Atomic Force Microscopy in Cell Biology Episode 2 Part 8 pdf

326 Altmann and Lenne may be interpreted as to represent a projection of a large volume of configuration space onto one of two preferred tracks. Paci and Karplus (1999) found two sets of unfolding pathways for fibronectin-type 3 modules by molecular dynamics simulations, which are analogous to those that we propose. The same authors have recently detected stable intermediates during unfolding of a single-spectrin domain (Paci and Karplus, 2000). Both tracks follow similar directions in real space, as defined by the direction of the applied force; however, according to our model, they may lead to two different unfolded states starting from the native folded state (Fig. 11). The intermediate state is conceptually available along both pathways, but each pathway by itself either leads from the native state 0 to the partially unfolded state 1 or the completely unfolded state 2. The relative difference of the height of the free energy barrier along either of the two pathways determines whether state 1 or state 2 is attained. The advantage of this strongly simplified modeling is that only one free parameter is needed for differentiating between the two averaged pathways. At the same time, we find this approach to be in good agreement with our data from the experiment and from Monte Carlo (MC) simulations (see following). In the native folded state, the protein is in state 0 at the bottom of the potential well. The directional mechanical stress applied by the AFM tip not only decreases the barrier height to thermally activated unfolding but also reduces the options of the protein to those of following either path 1 or path 2 during unfolding. The protein will follow only one path leading to a bimodal probability distribution with 35 and 65% probabilities for path 1 and path 2, respectively, according to our experimental data. The external stretching force reduces the effective energy barriers so that the system can cross them by thermal activation (Evans and Ritchie, 1997). As the applied force increases, the height of the energy landscape is reduced linearly along the generalized reaction coordinate. Along path 1 this reduction will lower the free energy barrier of the partially unfolded state below the thermal energy level and thereby grant access to this state. The remaining free energy difference of the totally unfolded state is too large, such that this state cannot be reached. The protein will therefore unfold only partially. Along path 2 the forced reduction will simultaneously lower the barriers of both states 1 and 2 below the thermal energy level, such that the barrier height of the intermediate state is still the one dominating the kinetics of the unfolding pathway. Along this path though, the barrier to the totally unfolded state is now lower than the barrier of the intermediate state, and the protein will unfold completely and at most stay only intermittently in the intermediate state, because the thermal energy will drive it immediately into the completely unfolded state. A similar concept has been proposed by Merkel et al. (1999) to explain the rupture of the streptavidin–biotin bond. Since the free-energy barrier for the intermediate state is higher along path 2 and also closer to the total unfolding barrier, a higher force is needed on average to reach the completely unfolded state than to reach the only partially unfolded state. The difference in free energy for state 1 along path 1 is lower than that along path 2. Because the height of the barrier to complete unfolding in state 2 is roughly the same along the very similar directions through the conformational space of the protein starting in the native folded conformation, state 1 will be accessible to the protein well before state 2. The thermal 15. Forced Unfolding of Single Proteins 327 energy will allow the protein to unfold partially into state 1, while state 2 is still hidden behind a barrier that cannot be overcome by thermal activation. Because the free-energy barrier to state 1 is lower along path 1, the average force needed to reach this state is lower than that for state 2. C. Monte Carlo Simulations We have included these two scenarios in a simple MC simulation (See Section VII,D) by testing the reaction kinetics simultaneously for the short and long elongation events. The kinetics can be characterized by two parameters: the width of the first barrier and an effective “attempt” frequency, which includes the barrier height as a multiplicative exponential factor, normalized by the thermal energy. The width of the first barrier was kept the same for both scenarios, while the attempt frequency was adjusted to agree with the relative difference in barrier height. Figures 12a to 12c show the force and elongation histograms obtained from 5000 consecutive runs of a Monte Carlo simulation. The simulations reproduced well the general features of the experimental data with a barrier width of 0.4 nm and an attempt frequency of 0.5 Hz along path 1 and 0.05 Hz along path 2 (corresponding to about a 2-kT difference in barrier heights). The selected pathway guides the folded domain either to a state where it is totally unfolded or to a state where it is partially folded. Fig. 12 Probability histograms of elongation (a) and unfolding forces for short elongation (b) and long elongation events (c). These were obtained by 5000 Monte Carlo simulations of unfolding of four domains placed in series. By testing the two reaction kinetics simultaneously associated with the two different pathways, short and long elongation events were allowed. A barrier width of 0.4 nm and an attempt frequency of 0.5 Hz along path 1 and 0.05 Hz along path 2 fitted best to the experimental data. 328 Altmann and Lenne VI. Conclusion and Prospects Although the molecular complexity of unfolding pathways can be very high, force spectroscopy of properly engineered single proteins can provide important clues to en- ergy landscapes on time scales from milliseconds to seconds and larger (the stability of the instrument permitting). In the future, we expect an increasing contribution by forced unfolding measurements to the understanding of protein folding as, on the one hand, proteins can be engineered to systematically perturb the unfolding pathways imposed by the real-space directionality and, on the other hand, instrument developments as, e.g., outlined in this chapter, will enable new types of measurements. This combination will be able to provide a more detailed understanding of the link between mechanical stability and folding features of proteins. The comparison of exper- imental results to increasingly available simulation results could offer a deeper insight into unfolding pathways. In particular, as we have shown, this technique can reveal— possibly functionally relevant—intermediates that were not detected thus far by other techniques. A. Biological Implications Molecular elasticity is a physicomechanical property that is associated with a number of proteins in both the muscle and the cytoskeleton. These new details about unfolding of single domains revealed by precise AFM measurements show that force spectroscopy can be used to not only determine forces that stabilize protein structures but also analyze the energy landscape and the transition probabilities between different conformational states. Applications of force spectroscopy on single molecules may thus lead to a better understanding about molecular biophysics in both the muscle and the cytoskeleton. VII. Appendices A. The Double-Sensor-Stabilized AFM We have designed a special AFM with a unique local stabilization system, which lends ultrahigh positional accuracy to forced unfolding measurements. It is made of two crossed, i.e., independent, optical detection systems (Figs. 13 and 14). The exact details of this double-detection system will be described elsewhere. In a normal AFM one lever is used simultaneously for the feedback that drives the displacement of the piezo-tube and the force measurement. This technique is being used with great success in various imaging applications of the AFM, but it has several serious drawbacks in forced unfolding applications. Because the AFM only knows where the surface is (as long as the lever is in sensory contact with it), the absolute distance between the free position of the lever and the surface is not known when the lever is not in contact with the surface. While the lever is out of contact, drifts and other low-frequency noise changing the distance between the tip and the sample cannot be detected. On approaching 15. Forced Unfolding of Single Proteins 329 Fig. 13 Our double-sensor atomic force microscope has two full crossed optical detection units. or retracting from the sample one controls the extension of the piezo only and not the distance between tip and sample. Compare the lower part of Fig. 15. This is why, in conventional dynamic force spectroscopy, force curves must be done fast enough, such that absolute and relative measurements on force curves can be carried out by basing them on the distance the piezo surface traveled during this time according to the voltages applied to it. 330 Altmann and Lenne Fig. 14 The two optical detection units are used to simultaneously detect the deflection signals from two levers on the same substrate independently. (See Color Plate.) The stabilization system we used in our instrument is based on the idea of using two levers simultaneously. This allowed us to split the feedback control system off from the one for the force measurements. In our double-sensor-stabilized AFM, (DSS-AFM) two sensors mounted side by side with a distance of few hundred microns on the same substrate carrier and slightly tilted with respect to the sample surface are used for this purpose. Because of the latter, one of the two sensors will make contact with the surface before the other. The distance between the second sensor and the sample surface can then actively be controlled with subnanometer resolution. Thus, measurement and distance controls are split up between the two levers. The first lever will detect all the noise that would change the distance between sensor array and sample. This can be controlled by a fast feedback. We eliminated all drift between the tip and sample by using a fast integral feedback. The second lever signal can be used to carry out measurements at any distance, mea- sured by the first lever, from the surface from milliseconds to hours at forces determined only by the sensitivity of the detection system (the thermal noise amplitude of the second cantilever, which was about 10 pN in our case) and by the average statistical error (which comes out to be about 4 at 30 pN according to the Gaussian law of error propagation), if we assume angstrom resolution and 10% uncertainty in the determination of the force constant of the cantilever by one of the calibration methods listed in the following. 15. Forced Unfolding of Single Proteins 331 Fig. 15 Force curve representation of the principle of the double sensor stabilization system in our AFM. After the first lever has contacted the surface, the distance between the second lever and the surface can be controlled with the typical subnanometer resolution. The distance between the sample and the second tip, which is used to do the actual unfolding experiments, can be controlled with the subnanometer resolution typical for AFM by selecting the proper setpoint, i.e., the normal force, of the first lever (Fig. 15). With this control one can do what is called “force clamping” a protein between the lever and the surface. As is shown in the Fig. 16, as long as the first lever is in contact with the surface, it is possible to stop the retract of the second lever at any time (e.g., t 01 ) for any duration (t 02 − t 01 ) while keeping the distance (d 0 ) and therefore the force (F 0 ) constant. B. Data Acquisition and Evaluation Techniques Data were acquired by a 32-bit PCI-M-I/O-16E-4 acquisition card (National Instru- ments) with 16 single-ended analogue inputs with a 12-bit resolution. The maximal speed of acquisition was 500 kSamples/s for single-channel acquisition. For most mea- surements, we recorded multiple channels at 100 kSamples/s. Force curves were recorded and saved on a Computer with a 266-MHz Intel Pentium II CPU with 128-MByte RAM. We implemented programs for digitally controlling the instrument and storing the data acquired with either Labview (National Instruments) 332 Altmann and Lenne Fig. 16 Force clamp based on the double sensor stabilization system. The force can be kept constant by simply keeping the distance constant. or Igor Pro using NI-DAQ tools (Wavemetrics). All force curves from an experiment were continuously recorded using FIFO-buffering and saved without prior sorting. After each experiment, data were separated, scaled, and sorted. A box-smoothing window (of variable width depending on the acquisition rate) or a 2-kHz low-pass filter was applied to reduce the laser noise and thermal noise on the force signals. This low-pass filtering does not alter the curves acquired with Hz-scanning. Positions and force were then analyzed manually with Igor Pro. C. Calibration 1. Thermal The analysis of the thermal fluctuations of the vibrating lever gives access to the stiffness of the latter. It is based on the equipartition theorem and may be performed as described in (Florin et al., 1995). However, this approach requires that no additional noise is added to the thermal noise. This would lead to an overestimation of the displacement of the lever and hence to an underestimation of the measured stiffness. 2. The B–S Transition of λ-Phage DNA When a single λ-digest DNA molecule is stretched it goes into a highly cooperative conformation transition (B–S). The well-pronounced transition force plateau provides a valuable method for lever calibration. This plateau is observed at 65 pN at room temperature of 20 ◦ C (see Fig. 17) (Rief, Clausen-Schaumann et al., 1999; Clausen- Schaumann et al., 2000). Practically, λ-BstE digest DNA was used (Sigma) (see (Rief, Clausen-Schaumann et al., 1999) for methods). The procedure is easy and at the same time constitutes a test for correct setup for force measurements. 15. Forced Unfolding of Single Proteins 333 Fig. 17 The B–S transition of λ-phage DNA measured by AFM. Fig. 18 Monte Carlo simulations of spectrin extension. 334 Altmann and Lenne D. Monte Carlo Simulations Monte Carlo simulations (Fig. 18) were set up analogously to Rief et al. (1998) by combining the WLC model to calculate the force with the kinetics governed by a two- state model. The method was developed further to a three-state model with a choice of two pathways. The unfolding rate ν u of a folded structure is the product of a natural vibration ν 0 and the likelihood of reaching the transition state with an energy barrier G u discounting by mechanical energy F · x u , where x u is the width of the activation barrier (Bell, 1978), ν u (F) = ν 0 exp(−(G u − F · x u )/k B T ) = ν eff exp(F · x u /k B T )(k B T = 4.1pN· nm at room temperature). 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[...]... obtained with the active-Q feedback activated The difficulties encountered in imaging living cells are similar to those experienced in imaging swollen gels The thickness of cells combined with their low stiffness results in large deformations, so that the tip can distort the structure locally to such an extent that lateral forces again become a problem and result in streaks in the image The value in using... the specimen resulting in a neck of water forming as the tip approaches the specimen The resultant surface-tension force will act to pull the tip of the probe into the specimen, increasing the normal force to about 50 nN The lateral force on the specimen is proportionally increased This capillary force can be virtually eliminated by working in a liquid environment so that the liquid interface is moved... addition of the feedback loop the phase of this oscillating signal shifted by π /2 so as to bring the signal in phase with the velocity of the cantilever In practice, the actual shift required to bring the displacement in phase with the velocity will not be exactly π /2 owing to other phase shifts in the system, particularly in the electronics The resulting signal is then added to the drive signal for the... greater forces are applied to the specimen during the tapping process, which results in distortion and lower resolution imaging of the specimen It also gives incorrect values for the heights of the specimens Higher values of Q in liquid bring many benefits to imaging The simplest method of increasing the value of Q is by designing the cantilever to present a low area in the direction of motion An alternative... contrast is not METHODS IN CELL BIOLOGY, VOL 68 Copyright 20 02, Elsevier Science (USA) All rights reserved 0091-679X/ 02 $35.00 337 3 38 Humphris and Miles usually necessary with AFM, and so the specimen is free to change with time This allows processes to be followed in situ There are exciting developments to dramatically increase AFM scan rates and these will be of great value in the study of biomolecular... stored in the cantilever and to increase its response time to allow scan rates to be increased The dramatic increase in effective Q of the fundamental resonance of a cantilever in a liquid environment as a result of the active feedback is shown in Fig 2 This effect is demonstrated using both the magnetic and the acoustic methods of driving the cantilever The initial breadth of the cantilever resonance in. .. Dynamic Force Techniques A Transverse Dynamic Force Spectroscopy B Application of Transverse Dynamic Force Spectroscopy and Microscopy V Conclusions References I Introduction The advantages of atomic force microscopy (AFM) for the study of biological specimens are unique and are discussed in many of the accompanying chapters The ability to image at molecular resolution in three dimensions in any environment... conventional tapping or intermittent contact mode in liquid, the energy stored in the oscillating cantilever is much less so that intermittent contact with the surface results in a nonsinusoidal motion of the cantilever; that is, the oscillation becomes anharmonic and higher modes become significant The decrease in the quality factor of the cantilever in liquid has the consequence that greater forces are... specimen in intermittent contact mode in liquid are, in fact, about an order of magnitude greater than those in simple contact mode in liquid, although the lateral forces are less This may account for the observed decrease in resolution compared to that in contact mode imaging The resonant peak in the frequency spectrum is now so broad that any shift in frequency due to the interaction between the tip and... further driving term is added to the right-hand side of Eq [2] : m d2z dz + kz = F0 eiωt + Fint (z) + Geiπ /2 z(t) +γ dt 2 dt [3] This term represents a positive feedback of the cantilever displacement with variable gain (G) and phase shifted by π /2 so as to be in phase with the velocity rather than the displacement of the cantilever Equation [3] can be rewritten as m dz d2z + kz = F0 eiωt + Fint (z), + . metal-chelating microscopy tip as a new toolbox for single-molecule experiments by atomic force microscopy. Biophys. J. 78, 327 5– 3 28 5. Speicher, D. W., and Marchesi, V. T. (1 984 ). Erythrocyte spectrin. expect an increasing contribution by forced unfolding measurements to the understanding of protein folding as, on the one hand, proteins can be engineered to systematically perturb the unfolding pathways. Biophys. J. 78, 1997 20 07. Djinovic-Carugo, K., Young, P., Gautel, M., and Saraste, M. (1999). Structure of the alpha-actinin rod: Molec- ular basis for cross-linking of actin filaments. Cell 98, 537–546. Dubreuil,