Complex systems, maths theories . . . and medical practice
Last week in Nature there was a very illuminating paper, called "Controllability of complex networks" by Liu, Slotine and -- particularly -- Barabasi.
Albert-Laszlo Barabasi has been in the complexity field for many years, and has brought illumination to many areas, from engineering and natural systems like ecology to complex social systems. (He also writes compellingly good books for the non-scientist.)
The idea of 'controlling complex systems' seems much too general to do any real mathematics with, but the authors of the Nature paper show very clearly that
there are general principles that can be deduced, and that several - counter-intuitive - proposals can be offered and tested.
Many, perhaps most, complex systems can be formalised as networks, with hubs (called 'nodes') and links (called 'edges' for geometric/topological reasons...). They call the nodes that can be affected to drive the system into alternate modes 'driver nodes'. They also consider systems that are 'sparse' (few nodes and links) or 'dense' (many nodes and links); sparse nodes are difficult to control compared to dense nodes, and high-degree nodes (with many links) are, surprisingly, not the best way to control systems. This is proved so both in theory and in practice.
Now what has this to do with the real world? Well, there are many complex systems that we would like to control. For example, and this is what caught my attention as a way to illustrate the point, this week's Nature Insight has four very complicated papers about our blood vascular system: one considers 'angiogenesis' ( the development of vessels to bring blood to organs - and to cancers), one considers aneurisms (large blood vessels may develop swellings that can burst, and this condition is somewhat heritable), one considers the biology of atherosclerosis (in which fatty deposits occlude arteries, particularly those that feed the heart muscles) and one considers prospects for curing - at least for ameliorating - the pathologies resulting from 'heart failure'.
Each of these papers is a classic consideration of a complex system, and to my eye they could all be expressed (at least partly) as networks and made amenable to the kind of control Barabasi et al talked about last week.
There is, of course, a tremendous gap between mathematical theories of complex networks and medical practice - or theory. But there is another, more imminent, problem.
The people who read the complexity paper simply won't turn their attention to the blood vascular system (except when they themselves become sick, and they won't think 'network' then!). And the people who write -- and read -- the medical papers simply will flip over the pages of Network Theory just as they do for the papers about anti-matter Helium4, or the rate of ice loss from North Canadian islands because of warming temperatures, both in this week's Nature.
There are very few of us who read all of Nature, and we all skip lots of stuff, only read the summaries. Perhaps in the future someone will pick up on ways to control blood system diseases by drawing out the web of interactions and finding those nodes that can be altered to change the system. Let's bet our lives on it!