Magnetic Tape Head Tweezers for Novel Protein Nanomechanics Applications

Abstract

Over the past few decades, magnetic tape heads have been perfected to allow for the application of strong magnetic fields that can be modulated at very high frequencies, meeting the technological demands of high-density magnetic recording. Hence, exploring their implementation in modern magnetic tweezers force spectroscopy seems like a natural approach. Here, recent developments in magnetic tweezers instrumentation related to the use of magnetic tape heads will be reviewed.

Over the past few decades, magnetic tape heads have been perfected to allow for the application of strong magnetic fields that can be modulated at very high frequencies, meeting the technological demands of high-density magnetic recording. Hence, exploring their implementation in modern magnetic tweezers force spectroscopy seems like a natural approach. Here, recent developments in magnetic tweezers instrumentation related to the use of magnetic tape heads will be reviewed. Classic magnetic tweezers technology typically employs a pair of permanent magnets to apply pulling forces on tethered molecules, and force changes require to physically displace the magnets, a slow and often inaccurate process. By controlling force through the electric current supplied to the tape head, novel magnetic tweezers designs overcome this limitation, enabling swift force changes and opening new avenues to explore protein nanomechanics under rapidly changing forces. To illustrate the potential of this instrumental approach, two practical examples, respectively studying protein folding over short timescales and under complex force signals, will be discussed.

1 Introduction

Mechanical forces are a key player across all biological scales. At the macroscopic scale, our bodies are entirely accustomed to responding to mechanical forces—walking, lifting a weight, or playing sports. Similarly, mechanical forces play a fundamental role at smaller biological scales, including tissues, cells, and even single molecules [1]. Common physiological processes such as muscle contraction, tissue integrity, or cell motility are finely regulated by mechanical forces. At the molecular level, many of these processes are underpinned by force-bearing proteins, with the ability to detect and respond to mechanical cues to trigger signaling pathways that eventually result in the modulation of mechanosensitive gene-expression programs [1, 2]. In this sense, understanding the molecular underpinnings of such force-sensing processes requires measuring the nanomechanical response of the key protein players. While classical biochemical assays have provided a wealth of knowledge about protein function, unfortunately, they are of little help here simply due to their inability to apply forces to a collection of proteins in the bulk.

In this context, single-molecule force spectroscopy techniques enable us to subject individual proteins to pN-level forces and measure their force-dependent conformational dynamics, which underpin, in many cases, their function [3, 4]. In a nutshell, force spectroscopy techniques—namely atomic force microscopy (AFM), optical tweezers, and magnetic tweezers—are based on the same concept: anchoring an individual molecule between its termini to apply a stretching force while monitoring its dynamics in terms of end-to-end length changes. For the study of protein nanomechanics, AFM and optical tweezers have traditionally been the techniques of choice [5], while magnetic tweezers have been mostly devoted to studying nucleic acids [6]. This likely owes to the low temporal and spatial resolution of the early magnetic tweezers designs, sufficient to capture the dynamics of the very stiff and long DNA molecules, in contrast to the more subtle nanomechanical behavior of most proteins. However, recent instrumental advances and the development of novel chemical strategies for protein anchoring are now demonstrating the expediency of magnetic tweezers for measuring protein nanomechanics [7,8,9,10].

Magnetic tweezers offer some natural advantages for studying protein dynamics under force. First, it is an intrinsically very stable technique, which has recently achieved very long measurements of protein dynamics over several hours or even days, hence allowing us to monitor single proteins over physiologically relevant timescales [7, 8, 10, 11]. Additionally, and in contrast to AFM and optical tweezers that generate force by displacing a force-probe, magnetic tweezers offer intrinsic force clamp conditions due to the very soft trap created by the magnetic field (typically ~ 10^–6 pN/nm). This affords direct control of the intrinsic variable (force) while the extensive variable (molecular extension) is measured, hence providing the natural statistical ensemble to measure protein dynamics in equilibrium. However, despite these advantages, being able to apply calibrated forces and, more specifically, to accurately and quickly change them has been a classical limitation in magnetic tweezers instrumentation. In its most typical configuration, magnetic tweezers use a pair of permanent magnets placed on top of the fluid chamber containing the proteins tethered to superparamagnetic beads. While this simple strategy excels at applying constant forces (provided that the magnets are accurately positioned without any vertical drift), changing the force involves a physical displacement of the magnets, an intrinsically slow process that greatly limits how fast force can be modulated. This technical caveat prevents, for example, capturing early protein folding events that can occur shortly after fast force quenches or studying protein dynamics under complex force protocols, limiting the scientific scope of this technique.

This chapter will review recent advances in magnetic tweezers instrumentation focused on implementing a magnetic tape head as the force-generating apparatus. This technical development provides accurate control of the pulling force, which can now be changed very rapidly (~10 kHz), granting access to previously inaccessible force protocols for studying protein nanomechanics. The chapter starts with a brief instrumental revision, stressing the calibration problem and how this is addressed when using the magnetic tape head. Finally, two practical applications that take advantage of the tape head’s features are presented, both highlighting the potential of this technique to undercover new properties in the response of individual proteins to force.

2 Magnetic Tape Head Tweezers—Instrumental Description and Calibration

2.1 Implementation of a Tape Head in a Single-Molecule Magnetic Tweezers Design

In magnetic tweezers, magnetic fields are used to apply forces of a few piconewtons (pN) to individual molecules tethered to micron-sized superparamagnetic beads. By tracking the vertical position of the bead (typically recording its interference or diffraction ring patterns), the molecular extension is measured, which allows for studying single-molecule dynamics under constant-force conditions [6, 8].

In most instrumental designs, the magnetic field is applied using a pair of permanent magnets placed on top of the fluid chamber, which directly exposes the magnetic beads to a constant force. By vertically displacing the magnets using a motor or a voice coil, the force is changed. The accessible range of forces depends on the magnets’ (geometry, material, etc.) and the bead’s properties (diameter, maximum magnetization, composition, etc.) While forces of several pN can be reached with some magnets-bead combinations [8, 12], magnetic tweezers are naturally suited to accurately manipulate low forces (<15 pN), in contrast to other techniques like AFM. This makes magnetic tweezers particularly appropriate for studying nucleic acids (typically very stiff molecules, which implies that most relevant conformational changes occur at very low forces) or proteins with low mechanical stability.

Recently, we introduced a new instrumental magnetic tweezers design, which implements a magnetic tape head as the force-generating apparatus [7, 10]. Magnetic tape heads have been developed and employed for decades in the perhaps now obsolete field of magnetic head recording [13]. Magnetic recording requires the application of intense magnetic field pulses at very high rates, essential for achieving high-density recording. This technological necessity pushed the industry to develop tape head devices with the ability to change the magnetic field very rapidly and with minimal thermal dissipation. In our context, this capability is particularly convenient as it overcomes one of the intrinsic limitations of magnetic tweezers: changing the force at high rates. Since most magnetic tweezers instruments use permanent magnets, force changes require physically displacing them, a generally slow process, taking up to ~ 100 ms in the best-case scenario. Due to this limitation, fast molecular events can be lost during the force change, where the force is ill-defined. Additionally, this limitation has restricted the set of applicable force protocols to either constant force pulses or slowly changing force ramps, limiting our understanding of how proteins can respond to more complex force signals.

A magnetic tape head is simply an electromagnet consisting of a toroidal core of magnetic material with large permeability, split by a narrow gap (generally containing a diamagnetic material) over which a strong magnetic is generated when applying electric current to the coil tightly wrapped around the tape head’s core [13]. In our instrumental design, we implemented a commercial magnetic tape head (Brush Industries, 9022836), which we selected to achieve forces comparable to those reached with the permanent magnets approach [8]. Among other commercially available tape heads, this specific model has a high maximum gap field (0.5 T) and strong gradient owing to its narrow gap (25 µm) that makes it suitable for our application, providing a working force range between 0 and 44 pN when applying electric currents between 0 and 1000 mA, above which the tape head saturates. To control the magnetic field at high rates, we connect the tape head to a custom-designed current-clamp PID circuit that maintains under feedback a high-precision 2 Ω resistor connected in series with the tape head (Fig. 12.1a). Our interest is being able to manipulate the magnetic field (force) only by controlling the electric current; hence, it is critical to position the tape head accurately at a fixed position over the fluid chamber. In particular, the magnetic field changes in the vertical coordinate over a length scale defined by the head’s gap width (25 µm in our case), which requires positioning the tape head with micron accuracy. To this aim, we designed a mounting piece manufactured using high-precision CNC [10] (Fig. 12.1b). When mounted in this piece, the tape head is positioned 450 µm away from the bottom surface (this is, 300 µm away from the magnetic beads when using standard 150 µm-thick bottom glasses to assemble the fluid chambers), which allows the accurate application of mechanical forces between 0 and ~ 44 pN only by controlling the electric current. By assembling the mounting piece on top of an inverted microscope, the vertical position of the magnetic beads can be tracked using a standard image-analysis algorithm [8], which allows for measuring the molecular extension of single proteins subjected to mechanical forces.

Fig. 12.1

Implementation of a magnetic tape head on a single-molecule magnetic tweezers instrument. a Schematics of the electronics and microscope design. The tape head is connected in series with a high-precision resistor, which is maintained under feedback with a current-clamp PID circuit powered by a 60 W amplifier. With this strategy, the electric current through the tape head is controlled, and, hence, the mechanical force. The tape head is positioned above the fluid chamber, placed on top of an inverted microscope, which allows for measuring the molecular extension. b The tape head is mounted on a high-precision piece fabricated with CNC, which allows positioning it 450 µm away from the bottom surface, hence, 300 µm from the magnetic beads, when using standard #1 bottom glasses. c Schematics of the molecular anchoring. The protein of interest is flanked by two stiff protein domains (typically Ig32, or Spy0128), which serve as molecular anchors. At the N-terminus, a HaloTag allows covalent anchoring of the construct to a glass substrate functionalized with the HaloTag Amine O4 ligand. At the C-terminus, a biotinylated AviTag closes the tether by interacting with streptavidin-coated superparamagnetic beads. The tape head is positioned 300 µm away from the bead/glass substrate, which allows the application of magnetic fields in the ~ mT range, which generate highly-controlled pN-level forces (diagram not at scale, the bead’s diameter is ~ 2.8 µm, while the protein construct extension is ~ 20 nm)

2.2 Anchoring Chemistry

Developing specific and stable chemical anchors is a crucial endeavor in single-molecule force spectroscopy. Over the past few years, there has been significant effort in designing new strategies for tethering protein constructs for magnetic tweezers [8, 9]. Among these, the HaloTag chemistry has been proven to be one of the most effective ones, as it allows for covalent and highly specific anchoring of individual proteins to glass coverslips that can be functionalized following a simple protocol [8, 14]. Tethering the protein construct to the superparamagnetic bead relies on the chemical coating of the commercially available beads. In the simplest and most used approach, the protein construct is capped with a biotinylated AviTag that permits binding to commercially available streptavidin-coated beads. The streptavidin–biotin interaction, albeit not covalent, is strong enough to resist forces of a few pN (< 65 pN) for extended times. However, if higher forces are required, it is possible to use double-covalent anchors by combining HaloTag chemistry with the SpyCatcher-SpyTag protein fusion system [15].

Another aspect to consider, particularly when studying protein monomers, is to develop suitable molecular handles to space the protein interest from the glass surface and bead to avoid spurious non-specific interactions. While DNA handles are often used in many applications, in our approach, we flank the protein of interest between two mechanically stiff protein domains (typically the titin Ig32 domain), which require very high forces to unfold, hence, not interfering with the dynamics of the protein of interest.

2.3 Calibration

An intrinsic challenge in any single-molecule force spectroscopy technique is accurately determining the applied force. In magnetic tweezers, this requires relating the applied magnetic field with the force acting on the bead to which the single protein is tethered. When using permanent magnets, while developing an analytical expression for the magnetic force is possible (see, for example, [16, 17] for discussions in this regard), an empirical exponential dependence is typically employed [8]. Although this approach lacks a rigorous physical basis, it works in practice, at least within the required force precision and range.

For a magnetic tape head, there is a general expression for the magnetic field as a function of the electric current and distance to the tape head’s gap; the so-called Karlqvist approximation predicts the magnetic field as [11, 18, 19]:

$$B_{x} = \frac{{B_{g} }}{\pi }\left[ {\tan^{ - 1} \left( {\frac{{{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2} + x}}{z}} \right) + \tan^{ - 1} \left( {\frac{{{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2} - x}}{z}} \right)} \right]$$

(12.1)

$$B_{z} = \frac{{B_{g} }}{2\pi }ln\frac{{\left( {{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2} + x} \right)^{2} + z^{2} }}{{\left( {{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2} - x} \right)^{2} + z^{2} }},$$

(12.2)

where B is the magnetic field, x is the lateral coordinate and z is the vertical one (we assume symmetry in y), g is the width of the tape head’s gap, and B_g is the gap field, which depends on the properties of the tape head:

$$B_{g} = \mu_{0} \frac{NI}{g}\eta ,$$

(12.3)

being N the number of wire turns around the head core, I the applied intensity, µ₀ = 4π × 10^–7 Tm/A the vacuum permeability, and η the field efficiency, defined by the specific geometry of the tape head. For a given magnetic field $\overrightarrow {B}$, the force acting on a superparamagnetic bead is:

$$\overrightarrow {F} = \left( {\vec{m} \cdot \nabla } \right)\overrightarrow {B}$$

(12.4)

Since, in practice, we cannot neglect an initial magnetization of the bead M₀, the total magnetization of the bead [20]:

$$\overrightarrow {M} = \overrightarrow {{M_{0} }} + \frac{{\chi_{b} }}{\rho }\frac{{\overrightarrow {B} }}{{\mu_{0} }},$$

(12.5)

where ρ is the density of the bead and χ_b its initial susceptibility. Thus, the magnetic force acting on the bead:

$$\overrightarrow {F} = \rho V\left( {\overrightarrow {{M_{0} }} \cdot \nabla } \right)\overrightarrow {B} + \frac{{V\chi_{b} }}{{\mu_{0} }}\left( {\overrightarrow {B} \cdot \nabla } \right)\overrightarrow {B} ,$$

(12.6)

being V the bead’s volume. When working right under the tape head’s gap, there is no lateral component of the field gradient, so the only force component will be in z (pulling force), which is the desired experimental situation. Here, we can write the pulling force as a function of the distance z and the electric current I [7]:

$$F\left( {z,I} \right) = AI^{2} \tan^{ - 1} \left( {\frac{{{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2}}}{z}} \right)\frac{1}{{1 + \left( {\frac{z}{{{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2}}}} \right)^{2} }} + BI\frac{1}{{1 + \left( {\frac{z}{{{g \mathord{\left/ {\vphantom {g 2}} \right. \kern-0pt} 2}}}} \right)^{2} }} ,$$

(12.7)

where A and B are coefficients that depend on the bead’s and head’s properties, namely:

$$A = 8V\chi_{b} \mu_{0} \frac{{N^{2} }}{{g^{3} }}\frac{{\eta^{2} }}{{\pi^{2} }}$$

$$B = 4\rho \mu_{0} \frac{N}{{g^{2} }}\frac{\eta }{\pi }M_{0x}$$

Therefore, provided we know g, we can leave A and B as free parameters to determine our force calibration curve (they are difficult to calculate as they depend on magnitudes such as η, which are hard to estimate). To determine A and B, we need some molecular quantity whose force dependence is well-described and easily measurable. In our case, we employ the force-dependent extension changes of a folding/unfolding protein (step sizes) as a molecular ruler to relate force with the magnetic field [8].

When a protein unfolds under force, it becomes an unstructured polypeptide that quickly equilibrates to an average extension (<x > ) that depends on the pulling force (F) following standard polymer physics models, such as the freely-jointed chain (FJC) model [7, 8, 21]:

$$\textless x\textgreater\left( F \right) = \Delta L_{C} \left[ {coth\left( {\frac{{Fl_{K} }}{kT}} \right) - \frac{kT}{{Fl_{K} }}} \right],$$

(12.8)

where kT = 4.11 pN nm is the thermal energy, ΔL_C the change in contour length (total extension of the unfolded protein minus the size of the folded structure), and l_K the Kuhn length (related to the protein stiffness, for an unfolded protein l_K = 1.1 nm). Hence, < x > (F) provides a good observable, which is simple to measure experimentally, and that, from its force dependence, allows calibrating by determining the parameters A and B. If we position the tape head at a fixed distance, in our case z = 300 µm, simply by measuring the average step sizes < x > as a function of the applied electric current I, we can determine the calibrating parameters A and B.

We used a protein L octamer construct (eight identical repeats of the bacterial protein L protein arranged in tandem) as a molecular ruler [7] (Fig. 12.2a). Protein L is a standard protein folding model that exhibits a clear folding/unfolding signature over a broad range of forces, providing a robust molecular observable to determine the calibration parameters A and B. Based on previous studies, the elastic properties of protein L have been accurately described by the FJC model with ΔL_C = 16.3 nm and l_K = 1.1 nm [22].

Fig. 12.2

Calibration Strategy for Single-Protein Magnetic Tweezers. a Schematics of a protein L octamer construct for magnetic tweezers. b Representative magnetic tweezers recording of a protein L octamer. A high current (force) pulse, unfolds the full polyprotein, showing eight discrete steps associated with the extension of each protein L domain (stars). A subsequent lower current (force) pulse reveals the reversible folding/unfolding dynamics as downwards (red arrow) and upwards (blue arrow) steps. The step sizes scale with force following the freely-jointed chain model, which allows us to associate electric current with the pulling force. c Step sizes of protein L as a function of the applied current. Error bars are the standard deviation. The dotted line is the fit to Eq. (12.8), which provides the calibration parameters A and B. d Force law as derived from c. Using the M270 beads and positioning the tape head at 300 µm from the surfaces enables the application of forces between 0 and 44 pN

Figure 12.2b shows a typical recording of a protein L octamer using magnetic tweezers. First, we applied a high electric current pulse of 932 mA, which readily unfolds the eight domains, appearing as discrete ~ 14.5 nm steps that increase the protein extension. We then lowered the current (force) to 371 mA, and the extended polypeptide collapsed under force, to then show stochastic folding/unfolding dynamics of its domains, appearing as downward (red arrow, folding) and upward (blue arrow, unfolding) steps, with a change in extension of ~ 8.5 nm. With this procedure, we explored different values of I and measured the step sizes of protein L to relate them with the pulling force, given its well-known molecular properties. Figure 12.2c shows the step sizes of protein L as a function of the applied electric current I fitted to Eq. 12.9, which provides the calibration parameters: A = (2.952 ± 0.853) × 10⁻⁵pN/mA² and B = 0.016 ± 0.005 pN/mA. These parameters define our current law that allows us to calculate the pulling force as a function of the applied current (Fig. 12.2d), provided that the tape head is fixed at a position of z = 300 µm. A more general calibration, probing different tape head positions z was described in Ref. [7].

The values of A and B depend on the specific magnetic tape head model and the beads’ properties (here, Dynabeads M270); therefore, the parameters discussed here are specific to our configuration. Using tape heads with stronger gap fields or bigger beads would allow for a broader range of forces. For instance, the commercially available M450 beads have also been proved in our experimental system, allowing us to reach forces up to ~ 240 pN [12].

3 Applications

Here, two practical examples highlighting the application of our tape head-based magnetic tweezers approach will be discussed.

3.1 Dissecting the Folding Pathway of a Single Protein on the Millisecond Timescale

The protein folding problem—this is, how an unfolded protein statistically samples its very large conformational space to find the unique native folded state—remains a key question in biophysics, which still attracts significant experimental and computational efforts [23, 24]. When folding, it is now generally accepted that the unfolded polypeptide will traverse a progressively narrower conformational space (in the entropic sense) that will eventually lead to the unique native folded state that minimizes the protein’s free under the given folding conditions. This is known as the now-classic funnel vision of protein folding [22, 25]. In this context, the first stage in the folding pathway is assumed to be an entropy-driven hydrophobic collapse of the polypeptide, where all the non-polar side chains clump together away from the polar solvent. This still immature protein structure is generally known as the molten globule state [26]. From the molten globule state, the protein conformation eventually evolves to establish the specific and unique interactions that define the native structure—such as hydrogen bond networks, salt bridges, etc.

Although this vision of protein folding agrees with statistical mechanics and computational models and simulations, it has been challenging to demonstrate it from an experimental perspective. In biochemical bulk studies, the diversity of folding reactions in an ensemble of folding proteins is averaged out, typically rendering the classic two-state picture of protein folding. On the other hand, while force spectroscopy studies enable direct observation of the folding pathway of an individual protein, the collapse transition to the molten globule is typically very fast, being invisible to most experimental techniques. Previously, an on-pathway molten-globule state in the RNase H protein was captured using optical tweezers [27]; however, this mechanically labile state was strikingly long-lived (~seconds), allowing its direct visualization. Over the past few years, instrumental developments have allowed a higher-resolution inspection of folding proteins. The development of high-speed force-clamp AFM enabled the detection of an ensemble of mechanically weak states in folding ubiquitin polyproteins that preceded the native folded state [28]; however, the AFM has limitations in the low-force range, which prevents precisely ascertaining the folding forces and thus, to directly monitor the folding reaction.

The implementation of the magnetic tape head overcomes many of these limitations by now allowing us to carry out swift force changes in the microsecond timescale and thus to finely sample the folding pathway of an individual protein. Here, we used protein L as a classic protein folding model, widely reported to fold in an uncomplicated two-state fashion [22, 29]. In these experiments [7], we designed a force pulse protocol to allow a protein L octamer to fold at a very low force during a precisely controlled time Δt and then interrupted this reaction with a higher force pulse to interrogate the folding status of the protein. Figure 12.3a illustrates the pulse protocol: We started with an unfolding pulse at 40 pN, which readily unfolds all eight protein L domains, to then decrease the force to 10 pN, which sets the reference extension of the unfolded polyprotein at this force. We then lowered the force to 1 pN to allow folding during a time Δt (here 250 ms) and quickly interrupted the folding pathway with a second 10 pN pulse to probe the folding status of the protein L octamer.

Fig. 12.3

Direct detection of ephemeral molten globule states in the folding pathway of protein L. a Magnetic tweezers recording illustrating the pulse protocol for detecting molten globule states. b Square root histogram showing the unfolding kinetics of protein L at 10 pN after a brief quench pulse at 10 pN. The histogram clearly separates two populations, a set of mechanically labile states that unfold over a timescale of ~ 0.5 s (first peak) and a mechanically stiff set unfolding over ~ 50 s (second peak). c Probability of reaching the molten globule (red), native state (black), or remaining in the unfolded state (blue) as a function of the quench time. The data is well described with a first-order three-state kinetic model that allows extracting the folding rates of protein L. d Schematic description of the folding pathway of protein L. Starting from the unfolded state, the protein rapidly transitions to a mechanically labile molten globule-like state over ~ 0.09 s, followed by an entropy-driven hydrophobic collapse. Over a slower timescale of ~ 0.8 s, the protein forms the enthalpic interactions that define the native state, reaching the folded state

During the probe pulse, we can clearly distinguish between two different kinds of collapsed states by their mechanical stability. Shortly after the force increases to 10 pN, we can observe very rapidly unfolding events on a milliseconds timescale, indicative of mechanically labile protein states (Fig. 12.3a, inset, red arrows); then, over a longer timescale, there is an additional unfolding event that occurs at the expected rate for folded protein L at 10 pN (Fig. 12.3a). We repeated this protocol on several protein L molecules and measured the unfolding times of all events observed during the 10 pN probe pulse. The unfolding times—here plotted with logarithmic binning to facilitate identification of the involved timescales—are distributed as a double exponential, with a short timescale of τ ~ 0.5 s and a longer timescale of τ ~ 50 s (Fig. 12.3b). This mixed population of structures with such different mechanical stabilities indicates the presence of two different protein structures that are attained over the brief 250 ms-long folding pulse, likely a mechanically labile molten-globule-like state and the mechanically stiff folded state of protein L.

To understand the nature of this state, we varied our folding time Δt to sample the folding pathway of protein L. Figure 12.3c shows the probability of finding a protein domain in the unfolded state (no step), molten-globule (fast unfolding), and native (slow unfolding), which dissects the time-evolution of the folding pathway of protein L. Over 10–25 ms, we found only unfolded domains, indicating that over these short times, protein L has simply no time to reach any mechanically stable state. As we increased the quench time to 100–500 ms, we observed a maximal population of molten-globule states, with a small fraction of native states. Finally, when quenching for a few seconds, we only found natively folded proteins. This time evolution in the relative populations of the molten globule/native state suggests that the molten globule is an immature protein state that precedes the transition to the native state, in accord with the idea of a collapsed protein conformation, yet to establish the native contacts. Thus, we can model the folding pathway of protein L as a simple three-state kinetic model:

$$U{\xrightarrow{{r_{{MG}} }}}MG{\xrightarrow{{r_{N} }}}N$$

where r_MG is the kinetic rate to form the molten globule (MG), and r_N is the maturation rate from the molten globule state to the native one (N). By solving this kinetic model, we can work out the probability of reaching the molten globule state (P_MG) or the native state (P_N) as a function of the folding time Δt [7]:

$$P_{U} (t) = e^{{ - r_{MG} t}}$$

$$P_{MG} (t) = \frac{{r_{MG} }}{{r_{MG} - r_{N} }}[ {e^{{ - r_{N} t}} - e^{{r_{MG} t}} }]$$

$$P_{N} (t) = \frac{{r_{MG} }}{{r_{MG} - r_{N} }}\left( {1 - e^{{ - r_{N} t}} } \right) - \frac{{r_{MG} r_{N} }}{{r_{MG} - r_{N} }}te^{{ - r_{MG} t}}$$

Fitting our experimental data to the kinetic model allowed us to extract the rates of formation of the molten globule (r_MG = 10.97 ± 1.42 s⁻¹) and native state (r_N = 1.28 ± 0.24 s⁻¹). With this information, we can model the folding pathway of protein L as a two-step reaction, where the unfolded polypeptide first collapses to a molten-globule-like state over ~ 0.09 s, characterized by a low mechanical stability. From this immature folded state, and over a timescale of ~ 0.8 s, the protein reaches its native folded state (Fig. 12.3d).

3.2 Protein Folding Dynamics Under Complex Force Signals

Most force spectroscopy techniques rely on the application of simple force perturbations, typically force ramps, to test the mechanical stability of the studied protein or constant forces to monitor its equilibrium dynamics. However, mechanical cues inside the cell are unlikely to resemble such simple shapes; the cell environment is naturally noisy, and mechanical signals typically change quickly over time, so the ability to respond to such fast force fluctuations is a crucial capability of many biological systems [30,31,32]. The human auditory system is a formidable example in this context, capable of converting complex vibration patterns into electrophysiological signals with high sensitivity [32, 33]. Even more generally, cells are known to respond to force oscillations exerted by cyclic stretching of their substrate, and such complex stimuli can trigger mechanosignalling pathways to control cellular behavior [31]. Therefore, there exists a natural motivation to understand the response of individual proteins to complex mechanical signals, including mechanical noise and force oscillations.

The implementation of a magnetic tape head in our single-molecule magnetic tweezers unlocks the previous instrumental limitations, allowing us now to generate arbitrarily complex force signals that are directly applied to a tethered protein. To demonstrate our approach, we studied the dynamics of the talin R3 domain harboring the IVVI mutation, which increases its mechanical stability while maintaining its biological function [34, 35]. Talin is a key protein in focal adhesions, where it crosslinks active integrins with the actin filaments, regulating the engagement and maturation of the cell-substrate adhesion. In particular, the talin R3 domain is the weakest of the 13-rod domains and has been shown to regulate the cell’s sensitivity to the substrate stiffness, likely by unfolding at low mechanical forces and recruiting vinculin to focal adhesions [35, 36].

Under constant forces between 8 and 10 pN and over ~ minute timescales, the talin R3^IVVI domain behaves like a classic two-state folder, transitioning stochastically between its folded and unfolded states with well-defined rates [11]. At 9 pN, it populates the folded and unfolded states with equal probability, giving rise to its characteristic “hopping” dynamics (Fig. 12.4a, left). The dwell times in the folded (or unfolded) state are distributed exponentially, as expected for a simple two-state folder that switches between its folded and unfolded states by overcoming a single free energy barrier (Fig. 12.4a, right).

Fig. 12.4

Talin R3^IVVI responds to oscillatory force signals in a finely-tuned way. a (Left) Typical magnetic tweezers recording of R3^IVVI at 9 pN, where it populates the folded and unfolded states with equal probability. (Right) Distribution of dwell times in the open (unfolded) state. R3^IVVI transitions stochastically between the folded and unfolded state, giving rise to exponentially distributed dwell times. b (Left) Dynamics of R3^IVVI under an oscillatory force signal with a frequency of 1 Hz, an average value of 9 pN, and an amplitude of 0.7 pN. The folding and unfolding transitions get synchronized with the force oscillations. (Right) Distribution of dwell times in the unfolded state, which shows Gaussian peaks at 0.5, 1.5, and 2.5 s, arising from the synchronized transitions, and an underlying exponential contribution accounting for the remanent stochastic transitions. c Power spectrum of R3^IVVI folding dynamics under the 1 Hz force signal, indicating a clear resonant peak at the driving frequency. d Resonant fraction of R3^IVVI transitions as a function of the driving frequency for signals with an amplitude of 0.7 pN. Talin’s response is strongly frequency-dependent, and it only detects signals oscillating at ~ 1 Hz, filtering out higher or lower frequencies. e Dependence of talin’s response with the amplitude of the driving signal. Talin is highly sensitive, being able to detect signals as small as 0.3 pN

However, when we subjected R3^IVVI to a force signal of the same average force (9 pN) but oscillating with a small amplitude (0.7 pN) at a frequency of 1 Hz, we observed a dramatic change in R3^IVVI’s dynamics. Under this small oscillation, the folding and unfolding transitions are mostly synchronous with the driving force signal, indicating that talin can detect this low-amplitude force oscillation (Fig. 12.4b, left). This change in behavior is reflected in the distribution of dwell times, now showing Gaussian-like peaks centered at odd multiples of half the driving frequency (0.5, 1.5, 2.5 s), with an underlying exponential contribution, reflecting a remanent stochastic behavior. By fitting the distribution of dwell times to a combination of Gaussian peaks and an exponential function [37], we can characterize the strength of talin’s response to the force oscillations as the relative weight of the Gaussian peaks (entrained transitions) and exponential (stochastic transitions). Furthermore, calculating the power spectrum of talin’s dynamics (removing the elastic contribution of the polypeptide chain, which follows the force oscillations), we observe a clear peak at the driving frequency of 1 Hz, indicative of resonant dynamics (Fig. 12.4c).

Similarly, we explored the dynamics of R3^IVVI over a broad range of frequencies (spanning between 0.1 and 100 Hz) and characterized its response by the fraction of entrained transitions (resonant transitions). Figure 12.4d shows the resonant fraction as a function of the driving frequency for 0.7 pN amplitude signals. The peaked dependence, with an optimal response in the ~ 1 Hz range, reveals that R3^IVVI is exquisitely sensitive to the oscillation frequency of the applied force. Very low frequencies are not detected as the force changes too slowly, and most transitions are stochastic; similarly, very high frequencies are rejected as talin folding/unfolding dynamics cannot follow such rapid force changes. Importantly, the resonant frequency is related to the natural folding/unfolding rates of talin at the coexistence force. As we demonstrated, proteins with lower mechanical stability and faster folding/unfolding rates synchronize their dynamics at higher frequencies of the timescale of the natural transition rates [38]. This behavior suggests that talin operates as a “mechanical bandpass filter,” responding only to a narrow range of frequencies. When increasing the amplitude of the driving signal, we naturally increase talin’s response (Fig. 12.4e); yet, talin is capable of detecting very weak signals of just 0.3 pN of amplitude.

This behavior is reminiscent of the physical phenomenon of stochastic resonance, by which nonlinear systems exhibit an amplified response to a weak input signal thanks to the presence of noise [37]. Stochastic resonance requires three basic ingredients: (1) a bistable system; (2) a weak periodic input; (3) an intrinsic source of noise. All these conditions are fulfilled in our experiment since talin folding dynamics can be well-described as a simple two-state system, we are applying a weak periodic force perturbation, and the thermal bath provides the intrinsic noise source.

Stochastic resonance has been described in a broad range of physical problems, from climate dynamics to quantum systems [37]. Similarly, many biological systems, mainly in the context of mechanoreceptors, have been shown to take advantage of noise as a method of signal detection [39, 40]. Our experiments clearly show that the talin R3 domain, a key protein mechanosensor, detects not only the magnitude of the force perturbation but also its frequency of oscillation, adding a new layer to its previously known force sensing capabilities. While it remains unclear if stochastic resonance is a general phenomenon among force-sensing proteins, our experiments are strongly suggestive that proteins with similar folding properties will be able to respond to force oscillations similarly, being the responsive frequency range selected by their mechanical stability. Therefore, it is enticing to speculate that mechanosensing proteins composed of tandem repeats of different domains with different mechanical stabilities will be responsive to a broad range of mechanical signals, where each domain will detect a specific frequency range, providing a nanomechanical mechanism to Fourier-decompose complex mechanical signals.

4 Conclusion and Outlook

While traditionally devoted to the study of nucleic acids, magnetic tweezers have become, over the past few years, an ideal technique for studying protein nanomechanics. This owes mainly to the development of new anchoring strategies—such as the HaloTag chemistry—and instrumental developments that increased the stability and resolution of initial designs. In this chapter, we have focused on the improvement of the force-application strategy by implementing a magnetic tape head that substitutes the more usual permanent magnet approach. The ability to manipulate force through electric current provides a faster and more stable way of subjecting proteins to force in a highly controlled manner. This is particularly critical for the study of proteins with very low mechanical stability, such as those relevant in mechanotransduction, which are exposed to forces that rarely exceed 10 pN, being thus exquisitely sensitive to meager force changes [41]. Furthermore, the possibility of changing the force very quickly opens the gates to interrogating protein dynamics under novel force protocols, which could potentially undercover new biophysical phenomena, as demonstrated in the case of talin dynamics under force oscillations. An additional advantage of magnetic tweezers not discussed here is its great stability, which permits measuring protein dynamics over very long timescales, up to several hours or even days [10, 11]. Similarly, this opens up the possibility of exploring new questions in protein folding, such as molecular heterogeneity or the effect of damaging posttranslational modifications triggered by protein aging.

Still, there are several directions to further develop magnetic tweezers instrumentation and overcome some of its limitations. A disadvantage of magnetic tweezers compared to optical tweezers or the AFM is its lower temporal resolution, which owes to the slow image acquisition and analysis methods compared to laser-based detection. While current designs reach sampling rates up to 1.5 kHz, the implementation of faster cameras and new computing methods, such as FPGAs, could potentially increase the time resolution to capture µs-timescales. Likewise, the bespoke design of most magnetic tweezers models enables the easy implementation of novel instrumental capabilities, among which the single-molecule fluorescence is likely the most appealing one. Combined fluoresce-magnetic tweezers instruments have been previously demonstrated for the study of protein-DNA interactions [42], where a double-stranded DNA molecule is tethered to the magnetic bead and mechanically stretched while binding fluorescently-labeled proteins are detectable with, for example, TIRF microscopy, allowing to correlate binding reactions with molecular nanomechanics. In this sense, a natural evolution of the current magnetic tape-head implementation is to include fluorescence capabilities for the study of protein–protein interactions under force.