Copy Number Alteration

Summary

Copy number alterations (CNAs) are somatic gains or losses of chromosomal segments — ranging from focal events (single-gene amplification or deletion) to arm-level and whole-chromosome events. CNAs are the most genomically extensive form of somatic alteration in cancer: they affect a greater proportion of the cancer genome than any other mutation type (Gerstung et al., 2020). CNAs arise from two distinct mechanisms — single catastrophic events and ongoing chromosomal-instability (CIN) — and the distinction between clonal and subclonal CNA carries fundamentally different evolutionary and clinical implications. CNAs are measured through logR (read depth) and B-allele frequency (BAF) signals from sequencing data, and they critically confound VAF-based clone inference: without CNA correction via the CCF formula, SNV-based subclonal reconstruction produces misleading results (Turajlic et al., 2019; Tarabichi et al., 2021).

1. Definition and Types

A copy number alteration is a deviation from the diploid copy number (2 copies per autosomal locus) in a tumor cell’s genome. CNAs are classified by:

Scale:

Type	Size	Example
Focal amplification/deletion	Kilobases to a few megabases	ERBB2 amplicon, CDKN2A deletion
Chromosome-arm event	Tens of megabases	9p loss, 1q gain, 5q deletion
Whole-chromosome event	Full chromosome	Trisomy 7, monosomy 3

Direction:

• Gain — increase in copy number relative to diploid (3+ copies). Can be low-level (3–4 copies) or high-level amplification (5+ copies, often focal).
• Loss — decrease in copy number (1 copy = heterozygous loss; 0 copies = homozygous deletion).
• Copy-neutral loss of heterozygosity (cnLOH) — loss of one parental allele with duplication of the other, producing diploid copy number but uniparental origin. Invisible to read-depth methods; detectable only through BAF.

Clonality:

• Clonal CNA — present in all (or nearly all) cancer cells. Typically an early event, often truncal. Arises from a single missegregation event, catastrophic event (chromothripsis, whole-genome-duplication), or early selective sweep.
• Subclonal CNA — present in a subset of cancer cells. Evidence of ongoing chromosomal-instability — the CNA arose after the most recent common ancestor and has not yet reached fixation. Subclonal CNAs are the hallmark of CIN-driven tumors and carry distinct prognostic implications (see §4).

2. Mechanisms of CNA Generation

2.1 Chromosomal Instability (Ongoing)

CIN is the continuous process of chromosome segregation errors during mitosis, producing new CNAs with each cell division. CIN-driven tumors are heterogeneously aneuploid — different cells carry different CNA profiles. This ongoing generation of copy-number diversity is the primary source of subclonal CNA (chromosomal-instability).

2.2 Catastrophic Events (Single-Shot)

Single catastrophic events produce CNAs across large genomic regions in one cell division, without ongoing instability:

• chromothripsis — chromosome shattering followed by random religation, producing complex rearrangements with oscillating copy number states. Present in 22.3% of cancers, predominantly clonal (PCAWG Consortium, 2020).
• whole-genome-duplication (WGD) — tetraploidization producing a genome-wide doubling. Creates a permissive background for subsequent subclonal CNA (more copies = more tolerance for loss).
• Chromoplexy — chains of balanced rearrangements across multiple chromosomes, producing derivative chromosomes with altered copy number.

Tumors with catastrophic-event CNA but no ongoing CIN are homogeneously aneuploid — all cells share the same CNA profile from the founding event. This is the punctuated evolutionary pattern (Turajlic et al., 2019; punctuated-evolution).

3. Measurement

3.1 logR (Read Depth Ratio)

logR compares the observed read depth at a locus to the expected diploid depth:

$\text{logR}={\log }_2\left(\frac{\text{observed depth}}{\text{expected diploid depth}}\right)$

• logR = 0 → diploid (2 copies)
• logR ≈ 0.58 → gain (3 copies; log₂(3/2) ≈ 0.58)
• logR ≈ 1.0 → amplification (4 copies)
• logR ≈ −1.0 → heterozygous loss (1 copy)
• logR ≪ −1.0 → homozygous deletion

Subclonal CNAs produce intermediate logR values — e.g., a gain present in 50% of cells gives logR ≈ 0.32 (between the diploid 0 and the clonal gain 0.58). At low subclonal fractions, these intermediate values are challenging to distinguish from noise (Tarabichi et al., 2021).

3.2 B-Allele Frequency (BAF)

BAF measures the proportion of non-reference allele reads at heterozygous SNP positions. In diploid regions, BAF clusters at 0.5 (heterozygous). CNA shifts the BAF:

• Gain (3 copies, genotype AAB): BAF ≈ 0.33 or 0.67 (depending on which allele is duplicated)
• Loss (1 copy, genotype A): BAF → 0.0 or 1.0 (loss of heterozygosity)
• Subclonal CNA: BAF splits between the clonal cluster and the shifted cluster, producing skewed patterns

BAF is essential for detecting cnLOH (copy number = 2 but BAF = 0/1) — invisible to logR alone.

3.3 Subclonal CNA Detection

Subclonal CNAs are harder to detect than subclonal SNVs because:

• The signal is continuous (logR, BAF) rather than discrete (mutant read count)
• Intermediate logR values can arise from noise or purity misestimation
• BAF splitting is detectable only at sufficient sequencing depth and subclonal fraction

The minimum detectable subclonal CNA fraction is typically higher than the minimum detectable SNV subclone (~0.30 vs. ~0.10 CCF at 100×; Tarabichi et al., 2021).

4. Clinical and Evolutionary Significance

4.1 CNA-Based ITH vs. SNV-Based ITH

CNA-based ITH is often greater in magnitude than SNV-based ITH and carries distinct clinical information. In TRACERx Renal, the degree of subclonal copy-number complexity distinguished metastasis-competent from metastasis-incompetent clones more powerfully than SNV-based ITH. Specific CNAs — loss of 9p and loss of 14q — were enriched in metastasizing clones, while no evidence of selection for small-scale SNV mutations in metastasis was found (Turajlic et al., 2019).

4.2 The “Just-Right” CIN Level and CNA Burden

Not all CNA is equally deleterious. The pan-cancer analysis by Turajlic et al. (2019) found a non-monotonic relationship between aneuploidy burden and survival:

CNA burden (aneuploidy %)	Survival	Mechanism
Low (<25%)	Better	Insufficient diversity for adaptation
Moderate (25–75%)	Worse	Adaptive sweet spot — diversity without lethality
Excessive (>75%)	Better	Cell-autonomous lethality — mitotic catastrophe

Moderate CNA burden is the worst outcome because it represents the Goldilocks zone: enough genomic diversity to generate adaptable subclones (including therapy-resistant ones), but not so much that cells die from the fitness cost of extreme aneuploidy (chromosomal-instability).

This CNA-burden U-curve runs in the opposite direction from the ITH-outcome U-curve predicted by the compression-entrenchment hypothesis (intratumor-heterogeneity §5). CNA burden is a process rate (how much ongoing copy-number change); ITH is a state (how much diversity currently exists). The two curves are consistent: moderate CNA burden generates the ongoing adaptability that makes tumors dangerous, while at high CNA burden the process collapses under its own weight regardless of the ITH it generates.

4.3 Metastasis

CNA complexity is strongly associated with metastatic competence. Punctuated tumors with high clonal CNA (early catastrophic event, low subclonal CNA) grow fast, metastasize widely, and seed metastases monophyletically — a single clone from the primary tumor founds all metastases. Gradual tumors with ongoing subclonal CNA produce oligometastases with intermetastatic heterogeneity — different metastases carry different CNA profiles (Turajlic et al., 2019).

4.4 Immune Evasion

CNA enables immune escape through two routes:

• HLA LOH: Subclonal loss of heterozygosity in HLA genes removes the tumor’s ability to present neoantigens, enabling immune evasion without SNV-level changes in the antigenic repertoire (McGranahan et al., 2017, cited in Turajlic et al., 2019).
• Neoantigen depletion: Loss of chromosomal segments containing neoantigen-coding mutations eliminates the antigens that would otherwise mark the clone for immune clearance.

Conversely, high CNA burden may increase immune visibility: more chromosomal rearrangements → more frameshift peptides and abnormal proteins → more neoantigens presented on MHC-I. This may synergize with the cell-autonomous fitness cost of excessive CNA to improve outcomes at the high end (chromosomal-instability).

4.5 Therapy Resistance

CNAs can confer therapy resistance through:

• Amplification of drug targets (e.g., ERBB2 amplification driving trastuzumab resistance)
• Amplification of bypass pathways (e.g., MET amplification rescuing EGFR-mutant cells from EGFR inhibition)
• Loss of tumor suppressor genes (e.g., PTEN deletion activating PI3K pathway independently of targeted RTK inhibition)
• Pre-existing subclonal CNA: Resistance-associated CNAs frequently exist as minor subclones before treatment, expanding under the selective pressure of therapy (Turajlic et al., 2019)

5. CNA/SNV Interdependence

CNAs and SNVs are not independent measurements — they interact in ways that are critical for accurate clone inference.

5.1 CNA Confounds SNV VAF

The observed VAF of an SNV depends on the local copy number, not just on the fraction of cells carrying the mutation. An SNV present in 100% of cancer cells at 50% purity has:

• VAF ≈ 0.25 if on one of two copies (diploid, heterozygous)
• VAF ≈ 0.20 if on one of three copies (gain, 3 total copies)
• VAF ≈ 0.17 if on one of four copies (amplification, 4 total copies)

The difference between one-of-three and one-of-four is only ~3% — at the edge of what moderate-depth sequencing (~100×) can resolve (Turajlic et al., 2019). Without accurate CNA correction, VAF-based clone inference can produce misleading phylogenies.

5.2 The CCF Correction Formula

The cancer-cell-fraction (CCF) corrects VAF for purity and local copy number:

$\text{CCF}=\frac{\text{VAF}\times (\rho \times N_T+2\times (1-\rho ))}{\rho \times m}$

Where:

• ρ = tumor purity
• N_T = total copy number at the locus in tumor cells (from CNA calls)
• m = multiplicity — how many allelic copies carry the SNV (typically assumed = 1)
• 2 × (1 − ρ) = contribution of normal diploid cells to total read depth

How CNA state changes the correction:

• Amplified region (N_T > 2): VAF is diluted across more wild-type copies → same VAF → lower CCF
• Deleted region (N_T < 2): VAF is concentrated on fewer copies → same VAF → higher CCF
• Unknown multiplicity: If m is unknown (amplified mutation — all amplified copies may carry it, or only one), the same VAF is consistent with a range of CCF values. The standard assumption m = 1 provides a lower bound on CCF (Tarabichi et al., 2021).

5.3 SNV Timing Relative to CNA

The order of SNV and CNA acquisition determines multiplicity:

• SNV before CNA gain: The SNV is present on the original copy; when that copy is amplified, all amplified copies carry the mutation → m > 1, high VAF relative to the gain size
• SNV after CNA gain: The SNV arises on one of the already-amplified copies → m = 1, lower VAF relative to the gain size

This timing information is critical for phylogenetic reconstruction: an SNV that occurred before a clonal gain is on the trunk of the tree; an SNV that occurred after is on a branch. This is encoded in the cancer evolution olog as the dependency relationship between PointMutation events and CopyNumber events (cancer-evolution-olog §CNA-SNV dependency).

6. CNA as a Phylogenetic Character

CNAs are more informative than SNVs for some phylogenetic questions and less informative for others:

Advantages of CNA:

• Larger genomic footprint → easier to detect at low coverage
• Fewer events per tumor → simpler phylogenies
• Less affected by sequencing error (logR is a continuous signal averaged over many loci vs. single-base SNV calls)
• Clonal CNAs are stable markers of the founding clone

Disadvantages of CNA:

• Subclonal CNAs are harder to call than subclonal SNVs (continuous signal, lower effective depth per event)
• Recurrent CNA at the same locus in independent subclones (convergent evolution) cannot be distinguished from shared ancestry — the same 9p loss arising independently in two subclones looks identical to a single 9p loss in their common ancestor
• CNA boundaries are imprecise (breakpoint uncertainty), making allele-specific copy number ambiguous at the margins
• CNA multiplicity (which amplified copy carries the SNV) is often unknown without long-read sequencing or SNP phasing

For these reasons, subclonal reconstruction typically uses SNVs as the primary phylogenetic character with CNA as an additional constraint, not the primary signal (Tarabichi et al., 2021; subclonal-reconstruction).

7. Limitations

CNA detection floor is higher than SNV. Subclonal CNAs below ~0.30 CCF are invisible at standard sequencing depths (Tarabichi et al., 2021). This means CNA-based ITH systematically underestimates the full extent of copy-number diversity.

Breakpoint uncertainty propagates. The boundaries of CNA events are inferred from segmented logR/BAF data with finite precision. Allele-specific copy number at CNA margins — exactly where SNV multiplicity matters most — is the least reliable part of the CNA call.

Multiplicity is assumed, not measured. The standard assumption m = 1 (heterozygous SNV on one copy) is violated when an SNV precedes a copy-number gain. Without long-read phasing or multi-sample data, m is unknowable — and incorrect m produces incorrect CCF.

Convergent CNA cannot be distinguished from shared ancestry. The same chromosome arm loss in two subclones may represent a single ancestral event (shared ancestry → related subclones) or independent deletions (convergent evolution → unrelated subclones). Resolving this requires multi-region sequencing or single-cell data (Turajlic et al., 2019).

The CNA background rate is unknown. Single-cell sequencing of normal tissues reveals copy-number variation at low frequency in apparently normal cells. The baseline CNA rate — the rate of segregation errors in cells without CIN — is not well characterized, making it difficult to determine whether an observed subclonal CNA reflects ongoing instability or background noise (Turajlic et al., 2019).