The results described above support the notion that aneuploid genomes are in general less stable than euploid genomes and prone to further karyotype changes. These findings in yeast are in agreement with recent observations that chromosomally stable pseudo-diploid human cells that accumulate aneuploid chromosomes frequently become chromosomally unstable 
. However, our results also indicate that different aneuploid karyotypes can exhibit different degrees of CIN, with some being more stable than others, suggesting that CIN is not a necessary outcome of aneuploidy. In other words, CIN does not appear to be caused by some general property of being aneuploid per se
but rather by determinants associated with specific aneuploid karyotypes. An advantage of our study is the carefully controlled genome variability among the strains analyzed. Because all aneuploid strains were derived from the same homozygous triploid parent and underwent minimal passage before their analysis 
, the different strains only differed in chromosome stoichiometry, minimizing the possibility that the observed CIN was due to other genetic variations or aberrations between different strains. Another advantage of our study was that CIN was assessed by examination of a wide range of spontaneously occurring karyotypic changes that include copy number gains and losses of native chromosomes. By analyzing aneuploid strains with randomly generated chromosome stoichiometries and the possibility of multiple chromosomes in aneuploid copy numbers, we were able to investigate the determinants underlying CIN in an unbiased manner and the effect of combinations of chromosomes in aneuploidy. We note, however, that our method presently does not allow analysis of those highly unstable karyotypes that quickly lead to considerable karyotype diversity within even a small population, and thus our results may not shed light on the determinants underlying extreme CIN. In addition, the qPCR-based karyotype method does not faithfully distinguish between whole-chromosome aneuploidy and partial chromosome aneuploidy and does not report on recombination events that may also be elevated in aneuploids 
Consistent with a recent report 
, we did not observe any correlation between fitness and CIN among the aneuploid strains. Whereas some aneuploid strains with non-observable CIN grew relative poorly, some strains with high CIN grew relatively well. This finding suggests that CIN is not necessarily a consequence of the growth defect caused by aneuploidy under standard laboratory growth conditions, or driven by the selection for improved fitness, but may be more intrinsic to specific features of an aneuploid genome. Analysis of the correlation between CIN and different parameters associated with specific karyotypes allowed us to observe two potential determinants of CIN. On the more global level, it was surprising to find that CIN was not necessarily linked to the distance of an aneuploid karyotype from the nearest euploid state. Instead, given that the analyzed aneuploid strains had a ploidy between 1N and 2N and that each chromosome exists in a copy number of either 1 or 2, we found CIN to be significantly linked to the distance of the karyotype from the haploid state. In other words, haploids with a few extra chromosomes tend to be more stable than diploids missing a few chromosomes. As the number of aneuploid chromosomes increases from 1N towards 2N, the level of CIN tends to increase until the ploidy reaches 2N, when the level of CIN is reset to a low level (). Future work will be necessary to test whether this trend continues beyond 2N. We propose to explain this trend by the disparity between the burden of segregating an increasing number of chromosomes and a lack of linear scaling of the capacity of the mitotic system with the aneuploid genome size. In this model, certain complex machineries, such as the kinetochore, or the mitotic spindle and the associated checkpoint mechanism, are composed of stoichiometric protein components encoded by genes distributed on all 16 chromosomes. This predicts that the functional scaling to increase the capacity of such machinery to segregate an increasing number of chromosomes from, e.g., a true haploid number might occur in a discrete rather than continuous manner and requires gaining of an entire chromosome complement (). As such, near-diploid karyotypes are predicted to be highly unstable owing to the largest disparity between the burden of having to segregate many extra chromosomes and the capacity of the mitotic machinery that, despite the near-diploid genome size, is still working with an efficiency close to that in a haploid genome (‘functional deficit’ in ). Only upon the chromosome number reaches a true diploid state, stoichiometries are reset to their basal level and mitosis can proceed with high fidelity. We note that “scaling” in our model differs from that in a previous study on CIN in polyploid yeast cells 
. “Scaling” in the Storchova model refers to a lack of scaling in the size of the pre-anaphase spindle with a euploid genome size (1N, 2N, 3N, 4N etc). The model intends to explain why polyploids are less chromosomally stable than haploids or diploids. Scaling in our model, on the hand, refers to the discrete increase in the functionality of the mitotic system with a linearly increasing number of chromosomes and intends to explain why certain aneuploid karyotypes are particularly unstable and why aneuploids are in general more karyotypically unstable than euploids.
Model of discrete scaling of the functionality of the mitotic system.
Although the global trend discussed above was statistically significant, exceptions to the rule could be found when comparing instability between specific karyotypes. This suggests that karyotype-specific effects may be superimposed on the global trend. Consistent with this idea, our analysis of relative dosage between pairs of chromosomes revealed an association of CIN with dosage imbalance between specific chromosome pairs. Because the level of gene expression largely scales with gene dosage at both the transcriptome and proteome levels 
, chromosome copy number imbalance is likely to directly lead to altered stoichiometry of proteins that interact physically or functionally. It has been shown that an unbalanced stoichiometry in specific proteins affecting mitotic spindle function is sufficient to drive chromosome mis-segregation in cancer cell lines 
. In yeast, one example is represented by the imbalance of MAD1
mitotic checkpoint genes 
. Although the precise molecular explanation remains unclear, it was shown that when MAD2
gene dosage was reduced relative to MAD1
, such as in the case of heterozygous gene deletion, chromosome instability ensued. Stability could be restored by further deletion of a copy of MAD1
to revert their ratio back to 1. Indeed, our data indicate that a ChrX (carrying MAD2
) to ChrVII (carrying MAD1
) ratio of 0.5 strongly predicts CIN. That dosage imbalance may be a prominent cause of CIN is also supported by the observation that many SAC components are deregulated at the gene expression level in several cancer cell lines without harboring sequence mutations in the corresponding genes 
. We note that there are likely to be many gene pairs whose imbalance could lead to CIN. For example, an imbalance between ChrII and VIII is also a predictor of CIN (), and the chromosome passenger proteins Sli15 (INCENP) and Nbl1 are encoded on ChrII and VIII, respectively. Whereas Sli15 and Nbl1 both interact with the Aurora kinase Ipl1, Nbl1 is the yeast borealin-like and bridges the interaction between Bir1 (survivin) and Sli15 
. It is conceivable that these chromosome passenger complex components need to be balanced in dosage to ensure proper chromosome segregation.
The flip side of the above finding is that relatively stable karyotypes may result from fortuitous but possibly complex balancing of certain key modules of the mitotic machinery. In an adaptive landscape, such metastable karyotypes may correlate with relatively stable, thus selectable, phenotypic states. This is consistent with the observation in mouse models or cancer cells that whereas moderate levels of CIN promote tumor formation or emergence of drug resistance, extremely high CIN could abate both processes 
. A recent large-scale analysis of aneuploid karyotypes in cancer cells revealed a high rate of co-occurrence of specific chromosome gains or losses 
. While this may be explained by a requirement for balanced gene function to maintain fitness, chromosome co-gain or co-loss may also be important for achieving relatively stable cancer karyotypes in order for persistent expression of cancer phenotypes given a certain tissue microenvironment. Further, the existence of relatively stable karyotypic and phenotypic states may explain why certain chromosome aberrations in cancer are clonal 
Finally, the observation of both global and chromosome-specific determinants of CIN may help to reconcile the chromosome/genome-centric theory vs. gene-centric theory in cancer evolution. First, our model of discrete and genome-dependent scaling of accurate chromosome segregation is consistent with the notion that complex cellular behaviors are non-linearly related to the sum of the function encoded by individual genes or even chromosomes. At the same time, the observation of different degrees of CIN associated with different aneuploid karyotypes, and more importantly with specific chromosome imbalances, highlights the exceptional impact of certain molecular components, such as Mad1 and Mad2, on the function and stability of the genome. However, even in this latter scenario, the impact of specific gene dosage is context-dependent, i.e. dependent on the dosage or activity of its partners in a manner that is potentially difficult to decode without a better knowledge of the entire cancer genome.