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Table 1 Scores and indices used to quantify aneuploidy

From: Aneuvis: web-based exploration of numerical chromosomal variation in single cells

Method Equation Support %-based? Reflects magnitude of copy number changes? Reflects variability in chromosomal states? Meaning and Considerations
Instability index (I) \( I=\left(\frac{\sum \limits_{t=1}^T{k}_t}{T}\right)\ast 100 \) I [0, ∞) No No Yes Calculates the sum of the percentage of abnormal chromosome counts across each chromosome.
Consider: I may increase with the # of chromosomes measured.
ANCA (A) \( A=\left(\frac{\sum \limits_{n=1}^N{q}_n}{n}\right) \) A [0, ∞) No No No ANCA = Average Number of Copy Number Alterations per cell.
Consider: A will ↑ as the # of measured chromosomes ↑s.
Normalized ANCA (AN) \( AN=\left(\frac{\sum \limits_{n=1}^N{q}_n}{T\ast n}\right) \) A [0, ∞) No No No AN is the ANCA score normalized for differences in number of chromosomes measured per experimental type (eg FISH vs sc-WGS).
Aneuploidy score (D) \( D=\frac{1}{TN}\sum \limits_{n=1}^N\sum \limits_{t=1}^T\mid {c}_{n,t}-{e}_t\mid \) D [0, ∞) No Yes No D increases with increased chromosome number.
Consider: Even a few cells with very large numbers of chromosomes will cause D to ↑ (not so with H)
Heterogeneity score (H) \( H=\frac{1}{TN}\sum \limits_{t=1}^T\sum \limits_{f=0}^{S-1}f\bullet {m}_{f,t} \) H [0, ∞) No No Yes Increases with greater ‘spread’ in the number of observed chromosomal states
Consider: H is maximized when each cell has a different number of chromosomes, regardless of absolute # of chromosomes.
Ploidy proportion PA + PD + PP = 1 PA, D, P [0, 1] Yes No Yes PD = 1, PA = 0, PP = 0 when population is diploid.
  1. For the instability index [7], T = the number of unique chromosomes examined. \( {\boldsymbol{k}}_{\boldsymbol{t}}=\frac{\mathbf{1}-\hat{\boldsymbol{p}}_{\boldsymbol{t}}}{\boldsymbol{N}} \), where p̂t is the number of cells containing the modal number of the tth chromosome. N is the number of cells examined. For the ANCA score [8, 9], qn is the number of non-diploid chromosomes observed in the nth cell. For the aneuploidy score [5], cn,t is the copy number of the nth cell at the ttth chromosome. et is the euploid copy number at the tth chromosome. For the heterogeneity score [5], S is the total number of copy number states. mf,t is the number of cells with copy number state s at bin t. mf,t is ordered such that mf =0,t≥ mf =1,t  …  ≥ mf = S −1,t. For the ploidy proportion, PA is the proportion of cells that are aneuploid, PD is the proportion of cells that are diploid, and PP is the proportion of cells that are polyploid