When metastable systems fail to become stable…

‘Metastable systems’ is a technical term for something you’ve definitely experienced in your daily life, as much as scientists often encounter it when studying subatomic particles.

Say you’re sitting on a chair and are getting comfortable. You realise you’d be even more comfortable on a bean bag but you don’t mind staying in the chair. You’re too lazy to get up. In this scenario, the you-chair system is metastable: while you’re stable (because you have low energy), you’re not as stable as you can be (you can have even less energy), but you don’t have enough energy to move from one state to the other.

The same thing happens to proteins inside your body. Proteins are really folded-up when they’re made and sometimes they need to unfold to work properly, like get inside a cell. Its folded form is metastable and it needs to unfold to attain a stable state, which happens by thermal fluctuations (random deviations from its folded form driven by temperature changes).

In fact, based on measurements of the Higgs boson (which gives ‘mass’ to many subatomic particles) and the top quark (the heaviest known subatomic particle), physicists currently believe our universe itself may be in a metastable state. It has some low level of energy but could have even less, and someday it may move to this state and doom us all.

Scientists have used the behaviour of metastable systems to explain a variety of phenomena in many fields, including reaction chemistry, radioactivity, the integrity of large metallic structures (like ships and statues), and glitches in semiconductor manufacturing.

They’ve often modeled these phenomena using Arrhenius’s law, which states that the likelihood a system can be found near the barrier separating the high-energy and low-energy states and how often the system tries to become metastable can together model the dynamics of the metastable system.

To explore this further, researchers from the University of Alberta in Canada tried something clever in a new study: they looked at how much a metastable system tries to escape to a more stable state before it ‘gives up’.

This is interesting because, unlike you in the chair or the universe, metastable-to-stable transitions matter greatly in protein-folding. Misfolded proteins are responsible for many terrible diseases and figuring out how a protein might have got that way – in the course of its attempted transition – may help set it right.

“The properties of unsuccessful crossing attempts remain largely unknown,” the researchers wrote in their paper, “even though they can contain information about regions of the barrier not explored during successful crossing events.” The paper was published in the journal Physical Review X on February 14.

To access the information contained in unsuccessful crossing events, the researchers conducted two experiments. In the first, they confined two small beads in a pair of optical traps next to each other and tracked how often the beads crossed over from one trap to the other. (The system could be made metastable by increasing the energy in one trap.)

Each bead had thermal fluctuations. A few attempts to cross over succeeded but more often the beads would wander into the region between the two traps, where the attractive potential exerted by the traps overlapped, linger there for a few microseconds, and fall back into their traps. By collecting data about the bead, the researchers found they could model its progress in the area of overlapping potential as Brownian motion (the seemingly random motion of microscopic particles in a fluid as a result of constantly colliding with other particles in the fluid).

In the second experiment, the team attached beads on to the two ends of a DNA molecule (using ‘handles’ made of a polymer) and confined the beads in adjacent optical traps. A crossover happened if the DNA molecule folded up. In this case, the distance between its ends, called the DNA extension, would decrease and the beads would move a little bit as a result.

In the first experiment, the two beads each moved a little bit randomly and eventually did or didn’t get to the other side, and the researchers could understand the system just by keeping track of the distance between the beads. The second experiment is more complex: the distance between the beads and the DNA extension are both affected by thermal fluctuations of the beads, of the atoms and molecules in the polymer handles, and of the large number of atoms and molecules in the DNA.

To really understand this system, then, the researchers would have to track all of these movements in a large, sophisticated apparatus with many knobs and controls – or, fortunately for them, use the work of Dutch physicist Hendrik Anthony Kramers.

In 1940, Kramers postulated that it’s possible there is a distance between two objects in a metastable system such that the system’s dynamics can be modelled as Brownian motion along the direction of that distance, plus the effects of frictional forces and some noise. The trick lies in choosing this distance correctly.

In their second experiment, the researchers found this distance to be the DNA extension. They recorded the DNA’s failed attempts to fold (crossover) and the points in different attempts at which it gave up trying to fold and fell back. They also calculated the corresponding solutions according to the Kramers model. When they compared the two results, they reported a match to within a small amount of uncertainty. There had been some doubt as to whether the Kramers model could apply in systems that evolve rapidly, in the order of microseconds, and the match proved that it could.

More importantly, the team also found the frequency with which the metstable system tried to become stable in the Arrhenius model couldn’t fully explain the dynamics, and that its role in the model would have to be reinterpreted through more experiments. Dmitrii Makarov, of the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin, wrote in Physics magazine that some of these experiments could combine “fluorescence experiments with force spectroscopy [to] provide a two-dimensional rather than one-dimensional picture of the dynamics”.

The study also opens the door to applications that involve metastable systems transitioning to stable ones. Consider molecular machines: assemblies of molecules that use mechanical forces to perform biological tasks. Last year, I reported the discovery of a particularly interesting kind of molecular machine for The Hindu. Excerpt:

In a 2016 paper, researchers from Australia and Germany reported that when an enzyme called Rab5 binds to a long protein called EEA1, the protein loses its taut and rigid shape and becomes floppy. This ‘collapse’ pulls two membranes inside a cell closer to each other.

In the new study, researchers have reported that EEA1 regains its rigid shape in another mechanism so that it can become floppy again to pull the membranes closer, creating a new kind of two-part molecular motor.

The researchers found that when it’s floppy, EEA1 can take one of several shapes, but when it becomes stiff, it has only one shape. Because the floppy state also has more entropy, they interpreted it mean it is also more “entropically favoured”, and when the protein goes from stiff to floppy, it exerts can “entropic force” on two membranes, which are pulled closer together.

Researchers can use the new study’s findings and the Kramers model to understand when, how, and why such molecular machines fail, and how their function can be restored.