Life as a complex system Frederick H. Willeboordse http://chaos.nus.edu.sg frederik@chaos.nus.edu.sg

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.

Is life a complex system? Yes! Examples of complex systems from 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

Aim: Argue that Life is a complex system 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.

Can Life be considered a complex system? 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

The physical/mathematical aspect 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!

The physical/mathematical aspect Is life a complex system? The physical/mathematical aspect Complex is not the same as complicated! Complicated: Microprocessor Function: difficult to design and understand Behavior: easy to understand Complex: Some double pendula linked by rubber bands Function: easy to design and understand Behavior: difficult to understand

The physical/mathematical aspect Is life a complex system? The physical/mathematical aspect An essential ingredient of complex systems is their built-in non-linearity. linear non-linear 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! A difference keeps on increasing A difference can increase but also decrease

The physical/mathematical aspect 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

Clearly, life is “built” up by combining many elements at many levels 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) Etc. Cell walls DNA (made of base-pairs) Multi-cellular organisms

Tristearin Fatty acid Glycerol C O H Hydrocarbon chain Is life a complex system? Tristearin Hydrocarbon chain Fatty acid H C O Glycerol

Chephalin (= Phosphatidyl ethanolamine) Is life a complex system? Chephalin (= Phosphatidyl ethanolamine) Hydrocarbon chain Fatty acid H C O H Glycerol C H H C O C H .. - N C O H P + H Fatty acid replaced by phosphate group and nitrogen containing molecule O C H H

Schematically, phospholipids can be drawn as Is life a complex system? The biological aspect Schematically, phospholipids can be drawn as The interesting thing is that phospholipids can from bi-layers ~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

They can also form micelles 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 …

A Cell behaves very differently from its components 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 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 ..and it is clear that cells posses the following qualities: Robustness Self-organization Adaptability Hence I believe it is fair to describe life as a complex system!

Life is a complex system. Is life a complex system? Life is a complex system. Common Points Differing Points Elements Collective Behavior Robustness Self-organization Adaptable Underlying equations not available in the Life Sciences Bio systems are not deterministic (at least not in the same way).

Examples of complex systems in Physics and Bio 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.

The logistic map is the element 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

The so-called bifurcation diagram 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

The marvelous bifurcation diagram Examples of complex systems in Physics and Biology The marvelous bifurcation diagram The bifurcation diagram exhibits unexpected properties. Let's enlarge this area

The marvelous bifurcation diagram Examples of complex systems in Physics and Biology The marvelous bifurcation diagram An almost identical diagram! Let's try this again...

The marvelous bifurcation diagram 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

The marvelous bifurcation diagram 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.

Our element is the logistic map 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.

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( ) f( ) f( ) Time n+1 Or in other words:

Coupled Map Lattices Frozen Random Pattern 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.

Even though the nonlinearity has increased and the logistic map is Examples of complex systems in Physics and Biology My Research Coupled Map Lattices Pattern Selection Even though the nonlinearity has increased and the logistic map is chaotic for a=1.7, the lattice is entirely periodic.

The coupled map lattice is symmetric, yet here we see a 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!

Spatio-temporal Chaos 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!

In this context it is particularly noteworthy that: 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.

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).

In fact there are many classes genomic information: ? 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: ? ?

start and stop sites for transcription 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).

A concrete example: The lac operon 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, 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.

And of course it wouldn’t end here: Examples of complex systems in Physics and Biology DNA as a ‘hard disk’ It’s not that simple! Y Z O A I 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: Y Z O A I 1990 O2 O3 CRP P O 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

Overall, the cell performs the following computation: 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.

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

Coupled Map Lattice with growth and death 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

Coupled Map Lattice with growth and death 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.

Coupled Map Lattice with growth and death 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”

Coupled Map Lattice with growth and death 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 cell splits when A cell dies when

Coupled Map Lattice with growth and death 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

Cells tend to be synchronized. 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

2) Partially Ordered Phase 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

3) Desynchronized Phase Examples of studies of life as a complex system from Physics and Biology 3) Desynchronized Phase Typically the cells are desyncronised. K = 4.0

Oxford English Dictionary: 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

Amoebae Darkfield Waves 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.

Lifecycle of Dictyostelium Examples of studies of life as a complex system from Physics and Biology Lifecycle of Dictyostelium

Amoebae Migrating Slug 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

Amoebae Cluminating Slug 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

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

Conclusion Conclusion Life IS a complex system!