SMFS of Proteins Physical Principles and Methodology

tte AFM, invented in 1986 by Binning and coworkers, is a relatively simple apparatus that allows the measurement of the mechanical properties of materials at atomic resolution. It is essentially a mechanical force transducer based on a flexible sensor (the cantilever) that ends in a sharp tip, which directly contacts the sample, tte forces are measured on the basis of the deflection of the cantilever, and distances are calculated from the travel of a high-resolution positioner. It works like a miniature record player or phonograph that connects our macroscopic world with the atomic world, ttis microscope ("nanoscope" may be a more appropriate word to describe it from a biologist's point of view) has been most widely used in its "imaging" configuration to mechanically map the topography of surfaces at atomic resolution. tte principle of this technique is more akin to touch than to vision. By using a 3D positioner, a sharp probe (the "eye" of this microscope) combs the surface of the sample recording the height at each point, yielding a topographic map of the surface (Bustamante et al. 1997). tte resolution gets only truly "atomic" in the z-axis for hard materials, whereas for soft biological material the typical lateral resolution in this mode is around 1 nm.

tte AFM is not just a high-resolution imaging tool, it can also be used to probe and manipulate atoms and molecules. Subsequently, the so-called force spectros--►

Fig. 8.3. Single-molecule force spectroscopy (SMFS): physical principle and the modes ofop-eration. a Schematic diagram ofthe physical principle oftypical AFM pulling experiments. The line depicts the laser light path before (dashed line; pale red) and after (solid lines; red) pulling on the protein system. The protein system connects mechanically the tip and the substrate, which is in turn attached to a piezoelectric positioner. In this setup the movement ofthe positioner along the z-axis results in bending ofthe cantilever along the same axis. This bending is tracked by changes in the reflected angle of a laser beam bounced off the cantilever, which in turn is detected by a split photodiode as a voltage difference between the two channels and is converted into force using Hooke's law (Eq. 8.1). SMFS is used to measure intra- and intermolecular interactions (red dots), which are represented as a protein and a protein-biomol-ecule pair, respectively (green), b 1 Typical force curve diagram in length-clamp SMFS showing different snapshots ofthe movement ofthe cantilever and tip as the positioner performs an approach-retraction cycle. When the substrate is not in contact with the tip (7); when in contact with the tip, which bends the cantilever (2); when it is withdrawn from the tip, which bends the cantilever the other direction (3); adhering to the tip, originating a force peak (4); on "jumping offcontact"fromthetip (5); when is not in contact with thetip (6). 2 Different schematic diagrams of force-extension showing recordings of nonspecific interactions, specific interactions, and atypical sawtooth pattern obtained by stretching ofa multidomain protein molecule. 3 Cartoon representing the different interactions depicted in 2. Top: nonspecific interactions between the protein and the tip, the substrate, or another protein are detected (redbars), but not intramolecular interactions (light brown bars). Center: a specific protein-protein interaction is detected (red bars). Bottom: intramolecular interactions in a multidomain protein are detected (red bars). Proteins or domains denatured by adsorption (to the substrate

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or the tip) are represented by amorphous symbols (modified from Zlatanova and Leuba 2003, with permission, copyright 2003 Elsevier Science), c Force-clamp mode of SMFS showing the typical staircase extension-time recording. This particular example shows a polyubiquitin protein (N-C linked) being stretched at a constant force (110 pN) (Schlierfet al. 2004)

copy or force-measuring configuration of the AFM was designed exclusively to record force-extension curves and, accordingly, it is based on a single piezoelectric positioner (z-axis; Fig. 8.3). ttese "force spectrometers" or "pullers" are typically more compact and rugged instruments (in which thermal drift and mechanical vibrations can be minimized) and they are used to measure the nanomechanical properties of immobilized materials such as biomolecules just by stretching them (Burnham and Colton 1989). ttey have been used in this way to mechanically unfold biopolymers and to determine the unbinding forces for various biomolecular pairs. Typically, this mode of SMFS is capable of measuring forces with a sensitivity of tens of piconewtons (Fig. 8.1b) and changes in length with nanometer resolution (Fig. 8.1a; Sects. 8.3.1, 8.6.1). tte timescale resolution of this technique is in the submillisecond range (Fig. 8.1c). tte resolution of this instrument allows the analysis of single-molecule unfolding events as well as single rupture events. In this way, the intermolecular binding forces of complementary DNA strands (Lee et al. 1994) and those of receptor-ligand systems (Florin et al. 1994) can be measured as can the intramolecular forces that maintain the conformation of polysaccharide rings (Rief et al. 1997a; Marszalek et al. 1998, 1999a) and the fold of the different domains of a modular protein (Rief et al. 1997b; Fig. 8.3b).

ttis section will mainly focus on the use of this technique to analyze intramolecular interactions in proteins since the systems involved for these studies are relatively simpler than those used to characterize intermolecular interactions.

Mechanical ForceTransduction byAFM

As shown in Fig. 8.3, the AFM transduces the forces exerted on its flexible cantilever by measuring the angular deviations of a laser beam bounced back off it. trough this optical method, deviations are converted into voltage differences by a split photodiode detector. However, the raw data provided by an AFM (photodiode voltage, AV, and positioner extension, Azv) have to be transformed in order to obtain the final force-distance plot (Sect. 8.3.1.2). tte cantilever of an AFM behaves as a Hookean spring. Following Hooke's law, the force is calculated as the product of the cantilever deflection (in the z-axis) and its spring constant:

where k is the spring constant of the cantilever and Azc is its displacement along the z-axis (Figs. 8.3a, 8.4a).

Cantilever and Tip Choices

In these experiments, proteins typically attach nonspecifically to the cantilever tip, which can pick out single molecules even from a dense layer of proteins. Although unsharpened cantilever tips are very much larger than the size of a typical protein (these tips have a radius of curvature of approximately 50 nm while the major dimension of a typical protein is approximately 5 nm), they are preferred to sharpened ones, tte reason for this is because the larger tips have a better chance of finding single-molecule events, which as we will see later, is a process of trial and error, tte spring constant of the cantilever, k, is typically in the range of 10-100 pN nm4. For a typical cantilever of 60 pN nm"1 the thermal noise of the force measurements is calculated to be approximately 16 pN (the root-mean-square force fluctuation; Bustamante et al. 2000). In SMFS of proteins the use of a stiff cantilever simplifies the analysis by ensuring that the macromolecule is the dominant elastic component in the whole system. As we will see later, this is the main assumption in the Monte Carlo simulations used to obtain the kinetic parameters of the unfolding process.

Calibration of the AFM

tte mechanical resistance (restoring force) of a protein bond probed with this sensor is obtained using Eq. 8.1. However, the photodiode voltage (AV) and positioner extension (Azp) should be transformed to get the final force-distance plot. In order to do that, prior to an SMFS experiment two constants have to be determined: the ratio of photodiode output voltage to cantilever deflection (AV/Azv) to obtain the Azc values, and the spring constant of the cantilever (k) (Fig. 8.4a).

Determination oftheOptical LeverSensitivity tte split photodiode detector converts the incident light in each half of the split photodiode into voltage and then outputs the voltage difference, tte ratio between the photodiode output voltage and the displacement of the piezoelectric positioner in the z direction (AV/Azv) is determined by performing an approach-retraction cycle and measuring the slope of AV vs. A zp when the tip is in contact with a hard "substrate" (also called sample stage, typically made of glass or mica) at high applied forces (high compliance region), assuming that there is no deformation of the substrate. In these conditions the displacement of the cantilever, Azc, equals that of the piezoactuator, Azp. tte value of this slope is often called optical lever sensitivity or sensitivity for short, C (in units of volts per nanometer), which depends on the dimensions and the shape of the laser spot on the photodiode and on the refractive index of the medium used, ttis proportionality factor allows the raw photodiode data, AV, to be transformed into the cantilever deflection, Azc:

tten, from Eq. 8.1 the force value can be calculated as long as the spring constant of the cantilever is known (see next section).

Determination ofthe Spring Constant ofthe Cantilever tte most commonly used method for determining the spring constant of a cantilever is the thermal method, which models the cantilever as a damped simple har-

monic oscillator fluctuating in response to thermal noise, tte mechanical properties of the cantilever are related to the frequency and amplitude of these oscillations. Hence, its spring constant can be calculated using the so-called equipartition theorem:

where the first member of the equality represents the mean-square displacement noise, ttis calculation has a typical error of ±20% (Hutter and Bechhoffer 1993; Florin et al. 1995). It must be noted also that the position of the spot on the back of the cantilever has an influence on the determination of its spring constant and that a method has been developed to correct this effect (Proksch et al. 2004). An alternative method to the thermal noise one is based on the shift in the resonance frequency of the cantilever after the addition of a small mass, ttis method is more accurate but it requires specialized equipment (Cleveland et al. 1993).

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