# Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech.

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Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech

Biology is the science of living things in all their complexity

Hey! Whats this Drosophila melanogaster doing in my soup?

To the death, Carlson! Hang on to the death!

April 26. After several months I now feel that these strange little rodents have finally accepted me as one of their own.

If there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers? Thomasina, in Tom Stoppards play, Arcadia

What good is mathematics?

Mathematics is a disciplined way of thinking... –about numbers –about shapes –about patterns … in space and time

Why the Disconnect? Until recently the complexity of most biological problems was too great for the mathematical tools available. Now we have the tools, but we dont speak a common language. My purpose is to open a serious dialog between mathematicians and biologists...

The Golden Rectangle L W WL-W

The GR is self-similar…expand by (1.618) 4 6.854

William Harvey, 1628 An Anatomical Treatise of the Motion of the Heart and Blood Harveys conclusion: blood must circulate!

Kermack & McKendrick, 1927 Infectious Diseases S = fraction of population that is susceptible I = fraction of population that is infectious dI/dt = S I - I

Plague in Eyam, England, 1666 = 0.14 per day = 0.09 per day Susceptibles Infectives

Basic reproductive rate For infection to spread, rate of new infection > rate of removal R o = 1.6 for plague

Can we stop the spread of infection by immunization?

The Overcrowding Game... space = available = occupied

time space

time space overcrowded

space time

Pascals Triangle

Bushes and Trees Arteries and Veins Bronchial tubes Self-similar, One-dimensional (lines) Pascals Tree

Olivia (mollusc)

Hans Meinhardt, The Algorithmic Beauty of Sea Shells

Johnson Hall Human geometry is Euclidean Wild Carrot Lifes geometry is fractal P. Prusinkiewicz, Univ. Calgary

By this time everyone had learned how careful you have to be when dealing with numbers. E.B. White The Trumpet of the Swan Fractional dimension???

Excitable medium... = resting = excited = refractory space

J. Keener A. Panfilov

DNA Sequence Analysis New sequence: …AGAACCCTAG… …GACCATAGCG… Dictionary sequence:

A G A A C C C T A G G A C A T A G C G The DNA sequence game...

A G A A C C C T A G G A C A T A G C G

A G A A C C C T A G G -1 -1 -5 -6 -7 -8 -9 -10-11-9 A -1 -2 2 -2 -3 -4 -5 -6 -8 -7 C -5 -2 -2 1 1 0 -1 -5 -6 -7 C -6 -6 -3 -3 4 4 3 -1 -2 -3 A -4 -7 -3 0 0 3 3 2 2 -2 T -8 -5 -5 -4 -1 -1 -1 6 2 1 A -6 -9 -2 -2 -2 -2 -2 2 9 5 G -10 -3 -6 -3 -3 -3 -3 1 5 12 C -11 -7 -4 -7 0 0 0 0 4 8 G -12 -8 -8 -5 -4 -1 -1 -1 3 7

A G A A C C C T A G G -1 -1 -5 -6 -7 -8 -9 -10-11-9 A -1 -2 2 -2 -3 -4 -5 -6 -8 -7 C -5 -2 -2 1 1 0 -1 -5 -6 -7 C -6 -6 -3 -3 4 4 3 -1 -2 -3 A -4 -7 -3 0 0 3 3 2 2 -2 T -8 -5 -5 -4 -1 -1 -1 6 2 1 A -6 -9 -2 -2 -2 -2 -2 2 9 5 G -10 -3 -6 -3 -3 -3 -3 1 5 12 C -11 -7 -4 -7 0 0 0 0 4 8 G -12 -8 -8 -5 -4 -1 -1 -1 3 7 AGAACCCTAG... GA. CCATAGCG

Mycoplasma genitalia 600,000 nucleotides (letters) 500 genes (words), 2/3 recognized How are the words organized into meaningful sentences and paragraphs?...ATAGCCCTAGTCAAGTCATGGTCGAAC... Human genome 3,000,000,000 300,000

Lab for Bioinformatics, Keio University, Japan The Institute for Genomic Research, Rockville MD

Do we really need an equation for every gene???

Solar System 9 planets + assorted moons 20 bodies x 3 degrees of freedom x 2 diff eqs = 120 differential equations (comparable to 1/4 Mycoplasma genitalia) We do not have to solve all these equations in order to put a man on the moon or send an orbiter to Jupiter and beyond!

Mathematics is a tool for thinking about complex patterns in a precise yet creative way.

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