Biomathematics: Using Graph Models

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Biomathematics Using Graph Models
Biomathematics  Using Graph Models for High
School
DIMACS Conference on Linking Mathematics
Biology In High Schools
29 April 2005
L. Charles (Chuck) Biehl The Charter School of
Wilmington Wilmington, DE cbiehl_at_charterschool.org

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What Are These?
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Haeckels tree
The phylogeny and classification of life as
proposed by Haeckel in 1866
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A Possible Evolutionary Phylogenetic Tree
http//www.talkorigins.org/faqs/comdesc
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Accugenix Tree Report
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A Sample of a Computed Tree
Leaves are species internal vertices minimize
differences
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Constructing Phylogenetic Trees
Actual Tree (yellow) Distance matrix
(pink) Reconstructed tree from mutations (blue)
David E. Joyce, Dept. of Mathematics Computer
Science, Clark University
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Epidemic Model Basic Majority Process Model
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Digraph as a State Modelfor Smallpox(Kaplan-Craf
t-Wein 2002)
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Dynamic Programmingfor Path Problems
Dynamic Programming for Path Problems  
A
6 3 2 1 3 B
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Dynamic Programming for String Alignment
Image Source Christopher Lewis, bioinformatics
analyst, Saskatoon Research Centre of Agriculture
Agri-food Canada
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Voronoi Diagram model for Cell Growth, Mitosis,
and Interaction
http//biology.beloit.edu/students/zdravko/vor_gal
lery_bio.html
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The Internet (at night)
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Protein-Protein Interactions
Pathmap Protein-Protein Interaction Data Set for
Yeast http//www.protana.com
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Proteome Interaction Network(Protein
Genome)