A candidate reference method for quantification of low concentrations of plasmid DNA by exhaustive counting of single DNA molecules in a flow stream

Fluidics. A piece of ∼1 m long square-form fused silica tubing (50 µm × 50 µm i.d.; 375 µm × 375 µm o.d.: WWP050375; Polymicro Technologies, Phoenix, AZ) was used as the fluidic channel. The DNA stream was focused on the centre axis of the fluidic channel by applying 0.07 MPa, whereas 20 kV was applied across the capillary. An electroosmotic flow directed against the hydrodynamic flow was accordingly established. If a different pressure or voltage was applied, the change is described in the text. The fluidic channel also served as a sample cell. The entire capillary volume was filled with a sample solution and then counting was started by pushing the sample solution with a blank buffer until the sample solution was completely pushed out. The sample volume was the volume of the capillary from the injection end to the detection window. All DNA molecules in the sample volume were counted as they passed the detection window ('exhaustive counting'). The detection window was implemented ∼60 cm away from the injection end of a ∼1 m long capillary tube. The schematic description of the fluidic arrangement is shown in the online supplementary figure S-1 (stacks.iop.org/Met/51/491/mmedia).

Detection. Sybr-Gold dye (S-11494; Molecular Probes, Eugene, OR)-stained DNA molecules were detected by LIF. A water-cooled argon ion laser (Model 95; Lexel Laser, Fremont, CA) was initially used but was replaced with a diode laser (Spectra-Physics Cyan™ 488; Newport Co. Irvine, CA) for a 488 nm laser beam with a ∼150 mW output. A laser-beam stabilizer (Compact model; MRC Systems, Heidelberg, Germany) was implemented just after the laser source (figure 1). The stabilized laser beam was then expanded using a Keplerian beam expander to be delivered to the back aperture of a 4× objective lens. The objective lens was placed on a micro-translation stage to adjust the relative position of the focal volume, by which the size of the effective excitation volume was precisely adjusted. The lateral beam diameter at the detection point was typically set to ∼20 µm. The fused silica tubing of the flow channel was held vertically to expose the flow channel normal to the incident laser beam. The emitted fluorescence light was collected at the normal angle to the incident beam using a 60× objective lens. A flip-mirror was placed to switch the direction of the fluorescent light either to a charge-coupled device (CCD) camera (Cascade II; Photometrics, Pleasanton, CA) or to the APD detector (SPCM-AQR12; PerkinElmer, Fremont, CA). The CCD camera was used for the real-time visualization of the DNA stream, whereas the APD detector was used to count individual DNA particles by tracking the change in fluorescence emission intensity as single DNA molecules travel through the focused excitation field. The resulting fluorescent intensity peak is used as the indicator for DNA counting. A 488 nm rejection filter and a 520 nm band-pass filter (20 nm bandwidth) were placed in front of each detector. As the APD has a very small active area (∼180 µm in diameter), the fluorescent light was focused onto the active area using a set of collection lenses. The whole detection system was installed in a darkroom to minimize stray light.

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Signal processing. The output pulses of the photon-counting APD responding to fluorescent photons were fed into a 16-bit frequency-to-voltage converter (AD9525; Analog Devices Inc., Norwood, MA) to generate analogue signal traces of the fluorescent intensity. The output pulses of the APD were integrated for 80 µs at every 100 µs. The analogue signal was compared with a preset threshold using an analogue comparator for the detection of meaningful events with the intensity higher than the threshold level, regarding only them as true events (the passage of a DNA molecule) and traced the rise of the fluorescent intensity to capture the peak of the curve involving a series of consecutive events. The peak intensity of each curve was then recorded. The data system checks if the signal rises again before it reaches the level below the threshold level. If it happens, the data system regards it as a new event involving the passage of a different DNA molecule, which means more than one DNA molecules contribute to a single intensity distribution curve. Peaks with durations greater than the normal duration were counted as events of double molecules (number of events of 'double molecules by width', N_dw). In addition, peaks with significantly larger heights than normal were also counted as events of double molecules (number of events of 'double molecules by height', N_dh).

Criteria for such events of double molecules were experimentally adjusted for optimization for the given experimental conditions where applied pressure and signal amplification were highly influential. For determining an event of double molecules by width, an average time span for the most frequent events was a starting point. Typically, a peak of a popular event lasted for 8 data sampling points for digitizing (∼3 ms). Therefore, the optimum criterion was sought among 7, 8, 9 or 10 data sampling points. Appropriateness of such a setting was determined by monitoring the screen of a digital oscilloscope that indicated events of double molecules in real time (online supplementary figure S-5 (stacks.iop.org/Met/51/491/mmedia)). In determination of an event of a double molecule by height, the criterion was first set to peak heights greater than 1.8-fold of the height of the most frequent events. This criterion was adjusted by 0.1-fold to result in the best measurement linearity together with the optimized criterion for calling events of double molecules by width. Multiple combinations of these criteria set were tried until a satisfactory measurement linearity (e.g. R² = 0.999) up to 8000 counts was achieved.

In addition to events of double molecules, events possibly attributed from dye-containing background were also corrected. At the beginning and end of the experiment, a dye-blank solution (a solution containing everything including the fluorescence-dye but DNA) was measured. The averaged results of these measurements (N_dye) were subtracted from the results of sample measurements. Even after subtraction of dye-background counts, small numbers of events were occasionally observed at the weaker signal region on a histogram. In such a case, the counts of such events (N_noise) were regarded as noise and subtracted from the total counts. Therefore, the finally adjusted counts (N_c) was determined by the following equation.

$$\begin{equation} N_{{\rm c}} = N_{{\rm c}}^{{\rm o}} +N_{{\rm dw}} +N_{{\rm dh}} -N_{{\rm dye}} -N_{{\rm noise}} , \end{equation} \tag{ 2 }$$

where $N_{{\rm c}}^{{\rm o}}$ is the number of events counted, N_dw is the number of events of double molecules determined by width; N_dh is the number of events of double molecules determined by height, N_dye is the number of events counted with a dye-blank solution and N_noise is the number of events gated out as noise signals

Multiple runs, typically 10 runs, were made for each sample, and the results were averaged to obtain the value of N_c. Then, the final value of a measurement was calculated by the following equation to have a unit of (mol kg⁻¹).

$$\begin{equation} C=(N_{{\rm c}} /N_{{\rm A}} )/\left( {D\cdot V} \right), \end{equation} \tag{ 3 }$$

where C is the amount of substance of DNA in the unit of mole per sample mass, D is the density of a test solution and V is the sample volume.

If dilutions were necessary, dilutions were made gravimetrically in the fewest steps possible, and the dilution factor was reflected in the final value.

Histograms were generated on the x-axis of a 0.1 V step from 0 to 10 V, full scale. An in-house software program using Turbo-C language was utilized as well as Microsoft Excel and Microcal Origin for signal processing and data reduction.

Plasmid DNA pBR322 was purchased from Fermentas (Burlington, Canada). The initial stock solution was diluted 1 000 000-fold to 50 mL of 1X TE buffer (10mM Tris/HCl at pH 8.0 + 1mM EDTA). For counting, 1 to 120 µL of this solution was gravimetrically diluted into 1.5 mL of run buffer (10mM Tris/HCl at pH 9.5 + 10% dimethyl sulfoxide) that contained 0.1 X Sybr Gold dye (S-11494; Invitrogen, Carlsbad, CA). The well-mixed sample solution described above was introduced into the fluidic channel by applying 0.2 MPa for 1 min. The sample solution was replaced with a buffer solution, then 0.07 MPa was applied with 20 kV as counting started. Counting was performed for 1.5 min. For repeated counting, the fluidic channel was occasionally cleaned by flushing with 0.1 N NaOH.

d-PCR quantification of pBR322 DNA was performed at a laboratory in the Advanced Institute of Science and Technology in Tsukuba, Japan. A typical d-PCR protocol was performed by an experienced scientist using Fluidigm EP1™ System (South San Francisco, CA). The PCR amplification conditions with a Taqman® probe are as follows:

• Master mix: Taqman®
• Forward primer: TATCGACTACGCGATCATGG
• Reverse primer: GCGACTCCTGCATTAGGAAG
• Probe: FAM-CGGCCTCAACCTACTACTGG-BHQ1
• Preheating: 90 °C, 10 min
• 40 cycles of 2-step reactions
• (melting: 90 °C, 15 s; annealing and extension: 60 °C, 60 s).

About 10 000 000-fold concentrated pBR322 relative to the concentration for count-based measurement was quantified by our in-house CE-dNMP analysis protocol [8]. In brief, a sample solution of pBR322 in a Tris buffer was mixed with DNase I and phosphodiesterase, then incubated at 37 °C for 1 h followed by the deactivation of enzymes proceeded at 80 °C for 10 min. The resulting individual nucleotides were separated by electrophoresis and then detected at 260 nm by a UV–VIS system. The UV signal was transferred to the quantities of each nucleotide type that were calibrated by the reference materials of nucleotides, which were certified using phosphorus measurement by ICP-OES [5]. The original concentration of pBR322 was then calculated based on its base sequence (www.ncbi.nlm.nih.gov/nuccore/208958).

Three measurement methods were applied for determining the sample volume. First, fluorescent dye filling the given length of capillary tubing was completely expelled into the known volume of a buffer solution, then the concentration of the diluted dye solution was determined using a fluorescence measuring plate reader (Victor³; PerkinElmer, Walthem, MA, USA). Dilution factor calculated from the concentration led to the volume of the dye solution expelled from the capillary [19]. Second, a piece of about 7 m long fused silica capillary of the same batch as the capillary used as the fluidic channel was filled with deionized water by applying pressure. Then, the water filling the entire length of the capillary was pushed out to a water container to determine the mass of the water added to the container. The water container (a 1.5 mL Eppendorf tube) contained ∼1 mL of water beforehand for pre-equilibrium of water evaporation. The capillary tip was passed through a fine hole (∼1 mm in diameter) on the cap of the tube to be immersed into water in the container. This procedure was repeated four times, and the results were averaged (table 1). Third, the piece of fused capillary tubing used as a fluidic channel was prepared for imaging its cross section with scanning electron microscopy (SEM). The cross sectional area of the open channel was calculated by comparing the mass of its cut-out with that of a cut-out of a known area from a print of the SEM image of a reference standard (30 µm × 30 µm on the same SEM image, see the online figure S-8 (stacks.iop.org/Met/51/491/mmedia)). For comparing results of three methods using different capillary lengths, unit volume (volume for 1 cm in length) was calculated assuming that the channel is straight along the given length, which is highly likely. The gradation of the tubing dimension along the length of the tubing is typically ∼0.1 µm m⁻¹ according to the manufacturer's specifications. In calculation of the sample volume, the unit volume was multiplied with the length of capillary from the injection end to the detection window. The detection window is the position where the laser beam was focused for excitation. Results of three measurement methods are compared in table 2.

Overall measurement uncertainty of the proposed method was numerically driven using the Kragten method for spreadsheet calculation (www.uttv.ee/naita?id=17721). As the results vary along with the range of the final output value, we aimed at calculation of uncertainty for a sample of ∼5000 copies/mg, which is equivalent to ∼6 × 10⁻¹⁵ mol kg⁻¹. Uncertainty components in equations (2) and (3) were evaluated (table 3). Rationales or the basis of such estimations are described in section 3. Those uncertainties were then input to the Kragten method for a spreadsheet to produce the combined uncertainty of the overall measurement procedure. Coverage factor of 2 was used to calculate the expanded uncertainty.

Table 3. Uncertainty components of the count-based quantitation that were used as the input uncertainties to the Kragten method for spreadsheet calculation. The concentration of the exemplified sample was ∼6 × 10⁻¹⁵ mol kg⁻¹.

Quantity	Unit	Value	Uncertainty	Uncertainty sources
Nc		(5473.3)
$N_{{\rm c}}^{{\rm o}}$	(counts)	4691	51.5	Repeatability of multiple runs
Ndw		561.3	59.2
Ndh		114	34.5
Ndye		90.7	20
Nnoise		16.3	10
NA	mol−1	6.0221 × 1023		Not considered
D	mg µL−1	1.0202	0.0067
Dwater (22.3 °C)	g cm−3	0.999 16	0.000 01
T	°C	22.3	0.1	ΔD/ΔT (22 °C) = 0.000 097 g cm−3 °C−1
Wwater	g	0.199 37	0.000 25	From weighing
Wsample	g	0.203 56	0.001 31
V	μL	1.4167	0.0142
Vunit	μL cm−1	0.0243	0.000 27	Difference between two methodsa
l	cm	58.3	0.01	Determination of length
Output	mol kg−1	6.04 × 10−15	0.13 × 10−15	Combined using Kragten method

^aRefer to the corresponding text.

As reported previously by others [17, 25], real time-PCR or d-PCR may underestimate the concentration depending on the structure of the template DNA. For example, natural plasmid DNA is mostly in the form of supercoils, which may create difficulties when it comes to primers reaching the designated priming sites during the annealing step, or it may not melt completely to fully expose the designated template regions during the extension. In this study, the d-PCR measurement with intact pBR322 DNA yielded only ∼30% of the expected result (figure 2), whereas a closer agreement between yield and expectation was seen with linearized lambda phage DNA. One could fully optimize the PCR conditions for pBR322 DNA to avoid such underestimation. However, a near 100% success rate in the single-copy PCR may not be ensured unless it is confirmed with a reliable reference standard. The proposed direct counting method that does not include PCR amplification may serve as such a reference standard.

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The performance of the counting system had to be further optimized or improved from what has been reported previously [19] in order to ensure robust detection of substantially smaller plasmid DNA. Under the previous conditions optimized for lambda phage DNA, histograms for pBR322 were dramatically poorer, as shown in figure 3. Poor histograms indicate that electro-hydrodynamic focusing of the stream of pBR322 DNA molecules is not tight enough to maintain the trajectory of the molecules within the focal area of LIF detection that was set along the central axis of the channel. It was observed that smaller DNA particles easily escaped the pressure gradient formed by the hydrodynamic flow of a parabolic profile (Bernoulli's theorem). We have found the same trend with plastic beads. Plastic beads smaller than 1 µm were hardly focused in their trajectories, whereas larger beads were focused well under appropriate pressures and electric fields. Nevertheless, focusing of the trajectories of pBR322 DNA was improved with an increased pressure for faster hydrodynamic flow, which can be seen in the improved histogram (figures 3(b)-b relative to figure 3(b)-a). However, there was still a significant fraction of pBR322 DNA detected with weak fluorescence signals that substantially deviated from the intensity of the main population, which implies that those DNA molecules flow along in the proximity of the capillary wall. An increased electric field, however, reduced the fraction but did not narrow the peak width of the histogram (figure 3(b)-c relative to figure 3(b)-a). The two effects of faster flow and stronger electroosmotic flow (EOF) were additive, as seen in figure 3(b)-d. The rationale for the effect of faster flow is straightforward and relies on Bernoulli's theorem. However, a fast flow would still result in stagnant layers along the capillary wall; some of the DNA molecules may escape from the pressure gradient into these layers. Stronger EOF rising along the capillary wall might more effectively disrupt such stagnant layers as it is directed against the hydrodynamic flow. In this case, DNA molecules in the stagnant layers would fall back into the pressure gradient. This hypothesis is supported by occasional observations of turbulent motions of DNA particles close to the capillary wall. Although far inferior to the results for lambda phage DNA, the finally optimized conditions resulted in acceptable histograms for pBR322 DNA. However, too fast flows shortened the exposure time to the detector to degrade the detection sensitivity whereas the voltage for EOF was limited to 20 kV. Higher voltages made the system unstable by occasional arcs.

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Since the fluorescent signal decreased with the size of the DNA, the background noise became relatively significant in counting pBR322 DNA. Therefore, a fluorescent detection needed to be made at the best sensitivity. It was most critical to focus the fluorescent light onto the small active area of the APD (∼180 µm in diameter), which was ensured with the help of a CCD-equipped microscope where the fluidic channel was filled with a concentrated fluorescein solution to produce constant fluorescence emission to adjust the focusing optics (see the online supplementary figure S-2 (stacks.iop.org/Met/51/491/mmedia)). A combination of lenses for a short focal length (∼0.5 cm) was applied for this purpose. Then, the well-aligned optics for detection resulted in a satisfactory histogram even for pUC18 plasmid DNA of 2.69 kbp (see the online supplementary figure S-3 (stacks.iop.org/Met/51/491/mmedia)). However, such alignment was time consuming and painstaking. In particular, whenever the laser was turned on, some degree of deviation in the radiation direction occurred, which required repeated alignment. This problem has been overcome with a beam stabilizer equipped with a position sensor combined with a piezo-actuated mirror (the dotted section in figure 1). This approach considerably improved the efficiency of the operation of the measurement system.

The validity of the measurement principle of a newly proposed quantification method can be proved with its measurement linearity of an acceptable quality. The counting method did not result in satisfactory measurement linearity if a simple summation of the events ( $N_{{\rm c}}^{{\rm o}}$ in equation (2)) was used for quantitation. As shown in figure 4 (∘ symbols), counts for relatively concentrated pBR322 DNA (counts >5000) substantially curved downwards to result in underestimation. This result may be caused by the events of 'multiple DNA detection', opposed to the events of 'single molecule detection' assumed in the measurement principle. Unlike sheath flow-based flow cytometry, DNA particles were not accelerated to have enlarged interparticle distance in the suggested counting method. The absence of acceleration is advantageous to avoid shear stress on DNA chains but raises an issue of short interparticle distances for concentrated DNA samples. With an insufficient interparticle distance, chances are high to observe two or more DNA particles pass the detection zone together. If we assume equal spacing among linearly arranged DNA particles along the 60 cm long sample cell, 30 000 DNA particles can pass the detection zone that is 20 µm wide without simultaneous exposure to the detector. In reality, however, the spacing is randomly distributed, which causes simultaneous exposures for a number of DNA molecules. Furthermore, there could be a small but detectable portion of pBR322 dimer, as indicated in gel electrophoresis (see the online supplementary figure S-4 (stacks.iop.org/Met/51/491/mmedia)). We categorized the simultaneous exposures into three groups. In the first group, two DNA molecules pass the detection zone simultaneously but with a detectable space in between, which results in two local maxima within a single time-traced intensity curve (see the online supplementary figure S-5A (stacks.iop.org/Met/51/491/mmedia)). In this case, we simply separated this event as two independent events as we do for chromatographic peak separation. In the second group, there was no detectable space between the two molecules but the combined fluorescent signal peak was significantly wider than the ordinary peak of a single DNA molecule, implying the sequential passage of two molecules in a row (see the online supplementary figure S-5B (stacks.iop.org/Met/51/491/mmedia)). These events were counted as 'events of double molecules by width'. Finally, two DNA molecules passed with minimal space to result in a fluorescent peak with a regular width but of a substantially greater peak height. These events were counted as 'events of double molecules by height', implying possible aggregation of molecules (see the online supplementary figure S-5C (stacks.iop.org/Met/51/491/mmedia)).

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As described in section 2, criteria for determining the events of double molecules were experimentally optimized until satisfactory measurement linearity was achieved. Typically, the peak duration of nine or more data sampling points was the optimum criterion for events of 'double molecules by width' where the average peak duration of the most frequent events was eight data sampling points. The optimum peak height as the criterion for events of 'double molecules by height' was 2.1-fold of the peak height of the most frequent events. This set of criteria needed to be adjusted if the major experimental conditions such as flow rate and the gain of signal amplification were changed. The temporal resolution of data sampling point needed to be improved for finer adjustment of the criterion for double events by width.

The proportion of events of double molecules increased in an exponential manner as DNA concentration increased (see the online supplementary figure S-6 (stacks.iop.org/Met/51/491/mmedia)). For example, for 2000 event counts $(N_{{\rm c}}^{{\rm o}} )$, counts for events of double molecules by width (N_dw) and double molecules by height (N_dh) were 105 (5.3%) and 15 (0.7%), respectively. These increased to 560 (12.1%) and 114 (2.5%), respectively, for 4600 event counts. The CVs of counts of double events (N_dw + N_dh) were in the range 5% to 20% for multiple runs. The minimum CV (∼5%) was observed for ∼2000 event counts. As the final outcome of the correction of events of double molecules, the measurement linearity was dramatically improved up to 8500 counts (▵ in figure 4).

For samples of higher concentrations, however, the linearity was not maintained, which indicates imperfection of the current correction scheme for concentrated samples. At higher concentrations, there are increased chances of coincidental detection of triple or quadruple DNA molecules, which are not discerned by the current correction scheme. Application of Poissonian statistics instead may be more appropriate in this case. However, it does not seem to justify giving up the current correction scheme that works with real data. Dilution of samples to lower appropriate concentrations would provide better results than application of Poissonian statistics in terms of measurement uncertainty. The standard uncertainty of the current correction scheme was estimated as ∼2% of ∼5000 event counts. Nevertheless, this point needs to be studied further.

Considering counts in a weaker fluorescent intensity region, background counts prevailing in this region caused instability in the signal gating. The distribution of events for a dye-blank solution (a test solution containing everything, including dye, except for the sample DNA) was compared with other pBR322 solutions of different concentrations in figure 5. For less concentrated DNA solutions, the superposition of events with the background counting seemed unavoidable, but it became negligible with concentrated DNA solutions. Nevertheless, a background count was subtracted from the results of the sample counting as a simple data treatment. The background count of a dye-blank solution resulted in 20 to 80 exhaustive counts, being highly influenced by the day-to-day instrument setup. Therefore, the background count was determined in every new experiment. Such a treatment led to excellent measurement linearity in the plot of measured versus expected values down to 100 exhaustive counts (see the online supplementary figure S-7 (stacks.iop.org/Met/51/491/mmedia)). We estimated the measurement uncertainty due to the variation in background counts to be ±20 counts.

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Overall, an excellent measurement linearity (R² = 0.999) in the plot of measured versus expected values was achieved between 100 and 8500 exhaustive counts (0.1 × 10⁻¹⁵ mol kg⁻¹ to 10 × 10⁻¹⁵ mol kg⁻¹) with the data treatment described above, which strongly supports the validity of the accuracy of the measurement platform and data processing. In addition, potential adverse phenomena such as wall-adsorption, fragmentation or cluster forming by adhesion of multiple DNA molecules were shown not to occur in observable degrees.

In exhaustive counting, calculation of the molar concentration of DNA involves the sample volume (equations (1) and (3)). Therefore, an accurate determination of sample volume V is as crucial as the counts (N_c) of DNA. Considering a small sample volume close to 1 µL, its accurate determination was not a trivial task. Initially, we calculated the volume of the applied capillary of a given length by the fluorescent dye-dilution method [19]. However, the precision of this measurement was not satisfactory (up to 5% CV). A different approach of weighing water filling the given length of capillary tubing produced a surprisingly high precision (0.5% CV for n = 4), as seen in table 1. Pre-equilibrium of water evaporation in a virtually closed water container worked well to reduce water evaporation rate down to ∼0.08 mg min⁻¹, where the weighing procedure took 10 min to 15 min. Therefore, ∼185 mg of water from the capillary tubing could be weighed precisely. However, this result was noticeably different (6% less) from the result of the fluorescence measurement (table 2). The third method of determining the cross sectional area of the flow-cell capillary from a calibrated SEM image (see the online supplementary figure S-8 (stacks.iop.org/Met/51/491/mmedia)) resulted in acceptable agreement (1.1%) with the method of weighing water from capillary, which indicates a high possibility of the validity of two measurement methods. Furthermore, the result of the method of weighing water from capillary agreed within 1% with the dimensions claimed by the manufacturer (49 µm × 49 µm). As it was ensured that measured values were not unexpectedly false, we took the most precise result, 0.0243 µL cm⁻¹ (from the water weighing method), as the unit sample volume. The uncertainty of the method of weighing water from capillary was estimated as 0.7% including weighing repeatability, evaporation correction and length determination. The difference from the SEM image method, 1.1%, was taken as the uncertainty of determination of unit sample volume to avoid possible underestimation by unknown sources. The sample volume was then determined 1.42 µL by multiplying the length between the injection end and the detection window, 58.3 cm with the uncertainty of ∼0.1 cm. As samples were prepared gravimetrically, sample mass instead of sample volume was required for calculation of the concentration of an original sample. The density of the test solution (1.020 mg µL⁻¹) was measured to be slightly greater than pure water due to the addition of DMSO (density = 1.100 kg L⁻¹). Uncertainty in determination of the density of the test solution included repeatability and calibration uncertainty of weighing for determination of the relative mass of test solution to water as well as uncertainty in temperature that changes water density. Applying its exact density, the sample mass was determined to be 1.445 mg. The final results of flow cytometric measurement in table 4 were calculated using the test sample mass of 1.445 mg.

Uncertainty components in equations (2) and (3) were estimated and listed in table 3. The results for the sample of 6 × 10⁻¹⁵ mol kg⁻¹ (∼5000 counts) were exemplified. For the quantities of counts involved in determination of N_c, standard deviations in ten consecutive runs were used as their standard uncertainties. For N_dw and N_dh, uncertainty might be greater than just the standard uncertainties due to possible incorrectness in the criteria setting. For the time being, however, there was no clear evidence for such underestimation. As the concerned concentration range was covered with satisfactory linearity, such probability was ignored for now. Even so, uncertainty in determination of events of double molecules counted ∼40% of the overall combined uncertainty. Repeatability in event counting itself was 22% of the overall combined uncertainty whereas uncertainty in determination of sample volume took 27%. The uncertainty sensitivity calculated using the Kragten method is shown in figure 6. Considering the relatively even distribution of uncertainty among four different sources, the coverage factor of the expanded uncertainty (k) was set to 2.0. For the given case, the measured value and expanded uncertainty were (6.04 ± 0.13) × 10⁻¹⁵ mol kg⁻¹. The relative expanded uncertainty was 4.3%. Relative expanded uncertainties for other samples were in the range 3% to 6%. For samples of less than 1000 event counts, relative expanded uncertainties were substantially worse (e.g. ∼20% for the sample of ∼380 event counts) mostly due to relatively poor repeatability in event counts. On the other hand, underestimation obviously enlarged uncertainty.

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The proposed count-based quantification of pBR322 DNA was further validated by comparing with the predicted concentration of samples from the CE-dNMP analysis [8]. The CE-dNMP analysis method developed in this laboratory has been validated in terms of both perfection of enzymatic digestion of DNA to nucleotides and the accuracy of the capillary electrophoresis (CE) analysis. The calibration standards for CE analysis of nucleotides were certified with ICP-OES measurements of their phosphorus content in nucleotides, combined with phosphorus impurity analysis with HPLC-ICP-MS. Because of the lack of sensitivity, CE-dNMP analysis was performed with about 100 million-fold concentrated pBR322 solutions. Gravimetric dilution factors of the samples for counting were multiplied with the result of CE-dNMP analysis to directly compare with the result of count-based quantification. As shown in table 4, the results of the two methods agree to within their measurement uncertainties. Although such closeness (less than 1.3% deviation) could be led by statistical coincidence from the limited set of data, such agreement between two methods of totally different measurement principles strongly supports the validity of both analytical methods. This agreement also confirmed that the gravimetric dilution of DNA under the given conditions (a mildly alkaline solution in glassware with minimal dilution steps) worked as expected.

From this result, we also confirmed that the previously observed underestimation of lambda phage DNA by flow cytometric counting relative to CE-dNMP analysis was due to fragmentation of large linear DNA. In our previous work, a significant underestimation (∼30%) was found in count-based quantification of lambda phage DNA compared with the results of the CE-dNMP analysis [19]. The cause of this underestimation was hypothesized to be due to the fragmentation of linearized lambda phage DNA from routine sample handling. It has been confirmed that linear DNA is subject to fragmentation by routine manipulations if its length is greater than 20 kbps, whereas smaller DNA is quite immune to fragmentation [24]. Although it does not count as much as 30% of lambda phage DNA of its integrity, substantial amounts of fragments are visible in the histogram of lambda phage DNA samples (figure 3(a)). Smaller fragments could exist but be invisible due to the limited window of the fluorescence intensity. In contrast, pBR322 is not prone to such fragmentation as it is about 10-fold smaller than lambda phage DNA and is mostly in the form of tightly wound supercoils. Therefore, substantial fragmentation is not likely with pBR322, and no extra DNA was detected by the CE-dNMP analysis other than countable, intact pBR322. Consequently, underestimation should not be observed in this study.

An international measurement comparison has been organized among several national metrology institutes. In this comparison, the measurement performance for pBR322 plasmid DNA based on the direct counting method and d-PCR methods will be compared. Both the supercoiled form and the linearized form will be measured. The outcome of this study will ultimately prove the analytical validity and applicability of both enumeration-based DNA quantification methods.