Making use of molecular motions

Ludwig Boltzmann expressed the ambition to become a ‘Darwin of matter’ by explaining how random molecular fluctuations could give rise to organisation. He was deeply impressed by Darwin’s mechanism for converting random variations into what seemed like a progression towards order and complexity - he even called Darwinism a ‘fight for negative entropy’. Yet Boltzmann’s name is generally linked only to the first part of that equation: the nature of the thermal fluctuations that impose randomness at the molecular scale.

Over the past decade or so, it has become clear that this ‘noise’ can be harnessed to drive non-random processes. Brownian ratchets are devices that use Brownian motion to move molecules or small particles in a selected direction. They appear to violate the second law of thermodynamics, since they produce a kind of order ‘for free’. Rectifying the erratic drunkard’s walk of molecules to create directional transport appears to demand Maxwell’s demon, which opens a door to admit particles travelling one way but not the opposite. That is in a sense what Brownian ratchets do - but not without an expenditure of energy that keeps the second law intact.

The idea of a Brownian ratchet is so simple that it’s surprising they were not discovered by the likes of Boltzmann and Maxwell. The key to directionality is an asymmetric environment, in which it is harder for a randomly diffusing molecule to move in one direction than in another. The classic example is a saw-tooth-shaped potential, with a shallow slope up which a molecule can ‘climb’ quite easily, and a sharp slope that presents a less easily surmountable barrier in the other direction. Over time, the wandering molecule moves in the direction of the ascending shallow slope.

Tiny devices like this have been made by micromachining. In one example, a series of bottlenecks in a narrow silicon channel, with different tapers on each side of the necks, enabled one-way transport of microparticles when pumped with an oscillating pressure (there’s the second-law-preserving energy input).¹ Single molecules of DNA have been transported this way by using electric fields to bias the direction of diffusion.^2,3 A particularly intriguing variant, as yet purely theoretical, is a water pump that transports water through a carbon nanotube by means of three asymmetrically placed charges just outside the tube along its length.⁴ Simulations indicate that the charges (immobilised ions, say) induce ordering of the water molecules in the nanochannel, and spontaneously bias its flow. This architecture was inspired by the structure of the membrane protein aquaporin, which regulates water flow in cells. The directionality appears to challenge thermodynamic propriety, but the device is not truly passive: energy is needed to maintain the charges in position.

It looks virtually certain that nature uses Brownian ratchets. The movement of RNA polymerase on DNA during replication seems to use such a bias to keep the sliding enzyme moving the right way on average. Whether motor proteins harness the phenomenon has been a matter of much debate, but that now seems likely in some form. Biophysicist George Oster has gone so far as to dub them ‘Darwin’s motors’, alluding to the way they ‘select’ from Boltzmann’s variations.⁵

Luca Angelani and colleagues at the University of Rome ‘La Sapienza’ have described a new twist on such biologically driven micromotors. Their simulations suggest that tiny rotors with asymmetric teeth will turn in a chosen direction in a ‘bath’ of tumbling bacteria, owing to the way the saw-tooth structure converts random impacts of cells into one-way rotation.⁶ Here the directional motion is transferred to the asymmetric environment itself. It looks at first like more of the same, yet is subtly different because the impacting particles are not randomly diffusing but are self-propelled by their own energy source. In both cases directional motion is the result of the breaking of time-reversal symmetry, but whereas for Brownian diffusion this is due to an external energy source, the bacterial propulsion mechanism renders the basic particle motions themselves time-irreversible. The experiments themselves are not so hard, and rumour has it that these little wheels will soon be spinning for real.