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

by Hoffmann, Peter M.

  Soap, detergents, and lipids are all examples of linear molecules that have one hydrophilic and one hydrophobic end. But what makes molecules hydro phobic or hydrophilic in the first place?

  We know that oil and water don’t mix (unless you add eggs). Why? Water is a peculiar liquid, quite unlike any other liquid in the universe. For example, compared with liquids of similar molecular construction, water has to be heated to a much higher temperature to melt or boil. It also has the curious property that its solid form (ice) is lighter than its liquid form; this is why ice cubes float on your drink, rather than sink. For most other substances, the opposite is true: The liquid is lighter than the solid. All these strange properties of our favorite liquid are mainly due to hydrogen bonds. Hydrogen atoms of water molecules form strong bonds with oxygen atoms of neighboring water molecules, forming “bridges” between the molecules. Because these hydrogen bonds in liquid water are stronger than we would expect, water does not evaporate as easily as other liquids.

  Hydrogen bonds arise because in each water molecule, which is made up of one oxygen atom and two hydrogen atoms, the oxygen “steals” the hydrogen’s electrons. The leftover hydrogen ions are positively charged, while the oxygen atom, now having two excess electrons, is negatively charged. When two neighboring water molecules come close to each other, the positively charged hydrogen on one molecule is attracted to the negatively charged oxygen on a neighboring water molecule. In liquid water, these hydrogen bonds form and break continuously at a high rate. They are but fleeting couplings. Yet, they make a profound difference for the stability of the liquid and lead to its high boiling temperature. In ice, the hydrogen bonds are essentially permanent. They are also directional, that is, water molecules can only form hydrogen bonds in ice if the molecules are arranged in a certain way. This arrangement leaves large, molecule-sized voids in the ice structure, making ice less dense than liquid water. Hence, ice floats on water.

  Nonwater molecules can also form hydrogen bonds with water, as long as they have some negatively charged parts. This includes many acids, sugars, and alcohols (a good thing—it would be a shame if alcohol and water didn’t mix). Other molecules, while not forming hydrogen bonds, are still quite happy in water, because they can accommodate their charges by surrounding themselves with water molecules. This is what ions do, and it explains why salt dissolves in water. Oils do not have any charges; they are a neutral bunch of molecules. Thus water cannot form hydrogen bonds with oil; nor are there any charges to accommodate. Oil is a molecular party-pooper—not very sociable. If oil is placed into water, water molecules form a kind of cage around an intruding oil molecule, trying to maximize hydrogen bonding to their own kind. The cage structure they form induces order in the water and therefore decreases entropy. A decrease in entropy leads to an increase in free energy, which is a bad thing. Trying to put oil into water comes at high (entropic) cost. What’s an oil molecule to do? Get out of the water and find its own kind. Soon enough, oil molecules form droplets, and eventually the droplets coalesce and leave the water all together. Oil and water separate.

  The hydrophobic force, which is responsible for the separation of oil and water, is therefore another example of an entropic force. While the hydrophobic force separates oil from water, it also provides a powerful drive for oil molecules to come together and coalesce. In water, hydrophobic molecules attract each other. This attraction of hydrophobic molecules is an important mechanism for self-assembly. One tasty example of this is cheese. Cheese can be made by adding salt or acid to milk or, in a more modern approach, by adding rennin. Each method leads to essentially the same result, but interestingly, the physics of how each works is different. About 80 percent of the protein in cow’s milk is in the form of casein, a phosphorus-containing protein. Casein molecules are hydrophobic, but also negatively charged. Their hydrophobic nature means that if they could get close enough to each other, the hydrophobic force would make them stick to each other. However, their negative charge keeps them apart. Now comes the cheese maker. Adding salt provides free positively and negatively charged ions to the milk. The positively charged ions crowd around each negatively charged casein molecule and shield its charge. Now casein molecules can approach each other and start to stick, forming cheese.

  How about acid? Acid increases the amount of hydrogen ions in the milk, changing the milk’s pH. The positively charged hydrogen ions stick to the casein and neutralize it. Again the casein molecules start to stick and cheese is made.

  Adding salt or acid, of course, affects the taste of the cheese, making it taste salty or sour. Sometimes this is not desirable. This is where rennin comes in. Rennin is an enzyme, a protein that promotes a certain reaction that cuts off the charged part of the casein. Without its charged part, the casein molecules are quickly forced together by the hydrophobic force.

  The importance of hydrophobic forces is not limited to the kitchen. Hydrophobic forces play a crucial role in shaping the very molecules that keep us alive, as we will discuss in the following section.

  Molecular Origami

  A life-or-death example of a molecular self-assembly process is the folding of large biological molecules, especially proteins, into their active shapes. Proteins are made of long chains of chemical units called amino acids, strung together like pearls in a necklace (Figure 4.3). On Earth, every protein in every living organism uses just twenty different amino acids (there are many more amino acids that could in principle be used, but nature has decided to use only these twenty). The particular sequence of amino acids in each protein is encoded in the cell’s DNA. Different amino acids have different affinities, courtesy of the hydrophobic force. These tendencies to attract or repel determine the particular, coil-like shape of a protein. Get the folding of a protein wrong, and you could end up with Alzheimer’s disease, mad cow disease, or cystic fibrosis—examples of diseases in which certain proteins fold into nonfunctional or even dangerous shapes, as a result of mutations or other unknown reasons.

  FIGURE 4.3. Amino acids are molecules with identical backbones, but different side chains. The backbones can link together by peptide bonds, forming a peptide chain. This chain is pushed around by the molecular storm until it folds into a stable structure with hydrophobic side chains in the center (stars) and hydrophilic ones on the outside.

  How does a protein find its optimal shape? When a protein is made by the molecular machinery of the cell, it initially comes out as a long string of amino acid beads. Some of these beads are destined to bind to each other, but initially the amino acid string wiggles around aimlessly, pushed by the molecular storm of bombarding water molecules (Figure 4.3). A molecule does not “know” how to fold—it needs to find its shape through random changes in its shape.

  Even a small protein can fold into innumerable possible shapes, the number of which far exceeds the number of atoms in our universe. The energy of the protein depends on all the twists and turns of its chain and the contacts between amino acids along the chain. If we were to measure the twists of the chain (by assigning angles to each link of the chain), we could calculate the energy of the protein for any possible shape. Some shapes would have larger energies, some lower. The greatest number of amino acids bind together in the lowest-energy shapes. As shown in Figure 4.3, in the lowest-energy configuration, the hydrophobic amino acids are safely tucked inside, while the hydrophilic amino acids are found on the outside of the coil.

  Imagine a map representing the energy of any possible shape of a protein. The coordinates of the map (north, west, south, and east) represent the angles of the links, and the topographic height, at each coordinate, represents the corresponding energy. This creates what physicists call the energy landscape of the protein. Figure 4.4 shows possible shapes of a short protein chain with the associated energy shown as the height on the landscape. The protein shown in this schematic has just four links, while real proteins consist of thousands of amino acid links, making the energy landscape fantastically complicated. The
different links of the protein are randomly pushed around by the molecular storm, causing the protein to continuously change shape. This ongoing change in shape is represented by the white path across the landscape. Each location along the path corresponds to a specific shape of the protein (some examples are shown in the figure).

  Sometimes the molecular storm pushes the protein into an uncomfortable, high-energy shape (a hill in the landscape); quickly, the protein relaxes down the hill to a more comfortable configuration. When the protein shape approaches the optimal shape, its energy reduces and it falls into an energy funnel in the landscape. Further reduction in energy draws the protein to the bottom of the funnel, where it assumes its lowest-energy configuration and optimal final shape.

  As the molecular storm pushes the protein around, the succession of different protein shapes can be represented as a meandering path across the (abstract) energy landscape (the white path in Figure 4.4). Physicists talk about a diffusion across the energy landscape (diffusion here means random motion). Without the molecular storm, the molecule would be stuck in a fixed shape and would never find the optimal shape that minimizes its free energy. The diffusion across the energy landscape is a search that eventually leads the protein molecule to its optimal, lowest-energy shape. This optimal shape of the protein determines the function of the protein. Without its three-dimensional shape, a protein is nothing. The particular sequence of amino acids making up the protein has meaning only as far as it determines the protein’s 3-D shape.

  For some proteins, the search for the optimal shape would simply take too long. For such proteins, life invented smaller proteins that chaperone, or guide, the larger molecule toward its proper shape. These chaperonin molecules serve as local molds that preshape parts of a protein and help it find its way along the energy landscape more quickly.

  FIGURE 4.4. The energy landscape of folding a protein.

  Protein folding is possibly the best example of how physical laws, randomness, and information—provided by evolution—work together to create life’s complexities. The amino acid sequence of a protein is determined by the cell’s DNA, according to the genetic code. This information evolved over billions of years. But the information in our DNA only encodes the amino acid sequence; it does not encode the final 3-D shape of the protein. The 3-D shape is a result of the energy landscape, which is determined by physical forces (hydrophobic forces, electrostatic forces, bending energies, etc.) acting on the particular sequence of amino acids. This shape also depends on external conditions (pH, temperature, ion concentration). Thus a large part of the necessary information to form a protein is not contained in DNA, but rather in the physical laws governing charges, thermodynamics, and mechanics. And finally, randomness is needed to allow the amino acid chain to search the space of possible shapes and to find its optimal shape.

  Schrödinger’s Riddle

  Erwin Schrödinger wondered how life’s molecules, especially DNA, could remain stable under the onslaught of the molecular storm. He postulated that stability is provided by strong chemical bonds. He was partly right—there are strong chemical bonds along the backbone of both DNA and proteins—but he missed the most interesting point: The functional structure of the large molecules in cells is not held together by a few strong bonds, but by many relatively weak ones, especially hydrogen bonds, but also hydrophobic interactions and so-called disulfide bridges (bonds between sulfur atoms attached to sulfur-containing amino acids in a protein). If the unique coil shape of a protein and the double helix of a DNA strand are held together by weak bonds, why are these shapes so stable?

  If all bonds in the molecules of living organisms are too strong, there can be no motion or change. If they’re too weak, there can be no stability. The key is to find a middle ground between stability and flexibility. If things are too stable, they cannot function—imagine a car with lead wheels. If they are too flexible and fragile, they cannot function either. The solution that life has found is to capitalize on the cooperativity of many bonds. As we saw earlier, many weak bonds cooperating make a molecule very strong, while individually, the bonds can easily be broken, allowing for rearrangement when needed.

  How can bonds be cooperative? In the aforementioned micelle, molecules act cooperatively to form a larger structure. If we replace molecule with bond, we have a similar situation. Once a DNA molecule is formed, the two strands of the DNA are held together by numerous hydrogen bonds. A single hydrogen bond can easily break at room temperature. The average lifetime of a hydrogen bond in water at room temperature is in the picosecond range (that is, a thousandth of a billionth of a second). However, if we have many hydrogen bonds working together, the spontaneous separation of two DNA strands would require a simultaneous, cooperative breaking of a large number of bonds—and this will not happen spontaneously. Single bonds may temporarily break in a DNA molecule, but they will quickly reform—forced back together by the presence of neighboring hydrogen bonds, which keep the DNA molecule in shape. In living cells, DNA retains its double-helix structure when the molecule is not in use. However, when the information contained in DNA needs to be read out, the double helix must be opened up. This is achieved by specialized proteins, which locally lower the barrier to undo a number of hydrogen bonds and, like a zipper, unzip the DNA where needed and then close it back up (see Chapter 7 for more on this).

  Stability in DNA is also actively achieved by repair enzymes. If for some reason a part of the DNA molecule becomes corrupted, the repair enzymes will fix the mistake, using an adjacent section of the molecule that is undamaged as a chemical template to repair the corrupted part. The stability of DNA is therefore the result of bond cooperativity, complementarity of the two strands, and active repair by the cell’s machinery.

  The situation is similar for proteins. A protein’s shape is held together by hydrophobic, hydrogen, and disulfide bonds, again cooperatively stabilizing the shape of the protein. The protein’s particular amino acid sequence is chosen by evolution such that a protein is just flexible enough to do its job (we will find out in the next chapters what kind of jobs they do) while keeping its overall shape. If a protein does get out of shape, the cell quickly discards it and recycles it back into its components.

  The Emergence of Long Time Scales: Forcing Water Molecules to Cooperate

  Cooperativity is almost inevitable when you have many entities interacting with each other. I found this out in my own research when my students and I looked at simple liquids—water or oil—squeezed down to a few nanometers. While solids, in the form of crystals, have long-range order (atoms are arranged in an orderly pattern over large distances throughout the crystal), liquids have short-range order: If you were sitting on a water molecule in a pool of liquid water, you would see neighboring molecules at an average distance of 0.25 nanometer (nm). These neighbors would move around, but on average, there would be a cloud of water molecules surrounding you at this distance. Beyond this distance, the next-nearest neighbors would feel the presence of your neighbors, and you would see an excess of molecules at an average distance of 2 × 0.25 nm = 0.5 nm. However, because of the incessant motion of all molecules, this excess of molecules at 0.5 nm would be a little bit more smeared-out than the excess of molecules at 0.25 nm. Going even further, there would be an even more smeared-out excess at 0.75 nm and so on, until at a distance of five to six molecular diameters, thermal motion would have smeared out any semblance of order, and water molecules could be found with equal probability at just about any distance.

  In my laboratory, we are using a different method to probe the short-range order of liquids. When liquids encounter a solid surface, they arrange themselves into molecular layers. The first layer, closest to the surface, is well defined. There is a high probability that we find water molecules at 0.25 nm from the surface. The second layer is a little bit more diffuse, and as we move away from the surface, the layers become more and more smeared-out, until order vanishes altogether after about five or six layers, as discusse
d above. This layering can be measured by an AFM. In our lab, we immerse an AFM cantilever and probe tip into water and then slowly move the tip toward the surface. To measure the response of the intervening water, we oscillate the tip at an amplitude (size of oscillating motion) of less than 0.1 nm—the diameter of a single hydrogen atom! Monitoring the amplitude, which changes slightly as we push through the water layers, we measure the “springiness” of the water layers (or “stiffness,” as we call it), that is, the capacity of water to push back at the tip if we push the tip against it. The stiffness fluctuates up and down with a period of 0.25 nm—the size of the water molecules—illustrating the molecular graininess of the liquid. An example of such a measurement is shown in Figure 4.5.

  In 2006, my post-doc Shiva Patil and my student George Matei were performing such measurements on a silicone oil, octamethyl-cyclo-tetrasiloxane. OMCTS has large molecules (if you are a nanoscientist), with diameters of 1 nm. Together with the stiffness, we also measured the damping of the liquid layers. While the stiffness tells us how much the liquid layers spring back into their original shape (i.e., how much energy they store), the damping tells us how much energy is lost as we push on the layers. The damping also fluctuated with the spacing between the tip and the surface, with the same period as the stiffness. Looking at the data, Shiva noticed something peculiar: The damping fluctuation wasn’t always in line with the fluctuations of the stiffness. Sometimes the peaks in the damping lined up with the peaks in the stiffness, but sometimes they were switched—peaks in damping coincided with valleys in the stiffness. What was the difference between the measurements? We looked at everything—ion concentration, liquid purity, problems with the instrument. After two weeks, Shiva found that the difference between the measurements was in the speed at which the tip approached the surface. Yet, we were moving the tip so slowly in our measurements—the fastest speed we used was 1.2 nm per second—that it shouldn’t have mattered. At this extremely slow speed, it would take almost a second to push the tip through one layer of molecules. For liquid molecules at room temperature, a second might as well be an eternity. Thermal motion is much, much faster than this. Yet, we found that something quite dramatic happened when we went from a speed of 0.4 nm per second to 0.6 nm per second and beyond. At the slower speeds, damping and stiffness fluctuated together. This meant that the liquid behaved like a liquid—it just got thicker and thinner as we pushed the tip through. At faster speeds, the liquid assumed a new state; it became springy with very little energy loss. Usually, only solids could do this. Since then, we have found the same effect in liquid water, although here we have had to squeeze a little bit faster to make it happen. Water is still liquid at 0.8 nm per second and starts behaving like a solid beyond that speed. The transition between the two states of the liquid is extremely sharp: Below a critical speed, it always behaves like a liquid, and within a very small range of speeds, it completely switches to a solid-like response.