Counting individual DNA molecules by the
`stochastic attachment of diverse labels
`
`Glenn K. Fu, Jing Hu, Pei-Hua Wang, and Stephen P. A. Fodor1
`
`Affymetrix, Inc., 3420 Central Expressway, Santa Clara, CA 95051
`
`Edited* by Ronald W. Davis, Stanford Genome Technology Center, Palo Alto, CA, and approved March 22, 2011 (received for review November 27, 2010)
`
`We implement a unique strategy for single molecule counting
`termed stochastic labeling, where random attachment of a diverse
`set of labels converts a population of identical DNA molecules
`into a population of distinct DNA molecules suitable for threshold
`detection. The conceptual framework for stochastic labeling is
`developed and experimentally demonstrated by determining the
`absolute and relative number of selected genes after stochastically
`labeling approximately 360,000 different fragments of the human
`genome. The approach does not require the physical separation of
`molecules and takes advantage of highly parallel methods such as
`microarray and sequencing technologies to simultaneously count
`absolute numbers of multiple targets. Stochastic labeling should
`be particularly useful for determining the absolute numbers of
`RNA or DNA molecules in single cells.
`
`absolute counting ∣ digital PCR ∣ next-generation sequencing ∣
`single molecule detection
`
`Determining small numbers of biological molecules and their
`
`changes is essential when unraveling mechanisms of cellular
`response, differentiation or signal transduction, and in perform-
`ing a wide variety of clinical measurements. Although many ana-
`lytical methods have been developed to measure the relative
`abundance of different molecules through sampling (e.g., micro-
`arrays and sequencing), the only practical method available to
`determine the absolute number of molecules in a sample is digital
`PCR (1–3), a powerful analytical technique typically limited to
`examining only a few different molecules at a time.
`In 2003, a theoretical approach to measure the number of
`molecules of a single mRNA species in a complex mRNA pre-
`paration was proposed (4). To our knowledge no experimental
`demonstration of this idea has been published. We have general-
`ized this idea and have expanded it to a highly parallel method
`capable of absolute counting of many different molecules simul-
`taneously. The concept is illustrated in Fig. 1. Each copy of a
`molecule randomly captures a label by choosing from a large,
`nondepleting reservoir of diverse labels. The subsequent diversity
`of the labeled molecules is governed by the statistics of random
`choice, and depends on the number of copies of identical mole-
`cules in the collection compared to the number of kinds of labels.
`Once the molecules are labeled, they can be amplified so that
`simple present/absent threshold detection methods can be used
`for each. Counting the number of distinctly labeled targets
`reveals the original number of molecules of each species.
`We can generalize the stochastic labeling process as follows.
`Consider a given set of copies of a single target sequence
`T ¼ ft1;t2…tng; where n is the number of copies of T. A set of
`labels is defined as L ¼ fl1;l2…lmg; where m is the number of
`different labels. T reacts stochastically with L, such that each t
`becomes attached to one l. If the ls are in nondepleting excess,
`each t will choose one l randomly, and will take on a new identity
`litj; where li is chosen from L and j is the jth copy from the set
`of n molecules. We identify each new molecule litj by its label
`subscript and drop the subscript for the copies of T because they
`are identical. The new collection of molecules becomes T ¼
`fl1t;l2t;…litg; where li is the ith choice from the set of m labels.
`At this point, the subscripts of l refer only to the ith choice and
`
`Identical DNA
`target molecules {t1, t2 …. tn}
`
`Random
`labeling
`
`Amplification and detection
`of k distinctly labeled molecules
`
`Pool of labels
`{l1 , l2 …. lm}
`
`t1
`
`t2
`
`t3
`
`t4
`
`t1l20
`
`t2l107
`
`t3l477
`
`t4l9
`
`Fig. 1. A schematic representation of the labeling process. An example
`showing four identical target molecules in solution. Each DNA molecule ran-
`domly captures and joins with a label by choosing from a large, nondepleting
`reservoir of m labels. Each resulting labeled DNA molecule takes on a new
`identity and is amplified to detect the number of k distinct labels.
`
`provide no information about the identity of each l. In fact, l1 and
`l2 will have some probability of being identical, depending upon
`the diversity m of the set of labels. Overall, T will contain a set
`of k unique labels resulting from n targets choosing from the non-
`depleting reservoir of m labels. Or, T ðm;nÞ ¼ flktg; where k
`represents the number of unique labels that have been captured.
`In all cases, k will be smaller than m, approaching m only when
`n becomes very large. We can define the stochastic attachment
`of the set of labels on a target using a stochastic operator S with
`m members, acting upon a target population of n, such that
`SðmÞTðnÞ ¼ T ðm;nÞ generating the set flktg. Furthermore, be-
`cause S operates on all molecules independently, it can act on
`many different targets. Hence, by combining the information
`of target sequence and label, we can simultaneously count copies
`of multiple target sequences. The probability of the number of
`labels generated by the number of trials n, from a diversity
`of m, can be approximated by the Poisson equation, Px ¼
`½ðn∕mÞx∕x!Še−ðn∕mÞ. Then P0 is the probability that a label will
`not be chosen in n trials, therefore, 1 − P0 is the probability that
`a label will occur at least once. It follows that the expected num-
`ber of unique labels captured is given by:
`
`Author contributions: G.K.F. and S.P.A.F. designed research; G.K.F. and P.-H.W. performed
`research; G.K.F., J.H., and S.P.A.F. analyzed data; and G.K.F., J.H., and S.P.A.F. wrote
`the paper.
`
`Conflict of interest statement: The authors are employees of Affymetrix, Inc. and the
`subject matter of this article may be a future commercial product.
`
`*This Direct Submission article had a prearranged editor.
`
`Freely available online through the PNAS open access option.
`
`1To whom correspondence should be addressed. E-mail: steve_fodor@affymetrix.com.
`
`This article contains supporting information online at www.pnas.org/lookup/suppl/
`doi:10.1073/pnas.1017621108/-/DCSupplemental.
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`9026–9031 ∣ PNAS ∣ May 31, 2011 ∣ vol. 108 ∣ no. 22
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`www.pnas.org/cgi/doi/10.1073/pnas.1017621108
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`label, and counting k is equivalent to counting n. As n increases, k
`increases more slowly as given by Eq. 1. For example, when n∕m
`is approximately 0.01, the counting efficiency, which is defined as
`the ratio of unique labels to molecules k∕n is approximately 0.99,
`and we expect that an increase of 10 molecules will generate 10
`new labels. As n∕m approaches 0.5 (i.e., 480 molecules reacted
`with 960 labels), k∕n becomes approximately 0.79 and six new
`labels are expected with an increase of 10 molecules. At high
`n∕m, k increases more slowly as labels in the set are more likely
`to be captured more than once. The green curve in Fig. 2 shows
`the number of labels chosen exactly once, and the black curve
`shows the number of labels chosen exactly twice as n increases.
`A more complete description of the number of times a label is
`chosen and of the counting efficiency as a function of n is shown
`in Figs. S1 and S2.
`To demonstrate stochastic labeling, we performed an experi-
`ment to count small numbers of nucleic acid molecules in solu-
`tion. We used genomic DNA from a male individual with Trisomy
`21 to determine the absolute and relative number of DNA copies
`of chromosomes X, 4, and 21, representing one, two, and three
`target copies of each chromosome, respectively. The DNA con-
`centration in the stock solution was measured by quantitative
`staining with PicoGreen fluorescent dye, and dilutions containing
`3.62, 1.45, 0.36, and 0.036 ng were prepared. In each dilution, the
`number of copies of target molecules in the sample was calcu-
`lated from a total DNA mass of 3.5 pg per haploid nucleus
`(5), and represent approximately 1,000, 400, 100, and 10 haploid
`genome equivalents. As outlined in Fig. 3A, the genomic DNA
`sample was first digested to completion with the BamHI restric-
`tion endonuclease to produce 360,679 DNA fragments. A diverse
`set of labels consisting of 960 14-nt sequences was synthesized
`as adaptors harboring BamHI overhangs (Table S1). This set
`of labels adequately addresses a broad dynamic range and was
`chosen for favorable thermodynamic properties as described in
`Materials and Methods. For the stochastic labeling reaction, each
`DNA fragment end randomly attaches to a single label by means
`
`At least once
`Exactly once
`Exactly twice
`
`1500
`1000
`500
`Number of target molecules (n)
`
`2000
`
`1000
`
`800
`
`600
`
`400
`
`200
`
`k)
`
`( slebal fo rebmuN
`
`0
`0
`
`Fig. 2. The number of stochastically captured labels for a given number of
`target molecules calculated using a nondepleting reservoir of 960 diverse
`labels. The red curve represents the average number of labels observed at
`least once (calculated from Eq. S1); the green and black curves represent
`the number of labels observed exactly once and twice (calculated from
`Eq. S3), respectively. Error bars indicate one standard deviation (calculated
`from Eqs. S2 and S4) away from the corresponding mean values.
`
`k ¼ mð1 − P0Þ ¼m ½1 − e−ðn∕mފ:
`
`[1]
`
`Given k, we can calculate n. In addition to using the Poisson
`approximation, the relationship for k, n, and m can be described
`using the binomial distribution, or simulated using a random
`number generator, each yielding similar results (SI Text).
`
`Results
`The outcome of stochastic labeling is illustrated by examining the
`graph of k (the red curve in Fig. 2) calculated using a label diver-
`sity (m) of 960. The expected number of unique labels captured
`depends on the ratio of molecules to labels, n∕m. When n is much
`smaller than m, each molecule almost always captures a unique
`
`A
`
`Genomic DNA
`
`BamHI fragments
`
`Label ligation
`
`Universal PCR and circularization
`
`Gene-specific inverse PCR
`
`|||||||||||||||||||||||||
`Array Probe
`
`Fragmentation and array hybridization
`
`biotin
`Ligation to short 5’ biotin oligonucleotide
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`B
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`3.62 ng
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`1.45 ng
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`0.36 ng
`
`0.036 ng
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`0 ng
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`960 labels
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`n.s.
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`525
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`256
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`107
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`14
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`0
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`SCIENCES
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`APPLIEDBIOLOGICAL
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`(A) A schematic drawing of the method used to attach labels to fragments of DNA in the genome. Red bars represent a pool of synthetic deoxyo-
`Fig. 3.
`ligonucleotide adaptors incorporating a collection of 960 labels used as counting sequences. A common primer sequence flanks each unique label adaptor,
`allowing universal amplification of all fragments with PCR. Circularization of amplified DNA molecules simplifies the selection and amplification of label-
`ligated DNA fragments through inverse PCR with gene-specific primers. The identity of labels that have been ligated to the genomic DNA fragment is
`determined using microarray hybridization, or DNA sequencing. (B) Microarray scan images of the 960 tiled probes for chromosome 4 corresponding to
`the labels used, as well as an additional 192 nonspecific (n.s.) probes serving as negative controls. The amount of genomic DNA used in each experiment
`is given on the left side of each image and the number of labels detected on microarrays is provided on the right side.
`
`Fu et al.
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`PNAS ∣ May 31, 2011 ∣
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`of enzymatic ligation of compatible cohesive DNA ends. High
`coupling efficiency is achieved through incubation with a large
`molar excess of labels and DNA ligase enzyme (>1013 molecules
`each). At this stage, the stochastic labeling process is complete,
`and the samples can be amplified as desired for detection. A
`universal primer is added, and the entire population of labeled
`DNA fragments is PCR amplified. The PCR reaction preferen-
`tially amplifies approximately 80,000 fragments in the 150 bp–
`2 kb size range. After circularization of the amplified products,
`three test target fragments were isolated using gene-specific
`PCR; one on each of chromosomes X, 4, and 21, and prepared
`for detection.
`The three labeled targets were counted using two sampling
`techniques: DNA microarrays and next-generation sequencing.
`For the array counting, a custom DNA array detector capable
`of distinguishing the set of labels bound to the targets was con-
`structed by dedicating one array element for each of the 960
`target-label combinations. Each array element consists of a com-
`plementary target sequence attached to one of the complements
`of the 960 label sequences (Fig. 3A, Fig. S3). To maximize the
`specificity of target-label hybridization and scoring, we employed
`a ligation labeling procedure on the captured sequences (Fig. S3).
`We set thresholds to best separate the intensity data from the
`array into two clusters, one of low intensity and one of high
`intensity (Fig. S4A). We scored a label as “present” if its signal
`intensity exceeded the threshold. The number of labels detected
`on microarrays is summarized in Table S2. Fig. 3B shows exam-
`
`ples of microarray scan images where bright spots/features were
`counted as present. As an alternate form of detection, sequencing
`adaptors were added (Fig. S5) and the samples were subjected
`to two independent DNA sequencing runs. Between several hun-
`dred thousand to several million high-quality reads were used to
`score the captured labels (Table S3). Similarly, we set thresholds
`for the number of sequencing reads observed for each label, and
`scored a label as present if the number of sequencing reads ex-
`ceeded the threshold (Fig. S4B). The number of attached labels,
`k, detected for each target in each dilution either by microarray
`counting or sequence counting is presented in Table S4, and
`plotted in Fig. 4 A and B.
`The counting results span a range of approximately 1,500 to 5
`molecules, and it is useful to consider the results in two counting
`regimes, below and above 200 molecules. There is a striking
`agreement between the experimentally observed number of mo-
`lecules and that expected from dilution in the first regime where
`the ratio of molecules to labels ðn∕mÞ < 0.2 (Table S4). Below
`200 molecules the data are in tight agreement, including the data
`from the lowest number of molecules—5, 10, and 15—where the
`counting results are all within the expected sampling error for the
`experiment. (The sampling error for 10 molecules is 10  6.4,
`where 10 and 6.4 are the mean and two standard deviations from
`10,000 independent simulation trials.)
`In the second regime above 200 molecules, there is an approx-
`imate 10–25% undercounting of molecules, increasing as the
`number of molecules increases. We attribute this deviation to be
`
`B
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`50
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`40
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`30
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`20
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`10
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`800
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`600
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`400
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`200
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`800
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`600
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`400
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`200
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`50
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`40
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`30
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`20
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`10
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`A
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`Number of labels
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`0
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`0
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`0
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`500 1000 1500
`0
`40
`30
`20
`10
`50
`Number of target molecules
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`0
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`0
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`0
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`500 1000 1500
`0
`40
`30
`20
`10
`50
`Number of target molecules
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`C
`
`Chr4
`Chr21
`ChrX
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`6.67
`
`D
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`4.5
`
`Chr4
`Chr21
`ChrX
`
`6.67
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`4.5
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`3.62ng
`
`1.45ng
`
`0.36ng
`
`0.036ng
`
`01234
`
`3.62ng
`
`1.45ng
`
`0.36ng
`
`0.036ng
`
`01234
`
`Fig. 4. Absolute counting results for DNA molecules. 3.62, 1.45, 0.36, and 0.036 ng dilutions of DNA isolated from cultured lymphoblasts of a Trisomy 21 male
`individual were processed for microarray hybridization and DNA sequencing. Three gene targets were tested, one from each of chromosomes X, 4, and 21, and
`the numbers of detected labels (blue curve) are shown for microarray (A) and DNA sequencing (B). The number of target molecules for each sample was
`determined from the amount of DNA used, assuming a single haploid nucleus corresponds to 3.5 pg. For comparison, the calculated number of labels expected
`from a stochastic model is also plotted in red. Numerical values are provided in Table S2. Copy number ratios of the three gene targets ChrX (red bar), Chr4 (blue
`bar), and Chr21 (green bar) representing one, two, and three copies per cell, respectively, are shown in (C) and (D). The calculated number of target molecules
`was determined from the number of labels detected on microarrays (Table S2, column 9) or from DNA sequencing. For each sample dilution, the copy number
`ratio of each gene target relative to ChrX is shown for microarray (C) and DNA sequencing (D). For comparison, copy number ratios obtained from in silico
`sampling simulations are also shown; where circles indicate the median values from 10,000 independent trials and error bars indicate the 10th and 90th
`percentiles. The 90th percentile values of the ratios at the lowest concentration (0.036 ng) are explicitly labeled in the plots.
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`due to a distortion in the amplification reaction. PCR-introduced
`distortion occurs from small amounts of any complex template
`due to the differences in amplification efficiency between indivi-
`dual templates (6–8). In the present case, stochastic labeling will
`produce only one (at low n∕m ratios), and increasingly several
`copies (at higher n∕m ratios) of each template. Modeling suggests
`that simple random dropout of sequences (PCR efficiencies
`under 100%) generates significant distortion in the final numbers
`of each molecule after amplification. At any labeling ratio, ran-
`dom dropout of sequences because of PCR efficiency will result
`in an undercount of the original number of molecules. At high
`n∕m ratios, the number of labels residing on multiple targets will
`increase and have a statistical survival advantage through the
`PCR reaction causing greater distortion. In support of this argu-
`ment, we observe a wide range of intensities on the microarray
`and a wide range in the number of occurrences of specific
`sequences in the sequencing experiments (Fig. S4 A and B). This
`effect can be reduced by carrying out the reaction at n∕m ratios
`near or less than 0.2, increasing the number of labels m, further
`optimization of the amplification reaction, or by employing a
`linear amplification method.
`The lymphoblast cell line used in this study provides an inter-
`nal control for the relative measurement of copy number for
`genes residing on chromosomes X, 4, and 21. Fig. 4 C and D pre-
`sents the ratio of the absolute number of molecules from all three
`chromosomes normalized to copy number 1 for the X chromo-
`some. As shown, the measurements above 50 molecules all yield
`highly precise relative copy number values. At low numbers of
`molecules (0.036 ng) uncertainty results because the error asso-
`ciated with sampling an aliquot for dilution is significant. Numer-
`ical simulations were performed to estimate the sampling error,
`and summarized medians along with the 10th and 90th percen-
`tiles of the copy number ratios are shown in Fig. 4 C and D as
`circles and range bars, respectively. At the most extreme dilu-
`tions, where approximately 5, 10, and 15 molecules are expected
`for the chromosome X, 4, and 21 genes, the deviation in copy
`number ratio is within the expected sampling error.
`Overall, the identity of labels detected on the microarrays and
`in sequencing are in good agreement, with only a small subset of
`labels unique to each process (Fig. S4C). Despite a high sequen-
`cing sampling depth (Table S3), a small number of labels with
`high microarray intensity appear to be missing or underrepre-
`sented in the sequencing results. In contrast, labels that appear
`in high numbers in the sequencing reaction always correlate with
`high microarray intensities. No trivial explanation could be found
`for the labels that are missing from any given sequencing experi-
`ment. Although underrepresented in some experiments, the same
`labels appear as present with high sequence counts in other
`experiments, suggesting that the sequences are compatible with
`the sequencing reactions. We used PCR as an independent meth-
`od to investigate isolated cases of disagreement, and demon-
`strated that the labels were present in the samples used for the
`sequencing runs (Table S5). Although we can clearly confirm
`their presence in the sequencing libraries, it is unclear as to why
`these labels are missing or underrepresented in the sequencing
`reads.
`To test the stochastic behavior of label selection, we pooled the
`results of multiple reactions at low target concentrations (0.36
`and 0.036 ng), where the probability that a label will be chosen
`more than once is small. Fig. S6 shows that the number of times
`each label is used closely follows modeling for 1,064 label obser-
`vations from microarray counting. Furthermore, because each
`end of a target sequence chooses a label independently, we
`can compare the likelihood of the same label occurring on both
`ends of a target at high copy numbers. Table S2, columns 10–11
`present the experimentally observed frequency of labels occur-
`ring in common across both ends of a target and their expected
`
`frequency from numerical simulations. No evidence of nonsto-
`chastic behavior is observed in these data.
`
`Discussion
`It is interesting to contrast the attributes of stochastic labeling
`with other quantitative methods. Microarray and sequencing
`technologies are commonly used to obtain the relative abundance
`of multiple targets in a sample. In the case of microarray analysis,
`intensity values reflect the amount of hybridization bound target
`and can be used to compare to the intensity of other targets in
`the sample. In the case of sequencing, the number of times a
`sequence is found is compared to the number of times other
`sequences are found. Although the techniques differ by using
`intensity in one case and a digital count in the other, they both
`provide relative comparisons of the number of molecules in
`solution. To obtain absolute numbers, quantitative capture of all
`sequences would need to be assured, and distortions due to am-
`plification biases understood; however, in practice the efficiency
`of capture and/or distortions due to amplification biases with
`sequencing or other counting approaches (9–12) are unknown.
`With stochastic labeling, high-efficiency enzymatic reactions
`coupled with a large molar excess of labels ensures quantitative
`labeling, and after amplification, threshold detection diminishes
`the effects of distortions due to amplification bias.
`Digital PCR is an absolute counting method where solutions
`are stochastically partitioned into multiwell containers, typically
`until there is an average probability of less than one molecule
`per two containers, then detected by PCR (3). This condition
`is satisfied when, 1 − P0 ¼ ð1 − e−n∕cÞ ¼ 1
`2; where P0 is the prob-
`ability that a container does not contain any molecule, n is the
`number of molecules and c is the number of containers, or n∕c
`is 0.693. If quantitative partitioning is assumed, the dynamic
`range is governed by the number of containers available for
`stochastic separation. Once the molecules are partitioned, high-
`efficiency PCR detection gives the yes/no answer and absolute
`counting is enabled. To vary dynamic range, microfabrication (13)
`or picoliter droplets (14) can be used to substantially increase the
`number of containers. Similarly, in stochastic labeling, the same
`statistical conditions are met when 1 − P0 ¼ ð1 − e−n∕mÞ ¼ 1
`2;
`where m is the number of labels, and one half of the labels will
`be used at least once when n∕m ¼ 0.693. The dynamic range is
`governed by the number of labels used, and the number of labels
`can be easily increased to extend the dynamic range. The number
`of containers in digital PCR plays the same role as the number
`of labels in stochastic labeling and by substituting containers for
`labels we can write identical statistical equations. Using the prin-
`ciples of physical separation, digital PCR stochastically expands
`identical molecules into physical space, whereas the principle
`governing stochastic labeling is chemically based and expands
`identical molecules into chemical space.
`We have shown that a population of indistinguishable mole-
`cules can be stochastically expanded to a population of uniquely
`identifiable and countable molecules. High-sensitivity threshold
`detection of single molecules is demonstrated, and the process
`can be used to count both the absolute and relative number
`of molecules in a sample. The method should be well-suited for
`determining the absolute number of multiple target molecules in
`a specified container, such as high-sensitivity clinical assays, or for
`determining the number of transcripts in single cells. For exam-
`ple, counting on the order of 300,000 molecules of the approxi-
`mately 30,000 gene transcripts in the human genome in any given
`cell could be achieved with high efficiency using several thousand
`labels. We estimate that this experiment should require about
`10–30 million sequencing reads, falling within the capacity of
`modern sequencing devices (the number of reads required using
`sequencing technology depends on the number of molecules, not
`the diversity of labels). The number of array elements required
`depends on the number of different types of molecules times the
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`diversity of labels, or ∼107 array elements in this example, also
`within range of current technology. The approach should also
`be compatible with other molecular assay systems. For example,
`antibodies could be stochastically labeled with DNA fragments
`and those that bind antigen harvested. After amplification, the
`number of labels detected will reveal the original number of anti-
`gens in solutions. In the examples shown here, DNA is used as a
`chemical label because of the great diversity of sequences avail-
`able, it can be amplified, and because it is easily detectable. In
`principle, any stochastic chemical change could be used as long
`as it can be easily detected and generates sufficient diversity for
`the desired application.
`
`Materials and Methods
`DNA Samples. Genomic DNA isolated from cultured B-Lymphocytes of a male
`Caucasian with Trisomy 21 was purchased from Coriell Institute for Medical
`Research (Catalog no. GM01921). The DNA quantity was determined by
`PicoGreen (Invitrogen) measurements using the lambda phage DNA pro-
`vided in the kit as reference standard. DNA quality was assessed by agarose
`gel electrophoresis.
`
`BamHI Digestion and Ligation to Labels. Genomic DNA was digested to
`completion with BamHI [New England BioLabs (NEB)] and ligated to a pool
`of adaptors consisting of an equal concentration of 960 distinct labels
`(Fig. 3A). Each adaptor consists of a universal PCR priming site, a 14-nt long
`label sequence, and a BamHI overhang (Fig. S3). The sequence of the labels
`(Table S1) was selected from an all-possible 414 nucleotide combination to be
`of similar melting temperature, minimal self-complementation, and maximal
`differences between one another. Homopolymer runs and the sequence of
`the BamHI restriction site were avoided. Oligonucleotides were synthesized
`(Integrated DNA Technologies) and annealed to form double-stranded adap-
`tors prior to pooling. For ligation, the digested DNA was diluted to the
`desired quantity and added to 100 pmol (equivalent to 6 × 1013 molecules)
`of pooled label adaptors, and 2 × 103 units (equivalent to 1 × 1016 molecules)
`of T4 DNA ligase (NEB) in a 30 μL reaction. The reaction was incubated at
`20 °C for 3 h until inactivation at 65 °C for 20 min.
`
`Adaptor PCR. Adaptor-ligated fragments were amplified in a 50 μL reaction
`containing 1X TITANIUM Taq PCR buffer (Clontech), 1M betaine (Sigma-
`Aldrich), 0.3 mM dNTPs, 4 μM PCR004StuA primer (Fig. S3), 2.5 units Taq
`DNA Polymerase (Affymetrix), and 1X TITANIUM Taq DNA polymerase (Clon-
`tech). An initial PCR extension was performed at 72 °C for 5 min, 94 °C for
`3 min, followed by 5 cycles of 94 °C for 30 s, 45 °C for 45 s, and 68 °C for
`15 s. This step was followed by 25 cycles of 94 °C for 30 s, 60 °C for 45 s,
`and 68 °C for 15 s and a final extension step of 68 °C for 7 min. PCR products
`were assessed with agarose gel electrophoresis (Fig. S4) and purified using
`the QIAquick PCR purification kit (Qiagen).
`
`Circularization. The purified PCR product was denatured at 95 °C for 3 min
`prior to phosphorylation with T4 polynucleotide kinase (NEB). The phos-
`phorylated DNA was ethanol precipitated and circularized using the CircLi-
`gase™ II ssDNA Ligase Kit (Epicentre). Circularization was performed at 60 °C
`for 2 h followed by 80 °C inactivation for 10 min in a 40 μL reaction consisting
`of 1X CircLigase™ II reaction buffer, 2.5 mM MnCl2, 1M betaine, and 200U
`CircLigase™ II ssDNA ligase. Noncircularized DNAs were removed by treat-
`ment with 20U Exonuclease I (Epicentre) at 37 °C for 30 min. Remaining
`DNA was purified with ethanol precipitation and quantified with OD260
`measurement.
`
`Amplification of Gene Targets. Three assay regions were tested, one on each
`of chromosomes 4, 21, and X. Table S1 lists the genomic location, length, and
`sequences of these selected fragments. The circularized DNA was amplified
`with gene-specific primers in a multiplex inverse PCR reaction. PCR primers
`were picked using Primer3 (http://frodo.wi.mit.edu/primer3) to yield ampli-
`cons ranging between 121 and 168 bp. PCR was carried out with 1X TITA-
`NIUM Taq PCR buffer (Clontech), 0.3 mM dNTPs, 0.4 μM each primer, 1X
`TITANIUM Taq DNA Polymerase (Clontech), and approximately 200 ng of
`the circularized DNA. After denaturation at 94 °C for 2 min, reactions were
`cycled 30 times as follows: 94 °C for 20 s, 60 °C for 20 s, 68 °C for 20 s, and a
`68 °C final hold for 4 min. PCR products were assessed on a 4–20% gradient
`polyacrylamide gel (Invitrogen) and precipitated with ethanol.
`
`Array Design. For each gene target assayed, the array probes consist of
`all possible combinations of the 960 label sequences connected to the two
`
`BamHI genomic fragment ends (Fig. S3). An additional 192 label sequences
`that were not included in the adaptor pool were also included to serve as
`nonspecific controls. This strategy enables label detection separately at each
`paired end, because each target fragment is ligated to two independent
`labels (one on either end).
`
`Array Synthesis. Arrays were synthesized following standard Affymetrix
`GeneChip manufacturing methods utilizing contact lithography and phos-
`phoramidite nucleoside monomers bearing photolabile 5′-protecting groups.
`Array probes were synthesized with 5′ phosphate ends to allow for ligation.
`Fused silica wafer substrates were prepared by standard methods with trialk-
`oxy aminosilane, as previously described (15). After the final lithographic
`exposure step, the wafer was deprotected in an ethanolic amine solution
`for a total of 8 h prior to dicing and packaging.
`
`Hybridization to Arrays. PCR products were digested with Stu I (NEB), and
`treated with lambda exonuclease (Affymetrix). Five micrograms of the di-
`gested DNA was hybridized to a GeneChip array in 112.5 μL of hybridization
`solution containing 80 μg denatured Herring sperm DNA (Promega), 25% for-
`mamide, 2.5 pM biotin-labeled gridding oligo, and 70 μL hybridization buffer
`(4.8M TMACl, 15 mM Tris pH 8, and 0.015% Triton X-100). Hybridizations
`were carried out in ovens at 50 °C for 16 h with rotation at 30 rpm. Following
`hybridization, arrays were washed in 30 mM NaCl, 2 mM NaH2PO4, 0.2 mM
`EDTA, pH 7.4 containing 0.005% Trition X-100 at 37 °C for 30 min, and
`with 10 mM Tris/1 mM EDTA, pH 8 (TE) at 37 °C for 15 min. A short
`biotin-labeled oligonucleotide (Fig. S3) was annealed to the hybridized
`DNAs, and ligated to the array probes with Escherichia coli DNA ligase
`(Affymetrix). Excess unligated oligonucleotides were removed with TE wash
`at 50 °C for 10 min. The arrays were stained with streptavidin, R-phycoery-
`thrin conjugate (Invitrogen), and scanned on the GCS3000 instrument
`(Affymetrix).
`
`Counting Labels. We set thresholds for the array intensity, or the number
`of sequencing reads to classify labels as either being used or not (Fig. S4 A
`and B). Appropriate thresholds were straightforward to determine when
`used and unused labels fall into two distinct clusters separated by a signifi-
`cant gap. In situations where a gap was not obvious, the function normal-
`mixEM in the R package mixtools was used to classify labels. This function
`uses the expectation maximization (EM) algorithm to fit the data by mixtures
`of two normal distributions iteratively. The two normal distributions corre-
`spond to the two clusters to be identified. The cluster of labels with a high
`value is counted as used, and the other as not used. The average of the
`minimum and maximum of the two clusters,ðImin þ ImaxÞ∕2, was applied as
`the threshold for separating the two clusters.
`
`Sampling Error Calculation. A sam