1 Life as a complex system Frederick H. Willeboordse [email protected]

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Life as a complex system

Frederick H. Willeboordse

http://chaos.nus.edu.sg

[email protected]

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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.

Underlying 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.

Abstract

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Today’s 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

Today’s talk

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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.

Introduction

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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

The biological aspect

what is commonwhat is different

Can Life be considered a complex system?

Is life a complex system?

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Generally speaking a complex system is a system of interacting elements whose collective behavior cannot be described as the simple sum the elements’ behavior

Complex is not the same as complicated!

Hence many systems studied in physics are in that sense not complex. E.g. in Quantum Physics we can simply ADDthe 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.


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Complex:

Some double pendula linked byrubber bands

Function: easy to design and understandBehavior: difficult to understand

Complicated:

Microprocessor

Function: difficult to design and understandBehavior: easy to understand


Complex is not the same as complicated!


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An essential ingredient of complex systems is their built-in non-linearity.

A difference keepson increasing

A difference can increasebut also decrease

It’s 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!


linear non-linear

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Complex systems often exhibit the following characteristics:

RobustnessSelf-organizationAdaptability

Furthermore:

Clear mathematical definitionBasically deterministic


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Clearly, life is “built” up by combining many elements at many levels

Phospholipids Cell (intra)Cell (inter)Etc.

→ Cell walls→ DNA (made of base-pairs)→ Multi-cellular organisms


Next, let us investigate whether some of the characteristics of a physical complex system can be found in living systems.

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Glycerol

Fatty acidHydrocarbon chain


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HFatty acid replaced by phosphate group and nitrogen containing molecule


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The interesting thing is that phospholipids can from bi-layers

The properties of the bi-layer are rather different from those of its elements

Schematically, phospholipids can be drawn as

where the hydrocarbon chains are represented as wiggly tails.

The tails are hydrophobicThe heads are hydrophilic

~5nm


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They can also form micelles or vesicles

The bi-layer is semi-permeable,H2O, e.g., can diffuse through.

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 …

Giant vesicles can be larger than 1 m!


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Hence I believe it is fair to describe life as a complex system!

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

We have also seen that:

Phospholipids

can form membranes

A Cell behaves very differently from its components

DNA by itself is static

..and it is clear that cells posses the following qualities:

• Robustness• Self-organization• Adaptability

But the cell is alive


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Life is a complex system.

Common Points Differing Points

ElementsCollective Behavior

RobustnessSelf-organizationAdaptable

Underlying equations not available in the Life SciencesBio systems are not deterministic (at least not in the same way).


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Examples of complex systems in Physics and Bio

Coupled Map Lattice

DNA as a ‘hard disk’

Examples of complex systems in Physics and Biology

A coupled map lattice is a collection of individual (chaotic) elements connected by some sort of “rubber” bands.

Once the prevailing view was akin to “there’s 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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The logistic map is the element

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.

2n1n αx1x

223 αx1x

212 αx1x

201 αx1x

given

The logistic map is defined as:

Step 1

Step 3

Step 2


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Plot 200 successive values of xfor every value of

The so-called bifurcation diagram

As the nonlinearity increases we sometimes encounter chaos

21nn αx1x

nx

α

n


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The bifurcation diagram exhibits unexpected properties.

Let's enlarge this area

The marvelous bifurcation diagram


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An almost identical diagram!

Let's try this again...



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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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Amazing! It’s 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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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.

Our element is the logistic map


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Coupled Map Lattices

The coupled map discussed here is simply an array of logistic maps. The formula appears more complicated than it is.

Or in other words:

f is the logistic map

f( ) f( ) f( )Time n

Time n+1

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)()1( 111

i

nin

in

in xfxfxfx

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Frozen RandomPattern

Parts of the lattice are chaotic and parts of the lattice are periodic.The dynamics is dominated by the band structure of the logisticmap.



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Even though the nonlinearity has increased and the logistic map ischaotic for a=1.7, the lattice is entirely periodic.

My Research

Pattern Selection



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The coupled map lattice is symmetric, yet here we see atravelling wave. This dynamical behaviour is highly non-trivial!

Travelling Waves



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Of course we have spatio-temporal chaos too. No order to be foundhere ... or ??? . No, despite the way it looks, this is far from random!

Spatio-temporalChaos



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From Oxford English Dictionary:

1970 Sci. Amer. Oct. 19/1 The human genome..consists of perhaps as many as 10 million genes.

In this context it is particularly noteworthy that:

In fact:

The human genome has only about 30 thousand genes! This is a remarkably small number.


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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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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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• 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, doesn’t 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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A concrete example: The lac operon

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.

The lac operon encodes the capacity for lactose utilization in E. coli.

1947lac The operon is a small section

of the genome

What is interesting, though, is that E. coli can distinguish glucose and lactose. If available, they’ll first consume the glucose. Hence there must be some kind of mechanism to regulated this.


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1961

And of course it wouldn’t end here:

YZO AI

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

It’s not that simple!

YZO AI

O2O3 CRP P O

Co-operative binding site for the repressor together with O3The repressor binding site

A promoter siteBinding site for the transcription factor that mediates glucose control

Co-operative binding site for the repressor together with O2

1990


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Overall, the cell performs the following computation:

IF lactose presentAND glucose not presentAND 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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Digressing a bit, thinking of Life as a complex system we bring together:

Study of Life as a complex system

It is of course impossible to give even a remotely complete list. But topics will include:

Complex systems theory, developmental biology, biophysics and bio-molecular science

Construction of Artificial Life Systems Analysis of Dynamic Life Processes Robust Developmental Processes

Study of Life as a complex system

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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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)(ixn

Model by Kaneko 1997

We can represent the internal state by the variable.

Let us assume we have a system of very simple interacting cells that receive a fixed amount of “food” each unit of time.


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)(2sin2

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ixf nn

K is a “parameter”


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The formulas on the previous sheet are not enough to obtain ‘cell-type’ dynamics. In order to do so, we’ll need to have criteria for growth and death.

A) A cell splits when

B) A cell dies when 0)( ixn

10)( ixn


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For increasing K, there are three basic phases

1) Ordered Phase2) Partially Ordered Phase3) Desynchronized Phase


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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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2) Partially Ordered Phase

The number of clusters fluctuates between 1 and N

K = 3.3


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3) Desynchronized Phase

Typically the cells are desyncronised.

K = 4.0


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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/zoologie/dicty/dicty.html


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Amoebae

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.

Professor Cornelis WeijerProfessor of Developmental PhysiologyUniversity of Dundee

From his website


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Lifecycle ofDictyostelium

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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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Amoebae

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

Cluminating Slug


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Amoebae

Time-lapse video showing slug formation, migration and culmination. From R. Chisholm, Northwestern University

Lifecycle


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Conclusion

Life IS a complex system!

Conclusion

Documents

1 Life as a complex system Frederick H. Willeboordse [email protected]