Monday, October 05, 2009

What toys can tell us

[My latest Muse for Nature news…]

Sometimes all you need to do scientific research is string, sealing wax and a bit of imagination.

When Agnes Gardner King went visiting her uncle William one November day in 1887, she found him playing. He was, she wrote, ‘armed with a vessel of soap and glycerine prepared for blowing soap bubbles, and a tray with a number of mathematical figures made of wire.’ He’d dip these into the tray and see what shapes the soap films made as they adhered to the wire. ‘With some scientific end in view he is studying these films’, wrote Agnes [1].

Her uncle was William Thomson, better known as Lord Kelvin, one of the greatest scientists of the Victorian age. His ‘scientific end’ was to deduce the rules that govern soap-film intersections, so that he might figure out how to divide up three-dimensional space into cells of equal size and shape with the minimal wall area. It was the kind of problem that attracted Kelvin: simple to state, relevant to the world about him, and amenable to experiment using little more than ‘toys’.

This kind of study is brought to mind by a paper in the Proceedings of the National Academy of Sciences USA by George Whitesides and colleagues at Harvard University. In an effort to understand how polymer molecules fold and flex, they have built strings of beads and shaken them in a tray [2]. There are three types of bead: large spherical or cylindrical beads of Teflon and nylon, and small ‘spacer’ beads of poly(methyl methacrylate).

They are designed to mimic real polymers in which different monomer groups interact via forces of attraction and repulsion. When agitated on a flat surface to mimic thermal molecular motion, the Teflon and nylon beads develop negative and positive electrostatic charges respectively, and so like beads repel while unlike beads attract.

This simple ‘beads-on-a-string’ model of polymers replicates, in toy form, a mathematical description of polymers used to understand their conformational behaviour [3], such as the way the polypeptide chains of proteins fold into their compact, catalytically active ‘native’ structure. With some modification – using cylindrical beads of various lengths, so that optimal pairing of oppositely charged beads happens when they have the same length – the model can be used to look at how RNA molecules fold up using the principles of complementary base-pairing between the bases that form the ‘sticky’ monomers.

The beauty of it is that the experiments are literally child’s play (the interpretation requires a little more sophistication). Even the simplest formulations of the mathematical theory are tricky to solve – but the beads, say Whitesides and colleagues, act as an ‘analog computer’ that generates solutions, allowing them rapidly to develop and test hypotheses about how folding depends on the monomer sequence.

Whitesides has used this philosophy before, making macroscopic objects with faces coated with thin films that confer different types of mutual interaction so as to explore processes of molecular-scale self-assembly driven by selective intermolecular forces [4]. This sort of collective behaviour of many interacting parts can give rise to complex, often unexpected structures and dynamics, and is difficult to describe with rigorous mathematical theories.

It’s really a reflection of the way chemists have thought about atoms and molecules ever since John Dalton used wooden balls to represent them around 1810: as hard little entities with a characteristic size and shape. Chemists still routinely use plastic models to intuit how molecules fit together. And these investigations have long gone beyond the pedagogical to become truly experimental. The great crystallographer Desmond Bernal studied the disorderly packing of atoms in liquids using ball-bearings, and, with chalk-dusted balls of Plasticene squeezed inside a football bladder, repeated the 1727 experiment by Stephen Hales on packing of polyhedral cells that was itself a precursor to Kelvin’s investigations. (Bernal called them, apologetically, ‘rather childish experiments’ [5]).

In more recent years, model systems of beads and grains have been used as analogues of the most unlikely and complex of phenomena, from earthquakes and exotic electronic behaviour [6] to the phyllotactic growth of flower-heads [7]. Aside from the obvious issue of how closely these ‘toys’ mimic the theory (let alone how well the theory mimics reality), these approaches stand at risk of offering phenomenology without true insight: with an ‘analytical’ solution to the equations, it can be easier to discern the key physics at play. But when applied judiciously, they show that creativity and imagination can trump mathematical prowess or number-crunching muscle. And they also help underline the universality of physical theory, in which, as Ralph Waldo Emerson said, ‘The sublime laws play indifferently through atoms and galaxies.’ [8]

1. King, A. G. Kelvin the Man p.192 (Hodder & Stoughton, London, 1925).
2. Reches, M., Snyder, P. W. & Whitesides, G. M. Proc. Natl Acad. Sci. USA advance online publication 10.1073/pnas.0905533106 (2009).
3. Lifshitz, I. M., Grosberg, A. Y. & Khokhlov, A. R. Rev. Mod. Phys. 50, 683-713 (1978).
4. Bowden, N., Terfort, A., Carbeck, J. & Whitesides, G. M. Science 276, 233-235 (1997).
5. Bernal, J. D. Proc. R. Inst. Great Britain 37, 355-393 (1959).
6. Bak, P. How Nature Works (Oxford University Press, Oxford, 1997).
7. Douady, S. & Couder, Y. Phys. Rev. Lett. 68, 2098-2101 (1992).
8. Emerson, R. W. The Conduct of Life, p.202 (J. M. Dent & Sons, London, 1908).

1 comment:

JimmyGiro said...

OK, we have a salt crystal; each ion of sodium is symmetrically surrounded by chloride ions, and visa versa.

Classically, each ion is sitting in a zero electric field, owing to the laws of superposition and symmetry. Hence if we expand the structure by small steps; maintaining the symmetry; we can dissociate the crystal with no work done.

Does that mean that the only thing holding the crystal together are the ions at the surface?