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

by Hoffmann, Peter M.

  FIGURE 4.5. Measurement of the stiffness and damping of molecule-thick water layers, using an atomic force microscope (AFM). Each peak in the stiffness (filled circles) corresponds to a thickness of water between the AFM tip and a flat surface, which contains an integer (1, 2, 3, . . .) number of water molecules. The fact that the stiffness peaks and the damping peaks (open circles) don’t line up means that the few-molecules-thick water layer responded like a solid to being squeezed by the AFM tip.

  The same thing can happen for bulk liquids (i.e., liquids that are not confined to nanometer spaces), but only at very fast speeds. Our finding was that at the nanoscale, these dramatic changes happened at very, very slow speeds. But how is that possible? Molecules in a liquid move at incredible speeds, much faster than our AFM tip. They should have plenty of time to accommodate the approaching tip, and the liquid should remain liquid. The answer is—you guessed it—cooperativity. Once water is squeezed to just a few molecular layers between the surface and the tip, it becomes difficult for the water molecules to move out of the way of the approaching tip. Due to the confinement, the molecules don’t have the freedom of motion they enjoyed in the bulk. When confined to the nanoscale, many molecules have to move in concert to create a hole into which the tip will move—water molecules have to cooperate to move out of the way. What is truly remarkable about these results is that it takes water molecules extremely long, of the order of seconds, until they randomly happen to move in a coordinated manner to create a hole. That is a million billion times longer than the average time between water molecule collisions. A crude calculation indicates that thirty to forty molecules—not very many—would have to be involved in the collaborative motion to create such a long time scale. Cooperativity can create not only sharp transitions, but also large changes in time scales, making even molecular processes take seconds or even minutes.

  Molecular Switching

  Amphiphilic molecules, such as lipids and detergents, suddenly form micelles once they reach a critical concentration. This results in a sharp change in osmotic pressure. In our confined-water experiments, we saw a rapid switching from liquid-like to solid-like behavior in response to a small increase in squeeze rate. The occurrence of rapid changes at critical values for certain control parameters (concentration for micelles, speed for confined water) is a signature of cooperative behavior.

  Cooperative behavior is not restricted to molecular biology. It is a ubiquitous, but underappreciated facet of our world. For example, some economists have argued that the financial crisis of 2008 and others before it, including the Great Depression of the 1930s, were the result of a cooperative failure of banking. This is how it goes: There is always a low rate of bank failures. As long as that rate is low, the overall financial system is relatively unaffected. But if banks fail at a rate exceeding a certain critical threshold, the interconnectedness (cooperativity) of banks pulls the whole market into the abyss. Thus, what looks like another, albeit somewhat larger, fluctuation in the financial market suddenly leads to rapid, profound change. This is cooperativity at work.

  Cooperativity leads to switching. Yesterday everything was fine; today the economy has crashed. A second ago, lipid molecules were happily floating around, and then, suddenly, they form micelles, and osmotic pressure drops precipitously. Water acts like a liquid, but squeezed above a slow critical rate, it suddenly bounces like rubber. A DNA double helix was fine a second ago, but suddenly it catastrophically unzips when it is heated. The San Andreas fault was quiet an hour ago, and now all hell breaks loose. We should not underestimate cooperativity!

  Despite some of the negative examples of its effects, cooperativity is crucial for the function of living cells. Changes in a molecule’s shape are driven by cooperativity of many bonds, and the shape change, often sudden and dramatic, can be driven by a relatively small external change. This behavior allows for the creation of molecular switches, molecules that can effect large changes in response to small causes, such as the binding of a small molecule. This in turn allows the creation of molecular circuits, which control the activity in a cell. In electronics, a transistor is an element that allows a small change in a voltage to control a large current. Transistors are electronic switches, and they are the root of modern electronics, from radios to computers. Similarly, molecular switches in cells serve as control units to make cells work. They work on the principle of cooperativity, which in turn is made possible by the use of many small bonds, many of them of entropic origin.

  All Energies Are Created Equal—At Least at the Nanoscale

  Thermal motion, entropic forces, and cooperativity—some of the strange properties of nanoscale systems—are important for our understanding of life at the molecular scale. Another, truly astonishing property of the nanoscale is the key to understanding how the coordinated activity of cells is generated. This property relates to how energy is transformed from one form to another. One of the most astonishing features of life is that living beings can take energy from food and turn it into directed motion. Past generations attributed this magical feat to life forces. However, the continued search for physical explanations has brought scientists to the molecular scale. Proteins, DNA, RNA, and other large molecules inside cells seem to be the fundamental functional units that make the cells work. Some of these molecules must be able to convert energy from one form to another; they must be acting like molecular machines.

  Machines are energy-conversion devices—a car engine, for example, converts chemical energy into kinetic energy. However, a car engine sitting in a pool of gasoline with no connections would not jump to life. Yet, the molecular machines in our cells do just that: Pluck a molecular machine, such as myosin, out of a cell, give it some chemical fuel (called ATP in cells), and it will “come to life.” Molecular machines are autonomous machines. Why can molecular machines work autonomously, while our familiar, macroscopic machines cannot?

  It turns out there is something very special about the nanoscale when it comes to converting different forms of energy into each other. Intriguingly, only at the nanoscale are many types of energy, from elastic to mechanical to electrostatic to chemical to thermal, roughly of the same magnitude (Figure 4.6). This creates the exciting possibility that the molecules in our bodies can spontaneously convert different types of energy into one another. Molecules and small, nanoscale particles can have substantial fluctuations in energy as they take energy from the molecular storm (thermal energy), use it to convert, for example, chemical energy to electrical energy, and then release the energy again into the surrounding chaos. By contrast, smaller structures, such as atoms or nuclei, have binding energies that are too large to allow thermal energy fluctuations, unless the temperature (along with thermal energy) is extremely high (thousands or millions of degrees). At such high temperatures, molecules are unstable and the formation of complex structures needed for life is impossible. On the other hand, at scales much larger than a nanometer, mechanical and electrical energies are too high to be subject to thermal fluctuations. At this scale, everything becomes deterministic, and objects do not spontaneously change shape or assemble themselves—which are attributes needed for life.

  FIGURE 4.6. Electrostatic energy, chemical bond energies, and elastic energies all converge at the nanoscale (10−9 meters), where they meet thermal energy (the molecular storm) at room (or body) temperature. This confluence of energy scales at the nanoscale explains self-assembly and the possibility of molecular energy conversion devices and machines. Reprinted with permission from Rob Philips and Stephen R. Quake, “The Biological Frontier of Physics,” Physics Today 59 (May 2006): 38–43. © 2006, American Institute of Physics.

  Thus, the nanoscale is truly special. Only at the nanoscale is the thermal energy of the right magnitude to allow the formation of complex molecular structures and assist the spontaneous transformation of different energy forms (mechanical, electrical, chemical) into one another. Moreover, the conjunction of energy scales allows for the self-assembly, adap
tability, and spontaneous motion needed to make a living being. The nanoscale is the only scale at which machines can work completely autonomously. To jump into action, nanoscale machines just need a little push. And this push is provided by thermal energy of the molecular storm.

  But doesn’t the molecular storm always lead to chaos, as suggested in the discussion of the second law of thermodynamics in Chapter 3? The answer would be yes if the molecular machines of living cells were just any old molecules—but they are not. They are clever little machines that can sift order out of chaos. How? Let’s find out.

  Richard Feynman quotation by permission of California Institute of Technology, Engineering and Science Magazine. K. Eric Drexler quote courtesy of K. Eric Drexler.

  * Christopher Toumey, “Reading Feynman into Nanotechnology: A Text for a New Science,” Techné 12, no. 3 (fall 2008): 133–168. Tourney ascribes the quote to Paul Shlichta, then of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena.

  ** Richard Feynman, “There’s Plenty of Room at the Bottom,” Caltech Engineering and Science 23 (February 1960): 22–36, available at www.zyvex.com/nanotech/feynman.html.

  5

  Maxwell’s Demon and Feynman’s Ratchet

  Now let us suppose that . . . a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.

  —JAMES CLERK MAXWELL, THE THEORY OF HEAT

  The Moving Finger writes; and, having writ,

  Moves on: nor all thy Piety nor Wit

  Shall lure it back to cancel half a Line,

  Nor all thy Tears wash out a Word of it.

  —OMAR KAYYAM, 1048–1131

  JAMES CLERK MAXWELL (1831–1879) LEFT BEHIND A distinguished scientific legacy. He unified electricity and magnetism, discovered electromagnetic waves and explained the nature of light, solved the riddle of Saturn’s rings, developed modern color theory, laid the foundations for engineering control theory, and cofounded statistical mechanics. In addition to all this, he invented a demon.

  The Scottish physicist’s work on thermodynamics and statistical physics, The Theory of Heat, remains an example of clarity. Describing the second law of thermodynamics, Maxwell wrote: “One of the best established facts in thermodynamics is that it is impossible in a [closed] system . . . which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up.”

  This quote presents as clear a definition of the second law as we could hope for. The law forbids the creation of temperature or pressure differences in a uniform medium, unless work is expended to create the difference. Yet at the end of the quote, Maxwell included a caveat: As long as we deal with many molecules (“in mass”) and have no way to look at them individually, the second law is true. But what if we could look at molecules individually? Maxwell continued: “But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own, would be able to do what is presently impossible to us.” Could such a being violate the second law?

  Maxwell’s Demon

  The second law was invented to explain certain limitations of machines: It was well known that steam engines wasted a lot of energy—most of the energy supplied in the form of coal was wasted as heat and not turned into mechanical work. Physicists and engineers from the late 1700s to the mid 1800s were preoccupied with improving the efficiency of engines. The efficiency is the ratio of useful energy generated to the energy input in the form of fuel. For example, a car engine has an efficiency of about 25 percent. Only 25 percent of the gasoline we put into the tank is used for moving the car or running the electrical systems; the rest is lost as heat. Is there a limit to the efficiency of engines? Could a 100 percent efficient engine be made, at least in principle?

  The new science of thermodynamics, and the understanding that heat was a form of energy, led Helmholtz to his universal law of energy conservation. Helmholtz convincingly demonstrated that motion and growth of a living being had to be powered by chemical fuel—food. In this sense, a living organism was similar to an engine. Like an engine, it converted a high-quality form of energy to both motion and heat. Again the question arose: Was there a limit to the efficiency of life’s engines?

  By the beginning of the twentieth century, it was becoming clear that the engines of life operated at the molecular scale. How can we understand such machines, and how does their operation relate to the macroscopic machines of our everyday experience?

  Macroscopic machines—car engines, power plants, etc.—exploit gradients, that is, differences in temperature or pressure, to convert fuel into motion. This important observation was first made by a young French military engineer, Sadi Carnot (1796–1832), in 1824. Carnot laid the groundwork for modern thermodynamics when he realized that the efficiency of engines could not be increased to 100 percent, even in principle, but instead was limited by the temperature gradient they exploited. In other words, the hotter the fire, and the colder the surroundings, the more efficient a machine could become. When the inside of an engine approaches the temperature of the surroundings, no more work can be done by the engine, and the efficiency goes to zero. We then have the situation Maxwell described in his definition of the second law.

  In living cells, temperatures and pressures are uniform—there is no combustion chamber or pressure reservoir. There are no temperature or pressure gradients. According to Carnot, no engine should be able to operate in our bodies. The second law of thermodynamics allows us to extract work from gradients, at the cost of creating waste heat and the leveling of the gradient. The result is equilibrium—a state of uniform temperature and pressure, a state from which no further work can be extracted. How can molecular machines extract work from the uniform-temperature environment of cells without violating the second law of thermodynamics?

  When the second law was formulated in the nineteenth century, physicists were not certain if it was an incontrovertible law of nature. What was the basis of this law? Physicists like to employ many methods to get to the bottom of things: experiments, theoretical calculations, and gedankenexperiments. Gedankenexperiment is a German word, sometimes used in English, meaning “thought experiment.” It is a hypothetical situation, which can only exist in thought and is a stress test for physics theories. The idea is either to create a paradox—a contradiction between different physical theories—or to see how far you can stretch a theory or an experimental result into a realm that is inaccessible to the real world. Famous thought experiments include Schrödinger’s cat (which showed the absurdity of some interpretations of quantum mechanics); Galileo’s deduction of constant acceleration during free fall, irrespective of the mass of the falling object (Galileo never threw objects off the Tower of Pisa—he inferred what would happen from rolling balls down inclines); Newton’s cannonball (which showed that the motion of celestial objects is related to the falling of objects on Earth); and Maxwell’s demon, the little creature who could transfer heat from cold to hot.

  FIGURE 5.1. Maxwell’s demon sorts fast-moving molecules into the left chamber and slow ones into the right chamber by controlling a small trap door. After a while, he succeeds in creating a temperature difference between the chambers without expending work, thus seemingly violating the second law.

  Maxwell’s demon, which he devised in 1867, was a tiny
hypothetical creature who controlled a little door separating two gas-filled chambers, which initially have the same average temperature (Figure 5.1). The job of the demon was to separate gas molecules into fast and slow molecules. If, for example, a fast molecule approached the demon’s door from the right, the demon would let it through the door to the left chamber, but if it was slow, he would not. Conversely, he was happy to let slow molecules pass from the left to the right chamber, but not fast ones. Soon, the demon had sorted fast molecules into the left chamber, while leaving all the slow ones in the right chamber. Starting from a uniform-temperature system, the demon had created a temperature gradient—making one side cold and the other side hot (remember that the temperature of a gas is directly related to the speed of the gas molecules). This temperature gradient could now be used to do work if a little turbine were placed into the demon’s door. The result would be to extract useful work from a uniform-temperature system, in clear contradiction of the second law. On the other hand, such a molecular Maxwell demon would be just what is needed to explain molecular machines! Are our cells full of molecular Maxwell demons? Does life, deep down, violate the second law?