DEVELOPING THE BIOMEDICAL MATHEMATICS MAJOR AT FSU De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL 32306 [email protected].

DEVELOPING THE BIOMEDICAL MATHEMATICS

MAJOR AT FSU

De Witt Sumners

Department of Mathematics

Florida State University

Tallahassee, FL 32306

[email protected]

THE BOOK OF NATURE IS

THE BOOK OF NATURE ISWRITTEN 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 LabMath 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 PassageStrand Passage

TopoisomeraseTopoisomerase

Strand ExchangeStrand Exchange

RecombinaseRecombinase

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 HeartbeatNormal Heartbeat

Jim Keeener, U. UtahJim Keeener, U. Utah

Spiral Waves-TachycardiaSpiral Waves-Tachycardia

Jim Keener, U. UtahJim Keener, U. Utah

Onset of FibrillationOnset of Fibrillation

J. Keener, U. UtahJ. 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 CerebellumThe Cerebellum

Euclidean Flat MapEuclidean Flat Map

Monica Hurdal, Florida State U.Monica Hurdal, Florida State U.

Hyperbolic Flat MapHyperbolic Flat Map

Monica Hurdal, Florida State UniversityMonica Hurdal, Florida State University

Spherical MapSpherical Map

Monica Hurdal, Florida State UniversityMonica 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

• 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 UniversityJoel Cohen, Rockefeller University

Thank You

•National Science Foundation

•National Institutes of Health

•Burroughs Wellcome Fund