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Open Access Open Badges Research article

Differentiating Plasmodium falciparum alleles by transforming Cartesian X,Y data to polar coordinates

Jeana T DaRe1, Drew P Kouri12, Peter A Zimmerman1* and Peter J Thomas2345*

Author Affiliations

1 Center for Global Health and Disease, Case Western Reserve University School of Medicine, Wolstein Research Building, 4-125, Cleveland, Ohio 44106-7286, USA

2 Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7058, USA

3 Department of Biology, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7058, USA

4 Department of Cognitive Science, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7058, USA

5 Department of Neuroscience, Oberlin College, 119 Woodland Street, Oberlin, OH, 44074, USA

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BMC Genetics 2010, 11:57  doi:10.1186/1471-2156-11-57

Published: 29 June 2010



Diagnosis of infectious diseases now benefits from advancing technology to perform multiplex analysis of a growing number of variables. These advances enable simultaneous surveillance of markers characterizing species and strain complexity, mutations associated with drug susceptibility, and antigen-based polymorphisms in relation to evaluation of vaccine effectiveness. We have recently developed assays detecting single nucleotide polymorphisms (SNPs) in the P. falciparum genome that take advantage of post-PCR ligation detection reaction and fluorescent microsphere labeling strategies. Data from these assays produce a spectrum of outcomes showing that infections result from single to multiple strains. Traditional methods for distinguishing true positive signal from background can cause false positive diagnoses leading to incorrect interpretation of outcomes associated with disease treatment.


Following analysis of Plasmodium falciparum dihydrofolate reductase SNPs associated with resistance to a commonly used antimalarial drug, Fansidar (Sulfadoxine/pyrimethamine), and presumably neutral SNPs for parasite strain differentiation, we first evaluated our data after setting a background signal based on the mean plus three standard deviations for known negative control samples. Our analysis of single allelic controls suggested that background for the absent allele increased as the concentration of the target allele increased. To address this problem, we introduced a simple change of variables from customary (X,Y) (Cartesian) coordinates to planar polar coordinates (X = rcos(θ), Y = rsin(θ)). Classification of multidimensional fluorescence signals based on histograms of angular and radial data distributions proved more effective than classification based on Cartesian thresholds. Comparison with known diallelic dilution controls suggests that histogram-based classification is effective for major:minor allele concentration ratios as high as 10:1.


We have observed that the diallelic SNP data resulting from analysis of P. falciparum mutations is more accurately diagnosed when a simple polar transform of the (X,Y) data into (r,θ) is used. The development of high through-put methods for genotyping P. falciparum SNPs and the refinement of analytical approaches for evaluating these molecular diagnostic results significantly advance the evaluation of parasite population diversity and antimalarial drug resistance.