Life's Ratchet: How Molecular Machines Extract Order from Chaos (18 page)

The scientist who inspired the creation of the AFM was John Pethica, of the University of Oxford, who fifteen years later became my postdoc advisor. Gerber called him the godfather of the AFM. (Which makes me, by scientific genealogy, the nephew of the godfather of the AFM, which probably is not much to brag about.) At Oxford, under the benevolent, inspirational, and deliberately hands-off guidance of John Pethica, my friends Steve Jeffery, Ralph Grimble, Ahmet Oral, Özgür Özer, Chandra Ramanujan, and I learned how to be innovative scientists. We built and used STMs and AFMs (actually combining the two) and measured the nanomechanics of atoms on crystal surfaces and molecules in liquids. It was a good time.

John is an easygoing person, but he is an exacting scientist. When I visited Oxford for my interview, an envelope with instructions was waiting for me at the hotel. John had written “Dr. Peter Hoffmann, Esq.” on the envelope. I didn’t know that I was an Esquire, but it showed John’s respect for everybody, even a lowly postdoc looking for a job. When my wife and I finally arrived a few months later, it was the beginning of summer. John
typically disappeared for extended periods, only to reappear with a bagful of new ideas. After John’s return from his mysterious summer travels, I got into one of the typical—as I soon realized—conversations with him. These conversations always involved new ideas, connections, and recent publications. Listening to John, I would often be reduced to nodding and saying, “aha, yeah, mmmh,” only to scramble back to the office to look up the papers he was talking about.

John is particularly interested in how we make the transition from the noisy but reversible world of the atom, to the more ordered but typically irreversible world of macroscopic objects, a passion I inherited. In one experiment, we measured the loss of energy an oscillating AFM tip experiences when it interacts with randomly oscillating atoms on a surface, in a process we called
atomic-scale energy dissipation
. For small numbers of atoms involved, the motions of the atoms seemed structurally reversible. Each time we lowered the tip, we measured the same force curve. Yet when we pushed harder, we passed the threshold to permanent rearrangement of atoms. When too many atoms were involved, there were too many possible configurations, and the system did not find its way back to its original arrangement. At this point, our experiment had passed from the microscopic to the macroscopic.

The interaction of atoms and the myriad possibilities of atomic arrangements in modestly large systems is also of great importance in molecular biology, as we will see. So is the transition from noise to order. Small nanoscale systems, such as the molecules in living cells, are subject to influences and laws that are quite different from what we encounter in our familiar, macroscopic world.

When Feynman pushed for the creation of atomic-scale technology in his talk, he also pointed out unique challenges that come with building machines out of just a few atoms. Indeed, since nanoscience has become a serious science, the most interesting feature has been that tiny things play by different physical rules. This sometimes creates problems and, other times, opportunities, but it is a source of continuing fascination to nanotechnologists.

When systems are shrunk to the nanoscale, effects that play little or no role at the macroscale suddenly become important. In his famous lecture, Feynman mentioned a few of these: problems of lubrication—because he surmised that the effective viscosity of any lubricant is much higher at a small scale—and the observation that at small scales, things are more likely to stick together. These problems are due to two more general effects that are common at the nanoscale: the graininess of matter and the problem of interfaces.

Matter is grainy; it is made of atoms, molecules, and larger grains, such as small crystals. On a large scale, this graininess of matter averages out. Following the laws of statistical mechanics and
continuum physics
(in continuum physics, we ignore the fact that matter is made of particles, but treat it as a smooth continuum), we can determine such average quantities as Young’s modulus (which determines how springy a solid material is) or viscosity (how resistant to flow a liquid is). But once we reduce the size of a system to just a few, ten, or one hundred molecules, these averaged quantities become meaningless, and measurements of mechanical or electrical properties show jumps, rather than smooth, averaged-out changes. In my lab, we measure the graininess of simple liquids, such as water. When I measure the mechanical properties of water, it doesn’t matter if I take a bucketful of water, or a few cubic centimeters from a syringe. A cubic centimeter of water contains 3 × 10
²²
water molecules (that’s a 3 with 22 zeros behind it). Adding or subtracting a few million or billion molecules from such a giant number of molecules is not going to change the average properties of the liquid. In our lab, however, we can measure the mechanical properties of much smaller numbers of water molecules. We can squeeze water between an AFM tip and a surface until the water layer between the tip and surface is a single molecule thick (however, since the tip has an area of about 50 nanometers by 50 nanometers, the single molecule layer under the tip contains about 25,000 molecules). Now, adding or subtracting single layers of molecules makes a huge difference to the mechanical properties of the liquid. As a result, when we push from a layer 6 molecules thick to one 5 molecules thick, and then from 5 to 4, and so on, the stiffness and the apparent viscosity of the layers alternate between high and low values.

These experiments also illustrate the other nanoscale problem Feynman was talking about. When we make something smaller, its surface
to-volume ratio increases. A golf ball has a greater surface-to-volume ratio than does a bowling ball. Shrunk to the nanoscale, this ratio would be more extreme. As volumes become small, surfaces start to dominate and the forces that are important at the macroscale become irrelevant at the nanoscale, and vice versa. At the macroscale, forces associated with mass, such as gravity and inertia, dominate. Surface forces, such as stickiness, are usually unimportant, unless specifically engineered, as in a glue. For example, in a baseball game, inertia (when the bat hits the ball) and gravity (when the ball comes back down) dominate. But, typically, the baseball does not stick to the bat. In a game of nanobaseball, however, inertia would be unimportant, as the ball would weigh next to nothing. Ditto gravity. But the relatively large surface area compared with the tiny bulk of the nanobaseball would make it difficult to get the nanobaseball off the nanobat. This is an example of one peculiar property of nanoscale systems: profound changes in behavior depending on the size of the system.

Of course, not everything at the nanoscale sticks together. Otherwise, we’d be in trouble. Our cellular components have to be able to stick and separate when needed. This is achieved through a careful balance of forces between molecules and the surrounding salty water. In a vacuum, in the absence of water, most surfaces simply tend to stick.

At the nanoscale, there are some peculiarities that Feynman did not mention: quantum-mechanical effects, the importance of thermal noise and entropy, cooperative dynamics, large ranges of relevant time scales, and the convergence of energy scales. A daunting list of strange properties. We will discuss these peculiarities through different examples in the remaining chapter.

Most books on nanotechnology will focus on the strange quantum-mechanical effects we encounter at the atomic scale. I alluded to some of these in the discussion of tunneling. Indeed, a large part of nanotechnology relies on new quantum-mechanical effects. However, for molecular biology, these are almost irrelevant. Essentially all of molecular biology can be explained using classical physics (except bonding between atoms, which
requires quantum mechanics). Many of the more interesting quantum-mechanical effects in nanosystems are completely destroyed by thermal motion. Therefore, much research on quantum computing, spintronics, or other fancy new quantum electronics is done at low temperatures—much too low for any living system.

By contrast, thermal motion (or, what physicists like to call thermal noise), already discussed in the previous chapter, is of great importance in biology and most of room-temperature nanotechnology. So are questions of size dependence, cooperative dynamics and time scales (which go hand-in-hand), and the convergence of energy scales. To understand what these things are, and how they influence systems at the nanoscale, let us consider the important question: How can we make stuff at the nanoscale?

Feynman believed machines and structures at the nanoscale could be assembled by some kind of demagnifying technology that could turn a macroscopic template into a small pattern using electron or ion beams (now a reality in devices called electron-beam writers or focused-ion beams) or by building machines that make smaller copies of themselves ad infinitum until the nanoscale is reached (not yet a reality). Both of these approaches could be described as top-down: They start with a large template or machine and then miniaturize down to the nanoscale.

This top-down approach is still used in building electronic devices, such as computer memory or processors. Life, however, works differently: Plants, animals, and all other living organisms are built from the bottom up. We are all assembled atom by atom, molecule by molecule.

A common fallacy that people hear over and over is that our DNA contains all the information needed to make a human being. Nonsense! The amount of information contained in our DNA is staggering, but it is not nearly enough to specify each molecule’s or cell’s location, or even the shape of an organ. Rather than being a blueprint (as DNA is often mistakenly called), DNA is more like a cooking recipe. When I make a cake, I don’t have
to specify where each starch or sugar molecule goes. I just follow the instructions, and the molecules go where they are supposed to. Much of the information to make a cake or a human being is contained in the laws of physics and chemistry. Molecules “know” how to put themselves together.

This self-assembly of molecules is ubiquitous throughout nature and is a major research area in nanoscience. If we could coax molecules to arrange themselves into any structure we want—much like what we see in living organisms—we could make new devices incredibly cheaply, without million-dollar ion or electron-beam writers. We could simply put everything in a pot and stir. But it’s obviously not that simple.

One of my recent graduate students, Venkatesh Subba-Rao, likes to tell the following anecdote: He once listened to a talk by a visiting scientist about structures in liquid crystals. When Venkatesh asked him the reason why these structures arise, the scientist answered, “They minimize free energy!” Since then, if I ask my students why this or that is happening in their experiments, and they don’t know, this is their stock answer. Most of the time it’s correct. Everything that happens in nature minimizes free energy. But this answer does not tell us much. It is almost the scientific equivalent of “because God made it so.” A more useful answer would include the types of energies that make up the free energy of a system. An even more useful answer would identify how molecules move around and how energy is transformed as the system minimizes its free energy. Remember, free energy is the difference between the
total
energy of the system and
unusable
thermal energy, leaving the
usable
, free part of the energy. Unusable energy is the product of temperature and entropy. When we minimize free energy, we can either lower the total energy, increase the amount of unusable energy, or both. In self-assembly, all of these possibilities come into play.

One of the most familiar and most stunning examples of self-assembly is the aforementioned snowflakes. Snowflakes are crystals of water ice. If you ask my students why snow crystals form, they would answer that it minimizes free energy! And, indeed, as we saw in
Chapter 3
, there is a critical temperature below which the lowering of the free energy leads to the formation of snow flakes, while above that temperature, free energy is minimal when water remains liquid. Yet, we would like to have more information. Snowflakes are such beautiful, intricate structures, and
explaining their structure as a reduction in free energy seems like a copout. The result is a reduction in free energy, but how does it happen? How does the structure form?

The creation of snowflakes is a perfect example of the combination of chance and necessity, entropy and energy. The six-sided symmetry of snowflakes is a macroscopic representation of the underlying molecular symmetry of water ice. Water molecules like to arrange themselves in a hexagonal (six-sided) pattern, like a three-dimensional puzzle. Different external conditions of moisture, temperature, and pressure influence the growth of the crystal, leading to different branching patterns. Since all six sides of the growing crystal are subjected to the same conditions at any given time, they grow more or less (although not exactly) in the same pattern, creating the beautiful symmetry of a snow flake.

The growth of a snowflake shows how complexity and beauty can arise from cold physical principles (no pun intended). Freezing is accompanied by a release of heat. This heat has to be removed (increasing the entropy of the environment) to allow the water to freeze. Thus ice crystals will grow fastest at those places where heat is removed the fastest, namely, at the endpoints of any spiky features. Spikes, however, are already the result of rapid growth. This creates positive feedback: The locations on a crystal that grow the fastest become spiky, which allows better heat transfer from these locations, which makes them grow faster, and so on. The result is what physicists call an instability, leading to the formation of long, spiky features. But there is an opposing force as well: The local temperature also depends on the spikiness of the crystal; spikier parts (those with higher curvature) melt at lower temperatures, thus reducing the temperature difference between spiky parts and the environment. This reduction in temperature difference slows heat transfer, counteracting the effect of the exposure of the spikes. Once a spike becomes too pointy, growth will slow down—a negative feedback that counteracts the positive feedback. When this happens, the crystal develops branches. The combination of these two tendencies, to become spiky and to develop branches, leads to the dendritic growth of snowflakes.