Mathematics and Biology

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Mathematics and Biology

• Peter J. Thomas
• Case Western Reserve University

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http//www.case.edu/artsci/ribms/ribms.html
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Mathematics Malaria
Worldwide distribution of Malaria, 2004 Center
for Disease Control
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What kinds of mathematics are contributing to
malaria research?
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What kinds of mathematics are contributing to
malaria research?

• Differential Equations

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What kinds of mathematics are contributing to
malaria research?

• Differential Equations
• Linear Algebra

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What kinds of mathematics are contributing to
malaria research?

• Differential Equations
• Linear Algebra
• Probability

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What kinds of mathematics are contributing to
malaria research?

• Differential Equations
• Linear Algebra
• Probability
• Statistics

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What kinds of mathematics are contributing to
malaria research?

• Differential Equations
• Linear Algebra
• Probability
• Statistics
• Computational Mathematics

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What kinds of mathematics are contributing to
malaria research?

• Differential Equations
• Linear Algebra
• Probability
• Statistics
• Computational Mathematics
• High School Geometry!?

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DNA gt RNA gt Protein
Image courtesy of HBC Protocols, Inc.
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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.
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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'
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Reading a DNA sequence
Gap
A single mutation can make the parasite drug
resistant. Drug Resistant (59 T)
5'-TCACATATGTTGTAACTGCACG-3' Drug Sensitive (59
C) 5'-TCACATATGTTGTAACTGCACA-3'
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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'
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Drew P. Kouri CWRU 2008 BS/MS (Mathematics) now
at Rice University (Computational and Applied
Mathematics)
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Polar Coordinates
x fluorescence from normal sequence indicator y
fluorescence from mutant sequence indicator
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Malaria DNA fluorescence data plotted in polar
coordinates
x axis radius y axis angle
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Diagnosis Thresholds via Histogram Segmentation
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Diagnosis Thresholds in Original Coordinates
x fluorescence from normal sequence indicator y
fluorescence from mutant sequence indicator
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The Kouri Algorithm
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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
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http//www.case.edu/artsci/math/
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http//www.case.edu/artsci/biol/