Single-molecule magnetic tweezers to probe the equilibrium dynamics of individual proteins at physiologically relevant forces and timescales

Abstract

The reversible unfolding and refolding of proteins is a regulatory mechanism of tissue elasticity and signalling used by cells to sense and adapt to extracellular and intracellular mechanical forces. However, most of these proteins exhibit low mechanical stability, posing technical challenges to the characterization of their conformational dynamics under force. Here, we detail step-by-step instructions for conducting single-protein nanomechanical experiments using ultra-stable magnetic tweezers, which enable the measurement of the equilibrium conformational dynamics of single proteins under physiologically relevant low forces applied over biologically relevant timescales. We report the basic principles determining the functioning of the magnetic tweezer instrument, review the protein design strategy and the fluid chamber preparation and detail the procedure to acquire and analyze the unfolding and refolding trajectories of individual proteins under force. This technique adds to the toolbox of single-molecule nanomechanical techniques and will be of particular interest to those interested in proteins involved in mechanosensing and mechanotransduction. The procedure takes 4 d to complete, plus an additional 6 d for protein cloning and production, requiring basic expertise in molecular biology, surface chemistry and data analysis.

Extended Figure 1

Stiffness of the magnetic trap created by the (A) N52 magnets (voice-coil configuration) and (B) magnetic tape head. The magnetic trap stiffnesses can be simply calculated as dF/dz being z the distance between the gap (magnets or tape head) and the magnetic bead. Due to the non-linearity of the F(z), the stiffness changes over the control parameter (magnet position or electric current), but in the operating regime the trap this results in a very soft trap (~10^-4 pN/nm), resulting in effective force clamp conditions (no appreciable change in force over the range where the bead moves).

Extended Figure 2

Calibration of the (A) voice coil-based or (B) tape head-based magnetic tweezers using the worm-like chain model for polymer elasticity (left) and comparison of the calibration using the WLC and FJC (right). The FJC gives a lower contour length (⊿L_c=16.3 nm) compared to the WLC (⊿L_c=18.6 nm). All error bars are SD.

Extended Figure 3. Photograph of the magnetic tape head and voice-coil-mounted permanent magnets with a magnification of the gap region.

Figure 1. Schematics of the workflow to study the nanomechanics of an individual protein using single-molecule magnetic tweezers.

(A) From the protein of interest (PoI), (B) clone the PoI gene into the expression-modified pFN18A plasmid. (C) Express and purify the protein construct. (D) Assemble and functionalize fluid chamber for specific and covalent anchoring of the protein construct. (E) Conduct nanomechanical experiments using the magnetic tweezers (F) Analyze and interpret the magnetic tweezers data.

Figure 2. Overview of magnetic tweezers force spectroscopy.

(A) Schematics of the magnetic tweezers instrument using the permanent magnet configuration. The magnets are placed on top of the fluid chamber, and their position is controlled by a voice coil maintained under feedback with a PID circuit. A commercial inverted microscope, with an objective mounted on a piezo focus scanner, allows tracking the vertical position of micron-sized beads. (B) Photograph of the instrument using permanent magnets, with labelling of some of its components. (C) Schematics of the magnetic tweezers instrument using the magnetic tape head configuration. The tape head is placed on top of the fluid chamber at a fixed distance of 300 µm and the magnetic field is applied by controlling the electric current supplied to the tape head using a PID circuit. The custom-made inverted microscope follows a similar arrangement as that used for the permanent magnet configuration. (D) Photograph of the magnetic tweezers instrument based on tape head configuration.

Figure 3. Image analysis algorithm

(A) 60x image focusing on the bottom part of the fluid chamber displaying reference (smaller) and superparamagnetic (slightly bigger and brighter) beads (beads inside the blue and green square respectively). (B) The Fast Fourier Transformer (FFT) of the Region Of Interest (ROI) for the superparamagnetic and reference beads is calculated to integrate the pixel intensity at constant radial positions (green and blue lines), allowing (C) the calculation of the radial profiles, which are (D) correlated with a z-stack look-up library to obtain the bead height Δz (molecular extension) as the difference in position of the Gaussian fits (red dotted lines) to the correlation profiles.

Figure 4. Step-size-based calibration of magnetic tweezers

(A) A protein-L octamer is used as a molecular construct to derive a calibration law by correlating the sizes of the unfolding events with force. (B) Typical magnetic tweezers recording showing the dynamics of the protein L octamer under force. Upon a first high-force pulse (F = 40 pN—which corresponds to a magnet position of 1.5 mm in the voice-coil configuration (blue) or an electric current of 932 mA on the tape head setup (red)-, the eight protein domains readily unfold sequentially, showing a step-wise increase in the protein’s extension (stars). Subsequently, the force is lowered down to 8 pN (3.4 mm of magnet position (voice-coil) or 371 mA of electric current (tape head)), triggering the protein to refold, marked by a step-wise decrease in its extension (red arrow). Occasionally, a few unfolding events (blue arrow) are detected due to the competing unfolding and refolding kinetics at this force. The step-sizes scale with the applied force (~14.5 nm at 40 pN, and ~8.5 nm at 8 pN, insets) following polymer physics models of polymer elasticity such as the freely-jointed chain (FJC) model. The trace was smoothed with a 101-point 4th-order Savitzky-Golay algorithm. (C) Step sizes of protein L as a function of the magnet position for the voice coil configuration. Data from n=565 step sizes measured on N>3 molecules. Error bars are SD. (D) Calibration law for the voice coil configuration using a pair of N52 magnets, providing the applied force as a function of the magnet position relationship. (E) Step sizes of protein L as a function of the electric current measured with the tape head configuration. Data from n=1,563 step sizes measured on N>3 molecules. Error bars are SD. (F) Resulting calibration force law for the tape head configuration, relating the applied force with the electric current.

Figure 5. Protein construct designs and click-chemistry strategies.

(A) Schematics of the modified pFN18A expression plasmid used to engineer proteins to be stretched in magnetic tweezers experiments involving an N-terminal HaloTag and a C-terminal AviTag anchoring. Between the four Ig32 domains (stiff molecular handles), the BspEI and NheI restriction sites used to routinely insert the protein(s) of interest. The HisTag is added for purification purposes. (B) Schematics of the resulting protein construct, here, using a talin R3^IVVI monomer as the protein of interest (PoI), immobilized between a streptavidin-coated superparamagnetic bead and a functionalized cover slide. Inset i. shows the non-covalent interaction between the C-terminal AviTag and streptavidin from the superparamagnetic bead. Inset ii. shows the covalent attachment between the N-terminal HaloTag and the HaloTag Amine (O4) Ligand. (C) Schematics of the pFN18A expression plasmid used to engineer those proteins requiring an N-terminal HaloTag and a C-terminal SpyCatcher. Between the two inextensible Spy0128 domains (stiffer molecular handles), the BspEI and NheI restriction sites enable insertion of the protein of interest. (D) Schematics of the resulting protein construct, here using a protein L monomer as the PoI. The protein construct is covalently immobilized to the glass cover slide using the N-terminal HaloTag. The C-terminal SpyCatcher covalently binds to the SpyTag, attached to the functionalized amine superparamagnetic bead. The inset shows the intermolecular isopetide bond enabling the covalent click-chemistry reactivity between the SpyCatcher and the SpyTag. Plasmid sequences have been uploaded to Addgene (pFN18A-HaloTag-Biotin: Addgene plasmid #206039; pFN18A-HaloTag-SpyCatcher Addgene plasmid #206041).

Figure 6. Fluid chamber configuration and assembly.

(A) Photograph of a fluid chamber employed in our magnetic tweezers experiments. (B) Schematics of the assembly of a fluid chamber. (C) Surface chemistry employed in the functionalization of the bottom cover slide with the HaloTag O4 ligand.

Figure 7. Characterization of the mechanical stability of single proteins using the force-ramp mode

(A) Structure of the talin R3 domain (PDB: 2L7A). We use the IVVI mutant as a model protein, owing to its higher mechanical stability. Typical unfolding force-ramp trajectories of R3^IVVI at 1 pN/s, 5 pN/s, and 10 pN/s. The unfolding of R3^IVVI is characterized by a sudden ~20 nm step-wise increase in the protein’s extension. As the pulling rate is increased, the unfolding force shifts to higher values. (B) Distribution of unfolding forces measured at 1 pN/s, 5 pN/s, and 10 pN/s fitted to Eq. 6. Data from N=100 (1 pN/s), N=133 (5 pN/s), and N=95 (10 pN/s) unfolding events using 5 individual molecules. (C) Unfolding force as a function of the pulling rate. Fitting to Eq. 7, we characterise the unfolding nanomechanics of R3^IVVI as k_U⁰=(1.62±0.10)x10^-5 s^-1 and x_U^†=5.33±0.21 nm. (D) Structure of protein L (PDB: 1HZ6) and a typical protein L unfolding trajectories at 1 pN/s, 5 pN/s, and 10 pN/s. The unfolding of protein L is chacterized by a ~15 nm step. (E) Distribution of unfolding forces measured at 1 pN/s, 5 pN/s, and 10 pN/s fitted to Eq. 6. Data from N=211 (1 pN/s), N=192 (5 pN/s), and N=100 (10 pN/s) unfolding events and 6 molecules. (F) Typical unfolding force as a function of the pulling rate, fitted to Eq. 7, allowing us to characterise the unfolding nanomechanics of protein L as k_U⁰=(3.29±0.50)x10^-3 s^-1 and x_U^†=0.22±0.06 nm. All traces were smoothed with a 101-point 4^th-order Savitzky-Golay algorithm. Error bars are SD

Figure 8. Characterization of single protein folding dynamics using the constant force mode.

(A) Typical magnetic tweezers recordings of R3^IVVI pulled at 8 pN, 8.5 pN, and 9 pN. When held at a constant force, R3^IVVI reversibly switches between the folded state (lower extension state) and the unfolded state (higher extension state), hallmarked by a change in length of ~20 nm. As the force increases, the population quickly shifts from the folded to the unfolded state. (inset) Fragment of the 8.5 pN recording, showing the overlaid idealised trace calculated with a step-detection algorithm (thresholding). Measuring the residence times in the folded (t_f) and unfolded state (t_u), allows calculation of the folding and unfolding rates. (B) Folding (red) and unfolding (blue) rates as a function of force. The folding rates decrease exponentially with force, while the unfolding rates increase exponentially, following Bell-Evans model with k_U⁰=(4.61±2.52)x10^-6 s^-1 and x_U^†=4.27±0.34 nm and k_F⁰=(1.84±1.01)x10⁶ s^-1 and x_F^†=6.78±0.59 nm. Data obtained from 12 independent molecules amounting N>10⁵ transitions. (C) Probability of populating the folded state (folded fraction), showing a sigmoidal shape with a coexistence force of ~8.5 pN. (D) Typical magnetic tweezers recordings of protein L at 7 pN, 8 pN, and 9 pN. Similar to R3^IVVI, protein L switches reversibly between the folded and unfolded states, albeit with much slower kinetics and over a broader force range. (inset) Fragment of the 8.5 pN recording, showing the overlaid idealised trace calculated with a step-detection algorithm (thresholding). (E) Folding (red) and unfolding (blue) rates of protein L as a function of force, respectively decreasing (folding) and increasing (unfolding) exponentially with force. In contrast to R3^IVVI, the folding and unfolding rates have very different slopes (different force sensitivity) that hallmark the very different nanomechanical properties of both proteins. From fits to the Bell-Evans model, we obtain k_U⁰=(3.10±0.06)x10^-3 s^-1 and x_U^†=0.30±0.03 nm and k_F⁰=(8.96±0.05)x10³ s^-1 and x_F^†=7.51±0.38 nm. Data obtained from 12 individual molecules and N>10³ transitions. (F) Folded fraction of protein L as a function of force, showing a sigmoidal dependence with a coexistence force of ~8 pN, similar to R3^IVVI but broader, indicating a shallower force dependence. All traces were smoothed with a 101-point 4^th-order Savitzky-Golay algorithm. Error bars are SD.

Figure 9. Measuring long-equilibrium dynamics of individual proteins under force.

12-hour magnetic tweezers recording of talin’s R3^IVVI domain at 8.5 pN (A) and protein L at 8 pN (B). The insets show a detail of the protein’s dynamics. In the case of R3^IVVI, the long-lasting recordings unveil the appearance of rare conformational states, while protein L maintains its two-state folding dynamics. Data smoothed with a 101-point 4^th-order Savitzky-Golay algorithm. No drift correction has been applied.

Figure 10. Fluctuation analysis method to fingerprint protein conformations.

(A) Schematic conceptualization of the fluctuation analysis method. Upon unfolding, a protein becomes an unstructured polypeptide, resulting both in an increase of its end-to-end length and its molecular fluctuations. In a free-energy diagram (upper panel), this is reflected in a transition from a narrow minimum characterizing the folded state (red) to a wider basin representing the unfolded state (blue). If the protein acquires some conformational state composed of a combination of structured (red) and unstructured segments (green), its end-to-end is likely to be large, and only slightly shorter than that of the unfolded state, while its fluctuations would be greatly reduced. Therefore, the end-to-end length and molecular fluctuations can be employed in combination to fingerprint protein conformational states (lower panel). (B) Workflow of the fluctuation analysis method. (i) Raw fragment of a magnetic tweezers recording for R3^IVVI pulled at 8.5 pN and extension histogram indicating the end-to-end length of the folded (z_F) and unfolded (z_U) states. (ii) Analyzed recording highlighting the fragments of the trajectory assigned to the folded (red) and unfolded (blue) states, alongside the transition paths (green) between them. Histograms (right) indicate the average extension of the folded (<z_F>) and unfolded (<z_U>) conformations based on the average extension of each fragment. (iii) Difference in variance for each fragment in the folded (red) and unfolded (blue) states. The difference between the average fluctuations between states is proportional to the change in exposed contour length in each state, following Eq. 11. (C) Fluctuation analysis applied to a rare (low probability) conformational state in R3^IVVI, consisting of three different conformations characterized by end-to-end extensions ranging between those of the folded (F) and unfolded (U) states. Analysis of the molecular fluctuations allows estimation of the fraction of unstructured contour length of each conformation, enabling to propose plausible and compatible protein structures. (D) Fluctuation analysis as a method for detecting cryptic binding events. Upon binding of an interacting protein to the mechanically unfolded and stretched state (here vinculin), the substrate protein (R3^IVVI) undergoes a conformational change triggered by the binding event (indicated by an arrow). This new bound conformation (B) is detectable by a small change in the protein’s end-to-end length (~3 nm) and by a large change in its molecular fluctuations, which are reduced by ~50%. This is suggestive of a conformation where half of the protein’s contour length is trapped by the bound molecule (right).