*Nature*. This one was tough, but hopefully worth it. Possibly I ended up with a better explanation on the

*Nature*site than here of why reversibility is linked to the minimum heat output. But it’s a tricky matter, so no harm in having two bites of the cherry.

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*Bacteria replicate close to the physical limit of efficiency, says a new study – but might we make them better still?*

Bacteria such as

*E. coli*typically take about 20 minutes to replicate. Can they do it any faster? A little, but not much, says biological physicist Jeremy England of the Massachusetts Institute of Technology. In a preprint [1], he estimates that bacteria are impressively close to – within a factor of 2-3 of – the limiting efficiency of replication set by the laws of physics.

“It is heartening to learn this”, says Gerald Joyce, a chemist at the Scripps Research Institute in La Jolla, California, who work includes the development of synthetic replicating molecules based on RNA. “I suppose I should take some comfort that our primitive RNA-based self-replicator apparently operates even closer to the thermodynamic lower bound”, he adds.

At the root of England’s work is a question that has puzzled many scientists: how do living systems seem to defy the Second Law of Thermodynamics by sustaining order instead of falling apart into entropic chaos? In his 1944 book

*What is Life?*, physicist Erwin Schrödinger asserted that life feeds on ‘negative entropy’ – which was really not much more than restating the problem.

Life doesn’t really defy the Second Law because it produces entropy to compensate for its own orderliness – that is why we are warmer than our usual surroundings. England set out to make this picture rigorous by estimating the amount of heat that must unavoidably be produced when a living organism replicates – one of the key defining characteristics of life. In other words, how efficient can replication be while still respecting the Second Law?

To attack this problem, England uses the concepts of statistical mechanics, the microscopic basis of classical thermodynamics. Statistical mechanics relates different arrangements of a set of basic constituents, such as atoms or molecules, to the probabilities of their occurring. The Second Law – the inexorable increase of entropy or, loosely speaking, disorder – is generally considered to follow from the fact that there are many more disorderly arrangements of such constituents than orderly ones, so that these are far more likely to be the outcome of the particles’ movements and interactions.

The question is: what is the cheapest way, in terms of how much energy (technically free energy, which takes into account both the energy needed to make and break chemical bonds and the associated entropy changes) is involved, of going from one bacterium to two? That turns out to be a matter of how easily one can reverse the process.

For the analogous question of the minimal cost of doing a computation – combining two bits of information in a logic operation – the answer depends on how much energy it costs to reset a bit and ‘undo’ the computation. This quantity places a fundamental limit on how low the power consumption of a computer can be.

“The probability that the reverse transition from two cells to one could happen is the quantity that tells us how irreversible the replication process is”, says England. “Whatever this quantity is, it need not be dominated by the trajectories that would just look like the movie playing backwards: there are many ways of starting with two cells and ending up with one. I’m asking what class of paths should dominate that process.”

The problem is precisely those “many ways”. “You can drive yourself nuts trying to think of everything”, England says. But he considered the most general reversal route: if, by chance, the atoms in the replicated bacteria happen to move such that all its molecules disintegrate. That is, of course, immensely unlikely. But by figuring out exactly how unlikely, England can place a rough limit on how reversible replication is, and thus on its minimum energy cost.

By plugging some numbers into the equations describing the likelihood of a replication being reversed – how long on average the chemical bonds holding proteins together will last, say, and how many such bonds there are in a bacterium – England estimates that the minimal amount of heat a bacterium must generate to replicate is a little more than a third of the amount a real

*E. coli*cell generates. That’s impressive: if the cells were only twice as efficient, they’d be approaching the maximum efficiency physically possible.

“The weakest point in my argument is the assumption that we know what the ‘most likely very unlikely path’ for spontaneous disintegration of a bacterium is”, England admits. “We’re talking about things that simply never happen, so we can’t have much intuition about them.” As a result, he says that his treatment “certainly shouldn't be thought of us a proof as much as a plausibility argument.”

It’s precisely this that troubles Joyce, who compares the calculation with the joke about a physicist trying to solve a problem in dairy farming. “As an experimentalist, it is hard for me relate to this ‘spherical cow’ treatment of a self-replicating system”, Joyce says. “Here

*E. coli*seems to be nothing more than the equivalent of its dry weight in proteins.”

England says that we can hardly expect bacteria to do much better than they do given that they have to cope with many different environments and so can’t be optimized for any particular one. But if we want to engineer a bacterium for a highly specialized task using synthetic biology, he says, then there is room for improvement: such a modified

*E. coli*could be at least twice as efficient at replicating, which means that a colony could grow twice as fast. That could be useful in biotechnology. “We may be able to build self-replicators that grow much more rapidly than the ones we're currently aware of,” he says.

He also concludes that there’s a trade-off between speed of replication and robustness: a replicator that is prone to falling apart produces less heat, and so can replicate faster, than one that is more robust. The findings might therefore have implications for understanding the origin of life. Many researchers, including Joyce, suspect that DNA-based replicators were preceded on the early Earth by those based on RNA, which both encoded genetic information and acted as an enzyme-like catalyst for proto-biological reactions. This fits with England’s hypothesis, because RNA is less chemically stable than DNA, and so would be more fleet and nimble in getting replication started. “Something else than RNA might work even better on a shorter timescale at an earlier stage,” England adds.

References

1. England, J. L. preprint http://www.arxiv.org/abs/1209.1179 (2012).

## 2 comments:

"Life doesn’t really defy the Second Law because it produces entropy to compensate for its own orderliness – that is why we are warmer than our usual surroundings."Does that mean that plants, insects, and cold blooded reptiles are living exceptions to your postulate?

Anyhoo, if Maxwell had known about the shenanigans of RNA in cell formation, he might have called his Daemon by such a name. Come to think of it, Maxwell's thought experiment may have preceded the atomic and molecular understanding of matter and its 'phases'.

Which just goes to show you how much you can achieve in science if you don't let them pesky facts get in the way [and if your wife runs home to her mother :)) ].

cool math games kids find on giogamer.com

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