Instructions for Assembly

thesis Instructions for assembly

Creativity in science often emerges from and Mackay illustrate how the idea of paradox. The word ‘crystal’ captures the It is clear that biology assembly complexity frames some issues archetype of order — structures repeating exploits prior physical in an insightful way. For example, we may perfectly through space, each elementary generally attribute to biology, and to the unit giving a complete description of algorithms of assembly, genetic machinery of biological organisms, the whole. Thirty years ago, the French much as a chef uses the algorithmic capabilities behind all the mathematical physicist David Ruelle various complex substances and structures played imaginatively with paradox in a basic chemistry. they produce. The remarkably rich paper entitled ‘Do turbulent crystals exist?’ hierarchical structure of nacre (mother of Turbulence? Crystals? Together? (Phil. Trans. R. Soc. A 370, 2807–2822; pearl), seems to be all the product of the By this time, Ruelle had already made 2012), biology, physics and materials science genetic machinery of molluscs. But this isn’t seminal contributions to the theory now face the challenge of moving “beyond quite right. of deterministic chaos. In the 1940s, crystals” in a general way. The task is to Nacre is an assembly of hexagonal Lev Landau, aiming for a general theory bring some understanding to the world of platelets of aragonite, a form of calcium of the origins of turbulence, had suggested disordered biological materials, and bio- carbonate, stitched together into sheets that its profound dynamic disorder develops inspired synthetic systems. As they note, that are then separated by further sheets of progressively in a fluid as ever more the word ‘crystal’ is still defined by the biopolymers such as chitin. The combination Fourier modes get excited. In 1971, Ruelle, International Union of Crystallography as of brittle platelets and flexible biopolymer working with mathematician Floris Takens, “a structure giving a diffraction pattern with sheets makes the material remarkably showed that another ‘scenario’ for the discrete points”. This is far too limiting. strong and resistant to cracks. For this transition to turbulence was actually much The most famous aperiodic crystal is, rich assembly, the mollusc genome takes more likely in a mathematical sense. They of course, DNA, and there the varying some of the credit, but not all. From the showed that if an initially stable system structural pattern stores crucial information. information perspective, it is clear that undergoes four consecutive transitions But the role of information is more general, biology actually exploits rich prior physical to oscillatory behaviour, this is enough as virtually all structures in biology store algorithms of assembly, much as a chef uses to create deterministic chaos and erratic information in one form or another, and basic chemistry. Biology, as Cartwright unpredictable flow; later research reduced reflect some essential biological function or and Mackay note, takes for granted “all the the number to three. purpose. At the simplest level, for example, physics and chemistry of nucleation, growth Loosely speaking, three independent we have membranes and micelles that divide dynamics, fluid dynamics, solid and liquid oscillations are generically sufficient for the world into an inside and an outside, crystallization” and much more besides. chaos. In developing this idea — now known controlling flow between them. Biology is Hence, we should really attribute to the as the Ruelle–Takens–Newhouse route full of messy but still organized hierarchies genome only the same information we do to chaos — Ruelle and Takens coined the and systems of systems running all the way to a chef who exploits natural chemistry famous term ‘strange attractor’. from the atomic scale to the human — what to produce a tasty soufflé, but who doesn’t Chaos is a dynamical phenomenon — draws them all together is the purposeful carry out the underlying physics and that is, a process in time. Ruelle’s paper with processing of information. chemistry. Looking at information and the paradoxical title simply asked if there As Cartwright and Mackay propose, the where it resides in structures offers a way to might be analogues in space. If periodicity in relation between information and structure penetrate the middle world between physics- time can dissolve into erratic chaos, why not may offer a means of bringing some order based materials science, approaching from in space? Could there be crystals, structured to the world of messy bio-structures, or the simple world of pure crystals, and by deterministic rules, yet never repeating their analogues in synthetic materials. They biology, where complexity goes far beyond in space? introduce the ‘assembly complexity’ of a anything we can make artificially. This was only a couple of years before physical structure, this being a measure Yet we still don’t have a strict answer the discovery of quasicrystals — ordered of how much information it holds. The to David Ruelle’s original question: do atomic solids with a quasiperiodic pattern idea works as an analogue of the famous turbulent crystals exist? For all the myriad in space. Ruelle (who assumed in his paper Kolmogorov complexity-of-information amorphous structures known in biology, that quasicrystals would exist) was on theory. Whereas the Kolmogorov complexity physics and modern chemistry, all seem to something. In the temporal domain, of a numerical sequence is the length of the to be metastable states or states of systems quasiperiodic time series lie between simplest algorithm capable of producing well out of equilibrium. Ruelle, in contrast, periodic and erratic structures; they define that sequence, the assembly complexity of had envisaged turbulent crystals as the true a boundary between periodic regularity a structure is given by the simplest physical physical ground states of a system at some and chaos. Quasicrystals play a similar role algorithm capable of producing it. finite temperature. It remains unknown in the spatial domain. The rigid order of How useful this idea might be in whether such things may really exist. the classical crystal is as limiting as that of practice isn’t yet clear. One shortcoming Clearly, questions aren’t valuable only if predictable, regular dynamics. What might is that a realized process of assembly gives they can be answered. The act of trying is we find on the far side? only an upper bound to the assembly valuable in itself. ❐ Three decades later, we’re finding out. As complexity of the structure, as other simpler Julyan Cartwright and Alan Mackay argue methods might exist. Even so, Cartwright MARK BUCHANAN

NATURE PHYSICS | VOL 8 | AUGUST 2012 | www.nature.com/naturephysics 577