- Methodology article
- Open Access
An experimental loop design for the detection of constitutional chromosomal aberrations by array CGH
© Allemeersch et al; licensee BioMed Central Ltd. 2009
- Received: 6 January 2009
- Accepted: 19 November 2009
- Published: 19 November 2009
Comparative genomic hybridization microarrays for the detection of constitutional chromosomal aberrations is the application of microarray technology coming fastest into routine clinical application. Through genotype-phenotype association, it is also an important technique towards the discovery of disease causing genes and genomewide functional annotation in human. When using a two-channel microarray of genomic DNA probes for array CGH, the basic setup consists in hybridizing a patient against a normal reference sample. Two major disadvantages of this setup are (1) the use of half of the resources to measure a (little informative) reference sample and (2) the possibility that deviating signals are caused by benign copy number variation in the "normal" reference instead of a patient aberration. Instead, we apply an experimental loop design that compares three patients in three hybridizations.
We develop and compare two statistical methods (linear models of log ratios and mixed models of absolute measurements). In an analysis of 27 patients seen at our genetics center, we observed that the linear models of the log ratios are advantageous over the mixed models of the absolute intensities.
The loop design and the performance of the statistical analysis contribute to the quick adoption of array CGH as a routine diagnostic tool. They lower the detection limit of mosaicisms and improve the assignment of copy number variation for genetic association studies.
- Copy Number Variation
- Chromosomal Aberration
- True Positive Rate
- Loop Design
- Conventional Karyotyping
Array CGH mostly competes with and is complementary to conventional karyotyping and Fluorescent In Situ Hybridization (FISH). Compared to conventional karyotyping, it offers a resolution between 10 kb and 1 Mb, instead of about 5 Mb, and detects at least twice as many aberrations . Furthermore, it does not require the use of metaphase chromosomes, which makes it faster and less labor intensive. However, current array CGH techniques cannot detect balanced translocations, while this is straightforward with conventional karyotyping. Compared to FISH, array CGH provides genomewide coverage, instead of covering only a limited set of probes--so, it does not require prior knowledge of which aberration might be present (based on the phenotype of the patient).
The most frequent experimental setup for array CGH consists in comparing genomic DNA of a patient (test) with that of a normal individual (reference) using a two-channel microarray consisting of DNA segments spread across the whole genome. In the case of our clinical platform, the DNA segments consist in PCR-amplified BAC clones. However, the discussion applies equally to spotted long oligo platforms. So, we will refer to our probes as reporters. DNA from the test and reference samples is extracted, labeled with different fluorescent dyes (usually Cy3 and Cy5), hybridized to the microarray, and then scanned by two-channel laser scanner. Aneuploid chromosomal regions are detected as probes with a deviant log ratio of the intensities of the test against reference signal (approximately log2(1/2) for a deletion and log2(3/2) for a duplication). Usually the experiment is repeated in a dye-swap with the uorescent labeling of test and reference exchanged. The signals are then averaged over the dye-swap replicates to reduce the signal-to-noise ratio.
Extensive genomic variation (called copy number variation (CNV)) is also present in normal individuals [16–18]. The extent of this variation is surprising (covering at least 10% of the genome) and likely to have major implications for human variation and disease. In the classical dye-swap design, a deviant log ratio for one reporter in the test sample could just as well be associated with a variation in the reference sample. The difficulty in disambiguating deviations between the test and reference sample prevents us also from replacing the reference sample with a second test sample in the dye-swap design. The loop design, on the contrary, unambiguously associates a deviation to the correct sample by looking for a unique pattern of log ratios. For example, a duplication in Patient 1 will be associated approximately to a positive log ratio in the Patient 1 vs. Patient 2 hybridization, a negative log ratio in the Patient 3 vs. Patient 1 hybridization, and a null log ratio in the Patient 2 vs. Patient 3 hybridization. No deletion or duplication in another patient will display the same pattern, so the association is unambiguous. Another way to elevate this issue in dye swap experiments would be to use a DNA sample, pooled from several individuals. However, for frequently occurring CNVs, the intensity ratios will be reduced and, therefore, pooling will rather complicate data interpretation instead of simplifying .
For the statistical analysis, we consider two approaches for array CGH: linear modeling of the log ratios and mixed modeling of the absolute signal intensities. We compare both methods on a test data set consisting of 27 patients (9 loop designs) and we implement the method with the best signal-to-noise ratio as a user-friendly web application. Both methods analyze the data in a clone by clone way. On high resolution arrays, the resulting estimates can however be used as input for segment wise analysis techniques. Experimental designs that make the best use of available resources are essential for the widespread adoption of array CGH as a routine clinical tool for the diagnosis of constitutional chromosomal aberrations. Reduction of false positives and negatives guarantees the best service to the patient and the best use of economic resources, which are key factors in a clinical environment. Furthermore, correct assignment of "benign" copy number variations to the right sample will be important in upcoming studies of association between copy number variations and disease. Finally, this design will also lower the detection limit for mosaicism (i.e., chromosomal aberrations present in only a percentage of the cells).
Array CGH for the detection of congenital chromosomal aberrations is also a key method for the genomewide discovery of gene function. Patients with chromosomal aberrations provide a natural form of forward genetics screen. Through genotype-phenotype correlations, phenotypes can be associated to chromosomal regions containing only a few to a few tens of candidate genes . Further prioritization of candidate genes using bioinformatics approaches and validation in small animal models (for example, zebrafish or fruit fly) allows rapid identification of disease causing genes .
New statistical models for the analysis of loop designs for array CGH
Two main philosophies vie for dominance for the statistical modeling of microarray signal intensities: (1) linear models of log ratios of intensities and (2) mixed models of absolute intensities. Two-channel microarrays were originally developed so that taking the ratio between the Cy3 and Cy5 intensity of a spot would eliminate multiple sources of variations (in particular, the amount of DNA material per spot). Linear models of log ratios keep in track with this philosophy and extend it by observing that log ratio measurements from different hybridizations containing equivalent samples are interdependent. They formulate these dependencies as a set of linear relations that are then inverted to obtain tighter estimates for a smaller set of independent statistical effects (which remain in essence similar to log ratios). By contrast, mixed models of absolute intensities aim at disentangling the signals from the Cy3 and Cy5 channels by expressing the intensities as the sum of an extensive set of fixed and random effects dependent on many factors that systematically affect the microarray measurements (dye effect, array effect, spot effect, etc.). Although the mixed models we consider are linear mixed models and thus also linear models, we will for simplicity refer in this paper to the two classes of methods as being "linear models" vs. "mixed models", respectively.
Mixed model of absolute signal intensities
Classification of the reporters.
Log Ratio patient1/patient3
Log Ratio Patient2/patient1
Duplication for patient1
Duplication for patient2
Duplication for patient3
Deletion for patient1
Deletion for patient2
Deletion for patient3
Linear model of log ratios
where E denotes the expectation of a random variable, X is the matrix of linear dependencies, C c is the vector of contrasts for Reporter c, and y ci denotes the log2 ratio for Reporter c measured on the i th slide. For each reporter, the least squares estimates of the three contrasts are obtained. To classify the contrasts as significantly duplicated, deleted, or not changed in copy-number, we apply the moderated t-statistic as implemented in the Bioconductor package limma, which implements linear models for microarray data analysis . The p-values from the moderated t-test were corrected to control the false discovery rate with Benjamini-Hochberg . Similarly to the mixed model, we can detect reporters that are duplicated or deleted for a patient, based on the p-values of the contrasts. For a chosen cut-off value α, we decide whether a reporter is not differentially expressed (0), upregulated (positive), or downregulated (negative) for a contrast. Based on the two contrasts, we can again classify a reporter as duplicated or deleted for a patient according to Table 1. Again, we can on rare occasions obtain strange reporters.
Loop design test data set.
deletion on 13
duplication of X (sex mismatch)
duplication of 18
karyotyping and FISH
deletion on 10
duplication on 7
duplication on 15
deletion on 4
deletion on 12
deletion on 9
deletion on 12
duplication on 5
deletion on 18
duplication on 13
deletion on 13
balanced translocation (2;6)(q33,1;p23)
duplication on 7
deletion on 7
deletion of X (sex mismatch)
duplication on 21
True positive and false positive rate
Optimization of the linear model
In the previous section, we focused on how well the different methods fit the measurements by assessing their capabilities to divide the non-aberrant reporters from the deviating reporters and by comparing the FP and TP rates. This indicated that the linear model was best suited to distinguish these groups of reporters, although also the linear model has a fairly high FP rate. However, we did not yet benefit from all available information.
Completely and partially deleted reporters
The non-confirmed positives
The non-confirmed positives.
Genomic Database of Variants
Single clone deletion
Single clone deletion
Single clone deletion
Single clone deletion
Single clone duplication
Single clone deletion
Lack of DNA
Low spot quality
Low spot quality
Low spot quality
Low spot quality
At α = 0.001, also 13 clones were classified as being strange. Ten of these clones overlapped with CNVs that are present in the normal population, according to the Genomic Database of Variants. (Note also that not all normal CNVs have already been identified.) Therefore, we suspect that a strange clone can often be explained as a polymorphic clone that is shared by two patients. Taken together these results indicate that at α = 0.001 our procedure has both low false negatives (TP rate around 95%) and essentially no false positives for completely deleted or duplicated clones. Most clones detected as positive or strange outside the regions known in the benchmark have been confirmed by qPCR or FISH; several of them being known normal CNVs.
The method is implemented as a web application and is available at http://www.esat.kuleuven.be/loop. A demo account with test data is available. Currently, the application and the statistical analysis have been tested and refined on an in-house series of over 400 patients. Details on the implementation and the use of the web application can be found in Additional file 1.
A first point of discussion is to which platforms the proposed statistical models are applicable. Some array CGH platforms are available using single-channel microarrays. In this situation, the loop design is simply not applicable. The loop design is directly dependent on using a two-channel microarray.
A second point of discussion is a main assumption that underlies our analysis, that two patients never share the same aberration. If two patients have an aberration for the same reporter, the statistical model cannot correctly interpret the result|resulting mostly into a strange reporter. For the detection of congenital anomalies, this effect is prevented by putting into a loop design patients who have clearly distinct phenotypic patterns. The rare cases where a common aberration is still present can be rescued at the validation stage. Incorrect assignment to the third patient would not be validated by FISH or qPCR and, in this case, the possibility of a common aberration for the two other patients should be kept in mind. Reporters flagged as strange can be validated in all three patients to clear out the situation.
At our genetics center, the pick-up rate (i.e., the percentage of patients that show an chromosomal aberration) is around 20%. Hence, a loop design consisting out of three patients with a CNVs occurs only in one out of 125 cases. The likelihood of having patients that share an abnormality is even smaller. However, this assumption is unrealistic when studying tumors or when doing preimplantation diagnosis. In the case of tumors, many chromosomal regions can be affected and overlap between patients is essentially unavoidable. In the case of preimplantation diagnosis, we have developed a procedure where one of the eight blastomere cells of an 8-cell embryo from in vitro fertilization is assessed by single-cell array CGH . In this procedure it is essentially impossible to guarantee that the aberrations from different blastomeres do not overlap (for example, some aberrant embryos have chaotic genomes where many chromosomes are affected).
In some rare cases, deviating reporters cannot be assigned as duplicated or deleted, but are instead labeled as strange. We observed that the majority of these strange reporters corresponded to polymorphic reporters. This can correspond to the situation where two patients share a complex polymorphic reporter  and will be investigated more deeply in a subsequent study.
Our analysis was characterized by the fact that for our optimized threshold we have a low number of false negatives and close to no false positives. Given that a secondary validation is available through FISH, which can catch false positives but not false negatives, we would want to increase our threshold further to decrease the number of false negatives at the cost of a few false positives that can then be caught by the FISH validation. However, increasing the threshold further results rather in more reporters being labeled as strange, which we prefer to avoid.
At a significance level of 0.001, for 0.251% of the clones the intensity ratios were suggestive of partial deletions of duplications. Most likely, the intermediate intensity ratios reflect the presence of subclonal CNVs (i.e., only a part of the clone has been deleted/duplicated instead of the complete clone). Recently, several articles show high levels of small CNVs in the human genome [16–18, 26]. Moreover, we performed qPCRs on some of these clones using several PCR primers and could confirm such partial deletions (data not shown). However, since no systematic analysis of all these clones has been performed, we do not know the number of false positives.
In our specific setting and in our hands, linear models clearly outperformed mixed models. We do not draw any conclusion with regard to the suitability of one class of method versus the other in general. In our setting, we hypothesize that the mixed model was less robust to deviation from the underlying normality assumptions or that the more compact (fewer parameters) estimation procedure of the linear model increased its robustness. The improvement of the mixed model in this setting appears to be an interesting research direction.
Microarray CGH for the diagnosis of congenital chromosomal aberrations is progressing rapidly from the research lab to the clinic. What value do such improved statistical procedures add to the diagnosis? First of all, increasing the signal-to-noise ratio between aberrant and normal clones through our statistical procedure is likely to improve the detection of low-grade mosaicism (i.e., chromosomal aberrations present in only a percentage of all cells), which is currently difficult to detect by array CGH. In a previous study , we presented a power analysis model for the detection of low-grade mosaicism where the signal-to-noise ratio was a critical factor in determining the limit of detection for mosaicism.
Secondly, CNVs are hard to assign with certainty to the patient instead of the "normal" reference. While these CNVs are currently largely handled as noise, some of them are likely to act as genetic modifiers that are risk factors for disease or modulate its penetrance and phenotypic spectrum . Association studies are currently being started to evaluate the importance of such CNVs in both congenital and acquired disorders. Unambiguous assignment of the "normal" CNVs to the correct sample is therefore paramount. And as a last point, there is the issue of cost per experiment. To keep cost down, some laboratories do not perform a dye swap when using the basic array CGH setup (patient vs. normal reference). In this case, a single array is used per patient. However, only one measurement per patient will be available in this case instead of two with our design, which means a higher level of false positives and negatives. False positives will be caught by the secondary FISH or qPCR validation, but false negatives will not. This results in lower quality diagnostics for the patient.
In conclusion, our results indicate that the experimental loop design, together with a statistical analysis by a linear model, provides an efficient procedure for the detection of chromosomal aberrations in congenital anomalies by array CGH. It is significantly superior to the classical setup by doubling the use of resources and unambiguously assigning variation to the correct patient. These improvements have a direct impact on the diagnosis offered to the patient using the microarray technology that is closest to routine clinical use.
A 1 Mb resolution BAC array was performed as described in . In short, 3500 BAC en PAC clones from the Welcome Trust Sanger Institute were amplified by two rounds of DOP-PCR . The purified aminolinked PCR products were spotted in duplicate on 3-D CodeLink Bioarray System slides (Amersham Biosciences, Piscataway, NJ). 150 ng of patient DNA was labeled by random prime labeling system (BioPrime Array CGH Genomic Labeling System, Invitrogen) using Cy3- and Cy5-dCTPs (Amersham Biosciences). Probe concentration and labeling efficiencies were measured using the nanodrop ND-1000 spectrophotometer (Nanodrop Technologies, Rockland, DE). The probe was placed on the slide under a glass cover slip (24 × 24 mm). The slides were incubated for 42-72 hours at 37°C under humified conditions.
Post hybridization washing was performed by soaking in 1 × PBS for 10 minutes and followed by a stringency wash on 42°C for 30 minutes in 50% formamide 2× SSC solution and 10 minutes in 1× PBS at room temperature. To finalise, the slides were dried by centrifugation for at least 1 minute.
Image and data analysis
After the washing, a two-channel scan was performed with an axon laser scanner GenePix 4000B (Molecular Devices, Union City, CA) at 532 nm and 635 nm using GenePixPro 6.0 program. The results are converted into GPR format and can be directly uploaded to the web-based application. The median spot intensities were corrected with the local median background, and only those spots with a signal above background (i.e., foreground intensity larger than local background intensity plus twice the local standard deviation of the background) were retained for the analysis. In this way, only few spots are lost, as almost all spots are above background (on average 96.6%). The ratios of the Cy5 to the Cy3 intensities were computed for each reporter and base 2 log transformed. The log ratios are normalized using a 2D spatial loess normalization, in which one applies a loess regression to fit the log2-ratios (M-values) on the coordinates on the slide as predictor variables.
Benchmark data set
For the comparison of the analysis approaches, we consider a data set consisting out of nine loop designs or 27 patients with mental retardation (MR) and multiple congenital anomalies (MCA). The patients were seen at our genetics center (Center for Human Genetics, U.Z.Leuven). Conventional karyotyping showed chromosomal imbalances in 11 patients. Analysis of the patients was carried out with a 1 Mb BAC array. In first instance, the data analysis strategy that we had previously developed was applied to this data. In this procedure, a region is called aberrant, if one clone passes the threshold of 4 × SD and if two or more flanking clones were passing the threshold of log2 ( ) - 2 × SD as described in . If a deletion or a duplication larger then 3 Mb was detected, FISH was performed to confirm the results of the array. In case of a duplication smaller than 3 Mb, we performed quantitative PCR (qPCR) . 16 out of 27 patients show one or multiple clone anomalies, whereas 10 patients are apparently normal, at least according to the results of the array. One of the patients was a carrier of an inversion and another patient had a balanced translocation. Both aberrations cannot be detected by array CGH, but with conventional karyotyping; as such these patients did not contribute data to the benchmark. A short summary of the data set is shown in Table 2. In total, this data set comprises 635 aberrant clones: 274 deleted and 361 duplicated clones.
The study was approved by the institutional review board and appropriate informed consent was obtained from human subjects. The data set has been uploaded to the Gene Expression Omnibus (Accession number GSE6538) and is publicly available.
Written informed consent was obtained from the patient for publication of accompanying images. A copy of the written consent is available for review by the Editor-in-Chief of this journal.
The authors wish to thank the MicroArray Facility, Flanders Institute for Biotechnology (VIB) for their help in the spotting of the arrays and the Mapping Core and Map Finishing groups of the Wellcome Trust Sanger Institute for the initial clone supply and verification. This work was made possible by grants GOA/2006/12 and Centre of Excellence SymBioSys (Research Council K.U.Leuven EF/05/007), Catholic University of Leuven.
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