New Research In
Physical Sciences
Social Sciences
Featured Portals
Articles by Topic
Biological Sciences
Featured Portals
Articles by Topic
 Agricultural Sciences
 Anthropology
 Applied Biological Sciences
 Biochemistry
 Biophysics and Computational Biology
 Cell Biology
 Developmental Biology
 Ecology
 Environmental Sciences
 Evolution
 Genetics
 Immunology and Inflammation
 Medical Sciences
 Microbiology
 Neuroscience
 Pharmacology
 Physiology
 Plant Biology
 Population Biology
 Psychological and Cognitive Sciences
 Sustainability Science
 Systems Biology
Digital PCR for the molecular detection of fetal chromosomal aneuploidy

Contributed by Charles R. Cantor, June 21, 2007 (received for review May 9, 2007)
Data supplements
Lo et al. 10.1073/pnas.0705765104.
Supporting Information
Files in this Data Supplement:
SI Table 3
SI Table 4
SI Materials and Methods
SI Table 5
SI Table 6
SI Table 7
SI Figure 4
SI Table 8
SI Figure 5
SI Table 9
SI Figure 4Fig. 4. Computer simulation of digital RNA SNP analyses of samples from euploid and trisomy 21 fetuses. The plots of sequential probability ratio test (SPRT) curves show results from simulated digital RNA SNP experiments conducted at m_{r} values ranging from 0.1 to 2.0. Simulations were performed for 5,000 euploid and 5,000 trisomy 21 fetuses, respectively. Only an illustrative sample of 300 euploid and 300 trisomy 21 fetuses is shown.
SI Figure 5Fig. 5. Computer simulation of digital relative chromosome dosage (RCD) analyses of 100% pure fetal DNA samples from euploid and trisomy 21 fetuses. Plots of sequential probability ratio test (SPRT) curves show results from simulated digital RCD experiments conducted at m_{r} values ranging from 0.1 to 2.0. Simulations were performed for 5,000 euploid and 5,000 trisomy 21 fetuses, respectively. Only an illustrative sample of 300 euploid and 300 trisomy 21 fetuses is shown.
Table 3. Expected allelic ratio and proportion of informative wells positive for the overrepresented allele, P_{r}, in digital RNA SNP analysis of trisomy 21 cases for a series of average reference template concentrations per well, m_{r}
m_{r}
Proportion of wells positive for
Proportion of informative wells
Digital RNA SNP allelic ratio
P_{r}
Reference allele
Overrepresented allele
Both alleles
Reference allele only
Overrepresented allele only
0.1
0.0952
0.1813
0.0173
0.0779
0.1640
0.2419
2.11
0.68
0.2
0.1813
0.3297
0.0598
0.1215
0.2699
0.3914
2.22
0.69
0.3
0.2592
0.4512
0.1169
0.1422
0.3342
0.4765
2.35
0.70
0.4
0.3297
0.5507
0.1815
0.1481
0.3691
0.5173
2.49
0.71
0.5
0.3935
0.6321
0.2487
0.1448
0.3834
0.5282
2.65
0.73
0.6
0.4512
0.6988
0.3153
0.1359
0.3835
0.5194
2.82
0.74
0.7
0.5034
0.7534
0.3793
0.1241
0.3741
0.4983
3.01
0.75
0.8
0.5507
0.7981
0.4395
0.1112
0.3586
0.4698
3.23
0.76
0.9
0.5934
0.8347
0.4953
0.0981
0.3394
0.4375
3.46
0.78
1.0
0.6321
0.8647
0.5466
0.0855
0.3181
0.4036
3.72
0.79
1.1
0.6671
0.8892
0.5932
0.0739
0.2960
0.3699
4.00
0.80
1.2
0.6988
0.9093
0.6354
0.0634
0.2739
0.3373
4.32
0.81
1.3
0.7275
0.9257
0.6734
0.0540
0.2523
0.3063
4.67
0.82
1.4
0.7534
0.9392
0.7076
0.0458
0.2316
0.2774
5.06
0.83
1.5
0.7769
0.9502
0.7382
0.0387
0.2120
0.2507
5.48
0.85
1.6
0.7981
0.9592
0.7656
0.0325
0.1937
0.2262
5.95
0.86
1.7
0.8173
0.9666
0.7900
0.0273
0.1766
0.2039
6.47
0.87
1.8
0.8347
0.9727
0.8119
0.0228
0.1608
0.1836
7.05
0.88
1.9
0.8504
0.9776
0.8314
0.0190
0.1462
0.1652
7.69
0.88
2.0
0.8647
0.9817
0.8488
0.0158
0.1329
0.1487
8.39
0.89
Table 4. Expected proportion of informative wells positive for the chromosome 21 locus, P_{r} , for a series of average reference template concentrations per well, m_{r} , in trisomy 21 samples with fractional fetal DNA concentrations of 10%, 25%, 50%, and 100%
m_{r}
Percentage of fetal DNA in the sample, %
10
25
50
100
Proportion of
informative wellsP_{r}
Proportion of informative wells
P_{r}
Proportion of informative wells
P_{r}
Proportion of informative wells
P_{r}
0.1759
0.51
0.1813
0.53
0.1903
0.56
0.2079
0.61
0.2
0.3020
0.51
0.3097
0.53
0.3223
0.56
0.3465
0.61
0.3
0.3893
0.51
0.3971
0.53
0.4098
0.57
0.4337
0.62
0.4
0.4465
0.51
0.4531
0.54
0.4637
0.57
0.4834
0.63
0.5
0.4805
0.52
0.4851
0.54
0.4925
0.57
0.5059
0.63
0.6
0.4968
0.52
0.4991
0.54
0.5027
0.58
0.5091
0.64
0.7
0.4999
0.52
0.4997
0.54
0.4994
0.58
0.4990
0.65
0.8
0.4931
0.52
0.4905
0.54
0.4866
0.58
0.4799
0.65
0.9
0.4792
0.52
0.4745
0.55
0.4672
0.59
0.4550
0.66
1.0
0.4603
0.52
0.4537
0.55
0.4436
0.59
0.4268
0.67
1.1
0.4382
0.52
0.4298
0.55
0.4174
0.60
0.3971
0.68
1.2
0.4140
0.52
0.4043
0.55
0.3899
0.60
0.3669
0.69
1.3
0.3887
0.52
0.3779
0.55
0.3621
0.60
0.3373
0.69
1.4
0.3631
0.52
0.3515
0.56
0.3347
0.61
0.3087
0.70
1.5
0.3378
0.52
0.3256
0.56
0.3080
0.61
0.2815
0.71
1.6
0.3130
0.52
0.3004
0.56
0.2826
0.62
0.2560
0.72
1.7
0.2892
0.53
0.2764
0.56
0.2585
0.62
0.2322
0.73
1.8
0.2664
0.53
0.2537
0.57
0.2359
0.63
0.2103
0.73
1.9
0.2449
0.53
0.2322
0.57
0.2148
0.63
0.1901
0.74
2.0
0.2246
0.53
0.2122
0.57
0.1952
0.64
0.1716
0.75
Table 5. Comparison of the effectiveness of the new and old sequential probability ratio test (SPRT) algorithms for classifying euploid and trisomy 21 (T21) cases in 96well digital RNA SNP analyses
m_{r}
Classification
New algorithm, %
Old algorithm, %
m_{r}
Classification
New algorithm, %
Old algorithm, %
Euploid
T21
Euploid
T21
Euploid
T21
Euploid
T21
0.1
Correct
0
37
0
35
1.1
Correct
89
92
14
35
Incorrect
3
2
3
1
Incorrect
1
0
4
0
Unclassified
97
61
97
63
Unclassified
10
7
81
65
0.2
Correct
6
64
0
40
1.2
Correct
90
92
11
35
Incorrect
4
2
4
0
Incorrect
1
0
4
0
Unclassified
90
34
96
60
Unclassified
9
8
84
65
0.3
Correct
34
75
6
39
1.3
Correct
91
92
7
34
Incorrect
4
2
4
0
Incorrect
1
1
4
0
Unclassified
62
24
90
61
Unclassified
8
7
89
66
0.4
Correct
54
81
14
39
1.4
Correct
92
91
5
34
Incorrect
3
1
4
0
Incorrect
1
1
4
0
Unclassified
43
19
82
61
Unclassified
8
9
91
66
0.5
Correct
64
85
20
38
1.5
Correct
92
90
2
32
Incorrect
3
1
4
0
Incorrect
1
1
4
0
Unclassified
33
14
76
62
Unclassified
8
9
93
68
0.6
Correct
74
88
23
38
1.6
Correct
92
89
1
31
Incorrect
2
1
4
0
Incorrect
1
1
4
0
Unclassified
24
11
72
62
Unclassified
8
10
94
69
0.7
Correct
80
89
25
37
1.7
Correct
92
89
1
30
Incorrect
2
1
4
0
Incorrect
1
1
4
0
Unclassified
18
10
71
63
Unclassified
7
10
96
70
0.8
Correct
83
91
23
37
1.8
Correct
92
88
0
28
Incorrect
2
1
4
0
Incorrect
1
1
4
0
Unclassified
15
9
73
63
Unclassified
7
11
96
72
0.9
Correct
86
91
21
36
1.9
Correct
92
87
0
26
Incorrect
1
1
4
0
Incorrect
1
1
3
0
Unclassified
12
8
75
64
Unclassified
8
12
97
74
1.0
Correct
88
92
19
36
2.0
Correct
91
86
0
24
Incorrect
1
0
4
0
Incorrect
1
1
4
0
Unclassified
11
8
77
64
Unclassified
9
13
96
76
The new algorithm refers to the selection of SPRT curves specific for the m_{r} derived from the digital PCR data. The old algorithm refers to the use of a fixed set of SPRT curves for all digital PCR runs.
Table 6. Comparison of the effectiveness of the new and old sequential probability ratio test (SPRT) algorithms for classifying euploid and trisomy 21 (T21) cases in 384well digital RNA SNP analyses
m_{r}
Classification
New algorithm, %
Old algorithm, %
m_{r}
Classification
New algorithm, %
Old algorithm, %
Euploid
T21
Euploid
T21
Euploid
T21
Euploid
T21
0.1
Correct
57
88
48
89
1.1
Correct
100
100
92
90
Incorrect
3
1
3
1
Incorrect
0
0
1
0
Unclassified
40
11
49
10
Unclassified
0
0
7
10
0.2
Correct
89
98
79
90
1.2
Correct
100
100
90
90
Incorrect
1
0
2
0
Incorrect
0
0
1
0
Unclassified
10
2
19
10
Unclassified
0
0
9
10
0.3
Correct
96
99
88
90
1.3
Correct
100
100
89
90
Incorrect
0
0
1
0
Incorrect
0
0
1
0
Unclassified
4
1
11
10
Unclassified
0
0
10
10
0.4
Correct
99
100
92
90
1.4
Correct
100
100
87
90
Incorrect
0
0
1
0
Incorrect
0
0
1
0
Unclassified
1
0
7
10
Unclassified
0
0
12
10
0.5
Correct
100
100
94
90
1.5
Correct
100
100
85
90
Incorrect
0
0
1
0
Incorrect
0
0
1
0
Unclassified
0
0
6
10
Unclassified
0
0
13
10
0.6
Correct
100
100
94
90
1.6
Correct
100
100
82
90
Incorrect
0
0
1
0
Incorrect
0
0
1
0
Unclassified
0
0
5
10
Unclassified
0
0
17
10
0.7
Correct
100
100
95
90
1.7
Correct
100
100
79
90
Incorrect
0
0
1
0
Incorrect
0
0
2
0
Unclassified
0
0
5
10
Unclassified
0
0
19
10
0.8
Correct
100
100
95
90
1.8
Correct
100
100
74
90
Incorrect
0
0
1
0
Incorrect
0
0
2
0
Unclassified
0
0
5
10
Unclassified
0
0
24
10
0.9
Correct
100
100
94
90
1.9
Correct
100
100
70
90
Incorrect
0
0
1
0
Incorrect
0
0
2
0
Unclassified
0
0
6
10
Unclassified
0
0
28
10
1.0
Correct
100
100
94
90
2.0
Correct
100
100
67
90
Incorrect
0
0
1
0
Incorrect
0
0
3
0
Unclassified
0
0
6
10
Unclassified
0
0
30
10
The new algorithm refers to the selection of SPRT curves specific for the m_{r} derived from the digital PCR data. The old algorithm refers to the use of a fixed set of SPRT curves for all digital PCR runs.
Table 7. Computer simulation of accuracies of a 384well digital RNA SNP analysis for the classification of samples from euploid or trisomy 21 (T21) fetuses
m_{r}
Classification
Euploid, %
T21, %
m_{r}
Classification
Euploid, %
T21, %
0.1
Correct
57
88
0.9
Correct
100
100
Incorrect
3
1
Incorrect
0
0
Unclassified
40
11
Unclassified
0
0
0.2
Correct
89
98
1.0
Correct
100
100
Incorrect
1
0
Incorrect
0
0
Unclassified
10
2
Unclassified
0
0
0.3
Correct
96
99
1.1
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
4
1
Unclassified
0
0
0.4
Correct
99
100
1.2
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
1
0
Unclassified
0
0
0.5
Correct
100
100
1.3
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
0
0
Unclassified
0
0
0.6
Correct
100
100
1.4
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
0
0
Unclassified
0
0
0.7
Correct
100
100
1.5
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
0
0
Unclassified
0
0
0.8
Correct
100
100
2.0
Correct
100
100
Incorrect
0
0
Incorrect
0
0
Unclassified
0
0
Unclassified
0
0
Table 8. Computer simulation of accuracies of a 384well digital RCD analysis for the classification of pure (100%) fetal DNA samples from euploid or trisomy 21 (T21) fetuses
m_{r}
Classification
Euploid, %
T21, %
m_{r}
Classification
Euploid, %
T21, %
0.1
Correct
38
44
0.7
Correct
95
94
Incorrect
2
2
Incorrect
0
1
Unclassified
60
54
Unclassified
5
5
0.2
Correct
64
69
0.8
Correct
95
95
Incorrect
2
2
Incorrect
1
0
Unclassified
34
29
Unclassified
4
5
0.3
Correct
78
82
0.9
Correct
96
96
Incorrect
2
1
Incorrect
0
0
Unclassified
20
17
Unclassified
4
4
0.4
Correct
85
87
1.0
Correct
97
96
Incorrect
1
1
Incorrect
0
0
Unclassified
14
12
Unclassified
3
4
0.5
Correct
89
90
1.5
Correct
97
96
Incorrect
1
1
Incorrect
0
0
Unclassified
10
9
Unclassified
3
4
0.6
Correct
92
93
2.0
Correct
96
95
Incorrect
1
1
Incorrect
0
0
Unclassified
7
7
Unclassified
4
5
Table 9. Computer simulation of accuracies of digital RCD analysis at an m_{r} value of 0.5 for the classification of samples from euploid or trisomy 21 (T21) fetuses with different fractional concentrations of fetal DNA
No. of wells
Classification
Fetal DNA in the sample, %
10
25
50
100
Euploid, %
T21, %
Euploid, %
T21, %
Euploid, %
T21, %
Euploid, %
T21, %
Correct
0
0
6
7
47
49
89
90
Incorrect
0
0
0
1
2
2
1
1
Unclassified
100
100
93
92
51
49
10
9
768
Correct
0
0
23
24
73
76
98
99
Incorrect
0
0
2
2
2
1
0
0
Unclassified
100
100
75
74
25
23
2
1
1,152
Correct
1
1
39
40
86
87
100
100
Incorrect
0
0
2
2
1
1
0
0
Unclassified
99
99
59
58
13
12
0
0
1,536
Correct
2
2
50
51
93
93
100
100
Incorrect
0
0
2
2
1
1
0
0
Unclassified
98
97
48
47
7
6
0
0
1,920
Correct
4
4
60
60
96
96
100
100
Incorrect
0
1
2
2
0
0
0
0
Unclassified
96
95
38
37
4
3
0
0
3,840
Correct
18
19
84
83
100
100
100
100
Incorrect
1
1
1
1
0
0
0
0
Unclassified
81
80
15
15
18
22
0
0
7,680
Correct
43
45
97
97
100
100
100
100
Incorrect
2
2
0
0
0
0
0
0
Unclassified
55
53
3
3
0
0
0
0
SI Materials and Methods
Subjects. Institutional ethical approval was granted and subjects with singleton pregnancies were recruited with informed consent from the Department of Obstetrics and Gynaecology, Prince of Wales Hospital, Hong Kong. Maternal peripheral blood (12 ml) samples were collected into EDTA tubes before the performance of obstetrics procedures. Placental tissue samples were obtained by chorionic villus sampling, after elective cesarean section or after pregnancy termination. Full karyotyping was performed to ascertain the fetal karyotypes. All trisomy 21 placental and maternal plasma samples were collected in first or second trimesters at the time of pregnancy termination. Most placental tissues from the euploid pregnancies were collected after elective cesarean section at term. The only exception involved the two euploid placental RNA samples subjected to digital RNA SNP that were collected in the first trimester after chorionic villus sampling. All nine euploid maternal plasma samples tested by digital RNA SNP were collected in the first trimester.
Sample Processing. DNA and RNA extractions from placental samples were performed by using the QIAamp tissue kit (Qiagen, Hilden, Germany) and TRIZOL reagent (Invitrogen, Carlsbad, CA), respectively, as previously described (1). Plasma RNA was extracted by using a combination of TRIZOLLS followed by an RNeasy minicolumn (Qiagen) as previously described (1). The extracted placental and plasma RNA samples were subjected to DNase I (Invitrogen) treatment to remove contaminating genomic DNA (1).
SNP Genotyping. Genotyping of the rs8130833 SNP on the PLAC4 gene was carried out in placental DNA samples by using PCR, primer extension, and mass spectrometry as previously described (1).
Digital RNA SNP. All RNA samples were first reverse transcribed with a genespecific reverse transcription primer by using ThermoScript reverse transcriptase (Invitrogen). Sequence of the reverse transcription primer was 5'AGTATATAGAACCATGTTTAGGCCAGA3' (Integrated DNA Technologies, Coralville, IA). The subsequent treatment of the reverse transcribed RNA (i.e., the cDNA) samples for digital RNA SNP and DNA samples (e.g., placental DNA) was essentially the same. Before digital PCR analysis, DNA and the cDNA samples were first quantified by using a realtime PCR assay with an amplicon size of 87 bp toward PLAC4, consisting of primers 5'CCGCTAGGGTGTCTTTTAAGC3', 5'GTGTTGCAATACAAAATGAGTTTCT3', and the fluorescent probe 5'(FAM)ATTGGAGCAAATTC(MGBNFQ)3' (Applied Biosystems, Foster City, CA), where FAM is 6carboxyfluorescein and MGBNFQ is a minor groovebinding nonfluorescent quencher. A calibration curve was prepared by serial dilutions of HPLCpurified singlestranded synthetic DNA oligonucleotides (Proligo, Singapore, Republic of Singapore) specifying the amplicon. The sequence was 5'CGCCGCTAGGGTGTCTTTTAAGCTATTGGAGCAAATTCAAATTTGGCTTAAAGAAAAAGAAACTCATTTTGTATTGCAACACCAGGAGTATCCCAAGGGACTCG3'. The reaction was set up by using 2´ TaqMan Universal PCR Master mix (Applied Biosystems) in a reaction volume of 25 ml. In each reaction, the amount of each primer and the amount of the probe used were 400 and 80 nM, respectively. The reaction was initiated at 50°C for 2 min and continued at 95°C for 10 min, followed by 45 cycles of 95°C for 15 and 60°C for 1 min in an ABI PRISM 7900HT Sequence Detection System (Applied Biosystems). Serial dilutions of the DNA or cDNA samples were then undertaken such that the subsequent digital PCR amplification could be performed at approximately one template molecule per well. At such a concentration, it was expected that »37% of the reaction wells would show negative amplification, and this expectation was first confirmed by conducting a 96well digital realtime PCR analysis. This was followed by digital RNA SNP analysis conducted in 384well plates by using a set of nonintron spanning primers specifying an amplicon of 77 bp, the forward primer 5'TTTGTATTGCAACACCATTTGG3' and the genespecific reverse transcription primer described above. Two allelespecific TaqMan probes targeting each of the two alleles of the rs8130833 SNP on the PLAC4 sequence were designed. Their sequences were 5'(FAM)TCGTCGTCTAACTTG(MGBNFQ)3' and 5'(VIC)ATTCGTCATCTAACTTG(MGBNFQ3') for the G and A alleles, respectively. The reaction was set up by using 2´ TaqMan Universal PCR Master Mix in a reaction volume of 5 ml. Each reaction contained 1´ TaqMan Universal PCR Master Mix, 572 nM each primer, 107 nM the G allelespecific probe, and 357 nM the A allelespecific probe. The reaction was carried out in the ABI PRISM 7900HT Sequence Detection System. The reaction was initiated at 50°C for 2 min and continued at 95°C for 10 min and followed by 50 cycles of 95°C for 15 s and 57°C for 1 min. During the reaction, the fluorescence data were collected by the "Absolute Quantification" application of SDS 2.2.2 software (Applied Biosystems). The software automatically calculated the baselines and the threshold values. The number of wells which were positive for either the A or the G allele was recorded and subjected to sequential probability ratio test (SPRT) analysis.
Digital Relative Chromosome Dosage (RCD) Analysis. All placental and maternal buffy coat DNA samples used in this study were first quantified by the NanoDrop spectrophotometer (NanoDrop Technologies, Wilmington, DE). The DNA concentration was converted to copies per microliter by using a conversion of 6.6 picograms per cell. The amount of DNA corresponding to approximately one template per well was determined by serially diluting the DNA samples and confirmed with the realtime PCR assay in a 96well format, where we expected »37% of the wells to show negative amplification. The PCR setup for the confirmatory plate was the same as described below except that only the probe for the reference chromosome was added. In the digital RCD analysis, the paralogous loci on chromosomes 21 and 1 (2) were first coamplified by forward primer 5'GTTGTTCTGCAAAAAACCTTCGA3' and reverse primer 5'CTTGGCCAGAAATACTTCATTACCATAT3', resulting in an amplicon of 101 bp. Two chromosomespecific TaqMan probes were designed to target the chromosome 21 and 1 paralogs, and their sequences were 5'(FAM)TACCTCCATAATGAGTAAA(MGBNFQ)3' and 5'(VIC)CGTACCTCTGTAATGTGTAA(MGBNFQ)3', respectively. Each reaction contained 1´ TaqMan Universal PCR Master Mix (Applied Biosystems), 450 nM each primer, and 125 nM each probe. The total reaction volume was 5 ml per well. The reaction was initiated at 50°C for 2 min and continued at 95°C for 10 min and followed by 50 cycles of 95°C for 15 s and 60°C for 1 min. All realtime PCR experiments were carried out on an ABI PRISM 7900HT Sequence Detection System (Applied Biosystems), and the fluorescence data were collected by the "Absolute Quantification" application of SDS 2.2.2 software (Applied Biosystems). The default baselines and manual threshold values were used. The number of wells which were positive for either chromosome 21 or 1 was recorded and subjected to SPRT analysis. One or more 384well plates would be analyzed until disease classification was possible by SPRT.
SPRT Analysis. The experimentally derived P_{r} value would be compared with the expected value of P_{r} to accept or reject the null hypothesis. If the alternative hypothesis was accepted, the samples were classified as having been obtained from pregnant women with trisomy 21 fetuses. If the null hypothesis was accepted, the samples were classified as having been obtained from pregnant women with euploid fetuses. Alternatively, neither the null or alternative hypothesis could be accepted if the P_{r} for the given number of informative counts had not yet reached the required level of statistical confidence for disease classification. These cases were deemed unclassifiable until more data were available. The details of the calculations are shown below and in the supporting information (SI) Tables 3 and 4.
Comparing Two SPRT Approaches. In the present study, we used SPRT curves that were specific for the m_{r} of a given digital PCR run (see below). This is in contrast to the previously described approach of using a fixed set of curves (3, 4). To compare the effectiveness of the two approaches, computer simulations (see below) were performed for 96well and 384well digital RNA SNP analyses at m_{r} values ranging from 0.1 to 2.0 for both SPRT approaches. For the fixed approach, the SPRT curves for the theoretical degree of allelic imbalance of 2:1 in the fetal genome were used.
Explanatory Notes to the Data Tabulated in SI Table 3. Calculating the expected digital RNA SNP allelic ratio and P_{r} for trisomy 21 cases, we use a specific example for illustration. In this specific example, the average concentration of the reference template per well, m_{r}, is 0.5, and the genotype of the trisomy 21 fetus at the PLAC4 SNP, rs8130833, is AGG. Therefore, the reference template would be the A allele and the overrepresented template would be the G allele.
The Poisson equation is as follows:
_{,}
where n is the number of template molecules per well, P(n) is the probability of n template molecules in a particular well, and m is the average number of template molecules in a particular digital PCR experiment.
Accordingly, the probability of any well not containing any molecule of the A allele at an average A allele concentration of 0.5 would be the following:
_{} = = 0.6065.
Hence, the probability of any well containing at least one molecule of the A allele would be 1  0.6065 = 0.3935. Therefore, ≈39% of the wells would be expected to contain at least one molecule of the A allele.
For each cell of a trisomy 21 fetus, the genomic ratio of A to G would be 1:2. Assuming that the A to G ratio in the extracted RNA or DNA sample would remain unchanged, the average concentration of the G allele per well would be two times that of the A allele, i.e., 2 ´ 0.5 = 1.
Accordingly, the probability of any well not containing any molecule of the G allele at an average G allele concentration of 1 would be the following:
_{} = = 0.3679.
Hence, the probability of any well containing at least one molecule of the G allele would be 1  0.3679 = 0.6321. Therefore, ≈63% of the wells would be expected to contain at least one molecule of the G allele.
Assuming that the filling of the wells with the A allele and the G allele is independent, the probability of a well containing both alleles would be 0.3935 ´ 0.6321 = 0.2487. Therefore, ≈25% of the wells would be expected to contain both alleles.
The proportion of wells expected to contain the A allele, but not the G allele, would be the number of wells containing at least one A allele deducted by the number of wells containing both the A and G alleles: 0.3935  0.2487 = 0.1448.
Similarly, the proportion of wells expected to contain the G allele, but not the A allele, would be the following: 0.6321  0.2487 = 0.3834.
An informative well is defined as a well being positive for either the A allele or the G allele but not both. Hence, the expected A to G allelic ratio in digital RNA SNP analysis is 0.1448:0.3834. In other words, the proportion of wells positive only for the G allele is 2.65 times that of wells positive only for the A allele. This is in contrast to the fetal genomic ratio where the overrepresented allele is 2 times that of the other allele.
For SPRT analysis, the proportion of the informative wells positive for the overrepresented allele, P_{r}, would need to be calculated and interpreted by using SPRT curves. In the current example, the proportion of informative wells would be the following: 0.1448 + 0.3834 = 0.5282. Hence, the expected P_{r} of a trisomy 21 sample at m_{r} 0.5 is the following: 0.3834/0.5282 = 0.73.
As the average template concentration, m, is a key parameter in the Poisson equation, the P_{r} would vary with m. SI Table 3 tabulates the expected digital RNA SNP allelic ratio and P_{r} of trisomy 21 samples for a range of template concentrations expressed as the average reference template concentration per well, m_{r}.
Explanatory Notes to the Data Tabulated in SI Table 4. Calculating the expected digital RCD ratio and P_{r} for trisomy 21 cases, we use a specific example for illustration. In this specific example, the average concentration of the reference template, chromosome 1, per well, m_{r}, is 0.5 and 50% of the DNA in the sample is derived from the fetus and 50% of the DNA is derived from the mother.
The Poisson equation is as follows:
_{,}
where n is the number of template molecules per well, P(n) is the probability of n template molecules in a particular well, and m is the average number of template molecules in a particular digital PCR experiment.
Accordingly, the probability of any well not containing any molecule of the chromosome 1 locus when its average concentration is 0.5 per well would be the following:
_{} = = 0.6065.
Hence, the probability of any well containing at least one molecule of the chromosome 1 locus would be the following: 1  0.6065 = 0.3935. Therefore, ≈39% of the wells would be expected to contain at least one molecule of the locus.
For each cell of this trisomy 21 fetus, the genomic ratio of chromosome 21 to chromosome 1 would be 3:2. The ratio between chromosomes 21 and 1 in the DNA sample would be dependent on the fractional fetal DNA concentration (fetal DNA %) and would be 3 ´ fetal DNA % + 2 (1  fetal DNA %) : 2 ´ fetal DNA % + 2 ´ (1  fetal DNA %). Thus, in this case, when the fractional fetal DNA concentration is 50%, the ratio would be (3 ´ 50% + 2 ´ 50%)/(2 ´ 50% + 2 ´ 50%) = 1.25.
Hence, when the average concentration of the chromosome 1 locus per well is 0.5, the average concentration of the chromosome 21 locus per well is 1.25 ´ 0.5 = 0.625.
Accordingly, the probability of any well not containing any molecule of the chromosome 21 locus when its average concentration is 0.625 per well would be the following:
_{} = = 0.5353.
Hence, the probability of any well containing at least one molecule of the chromosome 21 locus would be 1  0.5353 = 0.4647. Therefore, ≈46% of the wells would be expected to contain at least one molecule of the locus.
Assuming that the filling of the wells with either loci is independent, the probability of a well containing both loci would be 0.3935 ´ 0.4647 = 0.1829. Therefore, ≈18% of the wells would be expected to contain both loci.
The proportion of wells expected to contain the chromosome 1 locus, but not the chromosome 21 locus, would be the number of wells containing at least one chromosome 1 locus deducted by the number of wells containing both loci: 0.3935  0.1829 = 0.2106.
Similarly, the proportion of wells expected to contain the chromosome 21 locus, but not both loci, would be 0.4647  0.1829 = 0.2818.
An informative well is defined as a well positive for either the chromosome 1 locus or the chromosome 21 locus but not both.
Hence, the expected chromosome 21 to chromosome 1 ratio in digital RCD analysis is 0.2818/0.2106 = 1.34. In other words, the proportion of wells positive only for the chromosome 21 locus is 1.34 times that of wells positive only for the chromosome 1 locus. This is in contrast to the ratio of 1.25 in the DNA sample.
For SPRT analysis, the proportion of the informative wells positive for the chromosome 21 locus, P_{r}, would need to be calculated and interpreted by using SPRT curves. In the current example, the proportion of informative wells would be 0.2106 + 0.2818 = 0.4924.
Hence, the expected P_{r} of a trisomy 21 subject with 50% fetal DNA at m_{r} 0.5 is 0.2818/0.4924 = 0.57.
Because the average template concentration, m, is a key parameter in the Poisson equation, the P_{r} would vary with m. SI Table 4 tabulates the expected P_{r} for the fractional fetal DNA concentrations of 10%, 25%, 50%, and 100% in trisomy 21 samples at a range of template concentrations expressed as the average reference template concentration per well, m_{r}.
Construction of SPRT Curves. SPRT allows testing of the hypothesis as data accumulate (3, 4). In digital PCR analysis for trisomy 21 detection, the null hypothesis is that there is no allelic or chromosomal imbalance (i.e., trisomy 21 is not detected). The alternative hypothesis is that allelic or chromosomal imbalance exists (i.e., trisomy 21 is detected). Operationally, SPRT is applied and interpreted through the use of graphs with a pair of SPRT curves (Fig. 2A) that are constructed to define the probabilistic boundaries of accepting or rejecting either hypothesis. The SPRT curves plot the required P_{r} (y axis) for a given total number of informative wells (x axis) when confident classification could be made. As depicted in Fig. 2A, the upper curve sets the probabilistic boundaries for accepting the alternative hypothesis while the lower curve sets the probabilistic boundaries for accepting the null hypothesis.
The equations for calculating the upper and lower boundaries of the SPRT curves are adapted from El Karoui et al. (5). Furthermore, the level of statistical confidence preferred for accepting or rejecting the null hypothesis could be varied through adjusting the threshold likelihood ratio in the equations. In this study, a threshold likelihood ratio of 8 was used because this value had been shown to provide satisfactory performance in the discrimination of samples with and without allelic imbalance in the context of cancer detection (3, 4). In future studies, the use of different likelihood ratios could be evaluated and compared. The equations for calculating the upper and lower boundaries of the SPRT curves are as follows:
upper boundary = [(ln 8)/N  ln d]/ln g
and
lower boundary = [(ln 1/8)/N  ln d]/ln g,
where d = (1  q_{1})/(1  q_{0})
and
g = q_{1}(1  q_{0})/q_{0}(1  q_{1}).
q_{0} is the proportion of informative wells containing the nonreference allele if the null hypothesis is accepted and is equal to 0.5 (see below). q_{1} is the proportion of informative wells containing the nonreference (i.e., overrepresented) allele if the alternative hypothesis is accepted. N is the number of informative wells or the number of wells positive for either allele only. ln is a mathematical symbol representing the natural logarithm (i.e., log_{e}).
Determination of q_{0}. For the null hypothesis, the sample is assumed to be obtained from a pregnant woman carrying a euploid fetus. Under this assumption, the expected number of wells positive for either template would be 1:1, and, thus, the expected proportion of informative wells containing the nonreference allele would be 0.5.
Determination of q_{1}. For the alternative hypothesis, the sample is assumed to be obtained from a pregnant woman carrying a trisomy 21 fetus. The calculations for the expected P_{r} of trisomy 21 samples for digital RNA SNP and digital RCD analyses are detailed in SI Tables 3 and 4, respectively. Hence, q_{1} for digital RNA SNP analysis refers to the data shown in the last column of SI Table 3. q_{1} for digital RCD analysis of samples with varying fetal DNA fractional concentrations can be obtained from the columns showing the corresponding expected P_{r} values in SI Table 4.
Use of SPRT Curves. As detailed in SI Tables 3 and 4, the expected P_{r} for a trisomy 21 sample would be dependent on the average template molecule concentration per well. We describe the template concentration based on the reference allele, i.e., the average reference template concentration per well, m_{r}. As shown in the above equation, the expected P_{r} determines the plotting of the upper SPRT curve. Because the expected P_{r} is in turn dependent on the m_{r} (SI Tables 3 and 4), the plotting of the upper SPRT curve would thus be essentially dependent on the m_{r}. Thus, in practice, a set of SPRT curves relevant for the actual m_{r} of a digital PCR data set would need to be used for the interpretation of the P_{r} from that particular run. The practical manner for interpreting the digital PCR data by using SPRT is illustrated below, using a hypothetical digital RNA SNP run.
After digital RNA SNP analysis of each case, the number of wells positive for the A allele only, the G allele only, or both alleles is counted. The reference allele is defined as the allele with the smaller number of positive wells. m_{r} is calculated by using the total number of wells negative for the reference allele, irrespective of whether the other allele is positive, according to the Poisson probability density function (6). The data of our hypothetical example are as follows.
In a 96well reaction, 20 wells are positive for the A allele only, 24 wells are positive for the G allele only, and 33 wells are positive for both alleles. The A allele is regarded as the reference allele because there are fewer Apositive than Gpositive wells. The number of wells negative for the reference allele is 96  20  33 = 43. Therefore, m_{r} can be calculated by using the Poisson equation: ln(43/96) = 0.80. The experimentally determined P_{r} of this case is 24/(20 + 24) = 0.55.
According to SI Table 3, the expected P_{r} of a trisomy 21 sample at an m_{r} value of 0.8 is 0.76. Thus, q_{1} is 0.76 for this sample. The SPRT curves based on a q_{1} of 0.76 would be used to interpret the experimentally derived P_{r} of this sample, which is 0.55. When a P_{r} value of 0.55 is fitted onto the relevant SPRT curves, the data point falls under the lower curve. Hence, the case is classified as euploid (Fig. 2A).
In summary, after a digital PCR run is completed, the wells positive for either template only and those positive for both templates are counted. The m_{r} and P_{r} are calculated by using the experimental data. The m_{r} determines the set of SPRT curves to be used. The P_{r} is then fitted onto the relevant SPRT curves for interpretation and disease classification.
Computer Simulation of Classification Accuracy. The computer simulation was performed with SAS 9.1 for Windows software (SAS Institute). Simulations of 384well digital RNA SNP analyses were performed for m_{r} values ranging from 0.1 to 2.0. Simulations for digital RCD analyses were performed at a fixed m_{r} of 0.5 for samples containing 10%, 25%, 50%, and 100% fetal DNA at total well numbers ranging from 384 to 7,680.
For each digital PCR condition simulated (i.e., m_{r}, fetal DNA fractional concentration, and total well number), two rounds of simulation were performed. The first round simulated the scenario in which the tested samples were obtained from pregnant women carrying euploid fetuses. The second round simulated the scenario in which the tested samples were obtained from pregnant women carrying trisomy 21 fetuses. For each round, 5,000 fetuses were tested.
Simulation of Digital RNA SNP Analysis. The simulation data were generated as described in the following steps.
(i) For each well, two random numbers were generated by using the Random (Poisson) function of the SAS program to represent the A and the G alleles, respectively. The Random (Poisson) function would generate positive integers starting from 0 (i.e., 0, 1, 2, 3, ...), and the probability of each integer being generated was dependent on the probability of this number according to the Poisson probability density function for a given mean value, which represented the average concentration of the alleles per well. A well was regarded as positive for the A allele if the random number representing the A allele was larger than zero, i.e., contained one or more molecules of the A allele. Similarly, the well was regarded as positive for the G allele if the random number representing the G allele was larger than zero.
To simulate the scenario of a pregnant woman carrying a euploid fetus, the same mean value was used for generating the random numbers for the A allele and the G allele. For example, in the analysis simulating digital RNA SNP analyses at an m_{r} value of 0.5, the mean value for either the A allele or the G allele was set identically at 0.5, which meant an average concentration for either allele of 0.5 molecules per well. When using the Poisson equation, at a mean concentration of 0.5, the proportion of wells being positive for the A or the G alleles would be the same and was 0.3935 (SI Table 3).
When simulating the digital RNA SNP analysis of a pregnant woman with a trisomy 21 fetus at an m_{r} value of 0.5, the average concentration of the overrepresented allele per well would be expected to be 2 times that of the reference allele, i.e., one. In this situation, the probability of a well being positive for the overrepresented allele was 0.6321 (SI Table 3).
After generating a random number for a digital PCR well, the well could be classified as having one of the following statuses: negative for both the A and G alleles, positive for both the A and G alleles, positive for the A allele but negative for the G allele, or positive for the G allele but negative for the A allele.
(ii) The first step was repeated until the desired number of wells, 384 wells for the current simulation, had been generated. The numbers of wells positive for the A allele only and the G allele only were counted. The allele with fewer positive wells was regarded as the reference allele, and the allele with more positive wells was regarded as the potentially overrepresented allele. The number of the informative wells was the total number of wells positive for only one allele. The proportion of informative wells containing the potentially overrepresented allele, P_{r}, was then calculated. The upper and lower boundaries for the relevant SPRT curves to accept or reject the null or alternative hypothesis were calculated as described above.
(iii) Five thousand simulations were performed for each of the two scenarios, the pregnant woman carrying a euploid or a trisomy 21 fetus. Each simulation could be regarded as an independent biological sample obtained from pregnant women. In SI Table 7, the correct classification of euploid cases refers to those euploid cases in which the null hypothesis was accepted, and the incorrect classification of euploid cases refers to those euploid cases in which the alternative hypothesis was accepted. Similarly, those trisomy 21 cases in which the alternative hypothesis was accepted were regarded as correctly classified and those trisomy 21 cases in which the null hypothesis was accepted were regarded as incorrectly classified. For both groups, those cases in which neither the null nor alternative hypothesis was accepted after the prespecified total number of wells had been simulated were regarded as unclassified.
(iv) The first through third steps were performed for m_{r} values ranging from 0.1 to 2.0 at increments of 0.1.
Simulation of Digital RCD Analysis. The procedures for simulating digital RCD analyses were similar to those described for digital RNA SNP analysis. The steps for the simulations are described below.
(i) Two random numbers under the Poisson probability density function were generated to represent the reference locus, chromosome 1, and the chromosome 21 locus. For subjects carrying euploid fetuses, the average concentrations of both the chromosome 1 and chromosome 21 loci were the same. In this simulation analysis, an average template concentration of 0.5 for each locus per well was used. For subjects carrying trisomy 21 fetuses, the m_{r} in this simulation was 0.5, but the average concentration of the chromosome 21 locus per well would depend on the fractional fetal DNA concentration in the tested sample (SI Table 4). The distribution of the reference and/or the chromosome 21 loci to a well was determined by the random numbers representing the respective locus, which were generated according to the Poisson probability density function with the appropriate average concentration of the locus per well.
(ii) The first step was repeated until the desired number of wells had been generated, e.g., 384 wells for a 384well plate experiment. The numbers of wells positive for chromosome 1 only and chromosome 21 only were counted. The number of the informative wells was the total number of wells positive for either one of the chromosomes but not both. The proportion of informative wells positive for chromosome 21, P_{r}, was then calculated. The upper and lower boundaries of the relevant SPRT curves to accept or reject the null or alternative hypothesis were calculated as described above.
(iii) Five thousand simulations were performed for each of the two scenarios, the pregnant woman carrying a euploid or a trisomy 21 fetus. Each simulation could be regarded as an independent biological sample obtained from pregnant women. In SI Tables 8 and 9, the correct classification of euploid cases refers to those euploid cases in which the null hypothesis was accepted, and the incorrect classification of euploid cases refers to those euploid cases in which the alternative hypothesis was accepted. Similarly, those trisomy 21 cases in which the alternative hypothesis was accepted are regarded as correctly classified, and those trisomy 21 cases in which the null or alternative hypothesis was accepted were regarded as incorrectly classified. For both groups, those cases in which the null hypothesis was neither accepted nor rejected after the prespecified total number of wells had been simulated were regarded as unclassified.
(iv) The first three steps were repeated for samples with 10%, 25%, 50%, and 100% fetal DNA at total well numbers ranging from 384 to 7,680.
1. Lo YMD, Tsui NBY, Chiu RWK, Lau TK, Leung TN, Heung MM, Gerovassili A, Jin Y, Nicolaides KH, Cantor CR, et al. (2007) Nat Med 13:218223.
2. Deutsch S, Choudhury U, Merla G, Howald C, Sylvan A, Antonarakis SE (2004) J Med Genet 41:908915.
3. Zhou W, Galizia G, Lieto E, Goodman SN, Romans KE, Kinzler KW, Vogelstein B, Choti MA, Montgomery EA (2001) Nat Biotechnol 19:7881.
4. Zhou W, Goodman SN, Galizia G, Lieto E, Ferraraccio F, Pignatelli C, Purdie CA, Piris J, Morris R, Harrison DJ, et al. (2002) Lancet 359:219225.
5. El Karoui N, Zhou W, Whittemore AS (2006) Stat Med 25:31243133.
6. Daser A, Thangavelu M, Pannell R, Forster A, Sparrow L, Chung G, Dear PH, Rabbitts TH (2006) Nat Methods 3:447453.