Our model utilizes the fact that the normalized aCGH ratio increases with increasing DNA copy number in a stepwise manner, where the step size is dependent on the DI, the tumor cell fraction, and the experimental bias (Figure 1). In near diploid tumors (DI = 1) without a contribution from normal cells or affected by experimental bias, an increment of 1 in the copy number increases the ratio by a value of 0.5, leading to a normalized ratio of 0.5, 1, 1.5, 2, and so on (-1, 0, 0.69, 1 on a log₂ scale) for a copy number of 1, 2, 3, and 4, respectively (see Equation 2 in Materials and methods). The corresponding increase in tetraploid tumors (DI = 2) is 0.25, whereas an increase between 0.25 and 0.5 occurs in tumors with a DI between 1 and 2. Baseline, at a log₂ ratio of 0, corresponds to 2, 3, and 4 DNA copies in near diploid (Figure 1a), triploid, and tetraploid (Figure 1b) tumors, respectively. For DIs between 1 and 1.5 or between 1.5 and 2, baseline represents a copy number between 2 and 3 (Figure 1c) or between 3 and 4. The presence of normal cells within the tumor sample reduces the increase in aCGH ratio with incremental copy number (Equation 3), as can be seen when comparing the ratios of two near diploid lymphomas with different tumor cell fractions (Figures 1a,d). Using common ratio levels for scoring gains and losses in tumors like those presented in Figures 1a-d leads, therefore, to different results with respect to copy number changes.

A further reduction in the ratio dynamics occurs due to experimental bias (Equation 4). The bias, as represented by the dynamic factor, q, can be determined from control experiments, where normal DNA from males and females is cohybridized (Figure 1e). Theoretically, the X-chromosome ratio is 0.5 (-1 on a log₂ scale), but the experimental bias reduces the ratio dynamics, leading to a ratio level closer to zero. The absolute value of the log₂-transformed ratio level was used as a measure of q (Figure 1e). This value differed little among the slide series used here, ranging from 0.75-0.85 with a mean ± standard deviation of 0.80 ± 0.04 based on 8 control experiments. A q-value of 0.8 and range of 0.7-0.9 was used in the GeneCount calculations in the cases of known and unknown tumor cell fraction, respectively.

To enable automatic calculation of the copy number associated with each array probe, we implemented GeneCount in a program to be run on top of statistical analysis packages for aCGH ratio smoothing and breakpoint detection (Additional data file 1). A separate algorithm was developed for samples with unknown tumor cell fraction, where the fraction was estimated based on two ratio levels and DI (panel B in Additional data file 1), as described in Materials and methods. One decimal was included in the calculated DNA copy numbers when evaluating the results in comparison with FISH data. Otherwise, the numbers were rounded off to the nearest integer values.

We compared the GeneCount results of 94 lymphomas with previously published FISH data from the same tumors 202122232425. The FISH probes were located at chromosomal regions with frequent copy number changes (Figure 1 and Additional data file 2), and copy numbers within the range of 0-8 had been measured. The DIs, ranging from 0.95-2.23, and the tumor cell fractions, ranging from 27% to 98%, were used as inputs to GeneCount, together with the smoothed aCGH ratios from the GLAD and CGH-Explorer packages. CGH-Explorer applied a more extensive ratio smoothing than GLAD, and this led occasionally to differences in the ratio levels and breakpoint detection between the two programs.

The feasibility of our method for analysis of solid tumors without information of tumor cell fraction was explored in 99 cervical cancers, for which the DI ranged from 1.00-3.16. The tumor cell fraction could be estimated for 93 and 89 tumors based on GLAD and CGH-Explorer, respectively, fulfilling the requirements for this estimation (Materials and methods). The tumor cell fractions were poorly correlated with the values determined by analysis of histological sections (Additional data file 5). In most cases, the histology result was higher than the GeneCount estimate, probably because immune cells infiltrating the tumor parenchyma were not properly quantified by the histological examination. In a few cases, however, the histology result was higher, probably reflecting that different parts of the sample were used in the aCGH and histology analyses. The tumors for which the tumor cell fraction could be estimated by GeneCount were included in the further analyses.

A higher number of genetic aberrations were generally found in the cervical cancers than in the lymphomas. High level amplifications with more than 2.5-fold increases in gene dosage (that is, copy number, N, relative to total DNA content given by two times the DNA index (N/(2.DI)), were found in about half of the tumors and most frequently on chromosomes 5p and 11q. GeneCount analysis showed copy numbers within the range of 5-80 in these regions, which were often surrounded by gains at lower levels.

The GeneCount results were compared with the outcomes of existing analysis methods, where gains and losses were scored from the smoothed ratio levels and breakpoints obtained by GLAD and CGH-Explorer. The log₂ transformed ratio levels of ± 0.2 (that is, approximately two times the ratio standard deviation (Additional data file 6)) were applied as cut-off levels for scoring aberrations. We selected genes that were shown to be affected by gains and losses in previous studies on a subgroup of the patients 27. Some of the genes showed only a small variation in the aCGH ratios, often within the level of ± 0.2, and only a few tumors with aberrations were identified (Figure 6a and panel A in Additional data file 7). A higher number of patients with changes in gene copy numbers and in the corresponding gene dosages were identified with GeneCount, using the cut-off levels of ± 0.2 for scoring gene dosage changes (Figure 6b,c and panels B and C in Additional data file 7). The gene dosage correlated significantly with gene expression (Figure 6c and panel C in Additional data file 7), making the copy number changes determined by GeneCount plausible.

The copy number changes of MRPS23 have previously been shown to correlate with survival probability 27. Survival analysis based on the GeneCount data of MRPS23 identified more patients with poor outcome than the corresponding analysis based on ratio levels (Figure 6d,e). Hence, 15 high risk patients were identified based on the GeneCount results, whereas only 5 patients were classified with high risk based on the ratio levels. Nine of the ten patients that were not identified based on ratio levels (blue curve in Figure 6d) had aneuploid tumors with a DNA index ranging from 1.10-1.92. The remaining diploid tumor had a relatively low tumor cell fraction of 23%.

Some tumors had genome regions for which the aCGH ratio was clearly different from that corresponding to an integer copy number. This probably reflected intratumor heterogeneity in the DNA copy numbers, that is, the existence of subpopulations with copy number changes that are not common for all tumor cells in the sample. The common aberrations can thus be considered homogeneous. Lymphomas and cervical cancers with heterogeneous DNA regions had ratio levels that fell in between, and were significantly different from, those corresponding to integer values (Figure 7). The actual ratio level reflected the proportion of cells with that aberration (Equation 1).

Nineteen (20%) lymphomas and 44 (50%) cervical cancers had one or more heterogeneous DNA regions with copy numbers 1&2, 2&3, or 3&4 (Additional data files 8 and 9). Reliable detection of heterogeneity required tumor cell fractions above 24% (Additional data file 10) and 5 out of 93 cervical cancers were therefore excluded from this analysis. Lymphoma L309/89 (Figure 7) had previously been identified as heterogeneous by FISH, showing one population with three and another with four copies of MYC and centromeres 8 and 17 20. Moreover, several of the heterogeneous aberrations in the cervical cancers, such as loss on chromosome 4 and X and gain on 11q and 17 in C005/01, loss on 6q and gain of 11q in C006/01, and loss on 4 in C023/01, were similar to those detected earlier by conventional CGH 14. The previous study was, however, based on a different set of biopsies, which probably explains the lack of consistency for some of the tumors.

In a few of the heterogeneous tumors, two different ratio levels were identified between one and two copies (Figure 8 and Additional data file 11). Thus, it appeared that the corresponding aberrations were present in different fractions of the tumor cell population. Lymphoma L008/92 had two intermediate ratio levels between one and two copies, corresponding to 70% and 30% of the tumor cells (Figure 8b, blue and red ratios, respectively), leading to the possible tumor evolutionary schemes depicted in Figure 8c. As the sum of the two fractions did not exceed 100%, the heterogeneous aberrations may be found in non-overlapping subpopulations of the tumor, where the subpopulations have evolved differently from a predicted common population containing the homogenous aberrations (parallel sequence). A serial sequence, where the populations have evolved in a linear manner from a common population, was also possible. In C024/01, however, the heterogeneous ratio levels corresponded to 78% and 44% of the tumor cells, and a serial sequence was the only one suggested (panel C in Additional data file 11).

Samples from 94 patients with B-cell non-Hodgkin's lymphoma and 99 patients with squamous cell carcinoma of the uterine cervix were analyzed. We used fresh frozen lymphoma cell suspensions for which the tumor subtype, stage, patient treatment, and follow-up have been presented previously 25. The cervical cancers were of FIGO (Fédération Internationale des Gynaecologistes et Obstetristes) stage 1b-4b, treated with radiotherapy. Tumor biopsies taken before the start of treatment were used.

The DI of the lymphomas and cervical cancers and the tumor cell fraction of the lymphomas were determined by use of flow cytometry, and most of these data have been published earlier 142325. The lymphoma cells were labeled with phycoerythrin-labeled antibodies to the tumor characteristic light chains for identifying the tumor cells and Hoechst 33258 for assessment of DNA content. The DI was determined from the G₁ peak position of the light chain positive cells relative to the light chain negative cells. Tumor cell fraction was determined as the fraction of light chain positive cells. The DI of the cervical cancers was assessed by preparing clean nuclei, stained with propidium iodide, using the detergent-trypsin method 41. Cells from a diploid cell line were used as an internal reference. Samples showing two distinct G₁ peaks in the DNA histogram were classified as aneuploid, and the DI was determined from the position of the G₁ peak of the aneuploid cells relative to the corresponding peak of the diploid cells. Samples with a single G₁ peak were classified as near diploid. An estimate of the tumor cell fraction was achieved for each cervical cancer sample by histological examination of hematoxylin and eosin stained sections derived from the middle part of the biopsies. These values were used to compare with the tumor cell fractions estimated by GeneCount.

Genomic array slides produced by the Microarray Facility at the Norwegian Radium Hospital were used 42. The arrays contained 4,549 unique genomic clones of BACs and P1 artificial chromosomes (PACs) (Wellcome Trust Sanger Institute, Cambridge, UK) that covered the whole genome with a resolution of approximately 1 Mb. The 1 Mb clone collection was supplemented with tiling path probes between 1q12 and 1q25, using overlapping BACs and PACs. The clones were from the RPCI-11 (BAC) and the RPC1-1, -3, -4, and -5 (PAC) libraries. Each clone was printed in 4-8 array spots. The genes covered by the clones were found from Ensembl 43.

Genomic DNA was isolated from the lymphoma cell suspensions and cervical cancer biopsies according to a standard protocol, including proteinase K, phenol, chloroform, and isoamylalcohol 44. DNA (1 μg) was digested overnight, using DpnII endonuclease (New England Biolabs, Beverly, MA, USA), and purified using the QIAquick PCR Purification Kit (Qiagen, Valencia, CA, USA). Digested and purified DNA and normal reference DNA (0.5 μg each) were labeled by a random primer reaction (BioPrime DNA Labeling System, Invitrogen, Carlsbad, CA, USA) with Cy3-dCTP and Cy5-dCTP (Perkin-Elmer Life Sciences, Foster City, CA, USA), respectively, and co-hybridized to the array slides 42. Scanning and image analysis were performed by use of an Agilent scanner (Agilent Technologies Inc., Palo Alto, CA, USA) and the GenePix 6.0 image analysis software (Axon Instruments Inc., Union City, CA, USA). The microarray management and preprocessing software BASE 26 was used for spot filtering and ratio normalization. The mean value of the 4-8 spots of each genomic clone was used, provided that the standard deviation was less than 0.2. Lowess normalization was performed so that the mean log-transformed ratio of all clones was equal to 0. The GLAD and CGH-Explorer algorithms were used for ratio smoothing and breakpoint detection 911. Default values of 8 (GLAD) and 1.5 (CGH-Explorer) for the statistical penalty, λ, were used. The smoothed ratios were inputs to GeneCount.

For a heterogeneous test sample consisting of several cell populations, like normal cells and distinct populations of malignant cells, the DNA of each cell population contributes to the aCGH ratio. Ideally (that is, in cases of no experimental bias), the normalized ratio of each array probe is given by:

R i d e a l = ∑ i = 1 n N i 2 ⋅ D I i ⋅ F i ⋅ D I i ∑ i = 1 n F i ⋅ D I i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@5AA2@

where R_ideal is the aCGH ratio of a sample with n cell populations, and N_i, DI_i, and F_i are the DNA copy number, DNA index, and tissue fraction of cell population i, respectively. We assume that: the reference sample is normal DNA with a copy number of 2 throughout the genome, except for the X and Y chromosomes in males; sex-matched hybridizations are performed; and DI is given relative to the DNA content of normal cells.

In cases of a homogeneous sample with a single cell population, for example, a cancer cell line, Equation 1 is reduced to:

R i d e a l = N 2 ⋅ D I MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaWGsbWaaSbaaSqaaiaadMgacaWGKbGaamyzaiaadggacaWGSbaabeaakiabg2da9KqbaoaalaaabaGaamOtaaqaaiaaikdacqGHflY1caWGebGaamysaaaaaaa@3CFE@

In clinical samples with two cell populations, that is, malignant and normal cells, the ratio is given by:

R i d e a l = N T 2 ⋅ D I T ⋅ F T ⋅ D I T F T ⋅ D I T + ( 1 − F T ) + 1 − F T F T ⋅ D I T + ( 1 − F T ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@660B@

where N_T, DI_T, and F_T are the DNA copy number, DNA index, and fraction of malignant cells in the sample, respectively. 1 - F_T represents the fraction of normal cells, which have a DI of 1 and DNA copy number (N) of 2.

It was clear from experiments where normal male DNA was hybridized against female DNA that the ratio dynamics were somewhat reduced (Figure 1e). A dynamic factor, q, was included in Equation 3 to compensate for this effect. Since the experimental noise was independent of the logarithm of the ratio (Additional data file 6), Equation 3 was rewritten to account for the reduced dynamic in the following way:

L o g 2 ( R ) = q ⋅ L o g 2 ( N T 2 ⋅ D I T ⋅ F T ⋅ D I T F T ⋅ D I T + ( 1 − F T ) + 1 − F T F T ⋅ D I T + ( 1 − F T ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@6EAF@

The dynamic factor represents the systematic, non-random reduction in the log-transformed ratios caused by the experimental bias and has a value between 0 and 1, where the latter value occurs in the ideal situation without any reduction in the ratio dynamics. The factor is a characteristic of the array slide series and the laboratory protocol and was determined from the ratio of the X chromosome in a control experiment hybridizing male versus female normal DNA (Figure 1e). Equation 4 was used in GeneCount to calculate F_T and N_T from the ratio profile of the sample.

Intratumor heterogeneity in the DNA copy numbers, that is, the cases of several populations of malignant cells in addition to the normal cells, was identified by selecting the tumors for which one or more of the aCGH ratio levels were different from that corresponding to an integer value by visual inspection. The ratio distributions of the potential heterogeneous regions were compared to the distributions of the adjacent homogeneous aberrations by ANOVA analysis, and a P-value of 0.05 was required to classify the aberration as heterogeneous. The fraction of tumor cells with a heterogeneous aberration was calculated, employing the more general Equation 1. The DI was assumed to be the same for all subpopulations of malignant cells.

We used BASE as a platform for GeneCount and linked the algorithm to the output of the GLAD and CGH-Explorer packages, which were implemented in our BASE version. The method can also be developed as a separate program or integrated in other aCGH analysis packages. The algorithm consists of three major steps: data input for all samples; estimation of tumor cell fraction in the cases when this parameter is unknown; and estimation of DNA copy number for each array probe (panel A in Additional data file 1). The smoothed aCGH ratios served as input, together with the DI, the q-value from control experiments with its lower and upper limits (q_min, q_max) and, if available, the tumor cell fraction.

In cases of unknown tumor cell fraction, this value was estimated in a simulation procedure based on two selected ratio levels, using the tumor cell fraction and DNA copy numbers as independent and q as dependent variables. The copy numbers and tumor cell fraction were increased in steps of 1 and 0.01, respectively, and the corresponding q-value was calculated (panel B in Additional data file 1). To ensure high accuracy in the estimated fractions, it was required that the absolute value of the selected ratio levels was larger than 0.15. This implied that samples with a tumor cell fraction lower than 24% in diploid and 36% in tetraploid tumors could not be analyzed when only aberrations involving one copy number change existed (Additional data file 12). Moreover, a minimum absolute difference of 0.2 - that is, approximately two times the standard deviation of the log-transformed ratio levels (Additional data file 6) - between the two selected ratio levels was needed. To further increase the reliability of the estimation, only ratio levels with more than ten probes were selected. We optimized q for each tumor by allowing the value to vary within the limited range of q_min to q_max, typically q ± 10%, leading to fairly stable estimates of the tumor cell fraction. The mean tumor cell fraction based on these estimates and the corresponding mean q-value was used in Equation 4 to estimate the DNA copy numbers of the tumor. In cases of known tumor cell fraction, this fraction and q from control experiments were used in Equation 4. The source code of the module is provided by communication to the authors. A demo version of GeneCount in BASE is also available 45.

GeneCount estimates for the lymphomas were compared with direct assessments of gene copy numbers by use of FISH. All FISH analyses have been published previously 202122232425. Dual-color FISH was applied to all 94 tumors. We used spectrum orange labeled locus-specific propidium iodide DNA probes for genes commonly aberrant in lymphomas (CCND3, BMP6, PIM1, MYC, CDKN2A, RB1, TP53, PMAIP1, and MALT1) and spectrum green labeled centromer probes (centromere 1, 6, 8, 17, and 18) (Vysis Inc., Downers Grove, IL, USA) for assessing the quality of the experiment. For exploring DNA copy number calculations in translocated chromosomal regions, BCL2, which is frequently involved in the translocation t(14;18)(q32;q21) in lymphomas, was considered. A dual-color translocation probe involving BCL2 and covering the breakpoint region was used (LSI IGH Spectrum Green/LSI BCL2 Spectrum Orange, Vysis Inc.). Due to splitting of the probe signal in cases of translocation, erroneous high BCL2 copy numbers were derived directly with this probe. The BCL2 copy number was therefore corrected based on the signals from the IGH and centromere 18 probes, as described 22.

Gene expressions were determined by microarray analysis of 89 of the cervical cancers and related to the GeneCount estimates. We used array slides produced at the Microarray Facility at the Norwegian Radium Hospital, containing 15,000 cDNA clones. The data from 48 of the patients, with a detailed description of the experimental procedures, have been presented 27. Cy3- and Cy5-labeled cDNA was synthesized from total RNA by anchored oligo(dT)-primed reverse transcription and co-hybridized with a reference sample (Universal Human Reference RNA, Stratagene, La Jolla, CA, USA) to the array slides overnight at 65°C. Scanning and image analysis were performed with an Agilent scanner and the GenePix 4.1 image analysis software, respectively. Data preprocessing, including correction of saturated intensities, filtering of weak and bad spots, and lowess normalization, was performed in BASE. All hybridizations were performed twice in a dye-swap design, and the average expression ratio based on the two experiments was used in the further analyses.

The array CGH raw data have been deposited to the ArrayExpress repository (E-TABM-398, E-TABM-399).