Life's Ratchet: How Molecular Machines Extract Order from Chaos

by Hoffmann, Peter M.

  The reset step, which we have found to be necessary for a molecular machine to work, can take many forms. This step is an example of a so-called irreversible step, because it degrades free energy into heat, and this heat cannot be turned back into free (usable) energy. Through this irreversible step, our molecular machine can extract energy from the molecular storm without violating the second law.

  In hindsight, this makes sense: A reversible machine is a machine in thermodynamic equilibrium, with no irreversible steps. But if a machine is reversible, it can just as easily move one way or the other. If it can move just as easily forward as it can move backward, it cannot do any useful work. For a machine to do useful work, we need irreversibility. This was the missing something we were looking for in Chapter 5.

  In Chapter 3, we found that living beings are open, dissipative, near-equilibrium systems. Now this statement takes on a new meaning: The irreversible steps needed to put our cellular machinery to work are paid for by a continuous supply of free energy. We must receive free (low-entropy) energy from the outside (food or sunlight), and this free energy is degraded (dissipated) by our molecular machines as they use it to harness the molecular storm.

  What Molecular Machines Eat

  Molecular machines need a supply of free energy. In some sense, they eat free energy. But how do they like their free energy served? On a bun with some ketchup? Joking aside, in animals, the free energy that feeds the molecular machines of cells comes from food. A bewildering network of enzymes in the stomach, intestines, and cells breaks down food as part of metabolism. The final product of this complicated process is a molecule called adenosine triphosphate, or ATP, the energy-storage molecule that brought myosin to life in the motility assay mentioned in Chapter 4. Three phosphates bind to adenosine to form ATP. With all three phosphates attached, ATP is a bundle of concentrated energy. Snapping off one or two of the phosphate groups releases a great deal of energy—only the molecule’s activation barrier keeps the phosphates from detaching right away. But once ATP binds to a molecular machine, the phosphate groups snap off readily, ATP turns into ADP (adenosine di-phosphate), and the machine is provided with a large amount of energy.

  What form does this energy take? It is vibrational energy; the release of the phosphate makes the enzyme shake and rattle. In some sense, we can think of it as local heating (higher temperature means more violent motion). The energy released by the loss of one phosphate is equivalent to heating the enzyme up to 7,000 degrees Fahrenheit. This additional shaking allows the molecular machine to overcome activation barriers that are otherwise unattainable.

  Once the ATP is broken down to ADP, the ADP goes back to the cell’s recharging station, the mitochondrion. The mitochondrion is a cellular factory where sugar provides the energy to reattach phosphates to ADP, reconstituting ATP.

  Tighty and Loosey

  Righty tighty, lefty loosey

  —GOOD ADVICE WHEN PUTTING TOGETHER IKEA FURNITURE

  Now that we know what is on a molecular machine’s menu, let us find out how real molecular machines implement the nano-Sisyphus method outlined above. As described earlier, nature has taken two major approaches to machine design: a robust (“super-Hummer”) strategy and a floppy (“If you can’t beat ’em, join ’em”) strategy. Scientists refer to these as tight and loose coupling, respectively. The boundaries between the two are not well defined and are vigorously debated in the scientific community. Each time a new molecular machine is identified, the tight-versus-loose debate flares up again, with both factions claiming the new machine for their camp. Before I try to weigh in on this debate, let me further explain the difference between the two mechanisms.

  When biophysicists talk of tight coupling, they are referring to two (related) ideas. First, they think of a close coupling between the supplied ATP and the work steps taken. Second, tight coupling refers to the machine’s being bound to a molecular track at all times. A tightly coupled motor uses one ATP molecule to make exactly one step while at least partially bound to a track. A loosely coupled machine, by contrast, may let go of the track from time to time. Detaching from the track allows a loosely coupled machine to make more than one step per ATP molecule, but it also allows the molecular storm to push the machine in an undesired direction.

  As discussed earlier, in the super-Hummer model (i.e., a tightly coupled machine), there must be some minimal degree of letting go—otherwise the machine would not move at all. A good analogy is a human walking. In order to move forward, we have to break contact with the ground from time to time (even when we shuffle, we shift from firm contact to sliding). We can do this because we always keep one foot firmly planted on the ground, while moving the other. This is, in essence, how a number of molecular machines, or motors, work. For example, a molecular motor called kinesin—a fifty-nanometer-long assembly of protein molecules—walks on two feet (or heads, as biologists confusingly call them) on a molecular track called a microtubule, always keeping one foot planted to the track. These motors are used to move cargo throughout cells—they are nanosize Sherpas, carrying heavy molecular loads along a one-way track to distant regions of the cell (Figure 6.8).

  FIGURE 6.8. A kinesin molecular motor carrying a vesicle filled with nutrients walks along a microtubule. The whole molecular motor is only about fifty nanometers in height. © 1999 Robert A. Freitas Jr., www.nanomedicine.com. Used with permission.

  FIGURE 6.9. Motion of a kinesin molecule (highly simplified). A: Foot 2 binds an ATP molecule, while foot 1 degrades ATP (T) to ADP (D) and detaches from the track. B: Binding ATP (T) causes foot 2 to clamp on tightly to the microtubule track and allosterically bend its leg forward. Meanwhile, foot 1 has released from the track (arrow a in step A) and dangles back and forth (arrow c). C: But because foot 2 and its leg have tilted the molecule forward, forward motion is favored for foot 1, and eventually it will weakly bind to the track in front of foot 2, releasing ADP, as seen in arrow d. The molecule has taken a step. Finally (not shown), foot 1 binds an ATP, clamps on tightly to the track, and tilts its leg forward. The cycle repeats with the roles of feet 1 and 2 reversed: Foot 2 degrades its ATP to ADP and detaches from the track, and so on.

  To see how kinesin motors work, let’s take it step-by-step (literally). Initially, both feet are attached to the microtubule, and one of them has bound to an ATP molecule. The ATP molecule releases its energy (turning into ADP), and this energy is used to detach the foot from the microtubule. Once this foot is detached, the molecular storm initially pushes the foot forward and backward, but it cannot go very far as the other foot is still holding on to the track. Now, the foot still planted on the track takes on an ATP molecule and by an allosteric shape change bends the whole kinesin molecule forward, forcing the dangling foot toward the forward direction. Now, the dangling foot latches on in front of the attached foot, and releases ADP. The attached foot degrades its ATP in turn, detaches from the track, and the cycle repeats (Figure 6.9).

  We find here a mechanism that is similar to our nano-Sisyphus model: The allosteric interaction plays the role of Sisyphus, not allowing the free foot to swing backward as it is randomly pushed by the molecular storm. Once the foot has made a step, the now lagging foot must be released in an irreversible reset step, requiring the breakdown of an ATP molecule to a lower-energy ADP molecule. As long as there is a supply of ATP molecules, the motor will keep walking.

  The hallmark of a tightly coupled molecular motor is that it goes through well-defined cycles, using up a fixed number of ATP molecules during each step. Nevertheless, random motion is the drive behind the motor’s locomotion, as it ultimately moves the legs of the motor forward—of course, rectified by the allosteric interaction of the motor’s legs with ATP.

  Loosely coupled motors, by contrast, rely more heavily on random motion and have no fixed-step cycle. And they are more difficult to understand.

  What Are the Odds?

  To understand loosely coupled motors, consider two ways that nanoscale objects c
an move while immersed in water. We have already encountered random motion, which is caused by collisions with fast-moving water molecules. Physicists call this random motion diffusion (Figure 6.10). When a molecule moves by pure diffusion, it executes a random walk: Each step it takes is in a random direction, independent of the step it took previously. As a result, the molecule wanders around aimlessly, like a drunk after a night of binge drinking (sometimes this motion is called the drunkard’s walk).

  FIGURE 6.10. Possible molecular motions: (A) Pure diffusion: The molecule moves along a random path and makes no net headway. (B) Pure drift: The molecule moves along a straight, deterministic path in the direction of an applied force. (C) Drift and diffusion: The molecule moves, on average, in the direction of the force, but superimposed is random, diffusive motion.

  The other type of motion occurs when a force is applied to the molecule. The molecule is still subject to random collisions from the molecular storm, but now, it is also dragged through the molecular tempest by the applied force. Physicists call this type of motion drift. What kind of forces can be applied to molecules? Ultimately, all forces in the molecular realm are of electrostatic origin. Even a chemical bond is ultimately due to electrostatic attraction (although some quantum mechanics is needed to fully explain the origin of a chemical bond).

  An important fact to remember is that forces drive systems toward reduced energy. If a molecule binds to another molecule, the two molecules will not initially bind perfectly to each other—there will still be some distance between them. But as soon as the molecules feel one another, their combined energy will start to reduce, and they’ll be compelled by a force of attraction. This force pulls the molecules in the direction of further energy reduction, that is, in the direction of completing the bond.

  In general, molecules experience both types of motion, diffusion and drift. Drift is a deterministic motion, always in the direction of reduced energy, while diffusion adds a random component to the molecule’s path (Figure 6.10). Because of this randomness, the best way to describe the motion of a molecule is to use statistical mechanics. The statement “in three seconds the molecule will move five nanometers to the left” becomes nonsensical, and we can merely state the probability that it may have moved to this position. Physicists can calculate the probability of a molecule’s moving to a certain location by using the so-called Fokker-Planck equation (a challenging equation usually solved by computers). This equation calculates the probability of motion on the basis of the energy landscape of the molecule. The energy landscape gives a conceptual picture of the molecule’s energy as a function of position and configuration. A steep slope in the landscape—that is, a strong dip in energy for small movements of the molecule—leads to drift. This is because steep changes in energy correspond to strong forces driving the system down the energy slope. On the other hand, on the flat parts of the landscape (where changes in the molecule’s position or shape do not change energy by much), forces are negligible, and diffusion will dominate.

  With this picture in mind, we can understand how the loosely coupled motor works. A loosely coupled motor is one that relies partly on random motion (diffusion), yet is still capable of performing directed motion. It can do this if it periodically attaches and detaches to a track. When it is attached to a track, it is subject to drift and feels a force directing it to the lowest-energy position on the track. When it is detached from the track, it diffuses freely. Loose coupling doesn’t violate the second law, because detaching from the track requires free energy, which is degraded into heat. The detachment is the irreversible reset step.

  How would such a machine move? We need to think of probabilities. Figure 6.11 shows a molecular motor on a track with an asymmetric energy landscape. The energy changes more steeply in one direction than the other, forming a saw-tooth pattern (similar to the teeth of the ratchet). On such an energy landscape, the combination of drift and diffusion will increase the probability that the machine will move one way rather than the other.

  The asymmetry of the track’s energy has two effects on the machine: First, the machine will spend most of its time near the energy minimum of the track. This minimum is at the lowest point of the track (Figure 6.11, step A). Now, when the machine detaches, it is just a short distance to the neighboring tooth on the left, but a larger distance to the tooth on the right. Second, once the motor reattaches to a random spot on the track, it will most likely end up on a gentle slope of the energy. This slope is also directed to the left, so the motor will experience a force pushing it to the left toward the minimum of the next tooth’s energy. The overall result is that the asymmetry of the track’s energy biases the motion of the motor to the left.

  In Figure 6.11, the bottom three graphs represent this motion by plots of probability, each plot corresponding to a step in the cartoon above. Initially, if we know the motor is attached at a certain energy minimum, the probability that it is at this location is 100 percent (plot A). Then, the motor detaches and freely diffuses. This is represented by the flattened-out peak in the probability shown in plot B. When the motor reattaches, it quickly finds the nearest energy minimum. Because it was closer to the minimum to the left of its original position, the probability is somewhat higher that it ended up moving left rather than right. This represented in plot C by the slightly larger peaks in the probability to the left of the starting position. Note that the largest probability peak is at the starting position, indicating that often the motor does not move at all, but reattaches at its original location. There is also a small peak to the right of the starting position, indicating the small, but nonnegligible probability that the motor moves backward. On average, however, after many steps, the motor will move to the left. That is, it will perform directed motion.

  FIGURE 6.11. Top: Motion of a loosely coupled motor. In step A, the breakdown of an ATP molecule and release of ADP detaches the motor from the track (arrow a). In step B, the motor diffuses freely. In step C, the motor reattaches (arrow b), binding ATP in the process. As it binds to the molecular track, it quickly moves to the lowest energy state by drift (arrow c). Bottom: Probability plots corresponding to the steps shown above. (A) A single probability peak corresponds to the motor initially positioned at the energy minimum (prior to detaching in step A). (B) The motor diffuses freely, leading to a broadening of the probability peak. (C) The motor reattaches. Because of the asymmetry of the track’s energy, the probability that it attaches to the left of the starting position is higher than the probability that it attaches to the right. The motor can also reattach at the same position where it started. However, leftward motion is more probable than rightward motion, and, on average, the motor will move to the left.

  If this model sounds eerily similar to our ratchet in Chapter 5, consider that physicists refer to this type of loosely coupled machine as a Brownian ratchet. The Brownian ratchet, unlike Feynman’s passive ratchet, uses an irreversible step: the detachment from the track, fueled by the breakdown of an ATP molecule. 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 an irreversible, energy-degrading step can extract useful work from the molecular storm.

  Because the motion of a loosely coupled machine is dominated by diffusion, the machine can take several steps at once, but it can also move backward. Therefore, loosely coupled machines do not move as efficiently as tightly coupled machines. Moreover, they do not move along a track for long distances before completely detaching. A motor that can move long distances along a track, continuously stepping forward, is called a processive motor. Tightly coupled motors tend to be
processive; loosely coupled motors are not.

  The Controversy

  As mentioned earlier, there is an ongoing battle between scientists about whether molecular motors are tightly or loosely coupled. This fight has a deeper origin: Some scientists like the idea that the randomness of thermal motion plays a major role in molecular motors, while others prefer a more deterministic view. Loosely coupled motors have a clear dependence on random motion: The actual stepping is primarily done by random diffusion, with the asymmetric energy of the track providing the needed forward bias. Tightly coupled motors do not obviously incorporate random diffusion, so the tight-coupling mechanism is usually favored by many in the antirandomness camp.

  A particularly intense debate is over the molecular motor myosin II. There are approximately eighteen different myosins in nature, and myosin II molecules make animal muscles work. When we decide to lift an arm, we send signals to countless myosin motors in our muscles and tell them to pull on actin fibers. Myosins grab the fibers and pull them taught, as in a game of tug-of-war. As the myosin motors pull in the fibers, our muscles contract and our arm lifts up. Next time you lift an arm (or move any part of your body), remember that this is accomplished by an army of myosin nanobots.

  Measuring how these motors work at the single-molecule level is challenging, and unsurprisingly, different results have emerged from different laboratories. This has fueled the controversy. Until recently, most researchers believed that myosin II was a tightly coupled motor, making measured steps of five to ten nanometers per ATP molecule consumed. However, one of the pioneers of single molecular motors, Toshio Yanagida of Osaka University, produced repeated measurements that contradicted this claim. Yanagida claims that the distance myosin II moves fluctuates and can reach up to thirty nanometers per ATP molecule. This could only be possible if myosin were a loosely coupled motor.