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?

“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 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

DNA (2,13) TORUS KNOT

Toposides--ChemotherapyToposides--Chemotherapy

Replication ForkReplication Fork

TopoisomeraseTopoisomerase

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 & topology

•Visualization--computer graphics

The Human BrainThe Human Brain

The CerebellumThe Cerebellum

Euclidean Flat MapEuclidean Flat Map

Euclidean Map

Hyperbolic Maps

Hyperbolic Flat MapHyperbolic Flat Map

Spherical Map

Spherical MapSpherical 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 UniversityJoel Cohen, Rockefeller University

Thank You

•National Science Foundation

•National Institutes of Health

•Burroughs Wellcome Fund