Coping with Complexity April 1999 John J Tyson

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! What’s 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 Stoppard’s 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 don’t speak a common language. • My purpose is to open a serious dialog between mathematicians and biologists. . .

The Golden Rectangle L W W L-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 Harvey’s conclusion: blood must circulate!

Kermack & Mc. Kendrick, 1927 Infectious Diseases S = fraction of population that is susceptible I = fraction of population that is infectious d. I/dt = b. SI - g. I

Plague in Eyam, England, 1666 Susceptibles b = 0. 14 per day g = 0. 09 per day Infectives

For infection to spread, rate of new infection > rate of removal Basic reproductive rate Ro = 1. 6 for plague

Can we stop the spread of infection by immunization?

The Overcrowding Game. . . space mmmummm m = available u = occupied

space time mmmummm mmumumm

space time mmmummm mmumummmum overcrowded

space time mmmummm mmumummmum umumumu

u ummmu umumumu ummmmmmmu umummmmmumu ummmummmu umumumumu ummmmmmmmu umummmmmmmumu ummmmmmmummmu umummmmmumumumu ummmmmmmummmmmmmu umummmmmumummmmmumu ummmummmummmummmu umumumumumumumumu ummmmmmmmmmmmmmmmu umummmmmmmmmmmmmmmumu ummmmmmmmmmmmmmmummmu umummmmmmmmmmmmmumumumu ummmmmmmmmmmmmmmummmmmmmu umummmmmmmmmmmmmumummmmmumu ummmummmmmmmmmmmummmummmu umumumummmmmmmmmumumumumu ummmmmmmmmmmmmmmummmmmmmmu umummmmmmmmmmmmmumummmmmmmumu ummmummmmmmmmmmmummmmmmmummmu umumumummmmmmmmmumummmmmumumumu ummmmmmmummmmmmmummmmmmmummmmmmmu umummmmmumummmmmumummmmmumummmmmumu ummmummmummmummmummmummmummmummmu umumumumumumumumumumumumumumumumu Pascal’s Triangle

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

Olivia (mollusc)

Hans Meinhardt, The Algorithmic Beauty of Sea Shells

Cymbiola (pattern = Serpinski’s gasket)

Serpinski’s Gasket

Johnson Hall Human geometry is Euclidean Wild Carrot Life’s geometry is fractal P. Prusinkiewicz, Univ. Calgary

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

Excitable medium. . . space mmmmmmmmmmmmm mmmmmmummmmmmmmmmmmm space m = resting u = excited z = refractory

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J. Keener A. Panfilov

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

The DNA sequence game. . . A G A A C C C T A G G A C C A T A G C G u u uuu uu u u u uuu u u

A G A A C C C T A G G A C C A T A G C G u u uuu uu u u u uuu u u

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

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

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.