calculating the secrets of life: mathematics in biology and medicine de witt sumners department of...
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Calculating the Secrets of Life: Mathematics in Biology and
Medicine
De Witt Sumners
Department of Mathematics
Florida State University
Tallahassee, FL 32306
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: 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
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
Mathematics in the Heart
•Arrythmias-chaos theory
•Signal conduction geometry--fractals
•Fiber structure--finite element methods
•Conduction waves--differential equations & topology
•Visualization--computer graphics
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