High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

All materials and equipment described in this protocol are listed in the Table of Materials. LabVIEW software to operate the high-speed MT setup described below, as well as the MATLAB scripts to analyze sample data, are deposited on GitHub (https://github.com/ShonLab/Magnetic-Tweezers) and publicly available.

1. Construction of apparatus

NOTE: The general principle of the high-speed MT construction is similar to standard, conventional MT systems, except for the use of a high-speed complementary metal oxide semiconductor (CMOS) camera and a high-power, coherent light source (Figure 1). Refer to other sources for more descriptions of standard MT instruments^5,26,27.

1. Set up an inverted microscope on an anti-vibration optical table. Install a high-speed CMOS camera and a frame grabber.
2. Build a translation stage for manipulating magnets in 3D. Mount a motorized linear stage (>20 mm travel) vertically on top of a manual XY stage.
   NOTE: The vertical movement controls force, whereas the XY stage is for the manual alignment of magnets to the optical axis for the initial construction of the setup.
3. Install a rotary stepper motor and a belt and pulley system for rotating magnets.
   NOTE: The belt transmits the rotary motion between the motor shaft and magnets that are a few centimeters apart. The rotation of magnets is internal to the translational manipulation.
4. Mount the magnets. Use an acrylic holder (ordered from a manufacturing company; see Supplemental Figure S1) that can tightly house two identical magnets in parallel, with a well-defined 1 mm gap between the magnets (Figure 1B). To utilize the maximum force obtainable with a given pair of magnets, adjust the vertical position of the translation stage so that the bottom surface of the magnets aligns with the sample plane when it is moved to the lowest position.
   NOTE: Refer to Lipfert et al. for more information on the holder design and configuration of magnets²⁸. The height and orientation of magnets are controlled by the LabVIEW software in conjunction with data acquisition.
5. Viewing with a low-magnification objective lens, align the magnets to the center of the field of view. Check that rotating the magnets does not cause a large displacement of the center of the magnet pair.
   NOTE: If the midpoint between the magnets rotates about the axis of rotation, it is likely that the magnets are off-centered due to an imperfect holder. A small level of misalignment relative to the gap size is tolerable, as the magnet rotation is only for checking tethers and applying torques in specific applications.
6. Install a superluminescent diode (SLD) for the illumination of beads. Pass the beam through the 1 mm gap between the two magnets. Make sure that the beam is properly collimated to fit in the gap and the illumination is not shadowed by the magnets.
7. Install a piezo lens scanner on the nosepiece and mount a 100x oil-immersion objective lens (numerical aperture [NA]: 1.45) for bead tracking. To avoid potential artifacts in tracking results, make sure that the illumination is maintained uniformly when the magnets are moved. Finally, adjust the light level to the maximum brightness without saturating pixels.
   ​NOTE: For the comparison of different light sources for the high-speed tracking of beads, refer to Dulin et al.²⁹.

2. Calibration of magnetic force

1. Using polymerase chain reaction (PCR; see Table 1), prepare 5 kbp dsDNA fragments (using Primer B, Primer Z_5k, and λ-DNA) that are labeled with biotin on one end (for surface attachment) and azide on the other end (for bead attachment).
2. Following section 6, prepare a flow cell with the 5 kbp molecules.
3. Following section 7, identify a good bead-tether construct by verifying its extension and rotation. In particular, make sure to choose a bead with a minimal rotational trajectory (i.e., with a radius <200 nm) to minimize the bead height offset due to off-centered attachment^30,31. Once a good tether is identified, start bead tracking, referring to section 9.
4. If the setup is new, characterize its noise and stability for reliable high-resolution measurements. Place the magnet ~3 mm from the flow cell surface (to apply >10 pN and suppress the Brownian motion of a bead), track the z-position of the bead at 1.2 kHz, and compute the Allan deviation (AD) from the z-coordinate time series^32,33 (Figure 2C). Check that AD values of a few nanometers are achievable in the high-speed regime (<0.1 s), and that differential tracking (magnetic bead position relative to a reference bead) reduces AD in the longer timescale.
   NOTE: We typically obtain an AD of <3 nm at the maximum rate (1.2 kHz or 0.83 ms resolution), and the AD keeps decreasing at least up to 10 s, implying a minimal drift. Others have reported similar values on similar setups^{9,10,11,12,34}.
5. With magnets in the resting position (F ~ 0 pN), record the x– and y-coordinates of the tethered bead at 1.2 kHz. Record the position for a sufficiently long period (that is, sufficiently longer than the characteristic relaxation time of fluctuation³⁵) so that the Brownian motion is sufficiently sampled.
   NOTE: Here, the x-direction is along the direction of the magnetic field, whereas the movement in y represents the transverse motion perpendicular to the field.
6. Move the magnets closer to the flow cell and repeat the bead-position measurements until the magnets gently touch the top of the flow cell. Move in large steps (e.g., 1-2 mm) when the magnets are more than 7 mm away from the sample plane (since the applied force increases slowly in the far field of magnets), but reduce the step size gradually (e.g., 0.1-0.5 mm) as they approach closer for finer calibration at higher force levels (Figure 2B).
7. Calculate the force at each magnet position, d, using either of the two alternative methods (a MATLAB script "force calibration.m" including both methods is provided; see Supplemental File 1).
   1. Measure the variance of the bead's y-coordinates, (Figure 2D) and the mean z-position of the bead relative to the lowest position (Figure 2B, bottom). Then, use equation (1)^7,27,36 to estimate the force (with a fixed bead radius R = 1,400 nm and thermal energy k_RT = 4.11 pN∙nm):
          (1)
   2. Alternatively, calculate the power spectral density (PSD) of the y-coordinates, S_y (Figure 2E). Determine the applied force F by fitting a double-Lorentzian model³⁷ to the measured S_y using equation (2).
          (2)
      Here, , R is bead radius, γ_y and γ_φ are the translational and rotational drag coefficients, respectively (estimated from the Stokes-Einstein equation), k_RT is the thermal energy, f₊ and f_– are two characteristic frequencies obtained using equation (3).
      (3)
      NOTE: Since the tether extension L is a function of force that follows the well-established worm-like chain (WLC) model, the above expressions leave F as the only fitting parameter (we fix R to be 1,400 nm for simplicity because it is shared across all force levels and the exact value does not influence the results appreciably). When necessary, motion blur and aliasing from camera-based image acquisition must be considered^38,39, but this effect is negligible in our high-speed measurements above 1 kHz with 5 kbp tethers.
8. Repeat steps 2.4-2.7 for a few more constructs. Probe three to five different beads to average out the force variability among the magnetic beads.
   NOTE: Force variation among the magnetic beads in use should be considered to determine the proper number of constructs for averaging. This variability is small but can lead to more than 1 pN of error in the measured force, even for commercial products³¹. For most applications, where the absolute determination of the forces involved is not crucial, averaging the calibration results of three to five beads is generally sufficient. An alternative approach to account for this variation is to measure the force with individual tethers at the beginning of the experiment, which can be time-consuming. Another option is to embed hairpin structures that unzip at known force levels in each construct³¹.
9. Plot the measured force as a function of magnet distance and fit a double exponential function to the data (Figure 2F) using equation (4).
       (4)
   Here, F₀ (baseline), A₁ and A₂ (amplitudes), and d₁ and d₂ (decay constants) are fitting parameters. Make sure that the force values from the two methods, as well as the resulting double-exponential fits, largely agree (Figure 2F,G).
   NOTE: To confirm that force calibration is conducted properly, verify the force-extension relationship of the probed constructs by plotting the extension versus the measured force.
10. To correct for the bead height offset z_off resulting from force-dependent tilting of the magnetic beads^30,31, estimate z_off from the lateral offset x_off, considering the geometry of an off-centered tether with a bead radius using equation (5), and apply the values to the measured extension values. This step is implemented in the MATLAB script "force calibration.m" (lines 252-254).
        (5)
    NOTE: Although this correction makes small changes to extension, especially for the beads with a small radius of rotation (<200 nm), this offset often critically affects the elastic response, as seen in the change from Figure 2H à Figure 2I^30,31.
11. Check the persistence length L_p by fitting an extensible WLC model to the data using equation (6).
        (6)
    Here, L₀ is the contour length (1.7 µm for 5 kbp) and K₀ is the modulus for enthalpic stretching.
    NOTE: Although the L_p of dsDNA is well-accepted to be 40-50 nm in a typical buffer such as phosphate-buffered saline (PBS), the WLC formula applied to short molecules (<5 kbp) systematically underestimates L_p as L₀ decreases^31,40. This is because the classical WLC model presumes a polymer whose chain length is sufficiently longer than its persistence length. Here, we obtained L_p = 40 ± 3 nm for the 5 kbp construct (Figure 2H), and the extension correction further yielded a homogeneous K₀ of 1,100 ± 200 pN (Figure 2I). Applying a finite WLC model^31,40, as well as a correction for non-Gaussianity in extension distribution⁴¹, will slightly increase L_p.
12. Once the force calibration is verified, apply the obtained fitting parameters of the double-exponential model to the provided LabVIEW software (Supplemental File 2) and wait for the software to compute the current force in real time from motor readings (i.e., magnet position). Since an analytic expression for the inverse function d(F) is not available, prepare a lookup table of d versus F in 0.1 pN steps by numerical estimation of for the d target force levels. Store this table in the software as well to command the force control.

3. Synthesis of DNA hairpins

NOTE: DNA hairpin constructs for MT experiments are prepared by PCR amplification of a 510 bp region in λ-DNA with two custom primers, one of which contains a hairpin structure on its 5′-end (Figure 3A). In this way, a hairpin motif is placed at one end of the PCR product.

1. Prepare the primers.
   1. Forward primer: Primer B_hp that is 5′-biotin-labeled for glass surface attachment and binds to λ-DNA. This primer contains a hairpin motif with an 8 bp stem and a 6 nt loop, 5′ to the λ-binding region.
   2. Reverse primer: Primer Z_hp that is 5′-azide-labeled for magnetic bead attachment and binds to λ-DNA 1 kbp away from the forward primer.
2. Set up and run the PCR with λ-DNA (template), nTaq polymerase, and standard PCR conditions (see Table 1). Clean up the product with a commercial purification kit.
3. Measure the DNA concentration by UV absorption at 260 nm (A260) and perform agarose gel electrophoresis (2% gel) (see Table 2) to verify the product size. A typical yield is ~35 µL of ~600 nM solution.

4. Preparation of SNARE proteins

NOTE: Neuronal SNARE complexes are assembled by combining three purified rat proteins expressed from E. coli: VAMP2/synaptobrevin-2, syntaxin-1A, and SNAP-25 (Figure 3B). To facilitate their assembly, syntaxin and SNAP-25 are co-expressed with a VAMP2 fragment (lacking the N-terminal region; termed "ΔN-VAMP2") into a structure called the "ΔN-complex", and then mixed with full-length VAMP2 after DNA handle attachment to form full complexes.

1. Prepare plasmids containing cDNA for the expression of SNARE proteins (DNA sequences for all plasmids are given in the Table of Materials).
   1. Prepare 6×His-tagged VAMP2 lacking the transmembrane domain (2-97; L32C/I97C for disulfide linkages) cloned into a pET28a vector.
   2. Prepare syntaxin-1A lacking the Habc and the transmembrane domain (191-267, I202C/I266C substitutions for disulfide linkages) cloned together with 6×His-tagged ΔN-VAMP2 (49-96) into a pETDuet-1 vector.
   3. Prepare the full-length SNAP-25 isoform b (2-206, all C to A) cloned into a pET28a vector. This will be used for preparing ΔN complexes.
   4. Prepare the 6×His-tagged full-length SNAP-25 isoform b (1-206, all C to A) cloned into a pET28a vector for direct addition to the MT assay buffer to reassemble the SNARE complexes after unfolding.
2. Prepare two tubes of Rosetta (DE3) E. coli cells. Transform one group with VAMP2 plasmids (from step 4.1.1), one with both syntaxin-1A/ΔN-VAMP2 and untagged SNAP-25 plasmids (from steps 4.1.2 and 4.1.3) for expressing the ΔN-complex, and the other with His-tagged SNAP-25 plasmids (from step 4.1.4).
3. Transfer the transformed cells into Luria-Bertani broth (LB) with appropriate antibiotics (here, kanamycin and chloramphenicol for VAMP2 and His-tagged SNAP-25; kanamycin, chloramphenicol, and ampicillin for ΔN-complex). Grow them at 37 °C in a shaking incubator (220 rpm) until the optical density (OD) of the broth reaches 0.7-0.9.
4. Add 1 mM isopropyl β-d-1-thiogalactopyranoside (IPTG) to induce protein expression and incubate the cells for 3-4 h at 37 °C in a shaking incubator (220 rpm).
5. Pellet down the cells by centrifuging the culture at 4,500 × g for 15 min at 4 °C.
6. Prepare buffers for protein purification (see Table 2).
7. Suspend SNARE-expressing cell pellets in 40 mL of ice-cold lysis buffer and lyse the cells by sonication on ice (15% amplitude, 5 s on and 5 s off, 30 min total).
8. Centrifuge the lysate at 15,000 × g for 30 min at 4 °C to remove insoluble materials.
9. Pass the supernatant through a gravity column filled with 1 mL of Ni-NTA resin. Wash the resin with wash buffer A, then with wash buffer B, and elute the proteins with 10 mL of elution buffer.
10. Remove tris(2-carboxyethyl)phosphine (TCEP) and imidazole from the eluent by using a desalting column (follow the manufacturer's instructions). Elute the sample with PBS.
11. Concentrate the proteins with centrifugal filters (10 kDa cutoff) to ~70 µM while maintaining the proteins in PBS (typically yielding 2 mL). Measure the protein concentration either by ultraviolet (UV) absorption at 280 nm (A280) or by the Bradford assay.
12. Prepare small aliquots, flash-freeze in liquid nitrogen, and store at -80 °C until use.
    ​NOTE: Full SNARE complexes will be assembled after conjugating ΔN-complex on a DNA handle (see below).

5. Attachment of DNA handles

NOTE: Two 510 bp dsDNA handles containing primary amine groups on one end are first prepared by PCR, and the amine groups are then converted to maleimide groups by using a bifunctional crosslinker, SM(PEG)₂. The two handles are then covalently linked to SNARE complexes via their cysteine groups for site-specific conjugation (Figure 3B).

1. Prepare primers.
   1. Prepare forward primers: Primer B (for amplifying Handle B) that is 5′-biotin-labeled for glass surface attachment and binds to λ-DNA; Primer Z (for amplifying Handle Z) that is 5′-azide-labeled for magnetic bead attachment and has the same sequence as Primer B.
   2. Prepare a reverse primer: Primer N (shared for Handle B and Handle Z) that is 5′-amine-labeled for protein conjugation and binds to λ-DNA 510 bp away from the forward primer.
2. Set up and run two sets of PCR reactions (18 tubes of 200 µL reaction for each handle) with λ-DNA (template), nTaq polymerase, and standard PCR conditions (see Table 1). Clean up the product with a PCR clean-up kit and elute each handle with 45 µL of ultrapure water. Use a minimal volume of water to obtain high concentrations of handles for an effective reaction in later steps.
3. Measure the DNA concentration by A260. The typical yield is ~650 µL of ~2 µM solution for each handle. Keep small samples apart for later verification in agarose gel electrophoresis.
4. React each handle (1 µM in PBS) with 5 mM SM(PEG)₂. Incubate at room temperature with gentle rotation. After 1 h, use a DNA purification kit to remove unreacted SM(PEG)₂. Elute each handle with 250 µL of PBS to obtain ~2 µM solutions.
5. Mix the solutions of Handle B and ΔN-complex at a molar ratio of 1:16 (e.g., 1 µM Handle B and 16 µM ΔN-complex) in PBS and incubate for 2 h at room temperature with agitation. Keep apart a small sample for agarose gel electrophoresis.
6. Add a solution of VAMP2 in a 2.5-fold molar excess over the ΔN-complex used in the previous step. Incubate the mixture for another 1 h at room temperature with agitation. Full SNARE complexes are assembled in this step.
7. Remove free proteins by buffer exchange with fresh PBS and a centrifugal filter (100 kDa cutoff): centrifuge at 14,000 × g for 5 min at 4 °C, repeat at least 6x, and run for 15 min for the last spin. Measure the increase in the A260/A280 ratio to monitor the removal of free proteins. Keep apart a small sample for agarose gel electrophoresis.
8. Add Handle Z to the solution in a 15-fold molar excess over Handle B. Keep the concentration of Handle Z at least above 1 µM to facilitate the reaction. Incubate the mixture overnight at 4 °C with agitation.
9. Verify the intermediates (Handle B and its protein conjugates) and the final product (SNARE complex with two handles) by agarose gel electrophoresis (Figure 3B, inset) (see Table 2).
   NOTE: If the proteins are successfully attached to Handle B, a mobility shift will be detected. In particular, the formation of full SNARE complexes on DNA handles can be confirmed by their resistance to sodium dodecyl sulfate (SDS), unlike ΔN-complexes, that are disassembled in SDS and leave only syntaxin bound to DNA (compare b and c in Figure 3B).
10. Prepare small aliquots, flash-freeze in liquid nitrogen, and store at -80 °C until use.
    ​NOTE: Although the final solution contains unreacted handles, only the wanted construct that is doubly labeled with biotin and azide will be selected during the sample assembly in a flow cell.

6. Fabrication of flow cells

NOTE: Flow cells for MT measurements are constructed from two glass coverslips bonded together by double-sided tape (Figure 3C). One coverslip is coated with a mixture of PEG and biotinylated polyethylene glycol (PEG) to avoid nonspecific binding and to enable specific tethering of target molecules via biotin-NeutrAvidin linkage (Figure 3D). Then, the solutions of materials for MT experiments are sequentially infused into a flow cell by using a syringe pump (Figure 3C,D).

1. Prepare two glass coverslips, one each for the top (24 mm × 50 mm, No. 1.5 thickness) and the bottom (24 mm × 60 mm, No. 1.5 thickness) surface. Clean the coverslips by sonication in 1 M KOH for 30 min. After sonication, rinse the coverslips with distilled water and keep in water until the following step.
2. PEGylate the bottom coverslip following published protocols^42,43. Use N-[3-(trimethoxysilyl)propyl]ethylenediamine for silanization and a 1:100 (ww) mixture of biotin-PEG-SVA and mPEG-SVA in 100 mM bicarbonate buffer. Keep the PEGylated coverslips dry at -20 °C and store them for a few weeks.
3. On the day of the experiments, take out the PEGylated coverslips and blow dry them with a nitrogen gun. Visually inspect them for dirt to make sure they are clean.
4. To make the sample channels, prepare ~2 mm wide strips of double-sided tape and lay down four strips on a bottom coverslip (PEGylated surface up), parallel to and separated from each other by ~5 mm (Figure 3C).
   NOTE: This way, three 5 mm wide sample channels can be created in a single flow cell.
5. Place a top coverslip in the center of the bottom coverslip, leaving ~5 mm of space on the short edges for channel inlets and outlets. Gently press the back of the top coverslip with tweezers to firmly seal the channels.
6. To make an inlet reservoir, trim the edge of a 200 µL pipette tip. Cut out ~10 mm from the wider opening to allow for holding ~200 µL of solution. Make three of them for the three flow channels. To configure the outlets, prepare three syringe needles that fit the tubing for the syringe pump.
7. Using 5 min epoxy, glue the reservoirs and needle hubs to the flow cell. Ensure a complete seal is formed to avoid leakage, and that the channels are not blocked with excess glue. Let it dry for at least 30 min.

7. Assembly of bead-tether constructs

NOTE: The solutions of materials for MT experiments, including the ones for bead-tether constructs, are sequentially introduced into flow cells by using a syringe pump (Figure 3C,D).

1. Prepare magnetic beads. Take 5 mg of M270-epoxy beads from a stock solution (~3.3 × 10⁸ beads in 167.5 µL of dimethylformamide) and replace the solvent with phosphate buffer (see Table 2) by magnetic separation of the beads.
2. Prepare the beads at ~1.1 × 10⁹ beads mL⁻¹ in a phosphate buffer with 1 M ammonium sulfate and react them with 2 mM dibenzocyclooctyne (DBCO)-NH₂. Incubate the mixture for 3 h on a rotating mixer at room temperature. After the reaction, wash the beads 3x with fresh phosphate buffer to remove unreacted molecules.
   NOTE: The washed beads can be stored without extra rotation at 4 °C for several weeks before use.
3. Connect a needle on the flow-cell channel exit to the syringe pump with polyethylene tubing. Equilibrate the channels with PBS.
4. Introduce the following solutions sequentially into the channel by suctioning with the pump: NeutrAvidin, target constructs (DNA hairpins or SNARE complexes with DNA handles), reference polystyrene beads, and DBCO-coated magnetic beads. Before use, vortex the bead solutions thoroughly to disperse potential bead aggregates.
5. Wash away unbound beads while applying 0.1 pN of force.
   NOTE: The application of a small upward force facilitates the removal of unbound beads and helps avoid the rupture of specifically bound bead-tether constructs.
6. For experiments with SNARE complexes, include 1.5 µM SNAP-25 in the final buffer.
   ​NOTE: The free SNAP-25 molecules can rebind SNARE complexes after unfolding and allow repeated measurements on a single complex.

8. Identification of target constructs

1. On the surface of a flow-cell channel, search for the magnetic beads that are tethered by single molecules of the target construct. Make sure a reference bead is located nearby.
2. Rotate a candidate bead and check that it swivels freely. If the bead is tethered by multiple molecules, it exhibits a constrained motion.
3. Rotate the bead for a few complete turns and find out the radius of rotation (this function is implemented in the provided software). Preferably, choose a bead with a small rotational radius.
   NOTE: This radius indicates how much the bead is off-centered from the tether axis, which is randomly determined during the bead-tether assembly^30,31. In all experiments, minimal off-centering of a bead alleviates many artifacts associated with the high bead radius to tether extension ratio we use.
4. Increase the force from 0 to 5 pN to identify good single-tethered beads. Look for a large change in the diffraction pattern of a bead resulting from the stretching of a 1 kbp tether (or the equivalent two 510 bp handles). If the diffraction pattern does not change significantly, lower the force to zero and scan for another candidate bead.
   ​NOTE: The ~300 nm lifting of a bead can be readily noticed from the raw images without actually starting the tracking process.

9. Bead tracking for extension measurements

NOTE: Tracking of beads is performed by analyzing bead images in real time in the LabVIEW software provided with this article. The tracking method and its variants have been used in most of the conventional MT systems and are explained in previous literature^2,5,7,26. By measuring the position of a magnetic bead relative to a fixed reference bead (i.e., differential tracking), the position measurements become extremely robust to an external perturbation.

1. Once a proper magnetic bead is located together with a reference bead, click on the Calibrate button to start preparing for bead tracking.
2. Click on the beads in the image to define the locations of the beads. The images will then be cropped to regions of interest (ROIs) (e.g., 150 x 150 pixels for a 3 µm bead) around the beads and then further analyzed to extract the precise bead coordinates.
3. Wait for the magnet rotation to complete. This process records the x– and y-coordinates of the bead (by computing 2D cross-correlation⁴⁴ or by using radial symmetry⁴⁵ of the bead images, with comparable performance) while rotating the magnets to document the off-centered attachment of the bead³¹.
4. For tracking in the z-direction, wait for the software to generate a lookup table of diffraction images of the beads at different distances from the focal plane. This is carried out by stepping the objective lens with a piezo scanner in equidistant steps and recording fluctuation-averaged bead images at each position. Then, the z-coordinates of the beads in actual experiments are determined by comparing the real-time bead images to the lookup table with interpolation⁷.
5. When the lookup table generation is finished, enable tracking and autofocusing (press the Track? and AF? Buttons) and click on the Acquire button to start recording bead positions.
   ​NOTE: Autofocusing is optional but recommended to correct for the stage drift in z during the acquisition.

10. Force application schemes

1. Force-ramp experiments: To verify the force-extension relationship of the construct, apply a force ramp up and down at a constant loading rate (± 1.0 pN s⁻¹) (Figure 4A). For example, apply three rounds of a 0-20-0 pN cycle to verify the overall length of the construct and the force-extension curve of the handles.
2. By specifying the tether parameters in the software, overlay a WLC force-extension curve on top of the measured data, and determine whether the target bead is tethered by a genuine sample construct with proper DNA handles. Use the known contour length (e.g., ~340 nm for 1 kbp dsDNA) and WLC persistence length (30-45 nm for short dsDNA³¹) of the construct as a starting point. Apply the extension correction method described in step 2.11 if necessary.
3. If the construct is verified, examine the force-extension response in detail to look for additional extension resulting from the target molecules-hairpins or SNARE complexes.
4. Constant-force experiments: Gradually vary the applied force in discrete steps to probe the force sensitivity of the target molecules (Figure 4B).
   NOTE: MTs enable simple and effective constant-force experiments because the applied force is maintained constant when the magnets are held still.
   1. For DNA hairpins, apply 4-8 pN of force with 0.2-0.5 pN steps, and measure the bead position for ~10 s at each force level.
   2. For SNARE complexes, apply 14-16 pN of force with 0.1-0.2 pN steps, and measure the bead position for ~10 s at each force level.
5. Force-jump experiments: Observe the transition events of SNARE complexes.
   NOTE: Force-jump experiments, like constant-force experiments, involve changes in force levels. However, force jumps employ more abrupt changes in the applied force, allowing for the monitoring of force-triggered events in the probed molecules, such as a sudden rupture of protein complexes. For example, since SNARE complexes exhibit structural hysteresis in force cycling²³, it is informative to perform force-jump experiments and measure the latency to transition (Figure 4C).
   1. Unzipping: Peeling off of a VAMP2 molecule from an intact, ternary SNARE complex, leaving a binary complex of syntaxin-1A and SNAP-25.
   2. Rezipping: Zipping of the unzipped VAMP2 molecule to regenerate an intact SNARE complex.
      1. Unfolding: Full disassembly of a SNARE complex accompanied by complete dissociation of SNAP-25. Only VAMP2 and syntaxin molecules remain in the construct after unfolding.
      2. Refolding: Regeneration of a SNARE complex upon binding of a free SNAP-25 molecule from the buffer.
6. At 2 pN, induce the assembly of an intact SNARE complex by waiting (~30 s) for the association of a free SNAP25 molecule. A sudden decrease in extension is observed upon the formation of a SNARE complex.
7. To observe unzipping events, wait for a few seconds at 10-12 pN, and then move to 14-15 pN abruptly with the maximum motor speed possible. Depending on the target force, the SNARE complex will exhibit either a reversible transition between partially unzipped intermediates (as in constant-force experiments) or a ~25 nm jump to a higher, unzipped state after a random waiting time (or latency).
8. To observe rezipping events, lower the force to 10-12 pN immediately after unzipping is observed. Again, the SNARE complex exhibits a stochastic transition to the lower, zippered state after some random latency. If unfolding has occurred after unzipping, the complex will fail to rezip, as a SNAP-25 molecule will be missing.
9. To observe unfolding events, wait for a longer period after unzipping is observed to detect a further increase in extension (~2 nm).

11. Data analysis

NOTE: The types of analysis one can conduct with MT data depend on the target system. However, there are common approaches to extracting useful information from the respective experiments described in Figure 4. All analyses are performed with MATLAB (R2021a) using the custom codes provided with this article. These codes generate plots by using the same data presented in this article. Note that while raw data from 100 Hz tracking was directly taken for analysis, data from 1.2 kHz tracking was typically median-filtered (with a five-point sliding window) prior to analysis to reduce noise (except for noise analysis).

1. Force-ramp experiments: Analyze the force-extension relationship (e.g., elasticity of polymers) and transition the force to extract information on nanomechanical properties.
2. Constant-force experiments: Analyze state populations and dwell time (or transition rate) as a function of force to extract structural (e.g., regions involved in transition), thermodynamic (e.g., free energy difference), and kinetic (e.g., energy barrier) parameters of the conformational changes.
3. Force-jump experiments: Analyze rupture kinetics (e.g., protein-protein interactions and receptor-ligand binding) or the lifetime of transient intermediates (e.g., unfolding of biomolecules) to extract the stability of target molecules and their states.
4. As representative applications, analyze the sample data for DNA hairpins and SNARE complexes:
   1. Two-state transitions of a DNA hairpin: unzipping force, opening distance, force dependence of population shift, and state assignment and transition rate measurements with a hidden Markov model (HMM) (MATLAB codes provided).
   2. Conformational changes of SNARE complexes: unzipping force, force dependence of intermediate states and unzipping latency, hysteresis in rezipping, and unfolding/refolding behavior.
      NOTE: Force-extension models for DNA handles, DNA hairpins, and SNARE complex conformations are given in previous references^14,31.