The Malaria TaqMan Array Card Includes 87 Assays for Plasmodium falciparum Drug Resistance, Identification of Species, and Genotyping in a Single Reaction

ABSTRACT Antimalarial drug resistance exacerbates the global disease burden and complicates eradication efforts. To facilitate the surveillance of resistance markers in countries of malaria endemicity, we developed a suite of TaqMan assays for known resistance markers and compartmentalized them into a single array card (TaqMan array card, TAC). We included 87 assays for species identification, for the detection of Plasmodium falciparum mutations associated with chloroquine, atovaquone, pyrimethamine, sulfadoxine, and artemisinin resistance, and for neutral single nucleotide polymorphism (SNP) genotyping. Assay performance was first optimized using DNA from common laboratory parasite lines and plasmid controls. The limit of detection was 0.1 to 10 pg of DNA and yielded 100% accuracy compared to sequencing. The tool was then evaluated on 87 clinical blood samples from around the world, and the malaria TAC once again achieved 100% accuracy compared to sequencing and in addition detected the presence of mixed infections in clinical samples. With its streamlined protocol and high accuracy, this malaria TAC should be a useful tool for large-scale antimalarial resistance surveillance.

days (11). Ex vivo assessment of Plasmodium falciparum sensitivity requires tissue culture facilities and fresh blood products for parasite propagation, which are not readily available in countries of malaria endemicity. Genetic markers of resistance have been identified for several clinical antimalarials, and assessment of parasite DNA for these markers is a useful method for resistance detection (12)(13)(14)(15)(16)(17)(18)(19)(20). Several molecular tools have been developed to detect these markers, including PCR-restriction fragment length polymorphism (RFLP) (21), high-resolution melt analysis (22), quantitative PCR (23,24), and loop-mediated isothermal amplification (LAMP) (25). Although accurate, these PCR-based methods are onerous because multiple markers need to be assessed. Luminex-based assays (26,27), microarrays (28), and whole-genome sequencing of clinical samples (29,30) can achieve greater throughput but are difficult to implement in field settings. We therefore sought to create a comprehensive, easy-to-perform method to track many resistance markers from multiple samples in a single run. The TaqMan array card (TAC) is a customizable 384-well card that compartmentalizes each sample into 48 different quantitative PCRs. TAC protocols are streamlined (due to several self-contained reagents), and eight patient samples can be run simultaneously. Our group has applied this technology successfully for detection of multiple tuberculosis (TB) drug resistance markers (31,32), syndromic pathogen detection (33,34), and pneumococcal serotyping (35) and has found excellent reproducibility between multiple laboratories across Africa, Asia, and America.
Here, we describe the construction and testing of the malaria TAC. This initial card design includes 70 assays for the detection of resistance-associated mutations in the P. falciparum CRT [pfCRT] chloroquine), pfCYTB (atovaquone), pfDHFR (pyrimethamine), pfDHPS (sulfadoxine), pfMDR1 (multidrug resistant), and pfKelch13 (artemisinin) genes. Additionally, assays for the detection of the five Plasmodium species targeting humans (falciparum, vivax, ovale, malariae, and knowlesi) and 12 genotyping single nucleotide polymorphisms (SNPs) were included to provide additional epidemiologic information about the samples.

RESULTS
TaqMan assay performance. The 35 duplex TaqMan assays for resistance markers, 6 duplex assays for SNP genotyping, and 5 singleplex assays for species identification as well as a control assay for human glyceraldehyde-3-phosphate dehydrogenase (hGAPDH) (Fig. 1) were first tested against 35 other blood pathogens, and no crossreactivity (detection of false positives) was observed (see Materials and Methods for a list of pathogens) (data not shown). Specificity was then tested against 11 P. falciparum lines, P. vivax, P. knowlesi, human DNA, and 17 synthetic plasmid controls in the 384-well plate format (see Fig. S1 in the supplemental material). For most assays (38/47), we detected no cross-reactivity between any of the duplexed assays (wild-type and mutant loci and major and minor SNP alleles) or among the five Plasmodium species. We observed minor cross-reactivity in 9 of 47 assays (pfCRT 73-76VMET, pfCRT 326S, pfCRT 356I, pfCYTB 268Y, pfCYTB 268C, pfDHPS 613A, pfMDR1 1246Y, SNP1-T, and SNP2-G) (Fig. S1). Such cases were observed only when high concentrations of DNA (Ͼ1 ng) were used and were eliminated by adjusting the threshold.
Next, the PCR performance of each primer/probe assay was determined on 384-well plates and then later with the TAC format. To test the amplification efficiency of each assay, DNA from either individual parasite lines or plasmid controls was tested in triplicate for six serial dilutions (see Materials and Methods for details). The overall linearity (R 2 ) of the 88 targets, including hGAPDH, was 0.990 Ϯ 0.01 and 0.994 Ϯ 0.01; PCR efficiencies were 90% Ϯ 6.4% and 92% Ϯ 7.9% for the 384-well plates and TAC formats, respectively (Tables S1 and S2). The limit of detection was similar on both 384-well plates and TaqMan array cards, ranging between 10 to 100 plasmid copies per reaction or 4.03 to 403 copy equivalent genomic DNAs (0.1 to 10 pg) per reaction (Tables S1 and S2).
Malaria TAC evaluation. The performance of the TaqMan array card was evaluated using genomic DNA from 18 laboratory parasite lines and 87 clinical samples. The malaria TAC successfully detected the correct wild-type or mutant loci in 99% Ϯ 4.1% of reaction products using 18 laboratory parasite strains; those that were left undetermined represented parasite lines with mutations other than those included in malaria TAC (Table 1, pfCRT 97 and pfDHPS 436 -437). The malaria TAC successfully detected either wild-type or mutant loci for 89% Ϯ 7.3% of reactions using 87 clinical samples ( Table 1). The pfCRT 72-76, pfCRT 97, pfDHFR 164, and pfDHPS 540 targets had the lowest rates of detection in this set of samples (Ͻ80%) ( Table 1). The undetermined samples were mostly from the Malawi repository, with an average detection level of 78% Ϯ 9.0%. Thailand-, China-, and Uganda-derived samples exhibited detection levels of 95% Ϯ 5.3%, 90% Ϯ 18.4%, and 100%, respectively (Table S3). The malaria TAC successfully detected two clinical samples that contained non-P. falciparum parasite DNA, including one each of P. vivax and P. ovale (Table 1).
The allelic distribution of the loci successfully detected by the malaria TAC is shown in Fig. S2. The majority of clinical samples showed pfCRT mutations, except for those from Malawi. All samples displayed pfDHFR and pfDHPS mutations, but none were observed in pfCYTB. The number and type of pfMDR1 and pfKelch13 mutations varied depending on the country of origin. The pattern of P. falciparum mutant alleles detected in our analysis is summarized in Table S4. Overall, we detected 13 distinct resistance marker genotypes from 16 laboratory parasite lines (data not shown). This The antimalarial resistance-focused TaqMan array card (malaria TAC) includes eight ports/card (one port is shown), and each port is connected to 48 assay wells. Each assay well contains prespotted primers and probes and is configured as shown on the basis of gene, codon, and wild-type/mutant-specific loci. The antimalarial to which resistance is conferred is listed next to each group of targets (MDR, multidrug resistance; Sulf, sulfadoxine; Pyr, pyrimethamine; Ato, atovaquone; CQ, chloroquine; Art, artemisinin). For genotyping, the SNPs are identified as follows: SNP1, Pf_01_ 000130573; SNP2, Pf_01_000539044; SNP3, Pf_02_000842803; SNP6, Pf_06_000145472; SNP7, Pf_06_000937750; SNP8, to Pf_07_000277104. Plasmodium species-specific probes are included to confirm the presence of P. falciparum DNA in each sample.
TaqMan Array Card for Drug-Resistant Malaria Antimicrobial Agents and Chemotherapy estimation was more difficult for clinical samples since some targets were not detectable and therefore yielded incomplete data. However, from clinical samples in which all drug resistance loci were detected, the malaria TAC successfully detected 13 distinct resistance marker genotypes or antibiograms (data not shown). For validation, Sanger sequencing was performed in parallel on all laboratory parasites and ϳ50% of clinical parasites. Results from the malaria TAC showed 100% sensitivity, specificity, and accuracy ( Table 2). One laboratory parasite sample was negative for both wild-type (H) and mutant (Q) probes by malaria TAC at pfCRT 97. Sequencing revealed that this sample harbored an alternative allele that was not tested in our current design (H97L) ( Tables 1 and 2). Similarly, four pfDHPS 436 -437 mutants had an alternative allele (FG) that was not covered by the malaria TAC and was therefore not detected with the wild-type (SG) or mutant (AG or SA) probe (Tables 1  and 2).  During the assessment of clinical parasite genotypes, we found that 7/85 (8%) clinical DNA samples were positive for multiple probes at a single locus (termed hetero-resistance [data not shown]). These findings were originally detected using the malaria TAC but were subsequently sequence confirmed ( Fig. 2 and S3). For example, DB133 was positive for both the wild-type (184Y) and mutant (184F) pfMDR1 probes; Sanger sequencing showed mixed T/A as position 184, which indicated the presence of both F(TTT) and Y(TAT) (Fig. 2).
Due to space limitations, only 6 of 24 original genotyping SNPs (36) could be included in this initial malaria TAC design. With this limited set, we detected 12 distinct barcodes from 16 laboratory parasite lines (data not shown) and 67 distinct barcodes from 85 clinical samples (Table 3) (18 samples exhibited incomplete data and were not included in this analysis). The set of distinct barcodes from clinical samples included 13 shared and 14 unique barcodes. Four of the 13 shared barcodes were found in multiple samples from the same country, 8/13 were shared across two different countries, and 1/13 (CATCAG) was found in all four countries. We also detected 14 (21%) barcodes that were unique and contained mixed alleles, which were also confirmed by sequencing ( Fig. 2 and S4). In one example, sample DB009 was positive for both the major and minor allele probes at SNP3 (Pf_02_000842803 T and C, respectively); Sanger sequencing also showed a mixed T/C at this position (Fig. 2).

DISCUSSION
In this study, we developed and tested a quantitative PCR-based TaqMan array card to detect the majority of known antimalarial resistance-associated mutations. The malaria TAC yielded excellent specificity, with no cross-reactivity to other pathogens or human genes and no unexplained cross-reactivity between alleles (Fig. S1 in the supplemental material; also data not shown). This tool displayed excellent sensitivity and accuracy when clonal laboratory parasites were the source of DNA and results were compared with results of Sanger sequencing (Tables 1 and 2). Additionally, the malaria TAC performed well when clinical samples were used (Tables 1 and 2), despite the presence of human DNA (ϳ80 copies/reaction volume or 4.0 ϫ 10 4 copies/100 l of DNA). Based on the detection of heteroresistance and mixed genotypes, this tool has the ability to detect mixed infections (Table 3 and Fig. 2, S3, and S4), which are common, but underappreciated, in clinical samples.
Despite many benefits, there are also some obvious limitations of the malaria TAC. Although future malaria TAC designs are customizable, we are limited to the detection of known loci. For the most part, mutations that contribute to clinical resistance are well known, but new mutations whose significance remains unknown are still being discovered (37). Design flexibility is particularly relevant for emerging artemisinin resistance where novel Kelch13 resistance mutations are being detected (38). As is, our initial design of the malaria TAC appears to be a good approximation of important mutations. For example, we detected only two alleles in parasite DNA that were not included in the initial design (pfCRT 97L and pfDHPS 436F) ( Table 1). These mutations were not originally represented because their global minor allele frequencies (MAF) were well below those for other alleles of these loci (39). Second, we detected ample diversity across the malaria TAC assays: (i) SNP barcodes were covered by 75% of From a genotyping standpoint, we were limited in the number of barcodes that could be interrogated. From just five loci, we detected distinct barcodes in ϳ61% (41/67) of clinical samples. Since ϳ19% of the barcodes were shared and since the majority of these were detected in at least two different countries, it is likely that an expansion of the number of barcodes tested would have revealed that many of these were indeed unique. For example, sample DB148 from Thailand had a genotyping barcode that was shared with two samples from China, three samples from Malawi, and one sample from Uganda. The malaria TAC also detected heteroresistance in this sample at two loci, indicating that it was likely a mixed infection. We propose that expansion of the number of SNP barcodes would have revealed a unique/mixed barcode in this sample that originated from Thailand. Future malaria TAC designs can augment this aspect of assay design.
A challenge to clinical infections is the detection of minor loci from mixed infections. Using the malaria TAC, we detected mixed infections in samples from all four countries. If we take into account both genotyping SNPs and observations of heteroresistance, Thailand exhibited ϳ31%, China exhibited ϳ10%, Malawi exhibited ϳ33%, and Uganda exhibited ϳ40% mixed infections. Of course, these were convenience samples that were not systematically collected for purposes of examining heteroresistance, so the absolute numbers are likely not representative of those regions. Four of seven cases of heteroresistance were also detected as mixed infections by genotyping SNPs, indicating that it is possible to accurately detect multiple alleles using the malaria TAC (down to ϳ10% [data not shown]). Future assessment of the malaria TAC will work to accurately determine the limit of detection for rare alleles.
Clinical samples also exhibit various levels of parasite densities and thus parasite DNA. Measuring the limit of detection, or LOD, allows the estimation and comparison of sensitivity for various methods. Most of the malaria TAC assays displayed an LOD of 40.3 copies/reaction volume (ϳ8 to 40 parasites/l, if single-copy genes were assessed on either the plate or TAC format). The malaria TAC LOD is similar to LODs of other TACs that we have developed (35). Additionally, the LOD is within range of other sensitive genotyping methods used in the malaria field (10 parasites/l) (24,40). Future work will explore the malaria TAC limit of detection using clinical samples.
One related concern that was revealed by these studies was the decrease in malaria TAC sensitivity when DNA derived from clinical parasite lines was used. This result is likely a limitation of the quality and quantity of the clinical samples that were used for this analysis. First, the amount of parasite-derived genomic DNA in these samples is unknown because of the presence of an abundance of human blood cell DNA. In order to correct for this, the maximum allowable sample volume was used when the clinical samples were used (20 to 50 l of a 100-l reaction mixture). Second, the format and age of the clinical samples varied, which could directly contribute to assay performance (see Materials and Methods for details). For example, the dried blood spots, remarkably, were collected 11 years ago in Thailand. Room temperature storage over long periods of time likely leads to some level of DNA degradation. Evidence for this was observed by the failure of amplification of long PCR product sizes suitable for Sanger sequencing (data not shown). Additionally, most of the undetectable samples were from Malawi; these purified DNA samples had the longest period ( While most assays on the malaria TAC performed very well, a few of the assays were problematic. pfCRT 72-76, pfCRT 97, pfDHFR 164, and pfDHPS 540 assays appeared suboptimal based on a sensitivity of Ͻ80% when they were tested with DNA from clinical parasites ( Table 1). Three of these assays were the most challenging to design and exhibited the highest limits of detection. Conversely, pfCRT 97 performed well using laboratory parasite-derived DNA and exhibited an LOD similar to that of most of the other assays. It is possible that the presence of human DNA in clinical samples affects the performance of this assay. Although we did not specifically test the pfCRT 97 assay, we investigated this possibility by running five randomly chosen duplex assays in the presence and absence of human DNA at multiple ratios. Overall, we did not detect statistically significant differences during this analysis (data not shown). These results indicate that the presence of human DNA in clinical samples likely does not have an impact on these assays, but there is room for future work to investigate this further.
Although not the main purpose of this study, the malaria TAC detected a number of different resistance markers from several clinical isolates. For the most part, our observations are consistent with what has been observed previously. First, we did not detect pfCRT mutations from Malawi samples, consistent with the return of chloroquine-susceptible malaria in Malawi after chloroquine use was abandoned (41). The pfDHFR-pfDHPS mutant patterns IRNL-SGEGA and IRNL-AGEAA (mutations are underlined), which are linked to high-level sulfadoxine-pyrimethamine (SP) resistance (42), were observed as predominant alleles in Thailand and China samples, respectively. The pfMDR1 Y184F was the most common mutation observed in this study and has been reported as a common mutation found in Asia and Africa (43)(44)(45). Last, we found that 83% of pfKelch13 alleles from China harbored the F446I mutation; this is the predominant Kelch13 mutation associated with delayed clearance of parasites in patients close to the China-Myanmar border (9,10).
Overall, our numbers of clinical samples from each country were small, and thus the sensitivity and specificity estimates of the malaria TAC are an approximation. It will be important to further evaluate this tool with additional clinical samples to fully explore its use for surveillance. Based on this pilot study of the malaria TAC, future design alterations could include more genotyping loci (perhaps a new format), removal of cytochrome b mutations, and alteration of Kelch13 loci to better detect newly emerging resistance. Additionally, we can replace/redesign suboptimal assays (pfCRT 72-76, pfCRT 97, pfDHFR 164, and pfDHPS 540). Deployment of this molecular diagnostic technology requires an expensive real-time PCR platform (Viia7; Applied Biosystems); however, these instruments are already present in a number of countries of malaria endemicity, and this enables testing in country. We are hopeful that the malaria TAC will accelerate the ability to track antimalarial-resistant populations and impact local and national treatment recommendations. were also obtained from this source, grown in our laboratory, and extracted for DNA as performed previously (46). Two non-P. falciparum species were also obtained for use as controls: genomic DNA of P. knowlesi (MRA-456G; BEI Resources) and cryopreserved P. vivax parasites (MRA-383; BEI Resources) from which DNA was directly extracted. Human control DNA was extracted from whole blood of healthy volunteers in our laboratory. All work was reviewed and approved by Institutional Biosafety and Human Investigation Committees at the University of Virginia.
Blood pathogens. We tested the specificity of our malaria-specific assays against 35 other blood pathogens. Genomic DNAs from 11 pathogens were obtained from BEI Resources Confirmation by Sanger sequencing. Mutations present in the control P. falciparum lines and a subset of clinical samples (42/87) were confirmed by Sanger sequencing. First, the resistance-associated genes and genotyping SNPs were PCR amplified using primers described in Table S5  . Each 25-l PCR mixture contained 12.5 l of HotStarTaq master mix (Qiagen, Valencia, CA, USA), 0.45 l of the forward and reverse 50 M primers (final concentration of 0.9 M), 6.6 l of nuclease-free water, and 5 l of genomic DNA (500 pg total for DNA derived from laboratory parasites). PCR was performed on a CFX96 instrument (Bio-Rad, Hercules, CA, USA) and included an initial denaturation step at 95°C for 15 min, followed by 40 cycles of denaturation at 95°C for 30 s, annealing at 59°C for 30 s, and extension at 72°C for 30 s, with a final extension step at 72°C for 10 min. Next, PCR products were analyzed on 2% agarose gels, and Pholwat et al.
Antimicrobial Agents and Chemotherapy verified PCR products were purified using a MinElute 96 UF PCR purification kit (Qiagen, Valencia, CA, USA) according to the manufacturer's protocol. Finally, purified PCR products were measured spectrophotometrically, diluted with nuclease-free water, mixed with primers, and then submitted to GeneWiz (Genewiz, Inc., South Plainfield, NJ, USA) for DNA sequencing. Sensitivity (the ability to correctly classify a mutant allele) and specificity (the ability to correctly classify a wild-type allele) were determined using a two-by-two table where the gold standard is Sanger sequencing. Accuracy (the ability to correctly classify both alleles) is an average of sensitivity and specificity values. Drug resistance loci and mutant allele selection. We selected the targets for the initial malaria TAC design by (i) identifying previously reported associations with antimalarial resistance and (ii) prioritizing candidates based on global minor allele frequencies (MAF) reported in the MalariaGEN database (39). For pfCRT, pfDHFR, pfDHPS, and pfMDR1, most of the selected targets displayed a global MAF of Ͼ0.1 (5 of 26 total alleles) (Table S6). Since pfKelch13 mutations have only recently arisen predominantly in Southeast Asia, global frequencies of all these are low (Ͻ0.1). We therefore included pfKelch13 alleles that have been confirmed to confer artemisinin resistance (Y493H, R539T, I543T, and C580Y) (14,49) as well as one allele that is associated with clinically delayed parasite clearance (F446I) (10). Additionally, in order to provide a complete picture of variation across this gene, we included mutations that have been observed in Asia and Africa but at the time of selection had an unknown association with resistance (N458Y, R561H, P574L, and A578S) (50)(51)(52). Since data were not available for pfCYTB mutations in the MalariaGen database, we directly selected atovaquone resistance-associated alleles from the literature (18)(19)(20).
Optimization of conditions and probe specificity testing were performed using the 384-well plate on the ViiA7 platform (Applied Biosystems, Life Technologies Corporation, Carlsbad, CA, USA). Each assay was amplified in duplex ( Fig. 1 shows pairings), except for assays involved in species identification and the hGAPDH control. Primer/probe sets (0.09 l of each forward and reverse primer, 0.025 l of each probe of 50 M stock, final concentrations of 0.9 M and 0.25 M, respectively) were assayed in a 5-l PCR mixture containing 2.5 l of 2ϫ TaqMan universal master mix II (Applied Biosystems, Life Technologies Corporation, Carlsbad, CA, USA), 1.27 l of nuclease-free water, and 1 l (1 ng/l) of genomic DNA. Cycling conditions included an initial denaturation at 95°C for 10 min, followed by 40 cycles of denaturation at 95°C for 15 s and annealing/extension at 59°C for 1 min. DNA sources included either P. falciparum 3D7 DNA as a wild-type control, 10 sequence-confirmed mutant P. falciparum lines (including Dd2, V1/S, 7G8, TMC90C6B, K1, HB3, PAIL, PUR, MON, and BAT), P. vivax, P. knowlesi, synthetic mutant control plasmids and species identification plasmids (P. malariae and P. ovale), a mixture of parasitehuman DNA to test the performance of assays in the presence of human DNA (see below for ratios), or nuclease-free water as a nontemplate control.
Assay amplification efficiency and limits of detection were first performed on the 384-well plate format and subsequently on the array card format. To do so, DNA from individual parasite lines or plasmid controls was 10-fold serially diluted (plasmid control range, 10 5 to 1 copy/l; parasite DNA range, 1 ng to 10 fg or the equivalent of 4.03 ϫ 10 4 to 0.403 copies/l). For 384-well plate assays, 1 l of diluted samples was tested in each 5-l reaction mixture in triplicate. Since the volume of DNA used in the array card is 5-fold lower (0.2 l/reaction mixture), dilutions for malaria TAC testing were prepared as 5-fold more concentrated to ensure equivalence on both formats. The copy number of plasmid controls and copy number equivalents for parasite DNA were calculated using an available online tool (University of Rhode Island Genomics and Sequencing Center calculator [http://cels.uri.edu/gsc/cndna.html]) by inputting the amount of DNA in nanograms and the length in base pairs (23 Mb was used for parasite DNA). The formula is a follows: number of copies ϭ (amount of DNA ϫ 6.022 ϫ 10 23 )/(length of template ϫ 1 ϫ 10 9 ϫ 650). To determine whether human DNA in the clinical samples impacted the performance of our assays, five randomly chosen assays were tested in duplicate in the presence and absence of human DNA (pfCRT 72C/72Stct, pfDHFR 164I/164L, pfDHPS 540K/540E, pfMDR1 86N/86Y, and P. falciparum). This was performed at multiple ratios of parasite/human DNA; human DNA was fixed at 10 ng (2,860 genome copies), and parasite DNA varied from 1 ng to 1 pg (40,300 to 40.3 genome copies), yielding the following ratios: 14:1, 1.4:1, 0.14:1, and 0.014:1.
Evaluation of the malaria TAC. Primer and TaqMan probe oligonucleotides were custom ordered, synthesized, and spotted into the microfluidic card by Applied Biosystems (Life Technologies Corporation, Carlsbad, CA, USA) as laid out in Fig. 1. Twenty to 50 l of input DNA (at 1 ng/l for culture parasite-derived DNA) was mixed with 50 l of 2ϫ TaqMan universal master mix II (Applied Biosystems, Life Technologies Corporation, Carlsbad, CA, USA) and 0 to 30 l of nuclease-free water to yield a 100-l final volume. This mixture was loaded into each port of the card; each card included a port for seven clinical samples and one synthetic positive-control plasmid (8 ports total). The loaded card was centrifuged twice at 1,200 rpm for 1 min and then sealed. The loading ports were excised, and the full card was inserted into a ViiA7 instrument (Life Technologies Corporation, Carlsbad, CA, USA) and run under the same cycling conditions as described above for 45 cycles. The results were automatically analyzed by ViiA7 software; the baseline and threshold were adjusted in cases where minor cross-reactivity occurred. Statistical analysis. Means or medians were compared using Student's t test or a Mann-Whitney test. Data are shown as means Ϯ standard deviations unless otherwise stated. A standard curve of hGAPDH was generated with known DNA concentrations and plotted against the C T value to yield the following equation: copy number per reaction product ϭ 10 (CT Ϫ 37.65)/Ϫ3.6425 .