Life's Ratchet: How Molecular Machines Extract Order from Chaos (25 page)

The impossibility of a vital force can be directly related to the impossibility of realizing a Maxwellian demon. This is the argument: Why did eighteenth-century biologists postulate a vital force? Because they were looking for something that could explain the “directed activity” seen in living organisms. It was a way to explain “purpose,” to explain the apparent “intelligence” that seemed to operate in humble cells and microbes. This directed activity had to ultimately stem from the directed activity of the molecules that made up the organism. Who could direct this activity? Only a molecular Maxwell demon, who, by using his intelligence, injects purpose into the otherwise senseless motions of molecules.

But a Maxwell demon is impossible, because a perpetual-motion machine is impossible. The connection between information and entropy, made clear by the thought experiment of the demon, shows that intelligence, purpose, or vital forces can play no role at the molecular scale if the statistical second law of thermodynamics is supposed to hold. Before Maxwell’s demon was conceived, Helmholtz and Mayer had already realized that vital forces had no place in the play of molecules, not even molecules that live in our cells.

Our discussion leaves us empty-handed: To make life work, we need something
like
a Maxwell demon—something that can create directed activity out of chaos. Yet, a Maxwell demon is impossible. The existence of such a being or object would lead to the creation of perpetual-motion machines and violate the second law. The fact that the second law can sometimes be seemingly violated does not help much, either, because it can only be violated by single molecules, at random, and not repeatedly.

Strictly speaking, the second law is a statistical law, that is, the result of averaging over long times or many molecules. It is therefore not truly violated by rare events that seem to run counter to it.
On average
, nothing, not even molecules, violates the second law. And you cannot make a functioning machine out of a molecule that only works occasionally and usually moves in the wrong direction.

Marian Smoluchowski devised another simplified version of Maxwell’s demon, which is very relevant to the mystery of molecular machines. Looking at Maxwell’s demon, he wondered if it would be possible to devise a tiny machine that could extract work from the random motions of molecules in a uniform-temperature environment. There is energy contained in the random thermal motion of atoms, the molecular storm. But how could we harness this energy? Smoluchowski’s machine consisted of a wire with a ratchet attached at the other end. Years later, physicist and Nobel laureate Richard Feynman read Smoluchowski’s work and devised a particularly fruitful incarnation of Smoluchowski’s machine:
Feynman’s ratchet
.

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 (
Figure 5.2
). Old-fashioned watches have ratchets in their windup mechanisms, as do pulleys. As the son of a watchmaker, I have seen tiny ratchets in windup wristwatches many times. The ratchet allows us to wind up our watch but not let it unwind. It allows easy motion in one direction, but blocks motion in the opposite direction. 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. This surely would be a nice way to harvest energy from random motion.

FIGURE 5.2.
Ratchet and pawl—a simple device designed to block motion in one direction (clockwise in this case), but allow it in the other direction (counterclockwise).

I am sure you already sense that there is something fishy about this suggestion. After all, every other attempt to make machines, doors, or demons that could extract useful work from the molecular storm has failed. But surely, this one looks promising: You just need to adjust the spring of the pawl to the right stiffness, and the wheel should block backward motion, while easily sliding in the forward direction. What could go wrong with this idea?

Alas, Feynman showed that this hypothetical machine was also impossible. To get a molecular-size ratchet and pawl to work, the pawl needs to be spring-loaded so that it moves up and down, notch after notch. To allow the ratchet to rotate, the pawl must be pushed up to the height of one of
the teeth. The backward step is restricted because a much larger force is needed to push the pawl up the steep edge of the tooth rather than the gentle incline on the other side. The energy or work is the same in either case, because work equals force times distance. Pushing the pawl up the gentle incline takes less force, but more distance, while pushing it up the steep edge takes more force and less distance.

FIGURE 5.3.
A molecular-size ratchet and pawl would need to have a weak enough spring to allow collisions with molecules to turn it. But such a weak spring would also allow the water molecules to randomly open the pawl, allowing the ratchet to slip backward.

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, as shown in
Figure 5.3
. Worse, because the spring is most relaxed when the pawl is at the lowest point between two teeth, 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, and the spring will push the pawl down the incline—rotating the ratchet backward! Feynman calculated the probabilities of the ratchet’s moving forward and backward and found them to always be the same. The ratchet will move, bobbing back and forth, but it will not make any net headway.

Any simple device, when stuck in an isolated, uniform-temperature bath can only move randomly—no matter how ingeniously designed. The impossibility of making simple, passive machines that can extract oriented work from random thermal energy, be it Smoluchowski’s trap door or Feynman’s ratchet, is a powerful illustration of the second law of thermodynamics. Work cannot be repeatedly extracted from an isolated reservoir at uniform temperature. If it were possible to make machines that could do this, our energy problems would be solved: Such machines would convert heat in our environment back into ordered mechanical energy. Imagine placing such a contraption into your backyard. It would make the air in the backyard colder and turn the extracted heat into electricity. That would be wonderful, but alas, nobody has been able to violate the second law of thermodynamics. At least nobody larger than ten nanometers. And even at ten nanometers, it only happens randomly and rarely.

So, we seem to have hit a snag: We know our cells are full of tiny machines, and we know they must be molecular in size—but we have not yet explained how they work. Does life have the mysterious power to defy the second law of thermodynamics—a law that rules supreme in the inanimate universe? Or are we missing a crucial ingredient that allows life’s molecular machinery to use the molecular storm without violating this all-powerful physical law?

What is the characteristic feature of life? When is a piece of matter said to be alive? When it goes on “doing something,” moving, exchanging material with its environment, and so forth, and that for much longer period than we would expect an inanimate piece of matter to “keep going” under similar circumstances.

—E
RWIN
S
CHRÖDINGER
,
W
HAT
I
S
L
IFE
?

For molecules, moving deterministically is like trying to walk in a hurricane: the forces propelling a particle along the desired path are puny in comparison to the random forces exerted by the environment. Yet cells thrive. They ferry materials, they pump ions, they build proteins, they move from here to there. They make order out of anarchy.

—R. D
EAN
A
STUMIAN
, “M
AKING
M
OLECULES INTO
M
ACHINES
”

M
OLECULAR MACHINES READ AND TRANSLATE DNA; MAKE new machines; operate the processes that makes cells reproduce, transport nutrients, and expel wastes; and help the cell change shape and move about. These tiny machines are the basis of life. But how do they work?

So far, our attempts to explain how molecular machines can do useful work in the midst of the molecular storm have been foiled by the second law of thermodynamics. No machine, however ingeniously designed, can directly convert the random thermal energy into “oriented, coherent activity,” in the words of Jacques Monod. What are we missing?