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Monte Carlo modeling-based digital loop-mediated isothermal amplification on a spiral chip for absolute quantification of nucleic acids Yun Xia, Shuangqian Yan, Xian Zhang, Peng Ma, Wei Du, Xiaojun Feng, and Bi-Feng Liu Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b00031 • Publication Date (Web): 17 Feb 2017 Downloaded from http://pubs.acs.org on February 19, 2017

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Analytical Chemistry

Monte

Carlo

modeling-based

digital

loop-mediated

isothermal amplification on a spiral chip for absolute quantification of nucleic acids Yun Xiaabc†, Shuangqian Yana†, Xian Zhanga, Peng Maa, Wei Dua, Xiaojun Fenga*, and Bi-Feng Liua*

a

The Key Laboratory for Biomedical Photonics of MOE at Wuhan National Laboratory for

Optoelectronics-Hubei Bioinformatics & Molecular Imaging Key Laboratory, Systems Biology Theme, Department of Biomedical Engineering, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China b

Central Laboratory of Health Quarantine, Shenzhen International Travel Health Care Center,

Shenzhen Entry-exit Inspection and Quarantine Bureau, Shenzhen 518033, China c

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055,

China.

† These authors contributed equally to this work. * Corresponding author Add: College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China Email: [email protected], [email protected] Tel:

+86-27-87793180

Fax:

+86-27-87792170

ACS Paragon Plus Environment


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ABSTRACT

Digital loop-mediated isothermal amplification (dLAMP) is an attractive approach for absolute quantification of nucleic acids with high sensitivity and selectivity. Theoretical and numerical analysis of dLAMP provides necessary guidance for the design and analysis of dLAMP devices. In this work, a mathematical model was proposed based on Monte Carlo method and the theories of Poisson statistics and chemometrics. To examine the established model, we fabricated a spiral chip with 1200 uniform and discrete reaction chambers (9.6 nL) for absolute quantification of pathogenic DNA samples by dLAMP. Under the optimized conditions, dLAMP analysis on the spiral chip realized quantification of nucleic acids spanning over 4 orders of magnitude in concentration with sensitivity as low as 8.7×10-2 copies/µL in 40 min. The experimental results were consistent with the proposed mathematical model, which could provide a useful guideline for future development of dLAMP devices.

KEYWORDS: Digital loop-mediated isothermal amplification; Numerical analysis; Absolute quantification; Microfluidic chip; Nucleic acid


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INTRODUCTION

Quantitative analysis of nucleic acids is essential for the practice of precision medicine,1-2 an emerging medical model that propose the customization of individuals' healthcare based on the context of their genetic or other molecular content.3 Currently, the kinetics-based real-time quantitative polymerase chain reaction (qPCR) is the gold standard for detecting and quantifying nucleic acids in clinical settings.4-6 This technique is built on the basis of relative quantification, requiring an external calibration with genetic standards or inner reference DNA templates.7-8 With the advances in microfluidic technology, the advent of digital polymerase chain reaction (dPCR) has revolutionized the quantitative analysis of nucleic acids by offering absolute quantification of genetic copies.9-14 The dPCR is based on single-molecule DNA amplification philosophy, in which diluted nucleic acid samples are distributed into hundreds to millions of discrete nanoliter-scale reactions containing only one or zero target DNA molecule according to Poisson distribution.15-16 Consequently, the absolute copy number of target DNA can be calculated from the number of positive and negative reactions based on the Poisson distribution formulas.17 Recently, the research group of Ismagilov reported a theory for the design and analysis of dPCR devices,18 which was validated using SlipChip platform.19

PCR is an enzymatic reaction that relies on thermal cycling, consisting of cycles of repeated heating and cooling of the reaction for DNA melting and enzymatic replication of the DNA template.5, 20 Alternatively, various isothermal amplification methods have been reported,21 such as loop-mediated isothermal amplification (LAMP),22 rolling circle amplification (RCA),23 recombinase polymerase amplification (RPA),24 strand displacement amplification (SDA),25 helicase-dependent amplification (HDA),26 and multiple displacement amplification (MDA)27



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eliminating the need for thermal cycling. Among these methods, LAMP is a well-established technique for the analysis of nucleic acids. LAMP can amplify nucleic acid sequence under 60-65°C with high sensitivity and selectivity.28 The reaction can be monitored optically by simply adding calcein, a fluorescence metal indicator, and magnesium ions to the reaction solution.29,30 In addition, LAMP is tolerant of common inhibitory compounds in clinical samples that typically inhibit PCR. 31

Recently, several research groups have demonstrated the feasibility of digital loop-mediated isothermal

amplification

self-digitization

chip,33

(dLAMP) self-priming

on

microfluidic

platforms,

compartmentalization

including

chip,34

and

SlipChip,32 droplet-based

microfluidics.35 These methods demonstrated the feasibility of LAMP-based digital assay on microfluidic chips, holding high potential for quantitative analysis of nucleic acids.36 However, theoretical and numerical analysis of dLAMP is still missing, which is necessary for guiding the design and analysis of dLAMP devices.

In this work, a mathematical model was established for dLAMP, which was investigated using Monte Carlo-based statistic modeling and further validated on a spiral chip for absolute quantification of nucleic acids. The mathematical model for dLAMP was built on the theories of Poisson statistics and chemometrics.37-38 Validity and reliability of maximum likelihood estimation (MLE) were demonstrated in theory by Monte Carlo method-based program. Further in silico results showed that 1200-plex digital assay has a competent quantification resolution comparable to qPCR. Based on the mathematical model, we designed and fabricated a spiral chip with 1200 uniform and discrete LAMP reaction chambers (9.6 nL) for absolute quantification of pathogenic DNA samples. Under the optimized conditions, dLAMP on the spiral chip realized quantitative


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analysis of nucleic acids spanning over 4 orders of magnitude in concentration with detection limit as low as 87 copies/mL. Meanwhile, the analysis time of dLAMP on the spiral chip was about 40 min. The experiment result was consistent with the theoretical analysis and our mathematical model provides a guideline for the design and analysis of dLAMP devices. EXPERIMENTAL Chemicals and reagents. Tris(hydroxymethyl)aminomethane and lysozyme were purchased from Biosharp Co., Ltd. (Hefei, China). Fluorescein, agar, betaine and Triton X-100 were obtained from Sigma–Aldrich (MO, USA). Agarose G-10 was bought from Gene Co., Ltd. (Hongkong, China). Proteinase K (recombinant), calcein, uracil-DNA glycosylase (UDG), dNTPs and all LAMP primers were obtained from Sangon Biotech (Shanghai, China). Tris-acetate-EDTA buffer premix powder was purchased from Dycent Biotech (Shanghai, China). Gel loading blue dye buffer, 100 bp DNA ladder plus and DNA extraction kit for detecting bacterial genomic DNA were purchased from Dongsheng Biotech (Guangzhou, China). Magnesium sulfate, ThermoPol II buffer and Bst 2.0 DNA polymerase were purchased from New England Biolabs (MA, USA). A fluorosilane polymer (Novec™ EGC-1720, 3M, USA) was employed as the waterproof fluorinating reagent and immiscible fluorinated oil (Fluorinert™ FC-40, 3M, USA) was used as the oil phase to partition the spiral chamber array. SU-8 (GM 1070) was purchased from Gersteltec Sarl (Switzerland). Other chemicals were obtained from Sinopharm Chemical Reagent (Shanghai, China). Water was purified by the Millipore-Q system (Millipore, USA) before use. All DNA fragment and primers and the typical LAMP reagent mixture was prepared according to our previous work.39 In order to visualize the dLAMP assay, an optimized concentrations of 0.125 mM calcein and 0.6 mM MnCl2 were used as the indicator and quencher,



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respectively. The reaction mixture (20 µL) for real-time qPCR was prepared according to the protocol proposed by Sangon Biotech (Shanghai, China) which consisted of 2× SG Fast qPCR Master Mix (High Rox, 10 µL), 1 µM forward primer (F3) and backward primer (B3) mix (4 µL), PCR-grade water (5 µL) and

1 µL of 10-fold diluted DNA template (5.23×106, 5.23×105,

5.23×104, 5.23×103, 5.23×102, 5.23×101 copies/µL). Real-time qPCR operation. Real-time qPCR was conducted on a StepOnePlus™ real-time PCR system (Thermal Fisher Scientific, USA) to validate the quantitative results from dLAMP. Outer primers including F3 (20nt, 50% GC content, Tm: 55°C) and B3 (18nt, 61% GC content, Tm: 56°C) were used as the forward and reverse primers. Temperature cycle was carried out as 95°C for 210s followed by 40 tri-temperature cycles (95°C for 5 s, 50°C for 20 s and 72°C for 20 s). Optical imaging and data processing. The end-point fluorescence images of dLAMP were captured under a fluorescence stereo zoom microscope (Axio Zoom.V16, ZEISS, Germany). The excitation and emission wavelength was 480 nm and 520 nm respectively. Fluorescence intensity of each chamber was obtained with Image-Pro Plus 6.0 software (Media Cybernetics, USA) and the final images were processed using a home-built program. RESULTS AND DISCUSSION Establishment of a statistical model. In order to depict the digital assay, a simplified ideal model was conceived on the basis of two hypothetical facts. Firstly, nucleic acid molecules driven by Brownian motion have a homogeneous distribution in solution. Secondly, the independent and identical distribution for each molecule is not biased due to the wide disparity of the length scale between nucleic acid and LAMP chamber. Despite the higher probability of the boundary absorption caused by the increasing specific surface area in micron scale, the molecules aggregation and boundary


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absorption however could be avoided by surface pretreatment (coating or modification) and preloaded surfactant.40 The probability of every molecule distributed to single partition was regarded as approximate consistent. Thus, the process that bulk volume solution was divided into numerous partitions was regarded as ideal multivariate Bernoulli trials, which can be described by the following equation:

m P{ X = k } =   × (1 / n ) k × (1 − 1 / n) m − k k

（1）

Where, m is the number of molecules, and n is the number of partitions. When m/ n is constant and n is large

enough,

P

approximates (m / n) k × e - ( m / n ) /k !, i.e., the number of molecules in a single partition follows a Poisson distribution. Furthermore, the probability that the frequency of k molecules (Ck) trapped in the same partition equivalent to i (i ≥ 0) is given by the following equation: k −( m / n) ( m / n) k × e − ( m / n ) n −i  n  (m / n) × e P{C k = i} =   × [ ]i × [1 − ] , k! k! i

（2）

Subsequently, we analyzed a variety of laws and quantitative parameters of the mathematics quantitative methods by a series of formula derivation and mathematical model (ESI). Based on above built supposes and mathematics quantitative models, the distribution regularities of DNA molecules in solution could be described with the homogeneous spatial point process. In order to concisely describe the mathematical model, a 256-plex (16×16) 2-D array was analyzed as an example to simulate the 2-D Poisson process with different number of molecules (from 1 to 2000). Each assay was repeated 6 times independently and the numbers of molecules in each grid partition as well as the total number of partitions containing 0 to 15 molecules were recorded. As shown in Figure



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1, the expectation of random variable Ck (the blue continuous curve) deduced from equation（2）was in accordance with the simulation result (histogram, k: 0 to 15), which verified the consistency between the simulation results and our mathematical model.

Furthermore, 11 sets of in silico experiments with a series of fixed input m (1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, and 1500) were carried out (Figure S1). The good linear correlation (R2 = 0.99953) of estimated value M and the original input m verified the validity of the quantification method based on maximum likelihood estimation and Poisson distribution. But results showed that when the input number m was fixed at 1500, sample observations of C0 began to drop to 0 and the estimated M would be infinite, leading to significant quantitative error (not showed in the figure). There is an upper limit molecule number that can be quantified to a given chamber number of the digital assay.

Quantitative resolution of a 1200-plex digital assay. The precision and dynamic range at varying partitions (120 - 120000) was discussed in Figure S2. In this section, we focused on discussing the precision and dynamic range of 1200 partitions. As shown in Figure S1A, the quantitative precision reached its extreme point when m/n (average molecules per partition) was 1.5702 and the percentage of negative partitions (PNP) was 0.203, resulting in the maximum quantitative precision, 14.12%. The theoretical quantitative calculation curve and confidence bound at 95% confidence level was shown in Figure S2. As illustrated in Figure S3B, the uncertainty of the Poisson estimation quantitative results was increasing when the PNP was at both ends of the abscissa. While the quantitative requirements can be satisfied when PNP was in a specific range. According to equation Mˆ = − n ln(i / n ) , the theoretical maximum number of molecules in the quantitative range of the 1200-plex chip was 1~8508 and the range was 37~1330 to the precision better than 20%. The theoretical dynamic range of the 1200-plex chip was 3.4


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(Figure S1E). Based on the proposed mathematical model, we further analyzed the quantitative resolution of a 1200-plex digital assay by Monte Carlo method. A series of simulations consisting of 10000 sets of independent point process tests were conducted with varying input m ranging from 1 to 10000. Figure 2A illustrated the simulation results with input m fixed at 3, 30, 300 and 3000 respectively. The negative count (C0) for each replicate plotted against m was shown in Figure 2B. The negative count was exponentially decreased with increasing m, which might influence the result of the dLAMP assay. In addition, a combination of segmented frequency histograms by plotting replicates counts (1000 in total) against negative count (from 0 to 1200) for selected input m demonstrated the quantitative resolution of 1200-plex digital assay (Figure S4). These results of mathematical simulation were following the Gaussian distribution with the same input m. It was difficult to distinguish two different molecular numbers if the overlap of gauss distribution was too large. By increasing the repetition times of the assay, it would help to distinguish two different molecular numbers with a better confidence level. Figure S5 showed how quantitative accuracy was affected by the partition density. Spiral chip design and fabrication. The 1200-plex spiral chip had a centro-symmetric layout with 8 spiral arms, each arm containing 150 separate chambers (310 µm in width, 310 µm in length and 100 µm in height) that were connected by a spiral channel (60 µm in width and 100 µm in height). A series of Tesla valves41 were located downstream the outlet of the spiral channels, preventing reversed flow due to pressure instability in the channel and cross contamination between adjacent chambers during incubation. A dead end circular chamber (2.5 mm in radius) was set as the reservoir for absorbing excessive liquid. The PDMS layer featuring 1200-plex chamber array was fabricated according to the rapid prototyping method. Briefly the SU-8 mold



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was fabricated on a 3-inch silicon wafer using standard soft lithography technique. The PDMS layer was fabricated by pouring a mixture of PDMS monomer and the curing agent (mass ratio 10:1) onto the mold. After degassing and curing at 85°C for 2h, the PDMS replica was gently peeled off from the mold and cut in round shape. A through-membrane hole (1.5 mm in radius) was punched at the center. The replica was then sealed to a glass slip (50 mm in diameter and 1 mm in thickness) by plasma treatment and incubated at 65°C for 4h. A quartz tube (4 mm in inner diameter and 6 mm in height) was finally attached onto the central hole with glue as the sample reservoir (Figure 3A). Microchip operation. Firstly, the spiral chip was degassed at 1 kPa for 2 min, enabling the loading of fluorosilane to hydrophilize the microchannel. After preparation, the microchip operation procedure was shown in Figure 3B. After degassing at 1 kPa for 5 min, LAMP mixture (25 µL) was loaded via the inlet port with a pipette. As soon as all the mixture was loaded into the spiral array, fluorinated oil (~50 µL) was added into the inlet and sequentially loaded into the channel to replace the reaction mixture in the channel, partitioning the spiral array into 1200 discrete chambers. A PDMS plug was pushed into the quartz tube to seal the inlet and drive all the excessive oil to the dead end reservoir. Finally, the spiral chip was encapsulated in an aluminum jar (51 mm in inner diameter and 2.1 mm in height) and immersed in pure water (~2 mL) to reduce evaporation. The dLAMP assay was then carried out at 65°C for 40 min in a water bath. Oil partitioning and water evaporation on the spiral chip. The absolute quantification result of copy number concentration is dominated by two factors: the estimated copy number by Poisson statistics and the total effective volume involved in each single dLAMP assay. According to the equation, Concentration

volume

= m /V = m /(n × v) , the total effective volume could be determined


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by multiplying the volume of each single chamber by the number of reaction chambers (n). However, the quantitative result might be seriously biased due to the uniformity of dLAMP mixture partitioned in each reaction chamber. To evaluate the partitioning performance, calcein solution of 0.125 mM was loaded into the spiral chip as the indicator and captured the fluorescence image of the partitioned spiral array using a stereo zoom microscope (excitation at 470 nm). Under such circumstance, the horizontally projected area could be interpreted as the captured fluorescence area while the mean excitation height is proportional to the mean intensity for each single reaction chamber. By interrogating the fluorescence area (pixels) and mean intensity (arbitrary unit) of each reaction chamber via a customized processing program, we obtained a frequency histogram as shown in Figure S6, which demonstrated the approximate Gaussian distribution of area and intensity for the 1200 reaction chambers. The coefficient of variation for excited chamber area and mean intensity was 2.27% and 0.676% respectively, which indicated a relatively good uniformity of partitioned reaction volume. A portable digital camera could also be used to image the fluorescence distribution of the spiral chip under UV flashlight excitation (Figure S7). Next, the water evaporation on the spiral chip was evaluated. After the calcein solution was loaded, the fluorosilane polymer-coating spiral chip was placed in a flat-bottom petri dish (60 mm in diameter) and immersed in adequate water. Water evaporation was monitored in real time under the inverted fluorescence microscope using a temperature-controlled stage. Due to the fluorosilane polymer coating on the inner surface of the reaction chambers, the reaction mixture was encapsulated as droplet in fluorinated oil and the evaporation loss at 65°C in the 45-min heating process had been significantly reduced. As shown in Figure 4, the evaporation loss of the 19



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chambers in the vision scope was recorded and calculated by an image processing program, and an average loss of 3.29% (pixels of fluorescence excited area) was achieved to ensure the dLAMP performance. Optimization of dLAMP on the spiral chip. In order to ensure the rapid and distinct response of LAMP reaction in 9.6 nL chambers on the 1200-plex spiral chip, a series of dLAMP tests using varying temperatures and concentrations of Bst 2.0 DNA polymerase were carried out. Since the activity of the non-warmstart Bst 2.0 DNA polymerase was extremely dependent on the external temperature, we conducted dLAMP assays at 4 different temperatures (50°C, 55°C, 60°C and 65°C) with undiluted genomic DNA as the template. The real-time image sequences indicated that when the temperature was below 55°C, there was no obvious increasing fluorescence until 15 min and a merely 2-fold end-point intensity was achieved after 45 min, resulting in lagging and poor response signal. However when the temperature was elevated to above 60°C, the resulting fluorescence signal was improved in both speed and intensity, as shown in Figure S8A. In another set of dLAMP assays with varying concentrations (0, 0.08, 0.16 and 0.32 U/µL) of Bst 2.0 DNA polymerase was performed and the real-time fluorescence was recorded to verify the optimal working concentration. Similar to the above experiment, undiluted genomic DNA was used as the template. The plotted curves in Figure S8B indicated that all 3 dLAMP assays with Bst 2.0 DNA polymerase successfully completed the amplification in 45 min, resulting in distinct end-point fluorescence. As the concentration of polymerase increased, the response time dropped quickly and the relative intensity increased slightly. It turned out that the outcome of dLAMP assay was detectable within 15 min with the highest working concentration (0.32 U/µL). Above results showed that the performance of real-time LAMP assay highly depended on the


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precise temperature control and the polymerase activity. Moreover, we discovered that when dLAMP reaction was maintained at the temperature between 60°C~65°C with the Bst 2.0 polymerase varying from 0.16 to 0.32 U/µL, the resulting fluorescence could achieve a 4-fold to 5-fold increase compared to the initial background, within a relatively short period of time no longer than 40 min. In the following dLAMP experiments, a polymerase concentration of 0.32 U/µL and a temperature of 65°C were employed as the optimal reaction condition. Absolute quantification by dLAMP on the spiral chip. In order to examine the capability of absolute quantification of DNA template on the spiral chip, a 10-fold serial dilution of VF genomic DNA sample spanning across 4 orders of magnitudes from 1:104 to 1:107 was prepared as the template. At very low sample concentration with small m, variation of initial DNA molecule number is dominated by Poisson uncertainty due to random subsampling process. However, the minimum concentration of template DNA is a single molecule in principle. For the most diluted sample, the outcome of dLAMP assay may possibly appear to be all negative or more than one positive, and we confirmed this phenomenon experimentally with several replicates (n = 6). As shown in Figure 5, representative fluorescent images of dLAMP assay on the spiral chip with 4 concentrations of DNA sample (including negative control) were captured under the stereo zoom microscope after 40-min water bath incubation at 65°C. The corresponding 2-D color scattergram (Figure S9) verified an approximately 4-fold increase in the end-point fluorescence compared to the negative control, which was consistent with our previous results.37 The total sample volume in the 1200-plex spiral array was about 11.5 µL. Consequently, the lowest detection amount was further reduced to 87 copies/mL, which was much lower than those achieved by microliter LAMP reactors. Figure S10 showed the digital image processing of the dLAMP assay. On the other hand,



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the quantitative dynamic range was narrowed due to the limited array size of (1200-plex) according to our theoretical results. DNA molecules in samples with minimum dilutions (1:104 and 1:105) was successfully quantified, which validated that the spiral chip allows us to reach a dynamic range of nearly 4 logs with a potentially competitive quantitative resolution compared to qPCR. Each set of dLAMP assays for different concentrations of diluted samples included 3 replicates to ensure the repeatability. A linear fit regression to the 4 dilutions was determined with a linear correlation coefficient R2 = 0.99973, as shown in Figure 6A. Furthermore, an absolute quantification assay by fluorescence dye based real-time qPCR was carried out to evaluate and validate the quantitative results of dLAMP assays. To ensure the optimal amplification efficiency, two sets of conventional PCR pre-experiments were performed with different cycling programs, whereas the running method with the annealing temperature at 50°C showed higher DNA yield and better efficiency (Figure S11). With these optimized conditions, the ten-fold serial dilutions of VF genomic DNA templates were used to evaluate the detection limit of PCR assay by agarose gel electrophoresis, and as shown in Figure S12, 1:104 diluted template sample was successfully detected. A standard curve (y = -3.49x + 36.67 with a correlation coefficient R2 = 0.997) for absolute quantification by qPCR was established covering 6 orders of magnitudes in concentration, and the quantification result (9.99 copies/µL) for the unknown sample by qPCR showed good consistency with that (9.46 copies/µL) measured by dLAMP (Figure 6B). These experimental results validated that the dLAMP assay performed on this spiral chip has the capability of rapid absolute quantification of DNA concentrations, demonstrating lower detection limit and better precision for minute amounts of samples.


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CONCLUSION

In this study, we established a mathematical model for dLAMP assay. The mathematical model illustrated the influential factors of the dLAMP assay. A spiral chip was subsequently designed and fabricated with 1200 uniform and discrete LAMP reaction chambers based on the mathematical model. The spiral chip was composed of only a PDMS layer with channels and chambers and a glass slide. By optimizing the temperatures and polymerase concentrations, dLAMP assay could be carried out within 40 min and the lowest detection amount as low as 87 copies/mL. The spiral chip realized quantitative analysis of nucleic acids spanning over 4 orders of magnitude in concentration. The experiment result was consistent with the theory analysis and our mathematical model provides a guideline for the design and analysis of dLAMP devices.

Acknowledgements

The authors gratefully acknowledge the financial supports from National Natural Science Foundation of China (21475049, 31471257 and 21275060) and National Key R&D Program of China (2016YFF0100801).

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: Information of the laws and quantitative parameters of the mathematics quantitative methods by a series of formula derivation and mathematical model (Figure S1-S5, Table S1-S2); Chip evaluation, optimization and digital assay (Figure S6-S12).



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Figure 1. Simulation and statistical analysis of 2-D poisson process using discontinuously varying input m ranging from 1 to 2000 in the 256-plex digital array. (A-L) Histograms embedded with scatter plots of 2-D poisson process showing the statistical results of the numbers of partitions for different input m while grey bar indicated the number of empty partitions that trapped no molecules. Each sets of in silico experiments included 6 replicates. Orange square dots denote the input molecules while the blue solid outlines indicate the empty partitions. Vertical axis Ck, horizontal axis k. Each assay was repeated 6 times.



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Figure 2. Prediction of quantitative resolution for 1200-plex digital assay by Monte Carlo simulation. (A) Simulation results when the input m value was fixed at 3, 30, 300 and 3000 respectively. (B) A box plot embedded with a scatter plot showed the overall result of the in silico experiment with 10000 sets of 1000 replicates for input m ranging from 1 to 10000.


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Figure 3. The spiral chip and its operation procedure. (A) Design and fabrication of the spiral chip. (B) The principle and operation procedure of sample introduction and partition on the dLAMP spiral chip. After sample loading a PDMS plug was used to seal the quartz inlet and push the oil to fill the channels.



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Figure 4. Evaluation of evaporation at 65°C immersed in water after fluorosilane polymer coating on the internal surface of the spiral chip. (A-D) Bright field fluorescence images captured at 0 min, 15 min, 30 min and 45 min, respectively. (E) Original fluorescence image captured in bright field. (F) Regions’ margin extracted and image binarized. (G) Fill in the closed regions. (H) Eliminate small regions and calculate the pixels of remaining regions. (I) Hardly any liquid evaporation was observed in the 19 chambers within 45 min heating.


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Figure 5. The dLAMP results on the spiral chip using a series of 10-fold diluted Vibrio fluvialis genomic DNA sample ranging from 0.21 copies/µL to 2100 copies/µL as the template. (A) Negative result. (B) 1-copy result using 107 diluted template. (C) 2-copy result using 107 diluted template. (D) 22-copy result using 106 diluted template. (E) 213-copy result using 105 diluted template. (F) 1907-copy result using 104 diluted template.



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Figure 6. Results comparison of digital LAMP and real-time qPCR. (A) dLAMP quantification curve of copy number from a series of samples with given 10-fold diluted VF gDNA concentrations. (B) Quantification of dLAMP and qPCR for the same sample with an unknown concentration.


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