Biomathematics: Using Graph Models for High School DIMACS Conference on Linking Mathematics & Biology In High Schools 29 April 2005 L. Charles (Chuck)

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Presentation transcript:

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 Biomathematics: Using Graph Models

What Are These?

The phylogeny and classification of life as proposed by Haeckel in 1866 Haeckel’s tree

A Possible Evolutionary Phylogenetic Tree

Accugenix Tree Report

A Sample of a Computed Tree Leaves are species – internal vertices minimize differences

Constructing Phylogenetic Trees David E. Joyce, Dept. of Mathematics & Computer Science, Clark University Actual Tree (yellow) Distance matrix (pink) Reconstructed tree from mutations (blue)

Epidemic Model: Basic Majority Process Model

Digraph as a State Model for Smallpox (Kaplan-Craft-Wein 2002)

Dynamic Programming for Path Problems A B

Dynamic Programming for String Alignment Image Source: Christopher Lewis, bioinformatics analyst, Saskatoon Research Centre of Agriculture & Agri-food Canada

Voronoi Diagram model for Cell Growth, Mitosis, and Interaction

The Internet (at night)

Protein-Protein Interactions Pathmap ™ Protein-Protein Interaction Data Set for Yeast

Proteome* Interaction Network (*Prote[in] + [Gen]ome)