CNV-seq, a new method to detect copy number variation using high-throughput sequencing - PMC

The Model

We have developed a method to detect CNV by shotgun sequencing, CNV-seq. The method is based on a robust statistical model that allows confidence assessment of observed copy number ratios and is conceptually derived from aCGH (Figure 1). The microarray-based procedure, aCGH involves a whole genome microarray where two sets of labeled genomic fragments are hybridized. Instead of a microarray, CNV-seq uses a sequence as a template and two sets of shotgun reads, one set from each target individual, X and Y (Figure 1). The two sets of shotgun reads are mapped by sequence alignment on a template genome. We use a sliding window approach to analyze the mapped regions and CNVs are detected by computing the number of reads for each individual in each of the windows, yielding ratios. These observed ratios are assessed by the computation of a probability of a random occurrence, given no copy number variation.

The random sampling in shotgun sequencing results in uneven coverage that may lead to observed coverage ratios that falsely imply CNV. Therefore, a statistical model is essential for the assessment of the probability of false positive ratios. The average number of reads in a region of a genome is dependent on the total number of reads sampled, the length of the genome and the length of the region. We use this relationship to compute a minimum sliding window size to achieve a desired minimum confidence level of the observations.

The mean number of reads for X and Y genomes in a sliding window determines the distribution of the ratios. The number of reads in a window is approximately distributed according to Poisson, Po(λ), where the mean number of reads per window is λ, given by

where N is the total number of sequenced reads, G is the size of the genome and W is the size of the sliding window, and W < <G. We use the Gaussian distribution to approximate the Poisson distribution with mean and variance λ = μ = σ². This approximation is good when the mean number of reads per window is greater than 10 with continuity correction.

The predicted copy number ratio, r in each sliding window can be computed by

where z is the ratio of read counts in the window and N_X and N_Y are the total number of reads in the genomes X and Y respectively. Assuming an independent distribution of the read counts, we can obtain a probability, p of a copy number ratio being r or divergent from 1:1 ratio by a random chance. For this purpose, we need the distribution of the read count ratio z. This distribution is given by Gaussian ratio distribution [25]. The computation of this distribution is cumbersome, but it can be transformed to another variable, t, by Geary-Hinkley transformation [26]:

where μ_X, ${\sigma }_X^2$, μ_Y and ${\sigma }_Y^2$ are the means and the variances for X and Y respectively. The new variable t approximately have a standard Gaussian distribution when the mean number of reads per window is greater than 6 in Y and less than 40,000 in X. The p-value can be computed by

where Φ (t) is the cumulative standard Gaussian distribution function. The probability p decreases with increasing sliding window size (Figure 2) and we would like p to be as low as possible. Conversely, increased sliding window size leads to a decreased resolution of CNV regions. Therefore it is advantageous to compute a window size, which yields the best possible resolution according to a preset threshold of p for r. Based on the above equations, We can calculate the best possible resolution, or the theoretical minimum window size, W by

and

where p' is the desired significance level, and r' is the CNV detection threshold ratio. Φ^-1 is the inverse function of Φ. The number of reads sampled will affect the minimum window size. For example, if one wants to detect CNV with ratio ≥ 3 : 2 at significance level 0.002, a genome size of 3 G bases and 10 M reads in both genomes will yield the minimum window size of 37,243 bases, while 1 M reads will yield the window size of 372,431 bases. The use larger number of reads allows detection of ten times shorter CNV.

An alternative approach is to calculate the range of copy number ratios that can be detected at a certain significance level p', with a predefined window size W':

where

and

Validation

In order to assess the performance of CNV-seq, we used simulated and real human data. For the simulation of shotgun data, in total of 101 genomes were constructed, containing varied number, sizes and locations of CNV regions, SNP and short insertions/deletions (indels). We simulated three sequencing methods, Solexa, 454 and Sanger [27] for each constructed genome on 0.1× to 8× coverage. This resulted in the total of 8,400 simulations.

The Figure 3 shows the results of the simulations on varied coverage and varied p' for constant log₂(r') = 0.6. Each dot represents an average of 100 simulations and the sizes of the dots reflect the sizes of the lengths of the sliding windows that are the theoretical minimum lengths, given by equation (5). The overall specificity for our method is between 91.7 – 99.9%, the sensitivity between 72.2 – 96.5% with the median of 99.4% and 89.9% respectively. The mean sequence length is dependent on the technology simulated. Thus, in order to reach the same coverage, a larger number of fragments need to be sequenced when sequencing is performed with Solexa, which produces short reads compared to the Sanger and 454 methods. According to our model, the largest number of sequenced reads yields the shortest length of the sliding window and thus the best resolution. The range of window sizes in our simulations varies from 1,103 bases to 2,951,792 bases, decreasing with increasing average sequencing coverage. The results show that our model performs well in the presence of errors. Despite of increased resolution due to shortening of the sliding window size, the sensitivity is increased together with increased sequencing coverage. Slight drop in specificity with increasing sequencing coverage can be observed (Figure 3). This is likely to be due to SNPs, short indels, and read mapping errors, that are not considered in our statistical model and have a more profound effect on small windows. The specificity does not drop in error free data. The effect of errors may be reduced by using a window size that is larger than the theoretical minimum. For example, the theoretical minimum window for 8× Solexa sequencing at p = 0.001 is 1947 bases. This window size gives a specificity of 95.4%, while a 2 times larger window yields specificity of 97.8% (Figure 4).

Analysis of human data

The genomes of two individuals, Dr. Craig J. Venter and Dr. J. Watson were recently sequenced on 7.5× and 7.4× coverage respectively [21,24]. The genome of Dr. Craig J. Venter is sequenced using Sanger method and Dr. J. Watson's genome using 454 technology. We compared the two genomes using CNV-seq (Figure 5 and Additional File 1). The thresholds p' = 10^-5 and log₂(r') = 0.6 yield sliding window size of 26,481 bases for autosomal chromosomes. The sex chromosomes have a lower sequencing coverage than autosomal chromosomes, therefore larger window sizes are used: 72,044 bases for chromosome X and 269,032 bases for chromosome Y. We identified 174 contiguous regions covered by four or more consecutive windows. The sizes of these regions range from 66,202 bases to 941,612 bases.

The comparison of the 174 CNV calls with those in the Database of Genomic Variants (DGV) [2] revealed 142 of the CNV calls to overlap more than 50% with previously reported CNV regions. In order to asses the significance of CNV calls, we performed 5,000 permutation tests, using 174 randomly distributed CNV regions of the same sizes as in the original experiment. In average, only 56 and maximum 78 of 174 regions overlap more than 50% with CNV in DGV (Figure 6) 5,000 random sets. The real CNV calls have significantly larger overlap with DGV (p = 0).

We also intersected the CNV calls with the CNVs identified by aCGH in the two genomes. There are 23 and 45 CNV regions reported in Watson's and Venter's genome respectively [21,24]. We found 15 of our CNV calls overlap with 10 of previously reported Watson's CNV regions, and only 11 of our CNV calls overlap with 5 of Venter's. The low overlap with Venter's CNV calls made by aCGH is not surprising, for the reason that the majority of the CNV regions were detected by only one of three microarray platforms [24]. There are 121 CNV calls that made by CNV-seq but not aCGH and overlap with DGV data, suggesting that CNV-seq can detect CNV regions that were missed by aCGH. One of these regions is shown in Figure 5 (bottom panel), a 238 kb region (copy number ratio 6:1, p = 0) containing two genes (FAM23B, MRC1L1) and one miRNA (hsa-mir-511-2). We have used stringent thresholds in our analysis, thus by lowering thresholds, such as p-value and the number of consecutive windows, will increase the number of reported CNV calls.

A major assumption in CNV-seq is that shotgun sampling of DNA fragments is random, and therefore the CNV calls made by CNV-seq are not due to different sequencing bias between the two sets of data compared. When the two sets of data are prepared in the same way, this assumption is valid. However, when the shotgun sequences are generated using two different sequencing methods, the assumption may not hold any more. Solexa sequencing reads are recently reported to be GC-biased dependent on a library preparation procedure [28]. Venter's genome was sequenced using 454 and Watson's genome was sequenced using the Sanger method. We compared the distribution of GC frequencies in the shotgun reads in both genomes. There are no significant differences between the two distributions (p = 0.2106, Kolmogorov-Smimrov test).