Coping with Complexity

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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 isa 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
W
L-W
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The GR is self-similarexpand by (1.618)4 _at_
6.854
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William Harvey, 1628An Anatomical Treatise of
the Motion of the Heart and Blood
Harveys conclusion blood must circulate!
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Kermack McKendrick, 1927Infectious Diseases
S fraction of population that is susceptible I
fraction of population that is
infectious dI/dt b S I
- g I
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Plague in Eyam, England, 1666
b 0.14 per day g 0.09 per day
Susceptibles
Infectives
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For infection to spread, rate of new infection gt
rate of removal
Ro 1.6 for plague
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Can we stop the spread of infection by
immunization?
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The Overcrowding Game...

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mmmummm
m available u occupied
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mmmummm mmumumm
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mmmummm mmumumm mummmum
overcrowded
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mmmummm mmumumm mummmum umumumu
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u umu ummmu umumumu ummmmmmmu umummmmmumu ummmummm
ummmu umumumumumumumu ummmmmmmmmmmmmmmu umummmmmmm
mmmmmmumu ummmummmmmmmmmmmummmu umumumummmmmmmmmum
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ummmmmumu ummmummmummmummmummmummmummmu umumumumum
umumumumumumumumumumu ummmmmmmmmmmmmmmmmmmmmmmmmmm
mmmmu umummmmmmmmmmmmmmmmmmmmmmmmmmmmmumu ummmummm
mmmmmmmmmmmmmmmmmmmmmmmmummmu umumumummmmmmmmmmmmm
mmmmmmmmmmmmumumumu ummmmmmmummmmmmmmmmmmmmmmmmmmm
mmummmmmmmu umummmmmumummmmmmmmmmmmmmmmmmmmmumummm
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u umumumumumumumummmmmmmmmmmmmmmmmumumumumumumumu
ummmmmmmmmmmmmmmummmmmmmmmmmmmmmummmmmmmmmmmmmmmu
umummmmmmmmmmmmmumummmmmmmmmmmmmumummmmmmmmmmmmmum
u ummmummmmmmmmmmmummmummmmmmmmmmmummmummmmmmmmmmm
ummmu umumumummmmmmmmmumumumummmmmmmmmumumumummmmm
mmmmumumumu ummmmmmmummmmmmmummmmmmmummmmmmmummmmm
mmummmmmmmummmmmmmu umummmmmumummmmmumummmmmumummm
mmumummmmmumummmmmumummmmmumu ummmummmummmummmummm
ummmummmummmummmummmummmummmummmummmummmu umumumum
umumumumumumumumumumumumumumumumumumumumumumumumum
umumu
Pascals Triangle
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Pascals Tree
Bushes and Trees Arteries and Veins Bronchial
tubes
Self-similar, One-dimensional (lines)
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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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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
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Excitable medium...

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mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmum
mmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm
m resting u excited z
refractory
space
space
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mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmummmmmm mmmmmuzu
mmmmm mmmmmmummmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm
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mmmmmmmmmmmmm mmmmmmummmmmm mmmmmuzummmmm mmmmuzmz
ummmm mmmmmuzummmmm mmmmmmummmmmm mmmmmmmmmmmmm
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mmmmmmummmmmm mmmmmuzummmmm mmmmuzmzummmm mmmuzmmm
zummm mmmmuzmzummmm mmmmmuzummmmm mmmmmmummmmmm
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mzumm mmmuzmmmzummm mmmmuzmzummmm mmmmmuzummmmm
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mmmmuzmzummmm mmmuzmmmzummm mmuzmmmmmzumm muzmmmmm
mmzum mmuzmmmmmzumm mmmuzmmmzummm mmmmuzmzummmm
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mmmuzmmmzummm mmuzmmmmmzumm muzmmmmmmmzum uzmmmmmm
mmmzu muzmmmmmmmzum mmuzmmmmmzumm mmmuzmmmzummm
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mmuzmmmmmzumm muzmmmmmmmzum uzmmmmmmmmmzu zmmmmmmm
mmmmz uzmmmmmmmmmzu muzmmmmmmmzum mmuzmmmmmzumm
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muzmmmmmmmzum uzmmmmmmmmmzu zmmmmmmmmmmmz mmmmmmmm
mmmmm zmmmmmmmmmmmz uzmmmmmmmmmzu muzmmmmmmmzum
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uzmmmmmmmmmzu zmmmmmmmmmmmz mmmmmmmmmmmmm mmmmmmmm
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zmmmmmmmmmmmz mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmm
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mmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm
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mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm m
mmmmmmmmmm mmmmmuuuuuu mmmmmzzzzzz mmmmmmmmmmm mmm
mmmmmmmm mmmmmmmmmmm mmmmmmmmmmm
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mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm m
mmmmuuuuuu mmmmuzzzzzz mmmmmmmmmmm mmmmmmmmmmm mmm
mmmmmmmm mmmmmmmmmmm mmmmmmmmmmm
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mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmuuuuuu m
mmmuzzzzzz mmmuzmmmmmm mmmmummmmmm mmmmmmmmmmm mmm
mmmmmmmm mmmmmmmmmmm mmmmmmmmmmm
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mmuzmmmmmm mmuzmmmmmmm mmmuzummmmm mmmmummmmmm mmm
mmmmmmmm mmmmmmmmmmm mmmmmmmmmmm
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muzmmmmmmm muzmmummmmm mmuzmzummmm mmmuzummmmm mmm
mummmmmm mmmmmmmmmmm mmmmmmmmmmm
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uzmmummmmm uzmmuzummmm muzmmmzummm mmuzmzummmm mmm
uzummmmm mmmmummmmmm mmmmmmmmmmm
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mmmmuzzzzzz mmmuzmmmmmm mmuzmmmmmmm muzmmummmmm u
zmmuzummmm zmmuzmzummm uzmmummzumm muzmmmzummm mmu
zmzummmm mmmuzummmmm mmmmummmmmm
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mmmuzmmmmmm mmuzmmmmmmm muzmmummmmm uzmmuzummmm z
mmuzmzummm mmuzmmmzumm zmmuzummzum uzmmummzumm muz
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J. Keener A. Panfilov
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DNA Sequence Analysis
New sequence AGAACCCTAG GACCATAGCG Dictiona
ry sequence
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The DNA sequence game...
A G A A C C C T A G G u u A
u uu u C uuu C uuu A uu u T
u A u uu u G u u C uuu G u
u
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A G A A C C C T A G G u u A
u uu u C uuu C uuu A uu u T
u A u uu u G u u C uuu G u
u
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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
...ATAGCCCTAGTCAAGTCATGGTCGAAC...
Human genome 3,000,000,000 300,000

• 600,000 nucleotides (letters)
• 500 genes (words), 2/3 recognized
• How are the words organized into meaningful
  sentences and paragraphs?

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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.