Abstract:
Massively parallel sequencing of cell-free, maternal plasma DNA was recently demonstrated to be a safe and effective screening method for fetal chromosomal aneuploidies. Here, we report an improved sequencing method achieving significantly increased throughput and decreased cost by replacing laborious sequencing library preparation steps with PCR employing a single primer pair. Using this approach, samples containing as little as 4% trisomy 21 DNA could be readily distinguished from euploid samples.

Description:
[0001]    This invention was made using funding from the U.S. National Institutes of Health, grants CA62924, CA43460, and CA57345. The U.S. government therefore retains certain rights in the invention. 
     
    
     TECHNICAL FIELD OF THE INVENTION 
       [0002]    This invention is related to the area of genetic analysis. In particular, it relates to assessment of relative copy number of chromosomal sequences. 
       BACKGROUND OF THE INVENTION 
       [0003]    A major chromosomal abnormality is detected in approximately 1 of 140 live births 1  and in a much higher fraction of fetuses that do not reach term or are still-born 2 . The most common aneuploidy is trisomy 21, which currently occurs in 1 of 730 births 1 . Though less common than trisomy 21, trisomy 18 (Edwards Syndrome) and trisomy 13 (Patau syndrome) occur in 1 in 5,500 and 1 in 17,200 live births, respectively 1 . A large variety of congenital defects, growth deficiencies, and intellectual disabilities are found in children with chromosomal aneuploidies, and these present life-long challenges to families and societies 3 . For these reasons, much effort has been devoted to detecting chromosome abnormalities during early fetal life, at a time when therapeutic abortions can be offered as an option to prospective parents. 
         [0004]    There are a variety of prenatal diagnostic tests that can indicate increased risk for fetal aneuploidy, although invasive tests such as amniocentesis or chorionic villus sampling are the current gold standard 4  and are associated with a non-negligible risk of fetal loss. More reliable, non-invasive tests for fetal aneuploidy have therefore long been sought. The most promising of these are based on the detection of fetal DNA in maternal plasma, as pioneered by Lo&#39;s group 5 . It has been demonstrated that massively parallel sequencing of libraries generated from maternal plasma can reliably detect chromosome 21 abnormalities 6,7 . In the most comprehensive study to date 8 , 98.6% of fetuses with trisomy 21 were detected in maternal plasma, with a false positive rate of 0.2 percent. In an additional 0.8 percent of samples, the test failed to give a result. These exciting studies promise a new era of non-invasive prenatal testing. 
         [0005]    Currently, almost half of trisomy 21 babies are born to mothers less than 35 years of age, as more than 80% of pregnant women are under 35 9,10 . Though the risk of invasive procedures is thought to outweigh the benefit of invasive testing for eligible young mothers, it is clear that the vast majority of births associated with chromosomal aneuploidies could be safely prevented with reliable non-invasive tests that could be safely administered to all pregnant women. Prenatal testing is an extraordinarily stressful exercise for pregnant mothers and their families, and the more rapid the process, the better. 
         [0006]    To achieve this goal with circulating fetal DNA testing, decreases in cost and increases in throughput will be necessary. There are three major components of plasma DNA testing: preparation of DNA libraries for loading on the sequencing instrument, the sequencing of these libraries, and their analysis. The second component is being addressed by instrument manufacturers, who have made remarkable progress over the last few years. Potential improvements in the first and third components are the subject of the current study. 
         [0007]    The only commercially available test for circulating fetal DNA aneuploidy involves the preparation of whole genome libraries and the analysis of a sufficient number of sequences on the relevant chromosomes to reliably detect small differences in copy number. The preparation of whole genome libraries involves several sequential steps, including end-repair, 5′-phosphorlyation, addition of a terminal dA nucleotide to the 3′ ends of the fragments, ligation of the fragments to adapters, and PCR amplification of the ligated products, many of which require intervening purifications. The PCR products are then quantified and loaded on the sequencing instrument. Following the sequencing run, the tags are aligned to the human genome and assessed with Digital Karyotyping 11 , i.e., the number of tags per genomic locus is used to construct a virtual karyotype. Another recently described test involves fewer, but still a large number of, steps to prepare libraries for sequencing 12 . 
         [0008]    There is a continuing need in the art to rapidly and non-invasively detect genetic abnormalities. 
       SUMMARY OF THE INVENTION 
       [0009]    According to one embodiment of the invention a method is provided for testing a human for aneuploidy. A plurality of chromosomal sequences in a DNA sample from a human are amplified with a single pair of primers complementary to said chromosomal sequences to form a plurality of amplicons, wherein the plurality of amplicons are not identical, and wherein the plurality of amplicons include sequences on a query chromosome and sequences on a plurality of reference chromosomes. Reactions are performed to determine the nucleotide sequence of at least 3 nt of the plurality of amplicons. Amplicon nucleotide sequences are matched in silico to genomic sequences at genomic loci. Numbers of matching amplicons at individual genomic loci are counted. Numbers of amplicons matched to genomic loci on the query chromosome are compared to numbers of amplicons matched to genomic loci on the reference chromosomes. 
         [0010]    According to another embodiment a method is provided for testing a human for DNA copy number changes. A plurality of chromosomal sequences in a DNA sample from a human are amplified with a single pair of primers complementary to the chromosomal sequences to form a plurality of amplicons, wherein the plurality of amplicons are not identical, and wherein the plurality of amplicons include sequences in a query chromosomal region and sequences in a plurality of reference chromosomal regions. Reactions are performed to determine the nucleotide sequence of at least 3 nt of the plurality of amplicons. Amplicon nucleotide sequences are matched in silico to genomic sequences at genomic loci. Numbers of matching amplicons at individual genomic loci are counted. Numbers of amplicons matched to genomic loci in the query chromosomal region are compared to numbers of amplicons matched to genomic loci in the reference chromosomal regions. 
         [0011]    A pair of primers is provided which is useful for analyzing human aneuploidy. A first primer comprises SEQ ID NO: 1 and a second primer comprising SEQ ID NO: 2. 
         [0012]    A method of selecting primers is provided for use in detecting human aneuploidy. A pair of primers is identified in which the primers are complementary to a plurality of pairs of chromosomal segments that are separated by 3 to 10,000 nt of intervening sequence in a human genome. The intervening sequences are distributed on at least three human chromosomes. The pairs of chromosomal segments and their intervening sequence are amplified to form a population of amplicon molecules whose representation in the population reflects representation of the chromosomal segments and their intervening sequences in the human genome. 
         [0013]    These and other embodiments which will be apparent to those of skill in the art upon reading the specification provide the art with new tools and methods for assessing genomic copy number sensitively and rapidly. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIGS. 1   a - 1   d : Comparison of observed and predicted distributions of FAST-SeqS amplification products. ( FIG. 1   a ) A density plot of the expected distribution of fragment lengths, with peaks at 124 and 142 bp. ( FIG. 1   b ) A density plot of the actual tag counts obtained in eight normal plasma DNAs. The 124 by fragments are preferentially amplified compared to the 142 by fragments. Inset: polyacrylamide gel of a representative FAST-SeqS sequencing library. Note that the amplification products contain an additional 121 by of flanking sequence to facilitate sequencing (Supplementary Table 3). ( FIG. 1   c ) The average representation of L1 retrotransposons within repetitive DNA in eight normal plasma samples. Roughly 97% of tags align to positions representing only seven L1 retrotransposons. ( FIG. 1   d ) A detailed examination of the observed distribution from eight normal plasma DNAs compared with the distribution of each of the seven L1 retrotransposons predicted by RepeatMasker. Error bars in each panel depict the range. 
           [0015]      FIGS. 2   a - 2   c : Demonstration of FAST-SeqS reproducibility. ( FIG. 2   a ) Calculated z-scores for each autosome from eight normal plasma DNA samples. No chromosome had a z-score&gt;3.0 (range: −2.1 to 1.9). ( FIG. 2   b ) Comparison of z-scores from patients with trisomy 21 (n=4), trisomy 18 (n=2), and trisomy 13 (n=1) with eight normal spleen or WBC DNAs. The z-scores displayed represent the relevant chromosome for the comparison. The maximum z-score observed for any of the compared normal chromosomes was 1.9 (chr13). ( FIG. 2   c ) Control WBC DNA was analyzed alone (z-score range: −0.8 to 1.3) or when mixed with DNA from a patient with trisomy 21 at 4% (z-score range: 4.5 to 7.2) or 8% (z-score range: 8.9 to 10.) levels. Each experiment in ( FIG. 2   c ) was performed in quadruplicate. 
           [0016]      FIG. 3   a - 3   b  (Supp.  FIG. 1 ) Further demonstration of FAST-SeqS reproducibility using different instruments, samples, and sequencing depth. ( FIG. 3   a ) Matched peripheral blood white blood cell (WBC) DNA from eight samples whose plasma DNA was sequenced in  FIG. 2   a  was also sequenced on one-quarter of an Illumina HiSeq 2000 lane. Plotted are the calculated z-scores for each autosome. No chromosome had a z-score&gt;3.0 (range: −2.2 to 1.9). ( FIG. 3   b ) Eight samples of either splenic or WBC DNA were sequenced on one-half of an Illumina GA IIx lane, designed to yield less tags than the aforementioned plasma and WBC samples ( FIG. 2   a  and (a)). Displayed are the z-scores calculated for each autosome. Despite three-fold less sequencing, no chromosome had a z-score&gt;3.0 (range: −2.2 to 2.1). 
           [0017]      FIG. 4  (Supp.  FIG. 2 ) Pilot mixing experiment of trisomy 21 and euploid DNA. Control peripheral blood white blood cell (WBC) DNA was analyzed alone (n=2) or when mixed with DNA from a patient with trisomy 21 at 5% (n=2), 10% (n=1), or 25% (n=1) levels. A tight correlation exists between the expected and observed fractions of extra chromosome 21 (r=0.997 by Pearson correlation test, n=6). 
           [0018]      FIG. 5 . (Supplementary Table 1.) Samples analyzed in this FAST-SeqS study 
           [0019]      FIG. 6A-6B . (Supplementary Table 2) Sequencing characteristics of FAST-SeqS 
           [0020]      FIG. 7 . (Supplementary Table 3.) Oligonucleotides used to prepare and sequence FAST-SeqS samples (SEQ ID NO: 4-14 consecutively) 
           [0021]      FIG. 8 . (Table 1) Samples analyzed in this FAST-SeqS study 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0022]    The inventors have developed a method that rapidly and non-invasively detects genetic abnormalities, in particular copy number abnormalities. We reasoned that the process in the commercially available test could be simplified if a defined number of fragments from throughout the genome could be amplified using a single primer pair, obviating the need for end-repair, terminal 3′-dA addition, or ligation to adapters. Furthermore, the smaller number of fragments to be assessed (compared to the whole genome) would streamline the genome matching and analysis processes. The method developed was capable of detecting trisomies in a reproducible fashion in pilot experiments. It has advantages over unbiased whole genome sequencing in ease of implementation, cost, analysis time, and throughput. 
         [0023]    Our approach to achieving the goals was based on the use of specific primers that anneal to a subset of human sequences dispersed throughout the genome. We named this approach “Fast Aneuploidy Screening Test-Sequencing System (henceforth FAST-SeqS). For maximum utility, we sought to identify regions with enough similarity so that they could be amplified with a single pair of primers, but sufficiently unique to allow most of the amplified loci to be distinguished. To be compatible with the degraded DNA found in plasma 8 , we further required that the amplified sequences be ≦150 bp. Using the BLAST-Like Alignment Tool (BLAT) algorithm 13 , we iteratively searched fragments of a small portion of chromosome 21 (˜6.8 Mb) containing the Down&#39;s Syndrome critical region to identify suitable primer pairs, i.e., primer pairs that would amplify many distinct fragments of DNA from throughout the genome as well as throughout the Down&#39;s Syndrome critical region. Three such primer pairs were identified, and after testing these primers in silico (using In Silico PCR 14 ) as well as in pilot sequencing experiments, we found one of the three primer pairs (henceforth FAST-1) to be optimal (Online Methods). The FAST-1 primer pair was predicted to amplify subfamilies of long interspersed nucleotide elements (L1 retrotransposons) which, like other human repeats, have spread throughout the genome via retrotransposition, particularly in AT-rich regions 15 . As it is generally more difficult to uniformly amplify and sequence regions that vary widely in their GC content 8,16 , we expected that this differential localization would work in our favor. 
         [0024]    Any chromosome or chromosome region can be queried. Non-limiting examples of useful query chromosomes and regions are chromosome 21, chromosome 13, chromosome 18, the X chromosome, the Y chromosome, Down&#39;s Syndrome critical region on chromosome 21. The query and reference chromosomes may be nuclear. In some embodiments at least two, three, four, or five amplicons tested match a genomic sequence within a query chromosome or query region. 
         [0025]    The amplicons may be relatively small so that the degraded nature of some samples is not an impediment to detection. The amplicons may be less than 1 kbp, less than 500 bp, less than 250 bp, less than 180 bp, less than 150 bp, less than 120 bp, less than 100 bp, or less than 50 bp. In one embodiment the pair of primers comprises a first and a second primer in which the first primer comprises SEQ ID NO: 1 and the second primer comprising SEQ ID NO: 2. 
         [0026]    The DNA sample may come from any source, but preferably is from a mammal and more preferably is from a human. In certain embodiments the sample is from a gravid female and the DNA sample comprises maternal and fetal DNA. The DNA sample may be from plasma or from serum, for example. Other body fluids such as saliva, tears, sweat, lymph, urine, may be used. Tissue samples may be used as a source of DNA. Cord blood may be used as a source of DNA. Because fetal DNA is only a small fraction of maternal plasma DNA, maternal DNA could mask a fetal abnormality. Therefore a sufficient number of amplicons must be counted to detect fetal aneuploidy if present. 
         [0027]    Although the amplicons may be larger, the entire amplicon need not be sequenced to identify an amplicon. In some embodiments as few as 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, or 30 nt of nucleotide sequence is determined of the plurality of amplicons. More may be determined if desired. 
         [0028]    Useful primer pairs may be complementary to sequences that are distributed on at least 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, or 23 human chromosomes. The complementary sequences may be separated by at least 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 or more nt. 
         [0029]    The above disclosure generally describes the present invention. All references disclosed herein are expressly incorporated by reference. A more complete understanding can be obtained by reference to the following specific examples which are provided herein for purposes of illustration only, and are not intended to limit the scope of the invention. 
       EXAMPLE 1  
     Methods 
     Primer Selection 
       [0030]    We began by searching a −6.8 Mb region of chromosome 21 containing the Down&#39;s Syndrome critical region (hg19 17  coordinates 35,888,786 to 42,648,523) for sequence blocks of ˜150 by that were similar but not identical to those present on all chromosomes. Using 150 by sliding windows incremented by 50 by (135,186 sequences of 150 by in length), we queried sequences with the BLAST-Like Alignment Tool (BLAT) algorithm 13  to identify such blocks. We also required that at least three of the blocks were present on chromosome 21 in addition to the one within the ˜6.8 Mb region described above. 
         [0031]    Out of the 135,186 queried blocks, we found only 56 that met the following criteria:
       contained at least 11 variant bases from the query sequence, to aid in distinguishing amplified loci;   contained no more than 30 variant bases from the query sequence, to increase the chance of uniform amplification; and   spanned no more than a total of 180 bases, to be compatible with the analysis of degraded DNA.       
 
         [0035]    We then manually scanned the BLAT alignments of these 56 blocks to search for those that had highly similar 5′ and 3′ ends. At least three of the 56 sequences met our criteria and we designed primers for them. In Silico PCR 14  verified that each theoretical primer pair would amplify many distinct sequences from every nuclear chromosome. 
       Ascertainment of Amplification Product Uniqueness. 
       [0036]    Sequences that were too similar could pose a problem during alignment because of the inevitable errors introduced during library preparation or sequencing. We therefore wrote a custom script to assess how many distinct sequences would remain after allowing one, two, or three errors in each ˜150 by sequence. The theoretical amplification products of one primer pair (FAST-1) greatly outperformed the other two, and the superiority of FAST-1 was confirmed in pilot sequencing experiments. In Silico PCR 14  predicted a bimodal distribution of PCR fragments, and this was confirmed by size separation of the amplified PCR products on a polyacrylamide gel and through the observed distribution of counts per position ( FIG. 1   b ). 
       Templates. 
       [0037]    Control DNA was obtained from normal spleen, peripheral blood white blood cells (WBCs), or plasma (Supplementary Table 1). Fibroblast DNA from five individuals with trisomy 21 (NA02767, NA04616, NG05120, NG05397, and NG07438), two with trisomy 18 (NA03623 and NG12614), and one with trisomy 13 (NA03330) were purchased from the Coriell Institute for Medical Research (Camden, N.J.). A total of 33 ng of DNA was used for each experiment. All templates were quantified by OD, except for the mixing experiments in which the templates were quantified by Digital PCR 20  to achieve a more accurate estimate of concentration. 
       Sequencing Library Preparation. 
       [0038]    The significant savings in time in FAST-SeqS is due to the replacement of a traditional whole genome amplification library preparation with an amplification using a single primer pair. Templates were amplified with FAST-1 primers as described by Kinde et al 21  in which individual template molecules are tagged with a unique identifier DNA sequence. Though the unique identifier sequences turned out to be not necessary for FAST-SeqS (see Precise template counting section below), we included them in the initial experimental design and continued to use them once they were observed to provide robust PCR products in our initial experiments. Briefly, the FAST-1 amplification primers each contained a different 5′ universal primer sequence (UPS) followed by the sequences allowing amplification of the repeated elements described above (Forward: ACACAGGGAGGGGAACAT; SEQ ID NO: 1; Reverse: TGCCATGGTGGTTTGCT; SEQ ID NO: 2) (Supplementary Table 3). Additionally, the forward primer contained a stretch of 16-20 degenerate bases immediately 3′ to its UPS (Supplementary Table 3). PCR was performed using Phusion Hot Start II Polymerase (Thermo Scientific, cat. no. F-549L) in 1× Phusion HF buffer, 0.5 μM each primer, and two units of polymerase in a total of 50 μL under the following cycling conditions: 98° C. for 120s, followed by two cycles of 98° C. for 10s, 57° C. for 120s, and 72° C. for 120s. The initial amplification primers were removed with AMPure XP beads (Beckman Coulter Genomics, cat. no. A63880) according to the manufacturer with the exception that the beads were added at only 1.4× the PCR volume and the elution volume was reduced to 10 uL of TE. The elution was used directly for a second round of amplification using primers that annealed to the UPS site introduced by the first round primers and that additionally contained the 5′ grafting sequences necessary for hybridization to the Illumina flow cell (Supplementary Table 3). Further, we introduced one of five indexes (“barcodes”) (Supplementary Table 3) to each sample in the reverse primer to later allow multiplexed sequencing. The second round of PCR was performed using Phusion Hot Start II Polymerase in 1× Phusion HF buffer, 0.5 μM each primer, and two units of polymerase in a total of 50 μL under the following cycling conditions: 98° C. for 120s, followed by 13 cycles of 98° C. for 10s, 65° C. for 15s, and 72° C. for 15s. Amplification products were again purified with AMPure XP beads and were quantified by spectrophotometry, real time PCR or on an Agilent 2100 Bioanalyzer; all methods of quantification yielded similar results. Oligonucleotides were purchased from IDT (Coralville, Iowa). 
       Data Analysis Overview 
       [0039]    As opposed to traditional whole genome amplification libraries, where the vast majority of tags align to the genome in unique positions and thus each tag needs an independent alignment, FAST-SeqS yields sequences that aligned to an average of only 21,676 positions; Supplementary Table 2). The number of positions to which the sequences aligned varied little compared to the range of sequence data obtained across all experiments. Though the number of uniquely aligned tags per experiment spanned a 12-fold range (1,343,382 to 16,015,347) the number of positions varied only by 0.25-fold (range: 18,484 to 24,562 positions; Supplementary Table 2). Raw reads from all experiments (Supplementary Table 2) can be downloaded from the domain sagenet.org, subdomain fast, document fast.htm. 
       Sequence Tag Filtering and Alignment 
       [0040]    Thirty-seven base sequence tags passing the Illumina chastity filter and containing at least three correct terminal bases of the amplification primer were filtered for quality by masking any base with a quality score &lt;20 with an N using a custom script. Thus, tags with low quality bases were given the opportunity to align by considering only their most reliable bases. After quality masking, only the distinct sequences were aligned to the human genome (hg19 17 ) using Bowtie 0.12.7 18 . When building the reference index for Bowtie, we included unresolved or unplaced contigs 22  to ensure the most accurate alignments. Sequences that aligned uniquely with up to one mismatch (using the flags −m 1 and −v 1, respectively) were retained and their alignments were matched back to the original data. An average of 38% of tags across all samples could be uniquely assigned to a genomic position (range: 31% to 45%; Supplementary Table 2). 
       Estimating the Distribution of Sequenced Fragments. 
       [0041]    After confirming the in silico prediction of a primarily bimodal distribution of FAST-SeqS amplification products by gel electrophoresis, we investigated whether the counts of sequenced fragments that aligned to unique positions were similarly distributed. Though we only sequenced 37 bases, we could estimate the relative size of each tag from In Silico PCR 14  and its unique position in the genome. This exercise could provide additional evidence that the actual amplification products matched those that were predicted and could alert us to any amplification bias (see Normalization section below). 
         [0042]    First, we transformed the tag counts per uniquely aligned position to a log scale, a transformation frequently performed to this class of data to induce symmetry 23 . We performed this transformation for each group of experiments (e.g., from eight normal plasma samples analyzed in the same instrument run; Supplementary Table 2). Next, we used a nonparametric method to estimate a smoothened distribution (a kernel density estimator, implemented in R 24  using the density function), which made it straightforward to visualize the modality of our data. After plotting the distribution using ggplot2 25  (an R 24  package), we observed that each group of experiments showed a similar clustering of tag counts per position, consistent with a primarily bimodal distribution with a negative skew. A representative plot is displayed in  FIG. 1   b.    
       Normalization.  
       [0043]    Massively parallel sequencing will generate a different number of sequence tags from each sample, as well as from different sequencing runs of the same sample, due to stochastic and experimental variations. Thus, it is essential to normalize the data to make meaningful comparisons of the type used here. Although it would be most straightforward to simply express tag counts as a fraction of the total number of tags sequenced in an experiment, this normalization is too simplistic and is highly susceptible to systemic biases that frequently plague next generation sequencing of both DNA and RNA templates, and these are routinely used in digital karyotyping analyses such as that used for the diagnosis of trisomy 21 8,16 . 
         [0044]    Because of the bimodal size distribution of the amplicons obtained with the FAST-1 primer pair, we predicted that the majority of bias in FAST-1 amplifications would be due to the potential over-representation of the smaller-sized fragments. This bias could either occur during library preparation or during solid-phase bridge PCR on the Illumina flow cell. We found that an appropriate normalization for this distribution could be obtained using the quantile method 19 , used extensively within the microarray community. By organizing our data into a list of positions (equivalent to probes in microarray data), each associated with a tag count (equivalent to intensities in microarray data), we were able to apply standard quantile normalization to FAST-SeqS data. To best approximate the microarray data format, we chose to only analyze positions that were shared within each experimental group (e.g., the data from eight normal plasma samples). As the FAST-1 primers amplified a highly reproducible set of positions, this generally only eliminated &lt;1% of the data. To maximize reproducibility, we excluded positions aligning to unresolved or unplaced contigs and those aligning to sex chromosomes, although inclusion of these chromosomes only marginally increased variability between experiments (e.g., in eight normal plasma samples, the maximum z-score from any chromosome rose from 1.9 to 2.3). The inclusion of sex chromosomes could be useful for other applications, such as detecting aneuploidies involving chromosome X or determining the gender of a sample (i.e., by the presence or absence of sequences aligning to chromosome Y). 
         [0045]    We implemented the quantile normalization 19  for each experimental group (each of which contained multiple samples; Supplementary Table 2) by performing the following steps:
       generating a sorted array of tag counts representing each position for every sample (all of equal length as only the shared positions in each experiment were analyzed);   combining these sorted arrays into a 2×2 matrix, where each experiment is represented in its own column and the shared positions constitute the rows;   replacing an individual sample&#39;s count with the mean count for all samples at that particular row; and   re-sorting the counts back to their original order.       
 
         [0050]    The distribution of our data was always negatively skewed (see  FIG. 1   b  for a representative example). We excluded the positions falling within the left tail of each experiment&#39;s distribution (the positions containing the smallest number of tags) from our analysis by:
       estimating the distribution of normalized values as described above;   determining the inflection point between the two peaks of the bimodal distribution; and   considering the positions that had a relative density below the inflection point as the left tail.       
 
         [0054]    Once the left tail was determined and positions within it discarded, the quantile normalization was repeated. Through this process, each sample within an experimental group had the same sum total of tags and an identical distribution of counts, so direct comparisons could be made. We automated the quantile normalization in R 24 . The entire normalization procedure routinely took less than a few minutes to complete. 
       Quantitative Determination of Aneuploidy Status. 
       [0055]    A common method of determining the aneuploidy status of a particular sample in Digital Karyotyping-based 11  assays is by comparison of z-scores 6,8,26 . Through this method, one determines the mean and standard deviation of tag counts lying within a chromosome of interest in a group of reference samples (e.g., samples with known euploid content), and then creates a standardized score (i.e., z-score) for a chromosome of interest for each sample as follows: z-score i,chrN =(chrN i −μ chrN )/sd chrN , where i represents the sample to be standardized, chrN represents the normalized tag count of the sample&#39;s chromosome, and μ chrN  and sd chrN  represent the mean and standard deviation of the normalized tag counts, respectively, of chrN in the reference group. When all samples are standardized in this way, outliers are easily detected because they have a z-score&gt;3.0. This indicates that the normalized tag count of the outlier exceeds the mean of the reference group by at least three standard deviations. 
       Precise Template Counting. 
       [0056]    Finally, we evaluated whether precisely counting template molecules could further increase reproducibility. By incorporating 16-20 degenerate bases at the 5′ end of one of the two FAST-1 primers (Supplementary Table 3), it is possible to uniquely identify each template molecule giving rise to a PCR product 21 . This could potentially increase accuracy by minimizing the possibility that the same template molecule was counted more than once in the final tally for each chromosome. We found that this enhancement did not significantly alter the consistency of normalized counts per chromosome among the eight normal plasma samples: the maximum z-score for any chromosome was slightly increased from 1.9 to 2.0. By performing a two-tailed t-test on the absolute values of the z-scores for all autosomes comparing analysis methods, we found no statistically significant difference between the two methods (p=0.759, n=22×8 for each group). 
       EXAMPLE 2 
       [0057]    As an initial test of the performance of FAST-SeqS, we examined the representation of each autosome in the plasma DNA of seven normal females, including one biologic replicate (Supplementary Table 1). Using only 37 cycles of sequencing in one-quarter of a lane on an lumina HiSeq 2000 instrument, we recovered an average of 31,547,988 high quality tags per individual (range: 27,179,424 to 36,0418,017 tags; Supplementary Table 2). An average of 35% of these tags (range: 31 to 37%) could be uniquely mapped to one of an average of 23,681 unique chromosomal positions (range: 22,589 to 24,562 positions) when allowing up to one mismatch during alignment to hg19 17  using Bowtie 18 . The theoretical in silico ( FIG. 1   a ) and observed distribution of tag counts ( FIG. 1   b ) both showed a bimodal distribution of sizes. Of the uniquely aligned tags, 99.1% aligned to positions predicted to be repetitive DNA by RepeatMasker (http://www.repeatmasker.org), 97.5% of which fell into just seven L 1  retrotransposon subfamilies ( FIG. 1   c ). Additionally, the distribution of each subfamily agreed with that predicted by RepeatMasker ( FIG. 1   d ). Because tag alignment to a discrete set of chromosomal positions is simpler than alignment to the entire genome, the post-sequencing analysis process was very rapid. In fact, this mapping plus subsequent statistical analysis could be completed in less than 30 min per sample with a single computer housing two six-core CPUs (Intel Xeon X5680). 
         [0058]    Most importantly, the relative fraction of tags mapping to each chromosome was remarkably similar among the individual samples after normalizing 19  to compare chromosome tag counts among different samples (Online Methods). In particular, the fraction of tags that matched to any of the autosomes in any of the eight samples studied never deviated from the average by a z-score&gt;3.0 ( FIG. 2   a ). Of particular note, the maximum z-scores observed among the eight samples for chromosomes 21, 18, and 13 were 1.3, 1.4, and 1.0, respectively. 
       EXAMPLE 3 
       [0059]    We next studied the reproducibility of chromosome representation in two additional experiments employing different types of samples, different instruments, and different depths of sequencing. In the first experiment, we analyzed DNA from peripheral blood white blood cells (WBCs) from the same seven individuals who contributed plasma. Four samples were sequenced on a single lane of an Illumina HiSeq 2000, yielding a mean of 10,835,559 uniquely aligned tags per sample (range: 4,905,067 to 16,015,347 tags). The maximum z-scores for any of the samples were 1.0, 1.2, and 1.6 for chromosomes 21, 18, and 13, respectively (Supplementary  FIG. 1   a ). 
       EXAMPLE 4 
       [0060]    In the next experiment, we analyzed splenic or WBC DNA from an additional eight individuals using one-half of a lane of an Illumina GA IIx instrument per sample (Supplementary Table 2). We obtained a mean of 4,013,951 uniquely aligned tags per sample (range: 2,847,661 to 4,645,608 tags). Despite almost 3-fold less sequencing, the maximum z-scores among the samples were still only 1.3, 1.5, and 1.9 for chromosomes 21, 18, and 13, respectively, well below the widely used cutoff of 3.0 (Supplementary  FIG. 1   b ). 
         [0061]    Given the tight distributions of tags evident in  FIG. 2   a , we expected it would be straightforward to distinguish the DNA of patients with trisomies from those of normal individuals with euploid chromosome constitutions. The data depicted in  FIG. 2   b  demonstrate that this expectation was realized in each of four patients with trisomy 21. The z-scores among these trisomy 21 patients ranged from 32 to 36, while the maximum z-score among eight normal individuals was 1.3. Similarly, the z-scores of DNA from two patients with trisomy 18 and one from trisomy 13 were 51, 56, and 36, respectively, far exceeding the maximum z-scores for these chromosomes in normal individuals ( FIG. 2   b ). 
       EXAMPLE 5 
       [0062]    Fetal DNA accounts for a geometric mean of 13.4% of maternal DNA, depending largely on maternal weight rather than gestational age 8 . To investigate whether FAST-SeqS could distinguish samples that contained mixtures of disomic and trisomic DNA, we performed mixing experiments using DNA from patients with trisomy 21 and normal individuals. In a first experiment of this type, we mixed 5% (n=2), 10% (n=1), and 25% (n=1) trisomy 21 DNA into normal WBC DNA alongside two controls (Supplementary  FIG. 2 ), and found a tight correlation between the expected and observed fractions of extra chromosome 21 (r=0.997 by Pearson correlation test, n=6). In a second experiment, we evaluated mixtures that contained 4% or 8% trisomy 21 DNA. As shown in  FIG. 2   c , there was a clear distinction between the samples containing 4% trisomy 21 DNA vs. those from normal individuals (p=2×10 −4  as determined by two-tailed t-test, n=4 in each group). The samples containing 8% trisomy 21 DNA were of course even more easily distinguishable (p=4×10 −6  when compared to the euploid group and p=1×10 −3  when compared to the 4% trisomy 21 samples, both by two-tailed t-test with n=4 for each group). 
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