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Ferrodrop dose-optimized-digital quantification of biomolecules in low-volume samples Soroush Kahkeshani, Janay Elise Kong, Qingshan Wei, Derek Tseng, Omai Brandt Garner, Aydogan Ozcan, and Dino Di Carlo Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b00958 • Publication Date (Web): 13 Jul 2018 Downloaded from http://pubs.acs.org on July 13, 2018

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Analytical Chemistry

Ferrodrop dose-optimized-digital quantification of biomolecules in low-volume samples Soroush Kahkeshani†, Janay E. Kong†, Qingshan Wei‡, Derek Tseng‡, Omai B. Garner§, Aydogan Ozcan†‡⊥, and Dino Di Carlo†^¶⊥*

†

Department of Bioengineering, ‡Department of Electrical Engineering, §Department of Patholo⊥

^

gy & Laboratory Medicine, Department of Mechanical and Aerospace Engineering, California NanoSystems Institute, and ¶ Jonsson Comprehensive Cancer Center, University of California, Los Angeles, 90095, USA * [email protected]

ACS Paragon Plus Environment

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ABSTRACT We present an approach to estimate the concentration of a biomolecule in a solution by sampling several nanoliter-scale volumes and determining if the volumes contain any biomolecules. In this method, varying volume fractions (nanoliter-scale) of a sample of nucleic acids are introduced to an array of uniform volume reaction wells (100 μL), which are then fluorescently imaged to determine if signal is above a threshold after nucleic acid amplification, all without complex instrumentation. The nanoliter volumes are generated and introduced using the simple positioning of a permanent magnet, and imaging is performed with a cellphone-based fluorescence detection scheme, both methods suitable for limited-resource settings. We use the length of time a magnetic field is applied to generate a calibrated number of nanoliter ferrodrops of sample mixed with ferrofluid at a step emulsification microfluidic junction. Each dose of ferrodrops is then transferred into larger microliter scale reaction wells on chip through a simple shift of the external magnet. Nucleic acid amplification is achieved using loop-mediated isothermal amplification (LAMP). By repeating each nanoliter dosage a number of times to calculate the probability of a positive signal at each dosage, we can use a binomial probability distribution to estimate the sample nucleic acid concentration. Using this approach we demonstrate detection of lambda DNA molecules down to 25 copies per microliter. The ability to dose separate nanoliter-scale volumes of a low-volume sample across wells in this platform is suited for multiplexed assays. This platform has the potential to be applied to a range of diseases by mixing a sample with magnetic nanoparticles. Keywords: droplet microfluidics, magnetic nanoparticles, point-of-care assays, mobile-phone fluorescence microscopy, nucleic acid quantification, ferrofluidics


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Introduction Digital (droplet)-based approaches to analyze molecules such as nucleic acids and proteins can lead to individual molecule-level sensitivity and high quantification accuracy1. These unique features can be extremely important in developing molecular diagnostics, however, digital approaches have not yet displaced bulk analysis approaches in the clinical lab. This may be partly due to the complex equipment and manual processes needed to generate small nanoliter-scale compartments, such as drops or sealed wells, as well as complex microscopy-based fluorescence readers for large fields of view. These large instruments and the need for liquid manipulation steps to prepare samples also have hindered use of these approaches in point-of-care diagnostics26

.

Translating digital (droplet) diagnostic technologies for point-of-care applications requires new technological innovations to address a range of challenges. Solutions are needed to achieve sample preparation7 without complicated systems, droplet generation or compartmentalization without bulky equipment to control flow, especially for low-volume samples, precise temperature control for assay reactions, as well as portable and cost-effective imaging and computational systems that can be assembled from low-cost consumer electronics such as cell phones8-11 for readout and transfer of data.12-15

New approaches are starting to reduce the need for bulky and costly pressure control systems to control flow in digital microfluidic systems. The SlipChip8,16,17 was developed to overcome some of the liquid handling challenges associated with droplets, allowing for reagent mixing and dilution by mechanically sliding and merging the sample and reagent wells without pumps. Still


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sample introduction requires some manual steps to precisely fill the initial sample wells using pipetting.16 Other approaches such as the SIMPLE18 device that uses vacuum filling with a battery and reagent microfluidic patterning are also using wells (100nl) for digital quantification of molecules, and unlike with droplets, which can be moved to separate locations on a chip for reaction or readout, the location and size of the wells remains fixed.16 Kahkeshani and Di Carlo3 have recently shown a drop formation technique in a step emulsification geometry operated by a permanent magnet that is suitable for point-of-care devices. When sample is mixed with magnetic nanoparticles (ferrofluids), for example using the motion of a permanent magnet, the magnetic body force acting on the fluid is sufficient to drive a flow from a reservoir into a narrow channel or channels and into a taller oil-filled reservoir. The ferrofluid stream breaks-up in this reservoir generating monodisperse pico/nanoliter scale ferrodrops, which can also be steered postgeneration using the same external magnetic field. The whole process operates without pressure control systems and only a permanent magnet is required.

Cost-effective optical analysis systems based on consumer electronics are also now being explored to readout arrays of droplets or wells. Point of care imaging of pico- and nanoliter droplets using these systems is still challenging due to movement and small size of drops, however larger wells (mm) can be accurately imaged as shown in previous works.8,9 In this work we accurately dispense nanoliters of sample into large reaction mixture wells for easier imaging and quantification avoiding imaging of individual drops.

Here, we show progress towards a low-cost point-of-care dose-optimized-digital nucleic acid analysis system using ferrofluidics for nanoliter-scale sampling and a demagnification mobile


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phone-based fluorescence reader device for assay result quantification. As shown in figure 1, after emulsifying a desired number of nanoliter ferrodrops (supplementary video 1) to achieve the desired dosage (step 1) by controlling the length of time that the magnet is placed below the step, delivery of this combined sample volume is achieved by placing a second magnet on top of a target reaction mixture well, while the first magnet is removed. This change in magnetic field gradient direction merges the ferrodrops with the other assay components for amplification (step 2). Then the process is repeated and another dosage of sample droplets is delivered to a second well. This continues until different dosages are delivered to the remaining wells. Each reaction mixture well contains 100 μl of a reagent solution for loop-mediated isothermal DNA amplification (LAMP)19-20 that also contains hydroxynaphthol blue (HNB)21 and EvaGreen to enhance signal to noise and temperature stability for point-of-care applications22, and each reaction mixture well is separated by a high-density oil. Following LAMP22, the intensity increase in each of the wells (step 3) is analyzed using a mobile-phone based reader, and the solution concentration can be estimated based on the probability of obtaining an amplified fluorescence signal above threshold for each dosage of drops and comparing it with the predictions for the binomial probability distribution across a range of concentrations. It should be noted that the presented approach can be generally applied to other nucleic acid amplification assays or even immunoassays such that this platform can be adapted for quantification of different biomolecules by changing the assay components in the reaction mixture wells. The magnetic nanoparticles used in this work are coated with dextran and were found to not interfere with the assays (figure S3). The LAMP assay that we have used here has been extensively validated in our previous work (Kong et al.22) using a hand-held plate reader.


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Theory for dose-optimized-digital assays In contrast to many digital assays where the entire sample is emulsified and then based on the fraction of droplets that have amplified signal above a threshold the concentration of the biomolecule is estimated using the Poisson distribution23-27, here the goal is to estimate concentration of a biomolecule in a sample with a minimum number of fractions of the sample, each which may be of different volume. Importantly, unlike previous work28 the reaction volume remains the same for each of these separate sample fractions, minimizing volume-dependent effects on reaction conditions. We explored several questions related to this dose-optimized-digital approach: 1. How can the concentration be determined based on the generated signal of each dosage? 2. How should we determine the dosages to maximize the dynamic range of concentration that is measurable while maintaining a level of accuracy in the estimation of concentration?

We first explore these questions theoretically, based on the properties of the binomial distribution, which should apply generally and is not limited to our platform. In order to use this model, the platform should be able to generate controlled fractions of the sample. The number of fractions is adjustable if more precision in quantification is required, or multiplexing of separate reactions is desired.

Because we aim to analyze only several nanoliters from low-volume samples, we should obtain accurate probabilities with a minimum number of sample fractions. Due to the limited number of fractions of the sample the binomial distribution more accurately represents the distribution of volumes that contain analyte molecules1. Using the binomial probability distribution we can determine analytically the probability of having at least one biomolecule in a specific fraction of


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sample droplets. Equation 1 describes the probability of having k molecules with a selected dose of sample volume (V), where C is the total number of molecules in 1 microliter of the original sample and V/1000 is the fraction of the entire sample (1000 nanoliters in this case) contained in the nanoliter dose volume (V )1:

𝑝 𝑘 =

! !

! !"""

!

1−

!!!

! !"""

(1)

Thus P=1-p(0) gives the probability of having at least one molecule within the selected dose and an amplified signal, assuming an amplified signal results from one or more molecules, and it can be written as: 𝑃 = 1 − 𝑝 0 = 1 − (1 −

! !"""

)!

(2)

By repeating the measurement for each dosage one can determine the probability (P) which corresponds to a particular C in the original sample for each dosage and therefore, concentration (C) can be estimated as shown in figure 2A. For multiple sample dose fractions the sample concentration can be estimated by using the combination of probabilities of a positive signal for each dose. For each dosage a measurement is repeated and the probability of an amplified signal is determined experimentally. This yields a set of points that overlay the graph in figure 2A corresponding to a particular dosage on the x-axis and measure of probability (P) along with a confidence interval of this probability, which sets a location along the y-axis. A line can be best fit to these points with a slope constrained to be zero (i.e. a single concentration) and the y intercept of this line provides the estimate of concentration (C). This process is shown and explained in detail in figure 1 (step 3) for measurements from our platform.


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The error in correctly identifying the probability of a positive signal from a sample fraction drives the accuracy of the concentration measurement. Near probabilities of 0 and 1, the change in probability with changing concentration (dP/dC) is low, meaning the precision of the measurement decreases in these regimes. The largest gradient (dP/dC) in the binomial probability distribution occurs at P=0.5. One can define a line at P=0.5 in a graph of sample dose fraction versus concentration (figure 2B), which can be used to pick doses optimized for a specific dynamic range of interest. A trade-off can be made to emphasize accuracy of concentration determination in a specific range vs. less accuracy but increased dynamic range when constrained to the same number of sample doses. Our graphical approach provides a simplified method to select fractions for sensitivity in an expected concentration range. Error in measurement of concentration can also be predicted analytically. The accuracy of the concentration measurement depends on the number of repeat measurements, dose/fraction volume, and concentration, according to equation 3, derived by Kreutz at al.28 for multi volume droplets. 𝜎 is the standard error for ln(C), C is the estimated concentration, 𝑉! is the volume of each dosage, and 𝑁! is the number of repeat trials for each dosage: !

𝜎= ! !.

!! ! .!! !!! ! !!

(3)

For a fixed small number of repeat trials of each dosage, equation 3 also predicts that the error in concentration determination is minimized around a dose that intersects the P=0.5 curve (figure 2C). For a concentration of 50 copies/μl, error is minimized using 10 nl volumes, which is near the value predicted by the P=0.5 curve (figure 2B) for this concentration. By decreasing the con-


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centration to 25 and 5 copies/μl, minimum standard errors also shift to dosages of 40 nl and 100 nl respectively, which are also the values predicted graphically on the P=0.5 curve. Importantly, the analytical solutions also predict a minor level of error will be observed for the small number of trials performed per dose (4 trials). As trial number increases (e.g. increases 9-fold, 36 trials) the error in measurement only decreases ~3-fold. In previous digital molecular analysis work, a large number of repeat fractions of the sample are measured to obtain concentration measurements, however, we find that if operating close to P=0.5 in the binomial distribution that only a small number of trials is needed to obtain an accurate concentration estimate. Therefore, we anticipate that the graphical approach to select sample fractions can be useful for quickly designing dose-optimized-digital assays which only operate with a few repeat trials while maintaining accuracy. In this study we are targeting quantification of DNA in the range from 5 to 50 copies per microliter and chose operating parameters that follow the guidelines outlined above for doseoptimized-digital assays. In the range of 5 to 50 copies per microliter, sample doses of 10 ferrodrops (10 nl), 40 ferrodrops (40 nl), and 100 ferrodrops (100 nl) approximately equally span the concentration range. However, if the goal is to detect concentrations in the regime between 50 to 500 copies per microliter, then dosages lower than 10 drops (10 nl) need to be chosen. By delivering each dosage once, 150 nl of the sample (10+40+100) is used, and if the process is repeated 4 times to calculate a probability of an amplified signal, then 600 nl of the sample is used in total. Finally, if quantification in the range of 500 to 5000 copies per microliter is desired then dosages in the picoliter range should be chosen to operate in accordance with the P=0.5 curve. Of course an initial dilution of sample can also enable better sparse sampling of higher concentration samples. This could be done by magnetically mixing the ferrofluid buffer with the sample


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ferrofluid in known ratios. In our previous work3 we showed mixing of two ferrofluid solutions magnetically in a ratio of 1:1 using a 2-inlet design. If the lengths of the channels are different, the flow rates (and subsequently ratios) could be controlled based on the differences in fluidic resistance of the channels. Experimental section The LAMP assay used in this study is similar to the assay reported in the work of Kong et al.22 using the HNB and Evagreen dye combination in a loop-mediated isothermal DNA amplification of lambda DNA template. The mobile phone reader device was prepared by integrating a 3D printed opto-mechanical attachment with the camera module of a smartphone and to increase the signal-to-noise ratio of the low-magnification detection system, a strategy of using oblique illumination of the sample substrate with a high-power laser diode was adopted. The entire assay from ferrofluid mixing with sample solution, through dosing, LAMP-based amplification, and cellphone readout is completed within 1.5-2 hours. The assay components and the cell-phone reader components are detailed in the supplementary materials section.

Results and discussion Controlled emulsification and delivery of a collection of ferrodrops is an important capability of our device that is valuable for point-of-care applications. Following mixing of the sample with ferrofluid (figure S4) we create well-defined nanoliter-scale doses using magnetic-field induced emulsification. The average droplet generation rate is 4 droplets per second (4 nl/sec), and the number of generated droplets can be easily adjusted by controlling the time a magnetic field is applied. The droplet size, as we have previously shown3, is dependent on channel geometry. By decreasing the channel height, smaller droplets can be generated. This ultimately results in a


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lower limit for a sample dose in the range of hundreds of picoliters from a single ferrodrop. The upper limit, as shown in figure 3, is dependent on the interval that the magnet is located near the step emulsification junction. For example, thousands of droplets can be generated in a few minutes, leading to an approximately three orders of magnitude range in sample fraction size. The standard deviation for each dose volume is less than 10 percent, and the discrepancy is most likely due to the manual nature of placing and removing a magnet that could be resolved using a more precisely controlled electromagnet. As shown in Figure 2A, a 10% change in the volume of delivered dosage, at maximum will lead to ~0.05 change in the probability of obtaining an amplified signal (P) near the P=0.5 curve, where the maximum dP/dC and error is possible. We consider this level of error to be small compared to the probability differences among the wells with different dosages. The generation rate of droplets and therefore total volume of a dose in a particular time is driven by several parameters of the system. The total volume of a sample dose (V) can be estimated to be proportional to the magnetic moment of the ferrofluid (m), change in magnetic flux density across the channel (ΔB), and also the time that the magnet is placed near the step (∆t).3 The other parameters affecting the flow of the ferrofluid and therefore the dose size in a given time are surface tension (γ), channel height (H), width (W), length of the channel occupied by ferrofluid (L1), length of the channel occupied by oil (L2), ferrofluid viscosity (µ! ), and oil viscosity (µ! ) (we assumed the thickness of the oil film between the ferrofluid and the narrow channel walls is negligible).

V=

!∆!!!! ! ! !!! ! !"( ! ! ! ! )

∆t

(4)

!"


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Following the generation of a controlled dose consisting of a collection of ferrodrops (figure 1,3) we can deliver this sample fraction to a separate reaction well also using magnetic field control. The magnetic field required for moving generated droplets from the oil phase to one of the aqueous reaction solution wells is about 0.1 Tesla. In order to establish this dosing field we place a magnet on top of the designated well within a distance of ~1.5 cm. Once the ferrodrops move to the interface between the oil and the reaction well fluid, they merge because both ferrodrops and the reaction mixture are aqueous solutions and no surfactants are used to stabilize the ferrodrops. Merging and mixing of the sample dose with the wells was also observed to accelerate when the reaction wells were incubated at 65C to initiate nucleic acid amplification, presumably due to the reduced interfacial stability and enhanced thermal motion of magnetic nanoparticles as temperature increases.

Following delivery to the reaction wells, nucleic acid amplification and readout can be performed. We first evaluated whether the addition of ferrofluid would affect the kinetics of loopmediated isothermal amplification (LAMP), and measured intensity every 5 minutes in a wellplate format (figure S5) to identify the optimum readout times using our cellphone-based imager. We found that the LAMP reaction proceeds in the presence of ferrofluid in a dose dependent manner. For samples with different concentrations of lambda DNA amplified fluorescence signal above background is detected after 55 minutes (figure S5) and reaches its maximum after 95 minutes for doses of 10 nL, 40 nL, and 100 nL of ferrodrops. The no DNA template control sample generates signal at a much later timepoint >>100 mins, which leads to a clear measure-


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ment window to differentiate positive signals from false positive signals.22 Balancing assay time while limiting false positive readings from nonspecific amplification, a 75 minute endpoint was chosen for mobile phone-based intensity measurements.

Mobile phone-based readout of the dose-optimized-digital assay following LAMP on-chip was performed using a sample with 50 copies per microliter of DNA mixed with ferrofluid. Ferrodrops were generated, moved to reaction wells with doses of 0, 10, 40, and 100 nLs per device and amplified using LAMP. Amplification was followed by cellphone imaging of the reaction wells. In this proof-of-concept we used an oven set to 65C for amplification, although other thermal control systems such as phase-change materials could be used in low-resource settings29,30. Figure 4A shows a representative snapshot of the cell phone imaging device with 3D printed attachments. To increase the signal-to-noise ratio of the low-magnification detection system, a strategy of using oblique illumination of the sample substrate with a high-power laser diode was adopted. Images collected with the device show distinct fluorescence intensity differences that vary between wells expected to be negative and those dosed with higher levels of target DNA (Figure 4B). The intensity of a positive well (55 ± 5) was found to be about double the intensity of a well without amplification (26 ± 5) (Figure 4C), which allowed us to set a threshold at 35 to determine whether a well contained one or more target DNA molecules.

Using 4 repeat measurements of each dose, we calculated based on figure 4C, the concentration of DNA in the sample. This proceeded as discussed in the theory section: for each dosage and positive probability estimated with 4 experimental trials, we plotted a location in the binomial probability distribution graph (Figure 4D). By fitting a horizontal line through these points across


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doses, we estimated the concentration of DNA in the original sample to be around 30 ± 5 copies per microliter (with error calculated based on the line fit). Our approach appears to yield an accurate estimate, comparable to estimates using the theory presented in Kreutz et al.28 for multivolume analysis of digital assays (18 copies per microliter). Based on equation (3) for a 95% confidence interval with 4 repeats for each dosage, the estimated concentration is in the range of (20,45) molecules per microliter. Thus, by operating near P=0.5 each fraction can have minimal redundancy to accurately calculate a probability and estimate the sample concentration.

We extended our analysis to quantify a much larger range of DNA concentrations. Figure 5 summarizes these experiments for concentrations from 5 to 100 copies/µl with 4 repeats for each dosage and two repeat trials per concentration demonstrating the reproducibility of our quantification process. For each experiment, the original concentration of DNA is known and dosages are chosen based on the guidelines introduced in the theory section for minimizing sample volume used for quantification. In the right column, concentrations are estimated based on the method reported in figure 1 (step 3) and figure 4D. We find that the estimated concentration based on the fraction of positively amplified wells obtained with the dose-optimized-digital assay correlates well with the expected concentration (correlation coefficient=1.9), however the expected concentration is systematically underestimated, which could be partly due to adsorption of DNA to PDMS surfaces (hydrophobic). Importantly, our measurements show the ability to quantify small differences in concentration accurately (e.g., 2 fold), with a limit of detection (LOD) of 25 copies/µl when a maximum dose of 400 nL is used (figure 5). For higher concentrations and doses higher than 400 nL the probability of obtaining an amplified signal is 100% (red region in Fig. 2A), and this result does not give us any additional information for determin-


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ing the concentration of the sample because P=1 corresponds to a large region rather than a point on the graph in Fig. 2A. Therefore we chose the optimal dosage volumes based on P=0.5. Our current limit of detection for nucleic acid testing is sufficient for a range of clinical applications such as identifying microbial populations, or rare gene mutations, however further improvements in the assay could lead to even lower detection limits22.

Conclusions We present a platform that uses only a small external magnet for controllable emulsification and dosing of fractional volumes of a sample to different reaction wells prefilled with assay components for nucleic acid amplification. Amplification and detection of bright (fluorescent) wells, yielding a probability of DNA molecule presence as a function of dose, using a cell phone-based fluorescent microsope allowed for an estimate of the number of target molecules in the sample based on the binomial probability distribution. Since only nanoliters of sample is used for quantification, this platform could be used for low volume samples following DNA extraction (e.g. fingerpicks of blood, sweat, saliva, tears) even in the presence of background molecules (figure S1). The overall reaction volume in the wells was greater than 99% controlled by the initial reaction solution volume (100 μl). This extreme dilution of the sample also can prove beneficial in reducing sample matrix effects which can interfere with assays in a random manner depending on the sample. The use of nanoliters of precisely dosed sample also allows for multiplexing of reactions with low sample volumes. Especially for point-of-care platforms, there is a need for a self-contained system where contamination is avoided and many different assays could be tested on the same sample31,32.


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The dose-optimized-digital approach also greatly improves simplicity of readout. A single measurement, as opposed to tens to hundreds of thousands of measurements using standard digital assays, only slightly decreases the accuracy of nucleic acid concentration determination. Amplification and signal generation occurs in a small number of larger wells, which removes the need for stabilizing droplets during imaging and alleviates well- or droplet-surface-based interference with reaction conditions, while still maintaining nanoliter-level sample volumes, ultimately enabling the use of a hand-held imaging system. It should be noted that one important difference in our work compared to the work of Kreutz et al.28 is that instead of having separate volumes for reaction, different fractions of the sample are mixed into the much larger scale reaction wells for easier imaging which eliminates volume-dependent effects on the reactions. In addition, because we are able to produce nanoliter-scale ferrodrops, much smaller sample volumes can be used to start with without the worry of significant dead volume in the device.

LAMP assays targeting different nucleic acid sequences (figure S2) can also benefit from this platform for minimizing the volume of the sample used for accurate quantification of biomolecules. For example, we have shown LAMP primer sets suitable for influenza cDNA (figure S2); similarly we could adopt the primers and reaction mixes used for accurate detection and quantification of Malaria and Zika virus used in the work of e.g., Modak et al.37 and Song et al.38, respectively. DNA purification steps could also be added to the presented platform using techniques such as the work of Min et al.39 which used coated magnetic nanoparticles for this purpose.

Some limitations of the current platform can be easily addressed in the future. It should be noted that instead of testing 4 devices (4 separate trials) to calculate probabilities, more wells could be


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used in a device (e.g. deeper wells to fit more volumes in one field of view). If deeper wells are used mixing of assay components and sample could be enhanced by movement of a magnet. It is also important to note that the use of multiple larger wells comprising nucleic acid amplification reagents can increase the overall reagent cost of an assay. Still, reagent cost can be comparable to current droplet digital PCR (ddPCR) per test costs if smaller volumes closer to 5 µL per microwell are used, which is feasible given the limited dilution that is caused by sample doses of ~ 100 nL. In order to continue development for point of care usage, reagents should be implemented in a dried format33-36, temperature control systems such as phase-change materials could be implemented29,30 and also electromagnets can be used to drive droplet motion instead of permanent magnets, to achieve a completely automated and closed system for molecular detection with improved dynamic range and multiplexing capabilities.

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ACKNOWLEDGMENT The work is funded by NSF grant No. 1332275. ASSOCIATED CONTENT Supporting Information Supplementary materials: Mixing efficiency of magnetic nanoparticles and DI water using motion of a magnet for point-of-care applications and plate reader results for determining the best end-point time for measurement using the cell-phone reader, cell-phone imaging system details, oils and magnets/ferrofluids used, mechanism of drop formation, assay components, and the assay performance in presence of background molecules and ferrofluids, dP/dC curve. Supplementary video 1: controlled droplet formation by positioning a permanent magnet in proximity.

Conflict of Interest Disclosure The authors declare no competing financial interest.


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Figure 1: Operation of dose-optimized-digital assay using ferrodrop dosing device. A connecting channel from the sample reservoir to a high-density oil reservoir terminates at a junction where drops are created using step emulsification. Flow into the junction for precise nanoliter dosing is achieved using an external magnet to generate magnetic force on the sample fluid mixed with magnetic nanoparticles. The sample fluid with magnetic nanoparticles mixed with lambda DNA sample occupies the sample reservoir. Step 1) A magnetic field is applied and fluid is attracted toward the magnet such that ferrodrops are generated as the fluid reaches the step junction. The number of generated ferrodrops depends on the actuation time of the magnet. Step 2) The magnet


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is placed on top of one of the reaction wells containing amplification and readout reagents and the generated ferrodrops from the previous step are delivered to the well and merged with the solution containing assay components. This step is repeated for a set of sample dosages and designated reaction wells. Following dosing of sample to reaction wells, amplification of nucleic acids is initiated at 65̊C. Step 3) The reaction outcome is imaged and the probability of an amplified signal for each dosage is estimated from experimental trials. The concentration of the lambda DNA in the original sample is determined by assessing the probability as a function of dose and fitting a line to a set of predicted concentrations from the binomial probability distribution. The number of wells and the delivered sample dosages can be easily adjusted and increased for multiplexing of reactions to assay different biomolecules simultaneously.


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A

P: Probability of amplified signal

1000

B

C

P=1 500

100 P=0.5 10

Dosages that intersect P=0.5 from 5 to 50 copies/microliter

50 P=0.5

1 0

20 40 60 80 100 Dosage volume (V) (nanoliter)

P=0

5

1

20 40 60 80 100 Dosage volume (V) (nanoliter)

(standard error)

Concentration (C) (copies/microliter)

6 Concentration (C) (copies/microliter)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4 trials each

5

50 copies/μl 25 copies/μl 5 copies/μl

4 3 2 1 0

0

20 40 60 80 Dosage volume (V) (nanoliter)

100

Figure 2: Theory for dose-optimized-digital assays: A) Probability of an amplified signal for different concentrations and dosages or sample fractions are shown following the binomial distribution and assuming a 1 µL total sample volume. B) Dosages used in this study for detection of 5 to 50 copies per microliter are chosen based on maintaining proximity to the P=0.5 curve over this concentration range. P=0.5 in the binomial distribution is where the largest gradient of P with respect to C occurs which is optimal for distinguishing between different concentrations with a smaller number of sample fractions. C) Standard error (σ) of ln(C) for concentrations in the range of 5 to 50 copies per microliter when considering 4 repeat measurements at each dose. Minimum error occurs at 10nl dosage for 50 copies per microliter. For lower concentrations the minimum error is found at higher 100 nl dosages.


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A

Dosing volume (1 nl per drop)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1000

Controlled nanoliter dosing of sample

100

10

1

t=0.2 sec

t=0.25 sec

Magnetic force direction 0

20

40

60

80

100

Actuation time (sec)

B 10 drops (10 nl)

40 drops (40 nl)

100 drops (100 nl)

Figure 3: Dosing process: A) The number of generated nanoliter ferrodrops for different time intervals of the applied magnetic field are shown. Scale bar is 120 µm. B) Microscopic images of ferrodrops generated for different dosages before merging with the reaction well. The standard deviation is less than 10 percent (10 percent of total volume of generated ferrodrops for each case). Scale bar is 120 µm.


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A

Cellphone

Emission Filter

Cellphone Camera

Batteries

Cellphone

Z stage Laser Lens Reaction mixture wells

B

2 cm

Sample Holder

Sample Holder

Cell phone image Control

100 drops

22

57

20

60

Intensities

10 drops

40 drops

4 mm

D

60 50 40

Threshold (+)

30 20

0

50

Concentration (C) (copies/microliter)

C

Intensity after amplification

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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100

Total volume delivered to a reaction mixture well (nanoliter)


5000

500 P=1

50

P=0.8

30

5

P=0.6 P=0.4

P=0.2

0

20

40

60

80 100

Dosage volume (V) (nanoliter)

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Figure 4: Results of LAMP amplficiation and cell phone-based readout for concentration estimation: A) Components of the fluorescent cell phone imaging system. B) A representative image of the reaction wells following amplification showing corresponding intensities of each well (averaged over 20 pixels around the center of each well). C) Summary of intensity measurements following 4 trials using cell phone imaging after 75 minutes of amplification for a range of dosages of ferrodrops from 0 to 100 nl. D) Estimation of the concentration of the DNA in the original sample based on line fitting on the binomial probability distribution graph.


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Figure 5: Quantification of lambda DNA over various concentrations. For each case, the doses are chosen based on the guidelines explained in the theory section to minimize the sample volume used for quantification. Original concentrations are known (left column). Each dose has been repeated 4 times and the probability of an amplified signal is reported. From the probabilities across the doses, the concentration of each sample is estimated based on Figure 2A (right column). The error range for each sample concentration is also calculated based on equation 3. Two repeats are performed for each sample concentration demonstrating reproducibility.


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For TOC only:


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Ferrodrop dose-optimized-digital quantification of ... - ACS Publications

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