Biomathematics: Using Graph Models for High School

DIMACS Conference on LinkingMathematics & Biology

In High Schools

29 April 2005

L. Charles (Chuck) BiehlThe Charter School of Wilmington

Wilmington, DEcbiehl@charterschool.org

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

http://www.talkorigins.org/faqs/comdesc

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 Modelfor Smallpox

(Kaplan-Craft-Wein 2002)

Dynamic Programmingfor Path Problems

A

32

14

72

33

62 5

65

33

52

46

34 6

82

32

75

14

33 4

11

25

67

31

43 5

6 3 2 1 3 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

http://biology.beloit.edu/students/zdravko/vor_gallery_bio.html

The Internet (at night)

Protein-Protein Interactions

Pathmap™ Protein-Protein Interaction Data Set for Yeasthttp://www.protana.com

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