Mathematics and Biology

1. Mathematics and Biology • Peter J. Thomas • Case Western Reserve University

2. http://www.case.edu/artsci/ribms/ribms.html

3. Mathematics & Malaria Worldwide distribution of Malaria, 2004 Center for Disease Control

19. What kinds of mathematics are contributing to malaria research?

20. Differential Equations What kinds of mathematics are contributing to malaria research?

21. Differential Equations Linear Algebra What kinds of mathematics are contributing to malaria research?

22. Differential Equations Linear Algebra Probability What kinds of mathematics are contributing to malaria research?

23. Differential Equations Linear Algebra Probability Statistics What kinds of mathematics are contributing to malaria research?

24. Differential Equations Linear Algebra Probability Statistics Computational Mathematics What kinds of mathematics are contributing to malaria research?

25. Differential Equations Linear Algebra Probability Statistics Computational Mathematics High School Geometry!? What kinds of mathematics are contributing to malaria research?

26. DNA => RNA => Protein Image courtesy of HBC Protocols, Inc.

27. Drug Resistant Malaria Mutants A single mutation can make the parasite drug resistant! Plasmodium falciparum diagnosis via bloodsmear Image courtesy Centers for Disease Control Worldwide distribution of drug-resistant malaria Single mutations are invisible to bloodsmear microscopy diagnosis. Diagnosis is only possible by reading the malaria DNA sequence.

28. SNP PCR Product Reading a DNA sequence A single mutation can make the parasite drug resistant. Drug Resistant (59 T) 5'-TCACATATGTTGTAACTGCACG-3' Drug Sensitive (59 C) 5'-TCACATATGTTGTAACTGCACA-3'

29. Reading a DNA sequence PCR Product 5’ phosphate 3’ biotin Oligonucleotide tag (for Luminex® xMAP™ beads) Allele Specific Primer Common Primer Gap A single mutation can make the parasite drug resistant. Drug Resistant (59 T) 5'-TCACATATGTTGTAACTGCACG-3' Drug Sensitive (59 C) 5'-TCACATATGTTGTAACTGCACA-3'

30. Reading a DNA sequence PCR Product 5’ phosphate 3’ biotin Oligonucleotide tag (for Luminex® xMAP™ beads) Microsphere Allele Specific Primer Common Primer A single mutation can make the parasite drug resistant. Drug Resistant (59 T) 5'-TCACATATGTTGTAACTGCACG-3' Drug Sensitive (59 C) 5'-TCACATATGTTGTAACTGCACA-3'

31. Drew P. Kouri CWRU 2008 BS/MS (Mathematics) now at Rice University (Computational and Applied Mathematics)

35. Text Polar Coordinates x = fluorescence from normal sequence indicator y = fluorescence from mutant sequence indicator

36. Malaria DNA fluorescence data plotted in polar coordinates x axis = “radius” y axis = “angle”

37. Diagnosis Thresholds via Histogram Segmentation

38. Diagnosis Thresholds in Original Coordinates x = fluorescence from normal sequence indicator y = fluorescence from mutant sequence indicator

39. The Kouri Algorithm

40. References: For more information on malaria, see: Malaria Journal 2006; 5: 86. Dynamics of immune response and drug resistance in malaria infection David Gurarie and F Ellis McKenzie Journal of Clinical Microbiology, March 2007, p. 752-761, Vol. 45, No. 3A Multiplex Ligase Detection Reaction-Fluorescent Microsphere Assay for Simultaneous Detection of Single Nucleotide Polymorphisms Associated with Plasmodium falciparum Drug Resistance Eric P. Carnevale, Drew Kouri, Jeana T. DaRe, David T. McNamara, Ivo Mueller, and Peter A. Zimmerman

41. http://www.case.edu/artsci/math/

42. http://www.case.edu/artsci/biol/