losses.
4. Copy-Neutral Loss of Heterozygosity (CNLOH).

The model assumes that mutations accumulate over time and that any mutation appearing between time points $s-1$ and $s$ is captured in the sample at time $s$.

C. Likelihood Model

LoPhy utilizes a factorized longitudinal likelihood approach. Instead of modeling the joint likelihood of all samples simultaneously, it maximizes the product of sample-specific likelihoods:
$$\prod_{s=1}^{S} P(D_s, A_s | T_s)$$
Where $T_s$ is the clone tree representing evolutionary history up to time point $s$. Crucially, the trees are nested ($T_1 \subseteq T_2 \subseteq \dots \subseteq T_S$), ensuring temporal consistency.

The sample-specific likelihood ($P(D_s, A_s | T_s)$) consists of two components:

1. Read Depth Likelihood: Modeled using a Negative Binomial distribution to account for overdispersion in sequencing coverage across amplicons.
2. Allelic Read Count Likelihood: Modeled using a Beta-Binomial distribution to handle allelic bias and amplification noise. It explicitly incorporates allele-specific dropout rates ($\mu$) to account for false negatives in detecting alternative or reference alleles.

D. Optimization Strategy

LoPhy employs a sequential tree-building algorithm combined with stochastic search:

1. Initialization: Starts with a root node (germline/normal cells).
2. Sequential Growth: For each time point $s$, new SNVs detected for the first time are added to the tree $T_{s-1}$ to form $T_s$.
3. Stochastic Search: The algorithm performs $\eta$ epochs of stochastic search to refine the tree. Moves include:
   • Relocating an SNV.
   • Adding or removing a CNA.
   • Constraint: New mutations are restricted to descendant clones, and clones from previous time points ($T_{s-1}$) remain fixed.
4. Parameter Estimation: An Expectation-Maximization (EM) algorithm is used to jointly estimate clone assignment priors and global dropout rates.
5. Objective: Maximizes a factorized posterior that includes a penalty term for the number of clones and CNA events to prevent overfitting.

3. Key Contributions

• First Longitudinal Joint Inference: LoPhy is the first method to reconstruct phylogenies capturing the joint evolution of SNVs and CNAs specifically from longitudinal single-cell data.
• Novel Objective Function: Introduces a factorized tree reconstruction objective that enforces temporal constraints while modeling sample-specific technical variations (coverage and dropout).
• Robust Handling of Noise: Explicitly models allele-specific dropout and overdispersion, which are major confounders in single-cell amplicon data.
• Open Source: The source code is publicly available, facilitating reproducibility and further development.

4. Results

A. Simulation Studies

LoPhy was benchmarked against COMPASS (SNV+CNA, no longitudinal), SCITE (SNV only, no longitudinal), and LACE (SNV only, longitudinal) on 40 simulated datasets.

• Accuracy: LoPhy achieved the best performance across all metrics, including Mutant Copy Number Mean Absolute Error (MCN-MAE), Total Copy Number MAE (TCN-MAE), and Tree F1 Score.
• False Emergence Rate (FER): LoPhy achieved a near-perfect FER (0.0), whereas COMPASS frequently inferred mutations to appear earlier than they actually did (high FER) because it ignored temporal constraints.
• Speed: LoPhy was significantly faster than COMPASS (approx. 9.5 minutes vs. 1 hour 40 minutes for 5 time points).

B. Real-World Application (AML Cohorts)

LoPhy was applied to 19 Acute Myeloid Leukemia (AML) cases (15 from a diverse treatment cohort and 4 TP53-mutated cases pre/post-venetoclax).

• Biological Consistency: The inferred trees were consistent with clinical observations and orthogonal bulk sequencing data (e.g., ASCAT, CNVkit).
• Dominance of CNAs: The analysis revealed that clones dominating after therapy or at relapse are frequently defined by both SNVs and large-scale CNAs.
• Case Study (AML-99): LoPhy correctly identified two independent CNLOH events in the RUNX1 region (one early, one at relapse) and tracked the expansion/contraction of specific subclones in response to therapy.
• Comparison with COMPASS: In cases like AML-01 and AML-83, COMPASS produced biologically implausible trees (e.g., inferring mutations present at diagnosis that were not detected, or missing CNA gains due to unmodeled coverage shifts). LoPhy correctly reconstructed the temporal ordering and CNA events by leveraging longitudinal constraints.

5. Significance

• Clinical Insight: The study demonstrates that therapeutic resistance and disease progression in AML are often driven by the interplay of SNVs and CNAs. Ignoring CNAs or treating time points independently leads to an incomplete or inaccurate picture of clonal evolution.
• Methodological Advance: LoPhy sets a new standard for analyzing longitudinal single-cell data by integrating temporal structure with complex noise models, enabling researchers to track the "continuous joint history" of genomic alterations.
• Future Directions: The framework provides a foundation for extending longitudinal phylogenetic inference to whole-genome sequencing and more complex copy number models (e.g., homozygous loss).

In summary, LoPhy bridges the gap between high-resolution single-cell sequencing and longitudinal clinical data, providing a robust tool to decode the evolutionary trajectories of cancer under therapeutic pressure.