Calculating the Secrets of Life: Mathematics in Biology and Medicine De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL.

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Presentation transcript:

Calculating the Secrets of Life: Mathematics in Biology and Medicine De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL

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)

Mathematics in Florida –Farside--Larsen

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

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

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

DNA Replication

Strand Passage Topoisomerase

Strand Exchange Recombinase

Enzyme Bound to DNA

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

DNA Trefoil Knot

DNA (2,13) TORUS KNOT

Toposides--Chemotherapy Replication Fork Topoisomerase

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

Normal Heartbeat Jim Keeener, U. Utah

Spiral Waves-Tachycardia Jim Keener, U. Utah

Onset of Fibrillation J. Keener, U. Utah

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

The Human Brain

The Cerebellum

Euclidean Flat Map

Euclidean Map

Hyperbolic Maps

Hyperbolic Flat Map

Spherical Map

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

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

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

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