Friday, June 21, 2013

Life’s Ratchet

This week I finished reading Life’s Ratchet: How Molecular Machines Extract Order from Chaos, by Peter Hoffmann. This book is mostly about molecular biophysics, which Russ Hobbie and I purposely avoid in the 4th edition of Intermediate Physics for Medicine and Biology. But the workings of tiny molecular motors is closely related to thermal motion (Hoffmann calls it the “molecular storm”) and the second law of thermodynamics, topics that Russ and I do address. One fascinating topic I want to focus on is a discussion of Feynman’s ratchet.

Let us begin with Richard Feynman’s discussion in Chapter 16 of Volume 1 of the Feynman Lectures on Physics. I recall reading the Feynman lectures the summer between graduating from the University of Kansas and starting graduate school at Vanderbilt University. All physics students should find time to read these great lectures. Feynman writes
“Let us try to invent a device which will violate the Second Law of Thermodynamics, that is, a gadget which will generate work from a heat reservoir with everything at the same temperature. Let us say we have a box of gas at a certain temperature and inside there is an axle with vanes in it … Because of the bombardments of gas molecules on the vane, the vane oscillates and jiggles. All we have to do is to hook onto the other end of the axle a wheel which can turn only one way—the ratchet and pawl. Then when the shaft tries to jiggle one way, it will not turn, and when it jiggles the other, it will turn….If we just look at it, wee see, prima facie, that it seems quite possible. So we must look more closely. Indeed, if we look at the ratchet and pawl, we see a number of complications.

First, our idealized ratchet is as simple as possible, but even so, there is a pawl, and there must be a spring in the pawl. The pawl must return after coming off a tooth, so the spring is necessary….”
Feynman goes on to explore this device in detail. He concludes that, as we would expect, the device does not violate the second law. He explains
“It is necessary to work against the spring in order to lift the pawl to the top of a tooth. Let us call this energy ε….The chance that the system can accumulate enough energy ε to get the pawl over the top of the tooth is e-ε/kT [T is the absolute temperature, and k is Boltzmann’s constant]. But the probability that the pawl will accidently be up is also e-ε/kT. So the number of times that the pawl is up the wheel can turn backwards freely is equal to the number of times that we have enough energy to turn it forward when the pawl is down. We thus get a ‘balance,’ and the wheel will not go around.”
Hoffmann explains that a lot of molecular machines important in biology operate analogously to Feynman’s ratchet and pawl. He writes
“What kind of molecular device could channel random molecular motion into oriented activity? Such a device would need to allow certain directions of motion, while rejecting others. A ratchet, that is, a wheel with asymmetric teeth blocked by a spring-loaded pawl, could do the job…Maybe nature has made molecular-size ratchets that allow favorable pushes from the molecular storm in one direction, while rejecting unfavorable pushes from the opposite direction….

For the ratchet-and-pawl machine to extract energy from the molecular storm, it has to be easy to push the pawl over one of the teeth of the ratchet. The pawl spring must be very weak to allow the ratchet to move at all. Otherwise, a few water molecules hitting the ratchet would not be strong enough to force the pawl over one of the teeth. Just like the ratchet wheel, the pawl is continuously bombarded by water molecules. Its weak spring allows the pawl to bounce up and down randomly, opening from time to time, allowing the ratchet to slip backward… Worse, because the spring is most relaxed when the pawl is at the lowest point between two teeth [the compressed spring pushes the pawl down against the ratchet], the pawl spends most of its time touching the steep edge of one of the teeth. When an unfavorable hit pushes the ratchet backward just as the pawl has opened, it does not need to go far to end up on the incline of the next tooth—rotating the ratchet backward!...The ratchet will move, bobbing back and forth, but it will not make any net headway.”
How then do molecular machines work? They require in input of energy, which eventually gets dissipated into heat. Hoffmann concludes
“We could, in fact, make Feynman’s ratchet work, if from time to time, we injected energy to loosen and then retighten the pawl’s spring. On loosening the spring, the wheel would rotate freely, with a slightly higher probability of rotating one way rather than the other. Tightening the pawl’s spring would push the wheel further in the direction we want. On average, the wheel would move forward and do work. In fact, it can be shown that any molecular machine that operates on an asymmetric energy landscape and incorporates and irreversible, energy-degrading step can extract useful work from the molecular storm.”
This may all seem abstract, but Hoffmann brings it down to specifics. The molecular machine could be myosin moving along actin (as in muscles) or kinesin moving along a microtubule (as in separating chromosomes during mitosis). The energy source for the irreversible step is ATP. This step allows the motor to extract energy from the “molecular storm” of thermal energy that is constantly bombarding it.

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