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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 3 — Mar. 1, 2014
  • pp: 737–751
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Microdroplet temperature calibration via thermal dissociation of quenched DNA oligomers

Eric W. Hall and Gregory W. Faris  »View Author Affiliations


Biomedical Optics Express, Vol. 5, Issue 3, pp. 737-751 (2014)
http://dx.doi.org/10.1364/BOE.5.000737


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Abstract

The development of microscale analytical techniques has created an increasing demand for reliable and accurate heating at the microscale. Here, we present a novel method for calibrating the temperature of microdroplets using quenched, fluorescently labeled DNA oligomers. Upon melting, the 3′ fluorophore of the reporter oligomer separates from the 5′ quencher of its reverse complement, creating a fluorescent signal recorded as a melting curve. The melting temperature for a given oligomer is determined with a conventional quantitative polymerase chain reaction (qPCR) instrument and used to calibrate the temperature within a microdroplet, with identical buffer concentrations, heated with an infrared laser. Since significant premelt fluorescence prevents the use of a conventional (single-term) sigmoid or logistic function to describe the melting curve, we present a three-term sigmoid model that provides a very good match to the asymmetric fluorescence melting curve with premelting. Using mixtures of three oligomers of different lengths, we fit multiple three-term sigmoids to obtain precise comparison of the microscale and macroscale fluorescence melting curves using “extrapolated two-state” melting temperatures.

© 2014 Optical Society of America

1. Introduction

The advent of microscale analytical technologies promises new advances in detection and quantitation in a variety of fields, from medicine to environmental monitoring to food safety [1

1. Y. T. Atalay, S. Vermeir, D. Witters, N. Vergauwe, B. Verbruggen, P. Verboven, B. M. Nicolaï, and J. Lammertyn, “Microfluidic analytical systems for food analysis,” Trends Food Sci. Technol. 22(7), 386–404 (2011). [CrossRef]

3

3. G. B. Salieb-Beugelaar, G. Simone, A. Arora, A. Philippi, and A. Manz, “Latest developments in microfluidic cell biology and analysis systems,” Anal. Chem. 82(12), 4848–4864 (2010). [CrossRef] [PubMed]

]. However, as greater reproducibility and sensitivity are required for commercialization, there is a greater demand for more accurate and efficient methods of temperature control. Fulfilling this need is a non-trivial task, as many traditional techniques are incompatible with the confined spatial requirements of microfluidics [4

4. S. Mondal and V. Venkataraman, “Novel fluorescence detection technique for non-contact temperature sensing in microchip PCR,” J. Biochem. Biophys. Methods 70(5), 773–777 (2007). [CrossRef] [PubMed]

, 5

5. G. Velve Casquillas, C. Fu, M. Le Berre, J. Cramer, S. Meance, A. Plecis, D. Baigl, J.-J. Greffet, Y. Chen, M. Piel, and P. T. Tran, “Fast microfluidic temperature control for high resolution live cell imaging,” Lab Chip 11(3), 484–489 (2011). [CrossRef] [PubMed]

].

The wide variety of temperature control solutions that have been described in the literature can generally be sorted into contact and non-contact methods, though hybrid solutions also exist [6

6. C. Fang, L. Shao, Y. Zhao, J. Wang, and H. Wu, “A gold nanocrystal/poly(dimethylsiloxane) composite for plasmonic heating on microfluidic chips,” Adv. Mater. 24(1), 94–98 (2012). [CrossRef] [PubMed]

, 7

7. K. J. Shaw, P. T. Docker, J. V. Yelland, C. E. Dyer, J. Greenman, G. M. Greenway, and S. J. Haswell, “Rapid PCR amplification using a microfluidic device with integrated microwave heating and air impingement cooling,” Lab Chip 10(13), 1725–1728 (2010). [CrossRef] [PubMed]

]. Contact heating methods typically rely on resistive Joule heating or other solid-state elements to provide heating combined with thermometry feedback control. However, these are typically limited to integrated “lab-on-a-chip” microfluidic technologies, where the critical elements are integrated into the chip architecture [6

6. C. Fang, L. Shao, Y. Zhao, J. Wang, and H. Wu, “A gold nanocrystal/poly(dimethylsiloxane) composite for plasmonic heating on microfluidic chips,” Adv. Mater. 24(1), 94–98 (2012). [CrossRef] [PubMed]

, 8

8. B. Selva, J. Marchalot, and M.-C. Jullien, “An optimized resistor pattern for temperature gradient control in microfluidics,” J. Micromech. Microeng. 19(6), 065002 (2009). [CrossRef]

10

10. E. M. Graham, K. Iwai, S. Uchiyama, A. P. de Silva, S. W. Magennis, and A. C. Jones, “Quantitative mapping of aqueous microfluidic temperature with sub-degree resolution using fluorescence lifetime imaging microscopy,” Lab Chip 10(10), 1267–1273 (2010). [CrossRef] [PubMed]

]. For larger or more flexible systems in which the sample or reaction vessel is not limited to a pre-defined microscale area, this becomes prohibitively expensive or simply incompatible. Non-contact optical methods of temperature control are inherently more flexible and rely on radiation for heat delivery [7

7. K. J. Shaw, P. T. Docker, J. V. Yelland, C. E. Dyer, J. Greenman, G. M. Greenway, and S. J. Haswell, “Rapid PCR amplification using a microfluidic device with integrated microwave heating and air impingement cooling,” Lab Chip 10(13), 1725–1728 (2010). [CrossRef] [PubMed]

, 11

11. H. Kim, S. Dixit, C. J. Green, and G. W. Faris, “Nanodroplet real-time PCR system with laser assisted heating,” Opt. Express 17(1), 218–227 (2009). [CrossRef] [PubMed]

16

16. A. F. R. Hühmer and J. P. Landers, “Noncontact infrared-mediated thermocycling for effective polymerase chain reaction amplification of DNA in nanoliter volumes,” Anal. Chem. 72(21), 5507–5512 (2000). [CrossRef] [PubMed]

].

To provide accurate thermometry for infrared laser-assisted heating in microdroplet PCR [11

11. H. Kim, S. Dixit, C. J. Green, and G. W. Faris, “Nanodroplet real-time PCR system with laser assisted heating,” Opt. Express 17(1), 218–227 (2009). [CrossRef] [PubMed]

13

13. K. Hettiarachchi, H. Kim, and G. Faris, “Optical manipulation and control of real-time PCR in cell encapsulating microdroplets by IR laser,” Microfluid. Nanofluid. 13(6), 967–975 (2012). [CrossRef]

], we have developed a temperature calibration method that relies on the melting of contact-quenched fluorescently labeled DNA oligomers. An oligomer labeled with a 5′ fluorescent reporter is contact-quenched by a 3′ quencher on the reverse complement upon hybridization [21

21. S. A. E. Marras, F. R. Kramer, and S. Tyagi, “Efficiencies of fluorescence resonance energy transfer and contact-mediated quenching in oligonucleotide probes,” Nucleic Acids Res. 30(21), 122e (2002). [CrossRef] [PubMed]

24

24. A. T. Jonstrup, J. Fredsøe, and A. H. Andersen, “DNA hairpins as temperature switches, thermometers and ionic detectors,” Sensors (Basel) 13(5), 5937–5944 (2013). [CrossRef] [PubMed]

]. With heating and dissociation of the hybrid pair, the fluorescence of the reporter oligomer is detected and recorded. The melting points of several oligomer pairs are assigned with a traditional qPCR instrument and used to calibrate temperature in the microdroplet with laser heating when this process is repeated at the microscale. This method not only provides a reliable and consistent calibration for microdroplet heating, as demonstrated by proper selection of heating parameters for qPCR, but it is also simple and straightforward to perform. Although we use this method for system calibration, it could be applied to online temperature monitoring during PCR while consuming only a single fluorescence channel.

Because premelting of DNA oligomers prevents modeling the fluorescence melting curve as a conventional (one-term) sigmoid that applies to a two-state system, we have also developed a model based on a three-term sigmoid that allows determination of precise melting temperatures from a fluorescence melting curve using curve fitting even when the premelting fluorescence is quite large. Calibration over a broader temperature range is obtained using a mixture of multiple oligomer pairs. The three-term sigmoid fitting allows for the use of common fluorescent DNA labels, such as fluorescein amidite (FAM), that can induce non-two-state melting behavior [25

25. Y. You, A. V. Tataurov, and R. Owczarzy, “Measuring thermodynamic details of DNA hybridization using fluorescence,” Biopolymers 95(7), 472–486 (2011). [CrossRef] [PubMed]

] as well as the use of high melting temperatures (85 °C for our longest oligomer with 47 base pairs).

2. Materials and methods

2.1 Reagents and DNA oligomers

Three reverse-complement pairs of DNA oligomers were designed for contact-quenching based on the work of Marras et al. [21

21. S. A. E. Marras, F. R. Kramer, and S. Tyagi, “Efficiencies of fluorescence resonance energy transfer and contact-mediated quenching in oligonucleotide probes,” Nucleic Acids Res. 30(21), 122e (2002). [CrossRef] [PubMed]

]. The three sequences, hereafter referred to as Oligo 20, Oligo 27, and Oligo 47, are listed in Table 1

Table 1. DNA Oligomer Sequences

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. The sequences were labeled with 5′-6-FAM while their reverse complements were each labeled with 3′-Dabsyl, enabling each pair to engage in static-contact quenching when annealed. All oligos were synthesized by the Protein and Nucleic Acid Facility at Stanford University (Stanford, CA). Aqueous stock solutions of each oligo (100 – 500 μM) were prepared and stored in the dark at −20 °C. Because both the diameter of microdroplets generated and oligomer melting temperature depend on buffer conditions, all subsequent oligo solutions were created in PCR master mix at 1X concentration (TaqMan Fast Universal, Life Technologies).

Solutions containing 2 μM of each reporter oligo and 10 μM of its reverse-complement quencher were prepared. The five-fold excess of quencher both minimizes the influence of unquenched dye on the results and simplifies the determination of melting temperatures, as demonstrated below. Solutions were further diluted to create 40-μL samples containing individual reporter-quencher pairs as well as mixtures of all three pairs. In all final solutions, Oligo 20 was prepared at 0.67 μM/3.3 μM FAM/Dabsyl, Oligo 27 was prepared at 0.50 μM/2.5 μM FAM/Dabsyl, and Oligo 47 was prepared at 0.83 μM/4.2 μM FAM/Dabsyl. Solutions containing only the reporter oligo at the same concentrations were also prepared for correction of temperature-quenching of the dye.

All 40-μL samples were run on an ABI 7300 Real-Time PCR System (Applied Biosystems) in an ABI Prism 96-well Optical Reaction Plate using a dissociation curve protocol. After holding at 95 °C for 15 seconds, the samples were annealed by lowering the temperature to 36 °C for 1 minute and then they were melted by raising it to 96 °C for 15 seconds. The temperature was ramped at +/− 1.1 °C/s for both annealing and melting. Raw fluorescence data was exported from the instrument and analyzed using a three-term sigmoid model, described below, to extract the melting temperatures.

2.2 Microdroplet production and imaging

A clear, 35-mm polystyrene Petri dish (Nunc, Thermo Fisher Scientific) was cleaned with methanol and dried with compressed air. A Zerostat gun was used to minimize the surface charge on the dish. 1.5 mL of sterile-filtered embryo tested mineral oil (Sigma) containing 0.4 mL of lecithin / 5 mL mineral oil was pipetted into the dish. The Petri dish was placed on the platform of the imaging microscope described below.

Oligo sample solutions were prepared in the same manner (as above) for macroscale melting. Microdroplets of oligo samples in 1X PCR master mix buffer, approximately 250 μm in diameter, were deposited onto the Petri dish under the surface of the mineral oil to prevent evaporation and maintain a high contact angle. Microdroplet deposition was accomplished by injecting sample solution through a capillary via pressure while the capillary was dipped under the mineral oil, as described elsewhere [11

11. H. Kim, S. Dixit, C. J. Green, and G. W. Faris, “Nanodroplet real-time PCR system with laser assisted heating,” Opt. Express 17(1), 218–227 (2009). [CrossRef] [PubMed]

13

13. K. Hettiarachchi, H. Kim, and G. Faris, “Optical manipulation and control of real-time PCR in cell encapsulating microdroplets by IR laser,” Microfluid. Nanofluid. 13(6), 967–975 (2012). [CrossRef]

]. Mineral oil was used because it has a lower density (0.82 – 0.88 g mL-1) than water and has extremely low water solubility.

Microdroplets were imaged using an inverted fluorescence microscope (TE2000, Nikon Instruments) containing a dual filter-turret and fitted with a 10x Nikon objective. Figure 1
Fig. 1 Instrument schematic for microdroplet heating with an infrared diode laser and imaging of sample fluorescence.
illustrates the system design. The top filter cube is used for fluorescence excitation and emission collection and the bottom filter cube delivers an infrared (IR) beam from a diode laser (FOL 1402PLY-617-1457, Furukawa Electric) of wavelength 1.46 μm for heating the microdroplet. A current source (LDX-3620, ILX Lightwave) under computer control varies the laser power for thermal cycling. Band-pass filters are used for fluorescence detection with a 480/40-nm filter for excitation and a 535/50-nm filter for emission. All dichroics and filters were purchased from Chroma (Bellows Falls, VT).

A two-lens telescope and 4-f two-lens configuration based on Thorlabs cage systems are utilized to adjust collimation and couple the laser to the microscope. Defocusing the laser beam at the microdroplets is achieved by translating one lens in the telescope in order to achieve a ~300-nm beam size and obtain a relatively uniform temperature distribution. The laser beam position and size are monitored using a transparent tape coated with a thin layer of erbium upconverting phosphor powder. Brightfield and fluorescence images are acquired with a cooled charge-coupled device (CCD) camera (Retiga EXi, QImaging). For DNA oligomer melting curve studies, the power of the laser was ramped between 0 and 63 mW, stepping up by 0.15 mW and holding for 5 seconds at each step. Fluorescence and brightfield images were taken at 3 and 4 seconds into the hold, respectively. All experiments were conducted at ambient temperature (23 °C).

2.3 Microdroplet PCR

PCR reaction solutions were prepared by combining 20 μL of TaqMan Fast Universal 2X master mix with 4 μL human male DNA (Applied Biosystems), 2 μL FAM-labeled 18SRNA primer-probe (Hs03928985_g1 TaqMan Expression Assay, Applied Biosystems), and 14 μL PCR-grade water (Ambion). Microdroplets of the reaction mixture were deposited on a Petri dish coated in mineral oil as described above. No treatment is necessary to prevent adsorption of DNA to the polystyrene surface.

Thermocycling protocol for TaqMan Fast Universal PCR Master Mix was converted to laser power using the melting curve calibration described below. This PCR protocol, for an ABI 7300 instrument, consists of an activation and denaturation step of 30 seconds at 95 °C, followed by 40 cycles of 30 seconds at 60 °C (annealing/extension) and 1 second at 95 °C (denaturation). The data shown below was obtained using laser power settings corresponding to 60 °C and 95 °C, respectively. Additionally, tolerance of the PCR reaction in the microdroplet was explored by testing the reaction at various power settings corresponding to 5 °C steps in the annealing/extension and denaturing temperatures. The results of these reactions were then compared to 25-μL reactions of the same PCR mixture run in a desktop instrument (AB7300, Applied Biosystems).

Droplets were imaged after the first 3 seconds of the annealing phase of each cycle for real-time FAM and brightfield detection, controlled in LabVIEW. The average pixel intensity for each droplet is tracked through 40 cycles of PCR. Fluorescence images are acquired with a 300-ms acquisition time and brightfield images are acquired with a 5-ms acquisition time to avoid observable fluorescence bleaching effects. The fluorescence illumination source is blocked with an automated shutter between fluorescence measurements.

3. Results and discussion

3.1 Macroscale melting analysis of reporter-quencher DNA oligos

Individual contact-quenched hybrid pairs of Oligos 20, 27, and 47 in PCR master mix buffer solutions were analyzed via thermal dissociation to obtain their fluorescence melting curves. Samples of each oligomer pair, as well as a mixture of all three oligomer pairs, were analyzed in replicates of 5. Melting curves were divided by the fluorescence of solutions containing only the reporter-labeled oligos to correct for thermal quenching of the fluorescent dye.

As will be further discussed below, the plots of fluorescence as a function of temperature do not fit well to the simple single-term sigmoid shape expected for two-state bimolecular melting/hybridization of two complementary DNA oligomers [26

26. J.-L. Mergny and L. Lacroix, “Analysis of thermal melting curves,” Oligonucleotides 13(6), 515–537 (2003). [CrossRef] [PubMed]

]. This discrepancy is due to a “premelt” fluorescence contribution that arises from disruption of the static, contact-quenched dimer of the 5′-FAM reporter and 3′-Dabsyl quencher. This premelt fluorescence increases with temperature as the reporter and oligomer achieve greater average distances apart due to “breathing” motions of the hybridized pair [27

27. M. Peyrard, S. Cuesta-López, and G. James, “Nonlinear analysis of the dynamics of DNA breathing,” J. Biol. Phys. 35(1), 73–89 (2009). [CrossRef] [PubMed]

]. It is important that we include this effect in our model of the fluorescence temperature dependence to obtain accurate results.

To account for this premelt fluorescence, we approximate the system as an equilibrium of three states as shown in Fig. 2
Fig. 2 Three-state equilibrium that describes the melting process of a static-quenched DNA oligomer pair. The premelt fluorescence we observe is accounted for by the existence of an intermediate state FQ* in which distance-based fluorescence resonance energy transfer (FRET) quenching is in effect.
: the contact-quenched hybrid pair, FQ, a premelted pair in which the reporter and quencher are not in static contact; FQ*; and the completely unquenched, melted pair, reporter F and quencher Q. The system is described by the equations
K1=[F][Q][FQ]
(1)
K2=[FQ*][FQ]
(2)
K3=[F][Q][FQ*]
(3)
where K1, K2, and K3 are temperature-dependent equilibrium constants for each state change and the quantities in square brackets indicate temperature-dependent concentrations in each state.

Note that we are treating [FQ*] as a single state although the premelted molecules will actually have a continuum of dye-quencher distances with different levels of fluorescence: some fully-quenched, some fully unquenched with fluorescence similar to the denatured states, and some with partially quenched fluorescence. Treating [FQ*] as a single state is valid with the appropriate definition of the concentrations [FQ*] and [FQ]. In particular, we define [FQ*] as the combination of the fully unquenched premelt molecules with an appropriate fraction of the partially quenched premelt molecules such that the product of this combined concentration [FQ*] times the fully unquenched fluorescence per molecule is equal to the total premelt fluorescence. The remainder of the partially quenched states and the fully quenched states are included in the state [FQ] to account for all the annealed oligomers. This simplified accounting is similar in principle to the two-state equilibrium of Eq. (1) in which any given oligo is neither annealed nor free, but is annealed for part of the time or denatured for part of the time. This definition of [FQ*] and [FQ] accounts for the total number of premelted molecules (since the population of partially-quenched molecules is split into dark and unquenched subpopulations) and accounts for the total fluorescence, since we have defined the subpopulations to ensure the total fluorescence is the equal to the actual fluorescence. However, because this definition of [FQ*] does not correspond to a conventional molecular state, the associated enthalpy that defines its coordinate in the reaction, ∆Hp, is not a true enthalpy but is instead a mathematical construct that assigns the population with a partially-quenched fluorescence brightness to a smaller averaged population with a fluorescence corresponding to an unquenched state.

It is convenient to introduce a pseudoequilibrium constant, κ, which expresses the ratio of fluorescing states [FQ] + [FQ*] to the dark states [FQ]
κ=[F]+[FQ*][FQ]=K1[Q]+K2.
(4)
Note that from the rightmost equivalence in Eq. (4), κ has the approximate behavior of a sum of two equilibrium constants, though neither term in the sum is a true equilibrium constant since the first term includes the factor [Q] and the second term K2 couples [FQ*], which is not a single molecular state. However, as seen below, this framework provides a good description of our experiments.

We define the fractional concentrations of fluorescent states f as
f=[F]+[FQ*][F]+[FQ*]+[FQ]=κ1+κ=11+1/κ.
(5)
where the denominator is the total concentration of dye-labeled oligomers. Solving Eq. (5) for κ gives

κ=f1f.
(6)

Because of the way we have defined of [FQ*] and [FQ], f is both the fraction of dye-labeled oligomers in equivalent fluorescent states and the average fluorescence from a population of dye-labeled oligomers. Although not shown explicitly, all parameters in Eqs. (4)(6) are temperature-dependent, and f describes the fluorescence melting curve normalized from zero to one. When [FQ*] is negligible, the f and κ depend on melted ([F],[Q]) and annealed ([FQ]) states only, which is the two-state solution of Eq. (1). For the two-state solution and large excess of [Q], f takes the form of a sigmoid and κ has Arrhenius behavior (it is a straight line on an Arrhenius plot as described further below).

For our experiments, [FQ*] is not negligible, and f and κ have fluorescence contributions from both melting and premelting. Indeed, plots of the normalized experimental fluorescence melting curves, f, show strong departures from the sigmoid shape expected for a conventional two-state melting behavior, particularly for the 47-mer oligo, as shown in Fig. 3(a)
Fig. 3 Experimental data and theoretical fits for fluorescence melting curves. The same data are displayed in two parameterizations: normalized (dimensionless) fluorescence f versus temperature T in (a); and as an Arrhenius plot or ln(κ) versus 1/T in (b). Solid lines show five replicates of experimental data with a different color for each of the three oligos. Dotted lines show the three single-term κ or f for each oligo, labeled m (melt), p (premelt), or t (transition), appearing as straight lines on the Arrhenius plot (b) and sigmoids in (a). For clarity, κt is not displayed in (a). Dashed lines show the two-term calculations κ(2) = κm + κp, and f(2) in (b) and (a), respectively, demonstrating good fits to the experimental data in the high- and low-temperature regions, but poor agreement in the transition region. The three-term calculations κ(3) = κm + κp + κt and f(3) precisely overlap the data (not shown for clarity; see Fig. 4 for examples). Two points at T = Tm are shown: upward pointing triangles at κm = 1 or fm = 1/2 (which define Tm) and downward pointing triangles on κ(3) or f(3) at the same temperature. For comparison between the parameterizations κ or f and T or 1/T, the other parameterizations are shown on the opposing axes (right and top axes). While full experimental data sets are shown in (a), in (b) we only show data values for f < 0.995 to minimize the noise that would obscure part of the linear fits.
. Similarly, if we make Arrhenius plots of the same data. i.e., ln(κ) versus 1/T with T in Kelvin, we find two distinct regions, as shown in Fig. 3(b). In fact, the two regions are linear, indicating that they demonstrate Arrhenius-like behavior. We expect that the high-temperature Arrhenius-like region, denoted as κm, corresponds to melting, which we write as
κm(T)=κm(To)exp[Dm(1To1T)]equalforhighTK1[Q]=[F][FQ]
(7)
where the Arrhenius-like behavior is shown explicitly in terms of the Arrhenius plot slope Dm and the Arrhenius plot amplitude ln[κm(To)] at a reference temperature, To. Similarly, the low-temperature Arrhenius-like region κp corresponds to premelting with behavior

κp(T)=κp(To)exp[Dp(1To1T)]equalforlowTK2=[FQ*][FQ].
(8)

We expect strict equality between the left and right parts of Eqs. (7) and (8) only for the high- and low-temperature regions, respectively, because of the complications in the transition region as discussed below. The various pseudoequilibrium constants κ and associated sigmoid curves, f, are summarized in Table 2

Table 2. Pseudoequilibrium Constants κ and Associated Sigmoid Curves f

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. When κ is the sum of two or three Arrhenius terms, we refer to the resulting shape for f as a two- or three-term sigmoid, or f(2) or f(3) respectively. Although there are other asymmetric sigmoid or logistic functions [28

28. F. J. Richards, “A flexible growth function for empirical use,” J. Exp. Bot. 10(2), 290–301 (1959). [CrossRef]

, 29

29. J. H. Ricketts and G. A. Head, “A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies,” Am. J. Physiol. 277, R441–R454 (1999).

], the ones presented here are based on a physical model for our experiments and perform very well at all temperatures as shown in Figs. 3 and 4
Fig. 4 Fitting of three-term (f(3), a-c) and two-term (f(2), d-f) versions of the model to fluorescence melting curves of the 20-mer (a, d), 27-mer (b, e), and 47-mer (c, f) oligomer pairs. The f(2) fit experiences significant deviation from the data in the premelt and melting regions for the 27- and 47-mer data. This deviation is largely absent when the f(3) fit is applied. To minimize systematic effects from fluctuations in the saturated region (f ~1), fits were performed only up to a maximum temperature given by fm = 0.995 plus 5 degrees. The same experimental data has been presented in Fig. 3 as f and κ calculated using the A and B determined by the f(3) fits.
.

We would expect κm to follow Arrhenius behavior since it describes the proportion of [F] and [FQ] in the high-temperature region, and κm should follow K1 in behavior since [Q] is in excess and its value, compared to the range of K1, is relatively constant. The fact the κp follows Arrhenius behavior is unanticipated because [FQ*] is not a single well-defined state. Converting the high-temperature and low-temperature limiting cases, or κ ~κm and κ ~κp, respectively, of Fig. 3(b) into fluorescence melting curves fm and fp using Eq. (5) gives single-term sigmoids showing good agreement with the experimental data in these limits, shown as dotted lines in Fig. 3(a).

Anticipating that κ is a sum of κm and κp based on Eq. (4), we plot κ(2) = κm + κp and the associated f(2) as the dashed lines in Figs. 3(b) and 3(a), respectively. While both curves agree well with experiment in the high- and low-temperature regions, the transition regions do not have the proper shape. To better fit the entire data set, a third transition Arrhenius-behavior term, κt, is added to the κm + κp sum to better approximate the behavior of the transition region, giving a three-term expression for κ(3) = κm + κp + κt (Table 2). The physical behavior of this transition region is likely complex and beyond the scope of this paper. However, the κt term is useful for fitting the data and obtaining a reproducible melting temperature. The result from the three-term fit exactly overlaps with the data for both the Arrhenius plot and the fluorescence melting plot.

For fitting experimental data in which we are interested in extracting the melting temperature, Tm, it is useful to express κ and f in terms of this parameter. Thus, we will use Tm as the reference temperature To in Eqs. (7) and (8). The experimental definition of the melting point is complicated because: (a) the conventional melting point is only properly defined for a two-state model for which exactly half of the oligos are denatured, and (b) the details of the equilibria in the transition region are not well defined. Note that the high-temperature region is expected to correspond to the two-state conventional melting process as shown in Eq. (7). Indeed, the slopes of these high-temperature lines agree with calculated enthalpies to within 10-15 percent, as discussed below with respect to Table 3

Table 3. Three-Term κ Fit Parameters

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. Using this information, we define the melting point for these experiments as an “extrapolated two-state” melting temperature or the point at which κm would yield [F] = [FQ] in Eq. (7) or

κm(Tm)=1.
(9)

Note that there are eight fitting parameters in Eq. (10): the scaling factors A and B; the three slope constants Dm, Dp, Dt; the two pre-exponential factors κp(Tm) and κt(Tm); and the melting temperature, Tm. The sensitivity of the melting curve may be optimized by increasing the melting enthalpy, thus increasing the slope constant Dm, and minimizing pre-melt behavior so that more fluorescence signal is devoted to the main ‘melt’ slope. We determined the slope constants and pre-exponential factors from global fits to the five-replicate single-oligo data sets using the graphing analysis program Igor Pro, in which these values were linked to a single value for all five data sets while A, B, and Tm were allowed to change for each curve. Although the melting temperature for all five curves in a data set should, in principle, be the same, we found improved results by letting each fit to a different value for Tm. This led to only ~0.1 °C variation between curves within a set. The results from these fits are shown in Figs. 4(a)4(c), and the fit parameters are summarized in Table 3. The residuals at the top of each figure (i.e., data minus fit) show good agreement between experiment and fit. In particular, the residual variations are primarily random noise in nature. On the other hand, fitting of the two-term versions of the model using f(2) instead of f(3) do not agree with data nearly as well, as shown in Figs. 4(d)4(f). These fits produce residuals with pronounced oscillations for the 27-mer and 47-mer, demonstrating a poor agreement between data and fit. Because of the low melting temperature of the 20-mer, the f(2) fits perform reasonably well.

For a given oligomer, a rough estimate of the contribution of premelt to a measurement is the point where the premelt and melt terms are equal, or fm = fp. For T below this point premelting becomes more important, while above this point melting becomes more important. For our oligos, we find fm = fp = 0.07, 0.11, and 0.25 for the 20-mer, 27-mer, and 27-mer, respectively [see also Fig. 3(a)].

3.2 Temperature calibration of infrared heating laser

Microdroplets containing the same solutions of Oligos 20, 27, and 47 and a mixture of all three were analyzed via thermal dissociation to obtain their fluorescence melting curves using laser-assisted heating. As with the dissociation curves obtained from the qPCR instrument described above, the curves were corrected for thermal quenching. Figure 5
Fig. 5 Fluorescent melting curves of Oligos 20(a), 27(b), and 47(c) in a microdroplet heated by an infrared laser. Single-oligo premelt model fit is applied using parameters of Table 3 and similar results are obtained as from application to the macroscale melting curves. Note that discrepancies in fit become larger with the oligomer length. The temperature axis at the top of each graph is calculated from the calibration curve in Fig. 7.
shows the corrected microdroplet dissociation curves fitted using the same model described above and the parameters from Table 3 for melting curves obtained via macroscale melting. Since our measured parameter is laser power rather than temperature, we replace the temperature T in Eq. (10) with
T=Ta+αP
(11)
where Ta is the ambient temperature, P is the laser power, and α is the proportionality between laser power and droplet temperature. For the macroscale fits [Figs. 4 and 6(a)
Fig. 6 Fluorescent melting curves of samples containing all three oligo quenched pairs, both at the macroscale (a) and in microdroplets (b). Three-oligo premelt model fit is applied. The temperature axis in (b) is calculated from the calibration curve in Fig. 7.
], the independent variable is T, and Tm is a fitting parameter. For the microdroplet fits [Figs. 5 and 6(b)], P is the independent variable, Tm is fixed to the value in Table 3, Ta is set to 23 C, and α is a fitting parameter. From Fig. 5, we see that there is some increasing discrepancy between data and fit with increasing oligomer length, which may be due to deformation of droplet shape with increasing temperature. This is reflected in the increasing variance of the melting power with oligo length (0.06 mW for the 20-mer oligo versus 0.2 mW for the 47-mer oligo). However, the fit is sufficient for our purpose of calibrating the droplet temperature.

For a solution containing a mixture of all three quenched pairs, the same model may be applied by simply extending Eq. (10) to be a sum of four terms
A+f20B20+f27B27+f47B47.
(12)
where fi and Bi are the fractional fluorescence and maximum scaling factor for each oligo, respectively. Figures 6(a) and 6(b) show fluorescent melting curves of both macroscale and microdroplet samples that contained all three oligomer pairs fitted to this three-oligo version of the model and the parameters of Table 3. There is some non-random structure in the residuals. However, the root-mean-square (rms) values of the residuals for the macro droplets [Fig. 6(a)] are quite small (0.001, or 0.2% of the maximum fluorescence levels).

A calibration curve for microdroplet temperature under laser-assisted heating was constructed using the macroscale melting temperatures and the laser power on the microdroplet obtained from the samples containing mixtures of all three oligo pairs [Fig. 6(b)]. The fits give a simple linear relationship as shown in Fig. 7
Fig. 7 Calibration curve for heating a microdroplet with an infrared laser. A linear relationship (black) is obtained when oligomer melting laser voltages are plotted against oligomer melting temperatures (blue). The regression line is interpolated to obtain a laser power corresponding to 60 °C and extrapolated to obtain a laser power corresponding to 95 °C (red).
. This curve was used to obtain appropriate laser power settings for conducting qPCR.

3.2 Temperature-calibrated microdroplet PCR

Using the calibration curve obtained for microdroplet temperature under laser-assisted heating, a PCR protocol based on laser power was obtained in place of a conventional temperature-based protocol. This protocol was used to conduct qPCR of the 18S RNA gene (TaqMan Hs03928985_g1) in human male DNA at a concentration of 0.4 ng/μL or approximately 2 copies of the genome per 250-μm microdroplet. Figure 8
Fig. 8 Real-time qPCR amplification curves for macroscale (a, b) and microdroplet instrument (c, d) reactions. Effective ranges for the microdroplet around the calibration are explored and compared to the range of a qPCR instrument. The calibration curve for this experiment gives approximately a 1 °C / 0.66 mW slope.
shows both microdroplet qPCR amplification curves as well as those for replicate reaction samples run in a conventional real-time qPCR instrument (ABI 7300, Applied Biosystems). A range of annealing and extension temperatures was tested to determine the tolerance of this qPCR reaction in both reaction environments.

Calibration of laser heating gave effective qPCR without any additional adjustment. Exploration of the surrounding annealing and denaturation temperatures in the macroscale instrument by 5 °C increments reveals that reaction mixture used in this work tolerates a wide range of temperatures [Figs. 8(a) and 8(b)]. The microdroplet reaction appears to exhibit a lower tolerance in the microdroplet [Figs. 8(c) and 8(d)]. It is not clear whether the higher sensitivity to reaction temperatures for the microdroplet is due to the sample size, sample environment, or the temperature ramp rate, which is approximately 100 times faster for the microdroplets. It should be noted though that the standard calibration appears to give the most efficient (earliest amplification) protocol for a microdroplet among the tested values. Therefore, we believe that the calibration serves as an effective method for establishing an effective PCR protocol. Additionally, it has consistently produced such protocols even after alignment changes in the infrared laser.

4. Conclusions

We have developed a novel method for the calibration of heating microscale volumes via the fluorescent melting curves of static-quenched oligomers. This method allows for effective qPCR in microdroplets heated with an infrared laser and minimizes complications due to optical changes, including drift in infrared laser alignment and variation in the size of the absorbing microdroplet. The use of labeled oligomers is more expensive than common dyes such as rhodamine (roughly by a factor of 100), but because the measurements are performed in droplets with a volume of roughly 10 nL and the calibration remains valid for the duration of an assay, the calibration cost is very low (less than a penny for labeled oligos for a five-droplet calibration run). In conjunction with this method, we have also developed a model for the melting of quenched labeled oligomers that follow non-two-state melting behavior. This three-term sigmoid model extracts the two-state melting temperature from the melting curves, overcoming limitations from premelting to quantification of fluorescence melting curves. We believe that this method may be extended to other fluorescent studies of DNA hybridization, including hairpin folding [24

24. A. T. Jonstrup, J. Fredsøe, and A. H. Andersen, “DNA hairpins as temperature switches, thermometers and ionic detectors,” Sensors (Basel) 13(5), 5937–5944 (2013). [CrossRef] [PubMed]

, 32

32. J. Jung and A. Van Orden, “A three-state mechanism for DNA hairpin folding characterized by multiparameter fluorescence fluctuation spectroscopy,” J. Am. Chem. Soc. 128(4), 1240–1249 (2006). [CrossRef] [PubMed]

], as well as the array of other dye-quencher pairings that are available [21

21. S. A. E. Marras, F. R. Kramer, and S. Tyagi, “Efficiencies of fluorescence resonance energy transfer and contact-mediated quenching in oligonucleotide probes,” Nucleic Acids Res. 30(21), 122e (2002). [CrossRef] [PubMed]

, 22

22. M. Johansson, “Choosing reporter-quencher pairs for efficient quenching through formation of intramolecular dimers,” in Fluorescent Energy Transfer Nucleic Acid Probes, V. Didenko, ed. (Humana, 2006), pp. 17–29.

]. Implementation of calibration in the same droplet undergoing PCR during the initial ramp to heat activation of the polymerase may also control for variance in droplet size and shape by tuning the protocol on a per-droplet basis.

Acknowledgments

This research was supported by funds from the DOD Breast Cancer Research Program (grant number W81XWH-12-1-0076; the U.S. Army Medical Research Acquisition Activity, 820 Chandler Street, Fort Detrick MD 21702-5014 is the awarding and administering acquisition office) and internal research and development funds from SRI International. The content of this paper does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. We acknowledge experimental contributions from Bio Guo and Chia-Pin Pan.

References and links

1.

Y. T. Atalay, S. Vermeir, D. Witters, N. Vergauwe, B. Verbruggen, P. Verboven, B. M. Nicolaï, and J. Lammertyn, “Microfluidic analytical systems for food analysis,” Trends Food Sci. Technol. 22(7), 386–404 (2011). [CrossRef]

2.

D. Wlodkowic and J. M. Cooper, “Tumors on chips: Oncology meets microfluidics,” Curr. Opin. Chem. Biol. 14(5), 556–567 (2010). [CrossRef] [PubMed]

3.

G. B. Salieb-Beugelaar, G. Simone, A. Arora, A. Philippi, and A. Manz, “Latest developments in microfluidic cell biology and analysis systems,” Anal. Chem. 82(12), 4848–4864 (2010). [CrossRef] [PubMed]

4.

S. Mondal and V. Venkataraman, “Novel fluorescence detection technique for non-contact temperature sensing in microchip PCR,” J. Biochem. Biophys. Methods 70(5), 773–777 (2007). [CrossRef] [PubMed]

5.

G. Velve Casquillas, C. Fu, M. Le Berre, J. Cramer, S. Meance, A. Plecis, D. Baigl, J.-J. Greffet, Y. Chen, M. Piel, and P. T. Tran, “Fast microfluidic temperature control for high resolution live cell imaging,” Lab Chip 11(3), 484–489 (2011). [CrossRef] [PubMed]

6.

C. Fang, L. Shao, Y. Zhao, J. Wang, and H. Wu, “A gold nanocrystal/poly(dimethylsiloxane) composite for plasmonic heating on microfluidic chips,” Adv. Mater. 24(1), 94–98 (2012). [CrossRef] [PubMed]

7.

K. J. Shaw, P. T. Docker, J. V. Yelland, C. E. Dyer, J. Greenman, G. M. Greenway, and S. J. Haswell, “Rapid PCR amplification using a microfluidic device with integrated microwave heating and air impingement cooling,” Lab Chip 10(13), 1725–1728 (2010). [CrossRef] [PubMed]

8.

B. Selva, J. Marchalot, and M.-C. Jullien, “An optimized resistor pattern for temperature gradient control in microfluidics,” J. Micromech. Microeng. 19(6), 065002 (2009). [CrossRef]

9.

H. Reinhardt, P. S. Dittrich, A. Manz, and J. Franzke, “micro-Hotplate enhanced optical heating by infrared light for single cell treatment,” Lab Chip 7(11), 1509–1514 (2007). [CrossRef] [PubMed]

10.

E. M. Graham, K. Iwai, S. Uchiyama, A. P. de Silva, S. W. Magennis, and A. C. Jones, “Quantitative mapping of aqueous microfluidic temperature with sub-degree resolution using fluorescence lifetime imaging microscopy,” Lab Chip 10(10), 1267–1273 (2010). [CrossRef] [PubMed]

11.

H. Kim, S. Dixit, C. J. Green, and G. W. Faris, “Nanodroplet real-time PCR system with laser assisted heating,” Opt. Express 17(1), 218–227 (2009). [CrossRef] [PubMed]

12.

H. Kim, S. Vishniakou, and G. W. Faris, “Petri dish PCR: Laser-heated reactions in nanoliter droplet arrays,” Lab Chip 9(9), 1230–1235 (2009). [CrossRef] [PubMed]

13.

K. Hettiarachchi, H. Kim, and G. Faris, “Optical manipulation and control of real-time PCR in cell encapsulating microdroplets by IR laser,” Microfluid. Nanofluid. 13(6), 967–975 (2012). [CrossRef]

14.

H. Terazono, A. Hattori, H. Takei, K. Takeda, and K. Yasuda, “Development of 1480 nm photothermal high-speed real-time polymerase chain reaction system for rapid nucleotide recognition,” Jpn. J. Appl. Phys. 47(6), 5212–5216 (2008). [CrossRef]

15.

R. P. Oda, M. A. Strausbauch, A. F. R. Huhmer, N. Borson, S. R. Jurrens, J. Craighead, P. J. Wettstein, B. Eckloff, B. Kline, and J. P. Landers, “Infrared-mediated thermocycling for ultrafast polymerase chain reaction amplification of DNA,” Anal. Chem. 70(20), 4361–4368 (1998). [CrossRef] [PubMed]

16.

A. F. R. Hühmer and J. P. Landers, “Noncontact infrared-mediated thermocycling for effective polymerase chain reaction amplification of DNA in nanoliter volumes,” Anal. Chem. 72(21), 5507–5512 (2000). [CrossRef] [PubMed]

17.

J. Coppeta and C. Rogers, “Dual emission laser induced fluorescence for direct planar scalar behavior measurements,” Exp. Fluids 25(1), 1–15 (1998). [CrossRef]

18.

D. Ross, M. Gaitan, and L. E. Locascio, “Temperature measurement in microfluidic systems using a temperature-dependent fluorescent dye,” Anal. Chem. 73(17), 4117–4123 (2001). [CrossRef] [PubMed]

19.

M. A. Bennet, P. R. Richardson, J. Arlt, A. McCarthy, G. S. Buller, and A. C. Jones, “Optically trapped microsensors for microfluidic temperature measurement by fluorescence lifetime imaging microscopy,” Lab Chip 11(22), 3821–3828 (2011). [CrossRef] [PubMed]

20.

J. A. Richardson, T. Morgan, M. Andreou, and T. Brown, “Use of a large Stokes-shift fluorophore to increase the multiplexing capacity of a point-of-care DNA diagnostic device,” Analyst (Lond.) 138(13), 3626–3628 (2013). [CrossRef] [PubMed]

21.

S. A. E. Marras, F. R. Kramer, and S. Tyagi, “Efficiencies of fluorescence resonance energy transfer and contact-mediated quenching in oligonucleotide probes,” Nucleic Acids Res. 30(21), 122e (2002). [CrossRef] [PubMed]

22.

M. Johansson, “Choosing reporter-quencher pairs for efficient quenching through formation of intramolecular dimers,” in Fluorescent Energy Transfer Nucleic Acid Probes, V. Didenko, ed. (Humana, 2006), pp. 17–29.

23.

J. Jung, L. Chen, S. Lee, S. Kim, G. H. Seong, J. Choo, E. K. Lee, C.-H. Oh, and S. Lee, “Fast and sensitive DNA analysis using changes in the FRET signals of molecular beacons in a PDMS microfluidic channel,” Anal. Bioanal. Chem. 387(8), 2609–2615 (2007). [CrossRef] [PubMed]

24.

A. T. Jonstrup, J. Fredsøe, and A. H. Andersen, “DNA hairpins as temperature switches, thermometers and ionic detectors,” Sensors (Basel) 13(5), 5937–5944 (2013). [CrossRef] [PubMed]

25.

Y. You, A. V. Tataurov, and R. Owczarzy, “Measuring thermodynamic details of DNA hybridization using fluorescence,” Biopolymers 95(7), 472–486 (2011). [CrossRef] [PubMed]

26.

J.-L. Mergny and L. Lacroix, “Analysis of thermal melting curves,” Oligonucleotides 13(6), 515–537 (2003). [CrossRef] [PubMed]

27.

M. Peyrard, S. Cuesta-López, and G. James, “Nonlinear analysis of the dynamics of DNA breathing,” J. Biol. Phys. 35(1), 73–89 (2009). [CrossRef] [PubMed]

28.

F. J. Richards, “A flexible growth function for empirical use,” J. Exp. Bot. 10(2), 290–301 (1959). [CrossRef]

29.

J. H. Ricketts and G. A. Head, “A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies,” Am. J. Physiol. 277, R441–R454 (1999).

30.

J. SantaLucia Jr., “A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics,” Proc. Natl. Acad. Sci. U.S.A. 95(4), 1460–1465 (1998). [CrossRef] [PubMed]

31.

L. Movileanu, J. M. Benevides, and G. J. Thomas Jr., “Temperature dependence of the Raman spectrum of DNA. II. Raman signatures of premelting and melting transitions of poly(dA).poly(dT) and comparison with poly(dA-dT).poly(dA-dT),” Biopolymers 63(3), 181–194 (2002). [CrossRef] [PubMed]

32.

J. Jung and A. Van Orden, “A three-state mechanism for DNA hairpin folding characterized by multiparameter fluorescence fluctuation spectroscopy,” J. Am. Chem. Soc. 128(4), 1240–1249 (2006). [CrossRef] [PubMed]

OCIS Codes
(120.6780) Instrumentation, measurement, and metrology : Temperature
(170.2520) Medical optics and biotechnology : Fluorescence microscopy
(170.3890) Medical optics and biotechnology : Medical optics instrumentation

ToC Category:
Biosensors and Molecular Diagnostics

History
Original Manuscript: October 9, 2013
Revised Manuscript: February 4, 2014
Manuscript Accepted: February 7, 2014
Published: February 13, 2014

Citation
Eric W. Hall and Gregory W. Faris, "Microdroplet temperature calibration via thermal dissociation of quenched DNA oligomers," Biomed. Opt. Express 5, 737-751 (2014)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-5-3-737


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References

  1. Y. T. Atalay, S. Vermeir, D. Witters, N. Vergauwe, B. Verbruggen, P. Verboven, B. M. Nicolaï, and J. Lammertyn, “Microfluidic analytical systems for food analysis,” Trends Food Sci. Technol.22(7), 386–404 (2011). [CrossRef]
  2. D. Wlodkowic and J. M. Cooper, “Tumors on chips: Oncology meets microfluidics,” Curr. Opin. Chem. Biol.14(5), 556–567 (2010). [CrossRef] [PubMed]
  3. G. B. Salieb-Beugelaar, G. Simone, A. Arora, A. Philippi, and A. Manz, “Latest developments in microfluidic cell biology and analysis systems,” Anal. Chem.82(12), 4848–4864 (2010). [CrossRef] [PubMed]
  4. S. Mondal and V. Venkataraman, “Novel fluorescence detection technique for non-contact temperature sensing in microchip PCR,” J. Biochem. Biophys. Methods70(5), 773–777 (2007). [CrossRef] [PubMed]
  5. G. Velve Casquillas, C. Fu, M. Le Berre, J. Cramer, S. Meance, A. Plecis, D. Baigl, J.-J. Greffet, Y. Chen, M. Piel, and P. T. Tran, “Fast microfluidic temperature control for high resolution live cell imaging,” Lab Chip11(3), 484–489 (2011). [CrossRef] [PubMed]
  6. C. Fang, L. Shao, Y. Zhao, J. Wang, and H. Wu, “A gold nanocrystal/poly(dimethylsiloxane) composite for plasmonic heating on microfluidic chips,” Adv. Mater.24(1), 94–98 (2012). [CrossRef] [PubMed]
  7. K. J. Shaw, P. T. Docker, J. V. Yelland, C. E. Dyer, J. Greenman, G. M. Greenway, and S. J. Haswell, “Rapid PCR amplification using a microfluidic device with integrated microwave heating and air impingement cooling,” Lab Chip10(13), 1725–1728 (2010). [CrossRef] [PubMed]
  8. B. Selva, J. Marchalot, and M.-C. Jullien, “An optimized resistor pattern for temperature gradient control in microfluidics,” J. Micromech. Microeng.19(6), 065002 (2009). [CrossRef]
  9. H. Reinhardt, P. S. Dittrich, A. Manz, and J. Franzke, “micro-Hotplate enhanced optical heating by infrared light for single cell treatment,” Lab Chip7(11), 1509–1514 (2007). [CrossRef] [PubMed]
  10. E. M. Graham, K. Iwai, S. Uchiyama, A. P. de Silva, S. W. Magennis, and A. C. Jones, “Quantitative mapping of aqueous microfluidic temperature with sub-degree resolution using fluorescence lifetime imaging microscopy,” Lab Chip10(10), 1267–1273 (2010). [CrossRef] [PubMed]
  11. H. Kim, S. Dixit, C. J. Green, and G. W. Faris, “Nanodroplet real-time PCR system with laser assisted heating,” Opt. Express17(1), 218–227 (2009). [CrossRef] [PubMed]
  12. H. Kim, S. Vishniakou, and G. W. Faris, “Petri dish PCR: Laser-heated reactions in nanoliter droplet arrays,” Lab Chip9(9), 1230–1235 (2009). [CrossRef] [PubMed]
  13. K. Hettiarachchi, H. Kim, and G. Faris, “Optical manipulation and control of real-time PCR in cell encapsulating microdroplets by IR laser,” Microfluid. Nanofluid.13(6), 967–975 (2012). [CrossRef]
  14. H. Terazono, A. Hattori, H. Takei, K. Takeda, and K. Yasuda, “Development of 1480 nm photothermal high-speed real-time polymerase chain reaction system for rapid nucleotide recognition,” Jpn. J. Appl. Phys.47(6), 5212–5216 (2008). [CrossRef]
  15. R. P. Oda, M. A. Strausbauch, A. F. R. Huhmer, N. Borson, S. R. Jurrens, J. Craighead, P. J. Wettstein, B. Eckloff, B. Kline, and J. P. Landers, “Infrared-mediated thermocycling for ultrafast polymerase chain reaction amplification of DNA,” Anal. Chem.70(20), 4361–4368 (1998). [CrossRef] [PubMed]
  16. A. F. R. Hühmer and J. P. Landers, “Noncontact infrared-mediated thermocycling for effective polymerase chain reaction amplification of DNA in nanoliter volumes,” Anal. Chem.72(21), 5507–5512 (2000). [CrossRef] [PubMed]
  17. J. Coppeta and C. Rogers, “Dual emission laser induced fluorescence for direct planar scalar behavior measurements,” Exp. Fluids25(1), 1–15 (1998). [CrossRef]
  18. D. Ross, M. Gaitan, and L. E. Locascio, “Temperature measurement in microfluidic systems using a temperature-dependent fluorescent dye,” Anal. Chem.73(17), 4117–4123 (2001). [CrossRef] [PubMed]
  19. M. A. Bennet, P. R. Richardson, J. Arlt, A. McCarthy, G. S. Buller, and A. C. Jones, “Optically trapped microsensors for microfluidic temperature measurement by fluorescence lifetime imaging microscopy,” Lab Chip11(22), 3821–3828 (2011). [CrossRef] [PubMed]
  20. J. A. Richardson, T. Morgan, M. Andreou, and T. Brown, “Use of a large Stokes-shift fluorophore to increase the multiplexing capacity of a point-of-care DNA diagnostic device,” Analyst (Lond.)138(13), 3626–3628 (2013). [CrossRef] [PubMed]
  21. S. A. E. Marras, F. R. Kramer, and S. Tyagi, “Efficiencies of fluorescence resonance energy transfer and contact-mediated quenching in oligonucleotide probes,” Nucleic Acids Res.30(21), 122e (2002). [CrossRef] [PubMed]
  22. M. Johansson, “Choosing reporter-quencher pairs for efficient quenching through formation of intramolecular dimers,” in Fluorescent Energy Transfer Nucleic Acid Probes, V. Didenko, ed. (Humana, 2006), pp. 17–29.
  23. J. Jung, L. Chen, S. Lee, S. Kim, G. H. Seong, J. Choo, E. K. Lee, C.-H. Oh, and S. Lee, “Fast and sensitive DNA analysis using changes in the FRET signals of molecular beacons in a PDMS microfluidic channel,” Anal. Bioanal. Chem.387(8), 2609–2615 (2007). [CrossRef] [PubMed]
  24. A. T. Jonstrup, J. Fredsøe, and A. H. Andersen, “DNA hairpins as temperature switches, thermometers and ionic detectors,” Sensors (Basel)13(5), 5937–5944 (2013). [CrossRef] [PubMed]
  25. Y. You, A. V. Tataurov, and R. Owczarzy, “Measuring thermodynamic details of DNA hybridization using fluorescence,” Biopolymers95(7), 472–486 (2011). [CrossRef] [PubMed]
  26. J.-L. Mergny and L. Lacroix, “Analysis of thermal melting curves,” Oligonucleotides13(6), 515–537 (2003). [CrossRef] [PubMed]
  27. M. Peyrard, S. Cuesta-López, and G. James, “Nonlinear analysis of the dynamics of DNA breathing,” J. Biol. Phys.35(1), 73–89 (2009). [CrossRef] [PubMed]
  28. F. J. Richards, “A flexible growth function for empirical use,” J. Exp. Bot.10(2), 290–301 (1959). [CrossRef]
  29. J. H. Ricketts and G. A. Head, “A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies,” Am. J. Physiol.277, R441–R454 (1999).
  30. J. SantaLucia., “A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics,” Proc. Natl. Acad. Sci. U.S.A.95(4), 1460–1465 (1998). [CrossRef] [PubMed]
  31. L. Movileanu, J. M. Benevides, and G. J. Thomas., “Temperature dependence of the Raman spectrum of DNA. II. Raman signatures of premelting and melting transitions of poly(dA).poly(dT) and comparison with poly(dA-dT).poly(dA-dT),” Biopolymers63(3), 181–194 (2002). [CrossRef] [PubMed]
  32. J. Jung and A. Van Orden, “A three-state mechanism for DNA hairpin folding characterized by multiparameter fluorescence fluctuation spectroscopy,” J. Am. Chem. Soc.128(4), 1240–1249 (2006). [CrossRef] [PubMed]

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