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Calculating the Secrets of Life: Mathematics in Biology and Medicine

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. What is mathematics good for?.

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Calculating the Secrets of Life: Mathematics in Biology and Medicine

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  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 Topoisomerase Replication Fork

  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

  27. 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. 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 Where can math help out? Joel Cohen, Rockefeller University

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

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