Life as a complex system

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Life as a complex system

• Frederick H. Willeboordse
• http//chaos.nus.edu.sg
• frederik_at_chaos.nus.edu.sg

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Abstract
Abstract
Life is certainly complicated and indeed often
complex. However, is it a complex system in the
Physicists sense? In this talk it shall be
arguedthat the answer to this question is
affirmative by comparing certaincharacteristics
of life with those of physical systems. Underlyin
g the ideas of life as a complex system is the
notion that complex systems have intrinsic
properties that can lead to unexpected but robust
and adaptable dynamics. This is rather different
from the currently prevailing view that evolution
is a random walk over adaptation space. Thus,
whether this notion eventually will prevail or
not, the consideration of life as a complex
system clearly illustrates how the interaction
between seemingly radically different fields can
enrich the experiences of both. The complex
systems properties of life and their conceptual
parallels in Physics will be discussed through
selected examples and the live demonstration of
simulation programs used in my research.
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Todays talk
Todays Talk

• Introduction
• Is life a complex system? Yes!
• Examples of complex systems from
• Physics and Biology
• Study of life as a complex system
• Examples of studies of life as a complex system
  from Physics and Biology
• Conclusion

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Introduction
Introduction
Aim Argue that Life is a complex system
Give some illustrations using aniterative
approach
What does Physics have to do with this?
Physicists like to look for universalities (e.g.
laws of nature). Most theorists of biological
evolution, however, have thus far assumed a
random walk to new adaptations. If life is a
complex system, the physicists approach can
contribute significantly.
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Is life a complex system?
Can Life be considered a complex system?
Obviously, Life is complex but does that mean
that it is a complex system?
In order to answer this question, at least two
aspects need to be considered
The physical/mathematical aspect
what is common what is different
The biological aspect
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Is life a complex system?
The physical/mathematical aspect
Generally speaking a complex system is a system
of interacting elements whose collective behavior
cannot be described as the simple sum the
elements behavior
Hence many systems studied in physics are in that
sense not complex. E.g. in Quantum Physics we can
simply ADD the wave functions.
Five boys and five girls together on a deserted
island though will likely behave quite
differently from one boy or girl on the same
deserted island.
Complex is not the same as complicated!
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Is life a complex system?
The physical/mathematical aspect
Complex is not the same as complicated!
Complex Some double pendula linked by rubber
bands Function easy to design and
understand Behavior difficult to understand
Complicated Microprocessor Function
difficult to design and understand Behavior easy
to understand
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Is life a complex system?
The physical/mathematical aspect
An essential ingredient of complex systems is
their built-in non-linearity.
non-linear
linear
Its a bit similar to a winding mountain road.
Take the wrong turn or make the wrong step and
you could end up somewhere completely else!
A difference keeps on increasing
A difference can increase but also decrease
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Is life a complex system?
The physical/mathematical aspect
Complex systems often exhibit the following
characteristics
Robustness Self-organization Adaptability
Furthermore
Clear mathematical definition Basically
deterministic
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Is life a complex system?
The biological aspect
Next, let us investigate whether some of the
characteristics of a physical complex system can
be found in living systems.
Clearly, life is built up by combining many
elements at many levels
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Is life a complex system?
Tristearin
Fatty acid
Hydrocarbon chain
Glycerol
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Is life a complex system?
Chephalin ( Phosphatidyl ethanolamine)
Fatty acid
Hydrocarbon chain
H
Glycerol
C
H
H
C

H
Fatty acid replaced by phosphate group and
nitrogen containing molecule
H
C
O
H
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Is life a complex system?
The biological aspect
The interesting thing is that phospholipids can
from bi-layers
Schematically, phospholipids can be drawn as
5nm
where the hydrocarbon chains are represented as
wiggly tails.
The properties of the bi-layer are rather
different from those of its elements
The tails are hydrophobic The heads are
hydrophilic
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Is life a complex system?
The biological aspect
or vesicles
They can also form micelles
The bi-layer is semi-permeable, H2O, e.g., can
diffuse through.
Giant vesicles can be larger than 1 mm!
Hence at the molecular level, we already see that
the sum is different from the elements so lets
jump the gun and draw some conclusions
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Is life a complex system?
The biological aspect
A Cell behaves very differently from its
components
We have also seen that
Phospholipids
DNA by itself is static
can form membranes
But the cell is alive

• ..and it is clear that cells posses the following
  qualities
• Robustness
• Self-organization
• Adaptability

Let us look back at our definition A complex
system is a system of interacting elements whose
collective behavior cannot be described as the
simple sum the elements behavior
Hence I believe it is fair to describe life as a
complex system!
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Is life a complex system?
Life is a complex system.
Differing Points
Common Points
Elements Collective Behavior Robustness Self-orga
nization Adaptable
Underlying equations not available in the Life
Sciences Bio systems are not deterministic (at
least not in the same way).
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Examples of complex systems in Physics and Biology
Examples of complex systems in Physics and Bio
Coupled Map Lattice
A coupled map lattice is a collection of
individual (chaotic) elements connected by some
sort of rubber bands.
DNA as a hard disk
Once the prevailing view was akin to theres a
gene for everything a cell does. Now that we
know that there are less than 30K genes a
different picture is necessary.
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Examples of complex systems in Physics and Biology
The logistic map is the element
The logistic map is defined as
This means that one starts with a certain value,
calculates the result and then uses this result
as the starting value of a next calculation.
Step 3
Step 1
Step 2
given
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Examples of complex systems in Physics and Biology
The so-called bifurcation diagram
Plot 200 successive values of x for every value
of
n
As the nonlinearity increases we sometimes
encounter chaos
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Examples of complex systems in Physics and Biology
The marvelous bifurcation diagram
The bifurcation diagram exhibits unexpected
properties.
Let's enlarge this area
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Examples of complex systems in Physics and Biology
The marvelous bifurcation diagram
An almost identical diagram!
Let's try this again...
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Examples of complex systems in Physics and Biology
The marvelous bifurcation diagram
This time, let us enlarge a much smaller area.
Now let's enlarge this area
Hard to see, isn't it?
This is the region we enlarged before
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Examples of complex systems in Physics and Biology
The marvelous bifurcation diagram
Amazing! Its basically the same again.
Indeed, the bifurcation diagram contains an
infinite number of ever repeating structures.
Hence, even though the underlying equation is
very simple we have a source of limitless
complexity.
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Examples of complex systems in Physics and Biology
Our element is the logistic map
We can think of the logistic map as a simple
chaotic oscillator. Then we can construct a
system of interacting elements by simply tying
them together with rubber bands. This yields a
so-called coupled map lattice. A simple prototype
for a complex system.
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Examples of complex systems in Physics and Biology
Coupled Map Lattices
The coupled map discussed here is simply an array
of logistic maps. The formula appears more
complicated than it is.
f is the logistic map
f( )
f( )
f( )
Time n
Time n1
Or in other words
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Frozen RandomPattern
Examples of complex systems in Physics and Biology
Coupled Map Lattices
Parts of the lattice are chaotic and parts of the
lattice are periodic. The dynamics is dominated
by the band structure of the logistic map.
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My Research
Examples of complex systems in Physics and Biology
Coupled Map Lattices
Pattern Selection
Even though the nonlinearity has increased and
the logistic map is chaotic for a1.7, the
lattice is entirely periodic.
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Examples of complex systems in Physics and Biology
Coupled Map Lattices
Travelling Waves
The coupled map lattice is symmetric, yet here we
see a travelling wave. This dynamical behaviour
is highly non- trivial!
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Examples of complex systems in Physics and Biology
Coupled Map Lattices
Spatio-temporalChaos
Of course we have spatio-temporal chaos too. No
order to be found here ... or ??? . No, despite
the way it looks, this is far from random!
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Examples of complex systems in Physics and Biology
DNA as a hard disk
In this context it is particularly noteworthy
that
From Oxford English Dictionary 1970 Sci. Amer.
Oct. 19/1 The human genome..consists of perhaps
as many as 10 million genes.
In fact
The human genome has only about 30 thousand
genes! This is a remarkably small number.
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Examples of complex systems in Physics and Biology
DNA as a hard disk
Complementary to considering DNA as a hard disk
is the idea that evolution is a process of
natural genetic engineering. It should be
stressed that this is a complex systems view and
does not require intelligent as in divine
design. The genetic engineering properties are
simply consequences of (by natural selection)
surviving systems designs. The most simple ones
reflecting nothing but the chemical properties of
its constituents (e.g. bi-layers made of
phospholipids).
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Examples of complex systems in Physics and Biology
DNA as a hard disk
A genome consists of many parts. The most
commonly studied parts (due to their perceived
relevance for medical applications) are the
so-called coding regions that determine the
proteins that can be synthesized. The other
regions are often referred to as junk!Is that a
reasonable assessment though? In fact there are
many classes genomicinformation
?
?
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Examples of complex systems in Physics and Biology
DNA as a hard disk

• start and stop sites for transcription
• control signals for e.g. level of expression
• Signals for chromatin remodeling
• Signals for DNA replication
• Signals for DNA repair

It is very important to realize that the genome
only functions in response to its environment.
DNA, by itself, doesnt do anything, it is
inert. The information stored in the DNA is only
activated due to its interaction with the rest of
the cell (this should be obvious considering e.g.
cell differentiation).
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Examples of complex systems in Physics and Biology
DNA as a hard disk
A concrete example The lac operon
The lac operon encodes the capacity for lactose
utilization in E. coli.
The operon is a small section of the genome
lac
1947
What is interesting, though, is that E. coli can
distinguish glucose and lactose. If available,
theyll first consume the glucose. Hence there
must be some kind of mechanism to regulated this.
OED operon A unit of co-ordinated gene activity
which is believed to account for inducible and
repressible enzymes in bacteria and hence for the
regulation of protein synthesis, and is usu.
conceived as a linear sequence of genetic
material comprising an operator, a promoter, and
one or more structural genes.
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Examples of complex systems in Physics and Biology
DNA as a hard disk
Its not that simple!
1961
Structural genes for encoding the proteins of
lactose transport and metabolism
An operator here, the site where the repressor
binds to stop lacZYA (note this is not a gene!)
Regulator gene that encodes a repressor protein
And of course it wouldnt end here
1990
Co-operative binding site for the repressor
together with O3
The repressor binding site
A promoter site
Binding site for the transcription factor that
mediates glucose control
Co-operative binding site for the repressor
together with O2
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Examples of complex systems in Physics and Biology
DNA as a hard disk
Overall, the cell performs the following
computation
IF lactose present AND glucose not
present AND cell can actually synthesize active
LacZ and LacY THEN transcribe lacZYA from lacP
It is important to note that the computation
involves many molecules and compartments of the
cell, not just DNA. E.g. the availability of
lactose needs to be signaled to it.
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Study of Life as a complex system
Study of Life as a complex system
Digressing a bit, thinking of Life as a complex
system we bring together
Complex systems theory, developmental biology,
biophysics and bio-molecular science
It is of course impossible to give even a
remotely complete list. But topics will include
Construction of Artificial Life Systems
Analysis of Dynamic Life Processes
Robust Developmental Processes
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Examples of studies of life as a complex system
from Physics and Biology
Examples of studies of life as a complex system
from Physics and Biology
Coupled Map Lattice with growth and death
Amoebae
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Examples of studies of life as a complex system
from Physics and Biology
Coupled Map Lattice with growth and death
Model by Kaneko 1997
Let us assume we have a system of very simple
interacting cells that receive a fixed amount of
food each unit of time.
We can represent the internal state by the
variable.
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Examples of studies of life as a complex system
from Physics and Biology
Coupled Map Lattice with growth and death
Amount of foods such that the total food for all
cells is s.
K is a parameter
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Examples of studies of life as a complex system
from Physics and Biology
Coupled Map Lattice with growth and death
The formulas on the previous sheet are not enough
to obtain cell-type dynamics. In order to do
so, well need to have criteria for growth and
death.

• A cell splits when
• A cell dies when

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Examples of studies of life as a complex system
from Physics and Biology
Coupled Map Lattice with growth and death
For increasing K, there are three basic phases

• Ordered Phase
• Partially Ordered Phase
• Desynchronized Phase

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Examples of studies of life as a complex system
from Physics and Biology
1) Ordered Phase
Cells tend to be synchronized. When a cell
splits, there are two clusters for a short time.
K 2.0
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Examples of studies of life as a complex system
from Physics and Biology
2) Partially Ordered Phase
The number of clusters fluctuates between 1 and N
K 3.3
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Examples of studies of life as a complex system
from Physics and Biology
3) Desynchronized Phase
Typically the cells are desyncronised.
K 4.0
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Examples of studies of life as a complex system
from Physics and Biology
Amoebae
Oxford English Dictionary A microscopic
animalcule (class Protozoa) consisting of a
single cell of gelatinous sarcode, the outer
layer of which is highly extensile and
contractile, and the inner fluid and mobile, so
that the shape of the animal is perpetually
changing.
I would now like to show some of the dynamics of
the Dictyostelium amoebae. A good reference site
is http//www.zi.biologie.uni-muenchen.de/zoologi
e/dicty/dicty.html
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Examples of studies of life as a complex system
from Physics and Biology
Amoebae
Professor Cornelis WeijerProfessor of
Developmental PhysiologyUniversity of Dundee
From his website
Darkfield Waves
The coordinated chemotactic movement of cells can
be seen as propagating darkfield waves in
aggregates, where the waves propagate mostly as
spirals, in streaming mounds where the waves
appear as multiarmed spirals in the mound
transforming into single waves fronts in the
aggregation streams. In slugs waves can be seen
to propagate from the tip towards the end of the
prespore zone.
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Examples of studies of life as a complex system
from Physics and Biology
Lifecycle ofDictyostelium
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Examples of studies of life as a complex system
from Physics and Biology
Amoebae
Side view of an older Dictyostelium discoideum
slug stained with neutral red. The migration of
older slugs (48 h and more) is characterised by a
strong periodic up- and downward movement of the
whole prestalk region. This is accompanied by the
repeated aggregation of anterior-like cells at
the prestalk-prespore boundary, where they stop,
while at the same time the unstained prespore
cells continue to move over the pile. The tip of
the slug is lifted from the substrate into the
air until it becomes unstable and falls back onto
the agar surface. Time between successive images
20 seconds. Scale bar 100 µm, (see Dormann D.,
Siegert F. C.J.Weijer (1996), Development, 122,
761-769
Migrating Slug
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Examples of studies of life as a complex system
from Physics and Biology
Amoebae
Cluminating Slug
Side view of a culminating Dictyostelium
discoideum slug stained with neutral red. During
early culmination all cells in the prestalk zone
rotate. Later during stalk tube formation the
prestalk cells rotate most vigorous at the
prestalk-prespore boundary. Time between
successive images 5 seconds. Scale bar 50 µm,
(see Dormann D., Siegert F. C.J.Weijer (1996),
Development, 122, 761-769
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Examples of studies of life as a complex system
from Physics and Biology
Amoebae
Time-lapse video showing slug formation,
migration and culmination.  From R. Chisholm,
Northwestern University
Lifecycle
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Conclusion
Conclusion
Life IS a complex system!