DEVELOPING THE BIOMEDICAL MATHEMATICS MAJOR AT FSU De

DEVELOPING THE BIOMEDICAL MATHEMATICS MAJOR AT FSU De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL 32306 sumners@math. fsu. edu

THE BOOK OF NATURE IS WRITTEN IN THE LANGUAGE OF MATHEMATICS GALILEO GALILEI (1600)

I HAVE DEPLY REGRETTED THAT I DID NOT PROCEED FAR ENOUGH AT LEAST TO UNDERSTAND SOMETHING OF THE GREAT LEADING PRINCIPLES OF MATHEMATICS CHARLES DARWIN (1860)

FSU BIOMEDICAL MATH • Prepare undergrads for math or bio grad school, med school; Hughes Fellow opportunities • Interdisciplinary curriculum: mathematics, statistics, computer science: biology, biochemistry • 2 new biomed math courses: Biocalculus Lab Math Modeling in Biology

Biocalculus Lab • Required of all bio majors • Calculus I pre/co requisite • Matlab based • Integrates mathematics, computation and biology • Calculus I bio applications • Exponential functions • Linear regression • Derivatives • Related rates • Integrals • Differential equations • Dynamical systems

EARLY USE OF MATHEMATICS Galen (200): blood created 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) proves that blood circulates: by studying cadavers, heart pumps 27 lt/hr, average human has 5. 5 liters of blood

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

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

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 • Visualization--computer graphics

The Cerebellum

Euclidean Flat Map Monica Hurdal, Florida State U.

Hyperbolic Flat Map Monica Hurdal, Florida State University

Spherical Map Monica Hurdal, Florida State University

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 Joel Cohen, Rockefeller University • 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

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