# Fusing MEMS technology with lab-on-chip: nanoliter-scale silicon microcavity arrays for digital DNA quantification and multiplex testing

### Conceptualization of PCR array technology

Figure 1 shows a sketch that illustrates the basic concept of the PCR array technology. A microcavity array chip made from a silicon substrate is implemented into a polymeric LoC cartridge in such a way that it features three kinds of interfaces: a microfluidic interface to fill the microcavities with a sample liquid via an inlet channel and to subsequently seal the microcavities with a second immiscible sealant liquid; a thermal interface for an exchange of heat with an external Peltier device enabling a rapid and homogeneous thermal cycling of the liquid aliquots inside the microcavities; and an optical interface for optical excitation and real-time fluorescence read-out of the liquid aliquots allowing for a tracking of the individual qPCR amplification reactions. Inside the microcavities, dried reagents like target-specific primers and probes or template DNA can be prestored. A flexible adhesive is used to bond the silicon chip fluidically tightly to the polymeric LoC cartridge for temperatures up to 95 °C.

In the following, we will proceed with an in-depth experimental characterization of this PCR array technology. Details regarding the fabrication technology of the microfluidic chips, the test setup used for carrying out the experiments, as well as the methodology employed for data acquisition and analysis are described in the “Materials and methods” section. The reader is recommended to read this section at first before continue reading the “Results and discussion” section.

For a characterization of the PCR array technology, we performed several experiments in order to investigate the cross talk between adjacent reaction compartments during thermal cycling, the carryover of prestored reagents during microfluidic filling and sealing, and the target-specific PCR amplification in selected microcavities by means of prestored primers and TaqMan probes. Besides the characterization of the technology, we describe a novel method for the absolute quantification of DNA in a sample liquid. The method enhances the quantification capabilites of standard digital PCR by incorporating the detailed launch characteristics of an amplification reaction inside a compartment under defined environmental conditions. By applying this probability of detection (POD)-based digital PCR, an accurate DNA quantification can be accomplished in multi-compartment devices by making use of amplification reactions, with arbitrary sensitivity characteristics and a LOD greater than one.

### Absolute DNA quantification by POD-based digital PCR

For an experimental investigation of the PCR performance within the microcavity array chip, we introduced a liquid PCR master mix into the microcavities that contained primers and probes for the detection of the ABL (Abelson murine leukemia viral oncogene homolog 1, also known as ABL1) gene target associated with chronic myeloid leukemia (CML), as well as corresponding template DNA (see “Materials and methods” section and ref. 48 for further information). In this case, no PCR reagents were prestored inside the microcavities. However, different concentrations of ABL template DNA within the liquid master mix were used. The obtained test results are summarized in Fig. 2a–d showing four endpoint fluorescence micrographs acquired after thermal cycling at the annealing temperature (60 °C), which correspond to initial template DNA concentrations of (bar{c}=) 2, 5, 10, and 20 calculated copies “per” microcavity (cpc) on average; Fig. 2e–h shows the corresponding normalized fitted amplification curves (see “Materials and methods” section for data analysis methodology).

The endpoint fluorescence micrographs in Fig. 2a–c indicate the presence of different fluorescence signal levels inside the individual microcavities after thermal cycling. In particular, an amplification-related sigmoidal increase in the fluorescence signal is detected in a certain fraction of the microcavities only. The fraction varies from 42% for 2 cpc, over 77% for 5 cpc, and 93% for 10 cpc, up to 100% for 20 cpc (see bottom right corners of Fig. 2a–d). Hence, the measurements provide clear evidence that the portion of microcavities where a PCR takes place during thermal cycling is related to the initial average copy number per microcavity (bar{c}).

Since all experiments were conducted under the same environmental conditions, the observed variation of the positive rate must be ascribed to the specific amplification characteristics like the sensitivity and the selectivity of the used PCR. For a general quantitative analysis of the amplification results, the binomial distribution statistics ({B}_{n}(c,bar{c})) have to be taken into account, which describe the randomly generated initial copy number distribution inside the microcavity array. That is, ({B}_{n}(c,bar{c})) gives the probability for the case that a compartment comprises exactly c copies, if the average copy number in each of the n compartments is given by (bar{c}). Figure 2i illustrates the distribution statistics for a n = 96 compartmentalization, with (bar{c}=) 1, 2, 5, 10, or 20 cpc on average as given by the binomial probability density function

$${B}_{n}(c,bar{c})=left(begin{array}{l}ncdot bar{c}\ cend{array}right){n}^{-c}{(1-1/n)}^{ncdot bar{c}-c}$$

(1)

({B}_{n}(c,bar{c})cdot n) describes the number of microcavities comprising exactly c initial copies of DNA, which is plotted there. As indicated in Fig. 2i, the general binomial statistical description includes both Poisson and Gaussian distribution statistics as limiting cases. In contrast to the Poisson distribution, which is commonly used in digital PCR analysis, the more general binomial distribution is also valid for the case that the number of reaction compartments n is rather small. However, for a relatively large number or reaction compartments n, the Poisson distribution (P(c,bar{c})={bar{c}}^{c}/c! {e}^{-bar{c}}) serves a good approximation, i.e., ({B}_{n}(c,bar{c})to P(c,bar{c})) for n → , and might be used as well for calculation.

In order to relate the experimentally determined positive rates with the initial copy number distribution, it appears useful to introduce a characteristical POD function pd(c) that describes the probability for a launch of an amplification reaction inside a thermalized microcavity compartment (under defined environmental conditions) in dependence on the initial number of DNA copies c inside the compartment. By applying the binomial distribution statistics ({B}_{n}(c,bar{c})), the fraction r of compartments where an amplification reaction takes place may be described by a POD-based binomially estimated launch rate

$$r(bar{c})=mathop{sum }limits_{c=0}^{infty }{p}_{d}(c)cdot {B}_{n}(c,bar{c})$$

(2)

Besides the discrete formulation using sums an integral description can be employed as well as given in the Supplementary Information.

The POD function pd(c) may be approximated by a Heaviside function Θ with a step at the copy number c = cLOD corresponding to the LOD of the amplification reaction:

$${p}_{d,Theta ;{rm{LOD}}}(c)=Theta (c-{c}_{{rm{LOD}}})$$

(3)

In this simple approximation, the ratio r of reaction compartments where an amplification takes place, as given in Eq. (2), becomes

$${r}_{Theta ;{rm{LOD}}}(bar{c})=mathop{sum }limits_{c={c}_{{rm{LOD}}}}^{infty } {B}_{n}(c,bar{c})$$

(4)

For a more realistic description of the onset of an amplification reaction inside a compartment, it appears viable to include a detection uncertainty to the POD function by folding the Heaviside function pd,Θ;LOD(c) with a Gaussian probability density function of width w

$${G}_{w,{c}_{0}}(c)=1/sqrt{2pi {w}^{2}}cdot exp [-{(c-{c}_{0})}^{2}/(2{w}^{2})]$$

(5)

in order to incorporate a continuous onset of the amplification reaction around the LOD copy number cLOD into the POD function

$${p}_{d,G;{rm{LOD}},w}(c)={intnolimits_{!-infty }^{infty }}dc^{prime} {p}_{d,Theta ;{rm{LOD}}}(c-c^{prime} ) {G}_{w,{c}_{0} = 0}(c^{prime} )$$

(6)

yielding a POD-based binomially estimated launch rate of

$${r}_{G;{rm{LOD}},w}(bar{c})=mathop{sum }limits_{c=0}^{infty }left({intnolimits_{!-infty }^{c-{c}_{{rm{LOD}}}}}dc^{prime} {G}_{w,0}(c^{prime} )right)cdot {B}_{n}(c,bar{c})$$

(7)

The graph in Fig. 2j compares the experimental results with calculative results from the analytical model. The experimentally measured positive rates r are plotted as labeled colored dots in dependence on the calculated initial average copy number per microcavity (bar{c}). The POD-based binomially estimated launch rates (r(bar{c})) from the model described above are indicated by the gray and black line, representing the Heaviside and the Gaussian onset modeling, respectively. The fitting parameters are cLOD = 2.6 for the Heaviside onset model pd(c) and cLOD = 2.5, w = 2.95 for the Gaussian onset model pd,G(c). The inset in Fig. 2j indicates the two corresponding POD functions pd,Θ;LOD(c) and pd,G;LOD,w(c).

Both POD functions reproduce the increase in the positive rate r that is associated with the average copy number (bar{c}) inside the compartments. However, the Gaussian onset model with a continous probability variation shows a better quantitative agreement with the experimental data. The coefficients of determination R2 yield ({R}_{Theta }^{2}=88.19 % ) for the Heaviside onset model and ({R}_{G}^{2}=99.20 % ) for the Gaussian onset model, respectively. By applying the Gaussian onset model, a 50% LOD of about cLOD = 2.5 (see above) can be infered from the experimental data. The measured ci values given in Fig. 2e–h are consistent with the results and indicate an efficient amplification reaction. All in all, the model and the experimental results are in good agreement.

Notably, the positive rates obtained from the Gaussian onset model are similar to a heuristic approach based on the Poissonian fraction (1-{e}^{-bar{c}}) of compartments comprising at least one copy. By introducing a LOD copy number cLOD into the calculation of this fraction, one obtains a launch rate of ({r}_{P;{rm{LOD}}}(bar{c})=1-{e}^{-bar{c}/{c}_{{rm{LOD}}}}). The corresponding fit with cLOD = 3.5 is indicated by the dashed black line in Fig. 2j, and shows good agreement with both the experimental positive rates, as well as the Gaussian onset modeling approach. Accordingly, further experimental studies should investigate if an onset modeling based on a given LOD copy number might be sufficient for an accurate digital DNA quantification, or if a more general POD function-based approach is advantageous in particular cases.

### Estimation of the cross talk rate during thermal cycling

An important property of every compartment-based reaction device is the cross talk rate between adjacent reaction compartments. For our case, the cross talk rate may be defined as the fraction of PCR-generated amplification product in a microcavity that is accidentally transferred to another (adjacent) microcavity during one PCR cycle.

In general, cross talk might be a serious issue that crucially affects the occurence of false positives and the entire functionality of the reaction device. However, the experiments presented in Fig. 2 demonstrate that the cross talk rate of our microcavity arrays must be very low in general, in the order of only 10−3 per PCR cycle:

A significant cross talk between adjacent microcavities in the order of 10−1 per PCR cycle would lead to a high false-positive rate with the consequence, that all microcavities would generate a positive fluorescence signal within a certain amount of thermal cycles. The micrographs in Fig. 2a–c and the observed amplification statistics proof that this is not the case here. However, a close look onto the amplification curves in Fig. 2e–h reveals that there are bunches of amplification curves corresponding to an average ci value that is about ten cycles higher than the main amplification peak. The large shift of about ten PCR cycles cannot be explained by the (small) variation of the initial copy number inside the microcavities due to the binomial distribution statistics: even an initial copy number variation by a factor of 16 = 24 (see Fig. 2i) would lead to a shift of about four PCR cycles only. Hence, the delayed amplification signals have to be false positives that may be ascribed to a possible cross talk between adjacent microcavities. However, the large delay of about ten PCR cycles indicates a maximum cross talk rate in the order of only 1/210 = 1/1024 ≈ 10−3 per PCR cycle. Although the presence of a possible spatially confined cross talk between individual microcavities cannot be excluded by our methodology, the results proof a very low cross talk in general, which is acceptable for PCR-based testing.

### Determination of reagent carryover during microfluidic filling and sealing by the prestorage of template DNA in selected microcavities

In section “Absolute DNA quantification by POD-based digital PCR”, we derived from the amplification statistics a 50% LOD for the ABL gene target of ~2.5 cpc. Thus, due to the good sensitivity, the used PCR appears well suited for a characterization of a possible carryover of prestored reagents that may take place during filling and sealing of the microcavity array. For this purpose, we used a microcavity array where every second microcavity was loaded with 100 copies of ABL template DNA. The master mix, which was introduced into the flow chamber, contained no template DNA but the corresponding primers and probes for the amplification and detection of the ABL gene target.

Figure 3a sketches the chessboard-like spotting layout. Regarding a possible carryover of prestored reagents, this pattern represents the most critical scenario, where a carryover of only a few copies of DNA from one of four adjacent microcavities into another will cause a false-positive amplification signal in that microcavity (in the Supplementary Information another spotting layout is investigated in addition).

Figure 3b shows a fluorescence micrograph that was captured during thermal cycling at the annealing temperature (60 °C). The image illustrates that a positive PCR amplification signal is generated in every microcavity containing prestored template DNA (as marked by the orange circles). In contrast, the microcavities that does not contain template DNA at the beginning (marked by the gray circles) show an overall weaker fluorescence signal. Hence, considering the very low cross talk rate of our microcavity array (see last section), this observation indicates that also no significant carryover of prestored template DNA takes place during filling and sealing of the microcavity array chip.

However, to further investigate this issue, we analyzed the individual amplification curves in addition. Figure 3c shows a map of the measured ci values of the amplification reactions, that is the temperature cycle numbers that correspond to the inflection points of the fitted amplification curves. The used false color-scale representation is given on the right side of Fig. 3c. Evidently, the ci value false color map resembles a chessboard pattern. The microcavities with prestored template DNA inside show ci values in the range between 26.8 and 28.8 (colored in yellow, orange, and red), while the microcavities without prestored template DNA show predominantly no amplification within 50 cycles of thermal cycling (colored in dark blue), or a delayed amplification signal (ci ≥ 32, colored in light blue). All in all, the difference of the ci cycle values between adjacent true-positive and false-positive amplification reactions is at least about four. Hence, based on the difference of the ci cycle values corresponding to true-positive and false-positive microcavities, the maximum fraction of carried over template DNA can be estimated to some 1/24 ≈ 6%. In the predominant areas, where no false-positive amplification signal is generated the fraction is even smaller. Based on the LOD of the used amplification reaction of about cLOD = 2.5 determined in the previous section, the fraction can be estimated to a maximum of only some cLOD/100 = 2.5% in these areas.

In summary, the experiment demonstrated that the carryover of prestored reagents that takes place during filling and sealing of the microcavities is low in general. For multiplexing purposes with prestored target-specific primers and probes (but no DNA), the measured carryover rate should be fairly acceptable: even a carryover of some 10% would lead to concentrations of accidentally transferred primers and probes that are about ten times lower than the standard concentrations in an ordinary PCR master mix. Consequently, the primer and probe concentrations in such a microcavity were both far too low to facilitate an efficient PCR reaction and to generate a false-positive amplification signal. However, in the following section, we will address this issue experimentally.

### Multi-targeted sample analysis by the prestorage of specific primers and probes in selected microcavities

In the last two subsections, we demonstrated that the used microcavity chips enable a geometric multiplexing by means of qPCR with very low cross talk during thermal cycling, and minor reagent carryover during microfluidic filling and sealing. In the following, we will briefly address the possibility of a multi-targeted sample analysis by a prestorage of target-specific primers and probes inside single microcavities.

For a basic testing, we prestored two sets of primers and probes inside 12 specific microcavities each addressing the ABL or the e13a2 gene target, respectively. Both genes are associated with CML (ref. 48). For the ABL gene target, we used a Cy3 fluorescence TaqMan probe while for the e13a2 gene target a Cy5 TaqMan probe was used. The 12 microcavities used for each gene target were distributed in a hexagonal pattern across the entire microcavity array in such a way that all adjacent microcavities of a loaded microcavity are empty. Accordingly, a possible carryover of reagents to an adjacent microcavity or a cross talk between adjacent microcavities during thermal cycling should be clearly observable.

Figure 4a, b shows two two-channel fluorescence micrographs in a RGB false color-scale representation before and after thermal cycling, respectively. The greyscale signal of the Cy3 fluorescence channel related to the ABL gene TaqMan probe is shown in red, while the Cy5 fluorescence signal of the e13a2 gene TaqMan probe is colored in green. Both micrographs are in good agreement, which indicates that there is no significant cross-contamination of adjacent microcavities due to carryover or cross talk. However, the 12 microcavities corresponding to the ABL gene target exhibited an increase in the fluorescence signal during thermal cycling.

The graph in Fig. 4c depicts a typical amplification-related fluorescence curve that corresponds to the microcavity “G4”. Like before, a sigmoidal increase of the fluorescence signal is observed. The ci = 28.55 value is shifted to a lower value due to the higher concentration of ABL template DNA inside the master mix ((bar{c}=100 {rm{cpc}})).

Figure 4d shows a map of the ci value distribution inside the microcavity array, Fig. 4e a graph of the normalized fitted amplification curves. Evidently, an amplification is achieved in all microcavities with prestored ABL primers and probes while no false-positive amplification signals are generated. Hence, the microcavity chips used here appear well suited for multiplexing applications, where different sets of primers and probes are prestored in selected microcavities.

### Conclusions and outlook

Our experiments demonstrated that functionalized silicon-based microcavity array chips are an excellent component for PCR-based sample analysis in polymeric LoC cartridges. By a prestorage of specific primers and probes inside individual microcavities, multiple targets may be addressed within a single chip. Due to the established and highly developed silicon micromachining techniques, a further reduction of the reaction volumes and an increase in the degree of multiplexing seems possible. Hence, in this article, we introduced the concept of fusing MEMS technology with lab-on-chip. From our point of view, the used hybrid silicon–polymer approach is a key to combine the best of both worlds: a microcavity array chip made from silicon, on the one hand, featuring a metal-like heat conductivity for a rapid and spatially homogeneous thermal cycling of the reaction compartments, tailored wetting properties for a capillary-assisted, fully automatable, and temperature-stable microfluidic aliquoting of the sample liquid, a high fabrication accuracy to provide reaction compartments with a precisely defined volume, no significant self-fluorescence for precise fluorometric qPCR measurements, and an inert surface that facilitates miniaturized biochemical reactions. While a polymeric lab-on-chip cartridge, on the other hand, can provide active fluid management for pumping and valving of liquids, reservoirs for an on-chip long-term storage of reagents, a world-to-chip interface for an introduction of the sample, as well as an enclosure of the liquids for a safe and contamination-free sample processing. Following this approach, we will perform further tests inside a specifically designed Vivalytic LoC cartridge that enables a fully automated filling and sealing of the microcavity array in an external processing unit (see ref. 49). In this way, the filling and sealing dynamics become highly reproducible making an even more detailed investigation of reagent carryover possible. Within that context, different additives apart from polyethylene glycol (PEG) may be tested to further reduce the reagent carryover during microfluidic filling and sealing.

Furthermore, we described a digital DNA quantification method taking the assay-specific amplification characteristics like the LOD into account. It is likely that the description introduced here coincides well with the experimental results reported in previous studies (see, for example, Fig. 4 in ref. 8, Fig. 2 in ref. 9, Fig. 4 in ref. 11, and Table 1 in ref. 47). However, further studies should investigate if the introduced amplification onset modeling by a POD function pd(c) is a generally valid approach for a description of the assay-specific amplification characteristics, thus enabling an accurate quantification of DNA using different amplification reactions and compartment-based digital PCR devices.

In conclusion, by providing a highly parallelized and quantitative testing of a plurality of different gene targets, the here presented PCR array technology constitutes the basis for the implementation of complex bioassays into lab-on-chip systems with a broad range of possible applications in the PoC molecular laboratory diagnostics field.

Source Article