Single-Molecule Micromanipulation Techniques

Transcription

1 Annu. Rev. Mater. Res :33 67 First published online as a Review in Advance on January 11, 2007 The Annual Review of Materials Research is online at This article s doi: /annurev.matsci Copyright c 2007 by Annual Reviews. All rights reserved /07/ $20.00 Single-Molecule Micromanipulation Techniques K.C. Neuman, 1 T. Lionnet, 2 and J.-F. Allemand Laboratory of Molecular Biophysics, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland ; neumankc@mail.nih.gov 2 Laboratoire de Physique Statistique, 3 Département de Biologie, 4 Laboratoire Pasteur Département de Chimie, Ecole Normale Supérieure, Paris, France; lionnet@lps.ens.fr, allemand@lps.ens.fr 5 UMR8550 Associé au CNRS et aux Universités Paris VI et VII, Paris, France Key Words optical tweezers, magnetic tweezers, polymer elasticity, microrheology, biophysics, soft condensed matter physics Abstract Single-molecule micromanipulation techniques traditionally have been developed for biophysical applications, but they are being increasingly employed in materials science applications such as rheology and polymer dynamics. Continuing developments and improvements in single-molecule manipulation techniques afford new opportunities in a broad range of fields. In this review we present an overview of current single-molecule manipulation techniques, with an emphasis on optical and magnetic tweezers, followed by a description of the elastic properties of single biopolymers. We then review the use of micromanipulation techniques to locally probe material properties. To provide some insight into biophysical questions addressed by these techniques, we describe two applications, which further serve to illustrate the power and versatility of singlemolecule micromanipulation techniques. We conclude with a brief discussion of emerging applications and techniques. 33

2 INTRODUCTION Single-molecule manipulation techniques have evolved rapidly over the past 15 years and are finding an ever-increasing number of applications. Continuing technological improvements have facilitated progress in instrumentation that has been equaled by advances in sample preparation and in the theoretical underpinnings of these techniques. Application of pico-newton-scale forces and measurement of the displacement of single particles with a nanometer-or-better resolution are now relatively commonplace, and atomic-scale resolution (Å) has been achieved in some experiments. These techniques have been applied to the study of individual molecular motors (1 3) and polymer and biopolymer physics (4 10) as well as to colloid and interfacial physics (11, 12). In addition to providing detailed measurements at small length and force scales, single-molecule techniques provide a noninvasive probe of local properties that can be applied in very small volumes. These techniques are also uniquely capable of shedding light on the interplay between individual and collective behavior. For example, single-molecule techniques have been used to measure the elastic properties of single polymer molecules in isolation (13, 14), the behavior of individual polymer molecules in a polymer solution (15), and the rheological properties of the polymer solution (16, 17), providing an unprecedented view of polymer behavior. In this review, we describe and compare single-molecule manipulation techniques, providing an overview of how they are implemented, their relative strengths and weaknesses, and discussing relevant applications and results. MANIPULATING A SINGLE MOLECULE Many single-molecule manipulation experiments consist of attaching a single molecule of interest between a force probe and a support (Figure 1), which requires a means both of attaching the molecule and of ensuring that only a single molecule is attached. Many strategies have been developed to accomplish these tasks for different molecules and different manipulation techniques. Occasionally, the molecule will spontaneously attach to the surface and the probe. More commonly, however, the molecule must be attached in a specific manner to both the probe and the support. Although this attachment can be accomplished through purely chemical means, molecular biology offers a wide array of more versatile attachment options. For example, DNA can be labeled with ligands that are specifically recognized by their cognate receptors. When these receptors are chemically attached to or adsorbed on surfaces such as glass or micron-sized beads, it is possible to manipulate the molecule as illustrated in Figure 1. Biological polymers offer other advantages, including the ability to make large quantities of homogeneous molecules, which can be much larger and therefore easier to manipulate than most synthetic polymers. For these reasons, in addition to their biological importance, most single-molecule elasticity measurements have been made with biopolymers. A combination of approaches has been adopted to ensure that a single molecule is attached between the force probe and the support. Multiple attachments can be avoided by working with very small concentrations of the molecule of interest. In the event of multiple attachments between the probe 34 Neuman Lionnet Allemand

3 and the support, these would be reflected in the measured elastic properties, thereby providing a posthoc means of ensuring a single-molecule measurement. FORCES AT THE SINGLE-MOLECULE LEVEL As illustrated in Figure 1, in typical single-molecule manipulation experiments, force is applied on a single molecule to probe its mechanical properties. The maximum practical force that can be applied in this configuration is the force at which the molecule breaks, i.e., the rupture force of a covalent bond. To obtain an order-of-magnitude estimate of this force, we note that force has the dimensions of an energy divided by a distance. The energy of a covalent bond is on the order of 1 ev = J, and the typical length scale of this bond is 1 Å, leading to a force on the order of 1.6 nn (18). Below this force the chemical bonds in the molecule are slightly extended. This is the enthalpic elasticity regime in which the molecule behaves as a traditional spring. At low forces the elastic properties of the molecule are dominated by entropy. For DNA, this entropic elasticity regime extends up to forces of 0.1 pn. We discuss the elastic properties of single polymers in more detail below. The lower limit of measurable force is set by the thermal motion of the force probe. The Langevin force, which is the origin of Brownian motion, arises from the collision of solvent molecules on an object. These collisions occur on all timescales, and thus the Langevin force is a white noise, and to obtain a characteristic value one has to consider a specific measurement time or bandwidth. The Langevin force is given by F L = (4γ k B TB) 1/2, where γ is the drag coefficient that depends on the shape of the object, its proximity to walls, if any, and the viscosity of the fluid (for a sphere of radius r in an infinite medium with viscosity η, γ = 6πηr); B is the measurement bandwidth; and k B T is the thermal energy. For a measurement bandwidth of 1 Hz, a sphere of 1 μm in water at room temperature is subjected to a force of N. This force is important to consider in the measurement process because it will always be present on the force sensor and it limits the lowest measurable force. The dependence of the Langevin force on the particle size and measurement bandwidth implies that to measure very small forces, one has to reduce the bandwidth or, preferably, the size of the force sensor to keep the measurement bandwidth as large as possible. SINGLE-MOLECULE MANIPULATION TECHNIQUES How can such small forces be exerted and measured? Several techniques have been developed to apply and measure force on single molecules: optical tweezers, magnetic tweezers, atomic force microscopy (AFM), glass microneedle, and the biomembrane force probe. As illustrated in Figure 1, these techniques share a common geometry; one end of the molecule of interest is attached to the force probe, and the other is attached to a surface. The mechanical properties of the molecule are determined by recording the force extension. In each of these techniques the force probe is well described as an overdamped spring, with the exception of certain configurations of magnetic tweezers. The applied force is not measured directly but is typically determined via Hooke s law from independent measurements of the probe stiffness and the AFM: atomic force microscopy Single-Molecule Techniques 35

4 a Laser beam b N S Polystyrene bead DNA Magnetic bead DNA c e Surface Optical microscope Surface Optical microscope Electromagnetic coils Magnetic bead DNA d f Surface Optical microscope Laser Cantilever DNA Surface Piezoelectric stage Photodiode Optical fiber Micropipette DNA Micropipette DNA Vesicle Photodiode 36 Neuman Lionnet Allemand

5 Table 1 Comparison of single-molecule manipulation techniques. Typical values of bandwidth, stiffness, position resolution, and force range for the single-molecule manipulation techniques illustrated in Figure 1 Optical tweezers Magnetic tweezers AFM Glass microneedle Biomembrane force probe Bandwidth (Hz) Stiffness (pn nm 1 ) Resolution (nm) Force range (pn) deflection of the probe from its equilibrium position. Accurate measurement of the applied force therefore requires determining the stiffness of the probe and measuring the deflection of the probe. Table 1 provides a comparison of the relevant parameters describing these micromanipulation techniques: spatial and force resolution, stiffness, maximum force, and detection bandwidth. Optical tweezers and certain implementations of electromagnetic tweezers permit noninvasive, full three-dimensional control over the position of the trapped object. More generally, optical and magnetic tweezers are the only noncontact micromanipulation techniques, affording them wider applicability, particularly in the domains of microrheology and colloid science. Figure 1 Schematic representation of micromanipulation techniques (not to scale). (a) Optical tweezers. In optical tweezers, a micron-sized bead is captured in a three-dimensional harmonic potential formed near the focus of an infrared laser. Force on the DNA molecule that tethers the bead to the surface is applied by moving the trapping laser focus or the surface. (b) Magnetic tweezers, permanent magnet configuration. Here the magnetic field, and hence the force on the magnetic bead, is controlled by mechanically changing the distance between the bead and the magnets with motors, which also rotate the magnets. (c) Magnetic tweezers, electromagnet configuration described by Gosse & Croquette (43). The magnetic bead attached to DNA experiences a force because of the magnetic field gradient imposed by six electromagnetic pole pieces above the sample. (d ) Atomic force microscopy (AFM). In AFM, force is imposed on the DNA molecule by moving either the cantilever or the surface with a piezoelectric element. The applied force bends the cantilever, and the deflection is determined from the displacement of a laser reflected off the cantilever detected with a split photodiode. (e) Glass microneedle. The glass microneedle, or microfiber, technique is similar to the AFM except that the cantilever is replaced by an etched optical fiber whose deflection is measured through the deviation of the light conducted by the fiber. ( f ) Biomembrane force probe. The biomembrane force probe consists of a lipid vesicle held in a suction pipette. Modified lipids in the membrane specifically bind ligands attached to a small bead, to which the DNA is attached. Force on the DNA molecule is imposed by moving the micropipette holding the other end of the DNA. Applied force is determined from the movement of the attached bead and the stiffness of the membrane. Membrane stiffness is controlled through the pressure in the suction pipette. Table 1 compares the relevant parameters (spatial and force resolution, stiffness, and bandwidth) of these micromanipulation techniques. Single-Molecule Techniques 37

6 NA: numerical aperture OPTICAL TWEEZERS Optical tweezers, or optical traps (Figure 1a), can apply controlled forces up to 100 pn on micron-sized particles while simultaneously recording the motion of the trapped particle with subnanometer accuracy (19). These capabilities are well suited to applications in materials science, in which optical trapping approaches are increasingly being employed, particularly in the areas of colloid science and microrheology (9, 20). Here we give a brief overview of optical trapping. Additionally, the techniques for calibrating optical tweezers introduced in this section are similar to those used to calibrate other micromanipulation instruments. More in-depth discussion can be found in recent reviews on optical trapping (11, 19), in particular on the use of optical traps for microrheology (21). An optical trap is formed by focusing a laser to a diffraction-limited spot with a high numerical aperture (NA) microscope objective (22). A dielectric particle near the focus will experience a three-dimensional restoring force that keeps the particle near the focus. The force arises because a dipole in an inhomogeneous field experiences a force in the direction of field gradient (23). The laser induces a dipole in the dielectric particle that interacts with the steep electric field gradient at the focus of the laser, resulting in the trapping force. In addition to this gradient force, the dielectric also experiences a scattering force in the direction of light propagation (23). To achieve stable three-dimensional trapping, the gradient force must overcome the scattering force, which is achieved by tightly focusing the laser. As a result of the scattering force, the stable position of the trapped particle is slightly past the laser focus. For small displacements ( 150 nm), the optical trap acts as a linear spring, with a spring constant that depends linearly on the polarizability of the trapped particle and the intensity of the trapping laser beam. For a trapped sphere with radius r λ, the wavelength of the trapping laser, scattering, and gradient forces can be calculated (23, 24): F grad = 2πα I cn 2 0, 1. m ( ) m α = n m r3, 2. m F scatt = I 0σ n m, 3. c σ = 128π 5 r 6 3λ 4 ( ) m 2 2 1, 4. m where I 0 is the intensity distribution of the focused trapping laser, σ is the scattering cross section of the sphere, n m is the index of refraction of the medium, m = n p /n m is the ratio of the index of refraction of the sphere to that of the medium, and α is the polarizability of the sphere. For a trapped sphere with radius much greater than the trapping wavelength, r λ, the total force on the sphere can be calculated from geometric optics. For the intermediate regime in which r λ, the force on the sphere is much more difficult to calculate, as no simplifying approximations can be made. 38 Neuman Lionnet Allemand

7 However, significant progress has been made recently in the calculation of forces in this regime (25, 26). Dielectric particles ranging in size from several microns to 20 nm can be optically trapped. Such particles include bacteria (27); yeast (28); organelles within larger cells (29); lipid vesicles (30 33); microspheres including silica, polystyrene, gold (34, 35), and silver (36); and polymer molecules such as DNA (37). More recently, defects in nematic liquid crystals (38) and carbon nanotubes (39) have been optically manipulated. Calibration of force and displacement is straightforward for microspheres, which are relatively monodisperse and isotropic and for which the hydrodynamic drag can be calculated. Silica and polystyrene microspheres or beads are widely used alone or as handles linked to other molecules of interest. Fundamentally, a particle can be stably trapped if the depth of the optically induced potential is significantly greater than k B T, which at room temperature (290 K) is convenient to express as 4pN nm. This fundamental limit imposes two interrelated practical limits on the size and composition of particles that can be trapped. Because the polarizability and hence the trapping potential scale with the volume of the particle (Equation 2), a compositiondependent lower size limit is imposed. The composition of trapped particles is in turn limited by the requirement that the axial gradient force must be larger than the scattering force. Generally speaking, this requirement limits the possibilities to dielectric materials with small absorption and scattering cross sections. However, very small ( nm) gold and silver nanoparticles can be stably trapped (34 36) because the optical skin depth exceeds their diameter, which dramatically reduces their effective scattering cross section. High-index particles can be stably trapped by using two counter-propagating optical traps (40) that effectively eliminate the scattering force, a configuration pioneered by Smith and coworkers (41). Finally, the polarizability of the particle depends on its index of refraction relative to the surrounding medium (Equation 2). Typically this is an aqueous solution with a refractive index near 1.3. For nonaqueous environments, the index of refraction will, with few exceptions, be higher than that of water, resulting in degraded optical trap performance and further limiting the size and composition of particles that can be stably trapped. This limitation is of particular concern for optical trapping studies of colloid systems in which the medium is index matched to the colloidal particles that are interspersed with a low concentration of higher index particles that can be trapped (42). Whereas a basic optical trap provides a convenient means of noninvasive manipulation, combining an optical trap with sensitive position detection of the trapped particle turns the instrument into a force and displacement transducer and greatly enhances its capabilities. The optically trapped object and the surrounding environment can be imaged with the high NA objective used to focus the trapping laser. Video microscopy is therefore the simplest method of particle tracking. Resolution on the order of 5 nm at video rate (30 Hz) is readily achieved with centroid tracking algorithms (43, 44). In addition to offering simplicity and convenience, imaging-based methods can track the position of multiple particles in the field of view. Moreover, tracking of nonuniform particles is possible. However, video-based tracking has some drawbacks. The bandwidth is limited to video rates, typically Hz, which is well below the characteristic frequency of even a relatively weak optical trap ( 1 khz). Single-Molecule Techniques 39

8 QPD: quadrant photodiode The resultant aliasing, combined with the intrinsic temporal filtering characteristics of video-based acquisition, complicates analysis and can lead to significant artifacts. Several nonvideo-based detection schemes have been implemented with improved detection bandwidth and resolution. The most versatile of these techniques relies on the interference between forward-scattered light from the trapped bead and unscattered light collected by a high NA condenser (45 47). The interference signal is measured by a quadrant photodiode (QPD) placed in an optical plane conjugate to the back focal plane of the condenser. The four quadrants of the QPD are pairwise summed, and the differential signals for the x and y dimensions are obtained. The sum signal of all four quadrants can be used to normalize the x and y signals, and it also provides a measure of the axial or z dimension displacement. The most straightforward implementation of the QPD detection relies on the interference signal from the trapping laser, although in some instances it is advantageous to employ a second, low-power, detection laser (48). Subnanometer spatial resolution and bandwidths in excess of 100 khz have been achieved with QPD-based detection (49). The principal limitations of this method are that one or possibly a few beads can be tracked simultaneously, detector calibration is more involved than for video-based methods, and detection is limited to a region within 400 nm or less of the laser focus. High-bandwidth position detection of a trapped bead affords a convenient means of calibrating the stiffness of the optical trap by analyzing the Brownian motion of the trapped particle (19). A trapped bead, in a Newtonian fluid, is well described as an overdamped particle in a parabolic potential subject to thermal fluctuations. The one-sided power spectrum of the positional fluctuations of the trapped particle is a Lorentzian: k B T S xx ( f ) = π 2 γ ( ), 5. f 2 + f0 2 where k B T is the thermal energy, f 0 = α(2πγ) 1 is the Lorentzian corner frequency, α is the trap stiffness, and γ is the drag on the particle. For a bead of radius r, far from any surfaces, the drag is given by the Stokes relation: γ = 6πηr, where η is the viscosity of the medium. Thus, the trap stiffness can be determined from the power spectrum of a trapped bead or other simple object for which the drag can readily be calculated. One distinct advantage of this method is that the position calibration of the detector need not be known, as the spectrum of the voltage fluctuations suffices to determine the stiffness. In fact, the power spectrum of the trapped bead can be used to provide a fairly accurate linear calibration of the position detector (50). The Lorentzian spectrum of the trapped bead also determines the practical measurement bandwidth. Bandwidth, and hence time resolution, can be increased by increasing the trap stiffness or by decreasing the drag on the trapped particle. A related but somewhat less involved method of determining trap stiffness relies on the equipartition theorem. For a particle in a harmonic potential of stiffness α, equipartition dictates that 1/2 k B T = 1/2 α x 2. Alternatively, this result can be obtained by integrating the power spectrum, which from Parseval s theorem is equal to the positional variance. Thus, by measurement of the positional variance of the trapped particle x 2, the stiffness can be determined. This technique does not depend on the drag coefficient of the trapped particle; however, it does require a 40 Neuman Lionnet Allemand

9 well-calibrated position detector and, in general, provides less information than does the power spectral method. Once the stiffness of the optical trap is established, the applied force, F, can be determined by measuring the displacement, x, of the bead from its equilibrium position and applying Hooke s law: F = αx. Both the power spectrum and variance methods require a position detector and associated electronics with sufficient bandwidth to accurately record the Lorentzian spectrum at least an order of magnitude past the corner frequency. Slight deviations from idealized behavior can result in significant misrepresentation of the trap stiffness, particularly for stiff traps with high roll-off frequencies. Several recent reports provide detailed theoretical and experimental analysis of the power spectrum and position detection electronics (49, 51, 52). Although the analysis is primarily focused on optical trapping instruments, the results are generally applicable to spectral analysis and hydrodynamics of micronscale particles. Optical trap stiffness can also be determined by measuring the displacement resulting from a known hydrodynamic force applied by moving the trapped particle or the surrounding medium (19). These hydrodynamic calibration methods require a calibrated position detector and an accurate value for the drag on the particle, including the contribution of any nearby surfaces. The bandwidth requirements, however, are substantially relaxed in comparison with the thermal or passive methods presented above. The most rudimentary approach consists of introducing an increasing flow in the trapping chamber and recording the velocity of the trapped bead, e.g., by video tracking, as it escapes the trap. Owing to the low Reynolds number, the bead velocity immediately adopts the fluid velocity at escape, and the known drag coefficient of the sphere permits the calculation of the escape force. This provides an estimate of the maximum force that can be exerted by the optical trap. This technique is limited to escape force measurements, as it is difficult to determine accurately the fluid velocity prior to escape because of such complications as the Poiseuille flow profile in the trapping chamber. If, on the other hand, the entire trapping chamber is moved, to a very good approximation the fluid moves as a single entity, that is, it does not slosh around in the trapping cell (53). Controlled motion of the trapping cell, e.g., by affixing it to a piezoelectric stage, imposes a known force on the trapped particle, which in conjunction with the resulting displacement provides a measure of the trap stiffness. This technique permits measurement of the trap stiffness well beyond the small displacements obtained from thermal calibration methods. Therefore, this technique can be used to determine the linear range of the trap, i.e., the maximal displacement for which the trap acts as a Hookean spring. An equivalent calibration scheme involves rapidly scanning the optical trap through the fixed fluid, which can achieve higher relative velocity because the trap can be moved faster than the trapping chamber. Tolić-Nørrelykke and coworkers recently demonstrated an elegant method to calibrate both trap stiffness and position detection from a single measurement of the power spectrum of a trapped bead subjected to an oscillating hydrodynamic force (53). The functionality of an optical trapping instrument is further expanded with the addition of dynamic position control of the sample, the optical trap, or both. Moving the sample is accomplished by fixing the optical trapping chamber to a piezoelectric stage. The current generation of commercial stages incorporates capacitive position Single-Molecule Techniques 41

10 AOD: acoustic optic deflector SLM: spatial light modulator HOT: holographic optical tweezers detection in a feedback loop resulting in nanometer or better positional accuracy. These stages afford long travel ranges ( 100 μm) but are limited to frequencies below 1 khz. Scanning the position of the optical trap in the specimen plane with acoustic optical deflectors (AODs), or galvanometer mirrors, can be done much faster (tens of khz for AODs) and opens up new avenues of control and manipulation. If the trapping laser is scanned faster than the diffusion time of the trapped particle, multiple optical traps can be formed by time-sharing a single laser beam (54). Furthermore, through the combination of dynamic position and amplitude control complex, timedependent trapping potentials can be created (55, 56). Grier and coworkers (11, 57, 58) pioneered a complementary approach to generate multiple optical traps and complex trapping potentials through the use of holographic or diffractive optics. A diffractive optical element placed in the back focal plane of the objective will produce an intensity distribution in the specimen plane that is the Fourier transform of the intensity distribution imposed by the diffractive element. Through the use of an addressable liquid crystal spatial light modulator (SLM) as the diffractive element, arbitrary intensity distributions in the specimen plane can be created and modified with a refresh rate of 5 Hz (58). In one demonstration of these holographic optical tweezers (HOT), 400 independent optical traps were generated with a single trapping beam (58). One particularly interesting application of the HOT technology is the generation of optical traps carrying angular momentum (11, 59). In a recent example, arrays of optical vortices in which trapped particles move in circular orbits have been used as microfluidic pumps (60). OPTICAL TRAPPING MICRORHEOLOGY The ability to optically manipulate and track the position of micron-scaled objects has opened up new avenues in the study of rheology (9, 10). It is now possible to make rheological measurements in very small volumes, including the interior of cells, and test rheological properties at small length scales. The underlying principle of microrheology is that the mechanical properties of the material can be obtained from the motion of a test particle subjected to a known force. The elastic and dissipative parameters of the material determine the transfer function relating the imposed force to the resultant motion. Video tracking of the thermal fluctuations of embedded beads provides the material s small-amplitude elastic and dissipative parameters (16). Recent theoretical and experimental progress has extended and refined the analysis by considering the correlated motion of pairs of particles (61, 62). Laser-based particle-tracking techniques, discussed above, have been employed to obtain high-frequency measurements not possible with standard video-tracking techniques (9, 20, 63). Valentine and coworkers (64) employed optical tweezers to impose a sinusoidal driving force on a bead in a polymer solution. Active microrheology extends the measurement capabilities beyond the small-amplitude, linear regime. In a recent experiment, Helfer and coworkers (65) used a pair of optical traps to probe the mechanical response of an actin-coated vesicle (Figure 2). They probed the linear, small-amplitude, elastic regime of the coated vesicle, and by increasing the amplitude of the driving force, they observed a reversible buckling transition in the vesicle membrane (65). 42 Neuman Lionnet Allemand

11 Figure 2 Optical tweezer based microrheology of composite lipid-actin membrane. (a) Fluorescence microscopy image of a 15-μm lipid vesicle coated with fluorescently labeled actin. (b) Two beads are attached to opposite sides of the vesicle. One bead is held in a fixed optical trap while the second bead is oscillated by moving the second trap with a triangle wave either tangentially (in plane) or radially (out of plane) with respect to the vesicle. (c) Motion of a 3.1-μm bead either attached to the vesicle (black points) or free in solution (gray points) for an imposed in-plane triangle wave trap motion of 310-nm amplitude at 0.6 Hz with a trap stiffness of 10 2 pn nm 1. The in-plane shear modulus of the vesicle can be determined from the difference in the amplitudes of the bead motion in the two cases. Figure adapted from Helfer and coworkers (65). OPTICAL ROTATION AND TORQUE Over the past several years, it has become possible to apply and measure torque in optical traps. Optical trapping of a symmetric and optically isotropic particle, such as a polystyrene or silica bead, produces a rotationally symmetric potential in which the trapped particle is free to rotate. Owing to the scattering force, asymmetric Single-Molecule Techniques 43

12 particles tend to align with their long axis along the beam s propagation axis. Despite a significant amount of restoring torque applied to the trapped particle in this instance, it is difficult to calibrate and all but impossible to use this torque to rotate the particle. Optically anisotropic, or birefringent, particles will experience a torque aligning one of the optical axes with the polarization direction of the trapping laser (66). By rotation of the polarization direction, e.g., by the use of a circularly polarized trapping laser, the trapped birefringent particle can be made to rotate. The rotation induced by circularly polarized light can also be treated as the transfer of angular momentum from the photons to the trapped particle. For circularly polarized light, each photon carries ±h - of angular momentum, and the angular momentum flux in a circularly polarized Gaussian beam is ± Pω 1, where P is the optical power and ω is the optical frequency (67). Transfer of angular momentum from the laser beam to the trapped particles produces the torque, resulting in a change in the circular polarization of the light. The optical torque, τ, can be expressed as τ = σ Pω 1, where σ is the change in circular polarization of the light due to its interaction with the particle (67). This relation permits the calculation of the optical torque on a particle for which the optical activity is known, which is generally unfeasible. More importantly, this relation provides a means of measuring the applied torque on an arbitrary particle simply by measuring the change in the circular polarization of the trapping light, which is relatively straightforward. Moreover, the rotation frequency of the trapped particle can be measured from the polarization modulation (67). On the basis of these principles, Bishop and coworkers demonstrated optical rotational microrheology by measuring the torque-velocity relationship for micron-sized birefringent spheres of vaterite (68). LaPorta & Wang implemented a torque clamp by incorporating optical torque detection into a feedback loop controlling the input polarization state of the trapping light (69). Although they offer a powerful combination of precision and versatility, optical traps are not completely devoid of drawbacks, limitations, and nonideal behavior, all important considerations to be weighed prior to and throughout experiments in which they are employed. The high intensity at the focus of the trapping laser, typically W cm 2, leads to local heating of the sample and can cause optically induced damage in trapped specimens. Optical absorption in the trapped particle and the surrounding medium causes heating. For a transparent particle trapped in water, which for most commonly used trapping wavelengths is relatively transparent and a good heat conductor, sample heating is modest, on the order of 3 C per 100 mw of trapping power (70). Highly absorbing particles, such as gold, lead to significantly more heating, as much as 27 C per 100 mw at a trapping wavelength of 1064 nm (35). Local heating can perturb the environment in the vicinity of the trapped particle by generating convection currents and changes in the viscosity of the medium, which can be a strong function of temperature. Local heating may also directly affect the properties of the sample, such as the enzymatic activity of proteins attached to the trapped bead (71). Proteins and other biological samples are also susceptible to photodamage induced by the trapping laser (27, 72, 73). Photodamage is reduced for trapping wavelengths in the near-infrared ( nm). However, an oxygen-mediated photodamage process, 44 Neuman Lionnet Allemand

13 presumably due to the formation of excited state oxygen, persists throughout this region (27). Although the details of this process remain unclear, photodamage can be significantly reduced by removing molecular oxygen from the trapping medium (27). Because the optical trapping potential is proportional to the gradient of the field near the focus, it is sensitive to all manner of optical perturbations and aberrations that modify the intensity, or the intensity distribution, at the focus. Optical trapping efficiency and precision will necessarily be degraded in complex, heterogeneous environments, but more subtle aberrations can also affect the trap stiffness. For example, the spherical aberrations that arise when using an oil immersion objective to focus the trapping laser into an aqueous medium lead to a smearing out of the focus, particularly in the axial dimension, along the optical axis (74, 75). As a result, the axial trap stiffness, and to a lesser degree the lateral trap stiffness, depends on the depth of focus in the trapping chamber. Moreover, the stable axial position of the trapped particle also changes as a function of focus depth, which in turn further modifies the lateral trapping stiffness (19, 74). Such nonideal behavior is not insurmountable, but it does illustrate the need for thorough consideration of the experimental conditions in conjunction with careful calibration to ensure accurate results. MAGNETIC TWEEZERS Magnetic tweezers (Figure 1b,c) use the fact that a superparamagnetic bead in an external magnetic field experiences a force proportional to the gradient of the field. The magnetic field B induces a magnetic moment m in the bead: m = 4πr3 μ 0 ( ) μr 1 B, 6. μ r + 2 where μ 0 is the permeability of free space, μ r is the relative permeability of the bead, and r is the radius of the bead. The induced moment interacts with the external field, resulting in a potential U = 1/2 m B. The force F on the sphere is given by the gradient of the potential: F = 2πr3 μ 0 ( ) μr 1 (B 2 ). 7. μ r + 2 Equations 6 and 7 are valid for values of B below the material-dependent saturation field. Above this field strength, the magnetic moment of the bead no longer depends on the applied field, and the equations must be modified appropriately. Different sizes of superparamagnetic beads from a few nanometers to a few micrometers are commercially available. However, as optical microscopy is typically used to determine the position of the magnetic particle, the size of the magnetic particle must be at least a few hundred nanometers. Moreover, the force on a magnetic particle scales with its volume. As mentioned above, to reduce the Langevin force, it is advantageous to work with the smallest possible particle; however, the maximum applied force decreases precipitously as the size of the particle is reduced. Thus, the optimum particle size depends on the experimental force required, but it is typically on the order of one micron. The superparamagnetic micron-sized beads used for magnetic Single-Molecule Techniques 45

14 Magnetization Mm (emu g -1 ) a 10 7 b c 10 6 Force (pn) Magnetic field B (mt) Magnets / bead distance (mm) Manufacturer data Langevin function: M max = 22 emu g -1 B 0 = 18 mt Experiment Model Figure 3 Generation of force and torque on magnetic particles using magnetic tweezers. (a) Magnetization of typical particles used for magnetic tweezers (1-μm diameter, MyOne, Dynal). The magnetization curve is well fitted by a Langevin function, characteristic of paramagnetic behavior. The high magnetic susceptibility reflects the superparamagnetic properties of the particle. (b) Spatial variation of the magnetic field (red line) generated in a permanent magnet implementation of the magnetic tweezers. Magnets (NdFeB) are spaced by a 0.7-mm gap. The force-versus-distance curve predicted from the measured magnetic field and the magnetization of the bead (part a) is shown as a blue line. Experimental measurements of the force exerted on a single bead are shown as blue circles. (c) Representation of the magnetization generated in a superparamagnetic bead. The slight polarization anisotropy of the bead results in a small, extra component in the magnetization, fixed relative to the bead (purple arrow, top). In contrast with the paramagnetic contribution to the magnetization (black arrow), this component might not be initially aligned with the external field (red arrow), thus generating a torque Ɣ that tends to align the direction of this component with the external field. In most applications, this restoration of torque overwhelms all other torque experienced by the bead in the experiment, and therefore the bead follows the field direction. Magnetic field (mt) B B Γ tweezers combine a high magnetic susceptibility with a zero remnant magnetization (Figure 3a). Consequently, they do not exhibit spontaneous magnetization in the absence of an exerted field, thus avoiding unwanted aggregation. The beads typically consist of submicron-sized iron oxide domains embedded in a polymer matrix (76). The ferromagnetic nature of the iron oxide gives rise to the high magnetic susceptibility of the whole bead. However, the small size of these domains ensures that in the absence of an external magnetic field, thermal fluctuations will randomly reorient their magnetization, resulting in a zero net magnetization of the bead. Application of a magnetic field induces a magnetization in the bead aligned with the external field, thus generating a force on the particle (Figure 3b). For a true paramagnetic particle, one does not expect the generation of a torque Γ M B. Superparamagnetic 46 Neuman Lionnet Allemand

15 beads, however, display a slight magnetic polarization anisotropy, resulting in a small deviation from this ideal behavior. The magnetization of the bead consists of a major component, aligned with the external field, and a minor component, aligned along a preferred direction fixed relative to the bead. The latter gives rise to a restoring torque that tends to align the preferred magnetization direction of the bead along the applied field (Figure 3c). Typical values of the restoring torque exerted by the magnetic field on the bead are orders of magnitude larger than other torques experienced by the bead, e.g., the torque exerted by a single-molecule tether, or the viscous drag torque opposing the rotation of the bead imposed by an external rotating field. The bead therefore constantly aligns itself with the external field. Practically, this is equivalent to fixing the angular position of the bead. Magnetic tweezers based on either permanent magnets or on electromagnets have been implemented. We discuss each implementation in turn. PERMANENT MAGNET CONFIGURATION Permanent magnets offer the simplest means of implementing a magnetic tweezers instrument (Figure 1b) (77 79). In a typical configuration, permanent magnets a few millimeters per side are separated by a fraction of a millimeter. The field gradient is inversely proportional to the gap between the magnets, with a characteristic length scale comparable to the gap size. Consequently, the applied force on the magnetic particle changes as a function of displacement, with a characteristic length scale on the order of 1 mm (Figure 3b). Compared with other force probes, such as AFM cantilevers and optically trapped beads, for which the force varies over a nanometer scale, the effective stiffness of magnetic tweezers is vanishingly small. In a typical configuration, the applied force varies by 1 pn for a magnet displacement of 1 mm, resulting in an effective stiffness of 10 6 pn nm 1. This negligible stiffness has important consequences that distinguish magnetic tweezers from other force probe techniques. Foremost among these differences is the fact that magnetic tweezers are passive, infinite-bandwidth force clamps. If the position of the magnetic particle changes by a full 10 μm, the change in force is a mere 0.01 pn. Other techniques, such as optical traps and AFMs, require sophisticated feedback systems to impose a constant force (48, 80). Thus, magnetic tweezers provide a significant advantage in situations in which a constant force is needed. Magnetic tweezers employing permanent magnets are further distinguished by the fact that, unlike optical tweezers, they do not permit three-dimensional control over the position of the magnetic particle. Rather than imposing a three-dimensional harmonic potential, magnetic tweezers impose a onedimensional potential without a local minimum. Indeed, the magnetic Earnshaw theorem states that no configuration of time-independent magnetic fields can stably confine a magnetic particle. Consequently, the magnetic particle must be constrained. Typically, it is attached, or tethered, to the surface of a microscope chamber by a single molecule of DNA or other biopolymer, and the permanent magnets are placed above the sample chamber. In this configuration the magnets apply an upward force on the magnetic particle. Control over the applied force is achieved by displacing the magnets. Calibration of the force as a function of the magnet separation is achieved Single-Molecule Techniques 47

16 though a technique similar to the equipartition method used to determine stiffness in other techniques. The tethered magnetic particle subjected to an upward force can be treated as an inverted pendulum, which has a lateral stiffness α x = F z L 1, where F z is the upward force and L is the extension of the molecule, equal to the height of the particle above the surface. The lateral stiffness α x can be determined from the variance of the lateral fluctuations of the magnetic particle through the equipartition relation: 1/2α x x 2 =1/2k B T. The extension can be measured simultaneously with the variance (see below), and together they provide the force on the molecule. In principle, there is no lower limit on the measurable force. In practice, however, a lower limit is set by the fact that as the force is reduced, the extension of the molecule decreases to the point at which the particle begins to interact with the surface. The maximum force that can be measured in this manner is ultimately limited by the detection bandwidth, the length of the molecule tethering the magnetic bead to the surface, and the size of the bead. The sampling rate should be substantially faster than the Lorentzian corner frequency f 0 = F(L2πγ) 1 to avoid aliasing artifacts; however, if the frequency response of the detection system is well characterized, the measured spectrum can be corrected to some extent, thereby increasing the effective detection bandwidth (V. Croquette, unpublished data). In practice, video-based tracking at 60 Hz can measure a maximum force of approximately 100 pn on a 2-μm bead tethered to the surface with a 10-μm molecule (81). This force measurement method, as well as most magnetic tweezers applications, requires a three-dimensional measurement of the bead position. Croquette and coworkers have developed a method to track in real-time the three-dimensional position of the bead. It relies on illuminating the sample with parallel light, typically from a light-emitting diode (LED). The interference pattern of the illumination light with the light scattered by the bead in the focal plane generates a ring pattern around the image of the bead (Figure 4a,b). Whereas the position of the centroid of the rings in the image plane yields the lateral (x,y) position of the bead with 2-nm resolution, the shape of the rings yields information on the position of the bead along the optical axis, i.e., its z position (Figure 4b). Indeed, the variation of the ring pattern phase is approximately linear with z (Figure 4c). Calibration of this relationship for each bead prior to an experiment enables subsequent real-time video tracking of its z position with 2-nm accuracy (43). ELECTROMAGNET CONFIGURATION Electromagnets, which offer an alternative to permanent magnets (Figure 1c), have been incorporated in several designs for electromagnetic tweezers (43, 63, 82 84). In this case, force is controlled by the current in the coils generating the magnetic field. To increase the magnetic field and its gradient, the coils contain iron pole pieces. The pole pieces lead to significant hysteresis in the relationship between coil current and magnetic field (43). To overcome this nonlinearity, a magnetic field detector can be incorporated into a feedback loop controlling the coil current (82). In their simplest incarnation, electromagnetic tweezers can impose a current-dependent force on a magnetic particle. More sophisticated implementations incorporating multiple 48 Neuman Lionnet Allemand

17 Figure 4 Three-dimensional optical tracking of a micron-sized bead. (a) Schematic of the illumination pattern: Parallel light illuminates a bead, and the interference of the illumination light with the light scattered by the bead in the focal plane produces a pattern of concentric rings. (b) Typical images of a bead (1-μm diameter) using the parallel illumination scheme, for different objective positions along the optical axis. As the objective focus moves away from the bead, the radius of the ring pattern increases. (c) Radial intensity profiles of a bead (horizontal axis) asa function of the objective position (vertical axis). These profiles yield the relationship between the ring pattern shape and the vertical position of the bead, used as a calibration for the z tracking of the bead. electromagnetic pole pieces can achieve full three-dimensional control over the position of and force on a magnetic particle. Unlike optical tweezers, these magnetic tweezers do not create a stable three-dimensional attractive potential; rather, an effective potential is created by dynamically adjusting the coil currents in response to a feedback signal derived from the position of the magnetic particle. In one realization of this scheme, Gosse & Croquette (43) used six independently controllable electromagnetic coils arranged in a hexagonal pattern above a sample chamber placed on an inverted microscope (Figure 1c). The three-dimensional position of the magnetic particle determined by video tracking provided the feedback signal controlling the current in the coils to maintain the position of the particle. In this configuration, the coils applied force in the plane and vertically toward the coils. Gravity provided the required vertical force away from the coils. Electromagnetic tweezers employing four pole pieces in an equilateral tetrahedral configuration and employing laser-based position tracking (see section on Optical Tweezers) have recently been realized (83). These improvements permit the application of force in an arbitrary direction as well as high-bandwidth position tracking. The effective stiffness of electromagnetic tweezers is dominated by the characteristics of the position feedback loop (43). Electromagnetic tweezers capable of full three-dimensional control over the position of the trapped particle can be calibrated by the same techniques used to calibrate optical tweezers (43). In electromagnetic configurations that simply apply a force on the magnetic particle, these techniques are not applicable. However, in these configurations, force can be determined from the velocity of a magnetic bead moving Single-Molecule Techniques 49

18 through a static fluid of known viscosity through the Stoke s relation: F = v6πηr, where v is the bead velocity, r is the bead radius, and η is the fluid viscosity. Although the maximum force depends on the details of the electromagnet configuration, forces up to 1000 pn on a 4.5-μm magnetic bead have been achieved (85). Magnetic tweezers offer several advantages over other micromanipulation and force probe techniques. In a tethered particle geometry, as depicted in Figure 1b, the minimum applied force is much smaller than can be practically achieved by other techniques. Moreover, magnetic tweezers do not suffer from the problems of sample heating and photodamage to biological specimens that plague optical tweezers. Furthermore, as the vast majority of materials have vanishingly small magnetic susceptibility, the magnetic field and resulting force on a magnetic particle are therefore independent of the intervening material, in contrast to the optical field employed in optical tweezers. These properties of magnetic tweezers have been exploited to perform active rheological measurements in complex materials. Sackmann and coworkers, among others, have measured the viscoelastic properties of complex polymer solutions such as entangled F-actin networks by tracking the motion of paramagnetic particles subject to either a constant or an oscillating force (44, 82, 86). The main advantage of these techniques is that they permit rheology in very small samples, including the interior of cells (87, 88). Another advantage of magnetic tweezers is that because the magnetic particle is aligned in the magnetic field, it can be rotated by rotating the magnetic field. In the permanent magnet configuration, this is performed by physically rotating the magnets (79), whereas in the electromagnet configuration, an oscillating, out-of-phase current is imposed between the coils (43). This ability to control the rotation in addition to the tension in a single polymer has been extensively applied to the study of DNA topology (79, 81) and of the enzymes that control DNA topology (89). Rotational microrheology has also been achieved with magnetic particles, both in solution and in the interior of cells (90, 91). ATOMIC FORCE MICROSCOPY An atomic force microscope (AFM) (Figure 1d ) consists of a thin sharp tip at the extremity of a flexible element called a cantilever (92, 93). The cantilever can be displaced very accurately (with angstrom precision) with a piezoelectric stage. When the tip interacts with a molecule, the cantilever is deflected. Reflection of a laser beam from the cantilever onto a split photodiode allows sensitive measurement of the cantilever deflection. Over a reasonable deflection range, the system behaves like a spring, and thus deflection is proportional to the force. Although the AFM is used primarily as an imaging device, we concentrate on the related ability to apply controlled pulling forces. For this application the AFM tip is functionalized to either specifically or nonspecifically bind the polymer of interest. As mentioned above, the first task is to measure the spring constant. The cantilever stiffness is determined by analyzing the variance of thermal positional fluctuations of the unloaded cantilever, in a method analogous to that used to determine the stiffness of optical tweezers. The large and complex geometry of the force sensor precludes the use of hydrodynamic calibration methods such as the power spectral method or imposing a force with a controlled flow. 50 Neuman Lionnet Allemand

19 Typical cantilever stiffness values range from to 10 3 to 100 N m 1 (93). Optical detection affords AFM measurements a large bandwidth (few kilo-hertz), which allows the measurement of processes occurring on short timescales. The large forces that can be applied, combined with high spatial resolution that can be achieved with the AFM, make AFM a powerful tool to study the rupture of molecular bonds ranging from an individual covalent bond (18) to the controlled unfolding of single proteins (5, 94) and the elastic properties of single polymers (95, 96). Although the unfolding trajectories of single proteins are currently readily measured, the folding trajectories have been more difficult to obtain. Recently, the entire folding trajectory of a single protein was measured with an AFM incorporating a force feedback loop (80). The primary limitations of the AFM result from the relatively large force sensor that is subjected to a proportionally larger Langevin force, which precludes measurement of forces less than a few pico-newtons. Nevertheless, it can measure very large forces in excess of nano-newtons. Moreover, forces can be determined for configurations in which no molecule is attached to the cantilever, e.g., when the cantilever is probing a surface. GLASS MICRONEEDLE The method termed glass microneedle, or microfiber, micromanipulation (Figure 1e) is conceptually similar to the AFM (13, ). The stiffness of a rod is proportional to the fourth power of its radius and to the inverse third power of its length. Thus, by reducing the radius of an optical fiber with chemical etching, one can obtain a rod flexible enough to detect interaction with a single molecule. The advantages of using a glass optical fiber are that (a) its radius can be controlled with hydrofluoric acid treatment and (b) the light emitted from the end of the fiber projected onto a positionsensing photodetector provides an accurate measure of fiber deflection. Calibration of the microneedle, similar to other micromanipulation techniques, involves determining the stiffness of the fiber. The microneedle is calibrated in exactly the same manner as the AFM. However, owing to a larger sensor and lower spatial resolution than AFM cantilevers, glass microneedles do not achieve the same performance: The force sensitivity and bandwidth are reduced, although it is a cheaper option. BIOMEMBRANE FORCE PROBE The biomembrane force probe technique (Figure 1f ) is based on the fact that the deformability of a vesicle is related to the membrane tension (101, 102). The tension is proportional to the pressure in the vesicle, which can be controlled by capturing the vesicle in a pipette and varying the suction pressure (Figure 1f ). The membrane can then be used as a spring with an adjustable stiffness that can be varied over orders of magnitude. The stiffness can be determined from models relating stiffness to membrane geometry and measured directly from the thermal motion of a bead attached to the membrane (101). The force is then obtained by multiplying this stiffness by the change in extension of the membrane. Merkel and coworkers (103) pioneered the field of dynamic force spectroscopy using the biomembrane force probe to demonstrate that the rupture force of a molecular bond depends on the loading rate. Single-Molecule Techniques 51

20 FJC: freely jointed chain WLC: worm-like chain SINGLE-MOLECULE ELASTICITY The simultaneous measurement of force and extension possible with single-molecule techniques provides a natural measure of the elastic properties of single molecules. Molecular elasticity arises from two different effects. At low forces, extension of the molecule reduces the number of accessible conformations of the polymer chain, thereby decreasing the entropy. In this entropic elasticity regime, the molecular elasticity is reflected by the work done in reducing the polymer entropy. At higher forces, for which the polymer is largely extended, the elasticity is dominated by the work required to deform chemical bonds in the polymer. A third aspect of the elastic properties of single molecules involves the rupture of intramolecular bonds, i.e., the folding state of the molecule, a crucial parameter for biological activity in the case of proteins or nucleic acids. The entropic regime has been studied largely in the polymer elasticity and dynamics field (5, 13, 14, 78, 79, 81, 96, ), whereas breakage of molecular bonds by force has been progressively recognized as an important tool to probe molecular structures (80, 94, ). Double-stranded DNA (dsdna) constitutes a model system to test entropic elasticity theories. In addition, knowledge of the mechanical properties of dsdna has proven to be a powerful tool for biological studies of DNA-protein interactions at the single-molecule level, as illustrated below (114). The first model introduced to account for the entropic elasticity of dsdna was the freely jointed chain (FJC) model describing the polymer as a series of discrete independent segments (Figure 5a). Thermal fluctuations induce a random orientation of each segment. However, when submitted to a force, they will align along the direction of the constraint, in a fashion similar to Langevin s description of paramagnetism in which magnetic dipoles are oriented by the magnetic field but disoriented by thermal energy. However, dsdna is a rigid molecule and cannot be accurately considered as a chain of independent segments. A more complete description necessarily includes a bending rigidity that limits the orientation of consecutive segments. The continuous limit of such a model is the worm-like chain (WLC) model (Figure 5b). This model has been numerically solved and compared with the single-molecule stretching experiment performed in 1994 by Bustamante et al. (104). Fitting experimental force extension data have been facilitated by an accurate analytical approximation to the exact solution (108). Analysis of single-molecule experimental data provided a direct measurement of the persistence length ξ of dsdna, i.e., the typical length necessary for thermal fluctuations to bend the DNA (ξ 50 nm in standard ionic conditions, Figure 5c). Therefore, forces necessary to align the dsdna molecule against entropic elasticity are on the order of k B T/ξ 0.1 pn. The double-helical structure of DNA results in rich topological behavior. Magnetic tweezers permit exploration of this behavior through the study of dsdna elasticity as a function of over- or underwinding by rotating the magnetic bead to which the dsdna molecule is attached (79). At low forces, the DNA extension is largely insensitive to rotation up to a threshold at which a buckling transition occurs. At this point, the torque in the molecule is sufficient to induce a bend in the molecule. In other words, it is energetically more favorable to bend the DNA and reduce the 52 Neuman Lionnet Allemand

21 a FJC b WLC c d 10 Experimental data 15 F F FJC model WLC model a 1 10 t i θ i θ(s) t(s) Force (pn) 10-1 DNA extension (µm) 5 Denatured Denatured Force: 8 pn 1 pn 0.2 pn Plectonemes plectonemes P-DNA plectonemes Plectonemes F Figure 5 F Relative extension <z>/l0 Elasticity of a single double-stranded DNA (dsdna) molecule. (a) Schematic representation of the FJC model: DNA is modeled as a chain of consecutive segments of length a that assume an independent orientation θ i.(b) Schematic representation of the WLC model: dsdna is represented as a continuous curve. The local orientation θ(s) is constrained by the introduction of a bending rigidity. (c) Experimental force-extension curve of a single dsdna molecule (red circles). The fit to the WLC model (purple line, ξ = 51.6 ± 2 nm) is in good agreement with the experimental data. The fit to the FJC model (green line, segment length a = 103 nm) displays a poorer agreement with the data. (d ) Torsional elasticity of a single dsdna molecule. extension of the molecule, working against the applied force, than to further increase the torque in the DNA. Beyond this buckling threshold, additional turns applied to the molecule are converted to plectonemic loops (Figure 5d ), resulting in a linear decrease in extension with applied turns. The formation of plectonemes is observed symmetrically under positive and negative torsion as long as the stretching force is held below a (salt-dependent) critical force, typically 0.5 pn. However, above this force the chiral structure of DNA becomes apparent. When the DNA is negatively supercoiled (underwound), the applied torque is limited by the formation of denaturation bubbles (regions in which the hydrogen bonds between complementary bases are broken) rather than the formation of plectonemic loops. As the extension of the denatured regions is very close to the extension of unconstrained DNA (in the few pico-newton range), the overall extension of the molecule does not dramatically change (81). In contrast, when the DNA is positively supercoiled (overwound) in this force regime, plectonemes are formed at a somewhat higher critical number of turns past which the extension of the molecule decreases (81, 115). Elastic properties are much more complex when they involve intramolecular bonds. Nevertheless, this is an important and increasingly common area in which single-molecule manipulation techniques are being applied. In practice, the unfolding of these intramolecular bonds is limited to biomolecules such as single-stranded DNA (97, 116, 117), RNA (111), and proteins (80, 94, 113). In the case of RNA and proteins, these intramolecular bonds are responsible for the three-dimensional structure of the molecule. Proper folding of these molecules is required for their biological activity. The methodology that has been adopted to probe these intramolecular bonds n (turns) Single-Molecule Techniques 53

22 is independent of the precise technique or molecule studied (94, , ). A typical experiment consists of increasing the force on the molecule, gradually extending it until the point at which the bonds rupture. As a single bond breaks, the extension abruptly increases (and the force decreases if no force clamp is imposed). Loading rate, i.e., the rate at which force is increased, is a crucial parameter for these experiments if equilibrium conditions are not reached (123, 126). Indeed, fast, repetitive rounds of folding and unfolding of an RNA molecule proved to be a good experimental test for microscopic nonequilibrium models (122, 125). Pulling experiments are better understood in terms of bond energy rather than rupture force: The bond represents an energy barrier that must be passed for the molecule to unfold. Increasing the pulling force distorts this energy landscape, which reduces the energy barrier and decreases the bond lifetime. Thus, these experiments provide insight into the energy landscape of the folding process. BIOLOGICAL APPLICATIONS OF SINGLE-MOLECULE MICROMANIPULATION TECHNIQUES The micromanipulation techniques described were either specifically developed for single-molecule experiments or were pushed to the limit to manipulate single molecules. Whereas these techniques were developed principally for, and applied to, biophysical applications, they are increasingly being applied to other domains. In the following we summarize some of these applications of optical and magnetic tweezers. We concentrate on single-molecule in vitro experiments on DNA and enzymes that interact with DNA. This choice is arbitrary, and readers interested in other singlemolecule biophysical experiments will find a variety of other examples in References RNA polymerase is the enzyme responsible for translating the genetic code from DNA into RNA (a process called transcription), which is then read by the ribosome to Figure 6 RNA polymerase studied with optical tweezers. (a) Stage-based RNA polymerase optical trapping assay. RNA polymerase bound to the template DNA is specifically attached to a polystyrene bead through a specific ligand-receptor pair (not shown). The free end of the DNA is attached to the surface of the trapping chamber via a specific antibody-antigen pair. The bead is held in the optical trap (pink) at a predetermined position, which imposes a force on the RNA polymerase. As RNA polymerase transcribes DNA into RNA, it translocates along the DNA template. The position of the bead in the optical trap, and hence the force, is held constant by moving the trapping chamber to counteract the motion of the polymerase along the DNA. (b) Double optical trap and dumbbell RNA polymerase assay. The assay is identical to the previous assay except that the free end of the DNA is attached to a second polystyrene bead that is held in a second independently steerable optical trap. As the polymerase transcribes the DNA, one of the optical traps is moved relative to the other so that the force is held constant. The double-trap geometry significantly reduces the noise and drift associated with the motion of the trapping chamber. Abbondanzieri and coworkers (136) employed this assay to measure the individual 3.3-Å steps of RNA polymerase as it translocates along the DNA. 54 Neuman Lionnet Allemand

23 produce proteins. RNA polymerase can be thought of as an enzyme that catalyzes the synthesis of a biopolymer (RNA), but from a mechanical point of view, it is a molecular motor that translocates along DNA using the chemical energy of RNA synthesis as fuel. Yin et al. (130) performed the first experiment probing the mechanical properties of this motor. RNA polymerase from Escherichia coli was attached to a surface, and the free end of the transcribed DNA was attached to an optically trapped bead (Figure 6a). In this geometry, the speed of individual motors ( 16 nucleotides s 1 ) as well as the stall force ( 30 pn) could be measured (131). Whereas the average velocity can be obtained from ensemble biochemical experiments, single-molecule experiments can probe variability among enzymes. Moreover, they are well suited to studying pauses in motor activity that provide insight into the motor mechanism, and a b RNA polymerase Synthesized RNA DNA Antibody and ligand Single-Molecule Techniques 55

24 are biologically important ( ). Recently, Abbondanzieri et al. (136) achieved single base-pair (0.33 nm) position detection resolution, using a double optical trap and a dumbbell trapping geometry (Figure 6b). This extraordinary resolution allowed them to unambiguously differentiate between different models describing the translocation of RNA polymerase along DNA. These included a power stroke model, in which motor movement is strongly coupled to the chemical reaction cycle, and a Brownian thermal ratchet model, in which thermal fluctuations, i.e., diffusion, play an important role in the progression of the motor, unlike macroscopic motors (137). The authors concluded that RNA polymerase moves by a Brownian ratchet mechanism. Building on this work, Greenleaf & Block (138) demonstrated mechanically based single-molecule DNA sequencing. When the RNA polymerase transcribes in a solution in which one of the four RNA bases is at a much lower concentration than the others, the motor pauses each time it must incorporate the low-concentration base, thereby revealing the position of complementary base on the DNA. By correlating the position of the pauses for different solutions, each depleted of one of the bases, up to 30 bp of DNA could be sequenced. Single-molecule techniques have brought a host of novel experimental approaches for the study of another class of enzymes, the topoisomerases. Topoisomerases regulate and control the topology of DNA in all living organisms. They are responsible for untangling, unknotting, and unlinking DNA, and they also regulate the overand underwinding of the DNA double helix. Their importance is highlighted by the fact that potent antibiotics and cancer chemotherapy agents specifically target topoisomerases. Owing to the ease of rotating a magnetic particle, magnetic tweezers provide a convenient means of both controlling and measuring DNA topology. By tethering of the magnetic bead to the surface with a single molecule of DNA rotationally constrained at both ends, i.e., attached at multiple points to the bead and the surface, the DNA can be over- and underwound by rotating the bead. At low forces (F < 0.4 pn) over- or underwinding of the DNA leads to the formation of loops or plectonemes (79), which reduce the extension of the bead by 45 nm per added turn (Figure 7a). Topoisomerases specifically modify the degree of over- and Figure 7 Topoisomerase studied with magnetic tweezers. (a) Extension as a function of rotation for DNA. A single molecule of DNA is attached to a paramagnetic bead and to the surface of the cell through rotationally constrained bonds. Small magnets above the sample apply an upward force and torque on the bead. Rotation of the magnets in either direction rotates the bead and causes the DNA to buckle and form plectonemes (inset right and left) that decrease the extension of the bead. For a stretching force of 0.4 pn the extension-rotation relationship is symmetric (green dots). The slope of the linear regime of the extension-rotation relationship (green line) indicates the change in extension per plectoneme loop, which in this case is 45 nm. (b) Removal of plectonemes by topoisomerase IV. Topoisomerase IV (inset) removes DNA plectonemes by transiently breaking one strand of DNA, passing a second strand through the break, and then resealing the DNA. The trace shows the real-time extension of a molecule of DNA that has been underwound (negative rotation in part a) by 12 turns. Occasionally, topoisomerase IV binds to the DNA and relaxes a single pair of plectonemes, as evidenced by the abrupt transitions of 90 nm (arrows) (K.C. Neuman, G. Charvin, D. Bensimon, & V. Croquette, unpublished data). 56 Neuman Lionnet Allemand

25 a N S Extension (µm) b Magnet rotation (turns) Extension (µm) Time (s) Single-Molecule Techniques 57

26 underwinding of the DNA molecule, which can be observed owing to the large 45-nm extension change associated with the formation or loss of a plectoneme. Therefore, monitoring the extension of the DNA molecule permits direct observation of topoisomerase activity on a single molecule of DNA (Figure 7b). In a pioneering work, Strick et al. (89) measured in real time a single turnover of a single topoisomerase on a single DNA molecule. In addition to the advantages shared by all single-molecule measurements, the magnetic tweezers experiments offer several unique advantages for the study of topoisomerases. The rotation of the DNA can be controlled to onetenth of a rotation or better, and DNA over- and underwinding are both easier and can be extended over a much larger range than is achievable by biochemical means. PROSPECTS The past 15 years have witnessed rapid development of single-molecule manipulation techniques. As these techniques have matured, they have been adopted by an ever-increasing range of disciplines. These techniques will continue to develop through advances in technology and innovation. As they have become more familiar and more robust, some are even commercially available, aiding in broader use and facilitating cross-fertilization between disciplines. Additionally, existing techniques are now being combined to great effect. For example, single-molecule fluorescence (not discussed in this review owing to space constraints) which provides details about conformation, position, and environment and is complementary to and in some cases on a much faster timescale than manipulation techniques has recently been combined with optical tweezers (117, 139). The combination of these two single-molecule techniques offers great promise for a variety of applications. Advances in existing techniques will be matched by the development of new manipulation techniques. For example, using a low-powered LED, Chiou and coworkers (140) were recently able to produce thousands of independently controllable, optically patterned dielectrophoretic particle traps. This method offers an inexpensive means of producing a massively parallel, optically induced trapping array for use in such applications such as parallel micromanipulation or the sorting of particles and cells. Sorting of microscopic particles by size or by refractive index has also been demonstrated by MacDonald and coworkers (141), using a three-dimensional array of specifically tuned optical traps. Finally, Cohen (142) has pioneered a two-dimensional electrophoretic trap capable of directly manipulating microscopic particles including proteins. These novel techniques have yet to achieve their full potential or to be extensively applied. However, we expect that these advances will pave the way for novel applications and the continued refinement of techniques and experiments. SUMMARY POINTS 1. Single-molecule micromanipulation techniques allow a variety of length, force, and complexity scales to be probed with high spatial and temporal resolution. 58 Neuman Lionnet Allemand

27 2. Relevant forces for single-molecule manipulation range from fractions of a pico-newton required to extend a single polymer chain to thousands of pico-newtons required to break a covalent bond. 3. The measurement of the force-extension relationship of individual polymer molecules provides a direct determination of the complete nonlinear elastic response, comprising both enthalpic and entropic regimes. 4. Microrheology permits rheological measurements in small volumes and on short length scales, including the interior of cells, by tracking the motion of micron-scale objects subjected to thermally or mechanically imposed forces. 5. Single-molecule techniques have made important contributions to biophysics, including the elucidation of enzymatic mechanisms of RNA polymerase and topoisomerases. ACKNOWLEDGMENTS The authors thank members of the Bensimon and Croquette lab for advice and suggestions. In particular we thank V. Croquette for sharing results prior to publication and for many helpful discussions. We thank D. Chatenay for providing Figure 2 and G. Charvin for providing Figure 5. We are indebted to Grace Liou for critical reading of the manuscript and to Omar Saleh for insightful comments. K.C.N. was supported by a Long-Term Fellowship from the Human Frontiers Science Program. J.F.A. acknowledges support from ANR and DRAB. T.L. acknowledges support from ANR. LITERATURE CITED 1. Mallik R, Gross SP Molecular motors: strategies to get along. Curr. Biol. 14:R Ishijima A, Yanagida T Single molecule nanobioscience. Trends Biochem. Sci. 26: Bustamante C, Chemla YR, Forde NR, Izhaky D Mechanical processes in biochemistry. Annu. Rev. Biochem. 73: Zhang W, Zhang X Single molecule mechanochemistry of macromolecules. Prog. Polym. Sci. 28: Clausen-Schaumann H, Seitz M, Krautbauer R, Gaub HE Force spectroscopy with single bio-molecules. Curr. Opin. Chem. Biol. 4: Strick TR, Allemand JF, Bensimon D, Croquette V Stress-induced structural transitions in DNA and proteins. Annu. Rev. Biophys. Biomol. Struct. 29: Samori P, Surin M, Palermo V, Lazzaroni R, Leclere P Functional polymers: scanning force microscopy insights. Phys. Chem. Chem. Phys. 8: Bao G Mechanics of biomolecules. J. Mech. Phys. Solids 50: Single-Molecule Techniques 59

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36 Contents Annual Review of Materials Research Volume 37, 2007 MATERIALS CHARACTERIZATION Low-Temperature Degradation of Zirconia and Implications for Biomedical Implants Jérôme Chevalier, Laurent Gremillard, and Sylvain Deville 1 Single-Molecule Micromanipulation Techniques K. C. Neuman, T. Lionnet, and J.-F. Allemand 33 Spin-Polarized Scanning Tunneling Microscopy of Magnetic Structures and Antiferromagnetic Thin Films Wulf Wulfhekel and Jürgen Kirschner 69 Microscale Characterization of Mechanical Properties K. J. Hemker and W. N. Sharpe, Jr. 93 Three-Dimensional Atom-Probe Tomography: Advances and Applications David N. Seidman 127 The Study of Nanovolumes of Amorphous Materials Using Electron Scattering David J. H. Cockayne 159 Nanoscale Electromechanics of Ferroelectric and Biological Systems: A New Dimension in Scanning Probe Microscopy Sergei V. Kalinin, Brian J. Rodriguez, Stephen Jesse, Edgar Karapetian, Boris Mirman, Eugene A. Eliseev, and Anna N. Morozovska 189 AFM and Acoustics: Fast, Quantitative Nanomechanical Mapping Bryan D. Huey 351 Electron Holography: Applications to Materials Questions Hannes Lichte, Petr Formanek, Andreas Lenk, Martin Linck, Christopher Matzeck, Michael Lehmann, and Paul Simon 539 Three-Dimensional Characterization of Microstructure by Electron Back-Scatter Diffraction Anthony D. Rollett, S.-B. Lee, R. Campman, and G.S. Rohrer 627 vii