Page 1

Comparison of microfluidic digital PCR and

conventional quantitative PCR for measuring

copy number variation

Alexandra S. Whale1, Jim F. Huggett1,*, Simon Cowen1, Valerie Speirs2, Jacqui Shaw3,

Stephen Ellison1, Carole A. Foy1and Daniel J. Scott1

1LGC Limited, Queens Road, Teddington, Middlesex TW11 0LY,2Leeds Institute of Molecular Medicine,

University of Leeds, St. James’s University Hospital, Leeds LS9 7TF and3Cancer Studies & Molecular

Medicine, University of Leicester, Robert Kilpatrick Clinical Sciences Building, Leicester Royal Infirmary,

Leicester LE2 7LX, UK

Received January 5, 2011; Revised and Accepted February 14, 2012

ABSTRACT

One of the benefits of Digital PCR (dPCR) is the

potentialforunparalleled

smaller fold change measurements. An example of

anassessmentthatcould

improved precision is the measurement of tumour-

associated copy number variation (CNV) in the cell

free DNA (cfDNA) fraction of patient blood plasma.

To investigate the potential precision of dPCR and

compare it with the established technique of quan-

titative PCR (qPCR), we used breast cancer cell lines

toinvestigateHER2gene

modelled a range of different CNVs. We showed

that, with equal experimental replication, dPCR

could measure a smaller CNV than qPCR. As

dPCR precision is directly dependent upon both

the number of replicate measurements and the

template concentration,

method to assist the design of dPCR experiments

formeasuringCNV.Using

(based on Poisson and binomial distributions) to

derive an expression for the variance inherent in

dPCR, we produced a power calculation to define

the experimental size required to reliably detect a

given fold change at a given template concentration.

This work will facilitate any future translation of

dPCR to key diagnostic applications, such as

cancer diagnostics and analysis of cfDNA.

precisionenabling

benefitfromsuch

amplificationand

wealsodevelopeda

anexistingmodel

INTRODUCTION

A key measurement challenge in diagnostic research

involves identifying small changes in gene dosage or

nucleic acid sequence that are commonly associated with

genetic diseases. Copy number variations (CNVs) are

changes in the genomic DNA leading to an abnormal

number of copies of a DNA sequence (usually two

copies per diploid genome). CNVs are caused by deletions,

duplications or structural rearrangements of the genome.

CNVs are involved in a large number of complex human

diseases such as Down’s syndrome (trisomy 21) and many

cancers, for example HER2 gene amplification in breast

cancer (BC) (1–5). CNV measurements are used for

routinescreeninginclinical

analysis can assist in subsequent prognostic monitoring

(6,7). Clinical diagnostic methods currently include fluor-

escence in situ hybridization (FISH), comparative genome

hybridisation (CGH), single nucleotide polymorphism

(SNP) arrays, deep sequencing and real-time quantitative

PCR (qPCR) (8–10).

Quantitative PCR (qPCR) is currently the most sensi-

tive approach able to resolve ?1.5-fold changes (11,12).

The discovery of cell free DNA (cfDNA) in blood plasma

has provided a simple source of genetic material for

pre-natal and tumour diagnosis (13–18) that could poten-

tially enable routine minimally invasive sampling for

subsequent CNV analysis. qPCR has recently identify

amplified HER2 molecules in breast cancer patients

with good correlation between the levels of amplification

detected in the primary tumour and cfDNA (19).

However, as only a proportion of the cfDNA is derived

from the embryo or tumour, identification of an

associated CNV is more challenging as the target DNA

is effectively ‘diluted’ in a background of normal DNA.

Consequently, a tumour-associated 5-fold increase in

CNV becomes a 1.2-fold increase if only 5% of the

cfDNA sample is derived from the tumour; this magnitude

of CNV would be undetectable by current approaches.

One method that has shown promise for improving the

limit of detection for nucleic acid quantification is digital

PCR (dPCR) with a number of reports highlighting the

diagnosticsandtheir

*To whom correspondence should be addressed. Tel: +44 20 8943 7655; Fax: +44 20 8943 2767; Email: jim.huggett@lgcgroup.com

Published online 28 February 2012Nucleic Acids Research, 2012, Vol. 40, No. 11e82

doi:10.1093/nar/gks203

? The Author(s) 2012. Published by Oxford University Press.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/

by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Page 2

superior accuracy of dPCR for CNV analysis (20,21).

dPCR has been reported to detect a 1.25-fold difference

in copy number (21); however, to our knowledge, no direct

comparison between qPCR and dPCR has been per-

formed to ascertain if the latter is more sensitive.

Another aspect that is not extensively addressed in the

literature is that the ability of dPCR to measure small

CNVs is directly dependent upon template concentration.

This is a crucial consideration when considering cfDNA as

a template as its concentration can range considerably;

from 2 to 30ng/ml plasma in healthy individuals to

180–600ng/ml plasma both during pregnancy and in

cancer patients (13,16,18,22–24).

This study aimed to investigate this further using an

in vitro BC gene amplification model to identify when

a CNV is too small to be measured by qPCR and

dPCR. Subsequently, we developed a model, based on

the Poisson and binomial distributions, to determine the

variance inherent in dPCR, and used this to perform

power calculations which demonstrate the effects of the

DNA-template concentration on the sensitivity of CNV

measurements.

MATERIALS AND METHODS

DNA samples

Genomic DNA (gDNA) from three BC cell lines with

different levels of HER2 gene amplification were used;

high-HER2 amplification (SK-BR-3; ATCC HTB-30),

low-level HER2 gain (T-47D; ATCC HTB-133) and one

with a single HER2 allele deletion (MCF-7; ATCC

HTB-22). Control experiments were performed using

commercially available gDNA from pooled healthy

females that have two copies of each gene per diploid

genome (Promega G1521). gDNA concentrations were

determined by A260 measurements (Nanodrop, Thermo

Scientific) and purity was measured by A260/A280measure-

ment (all gDNA samples were between 1.93 and 1.96).

Haploid copy number dilutions were calculated based on

the molecular weight of one normal haploid female

genome equalling 3.275 pg.

Gene-specific assays

The TaqMan?copy number reference assay (Applied

Biosystems 4401631) contained 900nM each of RNase

P-specific forward and reverse primers and 250nM of a

VIC dye-labelled TAMRA hydrolysis probe. The RNase

P amplicon sequence was confirmed by clonal sequencing

(LGC Genomics; Supplementary Figure S1a). The HER2

assay, targeting intron 5 of the HER2 gene on chromo-

some 17q21.1, contained 900nM each of forward

(50-AAG CTA AGA AAT AAG GCC AGA TGG-30)

and reverse (50-CGC ACA GCA CCA AGG AAA

AG-30) primers and 200nM of hydrolysis probe (50

FAM-CAG CAG AAC

CCT-BHQ1 30) (20) (SIGMA). The amplification of a

single PCR product for both the RNase P and HER2

assays was confirmed using the 2100 Bioanalyzer and

DNA 1000 kit according to the manufacturer’s instruc-

tions (Agilent; Supplementary Figure S1b).

AACGCA GCCCTC

Real-time quantitative PCR

Real-time quantitative PCR was performed in accordance

with the MIQE guidelines (Supplementary Table S1 and

Supplementary Figure S1) (25). Ten microlitres reactions

contained 1? TaqMan?gene expression mastermix (ABI

4369016), 1? gene-specific assay and 2ml target DNA.

qPCR was performed using the Prism 7900HT Real

Time PCR system (ABI). Thermocycling conditions were

95?C for 10min, followed by 40 cycles of 95?C for 15s and

60?C for 60s. Quantification was performed with the

standard curve method using five standard dilutions, in

triplicate, of normal female gDNA ranging from 16.50

to 0.33ng (5000 to 100 haploid genome copies) per

reaction. Due to the differences in molecular weight

between the BC cell line gDNA, triplicate reactions were

performed on a range of gDNA concentrations (16.50 to

0.33ng per reaction) for HER2 and RNase P assays. This

allowed identification of the gDNA concentration that fell

within the range of the qPCR standard curves for both

HER2 and RNase P assays. Subsequently, eight HER2

and eight RNase P reactions (16 reactions in total) were

performed on the optimum weight of gDNA for each cell

line (normal female: 0.71ng, MCF-7: 0.60ng, SK-BR-3:

0.94ng and T-47D: 1.45ng). The SDS software v2.4 (ABI)

was used to calculate the quantification cycle (Cq) value,

that is defined as the number of cycles at which the fluor-

escence signal is significant above the threshold, which was

converted to copy number using the relevant standard

curve. Replicate HER2:RNase P ratios were calculated

by randomly pairing HER2 and RNase P copy numbers

and calculating the 95% confidence intervals (CI) from the

standard error of the mean and the two-tailed Student’s

t-test. No template control (NTC) reactions were per-

formed using water with no template; in all cases, no amp-

lification occurred (Supplementary Figure S1c and S1d).

Digital PCR

About 4.5ml reactions containing 1? TaqMan?gene

expression mastermix, 2? GE sample loading reagent

(Fluidigm 85000746), 1? gene-specific assay and 1.35ml

target gDNA was pipetted into each loading inlet of a

48.770 digital PCR array (Fluidigm). The BioMark IFC

controller MX (Fluidigm, San Francisco, CA) was used to

uniformly partition the reaction from the loading inlet

into the 770?0.84 nl chambers. dPCR was performed

usingtheBioMarkSystem

(Fluidigm). Thermocycling conditions were set as for

qPCR. For BC cell line gDNA analysis, reactions were

performed in quadruplicate panels for HER2 and RNase

P assays (eight panels in total) on 0.6ng BC cell line

gDNA, estimated using A260measurements. The Digital

PCR Analysis software (Fluidigm) was used to set the Cq

threshold and range (Supplementary Figure S2), and to

count the number of positive chambers (H) out of the

total number chambers (C) from which the Poisson distri-

bution was used to estimate the average number of mol-

ecules per chamber (l) so that l=?ln (1 ? H/C) (26).

HER2:RNase P ratio (lt/lr) and 95% CI were calculated

as described in this publication (Table 1). NTC reactions

were performed using water with no template; in all cases,

forGeneticAnalysis

e82 Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 2 OF 9

Page 3

no positive chambers were observed (Supplementary

Figure S2).

Establishment and analysis of copy number

variation ratios

The in vitro gene amplification model was established

by spiking T-47D gDNA into normal female gDNA at

various percentages to generate a theoretical range of

HER2:RNase P ratios between 1.00 and 2.00 based on

the dPCR analysis (Supplementary Table S2). All ratios

were diluted to give approximately 720 RNase P copies/ml.

For qPCR, four replicates were performed per ratio for

both HER2 and RNase P assays in two independent

experiments (16 reactions in total). All CNV ratios were

calculated by conversion of Cq values to copy numbers of

HER2 and RNase P using a standard curve generated

from five dilutions, in triplicate, of normal female

gDNA ranging from 1,000 to 20 haploid genome copies/

ml (Supplementary Figure S1c and S1d). For dPCR, four

panels were performed per ratio for both HER2 and

RNase P assays in two independent experiments (16

panels in total) to give approximately 155 RNase

P copies per panel (lr=0.2) where one panel on a

48.770 dPCR array contains 0.195ml of template. CNV

ratios were calculated using the equations described in

this paper (Table 1).

To investigate the number of dPCR panels (containing

770 chambers each) needed

differences, a pseudo-random number generator (the

‘Math.random()’ method in JavaScript) was used to

assign a number to each HER2 and RNase P panel. In

each case, the required numbers of panels were selected

from the eight panel data set.

to detectsmall ratio

Statistical analysis and power calculations

Statistical analysis was performed using the MS Office

Excel software (2003). Statistical comparisons to establish

CNV limit of measurement were performed using

the one-way analysis of variance test to compare the

RNase P counts (dPCR) or copy number (qPCR)

between the samples (in vitro gene amplification model

ratio). Two-way analysis of variance was used to test for

differences in the mean copy number between the respect-

ive replicate qPCR experiments. The two-tailed Student’s

t-test was used to analyse the difference in HER2 counts

or copy number between the sample and the calibrator

(normal female gDNA). Power and associated calcula-

tions reported in this paper were carried out using the R

statistical programming language (version 2.13, http://

www.r-project.org). All scripts were written and run on

a standard desktop personal computer (Optiplex, Dell

Corporation). Further details of the methods and theory

are given in the Statistical Supplementary Information.

RESULTS

CNV measurement by dPCR and comparison with qPCR

In order to investigate the accuracy of dPCR for CNV

measurement, we used three BC cell lines with different

HER2 gene copy number as a model of gene amplification.

The RNase P assay was used as the reference gene for the

diploid control. Assay optimization was performed using

qPCR for HER2 and RNase P assays (Supplementary

Figure S1). For dPCR, absolute quantification of HER2

and RNase P molecules were calculated from the number

of positive counts per panel based on the Poisson distri-

bution for the number of molecules in each chamber

(Figure 1a).

dPCR analysis of normal female gDNA had a

HER2:RNase P ratio of 1.03 and was not significantly

different from qPCR analysis that had a HER2:RNase P

ratio of 1.00 (P=0.39; Figure 1b). Analysis of MCF-7

gDNA, which has a single HER2 allele deletion, gave a

ratio of 0.44 by both dPCR and qPCR. T-47D gDNA,

which has low-HER2 copy gain had a HER2:RNase P

ratio of 2.00 and 1.96 for dPCR and qPCR, respectively.

There was no significant difference in HER2:RNase P

ratios between the two techniques when measuring

Table 1. Summary of equations derived in this study

DescriptionSymbolEquation Equation in MS ExcelWorked example

Number of chambers analysed

Number of positive chambers for reference

Number of positive chambers for target

Number of reference molecules per chamber

Number of target molecules per chamber

Log ratio estimate

C

Hr

Ht

lr

lt

R

770

140

180

0.201

0.266

0.283

?ln (1 ? Hr/C)

?ln (1 ? Ht/C)

ln (lt/lr)

1 ? e??t

C?2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C?2

R+1:960?R

R ? 1:960?R

eR

eRCI-H

eRCI-L

?ln(1 ? (Hr/C))

?ln (1 ? (Ht/C))

ln (lt/lr)

Variance for Log ratio estimate

?R2

te??t+1 ? e??r

C?2

re??r

(1 ? EXP(?lt))/(C?lt2* EXP(?lt))

+(1 ? EXP(?lr))/(C * lr2 * EXP(?lr))

SQRT(sR2)

0.002

Standard deviation for Log ratio estimate

?R

1 ? e??t

te??t+1 ? e??r

C?2

re??r

s

0.040

Log ratio 95% CI (one-tailed) - high

Log ratio 95% CI (one-tailed) - low

Ratio

Ratio 95% CI (one-tailed) - high

Ratio 95% CI (one tailed) - low

RCI-H

RCI-L

R

RCI-H

RCI-L

R+NORMSINV(0.975) * sR

R+NORMSINV(0.025) * sR

EXP(R)

EXP(RCI-H)

EXP(RCI-L)

0.361

0.205

1.327

1.435

1.227

For equations in MS Excel, an ‘equals’ sign must be inserted before the formula and symbols should be replaced with the experimental values.

A worked example is provided, with the values used to generate the variance model and to ensure correct equations are transferred

PAGE 3 OF 9Nucleic Acids Research,2012, Vol.40, No. 11e82

Page 4

MCF-7 (P=0.71) and T-47D (P=0.52). SK-BR-3

gDNA, which has high HER2 gene amplification, had a

HER2:RNase P ratio of 7.15 when measured by dPCR

which was significantly lower than the HER2:RNase P

ratio 9.43 observed by qPCR (P=0.00005). For all meas-

urements, the 95% CIs were slightly larger for dPCR,

where four dPCR panels were analyzed, when compared

with qPCR, where eight reaction wells were analyzed

(Figure 1b).

Limit of detection for analysing copy number variations

To determine the limit of detection for analysis of CNVs

by dPCR, an in vitro gene-amplification model was used,

whereby T-47D gDNA was spiked into normal female

gDNA to generate a theoretical range of HER2:RNase P

ratios between 1.00 and 2.00 at low copy number (2.1ng/

ml) for analysis using dPCR and qPCR (Supplementary

Table S2). Using dPCR, a ratio of 1.17 or more was sig-

nificantly different from the experimentally derived

normal female gDNA ratio of 1.03 (P<0.0003) when

eight panels where used (Figure 2a). There was good

linear correlation between the expected and the observed

ratios when measuring a CNV of ?1.17 (R2=0.9974) and

this linear correlation was maintained when the line was

extrapolated through the observed ratio for normal female

gDNA (Figure 2a; dashed line). Furthermore, the slope

and intercept of the linear correlation were measured as

1.05 and 0.05, respectively, demonstrating the accuracy in

the measured ratios, and that no bias was introduced. An

expected ratio of 1.12 was not significantly different from

normal female gDNA when using eight panels (P=0.67;

Figure 2a). In all cases, the RNase P counts observed for

each measurement were not significantly different from

oneanother(P?0.75).

gene-amplification model with qPCR demonstrated that

ratios of 1.27 or more were significantly different from

Analysingthein vitro

Real-time PCR

R2 = 0.9949

y = 1.01x + 0.0003

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

Expected ratio

Observed ratio (95% CI)

(a)

(b)

Digital PCR

R2 = 0.9949

y = 1.05x - 0.05

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

0.81.01.21.41.61.8 2.0

0.81.01.21.41.61.82.0

Expected ratio

Observed ratio (95% CI)

†

†

Figure 2. Determination of CNV detection of digital and quantitative

real-time PCR. Quantitation of HER2:RNase P ratios using (a) dPCR

and (b) qPCR generated from the in vitro gene-amplification model.

The x-axis shows the expected HER2:RNase P ratio and the y-axis

shows the observed HER2:RNase P ratios with the 95% CI. (a) For

dPCR, four panels for each assay were analyzed for ratios>1.5

(daggered symbol) and eight panels for each assay for ratios <1.5. In

all cases, lrwas approximately 0.2. The error bars represent the 95%

CIs. (b) For qPCR, eight reactions were performed for each assay and

all ratios. The error bars represent the 95% CIs calculated from the

standard error of the mean and associated T-value with 95% confi-

dence and seven degrees-of-freedom. Key: black triangle: normal

female gDNA, black diamond: significantly different from normal

female gDNA (P<0.05), gray diamond: not significantly different

from normal female gDNA (P>0.05). Solid line of linear correlation

is shown for those ratios that were significantly different from normal

female gDNA. Dashed line is the extrapolation of the linear correlation

showing intersection with HER2:RNase P ratio of 1.0. R2and equa-

tions are given for the linear correlation.

Normal

Female

MCF-7

SK-BR-3

T-47D

NTC

2REHPe s aNR

(a)

90

62

62

141

0

92

347

115

62

0

0.0

0.1

1.0

10.0

HER2:RNaseP (95% CI)

Log scale

Normal

Female

MCF-7SK-BR-3T-47D

Real-time PCR

Digital PCR

(b)

*

Figure 1. Comparison of HER2:RNase P ratio in breast cancer cell

line genomic DNA using digital and quantitative real-time PCR.

(a) Software-generated heat map showing a single panel in a 48.770

dPCR array that contains 770 chambers with positive (white) and

negative (black) amplification signals. One representative dPCR panel

is shown for each gDNA sample and assay with the number of positive

chambers shown in the top right corner of the panel. Positive and

negative chambers were used to calculate the number of molecules

per panel and the HER2:RNase P ratio for the gDNA sample. The

NTC panels for both assays had no positive chambers. (b) qPCR (n=8

wells) and dPCR (n=4 panels) gave similar HER2:RNase P ratios for

all BC gDNA except the SK-BR-3 gDNA that was significantly higher

by qPCR compared with dPCR (asterisk). Data is presented on a log

scale and error bars represent 95% CIs.

e82Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 4 OF 9

Page 5

normal female gDNA (P<0.0005) and maintained a

linear correlation (R2=?0.99; Figure 2b; dashed line).

As was observed with the dPCR analysis, the observed

ratios were accurate with no introduced bias as shown

by the slope (1.01) and intercept (<0.001) of the linear

correlation. Ratios of ?1.22 did not differ significantly

from female gDNA (P>0.05; Figure 2b). As with

dPCR, in all cases, the RNase P counts observed for

each measurement were not significantly different from

one another (P?0.27). Furthermore, no statistically sig-

nificant inter-run variability was observed for either the

RNase P or the HER2 assays (P?0.99 and P?0.15,

respectively).

Determination of the number of dPCR panels needed to

confidently detect small changes in copy number variation

From our data, when the CNV to be measured is

>1.5-fold, then four dPCR panels were sufficient while

CNVs<1.5-fold could be detected with up to eight

dPCR panels (Figures 1b and 2a). As CNVs of <1.17

were not measurable using eight dPCR panels, it would

be useful to be able to predict how many dPCR panels

would be needed to detect such small CNVs. For such a

prediction, we would need to assess discriminating power,

and therefore, the true copy number difference at which

we would reliably judge two materials to be different. This

was achieved with a statistical power calculation, which

required a test statistic and associated distribution.

The domain of interest in this study involved the refer-

ence RNase P assay adjusted to give an observed number

of positive chambers in the region of 100–200 per panel

(2.1ng/ml) to mimic the low concentration observed in

cfDNA samples (18). Based on the Poisson distribution,

this can be used to estimate the number of molecules per

chamber (l), and in this case, l was approximately 0.2 in a

48.770 dPCR array (Table 1). At this concentration, the

probability P that a chamber will give a positive signal is

1 ? e??and is the same for every chamber (26). The CNV

is the ratio of l estimates for the two groups being

compared and as such, it is highly non-Normal. By

taking the logarithm of the ratio for these two groups

(R), the data is transformed to produce a variable whose

distribution is very close to Normal (Supplementary

Figure S3a) and is given by the equation:

R ¼ ln?t

?r

ð1Þ

where ltand lrcorrespond to the l values of the target

and reference genes, respectively, and l=?ln (1 ? H/C)

[Table 1; (26)]. Consequently, power calculations can be

based on a t-test for a difference in the logarithm of the

observed ratio of target to reference gene from zero.

To calculate power, we first need an expression for

the variance (?2

R) of the log ratio R. This was derived

using first-ordererrorpropagation

Supplementary Information’) and is given here as:

(see ‘Statistical

?2

R?1 ? e??t

C?2

te??t+1 ? e??r

C?2

re??r

ð2Þ

Comparison of the theoretical standard deviation of R

[estimated from Equation (2) as ˇ?2

standard deviation of the experimental data (Figure 2a)

demonstrated good concordance (Supplementary Figure

S3b). With a valid estimate of the variance ?2

ratio, the upper and lower 95% CI can be calculated

(Table 1). Power calculations can also be derived to deter-

mine the number of chambers required for an experiment

capable of detecting a log ratio R with a defined test power

of 1 ? ? and at the 1 ? ? confidence level, where ? and ?

are the false-positive and false-negative rates, respectively.

Our experiment was one in which a positive R was the

expected result (an increase in copy number, so lt>lr),

so a one-tailed test was appropriate. Statistical significance

was declared at a P-value of ? or lower (<0.05) and the

testpower wasequalto

Supplementary Figure S4). Power calculations involving

a test statistic which has a Normal distribution can only be

carried out numerically, as there is no analytical solution

and details of the method are given in the ‘Statistical

Supplementary Information’.

Using the power curve, where lr=0.2, we found that

with 95% power, a fold change of 1.2 was easily detectable

with five 770-chamber panels per gene assay, while ratios

of 1.1 and below required greatly increased numbers of

panels (>15 panels; Figure 3a). Using the curve to

compare the data from the HER2 in vitro gene-

amplification model with the number of panels required

demonstrates that a ?1.17 ratio can be measured with

eight or fewer panels (Figure 3a); this is shown experimen-

tally (Figure 2a). However, from the curve, a ratio of 1.12

was predicted to need more than 10 panels (Figure 3a),

which is supported by our inability to measure with con-

fidence a 1.12 ratio with only eight panels (Figure 2a). Our

power curve predicts that when lris 0.2, the smallest CNV

ratio that could be measured using eight dPCR panels is

approximately 1.15 (Figure 3a). This lies between our two

experimental data points and therefore confirms the fitness

of our model for this template concentration.

To further test the power calculations, each HER2

dPCR panel was randomly paired with an RNase P

panel and the desired number of paired panels (1–8)

were selected and used to calculate their CNV ratio and

associated 95% CI (Figure 3b). Our power curve suggests

that approximately three panels are needed to detect a

ratio of 1.27 when lr=0.2 (Figure 3a) which was experi-

mentally measurable with four or more panels (Figure 3b).

Analysis of a fold difference of 1.17 predicted that

approximately six panels are needed (Figure 3a), which

is concordant with our experimental data (Figure 3b).

Power calculations were also performed for qPCR using

the Student’s t-statistic (see ‘Supplementary Statistical

Information’ for details) and the resulting power curves

demonstrated that ratios greater than 1.25 can be

measured with 95% power and eight replicate qPCR

wells (Supplementary Figure S7). This compared well

with the experimental data generated from the in vitro

gene amplification model where a ratio of 1.27 was

measured with eight qPCR wells but small ratios

were not (Figure 2b). From the power curve, it was

shown that using gDNA at the experimental defined

R] with the observed

Rin the log

95%(where

?=0.05;

PAGE 5 OF 9 Nucleic Acids Research,2012, Vol.40, No. 11e82

Page 6

concentration, an excess of 20 qPCR wells would be

needed to measure ratios of 1.17 or fewer (Supplementary

Figure S7).

DISCUSSION

We have investigated the measurement capabilities of

dPCR when investigating changes in CNV, described the

limit of detection for a given experiment and demonstrate

that dPCR exhibits greater sensitivity than qPCR when

investigating subtle fold-differences. The potential of

cfDNA as a source of template in minimally invasive diag-

nostics is becoming increasingly apparent. The measurable

resolution of qPCR in our gene-amplification model for

cfDNA, which we describe here as a ratio of 1.27, offers a

theoretical diagnostic potential, however, the reality is

that smaller CNVs, where the tumour contribution to

the cfDNA can be as little as 5% of the total cfDNA

(16,17) are still technically out of reach using qPCR.

Furthermore, one of the major differences between

qPCR and dPCR is that technical variability of qPCR

can be high between and within laboratories (27). dPCR

is notably less variable between experiments (28,29), which

offers the possibility of reproducibly more accurate

results. In this study, a CNV ratio of 1.17 was significantly

detected using eight panels and therefore, the ability of

dPCR to detect incrementally smaller fold differences

than qPCR demonstrates the potential of this method

for future CNV clinical diagnostics.

Recently, an error model relating to the 95% theoretical

CI for copy number versus number of chambers was pub-

lished (21). According to this model, approximately 1,200

chambers (equates to 1.5 panels) would be needed to

detect a CNV ratio of 1.25. However, when the authors

performed this in a real experiment, they were unable to

realise this predicted precision, requiring twice the number

of chambers/panels to measure the targeted difference

(21). The authors explain that this was directly due to

the fact that, for their model, they fixed the lrat a value

of 0.6, whereas the real experiment (where lrvalues were

0.18 and 0.37 for their two samples) was below this value

and so did not have sufficient power to resolve the given

difference with the predicted number of chambers.

When we used this model to estimate the number of

chambers needed for our experiments, we found that

this was also underestimated and due to the smaller lr,

which in the case of our experiment was about 0.2.

Weaver and co-workers (21) used the point (in observed

number of panels) at which calculated 95% CIs just

overlap, assuming a Poisson distribution for individual

counts. The point of theoretical CI overlap is an indicator

of discriminating power, in that it increases as precision

degrades and allows comparison

However, basic statistical theory shows that a significant

difference at the 95% confidence level would usually show

substantially overlapping CIs for the two independent

observations. In this case, statistical significance focuses

on the error rate under the null hypothesis; the probability

of wrongly declaring a result significant, or the false-

positive rate. In contrast, we were interested in assessing

discriminating power and therefore, the true copy number

difference at which will we reliably judge two materials to

be different, that is the false-negative rate. Therefore, we

generated a power calculation based on the variance and

false-negative rate of a given measurement of copy

number ratio.

Our power calculation method takes the DNA-template

concentration into consideration using the corresponding

lr and estimating the number of panels required.

Validation of the theory is demonstrated with our experi-

mental data (Figure 3b). Based on this, further theoretical

power curvesforarange

were derived and are given in Supplementary Figure S5

for researchers to use for future experimental design.

From these power curves, we predict that to investigate

a1.25-fold difference,where

(approximate values for lrof 0.18 and 0.37) with 95%

powerrequires afour-

betweensamples.

of

lr

values(0.1–0.8)

lr

is0.2 or0.4

ortwo-panelexperiment,

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

12345678

Ratio (95% CI)

1.27

1.17

1.00

Number of dPCR panels

Number of 770-chamber panels required

0

15

10

5

1.11.3 1.41.56 . 12 . 1

CNV ratio

*

*

****

**

(a)

(b)

Figure 3. Determination of the number of dPCR panels needed to

measure HER2:RNase P ratios. (a) Power curve to determine the

number of panels required to detect different ratios of ltto lr, where

lt>lrwith 95% power at a confidence level of 95% and lr=0.2. The

two horizontal lines show a single-panel and eight-panel experiment

where the intersections with the power curve indicates the lowest de-

tectable CNV. The vertical line shows the smallest CNV detectable is

approximately 1.15 when lr=0.2 and the number of panels is 8.

(b) The relevant number of dPCR panels (1–8) were selected and the

HER2:RNase P ratio and associated 95% CIs were calculated.

The graphs for the different ratios are slightly staggered to allow iden-

tification of the 95% CI error bars for each ratio. Ratios that are

statistically different from the normal female gDNA are shown for

ratios of 1.27 (gray asterisk) and 1.17 (black asterisk).

e82Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 6 OF 9

Page 7

respectively (Supplementary Figure S5), which was con-

sistentwith Weaver and

The power calculations described in this publication are

based on a one-tailed test as we were interested detecting

HER2 amplification (where lt>lr) which has clinical and

prognostic relevance (30,31). Further applications of this

model would include detection of trisomy, e.g. in Down’s

syndrome (32). However, a modification of this model to

include detection of both amplification and deletion of

gene copies would have a wider scope, e.g. in character-

ization of in vitro culture cells over time (33), detection of

polyploidy in plants (34) or as an alternative to CGH

analysis or FISH for cancer diagnostics. Therefore, we

have expanded our model to incorporate a two-tail test

(Supplementary Figure S6).

We also generated power curves for qPCR based on a

one- or two-tailed test (Supplementary Figure S7). These

curves demonstrates that while dPCR appears to detect

only incrementally smaller fold differences than qPCR

using a one-tailed test and eight replicate measurements

(1.17 versus 1.27 in this study), an additional 12 qPCR

wells per assay or more would be needed before qPCR

could potentially measure a similarly small ratio to

dPCR. This is dependent upon the standard deviation of

the qPCR (in this case, was approximately 10% for both

assays across all experiments) as the number of replicates

needed will increase if precision is reduced. The binary

nature of dPCR means that the precision is more inde-

pendent of variation in assay amplification, making it

easier to optimize and standardize between laboratories.

As conventional qPCR is currently approximately one

20th of the expense of an equivalent dPCR analysis, it

does still offer a practical alternative method to measure

smaller CNVs. However, the increased template required

to perform the larger number of replicate measurements

could be a disadvantage where sample is limiting. qPCR

has the benefit of being able to measure lower plasma

template concentration than the dPCR method used

here as its larger reaction volume facilitates the addition

of more template. qPCR is also scalable offering the

option of adding even more template, where sample

permits,by further increasing

reaction. This is not currently possible with the dPCR

approach used here; however, with the development of

higher volume and throughput dPCR methods this

option will also be possible (35–37) with comparable

accuracy (38).

Improvements to qPCR using similar technologies to

those advancing dPCR will increase the throughput of

qPCR, as has already been described (21), although this

is also at the cost of smaller input volume which often

requires pre-amplification (39); this is not routinely

needed for dPCR. It should also be noted that for

qPCR (conventional or high throughput) to measure

such small fold changes, it is not only important that

precise well-optimized assays are used, but it is also essen-

tial that some estimation of efficiency is made (25). This

can be done by standard curves to estimate copy number,

as described here, or by performing efficiency corrected

??Cq (40). However, this fact further complicates using

qPCR for small fold change measurement.

co-workersobservations.

the volumeofthe

Our model also raises the question of why variable

lrshould need to be considered at all when performing

dPCR. The alternative would be to ensure the optimum

concentration in the first place. However, this is only

possible when the sample DNA is at or higher than this

value, and if the concentration is lower than the optimum

lrthen more chambers would be needed, and therefore,

our model would provide an idea of how many. This issue

is applicable when using cfDNA as a template, which is by

nature low in concentration; around 2–30ng/ml blood

plasma in normal healthy humans (13,16–18,22,23),

which corresponds to approximately 600–9900 normal

haploid genomes per ml. Measuring HER2 status using

cfDNA offers considerable potential as a diagnostic and

prognostic test (19,30,31).

Our power calculation provides a good foundation

from which to design subsequent experiments; in our as-

sessment, we have used a high-quality DNA template in

our proof-of-principle experiments to model the cfDNA.

Additional factors that will need to be considered,

building on the findings of this study, include template

integrity, PCR-assay efficiency and the impact of matrix

effects as integral parts of subsequent translational

research, if this approach is to be used in the context of

HER2 and other clinical measurements. Recently, power

calculations based on a multivolume dPCR assays were

generated and demonstrated that different reaction

volumes influence the dynamic range and precision of

dPCR, could minimize the total number of dPCR reac-

tions needed and separated the upper and lower limits of

quantification. This would allow samples of differing con-

centration to be analyzed in parallel without compro-

mising one sample over the other (37).

An additional function of this study was to directly

compare microfluidic dPCR with conventional qPCR for

CNV using the same gDNA template and reaction assays.

Both methods gave similar HER2 CNV results using BC

cell line gDNA with varying numbers of HER2 gene

copies per diploid genome. Two BC cell lines were con-

current with the published data; MCF-7 gDNA, that has

monosomy for chromosome 17 assigned a HER2:RNase P

ratio of<0.5 (one copy per diploid genome) (41,42) and

T-47D gDNA gave a HER2:RNase P ratio of<2 (3–4

copies per diploid genome) (43–46). Analysis of the

SK-BR-3 gDNA identified high levels of HER2 amplifica-

tion that corresponds with the published copy number

range (14–24 copies per diploid genome) (41,43–45,47).

However,there wasa

HER2:RNase P ratio obtained by dPCR (7.15) and

qPCR (9.43).

This difference could be attributed to the large number

of HER2 gene amplifications occurring on the same

molecule (concatamers of HER2 molecules inserted at

the same point in the genome) that are observed in this

cell line using FISH (48,49) but do not occur in the

MCF-7 or T-47D cell lines. Unlike qPCR, dPCR may

be unable to accurately quantify this type of gene ampli-

fication as linked genes cannot be separated into individ-

ual chambers. Qin and co-workers (20) have suggested

that this problem can be overcome by a pre-amplification

step using gene-specific primers to separate the linked

discrepancybetweenthe

PAGE 7 OF 9 Nucleic Acids Research,2012, Vol.40, No. 11e82

Page 8

copies before performing dPCR. However, such a step

requires careful validation because of the potential bias

that can be introduced that may outweigh the necessary

precision for detecting small CNVs (29).

In conclusion, our data suggests as microfluidic dPCR

becomes more established, it will offer a new level of pre-

cision and the clinical benefits of measuring smaller CNVs

in more challenging samples like cfDNA, will become

possible. However, the pre-clinical and translational

research necessary for this to be realized will need to

consider the issues explored by this study. The model we

describe here both provides a mechanism to facilitate this

research and highlights the issues around ensuring the

template concentration is included as a central consider-

ation when preparing CNV studies using dPCR. This will

better enable dPCR experiments to be designed, increasing

the impact of future research.

SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online:

Supplementary Tables 1–2, Supplementary Figures 1–7

and Supplementary Statistical Information.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Dr Malcolm

Burns and Dr Alison Devonshire for critical review of

the manuscript.

FUNDING

The UK National Measurement System. Funding for

open access charge: UK National Measurement System

(UK Government).

Conflict of interest statement. None declared.

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