### TL;DR
In this paper Giorgio Parisi attempts to bring togethe...
Giorgio Parisi is an Italian theoretical physicist and Nobel laurea...
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E. coli was one of the first organisms to have its genome sequenced...
The Human Genome Project was a 13-year-long international scientifi...
> ***"The problem that biology must confront is how to move forward...
4 2 Physics World September 1993
Physics began with the study of simple models that became more
complicated as they became more realistic. Biology has followed the
opposite path but the two disciplines are now converging in the
study of complex systems
Statistical physics
and biology
The relationship between
biology and physics has
often been close and, at
times, uneasy. During this
century many physicists
have moved to work in
biology. Amongst the ^^^^^^^^^^^^^^^^^
most famous are Francis ^^^^^^^^^^^^^^^^B
Crick (the joint discoverer
of the DNA double helix with Jim Watson), and Max
Delbriick and Salvatore Luria (Nobel prize-winners for
their work on mutations). However, after these scientists
changed their research field, they worked in the same way
as other biologists and used their physics training to a
reduced extent.
An intermediate discipline is biophysics, but here physics
is often used as a tool to serve biology (a similar situation
exists in biochemistry). In both cases, chemistry and
physics provide explanations of what is happening at the
lowest level, that of molecules and forces, but these are
used in a biological framework.
The situation is now changing and scientists are using
physics methods and developments in theoretical physics,
such as statistical mechanics, to study certain fundamental
problems in biology. This phenomenon arises from reasons
common to both disciplines.
Current physics
One cycle in the history of physics has finished and a new
one with different problems is emerging. One of the key
problems in physics has been to discover the fundamental
laws of nature, that is the elementary constituents of matter
and the forces between them. Twenty years ago the
structure of the components of the nucleus (protons and
neutrons) and the origin of nuclear forces were unknown.
Intense debates took place about whether quarks were the
constituents of the proton and there was no clear idea of
the nature of the forces between these hypothetical quarks.
Now almost everything is known about quarks and their
interactions. The laws of
physics,
from the atomic nucleus
to the galaxy, appear to be firmly worked out and most
scientists do not expect the future to hold many surprises.
However, at scales much smaller than the atomic nucleus
and as large as the entire Universe, many things are still not
understood. In some cases we are still in almost total
ignorance. In physics possibly the greatest mystery
still
to be
unravelled is the origin of gravitational forces and their
behaviour over very short distances. This is a difficult
problem, since the crucial experiments may involve
particles with energies many billions of times greater than
currently produced in the laboratory. But, within the range
that affects normal human activities, from the physics of
elementary particles to the study of stellar evolution, we
GIORGIO PARISI
have a satisfactory formula-
tion of the laws.
However, a knowledge of
the laws that govern the
behaviour of the constitu-
ent elements of the system
^^^^^^^^^^^^^^^^ does not necessarily imply
^^^^^^^^^^^^^^^™ an understanding of the
overall behaviour. For ex-
ample, it is not easy to deduce from the forces that act
between molecules of water why ice is lighter than water.
The answer to such questions can be obtained from
statistical mechanics. This discipline, which arose in the
late 19th century from the work of Boltzmann and Gibbs,
studies systems of many particles using probability
methods rather than by determining the trajectories of
the individual particles.
Statistical mechanics has provided the fullest possible
understanding of the emergence of collective behaviour.
We cannot say whether a few atoms of water will form a
solid or a liquid and what the transition temperature is.
Such statements only become precise when many atoms are
being considered (or, more accurately, when the number of
atoms tends to infinity). Phase transitions therefore emerge
as the effect of the collective behaviour of many
components - for example, the transition in which a
normal metal suddenly becomes a superconductor - as the
temperature is lowered. Statistical mechanics has been used
to study
a
variety of phase transitions from which a range of
collective behaviours emerge.
The predictive capabilities of statistical mechanics has
increased greatly over the last 20 years, both through
refinements of the theoretical analyses and through the use
of computers. In particular, interesting results have been
obtained from the study of systems in which the laws have
been selected by chance - so-called disordered systems.
Effects of computers
The computer has produced great changes in theoretical
physics. Current computers can perform about a billion
operations a second on seven figure numbers, and tasks
that were once considered impossible have now become
routine. If one wanted to calculate theoretically the
liquefaction temperature of a gas (argon, for example)
and one already knew the form of the forces between the
atoms, then one had to make very rough approximations
and only under the above conditions could a prediction of
the liquefaction temperature be produced by simple
calculations. However, the prediction would not agree
with the experimental data (typically the error was about
10%).
The only way to improve the agreement between the
predictions and experiment was to remove the approxima-
tions gradually. This theoretical approach, known as
Physics World September 1993 43
perturbation theory, produced highly complex expressions
and tedious calculations which could be done by hand or,
if necessary, by computer.
The new approach, which spread
in
the 1970s, together
with the intensive use of computers, was to cease making
approximations
on
the motion
of
particles and instead
to
calculate their trajectories exactly.
For
example,
we can
simulate the
behaviour o f a certain
number of argon atoms (let's say
8000) inside
a box of
variable
dimensions
and
observe what
happens
-
whether
the
argon
behaves
as a
liquid
or
as
a
gas.
The computational load of s u ch
a
simulation
is
enormous.
The
trajectories
of
8000 particles
have
to be
calculated and these
have
to be
followed
for
long
enough
for
them
to
overcome
the dependence
on the
initial
configuration. Such an approach
could
not
even
be
imagined
without
a
computer.
One
of the
reasons
for the
interest aroused
by the
simula-
tions is that systems that do not
exist
in
nature,
but
which
are
simpler from a theoretical point
of view,
can
also
be
simulated.
Simulations thus become
the
prime laboratory
to
examine
new theories that could
not be
verified directly
in
the real, and
too complex, world. Obviously
the final
aim is to
apply such
ideas
to
real cases
but
this may
be
done only after
the
theory has been sufficiently strengthened and has gained in
confidence from being matched against simulations.
Complex systems
Computers have played
a
fundamental role
in the
development
of
modern theories
of
disordered systems
and complex systems. For complex systems the situation
is
delicate since this
is a
newer field with interdisciplinary
characteristics
- it
has connections with biology, informa-
tion technology, system theory
and
ecology.
It is
also
a
fashionable field, despite the fact that anyone who tries
to
define "complex" finds it hard to do. Sometimes its sense
of complicated is emphasised, meaning that it is composed
of many elements
(a
nuclear power station
is a
complex
system insofar
as it is
composed
of
many thousands
of
different pieces).
At
other times
the
sense
of
incompre-
hensible is stressed (the atmosphere is a complex system in
that one cannot make long-range forecasts). Often every
speaker at conferences
on
complex systems uses the word
complex with a different emphasis (see Livi
et
al.
and Peliti
and Vulpiani
in
Further reading).
The
real problems
emerge when, having declared that
a
given system
is
complex, one wishes to use this statement to obtain results
and not restrict oneself
to
saying that the system is complex
and therefore no prediction is possible.
The aim of
a
theory of complex systems is to find the laws
which govern the overall behaviour of such systems. These
are phenomenological laws which cannot
be
easily
deduced from
the
laws that govern
the
individual
components.
For
example,
the
behaviour
of
individual
neurons is probably well understood but it is far from clear
Arthur Lask/Sclance Photo Library
Computer graphic
of
myoglobin, the oxygen-storage protein
found
in
muscle. Biology must now move forward from
a
knowledge of the basic biochemical constituents
of
org a nis ms to
an understanding
of
such systems' overall behaviour
how
ten
billion neurons, linked
by a
hundred trillion
synapses, form a brain that thinks. As we have already seen,
the emergence
of
collective behaviours
is a
phenomenon
that has already been much studied
by
physics
in
other
contexts:
the
interaction
of
large numbers
of
atoms
and
molecules is responsible for phase transitions (of the water-
ice kind). Nevertheless,
for
complex systems,
the
overall
behaviour of the system
is
not as
simple as that of
water,
which,
at
a given temperature, may
be in
one,
or at most two, states (if one
ignores the critical point).
If we assume that
a
complex
system must display complex
behaviour, then most
of the
systems studied
in the
past
by
physicists have displayed simple
behaviour
and
cannot
be re-
garded
as
complex. However,
physicists, with
the aim of un-
derstanding
the
behaviour
of
some disordered systems,
for
example
the
spin glasses (alloys
of gold
and
iron that display
anomalous magnetic behaviour
at
low
temperature), have
re-
cently begun
to
obtain results
on
the
properties
of
relatively
simple systems which display
complex behaviour (see Mezard
et al.
in
Further reading).
The
techniques used during this
research were more general than
one might expect given their
rather esoteric origin
and are
now being applied to the study of neural networks.
Frequently
the
study
of
complex systems
has
been
advanced either
by
analysis
or by
computer simulation.
Moreover, these
two
approaches
can be
combined
synergistically. Computers enable simulations
of
complex
systems
of
moderate complexity
to be
carried
out so
that
quantitative
and
qualitative laws
can be
extracted from
these systems before tackling truly complex systems.
The
mixture
of
analytical results from simpler systems
and
numerical simulations performed on systems of intermed-
iate complexity is very effective.
A profound understanding of the behaviour
of
complex
systems would be extremely important. Attention has been
focused
on
systems composed
of
many elements
of
different types which interact on the basis of more
or
less
complicated laws and
in
which there are many feed-back
circuits that stabilise the collective behaviour. In such cases
a traditional reductionist point
of
view appears
to
lead
nowhere. An overall approach,
in
which the nature
of
the
interactions between
the
constituents
is
ignored, also
appears to be useless
in
that the nature of the constituents
is crucial
in
determining the overall behaviour.
The emerging theory
of
complex systems takes
an
intermediate point of
view.
It
starts from the behaviour of
the individual components,
as in a
reductionist approach,
but incorporates
the
idea that
the
minute details
of
the
properties
of
the components
are
irrelevant and that
the
collective behaviour does not change if the laws governing
the conduct of the components are changed slightly. The
ideal would be to classify the types of collective behaviour
and
to
see what position
a
system would occupy
in
this
classification
if the
components were changed
(see
Rammal
et
al.
and
Parisi 1992b
in
Further reading).
In
4 4 Physics World September 1993
other words, collective behaviours should
be
structurally
stable and therefore susceptible to classification, unfortu-
nately
a
much more complicated one than that made by
Rene Thorn of the Institut Hautes Etudes Scientifiques,
Paris,
in
the book Structural Stability and Morphogenesis
(1975,
Benjamin, Reading, MA).
Spin glasses: complex system exemplified
The theoretical study is not carried out on an individual
system,
but
instead
we
study
a
whole class
of
systems
simultaneously, which differ from each other in
a
random
component. This approach may be understood more easily
if I give a concrete example. Imagine a group of people in a
room who know and either like
or
dislike each other.
Suppose we divide them
at
random into two groups and
then ask each person whether they want to move from one
group
to
another (the person will answer yes
or no
according
to
their preferences).
If a
person says yes they
change groups immediately. After the first round, some
people will still not be satisfied. Some of those who moved
(or who did not move after the first round) might wish to
reconsider their own position after the moves made
by
others. A second round of changes is made and so on until
there are no further requests from individuals. In a further
stage, we could try moving not just individuals but whole
groups
of
peopl e , since
a
change
of
grou p may only
b e
attractive if made in the company of others, until a state of
general satisfaction is achieved.
The fact that after
a
finite number
of
rounds
all the
requests from individuals have been satisfied depends
crucially
on the
hypothesis that we have assumed that
relationships of like or dislike are symmetrical, i.e. that if
Caio likes Tizio then Tizio likes Caio. We could have
asymmetric situations: Caio likes Tizio but Tizio cannot
bear Caio.
If
such relationships
are
c o m m o n then
the
procedure above will never achieve
a
stable state
-
Caio
pursues Tizio, who flees, and the two never stop. It is only
when the relationships are symmetrical that the desires of
the individuals are all directed towards the same objective
-
the optimisation of general satisfaction.
Obviously, the final configuration will depend upon the
relationships between the various people and the initial
configuration, and it cannot therefore be calculated directly
without such information. Nevertheless, we can calculate
approximately the general properties
of
this process (f<