Download Spin Glasses, Biological Evolution Dynamics, Cancer, and New

Spin Glasses, Biological
Evolution Dynamics, Cancer, and
New Materials
Bob Austin
Dept. of Physics
Princeton University
Two parts to this crazy talk:
•My materials science theory can
shed new light on biology, maybe
•The challenge to materials scienc
to create truly complex 3-D
designed structures.
I. A Failed War
The National Cancer Institute (NC
just finished a series of 3
Workshops
on bringing the hard physical
sciences into oncology (study of
cancer), and not in the usual way
of building new ways to detect
cancer, but to understand cancer
Why? Aren’t we making fabulous
ression was typical: surgery, chemo, remissio
wed by relapse after 2 years, which was fatal.
e old story.
t happened to the War on cancer? Where is the
ory?
II. Darwin and Evolution: problem
and examine the mathematic
and biological foundations o
evolution and natural selectio
you can soon feel yourself
becoming dangerously close
the ranks of excommunicate
scientists who wonder: how
well do we really understand
the dynamics of evolution
under stress?
This I think is one of our gre
n random, point mutations explain the
dible rates of evolution observed in Natu
diverse beaks of Darwin’s finches were o
s keys to natural selection. But, it was a s
rvation.
But Peter and Rosemary Grant
Princeton) found that there was much
more to Darwin’s finches then even he
hought.
evoid of human interference into natural selection,
s documented some 13 species of "Darwin's Finch
ing:
that is flightless
that cohabits with
e iguanas
(the vampire finch)
ves on blood
that is entirely
arian;
es and traced their elaborate lineage,
ling them to document the changes that
idual species make, primarily to their bea
action to the environment.
ng prolonged drought, for instance, beak
become longer and sharper, to reach the
st of seeds.
is the problem: we are talking about
sands of birds, not millions. We are talki
t beaks that change over periods of year
mics of Darwin’s finches and the small population size pose a severe problem for this kind of a model.
mma’’.
simply put, it says that the number g of
rations needed to “fix” a mutation is abo
ulation of this magic number 300 is rathe
y, but it is roughly ln(1/su).
rse problem is then optimizing (fixing) 10
s: now we are talking about 300,000
rations. That’s too long.
t Darwin (actually the Grants) saw
pid evolution on his little islands.
hy?
hink 2 things are at work:
ess drives evolution (and stress
ves cancer) in a non-linear way.
mall heterogenous populations drive
olution (and drives the evolution of
II. Proteins, Energy landscapes and
spin glasses.
things happen:
system freezes into a distribution of sta
e is no one protein conformation, but a f
gy landscape of them.
n the frozen distribution of states the
ponse function” of the system is a powe
an exponential.
he groundwork for rough landscape mod
logy:
ostats rather than water baths as do
logists.
proteins have a distribution of conforma
es, it turns out that the probability distrib
ction (pdf) of the activation energies, g(H
notation, must be an exponential in Hba
hematically yield a power law in the tails
t is the origin of these probability distrib
ions?
pin
glass
is
a
system
of
coupled
spins
frustrated interactions.
-
+
+
?
eresting properties (hard to prove
alytically even for simplest systems):
Spin system has a freezing point, like
otein.
ollective spin “metapopulations”: energy
ndscape.
een spin metapopulations.
gle inequality, can be used for minimizing path
HKUST building labyrinths )
for spin space populations, “stronger”
ality:
d:
ese
y:
ct:
etric space:
nsider a sphere of radius R which
ntains all spin populations whose
utual distance is less then R.
en: Any other sphere must be either
ntained within R or be disjoint from
you can’t share populations
tween different spheres.
us, you have speciation in spinasses, and in biology.
V. Fitness landscapes and spin
glasses.
dscape by a metapopulation is
ually a subject of physics interest.
general field is called spin-glass
sics, and it is about the flow of
ormation”.
third Workshop that the NCI
nsored was called “Coding, Decodin
nsfer and Translation of information
cer.
w variables:
local number of individuals with a “quas
ecies” genome homology i.
= “interbreeding” between quasi-species
d j, which you can also view of genomic
rrangements on a metascale (not SNPs).
roenvironment is the local fitness aroun
quasi-species. In the valley: stress.
rugged field of this character, selection w
y carry the species to the nearest peak, bu
may be innumerable other peaks which a
er but which are separated by "valleys."
problem of evolution as I see it is that of a
hanism by which the species may continu
ts way from lower to higher peaks in such
In order that this may occur, there must b
e trial and error mechanism on a grand sc
h the species may explore the region
can design fitness landscapes micr
ia “learned” to grow more slowly and exploit stress
abitats. In this sense we see the evolution of resis
population sizes in microhabitats in
evolution dynamics.
elective advantage s to “fix” (dominate) i
ulation of N individuals?
is, the larger the population, the longer i
s to fix a mutation. Large populations bu
ution rates, and is connected to the powe
ys.
, evolution can proceed more rapidly if y
k up a population N into sub-populations
mbers, and let them interbreed at rate m
is is a very strange and important result
says that the combinatorics (entropy!) of
rogenous genome gives rise to slower fi
of a trait with increasing populations size
different then, say, radioactive decay, w
e mean lifetime for 1/2 the atoms to decay
independent of the number of atoms.
ce we can define distances and
rlaps amongst genomes using
uencing and mapping, evolution
amics has become quantitative. It
n’t with Darwin.
lution on a fitness landscape thus
omes a biased random walk problem
re the distance between genomes c
measured, with mutations acting as
V. Cancer and spin glasses: the
delicate balance between rapid
evolution, freezing, and melting
ibution of the little metapopulations
s that move evolution forward rapidl
t Wright called:
e trial and error mechanism on a
nd scale by which the species ma
ore the region surrounding the
ll portion of the field which it
upies.”
he selection s is too small, you
umulate
o may bad mutations and the popul
es a “mutational meltdown”.
nk of the Royal Families of Europe a
nce Charles.
us, you need a finite selection press
ntain a stable small population.
he metapopulation size n is too sma
y local maxima in local fitness you
e a “complexity catastrophe”
uffman) and the system is stuck in a
glass frozen state even at finite
perature:
n distance <d> to local maximum go
og(n), so always near local maximum
a catastrophic genomic delocalizatio
ike that expression because it soun
ike quantum mechanics).
nomic delocalization means that the
exist no stable solutions to populati
equations, no quasi-species, and the
systems wanders through sequence
space.
s occurs at an error threshold u* giv
s is an important result;
here is an analogy between phase
nsitions in physics and genomic
abilities in genomics. u* = melting
perature.
here is “danger” in too small a
per.
re is a dual purpose to stress (=
ction):
ess drives natural selection and
ution. No stress, no evolution.
ess causes mutations, and changes
eased stress = increased mutations
ally, stress drives individuals within
anisms to cheat, to defect, to gain
al fitness at the expense of others.
s is the province of Game Theory,
it really has no analogy that I am
re of to physical systems, but may
crucially
ortant in biology.
s is why biology may be deeper in a
Optimal
Solution
Nash Equilibrium
The role of deliberate mutational diversit
wall Wright’s “trial and error mechanism
grand scale”) is to accelerate evolution
possible that the germline
roductive/stem cell) genomic diversity o
anisms is generated deliberately in rapid
lving organisms....and that cancer is a
essary byproduct of rapid evolution whic
not be removed because of the fundame
ability of the individuals to cheat in a
price of high evolution rates of course
er: the heterogenous genomes and
esale genomic rearrangements neces
apid evolution means that occasionally
em will lose control, and that’s OK at th
ies level, just bad for you.
Thus, cancer IS necessary for high
ates of evolution and is not a
disease.
Think of it as Windows Vista.
VI. New Materials to Build New
Ecologies in Biology
The “death galaxy”
my design for a
physics-based-ecolo
which will show all t
features of what we
doing wrong in canc
therapy.
Chemical
coupling
is through t
(10 micron)
polymer
barrier.
g):
I rapidly evolve bacterial resistance
ntibiotic in my “death galaxy” using
s of biology and materials science
ics?
ut this is just 2-D! We need to build
omplex 3-D ecologies to really emula
tual biological ecologies.
elf-assembly of micropatterned 3-D
ructures is not something I do, but
hers are doing.
avis Garcias, Johns Hopkins
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Materials science will be driven by
biological questions and we will
learn how to design 3-D
construction of extremely complex
shapes with defined purposes.
At some point, we may begin to
rival Nature in her fantastic design
of “one-off” complex structures.
Thanks!!!