1. Calculating the Secrets of Life: Mathematics in Biology and Medicine De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL 32306 sumners@math.fsu.edu

2. What is mathematics good for? “No longer just the study of number and space, mathematical science has become the science of patterns, with theory built on relations among patterns and on applications derived from the fit between pattern and observation.” L.A. Steen, SCIENCE (1988)

3. Mathematics in Florida –Farside--Larsen

4. Mathematics: The Foundation for Scientific Discovery X Ray Crystallography: Group theory CAT & MRI: Radon Transform Weather Prediction: Navier-Stokes

5. Mathematics in Biology and Medicine DNA Enzymes: Chemotherapy Heart: Fibrillation Brain: Function and Malfunction

6. EARLY USE OF MATHEMATICS Galen (200 AD):blood created in the liver by eating food, ebbs and flows, goes from one side of heart to other via invisible pores in the heart wall, arteries and veins sealed and separate from each other William Harvey (1615) mathematically proves that blood circulates: by studying cadavers, heart pumps 27 lt/hr, average human has 5.5 liters of blood

7. DNA Replication

8. Strand Passage Topoisomerase

9. Strand Exchange Recombinase

10. Enzyme Bound to DNA

11. Topological Enzymology Mathematics: Deduce enzyme binding and mechanism from observed products

12. DNA Trefoil Knot

13. DNA (2,13) TORUS KNOT

14. Toposides--Chemotherapy Replication Fork Topoisomerase

15. Mathematics in the Cell Mathematics--the ultimate microscope Compute protein structure and function Understand viruses Design chemotherapy drugs

16. Normal Heartbeat Jim Keeener, U. Utah

17. Spiral Waves-Tachycardia Jim Keener, U. Utah

18. Onset of Fibrillation J. Keener, U. Utah

19. Mathematics in the Heart Arrythmias-chaos theory Signal conduction geometry--fractals Fiber structure--finite element methods Conduction waves--differential equations & topology Visualization--computer graphics

20. The Human Brain

21. The Cerebellum

22. Euclidean Flat Map

23. Euclidean Map

24. Hyperbolic Maps

25. Hyperbolic Flat Map

26. Spherical Map

28. Mathematics in the Brain Normal brain in silico--computational template for function and anatomy Clinical diagnosis and treatment--compare subject brain to template brain

29. Mathematics in Biology and Medicine Mathematics--the ultimate microscope Biological systems in silico--experiments possible Organ templates--computational diagnosis and treatment

30. Where can math help out? Too big--biosphere Too slow--macro evolution Too remote in time--early extinctions Too complex--brain, stock market Too small--molecular structure Too fast--photosynthesis Too remote in space--life at the extremes Too dangerous or unethical--epidemiology of infectious agents, war weapons and strategies Joel Cohen, Rockefeller University

31. Thank You National Science Foundation National Institutes of Health Burroughs Wellcome Fund