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The Manipulation of Single Biomolecules

Terence Strick, Jean-François Allemand, Vincent Croquette, and David Bensimon

Twenty-five years ago, neurophysiology was revolutionized by the invention of a clever way to record the electrical activity of a single ionic channel across a membrane.¹ This so-called patch-clamp technique earned its inventors, Erwin Neher and Bert Sakmann, a Nobel Prize. The statistical analysis of the current flowing like a noisy telegraphic signal through such a channel yielded precious and unique information on the dynamic states of these channels. That information had previously been blurred or lost when, as was the prior custom, one simply measured the average current flowing through a large ensemble of channels.

Biophysics is undergoing a similar transformation, thanks to the development of new tools for manipulating, visualizing, and studying single molecules and their interactions. The statistical analysis of the measured signals (often a sequence of noisy steps) lets the biophysicist learn about the step size of molecular motors, their energy consumption, and the rate-limiting transitions in their enzymatic cycles. One can thus build and verify better models of how these enzymes function.

In this way a great deal has been learned in recent years about the mechanochemical coupling in the enzymes responsible for muscle contraction (actin and myosin), transport in the cell (kinesin and tubulin), energy generation (F₁-ATPase), DNA replication and transcription (polymerases), DNA unknotting and unwinding (topoisomerases and helicases), and so on.

Moreover, one can now apply to single biomolecules forces large enough to induce structural deformations. That capability gives biophysicists a new tool to probe the structure of the molecule and tackle the question of how it folds into its normal "native" state. The folding of proteins and RNA molecules presents particularly important and difficult issues. For example, DNA molecules under extreme tensional or torsional stress have been shown to exhibit new phases that may be relevant to cellular processes. It has also been proposed that the mechanical unzipping of DNA could speed up the sequencing of the nucleotides that encode its genetic blueprint. And the force-induced folding and unfolding of proteins is being addressed by experiments and computer models.

Let us first consider the range of forces acting at the molecular level. The smallest measurable forces are the Langevin forces responsible for the Brownian motion of bacteria, pollen grains, and other small objects in water at room temperature. The average force buffeting a bacterium every second is comparable to its weight, about 10^-14 newtons (or 10 femtonewtons).

Almost a thousand times stronger are the forces typical of molecular motors, which convert chemical energy from adenosine triphosphate (ATP) into mechanical work. ATP is the common coin of stored chemical energy in all life on Earth. The hydrolysis of an ATP molecule yields an energy of about 14 k_BT, where the thermal energy k_BT at body temperature is 4 × 10^-21 J, and the molecular dimensions are of order 10 nm. So, the characteristic forces of such motors are of order 10^-11 N (10 piconewtons).

Next on the way up the force scale are the cohesion forces associated with hydrophobic interactions and cooperative hydrogen bonding. Such interactions contribute to the stability of biomolecules and their native folded configurations. These forces are of order 10^-10 N, the typical force required to break a noncovalent bond and denature a protein. The strongest forces at the molecular level, are the nanonewton forces (10^-9 N) required to break covalent bonds with dimensions on the order of an angstrom and typical binding energies of 1 eV.

Figure 1

There are now many ways to manipulate single molecules. One can use optical or magnetic tweezers, atomic-force-microscope (AFM) cantilevers, or glass microfibers. (Optical tweezers and traps exploit the restoring force that can be exerted on a dielectric microbead by the electric-field gradients at the focus of a laser beam.) In all of these techniques, a DNA molecule, a protein, or some other biopolymer has one end bound to a surface and the other to a force sensor (see figure 1). The force sensor is usually a micron-sized bead or a cantilever, whose displacement one can measure to determine the force.

The sensor behaves like a noisy damped oscillator. For any given temporal resolution, the root-mean-square noise δF in the force measurement depends solely on the dissipation due to viscous drag. The fluctuation-dissipation theorem tell us that

,

where γ is the viscous dissipation and Δf is the frequency bandwidth of the measurement. To reduce noise in the measurement of force, one wants to work with smaller sensors. To reduce noise in measurements of displacement, one wants to use shorter, more rigid molecules.

Different techniques address different scales of displacement, time, and force. AFM cantilevers, for example, can measure angstrom-scale, millisecond events and forces larger than 10 pN. Glass microfibers do not achieve such fine spatial and temporal resolution, but they can measure piconewton forces. Optical tweezers allow the measurement of piconewton forces and nanometer displacements. Magnetic tweezers can measure femtonewton forces. They can also twist a molecule by rotating the bead or an attached microfiber.

Whatever the technique, one either keeps the displacement constant and measures a force, or one fixes the force and measures a displacement. Cantilevers and optical tweezers are natural extension clamps, that is to say, devices that hold the position fixed while measuring the force. Magnetic tweezers, on the other hand, are fundamentally force clamps. But an appropriate feedback loop can convert a force clamp into an extension clamp and vice versa.

In the study of DNA molecules and their associated proteins and enzymes, we have found the magnetic-tweezer technique to be simple and powerful. Briefly, it consists of stretching a single molecule while it is anchored at one end to a surface and, at the other end, to a magnetic bead whose diameter is on the order of a micron (see figure 1). Small magnets whose position and rotation can be controlled are used to pull and rotate the microbead, thus stretching and twisting the molecule. The vertical magnetic force F causes the DNA to extend to length l, and it provides a restoring force to restrict the bead's transverse Brownian fluctuations δx. Measuring these fluctuations, one can invoke the equipartition theorem to determine the force from the mean square Brownian fluctuation:

,

The first molecular motors to be studied by one of these micromanipulation tools--optical tweezers--were the enzymes responsible for muscle contraction (myosin) and cellular transport (kinesin).² These proteins use the energy of ATP hydrolysis to move in one direction along individual fibers: myosin on an actin filament and kinesin on a microtubule. During muscle contraction, thick fibers of myosin molecules pull on the anchored thinner actin filaments, bringing them closer together.³ Until recently, most of our understanding of muscle activity (ATP consumption under load, contraction rates, and so on) had been obtained from studies of muscle fibers, that is, assemblies of myosin and actin filaments. The single-molecule experiments have gone further, demonstrating that motor proteins act in a discrete, stepwise fashion with very high efficiency.

• Myosin. In 1994, Jeffrey Finer, Robert Simmons, and James Spudich studied myosin by suspending a single rigid actin filament held between two optical traps above a single myosin molecule. Thus they were able to measure directly the force and displacement resulting from the interaction of the molecule with the filament. When the myosin pulled on the actin fiber, the force was transmitted to microbeads anchored at the fiber's ends and held in the optical traps. The displacement of the beads from their equilibrium positions, which gave the myosin-induced movement of the fiber, was found to be discrete and load-independent, with an average step size of about 11 nm for a myosin. The average interaction time between myosin and actin was measured as a function of ATP concentration and found to agree with the known rates of ATP hydrolysis, and the static force developed by the myosin was measured to be about 4 pN.

  In 1998, Toshio Yanagida and coworkers at Osaka University coupled a similar system to a fluorescence microscope to observe simultaneously the displacement of the actin fiber and the hydrolysis of a fluorescently tagged ATP molecule by the myosin. The goal was to determine whether, as generally believed, only a single ATP molecule was consumed per myosin step. What they found, instead, was that, on average, a single ATP molecule accounted for three myosin steps. This experimental tour de force still awaits independent confirmation.

• Figure 2

  Kinesin. In parallel to these myosin studies, Steven Block and coworkers have been investigating the kinesin-microtubule system responsible for the movement of proteins and vesicles within cells. Here too, the central issue has been the efficiency and step-size operation of the kinesin motor. By using optical tweezers to follow the progression of a single kinesin molecule on a microtubule rail (figure 2), Block and coworkers⁴ were able to show that the two-headed kinesin molecule progresses in steps of 8 nm for each ATP consumed. Because kinesin can take many steps before falling off its microtubule rail, one can deduce the number of ATP molecules consumed per step from a statistical analysis of the time between steps. If kinesin molecules require just one ATP per step, the step-time distribution will be exponential, reflecting a single rate-limiting biochemical reaction (ATP binding). But if n ATP molecules were needed, the step-time distribution would be a convolution of n exponentials. For kinesin, Block and company found single-exponential behavior.

• F₁-ATPase. In the cells of animals, plants, and bacteria, a protein machine known as the F₀, F₁-ATP synthase complex is responsible for generating ATP from the flow of protons across the mitochondrial membrane.⁵ Some 20 years ago, Paul Boyer suggested that this machinery worked a bit like a hydroelectric generator: The proton flow through the F₀ subunit embedded in the membrane rotates a shaft in the statorlike F₁ subunit to synthesize ATP. Conversely, ATP hydrolysis in F₁ causes a reverse rotation of the shaft and a reverse flow of protons. For this "rotational catalysis model," Boyer was awarded a Nobel Prize in 1997 (together with John Walker, who determined the structure of this cellular machine).

  Earlier in 1997, Kazuhiko Kinosita and coworkers reported the first real-time study of the so-called F₁-ATPase system.⁶ They attached the protein to a coverslip and anchored a rigid, fluorescently labeled actin molecule to the enzyme rotor. When they added ATP, Kinosita and company observed 120° step-wise rotation of the actin. The single exponential distribution of the dwell times between steps suggested that only a single ATP molecule was being hydrolized per step. In more recent experiments, the group has found 90° and 30° substeps associated, respectively, with the protein binding to ATP and the release of the ATP hydrolysis products. Those results, together with an estimate of the energy dissipated by the drag on the rotated actin, imply that the efficiency of the F₁ subunit is nearly 100%.

Such remarkable pioneering experiments demonstrated the power of single-molecule studies and generated a flurry of activity in the theoretical modeling of molecular motors.⁷ These very efficient energy transducers are isothermal machines working in conditions where Brownian noise dominates. The principles that govern their activity and efficiency have been addressed in the conceptual framework of an energy-consuming thermal ratchet. That concept is an extension of Richard Feynman's 40-year-old discussion of simple thermal ratchets.

As a bearer of genetic information, DNA is of central importance in biology. But DNA is also a physically remarkable molecule. It is an extremely rigid polymer, very much stiffer than most synthetic polymers; and DNA is one of the few polymers that can be twisted.

Nature has evolved a vast kit of enzymes to cut, paste, unwind, translate, replicate, unknot, and repair DNA. Some of these enzymes are used in experiments in vitro to edit and modify DNA, to cut it at specific places, or to insert desired genes. Others are used to modify the molecule's ends for anchorage to appropriate surfaces. This last technique allows one to manipulate, stretch, and twist single DNA molecules.

The elastic properties of a single DNA molecule have been extensively studied since the pioneering experiments of Steven Smith, Laura Finzi, and Carlos Bustamante in the early 1990s.⁸ We now have a thorough experimental and theoretical understanding of the elastic properties of stretched and twisted DNA molecules.^9-11 (See the article "Stretch Genes," by Robert Austin, James Brody, Edward Cox, Thomas Duke, and Wayne Volkmuth in Physics Today, February 1997, page 32^*.) That understanding provides a firm basis for the investigation of the interactions of DNA with proteins by monitoring the stretching of the DNA molecules.

• Lac-repressor. One of the first such studies was the measurement, by Finzi and Jeffrey Gelles, of loop formation in DNA mediated by the lac-repressor protein.¹² The lac repressor is one of the best-studied regulators of gene expression. The efficient regulation of gene expression often requires interactions between distant sites along the DNA chain, causing the DNA molecule to form a loop. That's what happens in the case of the lac-repressor, which represses the expression of the lac genes by binding to specific operator sequences on the DNA. So the bending--and perhaps twisting--of DNA is quite relevant to gene expression.

  Finzi and Gelles monitored the formation and breakdown of a DNA loop between two lac gene sites bridged by a single lac repressor by noting the change in the fluctuation amplitude of a microbead tethered by a small DNA molecule. A loop reduces the bead's fluctuations by shortening its leash to the surface. A statistical study of the dwell times in open- or closed-loop states revealed that the open state consists of at least two different configurations, whereas the looped state is characterized by a single configuration. What these states are, how strongly they interact with DNA, and how that interaction is modulated by tension and torsion in the molecule are still open questions.

• RecA. In 1998, Didier Chatenay and coworkers in France looked at the interaction between DNA and RecA, a protein involved in "homologous recombination," that is, the exchange of DNA segments between paired homologous chromosomes. They noticed that the structure of DNA in the DNA-RecA complex was similar to the structure of S-DNA, a new DNA phase 70% longer than the regular B-DNA phase they and Bustamante's group had discovered by stretching the molecule with a force of about 70 pN. The experimenters reasoned that spontaneous thermal stretching fluctuations may create an S-DNA region that could then be stabilized by its interaction with RecA. By increasing the applied force, they made favorable fluctuations more likely and found an increased rate of RecA polymerization along the DNA. These results suggest that binding of proteins to DNA might rely, in part, on flexibility and thermal fluctuations of the molecule's structure.

• RNA polymerase. RNAP was the first DNA-based molecular motor to be studied at the single-molecule level. This protein is responsible for the transcription of DNA into messenger RNA, the working blueprint of the genetic code for protein production. Gelles and Robert Landick anchored an RNAP-DNA complex to a surface and bound a polystyrene microbead to the far end of the DNA that was threaded into the protein.^13,14 The transcription of the DNA was activated by providing the required nucleotide building blocks. As the enzyme transcribed the DNA, the tethered bead was pulled closer to the surface. By trapping the bead with an optical tweezer, they could exert a force on the RNAP. Working together with Block and his collaborators, they found that the transcription stalled when the load reached about 25 pN. The dependence of the molecular motor's speed on the force suggested that stretching the DNA was affecting a state that branched off the main reaction pathway, for example, by increasing the likelihood of pauses in enzyme activity. (See the box at right.)

• DNA polymerase. DNAP is a protein that synthesizes a new DNA strand on a single-strand (ss)DNA template, matching each of the four bases of the genetic code with its complement: adenine (A) with thymine (T) and guanine (G) with cytosine (C). It can also detect and correct its errors. Single-molecule studies of replication by DNAP were done independently by Bustamante's group¹⁵ and by our group.¹⁶ In both cases, the groups stretched an ssDNA molecule and monitored the replication rate, taking advantage of the different extensions of ssDNA and double-strand (ds)DNA at a given force.

  While Bustamante and company studied a natural enzyme, we worked with two proteins deficient in error-correcting activity. Both groups found similar results. Essentially, the replication rate decays exponentially with increasing load from an initial rate of a few hundred bases per second, finally stalling at a force of about 30 pN. At forces greater than 35 pN, the error-correcting activity of the natural enzyme was enhanced, causing it to chew away at the strand it had just synthesized.

  These results once again imply that a state on the main reaction pathway is critically sensitive to any pulling (see the box). The findings support the "induced fit" mechanism for error correction, which supposes that several bases must be correctly matched to the template strand before one base is allowed to polymerize.

• Topoisomerases. These are essential proteins that can modify the topology of a DNA molecule. They are responsible for relieving the torsional stress that builds up in DNA during transcription and replication by polymerases, and they are also required for the proper disentangling of chromosomes during cell division. To study these enzymes, one needs a substrate of coiled or linked DNA molecules.

  Figure 3

  The coiling of a single DNA molecule is easily done and undone with magnetic tweezers. Once the coiled molecule has been relaxed and uncoiled by a topoisomerase, simply rotating the magnets will regenerate the coiling. We have studied the relaxation of coiled DNA by a fly's topoisomerase¹¹ (see figure 3). This protein consumes ATP to untangle or unknot DNA by creating a temporary break in one DNA segment through which it can pass a second DNA segment.

  Twisting a DNA molecule attached to a small magnetic bead results in the formation of "supercoil" loops that reduce the DNA's overall length. Adding topoisomerases and ATP undoes the supercoiling. This coiling and uncoiling can be monitored in real time by following the changing distance of the bead from the surface. Lowering the ATP concentration slows the enzyme down enough so that single relaxation events can be resolved. The observed exponential distribution of time intervals between such events suggests that a single ATP molecule is hydrolyzed per strand passage. The exponential decay of the reaction rate with increasing force implies that a critical step in the enzymatic pathway involves work against the load. Perhaps it's the step in which the cleaved ends of the DNA are rejoined.

We have seen that the statistical analysis of the signals obtained in single-molecule studies of motor proteins can yield crucial information on the efficiency of the enzyme, that is to say, the number of ATP molecules that are consumed per mechanical cycle. Bulk measurements of overall ATP consumption do not provide that kind of detailed molecular information. The force dependence of the enzymatic rates can test various mechanistic models of the enzymatic kinetics by identifying steps in the reaction pathway that are sensitive to load. And the controlled and reversible twisting of single DNA molecules makes it possible to carry out investigations that cannot be done by any other means.

Experiments with single molecules complement and enlarge the knowledge of molecular motors we derive from bulk studies. They also offer us the novel opportunity to use the forces we can exert on a single molecule to control its structure. In that context, the load plays a role akin to the magnetic field in magnetic transitions. We've already mentioned the new extended S-DNA structure one can get by pulling on the DNA molecule with a force greater than 70 pN. Similarly, by overtwisting DNA, we have discovered a new, highly twisted structure of DNA, called P-DNA,¹¹ whose phosphate backbone winds in such a way as to expose the coding bases in solution. That configuration has been observed by Loren Day and David Liu, at the Public Health Research Institute in New York, in the packing of the DNA of some viruses. But we don't know whether it has a wider role in vivo.

Figure 4

The mechanical unzipping of the DNA double helix has been proposed as a faster way to sequence the genetic code by recording force signals as the complementary base pairs on the two strands are pulled apart. The force depends on the number of hydrogen bonds between base pairs (2 for A-T and 3 for G-C), and on the stacking energies of nearest neighbors on the same strand. Such an experiment was done by Ulrich Bockelmann, Baptiste Essevaz-Roulet and François Heslot¹⁷ (see figure 4). They measured a sequence-specific stick-slip signal as the double helix was unzipped.

A simple theoretical model of the experiment explains these results as a buildup of elastic energy in the chain that is released in bursts of base-pair separations. Because the single DNA strands left by the unzipping of the double helix are very flexible, the desired single-base resolution might be attained only for the first 100 or so bases, when the stored elastic energy in the single strands is not yet large enough to wash out the energy stored in the binding of a single base pair. So, unless ways are found to make the single-strand DNA pieces more rigid (perhaps by using single-strand binding proteins), the mechanical sequencing of DNA is not going to be a realistic alternative to existing methods, which remain efficient for up to 1000 base pairs on a DNA segment.

The folding of proteins into their natural state is one of the most fundamental and complex open questions in biology. By allowing the controlled folding and unfolding of a single protein molecule, the new tools we have described may contribute to a better understanding of the folding problem. One powerful tool is the atomic-force microscope, with its subnanometer spatial resolution and its ability to subject single molecules to forces stronger than 30 pN. In pioneering studies at the University of Munich, Hermann Gaub and his collaborators¹⁸ have looked at the unfolding of titin, a protein consisting of many globular domains in tandem. Pulling on the protein with forces between 150 and 300 pN caused the successive all-or-nothing unfolding of isolated domains. When force was subsequently reduced, the protein partially refolded. In more recent experiments, Gaub and company also observed the unfolding of subdomains within a globular protein. Comparing the findings of such experiments with theoretical analyses of folding under load should help us to develop better, more predictive models of the three-dimensional structures of proteins.

In this cursory review, we have tried to give a flavor of the kind of investigations that single-molecule techniques have made possible. Brownian fluctuations impose fundamental constraints on the spatial and temporal resolution of such experiments. To achieve nanometer and millisecond resolution, we have to use submicron rigid sensors. That pushes the current technology to the limit. In some cases (optical or magnetic tweezers), it might even conflict with the goal of applying large forces to individual molecules.

We have not addressed the equally important advances in fluorescence techniques.² These advances now make it possible to observe single molecules, their interactions, and their structural changes by means of a variety of low-noise optical methods, such as total- internal-reflection microscopy, two-photon and confocal microscopy, fluorescence-correlation spectroscopy, and single-molecule fluorescence energy transfer. Combining the fluorescence techniques with the manipulation of single molecules should give us exciting new ways to explore the molecular world. As Feynman said 40 years ago, "There is plenty of room at the bottom."

We thank our colleagues, biologists and physicists, for their help, in particular: Aaron Bensimon, Steven Block, Claude Bouchiat, Gilles Charvin, Nick Cozzarelli, Nancy Crisona, Nynke Dekker, Marie-Noelle Dessinges, Driss Dohmi, Michel Duguet, Laura Finzi, Giuseppe Lia, Berenike Maier, Marc Mézard, Margerita Peliti, Valentin Rybenkov, and Michelle Wang. We also thank our funding agencies, in particular the Centre National de la Recherche Scientifique, the University of Paris VI and VII, the Cold Spring Harbor Laboratories, and the Association pour la Recherche sur le Cancer for their continuing support.

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