Transcript Life as a complex system Frederick H. Willeboordse
Life as a complex system
Frederick H. Willeboordse http://chaos.nus.edu.sg
[email protected]
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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 argued that the answer to this question is affirmative by comparing certain characteristics 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.
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Today’s talk 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 3
Introduction Introduction: Aim: Argue that Life is a complex system Give some illustrations using an iterative 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 The biological aspect what is common what is different 5
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!
Complicated: Microprocessor Complex: Some double pendula linked by rubber bands Function: difficult to design and understand Behavior: easy to understand Function: easy to design and understand Behavior: difficult to understand 7
Is life a complex system?
The physical/mathematical aspect An essential ingredient of complex systems is their built-in non-linearity.
linear non-linear A difference keeps on increasing A difference can increase but 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!
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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 9
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 Phospholipids Cell (intra) Cell (inter) → Cell walls → DNA (made of base-pairs) → Multi-cellular organisms Etc.
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Is life a complex system?
Tristearin Hydrocarbon chain Fatty acid H H H H H H H H H H H H H H H H H O H H C C C C C C C C C C C C C C C C C C O C H Glycerol H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H O H C C C C C C C C C C C C C C C C C C O C H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H O H C C C C C C C C C C C C C C C C C C O C H H H H H H H H H H H H H H H H H H H 11
Is life a complex system?
Chephalin (= Phosphatidyl ethanolamine) Hydrocarbon chain Fatty acid H H H H H H H H H H H H H H H H H O H H C C C C C C C C C C C C C C C C C C O C H Glycerol H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H O H C C C C C C C C C C C C C C C C C C O C H H H H H H H H H H H H H H H H H H Fatty acid replaced by phosphate group and nitrogen containing molecule H H + H N C H C H H H O O P O O C H H 12
Is life a complex system?
The biological aspect Schematically, phospholipids can be drawn as The interesting thing is that phospholipids can from bi-layers where the hydrocarbon chains are represented as wiggly tails.
The tails are hydrophobic The heads are hydrophilic ~5nm The properties of the bi-layer are rather different from those of its elements 13
Is life a complex system?
The biological aspect They can also form micelles or vesicles 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 … The bi-layer is semi-permeable, H2O, e.g., can diffuse through.
Giant vesicles can be larger than 1 m m!
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Is life a complex system?
The biological aspect A Cell behaves very differently from its components DNA by itself is static But the cell is alive 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!
We have also seen that: Phospholipids can form membranes ..and it is clear that cells posses the following qualities: • Robustness • Self-organization • Adaptability 15
Is life a complex system?
Life is a complex system.
Common Points Elements Collective Behavior Robustness Self-organization Adaptable Differing Points 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 “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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Examples of complex systems in Physics and Biology The logistic map is the element The logistic map is defined as: x n 1 1 αx 2 n 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.
x 1 Step 1 1 αx 2 0 x 3 Step 3 1 αx 2 2 given x 2 Step 2 1 αx 1 2 18
Examples of complex systems in Physics and Biology The so-called bifurcation diagram x n Plot 200 successive values of x
n
for every value of α x n 1 αx 2 n 1 As the nonlinearity increases we sometimes encounter chaos 19
Examples of complex systems in Physics and Biology The marvelous bifurcation diagram The bifurcation diagram exhibits unexpected properties.
Let's enlarge this area 20
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.
This is the region we enlarged before Now let's enlarge this area Hard to see, isn't it?
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Examples of complex systems in Physics and Biology The marvelous bifurcation diagram 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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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 Time n
f
( ) 2
f
( ) 1
f
( ) 2 Time n+1 Or in other words:
x n i
1 ( 1 )
f
(
x n i
) 2
f
(
x n i
1 )
f
(
x n i
1 ) 25
Examples of complex systems in Physics and Biology Coupled Map Lattices
Frozen Random Pattern
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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Examples of complex systems in Physics and Biology Coupled Map Lattices My Research
Pattern Selection
Even though the nonlinearity has increased and the logistic map is chaotic for a=1.7, 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-temporal Chaos
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 genomic information: 32
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, 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). 33
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.
lac
1947 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.
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. 34
Examples of complex systems in Physics and Biology DNA as a ‘hard disk’ I O Z It’s not that simple!
Y A 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 wouldn’t end here: I O Z Y A 1990 O3 CRP P O O2 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 35
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 37
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 38
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.
x n
(
i
) 39
Examples of studies of life as a complex system from Physics and Biology Coupled Map Lattice with growth and death
x n
1 (
i
)
x n
(
i
)
f
(
x n
(
i
))
S n
Amount of foods such that the total food for all cells is
s
.
S n
s
j f
(
x n
(
j
))
N f
(
x n
(
i
))
K
2 sin 2
x n
(
i
) K is a “parameter” 40
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, we’ll need to have criteria for growth and death.
A) A cell splits when
x n
(
i
) 10 B) A cell dies when
x n
(
i
) 0 41
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 1) Ordered Phase 2) Partially Ordered Phase 3) Desynchronized Phase 42
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/zoologie/dicty/dicty.html
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Examples of studies of life as a complex system from Physics and Biology Amoebae
Professor Cornelis Weijer Professor of Developmental Physiology University 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 of Dictyostelium 48
Examples of studies of life as a complex system from Physics and Biology Amoebae Migrating Slug 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 49
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 50
Examples of studies of life as a complex system from Physics and Biology Time-lapse video showing slug formation, migration and culmination. From R. Chisholm, Northwestern University Amoebae Lifecycle 51
Conclusion
Conclusion
Life IS a complex system!
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