developing the biomedical mathematics major at fsu de witt sumners department of mathematics florida...
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DEVELOPING THE BIOMEDICAL MATHEMATICS
MAJOR AT FSU
De Witt Sumners
Department of Mathematics
Florida State University
Tallahassee, FL 32306
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