Coping with ComplexityApril 1999

John J. TysonDepartment 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 strangelittle 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 isa 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

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

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

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!

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

time

1

susceptible fraction

infectious fraction

Plague in Eyam, England, 1666

= 0.14 per day

= 0.09 per day

Susceptibles

Infectives

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

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

( )( )

Disease Ro p

Plague 1.6 40%

Smallpox 4 75%

Polio 7 85%

Measles 20 95%

The Overcrowding Game...

space

= available = occupied

time

space

time

space

overcrowded

space

time

Pascal’s Triangle

Bushes and TreesArteries and Veins

Bronchial tubes

Self-similar, One-dimensional (lines)

Pascal’s Tree

Olivia(mollusc)

Hans Meinhardt, The Algorithmic Beauty of Sea Shells

Cymbiola (pattern = Serpinski’s gasket)

585.1log(2)

log(3) dimension

Serpinski’s Gasket

Johnson HallHuman geometry is Euclidean

Wild CarrotLife’s geometry is fractal P. Prusinkiewicz, Univ. Calgary

By this time everyone had learnedhow careful you have to bewhen dealing with numbers.

E.B. WhiteThe Trumpet of the Swan

Fractional dimension???

Excitable medium...

= resting = excited = refractory

space

space

J. KeenerA. Panfilov

DNA Sequence Analysis

New sequence: …AGAACCCTAG…

…GACCATAGCG…Dictionary sequence:

A G A A C C C T A G

GACCATAGCG

The DNA sequence game...

A G A A C C C T A G

GACCATAGCG

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

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

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

Lab for Bioinformatics, Keio University, JapanThe Institute for Genomic Research, Rockville MD

dR

dtdR

dt

dR

dt

1

2

127

...

...

...

...

glucose

protein

time

lipid

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

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!

Mathematics is a tool for thinkingabout complex patterns in a precise

yet creative way.