Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech
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Coping with ComplexityApril 1999
John J. TysonDepartment of Biology
Virginia Tech
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Biology is the science of living things in all their complexity
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“Hey! What’s 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 strangelittle 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 Stoppard’s 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 don’t 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
618.12
51
01
1
1
2
2
W
L
W
L
W
L
W
L
W
L
W
L
W
WL
L
W
W L-W
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The GR is “self-similar”…expand by (1.618)4 6.854
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William Harvey, 1628An Anatomical Treatise of the Motion
of the Heart and Blood
sinksource
1 50
190 1 600
gal
16 beats
beats
min
60 min
hour
gal
hour
pounds
hour
,
Harvey’s conclusion: blood must circulate!
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Kermack & McKendrick, 1927Infectious Diseases
S = fraction of population that is susceptibleI = fraction of population that is infectious
dI/dt = S I - I
deathor recovery by
infecteds of loss
infections
new of rate
fraction infectious
of change of rate
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time
1
susceptible fraction
infectious fraction
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Plague in Eyam, England, 1666
= 0.14 per day
= 0.09 per day
Susceptibles
Infectives
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SI I S
Ro
, when
1
1
Basic reproductive rate
For infection to spread,
rate of new infection > rate of removal
Ro = 1.6for plague
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Can we stop the spread of infection by immunization?
p
p
Rp
R p
pR
o
o
proportion immunized
proportion susceptible
1
11 1
11
( )( )
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Disease Ro p
Plague 1.6 40%
Smallpox 4 75%
Polio 7 85%
Measles 20 95%
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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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Pascal’s Triangle
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Bushes and TreesArteries and Veins
Bronchial tubes
Self-similar, One-dimensional (lines)
Pascal’s 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 = Serpinski’s gasket)
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585.1log(2)
log(3) dimension
Serpinski’s Gasket
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Johnson HallHuman geometry is Euclidean
Wild CarrotLife’s geometry is fractal P. Prusinkiewicz, Univ. Calgary
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By this time everyone had learnedhow careful you have to bewhen dealing with numbers.
E.B. WhiteThe Trumpet of the Swan
Fractional dimension???
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Excitable medium...
= resting = excited = refractory
space
space
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J. KeenerA. 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
GACCATAGCG
The DNA sequence game...
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A G A A C C C T A G
GACCATAGCG
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A G A A C C C T A GG -1 -1 -5 -6 -7 -8 -9 -10-11-9A-1 -2 2 -2 -3 -4 -5 -6 -8 -7C -5 -2 -2 1 1 0 -1 -5 -6 -7C -6 -6 -3 -3 4 4 3 -1 -2 -3A -4 -7 -3 0 0 3 3 2 2 -2T -8 -5 -5 -4 -1 -1 -1 6 2 1A -6 -9 -2 -2 -2 -2 -2 2 9 5G -10 -3 -6 -3 -3 -3 -3 1 5 12C -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 GG -1 -1 -5 -6 -7 -8 -9 -10-11-9A-1 -2 2 -2 -3 -4 -5 -6 -8 -7C -5 -2 -2 1 1 0 -1 -5 -6 -7C -6 -6 -3 -3 4 4 3 -1 -2 -3A -4 -7 -3 0 0 3 3 2 2 -2T -8 -5 -5 -4 -1 -1 -1 6 2 1A -6 -9 -2 -2 -2 -2 -2 2 9 5G -10 -3 -6 -3 -3 -3 -3 1 5 12C -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 genome3,000,000,000
300,000
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Lab for Bioinformatics, Keio University, JapanThe Institute for Genomic Research, Rockville MD
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dR
dtdR
dt
dR
dt
1
2
127
...
...
...
...
glucose
protein
time
lipid
Do we really need an equation for every gene???
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Solar System9 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 equationsin 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 thinkingabout complex patterns in a precise
yet creative way.