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

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Biology is the science of living things in all their complexity

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Hey! Whats this Drosophila melanogaster doing in my soup?

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

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

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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

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What good is mathematics?

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

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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...

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The Golden Rectangle L W WL-W

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

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

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

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

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

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Can we stop the spread of infection by immunization?

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The Overcrowding Game... space = available = occupied

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time space

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time space overcrowded

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space time

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Pascals Triangle

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

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Olivia (mollusc)

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Hans Meinhardt, The Algorithmic Beauty of Sea Shells

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Cymbiola (pattern = Serpinskis gasket)

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Serpinskis Gasket

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

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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???

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

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J. Keener A. Panfilov

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

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

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

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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

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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

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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

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

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

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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!

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

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