Single-molecule magnetic tweezers to unravel protein folding dynamics under force

Abstract

Single-molecule magnetic tweezers have recently emerged as a powerful technique for measuring the equilibrium dynamics of individual proteins under force. In magnetic tweezers, a single protein is tethered between a glass coverslip and a superparamagnetic bead, and by applying and controlling a magnetic field, the protein is mechanically stretched while force-induced conformational changes are measured by tracking the vertical position of the bead. The soft trap created by the magnetic field provides intrinsic force-clamp conditions, which makes magnetic tweezers particularly well-suited to measure protein conformational dynamics. Traditionally employed to study DNA due to their initially low spatial and temporal resolutions, magnetic tweezers instrumentation has experienced significant progress in recent years. The development of high-speed cameras, stronger illumination sources, advanced image analysis algorithms, and dedicated chemical functionalization strategies, now allow for high-resolution and ultra-stable experiments. Together with their ability to apply and control low forces, magnetic tweezers can capture long-term equilibrium protein folding dynamics, not possible with any other technique. These capabilities have proven particularly valuable in the study of force-sensing protein systems, which often exhibit low mechanical stabilities that are challenging to measure with other techniques. In this review, we will discuss the current status of magnetic tweezers instrumentation for studying protein folding dynamics, focusing on both the instrumental aspects and methodologies to interpret nanomechanical experiments.

Keywords: Magnetic tweezers; Protein folding; Protein nanomechanics; Single-molecule force spectroscopy.

Fig. 1

Schematics of a magnetic tweezers setup and experiment. A Schematics of a typical magnetic tweezers setup, involving an inverted microscope, a piezo-mounted objective lens, and a pair of permanent magnets mounted on a DC motor or voice coil, placed above the fluid chamber. Keeping the magnet position under electronic feedback using a PID circuit ensures accurate position and movement of the magnets. B Schematics of a magnetic tweezers experiment for measuring protein dynamics. A protein construct is anchored between a glass cover slide and the superparamagnetic (measuring) bead. By comparing the relative position of the magnetic and a reference bead attached to the glass, the protein extension is monitored. The magnets are positioned at distances of ~ mm, much larger than the molecular extension, creating a very soft trap that provides passive force clamp conditions. C Workflow of the image analysis algorithm. The beads region of interest (ROI) are imaged with the brightfield microscope (i), and the Fourier transform of the ROIs is calculated (ii). A piezo scan is done at the beginning of the experimen (iii), where the radial profiles for the measuring and reference beads are calculated by integrating the pixel intensity of the FFTs over constant radial positions. In this case, the piezo takes 100 radial profiles spaced by 20 nm. During the experiment, the real-time radial profiles are calculated (iv) and correlated with the z-stack library (v), allowing measurement of the beads’ position as the distance between the peaks of the Gaussian fits (vi)

Fig. 2

Step-size-based calibration of magnetic tweezers. A Schematics of a protein L octamer construct for calibrating magnetic tweezers. B Typical recording of a protein L octamer exploring different forces. The step sizes scale with force following the WLC model of polymer dynamics. C Calibration for a N52 permanent magnet setup using M270 superparamagnetic beads (upper) dependence of the step sizes with the magnet position, fitted to Eq. 4. (Lower) Force law. D Calibration for a tape-head setup using M270 superparamagnetic beads. (Upper) Step size dependence with the electric current, with the tape head placed at a position of 300 µm, fitted to Eq. 5. (Lower) Force law

Fig. 3

Elements of the energy landscape of a protein folding under force. A Schematics of an unfolded protein stretched at different forces. B Free energy landscape of an unstructured polypeptide chain at different forces, using $l_{\text{P}}$ = 0.58 and ${\mathrm{\Delta }L}_{\text{C}}$ = 19 nm. C Schematics of a two-state folded-unfolded transition for a protein. D Proposed free energy landscape for a folding protein, defining the relevant kinetic and energetic parameters. The parameter set here employed is as follows: U₀ = 50 pNnm, a = 1 nm⁻¹, G = 10 pNnm, z₀ = 2 nm, s = 1 nm⁻¹, $l_{\text{P}}$ = 0.58 and ${\mathrm{\Delta }L}_C$ = 19 nm. E Langevin dynamics simulations over the energy landscape shown in D. To mimic experimental recordings, we have added Gaussian noise with a SD = 1.5 nm (similar to the intrinsic noise in magnetic tweezers (Tapia-Rojo et al. 2024a)) and smoothed the recordings with a Savitzky-Golay 4th order algorithm with a box size of 51 points). F Folding (red) and unfolding (blue) rates measured from the Langevin dynamics simulations and fitted to different models. Fitting parameters are discussed in the text. E Folding probability calculated from the Langevin dynamics simulations

Fig. 4

Experimental modes in magnetic tweezers illustrated for a protein L octamer. A Typical recording of a force-ramp experiment, where force is linearly increased (here at 1 pN/s), which triggers the non-equilibrium unfolding of the protein, identified as a step-wise increase in the molecular extension. The force at which the unfolding occurs (F_U) is the experimental output. B Typical force-jump experiment. Starting at 4 pN with the protein folded, the force is increased to 30 pN, which triggers the unfolding of the protein, identified as a step-wise increase in the protein’s extension; subsequently, the force is reduced back to 4 pN, triggering the refolding of the protein which decreases the protein extension in a step-wise manner. The time to unfold (t_U) and to refold (t_F) are the experimental outputs. C Typical trajectories of protein L at different constant forces. Analysis of the dwell times in the folded (t_U) and unfolded states (t_F) allows for calculation of the unfolding and folding rates, respectively. D Histogram of unfolding forces as measured from force ramps at a pulling rate of a = 1 pN/s, fitted to Eq. 16, yielding $k_U^0=3.3\times {10}^{-3}$ s⁻¹ and $x_U^{†}=0.22$ nm. E Folding (red) and unfolding (blue) rates as measured from force jump and constant force experiments. The unfolding rates were fitted to a Bell model (Eq. 11), giving $k_U^0=2.8\times {10}^{-3}$ s⁻¹ and $x_U^{†}=0.31$ nm, in fair agreement with the force-ramp data. The folding rates were fitted to Eq. 14, giving $k_0=9.1$ s.⁻¹, ΔL_C = 16.5 nm, and l_K = 0.8 nm, in good agreement with the expected values of protein L using the FJC model. F Folding probability calculated using Eq. 15. The coexistence force for protein L is F_0.5 = 8.1 pN. Data adapted from Tapia-Rojo et al. (2024a)