Simply Complexity (30 page)

Cancer is a terrible and tragic example of a Complex System. In fact, it shows Complexity on all levels: from the set of microscopic and genetic processes that need to go wrong in order for it to start, right through to the way in which it manages to trick the body into supplying it with enough nutrients to grow and flourish – even though this may mean that the body itself could die. But exactly how it does all this is a mystery. As a result of the recent expertise in genetics which has arisen in the medical research community, there is a lot of effort being spent on trying to understand the first aspect of this Complexity – in other words, looking at what might be going on at the genetic and molecular level in order that the body then sets off on a course for cancer. The underlying hope which drives all this research is that cancer might conceivably be nipped in the bud before it fully develops.

However, the massive problem facing cancer researchers is that there are many reasons why a given cancer might start. This is why the media seem to be forever announcing that scientists have found a gene, protein or molecular process which could be important in the development of cancer. Unfortunately it is likely that even if we heard such announcements every day for the rest of our lives, scientists would still not have uncovered the full range of possibilities for how cancer can be produced. The point is that cancer tends to start like an error at the microscopic gene-protein level, and these errors can arise in presumably an infinite number of ways. It is like asking how many spelling mistakes can be made by someone copying a piece of text, where in this case the text corresponds to the DNA code or the molecular-level instructions for some protein production process. The chance of us ever being able to classify all possible errors is minimal – in fact, it seems to be true that among all the cancers ever studied, no exact same error has ever been observed.

Less attention tends to have been paid to the second aspect of Complexity mentioned above – the supply of nutrients which any given cancer, like a plant or fungus, needs in order to survive and grow. Yet this is precisely the area where the ideas of Complex Systems and networks, as described in
chapters 4
and
5
, might prove useful. This idea is being pursued by Sehyo Charley Choe, Alexandra Olaya Castro, Chiu Fan Lee, Philip Maini, Tomas
Alarcon and others – and it makes sense for the following reason. It is quite likely that many of us have very small, embryonic tumors already sitting inside us – yet they may never become life-threatening. Such small tumors are typically unable to grow any larger because they do not have a nutrient supply nearby. The nutrients for a tumor come in the form of oxygen and glucose which are carried in the blood. Hence blood vessels are needed to supply the tumor with these nutrients and to carry away any waste products. As an analogy, just think of a vehicular transport system by means of which food is supplied to a given town (i.e. tumor) and trash is carried away. If there is no road, there are no vehicles – and if there are no vehicles then there is no food and hence the town will not grow. Indeed, it seems that we can all survive quite happily with such small tumors and will remain oblivious to the fact that they even exist.

Unfortunately for us though, this situation of small but essentially static tumors may not last forever. At any particular time, the tumor may suddenly trigger the growth of blood vessels toward it. This is very much like our starved town managing to convince the roads to grow themselves toward it, and hence deliver nutrients as shown in
figure 10.3
. The tumor – or more precisely, the cancer cells within the tumor – perform this trick by releasing chemicals
which promote the growth of new blood vessels or capillaries near the tumor. This process is called angiogenesis. One of the first people to show the importance of this process was Dr. Judah Folk-man of Harvard University. The treatment which then suggests itself is to use drugs which reduce the effects of angiogenesis. This approach could run into trouble, however, since angiogenesis is also a process that helps heal wounds. The patient might then be in danger of dying from wounds that don’t heal. Indeed, this is why the skin around a cut turns red – blood vessels are being grown in order to help heal the wound.

Figure 10.3
Eating nutrients leads to growth. The nutrients are supplied through blood, which in turn flows along the “roads” formed by blood vessels and capillaries. The road network itself is called the “vasculature”.

As a result of angiogenesis, a growing tumor will tend to modify its underlying nutrient network, thereby giving rise to very strong feedback between the structure of the nutrient network, the size and shape of the tumor, its function and hence its lethality. And just as the efficiency of a transport network can be affected by the fact that short cuts may or may not exist – in other words, by the way in which it is wired – a tumor’s growth can be affected by the way in which the capillaries are arranged. In particular, going back to the discussion in
chapter 7
, we know that it is possible for two networks to have very different structures and yet have the same functional properties in terms of the average shortest path from one side to another. The same holds for cancer tumors – there can be arrangements of blood vessels and capillaries which are structurally very different, and yet which are equally efficient (and hence equally lethal) in transporting nutrients to all parts of the tumor. In other words, two blood-vessel – or so-called “vasculature” – networks in two different tumors may look very different, but they may have exactly the same functional properties and hence the same level of lethality. This is one of the reasons why it is so hard for doctors to predict how lethal a particular tumor will be.

The connection to topics discussed earlier in the book doesn’t stop there. It turns out that there is a war going on within the tumor at a more microscopic level. In particular at any given place within the cancer tumor itself, there are two competing populations of cells: cancer cells and normal cells. Cancer cells will do just about anything in order to survive. Not only do they fight to receive nutrients with which to grow, but they also fight for
space into which they can grow. Indeed, this sounds reminiscent of the competition for space in the bar problem in
chapter 4
, and the wars in
chapter 9
. More generally it is reminiscent of the competition for limited resources which this book has flagged as a fundamental feature of real-world Complex Systems. Indeed, the fact that cancer cells have such complicated interactions which can change in time means that we can usefully think of them as having strategies. Unlike normal cells, cancer cells evolve in such a way that regulatory mechanisms are avoided and they therefore represent a population of competitive individuals – very much like our agents or traders in a financial market, or drivers in traffic. And as we have seen throughout the book, a collection of such agents competing for limited resources can act in complicated ways. Hence it seems like the process of tumor growth should embody all the main features of Complex Systems discussed in this book.

Most previous mathematical models of cancer tumor growth have relied on treating this competition and nutrient-supply problem in an average way. In other words, just like the use of the bath in the colds project earlier in this chapter, the tumor is treated as a rather blurry object with no structure. However, for a tumor the devil is definitely in the details of how and where the nutrients are being supplied – so such an approximation will be unreliable in general. By contrast, Sehyo Charley Choe and Alexandra Olaya Castro have been developing a new model which combines all the elements of Complex Systems which we have discussed so far. In particular, it features agents (i.e. cells) fighting it out on the microscopic scale for space and nutrients. Their actions then feed back onto the underlying nutrient network which in turn feeds back onto the agents themselves. The idea is to use this model to see what changes in vasculature need to be made in order to stop a given tumor from growing. After all, if the tumor doesn’t grow and all activity ceases within it the patient is safe for an indefinite period of time – most importantly, that cancer won’t kill them.

Charley and Alexandra’s model allows us to examine the types of tumors (i.e. size, shape and growth-rate) which can emerge from the interplay between the competition among cancer and normal cell “agents”, and the underlying vasculature nutrient
network which is necessary for tumor growth. The case of skin cancers is particularly interesting – not only because it is one of the fastest growing forms of cancer in the population, but also since these tumors are usually more rugged in shape. It is hoped that an understanding of the interplay between the tumor’s functional and structural properties, and the underlying vasculature network, could help doctors in their important yet very difficult task of visually identifying possible skin cancers.

So how can we beat cancer? Charley and Alexandra’s model shows that if we can restrict the tumor’s nutrient supply by reducing the underlying vasculature, we may not only be able to stop the tumor from growing but may also help shrink it. They are now analyzing how different initial vasculature patterns may either favor or inhibit a given tumor’s growth, and how doctors might therefore be able to manipulate or re-wire this underlying vasculature network in order to effectively kill off the tumor. A sort of “tailor-made starvation”. This work is on-going, and has the potential to produce some very valuable diagnostic tools. But to help us understand how it might work, let’s just think back to
chapter 7
, where we saw the effects of adding a cost to a huband-spoke network. Thinking of the hub as the tumor (see
figure 10.4
), the implication of
chapter 7
is that if a “cost” can be introduced for transporting nutrients to the tumor then the number of
connections and hence nutrient pathways into the tumor can be kept small. More specifically, if the cost of connections to the hub can be made high, no new blood supply highways (i.e. major blood vessels which provide an influx of nutrients while simultaneously carrying off waste) would arise, and any existing ones would die out. In short, the tumor would become benign.

Figure 10.4
Starving the tumor. If the flow of traffic (i.e. nutrients) through the tumor could be reduced, the tumor could be starved and hence would stop growing.

Our body’s immune system is our first and last line of defense against all sorts of bugs (i.e. pathogens) that have the potential to make us seriously ill, and even kill us. Sounds important – and yet the mechanisms of the immune system are very complex and poorly understood, even by immunologists. This is because the immune system is actually a collection of objects which are themselves complicated – and the whole thing is held together by a remarkably intricate web of interactions and feedback processes. It is therefore a typical Complex System.

In computer systems and information systems, software equivalents of the immune system are being developed and employed on a daily basis in order to prevent contagion from the multitude of viruses being created. Our own bodies benefit from an immune system that can adapt itself to new challenges – or rather, can do so up to a point. However in computer systems, the software needs to be written each time a new virus appears. Hence there is an enormous amount of interest, both academic and commercial, in learning relevant tricks from our biological immune systems – in particular, how to build adaptability into software systems whose job it is to protect the system against present and future attacks by old and new viruses. We only have to look back to
chapter 9
and the tales of conflict to appreciate that there is also an important parallel with asymmetric wars whereby a small insurgent force might attack a large body with potentially lethal consequences. Interest in how to build a suitably adaptive and protective defense therefore also arises in the military domain. On a lighter note, we can also think of the dating example in
chapter 8
whereby we – presumably in the style of Victorian-age parents – might
wish to introduce a chaperone as “defense” to stop interested males/females from approaching our supposedly defenseless daughters/sons.