Force Measurement and Mechanical Imaging Apparatuses

CHAPTER THREE

Force Measurement and Mechanical Imaging Apparatuses A. Ikai Tokyo Institute of Technology, Yokohama, Japan

Contents 3.1 Mechanical, Thermal, and Chemical Forces 3.2 Laser Trap 3.3 Atomic Force Microscope 3.3.1 History and Principle 3.3.2 Mechanical Imaging by Atomic Force Microscope (AFM) 3.3.2.1 3.3.2.2 3.3.2.3 3.3.2.4 3.3.2.5

Contact Mode and Tapping Mode Noncontact Mode High-Speed AFM Scanning Ion Conductance Microscope MultiFrequency AFM

35 36 40 40 41 42 43 45 45 45

3.3.3 How to Use AFM for Force Measurement 3.3.4 Cantilever Force Constant 3.4 Surface Force Apparatus 3.5 Biomembrane Force Probe 3.6 Magnetic Beads 3.7 Gel Columns 3.8 Cantilever Force Sensors 3.9 Loading-Rate Dependence 3.10 Force Clamp Method 3.11 Specific Versus Nonspecific Forces Bibliography

47 49 51 51 53 53 54 54 57 57 59

3.1 MECHANICAL, THERMAL, AND CHEMICAL FORCES Force causes motions and deformations of material bodies and force can be applied in various different ways; force is force no matter what its origin is, just like energy is energy no matter how it is disguised. In practice, however, we distinguish different forms of energy such as heat, light, electric, etc. The World of Nano-Biomechanics ISBN: 978-0-444-63686-7 http://dx.doi.org/10.1016/B978-0-444-63686-7.00003-1

© 2017 Elsevier B.V. All rights reserved.

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Similarly, by knowing different origins of force, we may have access to control particular types of force. Force (F) is the negative derivative of potential energy (V (r)) with respect to the distance (r) of movement and it is expressed in various different ways as shown below. F¼

dV ðrÞ dr

When the distance is given by the three components, x, y, and z, 
vV ðx; y; zÞ vV ðx; y; zÞ vV ðx; y; zÞ ; ; Fðx; y; zÞ ¼  vx vy vz
 v v v ; ; ¼ V ðx; y; zÞ ¼ gradV ¼ VV vx vy vz

(3.1)

(3.2)

where V is called the gradient or nabla or del operator. Force is, thus, a vector and has a magnitude and a direction as it is derived from a scalar function V using the gradient operator as shown previously. Force played the central role in the Newtonian mechanics but gradually gave way to energy a more central stage in physics, especially in quantum mechanics. Measuring the magnitude of a force acting on experimental samples and extracting mechanical responses from the latter is the major concern of this section. If we can measure the magnitude and direction of a force acting on atoms and molecules, then we will be able to control the force that is influencing certain life processes while monitoring their behavior under a microscope. Measuring a small force acting at the molecular and atomic levels has been a difficult undertaking because the magnitude of the force involved is in the order of 109  1012 times smaller compared with newton (N)level force in our daily experiences. Recently, there has been an explosive development in the technology of measuring even smaller forces of 1012 N. Today, scientists are talking about measuring femtonewton forces, i.e., 1015 N. Let us take a look at some of the recently developed instruments with a capability of measuring such small forces acting in the invisible world of atoms and molecules, the nanoworld.

3.2 LASER TRAP One of the most sensitive force measuring devices is called the laser trap or laser tweezers consisting of a focused laser beam(s) and a microscope. The laser tweezers technique was developed by Ashkin [1,2] and has been

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greatly improved and widely used since then. It utilizes the force exerted by the light at the interface of two materials with different refractive indices. It has been shown that a metallic (conductive) or plastic (dielectric) particle whose diameter is less than the wavelength of light can be trapped by a focused laser beam. When a converging laser beam is irradiated on the particle, the scattering force, Fscat, and the gradient force, Fgrad, together work on the particle in two different ways. Fscat always pushes the particle in the direction of light propagation; thus a particle between the beam source and the focus is pushed to the focal area, but one on the other side of the focal area is pushed away. The gradient force, Fgrad, drives the particle to move in the direction of increasing electromagnetic field; therefore it is called the gradient force, and it pulls particles to the focal area from all directions. The gradient force, acting on a particle of polarizability, a, is given in the following form [3]. 1  2  Fgrad ¼  aV E  2

(3.3)

E is the electric field in the laser beam. For a spherical particle, the polarizability, a, is given by the following form: a ¼ 4pεr ε0

n2r  1 3 a n2r þ 2

(3.4)

where nr is the refractive index of the particle relative to that of the surrounding medium and a is the radius of the particle. The gradient force is thus dependent on the volume of the sample particle through the a3 term. In general, a is a complex number, but when its real part is positive, the particle is attracted to the stronger light field according to the gradient of the force. For example, a small gold particle with a  l is pulled into the beam focus by the gradient force because the real part of a is positive for gold. The variation of the gradient force and the scattering force in the vicinity of the laser focus is given in Ref. [2]. In Fig. 3.1, the laser beam is irradiated from the left to the right region, and its focal point is shown in the middle of the figure. If the latex bead is on the left of the focal point, the force operating at the interface pushes the bead to the right according to the force given by Eq. (3.4). If the bead is on the right of the focus, the force acts to push it to the left. Either way, the bead is pulled to the focal point. If the bead strays out of the focal point, there is always a force to pull the latex bead back to the center of the focus, and the bead is “trapped” there.

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Figure 3.1 Qualitative view of the trapping of a dielectric sphere in the focal point of laser beam. A converging beam comes in from the left, forms a focal point in the center, and leaves to the right. The refraction of a typical laser beam gives scattering and gradient forces whose vector sum always restores for axial and transverse displacements of the sphere from the focal point.

Thus, another term for this phenomenon is the “optical trap” method. As the laser focus is moved to left and right, the bead also moves as if it is picked with a pair of tweezers. Hence the method is also called laser or optical tweezers. Since the intensity of the laser beam has a somewhat Gaussian distribution in the 2D cross-section of the beam, the potential energy and the force associated with it can be calculated. There are two different ways to calculate the strength of the gradient force according to the relative size of the particle with respect to the wavelength of the laser light, l. The gradient force is in the “ray optics” regime when the radius of the particle (a) is much larger than the wavelength of the laser beam (a [ l) and in the Rayleigh regime when a  l. In the former case, the gradient force is independent of the size of the particle and proportional to the gradient of nP/c (n: refractive index of the medium, P: power of the laser beam, and c: the velocity of light), whereas in the latter regime, it changes with a3 because the polarizability is proportional to the volume of the particle as we have seen. In typical experimental cases in biology, a w l and the size dependence of the gradient force are not accurately known. The trapping force is then experimentally calibrated by dragging a spherical particle by laser tweezers and calculating the dragging force according to the hydrodynamic frictional force based on the Stokes’ law of spherical particle, i.e., F ¼ 6phav, where h and v are the viscosity coefficient of the medium and the constant rate of particle movement, respectively [4]. As an example of force measurement of laser trap, Hénon et al. reported the result of incident laser power versus trapping force on a latex bead of 1.05 mm as estimated by the hydrodynamic drag method (Fig. 3.2) [5]. The result in Fig. 3.2 shows that the trapping force is almost

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Figure 3.2 The relationship between the incident laser power (abscissa) and the trapping force (ordinate) in the focus of the laser beam at three different distances from the cover slip. Reproduced from S. Henon, G. Lenormand, A. Richert, F. Gallet, A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers, Biophys. J. 76 (1999) 1145e1151 with permission.

linearly proportional to the laser power but slightly dependent on the distance from the cover slip. The maximum force available in this case was approximately 80 pN. The magnitude of the gradient force and that of the scattering force depend on the laser power. If the laser power is high and if the difference in the refractive index of the particle is much higher than that of the medium, scattering force becomes larger than the gradient force and the laser trap fails. For a particle having only a slightly larger refractive index compared with that of the medium, the gradient force is not strong enough as a trapping device. If that is the case, two laser beams are employed in opposing directions both focusing at the same position. This setup would compensate for the scattering force while reinforcing the gradient force. This technique can be used to measure the force exerted to a bead trapped in the center of the focus. For example, suppose the bead in focus is tethered to a rigid wall via flexible polymer chain. As the laser beam moves horizontally, the bead trapped in the focus also moves, but its position does not exactly coincide with the center of the laser focus because of an extra force exerted from the polymer chain being stretched or compressed. The mismatching distance between the bead and the laser focus center coincides with the extension or compression of the polymer. It also gives the force

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acting on the polymer chain according the calibrated forceedistance curve of the laser trap. Thus one obtains a forceeextension curve for the polymer chain between the two beads.

3.3 ATOMIC FORCE MICROSCOPE 3.3.1 History and Principle In 1982 the invention of the scanning tunneling microscope (STM) was announced, and it was immediately welcomed by the researchers in surface science and related fields because of its superb capability of showing the arrangement of individual atoms on the metallic and semiconducting surfaces [6,7]. By measuring the magnitude of the tunneling current between an electrically conductive probe and a sample, which is exponentially dependent on the probe versus sample distance, the STM can provide a contour map of the sample surface in terms of the local density of states (LDOS) [8,9]. Special attention was paid to the arrangement of atoms in the reconstructed silicon (111) surface, where the STM clearly showed a real space image of the surface, which was very similar to the model that had been presented by Takayanagi et al. [10,11]. A few years later in 1986, the atomic force microscope (AFM) was invented by Binnig and colleagues [12], which was also capable of imaging atoms and molecules on a solid surface. One advantage of AFM is that it can operate on either conductive, semiconductive, or nonconductive materials, whereas the STM requires electron-conductive material as a sample. Comprehensive reviews of the mechanical imaging and force-mode operation of AFM, and the results reported in this area, have been given by Ikai et al. [13] and Butt et al. [14]. The AFM operates on the principle of mechanical rather than electrical interactions between the probe and the sample surface. Suppose both the probe and the sample are electrically neutral, dielectric materials. As the probe approaches within a few tens of nanometers, it comes into the regime of an attractive van der Waals force (including all of the dipoleedipole, dipole-inducededipole, and London dispersion interactions (see chapter 4). The probe is weakly attracted toward the sample surface, and as it approaches closer to the sample, it is in the repulsive regime in terms of LennardeJones potential [15], where the probe is strongly repelled from the sample surface. By measuring either an attractive or repulsive force at regularly positioned sites over the sample surface, one can reproduce the contour map of the sample.

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In most of the currently available commercial AFM instruments, the force sensor is a thin cantilever of approximately 100 mm in length (L), 20e30 mm in width (w), and less than 1 mm in thickness (t). When it is made of silicon or silicon nitride of Young’s modulus (Y) of 100e150 GPa, the spring constant (k) can be in the range of 0.01e10 nN/nm. It may be estimated from the following [16]. First, the relationship between the load, F, and the cantilever deflection at the free end, ymax, is expressed as ymax ¼

L3 4L 3 F¼ F 3YI Ywt 3

(3.5)

where I is the cross-sectional moment of the cantilever (in the case of crosssection of the rectangle of width, w, and thickness, t, I ¼ wt3/12). Therefore, the spring constant of the above mentioned cantilever is  3 Ywt 3 100  109  30  106  1  106 k¼ ¼ (3.6) 4L 3 4  ð1  104 Þ3 ¼ 0:75 N=m ¼ 0:75 nN=nm These equations are derived from the consideration of beam bending problem in mechanics, as detailed in Appendix 1. The optical lever system of AFM measures the displacement of the laser spot as it is reflected from the back of the cantilever. This displacement of the laser spot is proportional to the deflection angle of the cantilever, and it can be considered to be proportional to the vertical deflection of the cantilever. The 2D distribution of vertical deflection of the cantilever can thus be interpreted as representing a topography of the sample surface with atomic resolution.

3.3.2 Mechanical Imaging by Atomic Force Microscope (AFM) By using the mechanical principle of AFM, one may construct a 2D map of height distribution of the sample surface. This is a contour map, and just like an ordinary geographical map of a landscape, it may be color coded according to the height range. In practice, the lateral resolution of the resulting map depends on the sharpness of the AFM tip and the rigidity of the sample surface. The vertical resolution is determined by the sensitivity of the cantilever as well as the signal conversion system of cantilever deflection to the electrical signal. In a typical commercial instrument, the lateral and vertical resolutions are w0.1 and w0.001 nm, respectively. The effective diameter and the opening angle of a typical pyramidal-shaped AFM tip are w10 nm and

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35 , respectively. With this dimension, it is difficult to trace narrow and deep trenches accurately. Various types of highly sharpened probes have been produced. Another problem is soft samples. Since, in principle, AFM tip touches and pushes the sample though softly and slightly, it still deforms the sample, which results in an inaccurate estimate of the sample height. Some soft samples stick to the cantilever tip and are dragged around giving unwanted signals to the cantilever. This will again distort the accuracy and resolution of resulting images [17]. In spite of such difficulties as mentioned before, recent advancement of AFM instrumentation has produced remarkable results of biological molecules and structures. Some major topics are treated here under mechanical imaging by AFM. According to the principle of operation, at least four different types of AFM are available today. 3.3.2.1 Contact Mode and Tapping Mode This is the original method of obtaining a height image. In the contact mode, the AFM probe is pressed onto the sample surface with a small set point voltage, less than 1 nN in terms of vertical force. The probe is then scanned over the surface with constant set point voltage first in x-direction (commonly 256 points, but can be less or more) keeping y-direction unchanged. Then repeat this process after one-step increment in y-direction (xy raster scan). When the process is finished, sample height data are collected from 256  256 pixels in x-y plane of a prefixed area. Since biological samples are generally soft, it is important to use a very soft cantilever to avoid mechanical damage to the sample. In air under a relatively high humidity, sample, substrate, and probe surfaces are all covered with a thin layer of water. As the probe surface approaches the sample surface, the water layers on the two surfaces suddenly coalesce and a strong force is required to separate them. This event damages a soft sample and distorts images. It is manifested in the force curve as a “jump-in,” i.e., a sudden downward deflection of the probe. The retraction process of the probe from the sample surface is characterized by a prolonged tip-surface contact. The tip is freed from the surface only after a large deflection of the cantilever is reached, meaning after accumulation of a large force. This force is called “capillary force” or “meniscus force” because the phenomenon is due to the capillary effect of adsorbed water layers to keep the surface energy of the combined two surfaces at minimum [18e20]. The capillary effect is only existent in AFM operation in air. If a sample is submerged in water, there is no such effect, and contact mode imaging of

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biological samples can be done more easily in water than in air. For a soft sample, however, contact mode scanning still is hampered by sample dragging under the laterally moving tip. To avoid such deleterious effects observed in the contact made imaging, Hansma et al. introduced a new scanning method called “tapping” mode, which is usable both in air and in liquid [21]. In this mode, a relatively stiff cantilever is oscillated at near its resonance frequency with a large amplitude of w100 nm. When the cantilever comes close to the sample and “taps” on its surface, the amplitude begins to decrease. By keeping the amplitude decrease to a constant level through a feedback system, the tip is laterally scanned over the sample surface. In air, large amplitude oscillation of a stiff cantilever is strong enough to overcome the meniscus force during each approacheretraction cycle, making it easier to raster scan the sample surface. In liquid, because the tip does not drag the sample, sample damage is kept minimal. Contact and tapping modes are two fundamental methods in AFM. In these two methods the tip interacts with the sample surface in the repulsive regime of LennardeJones potential, hence called the “repulsive type” AFM. 3.3.2.2 Noncontact Mode From an early stage of AFM development, scanning over sample surface in the attractive regime of LennardeJones potential has been attempted. Giessble et al. and Morita et al. developed such instruments successfully [22,23]. In this scanning mode, a cantilever is oscillated at near-resonance frequency but with much smaller amplitude than in tapping mode. When the cantilever of force constant k comes into the region of attractive interaction with the sample surface, its oscillatory frequency is slightly reduced because the effective force constant k of the cantilever is now modulated to a new value K 0 by the gradient of the force field (¼ dF/dz which can be in a partial differential form as well), which is negative in this case. K0 ¼ k þ

dF dz

(3.7)

Since the oscillatory frequency of the cantilever is related to the spring constant through the following equation, rffiffiffiffi 1 k n0 ¼ 2p m

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1 n¼ 2p Dn ¼

n0 vF < 0; 4pk vz

rffiffiffiffiffi K0 m since

vF <0 vz

(3.8)

Reduction of K0 from k lowers n by Dn$Dn can be accurately measured with a precision better than 105 against n0 . Dn is thus related to the force gradient, not force itself. The previous equation was derived on the assumption that the force gradient is constant [23]. This detection method is used in the noncontact AFM (ncAFM), which has been shown to have a true atomic resolution and a capability of atom manipulation on metallic and semiconductor surfaces [22]. Initially, ncAFM was used under high vacuum because, under air or liquid conditions, the cantilever vibration is strongly damped (i.e., vibration under air or liquid conditions is energetically much less efficient compared with that under vacuum) and the signal-to-noise ratio is very low. The efficiency of transmitting supplied energy to the cantilever vibration is called Q-factor and is operationally defined as the ratio between the height against half width of the power spectrum of the cantilever vibration (see Fig. 3.3). It is difficult to physically increase Q-factor in air or in liquid, but it can be effectively increased by using an electronic control circuit called Q-control.

Figure 3.3 Q-factor represents the sharpness of the resonance peak and thus inversely the degree of energy dissipation in the form of (peak height)/(half width).

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3.3.2.3 High-Speed AFM In the just-discussed three modes of AFM operations, scan speed is slow. It usually takes several minutes to cover 256  256 2D points of the sample surface. To observe real-time dynamic movements of biological structures and molecules, AFM with much faster scanning speed was required. Ando et al. fulfilled this demand and announced a striking image of a walking myosin molecule along an immobilized actin filament [24e26]. The key points in this successful development were, first, fabrication of a small but stiff cantilever having a mega-Hz range high-resonance frequency for rapid tapping mode scanning and extra rigid setup of the scanning stage. Static images of myosin at work are reproduced in Fig. 3.4A. Readers are referred to the video film at: http://www.se.kanazawa-u.ac.jp/bioafm_center/index.htm http://www.se.kanazawa-u.ac.jp/bioafm_center/HS-AFM_Div.htm 3.3.2.4 Scanning Ion Conductance Microscope Another interesting development in AFM technology is based on, again, the original idea of Hansma [27,28]. The basic principle is scanning a glass capillary electrode near the sample surface keeping the ionic conductance at a constant level. While conducting ions flow into the capillary from its open end according to the set voltage difference, protrusions on the sample surface hinder a constant flow of ions by narrowing the space between the capillary tip and the sample surface. To keep the conductance at a constant level, the feedback system widens the tip-substrate distance. By recording feedback input voltage to keep the constant conductance level, topographic map of the sample surface is constructed. Recent advances in instrumentation produced surprisingly clear 3D images of live cell surface as reproduced in Fig. 3.4B [29e31]. 3.3.2.5 MultiFrequency AFM In conventional dynamic force microscopy, information about the sample that is encoded in overtone frequencies of cantilever vibration other than the excitation frequency is irreversibly lost. Multifrequency force microscopy involves the excitation and/or detection of the deflection at two or more frequencies, and it has the potential to overcome limitations in the spatial resolution and acquisition times of conventional force microscopes. The development of five different modes of multifrequency force microscopy is reviewed in Ref. [32]. Applications in studies of proteins, the imaging of vibrating nanostructures, measurements of ion diffusion,

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(A) (d)

(c)

(a)

(b)

(e)

(B)

(C) (a)

(b)

(c)

Figure 3.4 Results of mechanical imaging (A): Motion of myosin molecule by highspeed AFM. Tail-truncated myosin V (M5-HMM) movement on actin filament captured by HS-AFM. All of the images were taken at a frame rate of 7 fps. (a) Successive AFM images showing processive movement of M5-HMM in 1 mM ATP when positively charged lipid is absent in the planar lipid bilayer (PLB) surface. The arrowhead indicates one of the streptavidin molecules attached to the PLB surface. (b) Successive AFM images showing processive movement of M5-HMM in 1 mM ATP when positively

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and subsurface imaging in cells have been carried out. Results on imaging and elasticity mapping of IgM are given in Fig. 3.4C [32e35].

3.3.3 How to Use AFM for Force Measurement Since AFM is most favored by many researchers for the measurement of pN to nN level interaction force between biological macromolecules and structures, this section is devoted to the use of AFM in force measuring mode. In the operation of AFM, an accurate detection of the magnitude of cantilever bending (deflection) is most important because the deflection is directly proportional to the value of interaction force between the probe and the sample. To this day, a variety of methods of detection of cantilever deflection have been tested, but the most popular one involves the use of an optical lever. • Optical lever method utilizes a focused laser beam irradiated on the back of the mounted cantilever and reflected into a bisected or quadrisected photodiode detector. A small change in the cantilever deflection changes the incident angle of the laser beam to the back of the cantilever, and

=charged lipid is present in the PLB. The arrows indicate the coiled coil tail pointing to the minus end of actin. The arrowhead indicates one of the streptavidin molecules attached to the PLB surface. (c) Clips of successive images showing long processive run of M5-HMM in 1 mM ATP (14 steps are recorded). (d) Schematic explaining structural features of two-headed bound M5-HMM observed in the presence of nucleotides. (e) Successive AFM images showing stepping process in 1 mM ATP. The swinging lever is highlighted with a thin white line. (B): (a) Image of live cell by scanning ion conductance microscopy. Projections on the surface of HeLa cell. Lamellar projections with a range of topographies are clearly observed on the surface of the HeLa cell. (b) Luminal surface of rat trachea imaged by the ARS/hopping SICM mode. (C): High-resolution (height representation) AFM images of IgM antibodies in liquid. (a) IgM antibodies deposited on a mica surface. (b) High-resolution AFM image of a single IgM and cross-section along the dashed line. The pentameric structure is fully resolved. (c) High-resolution AFM image of a single IgM and cross-section along the dashed line. Full width at half-height maximum is provided. (A): Reproduced from T. Ando, T. Uchihashi, S. Scheuring, Filming biomolecular processes by high-speed atomic force microscopy, Chem. Rev. 114 (2014) 3120e3188 with permission. (B): Reproduced from T. Ushiki, M. Nakajima, M. Choi, S.J. Cho, F. Iwata, Scanning ion conductance microscopy for imaging biological samples in liquid: a comparative study with atomic force microscopy and scanning electron microscopy, Micron 43 (2012) 1390e1398 with permission. (C) Reproduced from A.P. Perrino, R. Garcia, How soft is a single protein? The stress-strain curve of antibody pentamers with 5 pN and 50 pm resolutions, Nanoscale 8 (17) (2016) 9151e9158 with permission.

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consequently the direction of the reflected beam is changed. The difference between the intensity of the light going into the upper and lower halves of the bisected detector gives a signal proportional to the cantilever deflection. To be accurate, a change in the cantilever angle against the horizontal line at the position where the laser beam hits is proportional to the displacement of the laser spot on the photodiode detector. The result is the same since the vertical deflection change can be linearly related to the angle change [36]. Since the direct output of photosensitive detector is the difference in its upper and lower panel voltage output (V), it should be translated to vertical cantilever displacement in nm (d) through determination of the cantilever “sensitivity” in terms of d/V (nm/V). By multiplying output voltage V with sensitivity, s in nm/V, one gets deflection in nm. The sensitivity is obtained as the reciprocal of the slope (V/nm) of a force curve measured on an undeforming solid surface. • Interference between the two laser beams, one reflected from the back of the cantilever and the reference beam can be used to detect the magnitude of cantilever deflection with a similar accuracy as optical lever method given previously [37]. • Change in capacitance due to the change in the distance between the cantilever and the substrate surface may be accurately monitored by placing an electrode against the back of the cantilever and may be used to record the cantilever deflection. • Tunneling current between the backside of a conductive cantilever and a sharp metallic probe positioned at a short distance to the back of the cantilever can give an accurate measure of the cantilever deflection. The prototype of AFM was built with this detection system. • Change in piezo resistance due to the deflection of a self-actuating cantilever is used in ncAFM. In Fig. 3.5, a schematic view of the optical lever method of detection of cantilever deflection is given. When the optical lever method is used, it does not record the magnitude of deflection itself but the slope of the cantilever at the position where the laser beam is irradiated. Since the relation between the deflection under an applied force F and the distance x from the free end and the maximum deflection at x ¼ 0 are given as

3 i FL 3 1 h x x y¼ (3.9) 23 þ L L YI 6 ymax ¼

1 FL 3 3 YI

at x ¼ 0

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Figure 3.5 The principle of the optical lever method used as a force transducer of AFM. The laser beam is reflected from the back of the gold-coated cantilever and reaches the quadrisected (A, B, C, and D) photodiode detector. The differential output (A þ D)(B þ C) is proportional to the vertical cantilever deflection from the equilibrium position, and (A þ B þ C þ D) gives the sum value.

Its slope is



2  dy FL 3 1 3 x ¼  þ3 3 dx L YI 6 L

(3.10)

FL 2 3 ¼ ymax 2YI 2L

(3.11)

which is equal to where x ¼ 0

Since the slope of the cantilever at x ¼ 0 is proportional to ymax as long as L is constant, it gives an accurate measure of its deflection.

3.3.4 Cantilever Force Constant In AFM operation, the cantilever property plays a central role in determination of the quality of the outcome. Thanks to the popularity of AFM in research and development field, high-quality cantilevers are commercially available from several companies. They are provided with calculated values of spring constant according to the geometric information of each lot of cantilevers using Eq. (3.5). k¼

Ywt 3 4L 3

where w, t, and L are the width, thickness, and length of the rectangular cantilever. Among the three geometric dimensions, the thickness is the

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source of a large error in production as well as characterization by scanning electron microscope. For AFM imaging, an accurate cantilever force constant is not needed but for force measurement it is desirable to determine the force constant experimentally. Force constant of a cantilever can be determined by several different methods but currently most favored is the one proposed by Hutter and Beckhoefer for relatively soft cantilevers, which measures the thermal fluctuation of an unloaded cantilever vibration [38]. At a finite temperature, the cantilever is constantly vibrating at its resonance frequency with a small instantaneous

amplitude of Dx. The one-dimensional vibrational energy is k < Dx>2 2 of the cantilever where k is the spring constant of the cantilever and was equated to the one-dimensional thermal energy that is equal to kB T =2. The result is kB T k¼ < ðDxÞ2 > < ðDxÞ2 > can be experimentally determined from the power spectrum of force fluctuation data. The area under the power spectrum is proportional to < ðDxÞ2 >. Most modern AFM instruments have a built-in program to determine cantilever force constant starting from sensitivity determination through power spectrum calculation. This method is not applicable to hard cantilevers because thermal fluctuation amplitude is too small to be accurately measured. Another simple method of cantilever calibration uses a commercially available precalibrated cantilever as a standard and determines that of a new cantilever by comparison. This method can be applied both for soft and stiff cantilevers if the reference cantilevers are available in the user’s requested range. In this method force curves are taken with a test cantilever on a solid surface and on the reference cantilever to give the spring constant of test cantilever using the following equation:
 Ss k ¼ kr 1 Sr where k, spring constant of the test cantilever; kr , spring constant of the reference cantilever; Ss, slope measured on a solid surface; and Sr, slope measured on the reference cantilever. For other methods, readers are referred to Ref. [39]. When either a calculated or an experimentally determined force constant is used, there are several corrections to be made [39]. Major factors that should be considered for correction are: (1) tilt angle of cantilever setup

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in AFM instrument (w10 in most commercial AFMs); and (2) difference in cantilever shape, whether rectangular or triangular. For detailed explanation of correction factors, which is reported to be w0.807, see Ref. [39] and references therein. For on line calibration of a cantilever force constant, the following URL should be referred: http://www.ampc.ms. unimelb.edu.au/afm/

3.4 SURFACE FORCE APPARATUS Surface force apparatus (SFA) was developed by Israelachvili et al. in the early 1970s [40,41]. In the SFA, two smooth cylindrical surfaces covered with thin layers of mica are positioned at 90 to each other. The two surfaces are moved to approach each other in a direction normal to the axes of the cylinders as close as a few nanometers. When the two curved cylinders have the same radius of curvature, R (w1 cm), in a “crossed cylinders” geometry, it is mathematically equivalent to the interaction between a flat surface and a sphere of radius R. The two surfaces can be modified with sample molecules, A and B, respectively. After contacting each other, the surfaces are separated by piezo motor system attached to one of the surface units. The other unit is attached to a force-sensing device such as a cantilever so that the force between two surfaces can be measured by a special optical system (SFA 3 brochure, SurForce LLC, Santa Barbara, CA). Some recent work performed with the SFM is found in Refs. [42,43]. The result of SFA measurement is given as a plot of [Force/Cylinder Radius (N/m)] vs. distance between two surfaces (nm). If the ordinate is in 1 mN/m and the radius of the cylinder is 1 cm, the actual force between the surfaces is 10 mN. Since the effective radius of the cylinder is much larger than the tip radius of AFM by an approximate factor of 106, the force would correspond to w10 pN in AFM experiment using a tip of effective radius of 10 nm.

3.5 BIOMEMBRANE FORCE PROBE Biomembrane force probe was introduced by Evans to measure the mechanical response of a live cell in a culture medium under constant monitoring by an optical microscope [44]. A live cell is immobilized on the tip of a glass capillary by sucking a part of the cell into the capillary under an application of a negative pressure. Force measurement manipulation on this target cell is performed on the opposite, i.e., exposed side of the cell. For instance, measurement of the interaction force between an intrinsic membrane protein on the cell surface and a chosen ligand or a specific antibody on a

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bead is carried out as follows. First, the ligand or antibody molecules were immobilized on a latex bead. Separately, a red blood cell (RBC) ghost was immobilized to the tip of a glass capillary in a similar manner and positioned face to face to the target cell. The bead was then bonded to the exposed side of the RBC as in Fig. 3.6. The blood cell is deformed to a spherical shape because of the negative pressure that acts to hold it at the mouth of the capillary. The latex bead is brought into brief contact with the sample cell, and after a specified time of contact, the two capillaries are pulled away from each other. As they are pulled away, both the target cell and the RBC are deformed due to the tensile force between the ligand and receptor molecules. The magnitude of the tensile force is estimated from the deformation of the spherical RBC. The suction force applied at the tip of the pipette can be lower than 0.1 pN [44,45]. When a force is applied at a single point on the immobilized RBC, the shape of the spherical RBC cell is slightly elongated or compressed. For a small displacement, the change in axial length is directly proportional to the axial force. The RBC working as a Hookean spring [45] can be used as a probe for force transduction. The axial change in the diameter, d, has been shown to be proportional to the applied force, F, as follows. F ¼ kf d s kf ¼ 2p  2 ; 4R0 ln Rp Rc

s¼

(3.12) Rp 1
 Dp Rp 2 1 R0

(3.13)

Figure 3.6 In biomembrane force probe, an emptied and resealed ghost RBC (red blood cell) is used as a force transducer. Top: actual setup of capillaries and cells. Bottom: RBC is depicted as a Hookean force transducer. Tensile force is calculated from the deformation of the spherical RBC ghost. Reproduced with permission of Professor Volkmar Heinrich.

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where R0, Rp, Rc, and Dp are the radius of the spherically swollen RBC, radius of the pipette, radius of the adhesive contact circle between the glass bead and the cell, and the suction pressure in the pipette.

3.6 MAGNETIC BEADS Small magnetic beads internalized into a live cell have been used to probe the local viscoelastic properties of the intracellular fluid [46]. By applying a magnetic field to twist a magnetic bead in the cell, one can measure the rotational frictional coefficient of the bead, hence the viscosity or viscoelasticity of the surrounding fluid is obtained.

3.7 GEL COLUMNS An interesting device for measuring the force exerted by a living cell as it slowly moves around the substrate surface has been fabricated using flexible gel columns [47]. In this method a sample cell is transferred from culture medium to cover an array of vertical gel columns prepared on a solid surface by a micromechanical method. A live cell is then placed over the vertical array of the columns and allowed to adhere to the columns. As the cell starts moving, a tensile force is created between the adhesive molecules of the cell surface and the upper end of the columns, consequently the columns are bent and/or elongated. The degree of column deformation is measured using an optical microscope and converted to the force under an assumption that the columns are linear cantilevers. Fig. 3.7 gives a schematic view of the experimental setup for this type of experiment. A recent paper gives experimental and theoretical details of the method, which is often called “traction force microscopy” [48].

Figure 3.7 Schematic view of the gel column method for force measurement between a moving cell and the column heads. The figure is from Dr. Ichiro Harada.

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3.8 CANTILEVER FORCE SENSORS The cantilever used in the AFM technology has been shown to be useful in a uniquely different way [49]. An array of cantilevers without the AFM probe part (tipless cantilever) was manufactured and their backside was chemically activated. Molecules of ssDNAs having a specific nucleotide sequence were then end grafted on them. After immersing the modified cantilever, ssDNA having a complementary sequence to those on the cantilever was added to the solution. When hybridization took place between the immobilized DNA and the complementary DNA in solution, newly formed dsDNA molecules tried to occupy a larger space on the cantilever and thus laterally push against each other. This lateral expansion of DNA volume caused downward deflection of the cantilevers, which can be easily detected by an optical lever system similar to the one used in commercial AFM instruments. The same principle can be applied to antigeneantibody systems. The idea has been used in the production of commercially available sensors for biological affinity measurements. Prospects of the method in the application of medical diagnostic direction are summarized in Refs. [50,51].

3.9 LOADING-RATE DEPENDENCE Since force is not a function of state, its value for bringing experimental system from one state to another depends on how the force is applied, for example, how fast the force is applied. Force measurement, therefore, does not stop at obtaining a particular force value under a specified condition. Once the force to break or distort a particular bond is measured, one can explore the dependence of the magnitude of the force on the rate of force loading, or simply loading rate. In daily life, we experience that tearing off an adhesive tape rapidly requires a larger force than doing so slowly. In more precise terms, it is not the speed of tearing but that of applying force in terms of force/time, and if the applied force increases linearly as a function of time, it is a constant value for a particular set of experimental parameters. The functional dependence of the mean force value on the logarithm of the loading rate (r) is expressed in Eq. (3.14) and schematically shown in Fig. 3.7 [52].
   0  kB T kB T kB T  F ¼ lnðrÞ  ln koff þ ln (3.14) Dx Dx Dx

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Figure 3.8 Plot of the mean rupture force on the ordinate and of the logarithm of the loading rate on the abscissa. The slope of the linear part of the plot is inversely proportional to the activation distance, and the intercept with the x-axis gives the unbinding rate constant in the absence of applied force. When the plot has two linear parts of different slopes, the energy diagram for unbinding is interpreted to have two energy barriers.

The parameter Dx that appears in Eq. (3.14) is shown to be synonymous with the “activation distance” and is schematically shown in Fig. 3.9 and Appendix 5. It is defined as the distance of the bond from its equilibrium position to the activated state for breaking. When the bond to be broken is uniquely defined as the bond between two atoms, the meaning of Dx (or xb ) is clear, but in many other reactions involving macromolecular species, the “bond” has a more conceptual picture. In general, (free) energy of the reacting system is plotted against an abstract concept of one-dimensional “reaction coordinate,” which represents collective deformation of the reactants in the direction of the applied force. Moreover, when the bond to be broken is not parallel to the direction of the applied force but inclined at an angle q, Dx measured in experiment corresponds to Dx0cosq, where Dx0 is the true length of the activation distance. The slope of the force-loading rate curve is steeper for a smaller value of Dx and vice versa. For example, for forced rupture of a covalent bond, Dx cannot be larger than 0.1 nm, but for the rupture of macromolecular bonds such as biotineavidin bond, Dx as large as 0.5 nm has been reported [53,54]. For proteineprotein interactions, it is even larger [55]. In such cases where the force-loading rate graph is divided into two curves with different slopes, the presence of two prominent activation barriers is postulated as shown in Fig. 3.9. The application of a tensile force to such a bond system, first lowers the outer energy barrier with a longer activation distance Dx2, and after sufficiently lowering the outer barrier, the presence of the inner barrier with a shorter Dx1 is exposed. Thus, the mechanical-rupture experiments of an interacting pair of molecules give a schematic view of the energy

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Figure 3.9 Energy diagram of reaction pathway for bond breaking showing the activation energy and activation distance. In this figure, there are two activation barriers designated as activated state 1 and 2. The applied force is assumed to decrease the activation barrier in proportion to the activation distance times the magnitude of force as shown by two dashed lines.

diagram of the reaction pathway. In short, at a lower and a higher loading rate, respectively, the outer and the inner barrier acts as the rate-limiting step. Since the rupture force is not a constant of a system, comparisons of different systems in terms of mechanical strength are not straightforward because a larger rupture force in one system may become smaller at a different loading rate. The other parameter in Eq. (3.14), k0off is the unbinding rate constant in the absence of externally applied force. It is, therefore, independent of loading rate but dependent on temperature and other environmental conditions. This is an important but not readily obtainable parameter by ordinary methods for surface-bound reactions. AFM-based force curve analysis, which is often called “(dynamic) force spectroscopy,” can make an important contribution in this respect. Detailed measurement of loading rate dependency may be avoided to obtain the two parameters mentioned herein by making a precise measurement of force distribution at a single loading rate [56]. The loading-rate

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dependence is observed not only in unbinding reactions but also in all the cases where force is used to deform or disrupt the mechanical system.

3.10 FORCE CLAMP METHOD It is also possible to use the force clamp method to obtain Dx and k0off . In this method, an applied force is kept at a constant level for a prolonged duration of time, and the time duration from the beginning of force application to the time of bond rupture is observed [57,58].

3.11 SPECIFIC VERSUS NONSPECIFIC FORCES One difficulty in force measurement is that force is force whatever its origin is, meaning that the probe senses all kinds of force working on it, whereas the experimentalists want to measure only one specific kind of force, i.e., the interaction force between A and B. We call the force we aim to measure the “specific force,” and all other interaction forces are “nonspecific” force or “noise.” Specific force is only based on the subjective choice of the experimentalist. The question is how to distinguish a specific force from nonspecific ones. Ideally, one should establish the following observations to claim measurement of a specific force between molecules A and B: • Observation of a positive interaction force between a probe modified with B against A on the substrate. • A probe modified and treated exactly the same way but without B does not have interaction with A on the substrate. • No interaction between a modified probe with B and a substrate without A. • Addition of an “inhibitor” of the interaction between A and B to the sample solution to see whether the inhibitor specifically inhibits the interaction between A and B. • Use of a force as small as possible in the initial contact of the probe with the sample, or use a cross-linker with a long spacer unit for the immobilization of B on the probe. This is to avoid pushing A on the substrate or B on the probe too hard so that they would not be damaged and would become the secondary source of adhesive interaction. In general, denatured proteins are stickier against almost any surfaces than native ones. Pushing sample proteins beyond their elastic limit may denature them and increase the probability of unwanted nonspecific adhesion events.

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Figure 3.10 Typical nonspecific adhesion curve with a large initial deflection of cantilever in the retraction regime.

Nonspecific interaction between the AFM probe and the substrate, if at all, is often revealed by the force curve as shown in Fig. 3.10. In the retraction regime of the force curve in Fig. 3.10, the probe stays in contact with the substrate for a prolonged time and then suddenly detaches from the substrate in a seemingly single step. This type of force curve likely represents nonspecific adhesion of the probe to the substrate. The use of spacer molecules between the sample and the substrate and/or the probe is desirable. In such a case, the initial phase of the retraction regime of the force curve should be similar to that shown in Fig. 3.11, where the force curve clearly has a nonlinear extension of the spacer before the probe is detached from the sample.

Figure 3.11 Spacer is valuable when force curves of interaction are obtained. The rupture event that appears after an extension of a long spacer of known length most likely corresponds to the unbinding of the focused pair. The nonlinear increase of the loading force, however, complicates the calculation of the loading rate.

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It is important to verify that the initial part has only a small or no “triangular” adhesion part before the spacer extension starts. If the initial triangle adhesion is small and the spacer extension part is clearly distinguished from it, the interaction force can be estimated from the rupture force after spacer extension, but it is important to exclude the initial one or two force peaks that are likely to involve nonspecific interactions.

BIBLIOGRAPHY [1] A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Observation of a single-beam gradient force optical trap for dielectric particles, Opt. Lett. 11 (1986) 288e290. [2] A. Ashkin, Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime, Biophys. J. 61 (1992) 569e582. [3] S. Kawata, M. Ohtsu, M. Irie, Nano-Optics, Chapter 4, Springer, Berlin, 2002, pp. 88e89. [4] A. Ashkin, K. Schutze, J.M. Dziedzic, U. Euteneuer, M. Schliwa, Force generation of organelle transport measured in vivo by an infrared laser trap, Nature 348 (1990) 346e348. [5] S. Henon, G. Lenormand, A. Richert, F. Gallet, A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers, Biophys. J. 76 (1999) 1145e1151. [6] G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Tunneling through a controllable vacuum gap, Appl. Phys. Lett. 40 (1982) 178e180. [7] G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Surface studies by scanning tunneling microscopy, Phys. Rev. Lett. 49 (1982) 57e61. [8] D. Bonnell, Scanning Probe Microscopy and Spectroscopy: Theory, Techniques, and Applications, Wiley VCH, New York, NY, 2000. [9] R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy, Cambridge University Press, Cambridge, UK, 1994. [10] G. Binnig, H. Rohrer, C. Gerber, E. Weibel, 7  7 Reconstruction on Si(111) resolved in real space, Phys. Rev. Lett. 50 (1983) 120e123. [11] K. Takayanagi, Y. Tashiro, M. Takahashi, S. Takahashi, Structural analysis of Si(111)7  7 by UHV-transmission electron diffraction and microscopy, J. Vac. Sci. Technol. A3 (1985) 1502. [12] G. Binnig, C.F. Quate, C. Gerber, Atomic force microscope, Phys. Rev. Lett. 56 (1986) 930e933. [13] A. Ikai, STM and AFM of bio/organic molecules and structures, Surf. Sci. Rep. 26 (1996) 261e332. [14] H.J. Butt, B. Cappella, M. Kappl, Force measurements with the atomic force microscope: technique, interpretation and applications, Surf. Sci. Rep. 59 (2005) 1e152. [15] K.A. Dill, S. Bromberg, Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology, Garland Science, New York, NY, 2002. [16] S.P. Timoshenko, J.M. Gere, Mechanics of Materials, PWS Publishing Co., Boston, MA, 2002. [17] H.G. Hansma, R.L. Sinsheimer, J. Groppe, T.C. Bruice, V. Elings, G. Gurley, M. Bezanilla, I.A. Mastrangelo, P.V.C. Hough, P.K. Hansma, Scanning 15 (1993) 296. [18] J. Jang, G.C. Schatz, M.A. Ratner, Capillary force in atomic force microscopy, J. Chem. Phys. 120 (2004) 1157e1160. [19] D.L. Malotky, M.K. Chaudhury, Investigation of capillary forces using atomic force microscopy, Langmuir 17 (2001) 7823e7829.

60

A. Ikai

[20] T. Ondarçuhu, L. Fabié, Chapter 14. Capillary forces in atomic force microscopy and liquid nanodispensing, in: P. Lambert (Ed.), Surface Tension in Microsystems: Engineering Below the Capillary Length (Microtechnology and MEMS), Springer, 2013. [21] P.K. Hansma, J.P. Cleveland1, M. Radmacher, D.A. Walters, P.E. Hillner, M. Bezanilla, M. Fritz, D. Vie, H.G. Hansma, C.B. Prater, J. Massie, F. L, J. Gurley, V. Elings, Tapping mode atomic force microscopy in liquids, Appl. Phys. Lett. 64 (1994) 1738e1740. [22] S. Morita, in: S. Morita, R. Wiesendanger, E. Meyer (Eds.), Noncontact Atomic Force Microscopy, Springer, Berlin, Germany, 2002 (Chapter 1). [23] F.J. Giessble, in: S. Morita, R. Wiesendanger, E. Meyer (Eds.), Noncontact Atomic Force Microscopy, Springer, Berlin, Germany, 2002 (Chapter 2). [24] T. Ando, N. Kodera, E. Takai, D. Maruyama, K. Saito, A. Toda, A high-speed atomic force microscope for studying biological macromolecules, Proc. Natl. Acad. Sci. USA 98 (2001) 12468e12472. [25] T. Ando, N. Kodera, Visualization of mobility by atomic force microscopy, Methods Mol. Biol. 896 (2012) 57e69. [26] T. Ando, T. Uchihashi, S. Scheuring, Filming biomolecular processes by high-speed atomic force microscopy, Chem. Rev. 114 (2014) 3120e3188. [27] P.K. Hansma, B. Drake, O. Marti, S.A. Gould, C.B. Prater, The scanning ionconductance microscope, Science 243 (1989) 641e643. [28] R. Proksch, R. Lal, P.K. Hansma, D. Morse, G. Stucky, Imaging the internal and external pore structure of membranes in fluid: TappingMode scanning ion conductance microscopy, Biophys. J. 71 (1996) 2155e2157. [29] Y.E. Korchev, C.L. Bashford, M. Milovanovic, I. Vodyanoy, M.J. Lab, Scanning ion conductance microscopy of living cells, Biophys. J. 73 (1997) 653e658. [30] A.I. Shevchuk, G.I. Frolenkov, D. Sanchez, P.S. James, N. Freedman, M.J. Lab, R. Jones, D. Klenerman, Y.E. Korchev, Imaging proteins in membranes of living cells by high-resolution scanning ion conductance microscopy, Angew. Chem. Int. Ed. Engl. 45 (2006) 2212e2216. [31] T. Ushiki, M. Nakajima, M. Choi, S.J. Cho, F. Iwata, Scanning ion conductance microscopy for imaging biological samples in liquid: a comparative study with atomic force microscopy and scanning electron microscopy, Micron 43 (2012) 1390e1398. [32] R. Garcia, E.T. Herruzo, The emergence of multifrequency force microscopy, Nat. Nanotechnol. 7 (2012) 217e226. [33] A.P. Perrino, R. Garcia, How soft is a single protein? The stress-strain curve of antibody pentamers with 5 pN and 50 pm resolutions, Nanoscale 8 (17) (2016) 9151e9158. [34] R. Garcia, R. Proksch, Nanomechanical mapping of soft matter by bimodal force microscopy, Eur. Polym. J. 49 (2013) 1897e1906. [35] D. Martinez-Martin, E.T. Herruzo, C. Dietz, J. Gomez-Herrero, R. Garcia, Noninvasive protein structural flexibility mapping by bimodal dynamic force microscopy, Phys. Rev. Lett. 106 (2011) 198101. [36] G. Meyer, N.M. Amer, Appl. Phys. Lett. 53 (1988) 2400. [37] C.A.J. Putman, B.G. De Grooth, N.F. Van Hulst, J. Greve, A detailed analysis of the optical beam deflection technique for use in atomic force microscopy, J. Appl. Phys. 72 (I) (1992) 6e12. [38] J.L. Hutter, J. Bechhoefer, Calibration of atomic-force microscope tips, Rev. Sci. Instrum. 64 (1993) 1868e1873. [39] JPK force spectroscopy notes, J. Instruments 2009 (2009). [40] J.N. Israelachvili, D. Tabor, The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm, Proc. R. Soc. Lond. Ser. A 331 (1972) 33119e33138.

Force Measurement and Mechanical Imaging Apparatuses

61

[41] J.N. Israelachvili, G.E. Adams, Direct measurement of long range forces between two mica surfaces in aqueous KNO3 solutions, Nature 262 (1976) 774e776. [42] Y. Kan, Q. Tan, G. Wu, W. Si, Y. Chen, Study of DNA adsorption on mica surfaces using a surface force apparatus, Sci. Rep. 5 (2015) 8442. [43] J. Israelachvili, Y. Min, M. Akbulut, A. Alig, G. Carver, W. Greene, K. Kristiansen, E. Meyer, Recent advances in the surface forces apparatus (SFA) technique, Rep. Prog. Phys. 73 (2010) 036601. [44] E. Evans, D. Berk, A. Leung, Detachment of agglutinin-bonded red blood cells. I. Forces to rupture molecular-point attachments, Biophys. J. 59 (1991) 838e848. [45] E. Evans, K. Ritchie, R. Merkel, Sensitive force technique to probe molecular adhesion and structural linkages at biological interfaces, Biophys. J. 68 (1995) 2580e2587. [46] N. Walter, C. Selhuber, H. Kessler, J.P. Spatz, Celluar unbinding forces of initial adhesion processes on nanopatterned surfaces probed with magnetic tweezers, Nano Lett. 6 (2006) 398e402. [47] J.L. Tan, J. Tien, D.M. Pirone, D.S. Gray, K. Bhadriraju, C.S. Chen, Cells lying on a bed of microneedles: an approach to isolate mechanical force, Proc. Natl. Acad. Sci. USA 100 (2003) 1484e1489. [48] S.V. Plotnikov, B. Sabass, U.S. Schwarz, C.M. Waterman, High-resolution traction force microscopy, Methods Cell Biol. 123 (2014) 367e394 (Chapter 20). [49] J. Fritz, M.K. Baller, H.P. Lang, H. Rothuizen, P. Vettiger, E. Meyer, H. Guntherodt, C. Gerber, J.K. Gimzewski, Translating biomolecular recognition into nanomechanics, Science 288 (2000) 316e318. [50] R. Datar, S. Kim, S. Jeon, P. Hesketh, S. Manalis, A. Boisen, T. Thundat, Nanomechanical tools for diagnostics, MRS Bulletin 34 (2009) 449e454. [51] R. Zhang, A. Best, R. Berger, S. Cherian, S. Lorenzoni, E. Macis, R. Raiteri, R. Cain, Multiwell micromechanical cantilever array reader for biotechnology, Rev. Sci. Instrum. 78 (2007) 084103. [52] E. Evans, K. Ritchie, Dynamic strength of molecular adhesion bonds, Biophys. J. 72 (1997) 1541e1555. [53] C. Yuan, A. Chen, P. Kolb, V.T. Moy, Energy landscape of streptavidin-biotin complexes measured by atomic force microscopy, Biochemistry 39 (2000) 10219e10223. [54] H. Sekiguchi, A. Ikai, A method of measurement of interaction force between ligands and biological macro-molecules (in Japanese), Hyoumenkagaku 27 (2006) 436e441. [55] M. Saito, T. Watanabe-Nakayama, S. Machida, T. Osada, R. Afrin, A. Ikai, Spectrinankyrin interaction mechanics: a key force balance factor in the red blood cell membrane skeleton, Biophys. Chem. 200e201 (2015) 1e8. [56] O. Takeuchi, T. Miyakoshi, A. Taninaka, K. Tanaka, D. Cho, M. Fujita, Dynamicforce spectroscopy measurement with precise force control using atomic-force microscopy probe, J. Appl. Phys. 100 (2006) 074315e074320. [57] J.Y. Shao, R.M. Hochmuth, Mechanical anchoring strength of L-selectin, beta2 integrins, and CD45 to neutrophil cytoskeleton and membrane, Biophys. J. 77 (1999) 587e596. [58] A.F. Oberhauser, P.K. Hansma, M. Carrion-Vazquez, J.M. Fernandez, Stepwise unfolding of titin under force-clamp atomic force microscopy, Proc. Natl. Acad. Sci. USA 98 (2001) 468e472.