Single Molecule Force Spectroscopy to Probe Intermediates and Energetics of Membrane Protein Folding

Abstract

Beyond structure, understanding membrane-protein folding and dynamics requires precise dissection of interaction energetics and mechanistic insight into the in-vivo folding process. Over the past 25 years, single-molecule force spectroscopy (SMFS) measurements, in which individual membrane proteins are probed by application of mechanical force, have emerged as a new way of probing these aspects of membrane proteins. The field has advanced both by focusing attention on increasingly biologically realistic (or increasingly ingeniously experimentally contrived) systems and by expanding the technical capabilities of single-molecule manipulation experiments. This review explores key developments along both lines. It begins with a discussion of SMFS experimental principles as applied to membrane proteins and how assay-design and instrumentation advances have enabled higher quality and novel measurements. The review then explores how these advances have led to—and will continue to enable—progress in understanding key questions in membrane-protein folding: the formation of folded structures, the adoption of topology, the individual contributions to thermodynamic stability, and the interactions between proteins.

Graphical Abstract

1. INTRODUCTION

Membrane proteins are essential to metabolism, transport, and signaling but are incompletely understood at the biophysical level. A desire to understand, predict, and modulate these functions motivates the study of membrane-protein folding. Beyond recent advances in experimental and computational structure determination,^1–4 investigators still seek to probe the mechanisms of folding, the conformational flexibility around the equilibrium structure, and the underlying energetics driving the process. In membrane proteins, these energetics arise from interactions with water, the lipid bilayer, the water/bilayer interfacial region, and also with other proteins.⁵ Deeper quantitative understanding of membrane-protein folding could answer key biological questions, including how to predict folded structures at levels relevant to catalysis and protein-protein interactions, to understand the mechanisms of membrane-protein topology formation and functional protein-protein interactions, and to dissect individual contributions to membrane-protein thermodynamic stability.

Over several decades, single-molecule experiments have proven to be a powerful method for probing biological systems. Examples of biophysical experiments with single-molecule resolution include fluorescence spectroscopy, scanning-probe and superresolution imaging, and force-application studies. All share a common strength when compared to traditional bulk experiments: rather than measuring average properties across an ensemble of molecules, they build up a full distribution of a given property by probing one molecule at a time. In this way, single-molecule experiments are sensitive to molecular heterogeneity.^6–8 Additionally, the specific implementation of a given single-molecule method can enable measurements that are not accessible by other methods.

In single-molecule force spectroscopy (SMFS) studies, mechanical force is applied to a specific site on a membrane protein in a native or synthetic bilayer or nanodisc.^{9, 10} As the force is increased, the folded state is destabilized and the membrane protein eventually unfolds, often via a series of partially unfolded intermediates. These intermediates represent particularly stable configurations of the protein and the magnitude of the force needed to unfold them is related to the degree of their stability. In cases where suitable thermodynamic arguments can be applied (see Sec. 2), these measurements are able to report on the free-energy landscape governing folding, including the relative stabilities of states and the positions and heights of activation barriers between states.¹¹ Measurements performed under perturbed conditions—such as in the presence of mutations, ligands, or chaperones—can probe how these intermediates and energetics are modulated by biologically significant factors.

SMFS studies differ fundamentally from—and overcome many limitations of—the chemical-denaturation experiments historically used to probe membrane-protein folding. In chemical-denaturation experiments, a membrane protein in a mixed detergent micelle is titrated with a denaturant such as sodium dodecyl sulfate (SDS) or urea.¹² These denaturants stabilize the unfolded structure of the protein and thus act globally to drive unfolding. Analysis of reversible two-state equilibrium unfolding curves, or of kinetic data,¹³ yields the thermodynamic stability of the protein. Measurements of this type represent the core of what is known about the energetics of membrane-protein folding to date, but are subject to several interpretational limitations. Except for $\beta$-barrel membrane proteins¹² (and one $\alpha$-helical example¹⁴), the measurements can only be made in micelles, not in bilayer, thus altering the chemical environment compared to the biologically relevant condition. There is a significant extrapolation involved in determining zero-denaturant energetics from unfolding at SDS mole fractions ≥ 0.5. Steric-trapping measurements have shown this extrapolation to introduce significant bias.¹⁵ Additionally, the energetic differences measured between folded and unfolded states are made ambiguous by the identity of the unfolded denatured state, which circular dichroism and electron paramagnetic resonance measurements have shown retains some, but not all, of its secondary structure.^16–18 Most profoundly, however, the requirement that the protein exhibit globally reversible refolding has limited this approach to certain model systems such as bacteriorhodopsin (bR),^19–26 lactose permease,²⁷ bacterial leucine transporter,¹⁴ diacylglycerol kinase,²⁸ and several $\beta$-barrel membrane proteins.^29–34 For example, no condition has been found under which any G-protein coupled receptor (GPCR) will reversibly refold in chemical denaturant.³⁵ This motivates the development of other methods, including the SMFS approaches reviewed here. SMFS studies can be performed in native or controlled bilayer, have a well-defined (mechanically stretched) unfolded state, and can probe the more-accessible reversible unfolding of small segments of the protein.

This review discusses the design and implementation of membrane-protein SMFS studies and how they have been applied to understanding membrane-protein folding. It begins by introducing the types of assays that have been applied to membrane proteins. It then explores assay-design, technology, and instrumentation considerations that can impact the quality of the SMFS data and the ability to probe specific biological questions. After establishing this background, a series of sections review how SMFS has been applied to understand key aspects of membrane protein folding, beginning with the seminal bacteriorhodopsin unfolding study of Oesterhelt et al.³⁶ (2000) and advancing through levels of increasing biological and technological sophistication to the present. While touching on a number of biological applications, the review’s primary goal is to illustrate the potential and limitations of SMFS techniques to address yet-unanswered biological and biophysical questions. The review concludes by discussing some of these questions in the context of existing methodologies and further technological improvements.

2. SINGLE MOLECULE FORCE SPECTROSCOPY ASSAYS

In an SMFS experiment, force is applied to the molecule of interest, causing it to stretch and unfold. In membrane-protein studies, both the cantilever of an atomic force microscope (AFM) and the superparamagnetic sphere of a magnetic tweezer (MT) have been used to apply force (Fig. 1A,B).^{36, 37} Both methods monitor the experimental parameters of force (F) and molecular extension (X), which can be plotted as force-extension curves (e.g., Fig. 1C,D). When the protein is fully folded (i.e., low X), the curve represents the elasticity of any unstructured tail or linker. The entropic elasticity of a disordered amino-acid chain is well described by the wormlike chain (WLC) model.³⁸ A sudden jump in the force-extension curve (Fig. 1C,D, asterisks), corresponds to a partial unfolding event; the amino acids liberated by unfolding are added to the disordered tail, increasing X (and, in the case of AFM, lowering F). The WLC model is parameterized in terms of the chain’s persistence length ($l_p\approx 0.4$ nm for amino acid chains)³⁹ and contour length ($L_c$), which increases with the number of amino acids (0.366 nm/amino acid)⁴⁰. Thus, fitting WLC models to curved regions of the force-extension curve (Fig. 1C,D, dashed lines) gives $L_c$ for each intermediate; taking differences between these values reveals the number of amino acids unfolded in each step. The rupture force at which each unfolding event occurs is related to the stability of the structural segment that is unfolding; however, because measurements are not necessarily performed close to equilibrium, it can be challenging to make this relationship quantitative.

FIGURE 1:

Examples of SMFS assays. (A) Most AFM assays unfold the membrane protein orthogonally out of a mica-supported bilayer by movement and deflection of a ~10–100 μm cantilever. X is read out by subtracting the cantilever deflection d from the cantilever height Z; F is obtained by modeling the cantilever as an ideal spring with calibrated spring constant. (B) MT assays generally unfold the bicelle- or liposome-stabilized membrane protein by pulling parallel to the membrane using a ~2.8 μm paramagnetic bead, via linkers. X is the measured bead height; F is set by the magnetic field gradient and does not change during unfolding events. (C,D) Example force-extension curves for the (C) AFM-based unfolding of bacteriorhodopsin⁴¹ and (D) the MT-based unfolding of GlpG.³⁷ In each, dashed lines highlight WLC elastic behavior in particular conformational states and asterisks denote unfolding events. The AFM trace ends with extraction of the protein from the bilayer, whereas the MT data show a cycle of increasing and then decreasing force (arrows). Panel C adapted from Ref. 41, which was published under the CC BY-NC-ND license. Copyright 2021, Jacobson and Perkins. Panel D adapted from Ref. 37. Copyright 2015, Springer Nature.

Historically, AFM has been used in most membrane-protein SMFS studies, although MT instruments have also been used in recent years to enable alternate pulling geometries and longer-duration single-molecule records. In AFM, forces from ~10 pN and up are exerted by bending a ~10–100 μm cantilever. Dynamics on μs timescales can be observed using modern methods and ultrashort cantilevers, although force drift becomes a problem for measurement times longer than ~1–100 s.^42–45 MT instruments, by contrast, are best suited for lower-force, longer-time measurements. They can exert forces in the range of ~0.01–100 pN and are stable for exceedingly long times. For example, Kim et al. have reported single-molecule membrane-protein records lasting 9 hours!⁴⁶ Although both methods are capable of implementing either geometry, most AFM studies of membrane proteins have extracted proteins orthogonally from surface-supported membranes of native or synthetic bilayer (Fig. 1A) and all MT studies have applying force to both termini of proteins in synthetic bicelle or liposome membranes. For proteins with an even number of $\alpha$ helices (e.g., GlpG, Fig. 1B,D), MT assays apply force parallel to the plane of the bilayer, whereas for proteins with an odd number of $\alpha$ helices (e.g., $\beta 2$ adrenergic receptor, $\beta$2AR), MT assays apply force orthogonal to the membrane but, unlike, AFM, from both ends.^{37, 47–49} Pulling direction and rotational freedom can all affect the unfolding pattern of a protein, as explored in comparative studies of membrane-spanning and soluble $\beta$ barrels.⁵⁰ Subtly, but fundamentally, AFM and MT differ in their thermodynamic ensemble (i.e., the constant parameter around which thermal fluctuations occur).⁵¹ In AFM experiments, it is the height of the base of the cantilever that is constant ($Z$ in Fig. 1A), leading a partial unfolding event to result in the concurrent increase in $X$ and decrease in $F$ as the system relaxes (see diagonal transitions in Fig. 1C). By contrast, MT experiments are inherently constant-$F$ because the magnetic field gradient does not appreciably change over experimental length scales, leading a partial unfolding event to result only in a change in $X$ (see horizontal transitions in Fig. 1D).

Other SMFS techniques also exist, although they have seen limited application to membrane-protein folding. Optical tweezers, which trap dielectric particles using focused laser beams and can apply forces in the 0.1–100 pN range,⁹ face practical challenges due to sample heating from the trapping laser beam, which must be separated from the molecule under study in a surface-supported assay by pulling with a long linker in a non-orthogonal direction. However, the feasibility of optical trapping has been demonstrated in recent studies of peripheral membrane proteins or domains using either a two-tether construct with long linkers⁵² or a bilayer-coated silica bead.^{53, 54} Acoustic force spectroscopy, which manipulates particles using standing acoustic waves, is an emerging technique with the promise of high parallelizability.⁵⁵ Lack of exploration of this method for membrane proteins could be due to technical challenges in establishing a standing wave without disrupting a stable, well-controlled membrane environment (e.g., supported bilayer, bicelle, or nanodisc).

Regardless of geometry, both AFM and MT are capable of implementing a variety of force-application protocols that can be interpreted to reveal different information about the underlying folding and thermodynamics. Three major classes of experiment are discussed in the following subsections: (2.1) constant-velocity pulling, which reports on the pathway of mechanical unfolding; (2.2) dynamic force spectroscopy, which reports on the activation barriers separating partially unfolded states; and (2.3) equilibrium measurements, which report on both kinetic barriers and thermodynamics.

2.1. Constant-velocity pulling

In a classic constant-velocity experiment, the control parameter is increased linearly, causing structural segments to sequentially unfold until, ultimately, the protein is extracted from the bilayer. Such studies principally reveal information about the loci of metastable structural intermediates along the unfolding pathway. To obtain this information, regions between unfolding events are fit using WLC models of suitable precision (Fig. 1C) to model the elasticity of the presently unfolded amino-acid chain.^{38, 56, 57} $L_c$ values from these fits can be converted into a number of amino acids unfolded up to that point. For example, in the first SMFS study of bacteriorhodopsin, Oesterhelt et al.³⁶ identified WLC-fit regions corresponding to 88, 148, and 291 unfolded amino acids, allowing them to identify unfolding transitions corresponding to extraction of pairs of alpha helices from the membrane ($\beta$-barrel membrane proteins tend to similarly unfold in pairs of beta strands).⁵⁸ The helix-pair major states in the unfolding of bR are “obligate”, in the sense that they occur in every single-molecule record. Some states, especially short-lived states resolved with the higher time-resolution methods of Section 3.1, are only occupied in a fraction of records. This can be because of the existence of multiple competing unfolding pathways or because the states are sometimes occupied for an undetectably short time.^{40, 59} Additional insight can be gained by performing pulling experiments as a function of other experimental conditions, such as pH, temperature, ligand concentration, or structurally convergent sequence.^{7, 60–68}

In addition to employing higher-resolution methods, partially occupied states can also be more readily identified using non-linear pulling protocols in which retraction of the cantilever away from the surface alternates with approach back towards the surface (Fig. 2B).⁶⁹ This has the effect of cyclically raising and lowering the tension on the protein. Since the probability of force-induced unfolding is expected to scale exponentially with F, a slight decrease in F may cause the protein to remain in a particular intermediate for significantly longer time.

FIGURE 2:

Differing SMFS pulling protocols probe the molecular energy landscape of bacteriorhodopsin in different ways.⁷⁰ (A) Schematic of AFM pulling from a supported lipid bilayer. (B) Once attached to the molecule, the cantilever can be retracted at constant velocity, held at a specific height, or dithered to drive sequential unfolding and refolding. (C) Transitions between states modeled as transitions on a free-energy landscape. Application of force tilts the landscape and promotes occupancy of partially unfolded intermediates. (D-F) Analysis of constant-Z data (D) to obtain the compliance-broadened (E, dashed) or deconvolved (E, solid) energy landscape under tension. (F) Data collected under various tensions can have force effects subtracted to recover the same underlying zero-force landscape. (G,H) Analysis of zigzag data showing many unfolding and refolding transitions (G) yields a transition rate map (H) that reveals the two-state coexistence force $F_{1/2}$ and, in turn, the free energy of folding. Reprinted in part from Ref. 70. Copyright 2020, American Physical Society.

Caution is called for in assigning biological meaning to the unfolding intermediates identified in a constant-velocity SMFS measurement. It is often useful to think of protein folding as occurring on a many-dimensional free-energy landscape in which the dimensions correspond to the degrees of freedom of the system.⁷¹ In this picture, the folded state corresponds to a global minimum of free energy and partially unfolded intermediates to local minima. When F is applied from one point, and X measured along one axis, this many-dimensional landscape is projected onto a single dimension (Fig. 2C).¹¹ The protein may encounter minima in this one-dimensional landscape that it would not encounter when taking a different (perhaps biologically relevant) path through the many-dimensional space. In other words, unfolding intermediates may be artifacts of the pulling geometry (see Sec. 4.1). That being said, membrane proteins do experience mechanical force in the biological context, such as when acted on by molecular motors like p97^{72, 73} or, most generally, in the presence of force exerted by the ribosome during cotranslational folding.⁷⁴

In contrast, the free-energy difference between states measured in an SMFS measurement is directly biologically relevant, since free energy is a path-independent state function. Free energies can be accessed from equilibrium (Fig. 2D–F) or near-equilibrium (Fig. 2G,H) reversible unfolding data by applying thermodynamic arguments and then subtracting the additional work done to bend the cantilever and to stretch the unfolded amino acid chain. These treatments of equilibrium data are discussed in Sec. 2.3.

In principle, it is also possible to obtain equilibrium energetics directly from non-equilibrium constant-velocity pulling data using the Jarzynski equality.⁷⁵ This result from thermodynamics relates a series of non-equilibrium works ($W$) to the underlying free energy of a process ($\Delta G$) via an average of exponentially weighted terms:

$$e^{-\frac{\text{Δ}G}{k_{B}T}}=\langle e^{-\frac{W}{k_{B}T}}\rangle$$ (1)

From a constant-velocity SMFS measurement, $W$ is obtained by integrating the area under the force-extension curve. A challenge in applying the Jarzynski equality (in its various practical forms)^76–78 is that the further the system is from equilibrium, the more data must be averaged to converge to the equilibrium result. Moreover, it is not trivial to figure out how much data is needed.⁷⁹ For unfolding of a small portion of bacteriorhodopsin that is close enough to equilibrium to show reversibility of unfolding and refolding, this method has been shown to agree with other inherently equilibrium approaches.⁷⁰ For unfolding of the entirety of bR, however, it is doubtful that the equilibrium value is truly recovered given that the dissipated work is many times $k_{B}T$.^{76, 79–81}

2.2. Dynamic force spectroscopy

A dynamic force spectroscopy (DFS) experiment measures changes in the distribution of unfolding forces of a given state to draw conclusions about the properties of the activation or transition-state barrier that must be crossed to unfold from that state.¹¹ Such distributions are measured by repeating unfolding experiments like those of Fig. 1C many times and building a histogram of unfolding forces for each unfolding event. The stochastic nature of barrier crossing confers an inherent width to these distributions and causes them to shift as the pulling rate is increased. A DFS plot typically refers to a graph of the distribution of most-probably unfolding force ($F_{\text{mp}}$) as a function of the loading rate of force application ($r=dF/dt$). Such a plot for a bR unfolding experiment is shown in Fig. 3, in which the unfolding forces of two of bR’s helix pairs are seen to vary with the rate of cantilever retraction ($dZ/dt$).⁸² In the high-force limit, this rate is linearly proportional to r, although at lower forces one much account for the WLC elasticity of the amino-acid chair (i.e., for the fact that the force initially increases slowly while the chain is still substantially a random coil).

FIGURE 3.

Dynamic force spectroscopy of bacteriorhodopsin.⁸² (A,B) bR was completely unfolded many times at various pulling speeds. The unfolding of certain regions was attributed, by WLC analysis, to the pairwise unfolding of helices E and D (blue box, arrow), of helices C and B (green box, arrow), or other pathways (not shown). (C) The dependence of the unfolding force on pulling speed (and thus loading rate) was fit with Eq. 3 to obtain properties of the free-energy landscape barrier crossed during unfolding: the distance to the top of the barrier ($\Delta X^{‡}$) and the zero-force unfolding rate ($k_0$). Reprinted from Ref. 82. Copyright 2004, Elsevier Science Ltd.

DFS data are interpreted in terms of models of activated barrier crossing. The simplest such model in the absence of force is the classic Arrhenius equation, $k_0=A{e}^{-\Delta G^{‡}/k_{B}T},$ in which the rate of barrier crossing $k_0$ is given in terms of the height of the barrier $\Delta G^{‡}$ and the attempt frequency A.⁸³ In the one-dimensional energy-landscape picture, applied force tilts the barrier to lower values. In the limit of a sharp barrier, Bell showed that this tilt leads to a new, force-dependent unfolding rate

$$k\left(F\right)=A{e}^{-\left(\Delta G^{‡}-F\Delta X^{‡}\right)/k_{B}T}=k_0{e}^{F\Delta X^{‡}/k_{B}T},$$ (2)

where $\Delta X^{‡}$ is the distance to the barrier along the reaction coordinate X.⁸⁴ Thus a plot of $\text{ln}k$ vs. F gives a straight line with slope equal to $\Delta X^{‡}/k_{B}T$. The y-intercept reports on a combination of A and $\Delta G^{‡}$, which cannot be separately resolved and are often treated as a zero-force rate $k_0$. Building on the Bell model and Kramers rate theory,⁸⁵ Evans and Ritchie derived an expression for the unfolding force histogram from which one can obtain the dependence of $F_{\text{mp}}$ on $r$ and energy-landscape properties:⁸⁶

$$F_{mp}=\frac{k_{B}T}{\Delta X^{‡}}\text{ln}\left(\frac{r\Delta X^{‡}}{k_0{k}_{B}T}\right).$$ (3)

Thus, the DFS plot of $F_{\text{mp}}$ vs. $\text{ln}r$ gives a straight line with slope equal to $k_{B}T/\Delta X^{‡}$ and a y-intercept that again gives information about $k_0.$ Both quantities are reported, for example, in the bR DFS data of Fig. 3. By further considering the shape of the barrier (rather than assuming it to be narrow), Dudko, Hummer, and Szabo derived further equations similar to the above that predict a degree of curvature in the $F_{\text{mp}}$ vs. $\text{ln}r$ plot for sufficiently broad domains of $r$ and that do allow separate determination of $\Delta X^{‡},\Delta G^{‡}$, and $k_0$ when such curvature is visible.⁸⁷

These theories have been applied to membrane-protein DFS data to characterize barriers along the mechanical unfolding pathway.⁸⁸ Such analyses have been performed by Müller and coworkers to yield $\Delta X^{‡}$ and $k_0$ for transitions between partially unfolded intermediates in bacteriorhodopsin,^{82, 89, 90} rhodopsin,^{89, 91–93} $\beta 2$ adrenergic receptor,^94–96 PAR1,^{97, 98} NhaA,⁹⁹ SteT,¹⁰⁰ OmpG,¹⁰¹ BetP,¹⁰² LacY,¹⁰³ Aac3p,¹⁰⁴ and BamA;¹⁰⁵ similar methods were applied by other groups to GlpG^{37, 49} and a de-novo designed protein.¹⁰⁶ The value of $\Delta X^{‡}$ can be interpreted as giving information about the extent to which the protein is ordered in the transition state. Such an analysis, however, is only biologically relevant if the mechanical unfolding/folding pathway mirrors the biological pathway. The biological interpretability of $k_0$ is limited unless it can be separated into $\Delta G^{‡}$ and $A$. This can be partially achieved by application of the Dudko-Hummer-Szabo model, which yields the barrier height if a particular barrier shape is assumed (e.g., linear-cubic or cusp-shaped). This height can be extracted from a fit only in the case where curvature is seen in the plot of $F_{\text{mp}}$ vs $\text{ln}r$; such curvature has not been identified in any membrane-protein SMFS experiment to date. $\Delta G^{‡}$ and $A$ can be trivially separated if a certain value of $A$ is assumed, an approach that has been taken in some works to enable $\Delta G^{‡}$ to be reported. However, this comes at the cost of relying on a value of $A$ from soluble-protein studies that could easily vary by multiple orders of magnitude.^107–111 The spatiotemporal resolution of the SMFS instrument can also impact the interpretation of energy-landscape parameters obtained from DFS: if limited time response causes multiple discrete conformational states to be misidentified as a single state or certain short-lived states to go unobserved, then the properties of the apparent transition-state barriers between these states, and the kinetics of barrier crossing, will not correspond to the underlying molecular landscape.^112–117

2.3. Equilibrium unfolding

It is sometimes possible to observe reversible unfolding and refolding of part of a protein by holding the control parameter fixed and allowing thermal energy to drive transitions between states. An example is the constant-Z bacteriorhodopsin AFM record of Fig. 2D. From such data, it is possible to directly measure the governing energy landscape without employing nonequilibrium thermodynamic theory or assuming a barrier-crossing model.

The most straightforward connection between experimental equilibrium data and the underlying molecular landscape is via inverse Boltzmann analysis. If each value of X corresponds to a certain macrostate of the thermodynamic system, then the probability of finding the molecule at that value of X is given by the Boltzmann distribution: $P_X=\text{exp}\left(-\frac{G_X}{k_{B}T}\right)/\mathbb{Z},$ where $G_X$ is the free energy corresponding to particular X and $\mathbb{Z}$ is the partition function. Inverting this expression gives

$$G_X=-k_{B}T\text{ln}\left(P_X\right)+C,$$ (4)

where the probability $P_X$ is the histogram of equilibrium data and the constant $C$ is common to all values of X and can thus be ignored.¹¹ In other words, taking the natural logarithm of an extension histogram and multiplying by $-k_{B}T$ returns the free-energy landscape of the system under tension. To recover the underlying zero-force landscape of biological interest, one must then subtract out the perturbations to the landscape due to force application. For a constant-force experiment (i.e., MT), this amounts to adding back in the “tilt” $F\cdot X$ (i.e., the opposite of the process illustrated in Fig. 2C). The treatment of AFM data is more complicated, since equilibrium data are taken in the constant-Z ensemble and both X and F vary between states (e.g., Fig. 2D). One strategy is to apply the argument of Eq. 4 to a force histogram ($P_F$) to obtain free energies of states at different forces $G_F$. $\Delta G$ between these states can then be corrected to the zero-force condition by accounting for both the Hooke’s-law elasticity of the cantilever and the work done on the polymer linkers connecting the molecule to the force transducer, as detailed by Yu et al.⁷⁰ Since each state in the constant-Z ensemble corresponds to a unique $L_c$, one can use a WLC model to transform the data into a function of $L_C$, rather than F or X, as in Figs. 2E,F. Linker compliance also blurs the features of the molecular landscape, although recent optical-trapping work shows that this compliance can be reduced by using DNA origami linkers.¹¹⁸ In mathematical terms, the observed landscape is a convolution of the underlying landscape and the linker landscape. In principle, one can recover the underlying landscape by measuring the linker landscape (e.g., from a construct containing linkers but no protein) and then performing a deconvolution,¹¹⁹ as has been demonstrated in nucleic-acid and protein systems (e.g., Figs. 2E and 2F).^{40, 70, 111, 120, 121} However, this is a mathematically ill-posed inverse problem and it can be challenging both to achieve convergence and to independently confirm the result.^{119, 122} Thus, claims to have fully reconstructed the energy landscape of membrane proteins must be approached with caution unless the work has been done with exceptional rigor. In contrast, reports of differences $\Delta G$ between stable minima are more robust.

Equilibrium thermodynamics can also be obtained from non-constant $F$ or $Z$ data that exhibit reversible transitions (e.g., Fig. 2G) using a rate-map analysis. In this analysis, Bell-model plots (Eq. 2) of force-dependent transition rates are made for both unfolding and refolding transitions. Such plots can be generated from non-constant-force data using the method of Zhang and Dudko or related approaches.¹²³ Essentially, from a series of unfolding/refolding trajectories, the transition rate from state i to state j in a given force bin, $k_{ij}\left(F\right)$, is found as the ratio of the number of transition events out of that bin $N_{ij}\left(F\right)$ to the total time spent in that bin in state i, $t_i\left(F\right)$. That is,

$$k_{ij}\left(F\right)=\frac{N_{ij}\left(F\right)}{t_i\left(F\right)}.$$ (5)

The crossing point of Bell-model curves for corresponding unfolding and refolding transitions gives $F_{1/2}$, the coexistence force in the constant-force ensemble (Fig. 2H). This force can be multiplied by the corresponding extension change between states, $\Delta X$, to give the mechanical work done on the system during the reversible transition, which is $\Delta G\left(F_{1/2}\right)$ in the presence of force. The same corrections for work done on the cantilever and the linkers discussed above can then be applied to obtain the zero-force $\Delta \text{G}\left(0\right)$. Dudko et al. also showed that rate maps can be obtained by applying a mathematical transformation to DFS data.¹²⁴

The use of any of the above methods to obtain $\Delta G$ between stable states rests on firm theoretical and empirical ground; measurements of the detailed structure of the transition-state barrier separating stable states are more fraught. Empirical success in obtaining $\Delta G$ was seen in comparison of the rate-map method, the inverse-Boltzmann method, and a method based on the Crooks Fluctuation Theorem (related to the Jarzynski equality, Eq. 1) in bacteriorhodopsin, which showed general agreement.⁷⁰ In terms of the transition barrier, however, a number of assumptions are implicit in the Bell model and related analyses: that the barrier is sharp or has a certain shape, that it has a single peak, that it is smooth, and that it represents the only accessible reaction pathway. Additionally, the projection of a multi-dimensional system onto a one-dimensional landscape can result in an X-dependent diffusion constant or attempt frequency.^{125, 126} That can occur, for example, if more conformations are accessible in the unfolded state than in the folded states. Furthermore, roughness of the landscape on small length scales can affect observed transitions across the barrier. Some theoretical work has explored how otherwise unobservable roughness can be teased out through temperature-dependent experiments, which have been performed for bacteriorhodopsin.^{127, 128} There is future hope in more rigorously characterizing the barrier by analyzing transition paths: single-molecule records confined specifically to the moment of barrier crossing. Such analyses have been performed in nucleic acids and some soluble proteins, but instrument response-time considerations have prevented such measurements, to date, in membrane proteins.^{110, 129–133}

3. ASSAY DESIGN AND INSTRUMENTATION CONSIDERATIONS

Because SMFS experiments indirectly detect conformational changes in the target protein under study through motion of the force transducer, their sensitivity depends on the transducer mechanical properties, on how the molecule is coupled to the transducer, and on how the molecule is coupled to the substrate. Choices made in assay design and improvements in instrumentation can cause the motion of the force transducer to follow the conformational changes of the subject molecule with higher fidelity and thus the resulting observations of folding intermediates, energetics, and kinetics to better reflect the underlying biological reality. This section discusses several key assay-design and instrumentation considerations, how they can be improved, and how these improvements lead to higher-quality membrane-protein SMFS data.

3.1. Spatiotemporal resolution: Noise and time response

The spatiotemporal resolution of an SMFS experiment is set by thermal energy and the viscous drag on the force transducer. Measurements are made in liquid at biologically relevant temperatures, and thus the AFM cantilever or magnetic bead is subject to random, Brownian motion. The equipartition theorem of statistical mechanics sets the average energy of these fluctuations at $k_{B}T/2$ per degree of freedom, and SMFS studies are typically sensitive only to one degree of freedom (i.e., extension along the pulling axis). Thus, if the system has an effective stiffness $k_{\text{eff}}$, which could arise either from the cantilever spring constant ($k_s$) or from polymer elasticity of the unfolded molecule, the corresponding noise in extension from Hooke’s law is $\delta X=\sqrt{k_{B}T/k_{\text{eff}}}$. Thus, a softer system will exhibit more noise in extension. However, in analysis of SMFS data it is often $F$, rather than $X$, on the ordinate axis. By a simple transformation of the $\delta X$ result using Hooke’s law, one finds the force noise:

$$\delta F=\sqrt{k_{\text{eff}}{k}_{B}T}.$$ (6)

Thus, a softer system will exhibit lower force noise. In AFM experiments where $k_s$ can be controlled, it can be lowered to improve resolution of states closely spaced in force. In general, resolution can also be improved by smoothing the data, although this comes at the cost of time resolution. One can represent the degree of smoothing by a frequency bandwidth $\Delta f$, in which case the force noise of the smoothed signal can be written as:⁹

$$\delta F_{\Delta f}=\sqrt{4\beta k_{B}T\Delta f},$$ (7)

where $\beta$ is the hydrodynamic drag.

The noise and time response of the force transducer are characterized by calculating the power spectral density (PSD) of its thermal Brownian motion. The PSD (Fig. 4A) is calculated as the norm squared of the Fourier transform of time-series fluctuation data. The PSD in a given frequency range corresponds to the power of the fluctuations in those frequencies; the integral of the PSD across all frequencies (the total power) corresponds to the expected equipartition result $k_{B}T/2$ and can be used to calibrate $k_s$. Soft AFM cantilevers, and all MT beads, are in the overdamped limit characterized by a frequency-independent PSD up to some corner frequency ($f_c$) beyond which the PSD falls off as $~f^{-2}$ (Fig. 4A, solid line). Thus, the cantilever is responsive to excitation at frequencies below $f_c$ and becomes unresponsive to excitations at frequencies above $f_c$. This critical frequency corresponds to the characteristic response time of the force probe, $\tau \approx f_c^{-1}$. For a damped harmonic oscillator, $f_c=k_{\text{eff}}/2\pi \beta$, which implies that

$$\tau \approx \frac{2\pi \beta }{k_{\text{eff}}}.$$ (8)

Stiff cantilevers are underdamped, show a resonance peak at $f_c$, but still fall off as $~f^{-2}$ at high $f$ (Fig. 4A, dotted line).

FIGURE 4.

(A) Power spectral density (PSD) of a free AFM cantilever or tethered magnetic bead subject to thermal fluctuations in the overdamped (solid black) or underdamped (dotted green) limit. The latter is relevant to AFM experiments with stiff cantilevers. In practice, experimental drift (red) can introduce additional noise at low frequencies. (B,C) Cantilever time response for small displacements can be modeled by treating the molecular linker (green) and cantilever or magnetic field gradient (yellow) as two springs in parallel. (B) In an example AFM measurement (details in main text), the linker is modeled as a WLC and the cantilever by Hooke’s law. The stiffness of the combined system (black line) can be found by fitting a parabola to the local minimum of the energy (inset). The result is in agreement with the expectation that cantilever and linker stiffnesses add. (C) In an example MT measurement, the magnetic field exerts a constant force on the bead, which results in a probe energy that has a constant slope (dashed yellow).

In principle, Equation 8 offers a way to calculate the time response of an SMFS experiment, although there is subtlety in understanding $k_{\text{eff}}$. The drag $\beta$ can be calculated directly from Stokes law ($\beta =6\pi \eta R$, where $\eta$ is the dynamic viscosity of water—0.89 mPa s at 25°C—and $R$ is the bead radius) in the case of MT and indirectly by treating the cantilever as an effective sphere with $R$ equal to half its width in the case of AFM.¹³⁴ The force probe stiffness (e.g., $k_s$ of AFM cantilever of $k_{\text{mag}}$ of MT magnetic force) and WLC elasticity of the molecular linker act as opposing forces that set the probe position. Both the linker and the force probe connect the end of the molecule being measured (Fig. 4B,C, blue circle) to the fixed Earth (Fig. 4B,C, double black lines). The overall stiffness of the system ($k_{\text{eff}}$) therefore adds like springs in parallel: $k_{\text{eff}}=k_{\text{linker}}+k_s$. It is thus dominated by the stiffer component. In MT measurements, the stiffer component will always be the linker, since $k_{\text{mag}}\to 0$ in a constant-force measurement. In the high-force limit, the WLC model of linker elasticity gives^{38, 135}

$$k_{\text{linker}}=\frac{d{F}_{\text{WLC}}}{dx}=\frac{4F}{L_c}\sqrt{\frac{F{l}_p}{k_{B}T}},$$ (9)

where $l_p$ is the persistence length (0.4 nm for amino acids) and $L_c$ is the contour length of the linker. Thus, at low force the overall stiffness of an AFM measurement is dominated by $k_s$ of the cantilever, whereas at high force the molecule approaches $L_c$ and the stiffness mostly derives from the molecule. Because the WLC elasticity is nonlinear, application of Eq. 8 to predict response times is only valid in the limit of small displacements. A solution for large displacements would have to account for the transient force during re-equilibration.

The two SMFS experiments of Fig. 1 can serve as examples to illustrate typical measurement response times, as calculated using Eq. 8. First, consider a traditional AFM-based unfolding experiment performed using an Olympus BL-RC150 cantilever, with $k_s=6$ pN/nm and cross-section dimensions of 100 × 30 μm. The indirect Stokes-law treatment gives $\beta =2.5\times {10}^{-4}$ pN s nm⁻¹ (based on $R=15$ μm). The first major unfolding transition (i.e., second asterisk from left in Fig. 1C) occurs at 275 pN with $L_c=28$ nm. Thus according to Equation 9, $k_{\text{linker}}=203$ pN/nm. Fig. 4B shows the potential energy associated with both the Hooke’s law cantilever and WLC linker as a function of extension. Interestingly, the cantilever is so comparatively soft under these conditions that its energy is nearly the straight line that would be expected for a constant-force measurement. The overall stiffness can be found by fitting a parabola to the sum of these energies in the vicinity of the local minimum corresponding to the equilibrium position (Fig. 4B, dashed blue). The value obtained from that fitting (209 pN/nm) precisely matches the springs-in-parallel expectation ($k_{\text{eff}}=k_s+k_{\text{linker}}$) and corresponds to a time response $\tau =8$ μs. This is in order-of-magnitude faster than the experimental $\tau =105$ μs measured for this cantilever when far from the surface and not attached to a molecule, consistent with substantial stiffening due to pulling on the linker.⁴²

Alternatively, consider a MT study using a bead of $R=1.4$ μm to exert $F=25$ pN to a membrane protein at the end of 348 nm of double-stranded DNA linkers (as in Fig. 1D). Here the drag can be calculated directly from Stokes law ($\beta =2.3\times {10}^{-5}$ pN s nm⁻¹) and $k_{\text{eff}}$ is now dominated by the linker elasticity since the constant magnetic force is equivalent to $k_{\text{mag}}\to 0$. This transition (asterisk of Fig. 1D) occurs from a state with $L_c=348$ nm. Taking $l_p=50$ nm (persistence length of double-stranded DNA, an approximation ignoring the unfolded amino-acid chain), $k_{\text{eff}}=k_{\text{linker}}=5.0$ pN/nm, corresponding to $\tau =29$ μs. Potential energy functions and a parabolic fit, also yielding $k_{\text{eff}}=5.0$ pN/nm, are shown in Fig. 4C. Whereas the lack of any transducer stiffness can lead one to intuitively suppose that MT assays are “floppy” and have poor time resolution, this argument shows that τ in the tens of μs can be achieved for small transitions at relatively high forces. In practice, however, MT instruments rely on video bead tracking and cannot access time resolutions shorter than the reciprocal of the camera frame rate. Typical 60–90 Hz frame rates correspond to 11–17 ms frame times,¹³⁶ but some advanced MT instruments have been implemented with frame rates as high as 10,000 Hz,¹³⁷ corresponding to 100 μs frame times.

In both of these examples, the time response could be improved by using a smaller force probe with lower $\beta$ (as per Eq. 8). In the case of MT, the maximum force that can be applied for a given magnetic field gradient scales with bead volume, so there is a lower limit on bead size that can still supply enough force to unfold the molecule. Thus, the time response of MT measurements is most readily improved by increasing the camera frame rate. By contrast, it is feasible to perform AFM experiments with short ($L\approx 40$ μm) and ultrashort ($L\approx 10$ μm) cantilevers if the detection laser spot size is reduced.⁴³ For example, the Olympus BL-AC10 cantilever has $k_s=100$ pN/nm and $\tau =0.4$ μs. This time response enables detection of events occurring on orders-of-magnitude faster time scales.¹³⁸ However, by the argument of Eq. 6, the higher $k_s=100$ pN/nm leads to greater force noise. To counteract this, Perkins and coworkers have shown that focused-ion-beam (FIB) lithography can be used to make cuts into the cantilever to tune its mechanical properties, lowering $k_s$ (and thus $\delta F$) while maintaining a reasonably low $\tau$.^{42–45, 139} Additionally, they have shown that removing most of the reflective gold coating on the back of the cantilever lowers its drift.¹⁴⁰ For example, modification of an ultrashort BL-AC10 cantilever reduces $k_s$ to about 15 pN/nm, increases $\tau$ to 2 μs, and leads to sub-pN drift up to ~10 s.^{43, 70, 139} Procedures have also been developed to modify other types of cantilevers to trade higher $\tau$ for longer-term drift stability or to utilize as starting materials cantilevers that are presently commercially available (e.g., the short PEAKFORCE-HIRS-F-B, Fig. 5).^{42, 45, 141}

FIGURE 5.

Illustration of FIB lithography steps used to modify a Bruker PEAKFORCE-HIRS-F-B cantilever to reduce its spring constant ~10-fold.¹⁴¹ The unmodified cantilever (A) is first etched with a partial-depth frame (B). A series of cuts (C) are then made to narrow the leg. The side pieces are folded back (D) and the leg is further thinned in elevation (E). Reductions in leg plan width and thickness (elevation) both reduce $k_s$; thinning in elevation also corrects for the bend induced by interaction with the Ga-ion beam of the FIB. Tungsten is deposited in (F) to protect a reflective gold patch when the remaining gold and chromium are later chemically etched; the partial-depth frame of (B) prevents undercutting during this etching. Adapted from Ref. 141, which was published under the CC BY license. Copyright 2025, Hatchell and Jacobson.

The power of optimizing cantilever mechanical properties in membrane-protein SMFS measurements was first demonstrated in the bacteriorhodopsin unfolding studies of Yu et al.⁴⁰ Earlier SMFS studies of bR had observed unfolding primarily in steps corresponding to pairs of $\alpha$ helices, with sometimes a few intermediates within a given helix pair. For example, SMFS studies with conventional cantilevers (Fig. 6A, inset) showed two intermediates in the unfolding of the E/D helix pair.¹⁴² By contrast, the study performed using modified ultrashort cantilevers revealed 13 intermediates in this region (Fig. 6A). Furthermore, the ability to detect occupancies in these states as short as a few μs led to the observation of equilibrium unfolding/refolding transitions between states (Fig. 6B), which were later exploited in energetics measurements using the approaches of Sec. 2.3.

FIGURE 6.

Enhanced resolution of bacteriorhodopsin unfolding enabled by FIB-modified cantilevers. (A) In constant-velocity unfolding at 300 nm/s using modified ultrashort cantilevers, bR was seen to unfold via 13 intermediates, only two of which could be resolved using cantilevers with higher noise and slower time response (inset, top-left). (B) Rapid time response enabled resolution of state occupancies of <10 μs and revealed reversible, refolding transitions amenable to energetic analysis. Reprinted from Ref. 40. Copyright 2017, AAAS.

3.2. Force drift

Whereas spatiotemporal resolution sets the fundamental sensitivity of an SMFS measurements, the drift in force over time limits the amount of interpretable data that can be collected from a single molecule. Unlike thermal noise, which is a fundamental property of any system at non-zero temperature, drift is an instrumental effect that can be reduced or, in theory, eliminated. The deleterious effect of drift can be understood in the context of an equilibrium measurement like Fig. 2D. In that measurement, the cantilever is held at fixed Z, tilting the energy landscape and resulting in transitions between states with rates that are not expected to vary with time. Such data could be analyzed to obtain those rates, the free-energy difference between states, and other quantities as discussed in Sec. 2. However, if the cantilever were actually drifting in position while it is believed to be held fixed, the force-dependent transition rates between states would erroneously appear to be changing with time. A large-enough drift could cause dynamic and energetic quantities to no longer reflect the underlying biological system. For example, in constant-Z equilibrium data with an unfolding distance of 1.5 nm, it would take a force drift of 6 pN to push the system from 50:50 to 90:10 equilibrium.

Drift can be readily quantified by analyzing the Brownian thermal fluctuations of the force transducer in terms of either the PSD or the Allan deviation (AD).¹⁴³ The PSD is a frequency-domain metric in which drift appears as anomalous signal at low frequency (Fig. 4A, red lines). The AD is a time-domain metric in which drift appears as an increase at large time (Fig. 7A). The AD is calculated by taking the standard deviation of time-series data that has been averaged with various bin sizes ($t_{\text{bin}}$). The AD point at the smallest $t_{\text{bin}}$ corresponds to the standard deviation of the raw data. As the data are smoothed with progressively larger $t_{\text{bin}}$, the AD decreases due to averaging out of thermal noise. For a system in which all noise is thermal, the AD would continue to decrease with $t_{\text{bin}}^{-1/2}$.¹⁴⁴ However, the presence of drift will lead to correlated motion on long timescales and an increased AD. For a given $t_{\text{bin}}$, the AD can be thought of as the force precision associated with measurements on that timescale. The performance of an SMFS instrument can be quantified by identifying a range of $t_{\text{bin}}$ over which the drift is below some acceptable value, often taken as 1 pN (Fig. 7A, gray line).⁴² In the aforementioned example of a 1.5-nm opening distance, 1 pN drift would shift the hypothetical two-state equilibrium from 50:50 to 59:41.

FIGURE 7.

Effects of force drift on AFM-based SMFS measurements and data-acquisition protocols enabled by low-drift cantilevers. (A) Allan deviation used to quantify the drift of unmodified and FIB-modified AFM cantilevers.⁴² The increase in AD at large times is due to drift, whereas a system with purely thermal noise would exhibit $~t_{\text{bin}}^{-1/2}$ decay (dashed line). (B) A FIB-modified BL-AC10 cantilever with sub-pN force stability to ~10 s enabled a data-acquisition protocol in which a single photoactive bacteriorhodopsin molecule was subjected to 60 sequential photoexcitation events (green arrows), each occurring during a 200 ms dwell at a particular constant Z (inset within).¹⁴⁵ The change in three-state equilibrium following a light pulse (inset below) can be analyzed to reveal the effect of the light-driven conformational change on intramolecular energetics. Panel A reprinted with permission from Ref. 42. Copyright 2014, American Chemical Society. Panel B adapted from Ref. 145, which was published under the CC BY-NC-ND license. Copyright 2024, Jacobson and Perkins.

While positional drift makes some contribution, the dominant source of drift in AFM-based SMFS studies is the cantilever itself, which exhibits top-bottom asymmetry and is thus prone to thermal and material relaxation on many-minute scales.^{146, 147} The large, soft cantilevers traditionally used in biological SMFS measurements exhibit sub-pN stability to ~1 s (Fig. 7A, magenta).⁴² Churnside et al. showed that this drift performance could be significantly improved by removing the reflective gold and chromium layers from the cantilever.¹⁴⁰ Smaller cantilevers (with faster time response) tend to drift more; for example, the Olympus BL-AC40 ($L=38$ μm) does not exhibit precision much below 1 pN on any timescale (Fig. 7A, gold).⁴² The combination of removing the gold coating and using FIB to modify the cantilever to have lower $k_s$ significantly improves the drift performance, enabling sub-pN drift up to ~100 s (Fig. 7A, green).^{42, 45} Similar modification of ultrashort ($L=9$ μm) cantilevers can achieve sub-pN stability to ~10 s with ~8-fold faster time response.^{43, 139} The latter low-drift, fast-response cantilevers have enabled individual bacteriorhodopsin molecules to be probed in excess of 10 s. Long-duration traces enable more data to be collected from individual molecules. For example, in a study of the effect of photon absorption on the folding energetics of bR (see Sec. 5.3), 60 light pulses could be applied to the same molecule under tension (Fig. 7B).¹⁴⁵

By contrast, the MT force probe is inherently stable against drift since the force-applying magnetic field is generated by permanent magnets and is essentially constant in time. Movement of the flow cell with respect to the objective lens can lead to drift in the measured bead height, but this can be effectively corrected for by simultaneously tracking a reference bead adhered to the surface of the flow cell (Fig. 8A, open vs. solid symbols).¹³⁷ Vertical movement of the flow cell is on length scales (nm) that are small compared to meaningful changes in the magnetic field gradient (μm–mm).¹⁴⁸ Thus, a key strength of MT-based SMFS is the ability to exert constant forces over long periods of time. This can allow thermal noise to be averaged down, enabling measurements at very low forces, or it can allow for many-hours-long data traces that capture rare folding and unfolding events of proteins with slow kinetics. A particularly striking example of this strength is a study of the de-novo-designed membrane protein scTMHC2, in which Kim et al. recorded equilibrium transitions in a single molecule between four conformational states at 12 pN over a span of 9 h (Fig. 8B).⁴⁶ Such a long record provides sufficient sampling of the rare transitions to enable determination of the relative energetics of the states via inverse Boltzmann analysis of the extension histogram (Fig. 8B, right).

FIGURE 8.

MT-based SMFS is capable of hours-long, drift-free measurements. (A) Allan deviation (position units) of vertical motion of a DNA-tethered magnetic bead, based on either the raw trajectory (open symbols) or the trajectory after subtraction of a reference bead attached to the surface (filled symbols).¹³⁷ (B) Nine-hour single-molecule trajectory of de-novo-designed protein scTMHC2 under 12 pN applied force.⁴⁶ Panel A adapted from Ref. 137. Copyright 2013, AIP Publishing LLC. Panel B reprinted from Ref. 46, which was distributed under the CC BY license. Copyright 2023, Kim et al.

3.3. Attachment chemistry

Membrane-protein SMFS studies depend on attachment of the molecule under study to the substrate and force probe. In the classic AFM-based study, the protein is embedded in a surface-supported bilayer adhered to the surface of mica and one end of the protein is attached to the AFM cantilever at its C- or N-terminal tail. In MT experiments, both ends of the protein must be attached by linkers, one to the surface of glass and the other to the magnetic bead. Single-molecule attachment is critical to the interpretability of the resulting data: if the force probe is tethered to the surface via multiple molecules at the same time, the force is divided across the molecules and it is impossible to assign observed unfolding events to specific molecules. Single attachment can be promoted by a sparse surface density of proteins or by partial labeling of dense proteins. Multiple attachments can be identified in experimental data by unusually high observed unfolding forces and by unusual and inconsistent numbers and locations of unfolding intermediates. In MT, one can also check for multiple attachments by rotating the magnetic field (and thus the bead). If there is a single attachment, the bead will rotate freely around the single bonds of the amino-acid backbone; if there is a multiple attachment, the amino acid chains will wind around each other and the bead will move closer to the surface.¹⁴⁹

The first AFM-based SMFS studies of membrane proteins relied upon nonspecific physical adsorption of the tail of the protein to the AFM tip, which has some advantages.^{36, 150} By not relying on chemical functionalization of the cantilever, the tip is not prone to fouling after repeated surface contact. By not relying on chemical labeling of the protein, SMFS can be performed on naturally occurring samples (e.g., studies of rhodopsin obtained from bovine and murine tissue^{92, 93, 151, 152}). By virtue of low attachment rates, multiple attachments can be avoided in protein-dense samples.

However, there are also disadvantages to nonspecific adsorption that have motivated the use of site-specific attachment chemistry. Nonspecific attachment is promoted by high tip-sample contact forces ($\gtrsim 1$ nN) and by the existence of large extramembrane domains. For example, in a study of E. coli lactose permease, Serdiuk et al. appended a 36-amino-acid Gly chain to the native C terminus to improve attachment efficiency.¹⁰³ The nature of the native N and C termini, without modification, will constrain where pickup occurs. In the outer membrane protein OmpA, nonspecific attachment always happens via the large C-terminal domain.¹⁵³ In cases where one end is not obviously preferred, experimental work is needed to identify which end is being pulled from. Nonspecific attachment is also short-lived and weak. Short lifetime prevents acquisition of the kinds of data-rich, long-duration traces shown in Figs. 7B and 8B. Weakness under tension can lead to bias in observed unfolding forces: if the tip-sample attachment is prone to rupture at high force, then the distribution of unfolding forces in molecules that survive the unfolding process will be skewed towards lower $F$. This bias can persist even when advanced data-reduction pipelines are employed.^{154, 155} Finally, variations in the exact locus of nonspecific attachment can lead multiple force-extension curves of a given system to be out of register, especially for the initial unfolding of the first helix. This is seen in comparisons of bR unfolding using site-specific and non-specific attachment chemistry.¹³⁹

The interpretational gains that can be made by adopting site-specific attachment chemistry are illustrated by comparing nonspecific and site-specific studies of bacteriorhodopsin. When bR was unfolded using non-specific adsorption, variation in attachment point led to broad scatter in extension (Fig. 9A, left), surface adhesion induced by 1 nN surface-contact force competed with the actual features of bR unfolding (Fig. 9B, left), and bias towards lower rupture forces led to the erroneous conclusion that the first helix pair unfolds at forces similar to the remaining five helices.^{36, 40, 139} Introduction of an engineered Cys residue at the C terminus of bR, subsequent treatment of the protein with a linker molecule, and azide functionalization of the cantilever via triethoxylsilane-derivatized polyethylene glycol (PEG)^{156, 157} allowed Yu et al. to site-specifically pull on bR using copper-free click chemistry (Fig. 9C).¹³⁹ In this approach, the registration of separate traces varied only by the variation in PEG linker length (although for commercially available PEGs this variation is typical non-negligible), a surface-contact force as low as 100 pN could be used to reduce adhesion, and the covalent chemistry persisted across all force scales relevant to membrane-protein unfolding. These advances allowed interpretation of the unfolding of the first two C-terminal helices (G and F helices), revealing that they are in fact the most mechanically robust of all bR’s helices (250 ± 6 pN rupture force, vs. 121 ± 2 pN for helices E and D) and that they exhibit reversible unfolding and refolding over an eight amino-acid span (Fig. 9D, dotted box) amenable to energetic analysis.^{70, 145} Moreover, the initial unfolding of a membrane protein is, in general, the most interesting to study, since whatever part of the protein unfolds first unfolds in the context of native tertiary interactions with the rest of the structure.⁶⁹

FIGURE 9.

SMFS characterization of bacteriorhodopsin improved by using site-specific attachment chemistry. (A) Early non-specific-attachment study of bR was unable to interpret the unfolding of helices G and F (gray) because force-extension curves were out of register in a heatmap representation. (B) Single high-resolution record of bR unfolding using non-specific attachment shows unreproducible features in helix-G unfolding (gray) due to surface adhesion. (C) Implementation of covalent site-specific attachment from an engineered Cys. (D) High-resolution unfolding using site-specific attachment reveals 8-amino-acid region of near-equilibrium unfolding in helix G (box). Panel A adapted from Ref. 36. Copyright 2000, AAAS. Panels B–D reprinted from Ref. 139. Copyright 2019, Wiley-VCH GmbH.

The click-chemistry approach based on an introduced Cys residue is restricted to proteins without native solvent-exposed cysteines and limits throughput as bound, unfolded proteins crowd the AFM tip; however, many complementary implementations of site-specific attachment have also been used. In early work, Ikai et al. demonstrated covalently crosslinked attachment to random sites in membrane proteins from natural sources.¹⁵⁸ Perkins and coworkers have used the engineered Cys strategy in studies of bR,^{41, 69, 70, 139, 145} Yang et al. have applied the same strategy to diacylglycerol kinase (DGK),¹⁵⁹ and a related approach of gold-thiol linkage was employed in the very first bR SMFS study of Oesterhelt et al.³⁶ MT experiments, where forces are typically lower, have utilized a variety of non-covalent attachments to both the surface and bead, including the biotin-neutravidin and dig-antidig receptor-ligand interactions, as well as the covalent SpyCatcher-SpyTag linkage.^{37, 49, 106, 160, 161} To enable data collection spanning many hours, Kim et al. utilized a combination of SpyCatcher-SpyTag, biotin-traptavidin, and copper-free click chemistry.⁴⁶

Beyond the approaches that have been applied to date, there is an entire toolbox of covalent and non-covalent attachment chemistries in use by the soluble-protein SMFS community that can be imported into membrane-protein studies. Many of these chemistries were reviewed by Yang et al.¹⁶² A number of chemistries center on genetically encoded multiple-amino-acid tags, which are less likely to conflict with the native sequence than is a single Cys. Of particular interest are adhesin tags (e.g., Fg$\beta$, DK) that form strong catch-bond linkages with adhesin proteins (e.g., SdrG, ClfB). Catch bond linkages are robust against force while the protein is being unfolded but come undone in the absence of force, preventing unfolded protein from blocking binding sites on the AFM tip.^{163, 164} While catch bonds can be used to form many sequential linkages from the same AFM probe, their activity is still expected to subside over time due to protein misfolding or aggregation; the highest per-cantilever throughput is thus still likely achieved using non-specific adhesion. In terms of attachment to the cantilever surface, cage-shaped 3-aminopropylsilatrane can overcome the crosslinking that leads to inconsistent results from triethoxysilane.^{165, 166} Compared to silanes, silatranes have an intramolecular coordinate bond between Si and N that resists hydrolysis.¹⁶⁷ Reuse of cantilevers is possible after removing chemical functionalization using UV/ozone treatment.¹⁶⁸

3.4. Pulling geometry

The effect of an SMFS pulling force depends on both the direction and locus of force application. The typical AFM and MT assays shown in Fig. 1 involve differing pulling geometries. In the AFM assay, force is exerted orthogonal to the plane of the membrane and each unfolding event corresponds to breaking secondary and tertiary structure as well as transferring some residues out of the bilayer and into the buffer. By contrast, in the MT assay force is exerted parallel to the plane of the membrane, which raises the possibility that tertiary structure could be interrupted by separating helices within the bilayer without unfolding or extracting the individual helices. Thus, the two stages of the classic “two-stage” model of membrane protein folding might be separated.¹⁶⁹ This occurred in the GlpG unfolding/refolding studies of Choi et al. (Fig. 10A), in which an anomalous loss of elasticity below ~10 pN during refolding was interpreted as “zig zag” insertion of the helices; partial penetration back into the bilayer without formation of tertiary structure.⁴⁹ When the protein was placed in a partially anionic bilayer that promoted folding, reversible transitions were observed between the zigzag state and several partially folded intermediates (Fig. 10B). More sophisticated analysis involving mutants and measurements of helix penetration depth suggested a degree of cooperativity between secondary and tertiary structure formation that is consistent with other biochemical evidence.^{5, 170, 171}

FIGURE 10.

MT SMFS study of GlpG using geometry of Fig. 1B.⁴⁹ (A) Unfolding proceeds from the native state (N) via several intermediates at high force. The average extension of the refolding protein (yellow line) passes continuously from an unfolded coil (U_c) through an unfolded chain of alpha helices (U_h) to a “zig zag” chain of membrane-spanning helices (U_z). (B) In a partially anionic membrane (30 mol% DMPG) that promotes folding, equilibrium refolding transitions were seen between the zigzag state and two partially folded intermediate states. Reprinted in part from Ref. 49. Copyright 2019, AAAS.

It has been challenging to disentangle the effects of pulling geometry from those of force-application technique, since all orthogonal-force assays to date have been performed by AFM and all parallel-force assays have been performed using MT. To explore the relative contributions of different effects, Wang et al. used Upside (a coarse-grained molecular dynamics model with membrane-burial potential) to simulate unfolding of GlpG under multiple conditions: (I.) a soft-spring potential applied to both ends, mirroring the parallel-force MT assay of Fig. 1B; (II.) a stiff-spring potential applied to both ends, as if that parallel-force assay were implemented using AFM rather than MT; and (III.) a stiff-spring potential applied orthogonally to GlpG in a supported bilayer, as if GlpG were subject to the classic orthogonal-force AFM assay.¹⁷² The unfolding patterns were different in all three cases. As shown in Fig. 11, assay I yields highly cooperative unfolding with a few briefly occupied intermediates, consistent with the experimental MT data (Fig. 10). Assay II, which has the same geometry but an AFM-like force probe, yields a diversity of unfolding pathways, each with many intermediates. Thus, the small number of intermediates seen in Fig. 10 are primarily a function of the constant-force nature (and possibly lower time resolution) of MT measurements. However, assay III illustrates that geometry also does affect the unfolding pathway: pulling GlpG with orthogonal force from either its N or C terminus yields yet additional unfolding pathways, also with multiple intermediates. This reinforces the important point that a molecule does not have one characteristic force-extension curve; rather, its unfolding behavior is a consequence of precisely how and from where force is applied. Additional insight into pulling-geometry effects was also obtained from comparative studies of structurally similar $\beta$-barrel proteins that either span the membrane (OmpG) or are water soluble (green fluorescent protein).⁵⁰

FIGURE 11.

Upside simulations of unfolding GlpG under various conditions.¹⁷² (I.) Parallel geometry with a soft spring, akin to the MT experiment of Fig. 1B. (II.) Parallel geometry with a stiff spring, akin to performing that same assay in an AFM. (III.) Orthogonal geometry with a stiff spring, akin to a GlpG study performed in the classic AFM geometry of Fig. 1A. Reprinted from Ref. 172. Copyright 2019, Biophysical Society.

The locus of tip-sample attachment is also an important consideration in SMFS study design. Section 3.3 discussed how variation in the site of non-specific attachment can make it challenging to interpret the initial unfolding of the protein. The specific amino acids that are the first to unfold can be changed by altering the attachment point, either by moving it from one terminus to the other¹⁷³ or by inserting attachment labels and proteolytic cleavage sites into interhelical loops.^{36, 69, 174} Like in the GlpG simulations of Fig. 11, experiments on bacteriorhodopsin pulled from different locations reveal different suites of unfolding intermediates.⁶⁹

3.5. Lipid and substrate effects

SMFS studies can be performed in native bilayer, accessing the biologically relevant energetics that affect stability and function,^{175, 176} or in controlled synthetic bilayer, isolating particular protein-lipid interactions. Studies of the bacteriorhodopsin model system have generally been performed in the native “purple” membrane extracted from lysed H. salinarum archaebacteria.³⁶ This is a membrane of high protein density that exhibits hexagonal packing order.^{177, 178} Other membrane proteins studied in native bilayer have included rhodopsin, several proteins involved in photosynthesis, and several bacterial outer membrane proteins.^{91, 179–183} The latter were studied in outer membrane vesicles that are naturally ejected by bacteria under stress. Most native membranes contain many different membrane-protein species. Specific genetically encoded tags could be used to isolate individual species. When non-specific attachment is used, Galvanetto et al.¹⁸⁴ developed a data-analysis strategy to handle the myriad resulting force-extension curves. Proteins that occur at low concentration in the bilayer are often purified into detergent micelles and then reconstituted into synthetic liposomes, which are then deposited on the surface to form supported lipid bilayers. MT experiments with sufficiently long linkers can accommodate membrane proteins in intact liposomes.⁴⁹ Detergent-solubilized proteins can also be reconstituted into bicelles or nanodiscs.^{37, 185} While the particular lipids into which the protein is reconstituted are frequently chosen for convenience or technical reasons, some studies have compared the unfolding of the same protein in native and non-native bilayers^{183, 185} and others have investigated how systematic changes in the composition of a synthetic bilayer alter membrane-protein properties.^{8, 49, 94, 96, 186}

Most AFM-based SMFS assays involve a supported lipid bilayer nonspecifically adhered to a mica substrate, which could lead to several possible experimental artifacts. First, protein-surface interactions could modulate the stability of different regions of the protein, resulting in observed unfolding intermediates or energetics that differ from the biologically relevant case without a mica substrate. The most extreme case would be protein-surface interactions that change the global fold of the protein. In cases where the native folded structure is known, the latter could be ruled out by careful contour-length analysis of the unfolding force-extension curve. For example, in retinal-containing proteins, one can look for telltale states stabilized by retinal interactions at their expected locations.^{60, 139} The primary evidence ruling out more subtle effects is the study of Petrosyan et al. that compared the force-extension curves of bacteriorhodopsin in surface-supported native bilayer and in a native bilayer spanning a nanoscopic pore in a PMMA surface; the study identified the same major unfolding intermediates in both cases.¹⁸⁷ However, this cannot be taken to mean that surface effects will not be seen in more modern measurements with higher spatiotemporal resolution or for proteins with larger interhelical loops facing the surface. Second, insufficiently strong interaction between the bilayer and the surface could cause it lift up under applied force. Such puckering of the bilayer could be identified, in principle, from anomalous deviations of the force-extension curve from expected WLC behavior and could be remedied through specific chemical tethering to the surface.

4. MEMBRANE PROTEIN FOLDING

SMFS studies probe membrane-protein folding by investigating the protein’s mechanical unfolding and, sometimes, refolding. Biologically relevant interpretation of the results, however, must bear in mind differences between the folding pathway along the force-application vector and the folding pathway in vivo, where the translocon plays a major role and folding occurs cotranslationally. Advanced assays sensitive to equilibrium energetics can provide a strategy for grappling with pathway dependence, since a free-energy difference between states is formally path independent.^{46, 70, 80} Sophisticated assays that explore alternate force vectors or that incorporate elements of the translocon can directly reproduce the biological folding context.^{37, 49, 188–190} With these assays, the tools are now in place to use SMFS studies to reveal quantitative details directly relevant to biological membrane-protein folding.

4.1. Force-induced unfolding does not necessarily recapitulate the biological folding pathway

The biological membrane-protein folding pathway is complicated and highly regulated.¹⁹¹ In eukaryotes, for example, an N-terminal signal peptide in the nascent polypeptide is recognized by the signal-peptide binding protein, which arrests translation until the ribosome docks with the Sec61 translocon in the membrane of the endoplasmic reticulum (ER). Once docked, translation resumes and the nascent polypeptide is cotranslationally inserted into the partially hydrated chemical environment of the translocon. In the translocon, alpha helices form, associate with each other, and are released into the ER bilayer. This is classically thought of in terms of the “two-stage” model of membrane protein folding, in which helices first form due to strong hydrophobic and hydrogen-bonding interactions and later associate due to weak van der Waals interactions.^{169, 192} Now, however, structural detail of the translocon reveals that there is more complexity to the process,^{193, 194} during which the topology of the helices in the bilayer is also established (see Sec. 4.5). Later, after surviving quality-control interactions with the ER-associated degradation (ERAD) machinery, folded membrane proteins are transported to the cell membrane.⁷³

Because neither Sec61 nor its prokaryotic analog, SecYEG, consume ATP, the folding process is fundamentally thermodynamically driven, meaning it should be possible to obtain insights from measurements sensitive only to the relative free energies of folded and unfolded states. However, most membrane-protein SMFS studies have been made under conditions that are not thermodynamically reversible (i.e., paths of maximum work or of microscopic equilibrium) and are thus path-dependent (see Sec. 5 for cases where reversibility has been achieved). There is a temptation to argue that an SMFS experiment in which the molecule is pulled from one end effectively mirrors cotranslational folding, since both cases involve interactions that either form or are disrupted starting at one end of the molecule. However, most unfolding assays (especially AFM-based assays) exhibit cooperative disruption of secondary and tertiary structure. There is not evidence that biological cotranslational folding proceeds in this way, counter to the two-stage model. Thus, most intermediates along observed mechanical unfolding pathways are likely not intermediates of the biological pathway and characterization of the transitions states^195–197 between these intermediates is likely not biologically relevant. That begin said, because the two membrane-protein folding stages are sometimes separately observed in MT assays, some of the intermediates seen in those studies may be biologically relevant. (Cotranslational folding is directly probed in the arrest-peptide experiments of von Heijne and coworkers).^{74, 198}

There are many examples of cases where different membrane-protein unfolding assays drive the system along different unfolding pathways. Already discussed was the distinction between parallel-pulling and orthogonal-pulling SMFS assays (Fig. 11). Another example is the distinction between mechanical unfolding and chemical denaturation, with is clearly illustrated by both the bR and GlpG model systems in which mechanical unfolding by either AFM or MT can be compared to classical biochemical phi-value analysis. A phi-value experiment uses chemical denaturation of wild-type and mutant proteins to determine whether a given residue is folded ($\Phi =1$) or unfolded ($\Phi =0$) in the transition state.¹⁹⁹ Phi-value studies of both proteins show that folding occurs in a single step with a transition state involving either a nucleus of interhelical contacts, in the case of GlpG, or “a loosely packed ensemble of configurations with a largely native topology”, in the case of bR.^{25, 200} This is true for a number of mutations in both proteins, although not for all: only mutants that exhibit two-state denaturation are amenable to $\Phi$-value analysis. It should also be remembered that the “unfolded” state of a chemical-denaturation experiment contains significant secondary structure and thus the experiment is primarily describing the second (tertiary structure formation) stage of the two-stage model.^{16, 17} Nonetheless, this apparent one-step folding, which can be loosely ascribed to part of the biological pathway, contrasts with the many-step unfolding of both proteins in SMFS studies.^{40, 49, 139} A further example of pathway dependence is seen in cases where a non-unique mechanical pathway is seen depending on experimental conditions. For example, the outer membrane protein LamB follows different mechanical pathways depending on the magnitude of applied force.²⁰¹ Simulated unfolding of bR spanning a large velocity range suggests velocity-dependent changes in the mechanical unfolding pathway.²⁰²

4.2. Refolding

Once unfolded, a reduction in force can permit a membrane protein to refold. If the reduction in force is gradual, the refolding process is also constrained to a mechanical pathway. However, this is not necessarily the same pathway as during mechanical unfolding. During mechanical unfolding tertiary contacts are in place between amino acids that are far apart in the primary sequence, whereas during mechanical refolding the applied tension makes interactions between far-removed residues unlikely because of the large work that must be supplied by thermal energy to bring them together.²⁰³ This effect was seen by Kessler et al. in a study of bR, where relaxing the cantilever back towards the surface after partial unfolding revealed refolding under tension into a mix of states along the mechanical unfolding pathway as well as two off-pathway states.²⁰⁴ If the force is quickly dropped (compared to the slow rate of refolding), tensile screening is no longer a factor and the protein can refold by any accessible pathway, possibly including the biological pathway. However, with $F=0$ there is no experimental SMFS readout and thus nothing is known about the progress of refolding until force is applied again. Subsequent application of force can reveal the extent of refolding and, through measurements made after different refolding times, its kinetics.

Single-molecule refolding into bilayers is illustrated by the E. coli sodium-proton antiporter NhaA experiments of Müller and coworkers.^{205, 206} After using constant-velocity SMFS measurements to establish the characteristic force-extension behavior of C- and N-terminal unfolding, they performed a refolding experiment in which they (i) unfolded 10 of the 12 transmembrane helices of NhaA, (ii) relaxed the cantilever back towards the surface, (iii) optionally waited for a period of refolding time, and (iv) again unfolded the protein (Fig. 12A). During the relaxation, they sometimes observed increases in force corresponding to helix pairs reinserting against the small applied force (Fig. 12B, dashed circles). Force-extension curves of subsequent unfolding enabled identification of these helix pairs. Measurements made after different refolding times established the folding rates of each helix pair (Fig. 12C). This approach constitutes a single-molecule method for identifying the structural elements of spontaneous membrane-protein insertion (i.e., helix pairs, consistent with the helical-hairpin hypothesis and subsequent evidence)^207–209 and the kinetics of this spontaneous process under the conditions of the refolding assay. However, it must be remembered that these kinetics do not necessarily recapitulate the biologically relevant rates due, for example, to the absence of the translocon machinery and the lack of complete refolding in many cases.

FIGURE 12.

Spontaneous refolding of NhaA at low force.^{205, 206} (A) Representation of the sequential unfolding/refolding assay. (B) Example force-extension curves showing initial unfolding of all helices III–XII $\left(A_1\right)$, refolding against applied force (dashed circles), and subsequent unfolding of only some helices ($A_2-A_6$). (C) Kinetics of individual helix pairs under the conditions of the refolding assay, extracted from measurements of the fraction refolded as a function of refolding time. Panels A and B adapted from Ref. 206. Copyright 2004, Elsevier Ltd. Panel C reprinted from Ref. 205. Copyright 2006, Elsevier Ltd.

Refolding of several other $\alpha$-helical species was seen in MT assays (e.g., Fig. 10), including GlpG, $\beta$2AR, GLUT3, and the computationally designed scTMHC2.^{46, 49, 106, 161} Comparison of refolding in this geometry has led to the identification of a common N-to-C-terminal folding pathway, which can be understood in terms of the N-to-C-terminal direction of translation.²¹⁰

SMFS refolding was extended to β-barrel membrane proteins in studies of OmpG by Damaghi et al.²¹¹ $\beta$ barrels often fold post-translationally after transport into the periplasm. Thus, an SMFS-based refolding experiment in which the entire polypeptide chain is present is perhaps a good model of $\beta$-barrel folding. In this OmpG study, after partial mechanical unfolding that left one β-hairpin anchored in the membrane, the authors observed refolding of individual β-hairpins back into the bilayer. The refolding pathway differed from the mechanical unfolding pathway, with the fourth β hairpin refolding faster than those before or after it in the primary sequence. This finding challenged the prevailing model that β-barrel proteins concertedly fold and insert into the bilayer in a single step,²¹² instead suggesting that individual β-hairpins can form stable folding units within the bilayer. Further details of the biological periplasmic folding pathway were obtained by Thoma et al., who showed that the chaperones Skp and SurA prevented misfolding of the E. coli receptor FhuA by stabilizing dynamic unfolded sates, with SurA specifically promoting stepwise β-hairpin insertion during refolding.²¹³ By contrast to OmpG, the larger outer membrane protein FhuA adopts misfolded conformations upon attempted refolding.²¹⁴ While biological insights can be obtained from studies of spontaneous refolding into membranes, these chaperone studies highlight that biologically relevant folding occurs in concert with other proteins. Especially relevant to $\alpha$-helical protein folding is the translocon, discussed in Sec. 4.4.

4.3. In-membrane helix-helix interactions

That mechanical unfolding using the orthogonal-pulling AFM assay does not recapitulate the biological folding pathway of a membrane protein has motivated other approaches to separate the high-energy effects of $\alpha$-helix formation from the comparatively low-energy effects of tertiary helix-helix interactions. The most direct approach has been to use the parallel-pulling MT geometry. For example, studies by Choi et al.⁴⁹ of GlpG (Fig. 10) revealed a transition to a zig-zag state with putative secondary structure but without tertiary structure (seen also in Upside simulations).²¹⁵ Under appropriate conditions, GlpG could be held at $F\approx 5$ pN and reversible transitions were observed between this state and multiple partially folded intermediates (e.g., Fig. 10B). Analysis of transition rates between states (e.g., using the Bell model⁸⁴) revealed a free-energy change associated with these transitions between native and zigzag states in GlpG of 15.2 $k_{B}T$ (9.0 kcal/mol), a direct measurement of the strength of in-membrane helix-helix interactions. These data were also analyzed to obtain the barrier heights ($\Delta G^{‡}$) separating states, although the interpretation is subject to the serious concerns of Sec. 2.2 because a pre-exponential factor value is assumed, obtained from soluble-protein measurements. Some evidence was also seen for a zig-zag state in $\beta$2AR, although the non-parallel pulling geometry in that GPCR (with an odd number of helices) complicates the interpretation.⁴⁹

Even in cases where helix-helix dissociation cannot be directly observed in an SMFS experiment, however, it is still possible to draw conclusions about tertiary interactions from studies of mutants. This can be done using an SMFS realization of the classic biochemical assay of alanine scanning mutagenesis. In such as study, replacement of a given side chain with the small methyl group of alanine disrupts van der Waals packing interactions between helices. Since free energy is a state function, a thermodynamic cycle can be used to isolate this effect by taking the difference in free energy of unfolding of wild-type and mutant proteins. This $\Delta \Delta G$ value will include all effects of side-chain substitution: altered helix-helix van der Waals interactions, changes in helix-formation propensity,²¹⁶ and differing hydrophobicity.³³ As discussed in Sec. 5.2, the latter effects can be estimated and subtracted to give the contribution of the side chain in question to the energetics of the tertiary structure.

It is also possible to make some observations about helix-helix interactions from non-equilibrium unfolding measurements that do not admit determination of $\Delta \Delta G$. For example, Voitchovsky et al. were able to identify electrostatic and non-electrostatic helix-helix interactions by measuring bacteriorhodopsin unfolding at different salt concentrations.²¹⁷ In another example, altered locations of intermediates when bR was cleaved and unfolded from the internal E-F helix loop (leaving helices G and F folded) indicated tertiary interactions between helices G and F and the other helices.^{36, 69} Sapra et al. showed that bR unfolding forces were higher in trimers than in monomers, suggesting an effect of quartenary helix-helix interactions; higher forces were likewise seen at the trimer interface of aquaporin-1.^{142, 218} However, unlike for formally path-independent measurements of $\Delta G$ and $\Delta \Delta G$, such non-equilibrium results along the mechanical unfolding pathway are challenging to generalize to reach biologically relevant conclusions.

4.4. Folding in the translocon context

A direct connection to biologically relevant membrane-protein folding pathways can be obtained by making measurements in the specific chemical environment of the translocon (Sec61 in eukaryotes, SecYEG in prokaryotes) or other insertases (e.g., YidC). Such studies build on work studying unaided peptide insertion into the bilayer^219–226, work studying peptide interactions with YidC,²²⁷ and the refolding studies of Sec. 4.2. For example, Serdiuk et al.¹⁸⁸ performed refolding experiments on LacY, unfolding it to the point of leaving a single intact structural segment spanning the bilayer and then lowering the force to induce refolding. They then performed the same measurement in a bilayer into which the insertase YidC had been co-reconstituted. Comparing the structural elements that refolded after different waiting times allowed several conclusions to be drawn about LacY folding in the biologically relevant context of YidC. These included that YidC acted to prevent misfolding of LacY and that YidC promoted insertion of individual structural segments one at a time, although not in a particular order.¹⁸⁸

In subsequent papers, Serdiuk et al. extended these studies through the “pull and paste” assay, which allowed complete refolding of a protein to be observed in a variety of chemical contexts.^{189, 190} In this assay (Fig. 13A), multiple patches of bilayer containing different proteins were deposited on the same surface. One contained the folded protein of interest (e.g., LacY) and others contained insertase and/or translocon proteins (e.g., YidC, SecYEG, or both). Here, LacY was completely unfolded and extracted from the donor membrane (Fig. 13B), then translocated to the target membrane where refolding was attempted. The studies relied on non-specific tip-sample adhesion, limiting refolding duration. They found that fully unfolded LacY did not spontaneously refold into a lipid-only bilayer (Fig. 13C). Either YidC or SecYEG was sufficient to enable refolding (e.g., Fig. 13D). However, they were able to observe differences that spoke to the mechanisms of the two proteins: (i) as in the 2016 study,¹⁸⁸ YidC promoted insertion of structural segments in random order at 0.96 segments per s, but falling off after 5 s; (ii) SecYEG promoted sequential insertion of structural segments at 0.42 segments per s, but maintained beyond 5 s; (iii) when both were present, SecYEG dominated the behavior, with sequential insertion and a steady 0.42 segments/s rate (Fig. 13E).^{189, 190}

FIGURE 13.

“Pull-and-paste” SMFS assay.^{189, 190} (A) AFM topograph and force-extension curves showing how the subject protein LacY is extracted from one bilayer patch (B) and then either refolded into that patch (C) or translocated another membrane patch containing an insertase (D) such as YidC. (E) The extent of refolding is monitored by subsequently attempting to unfold the protein after a period of time. The likelihood of refolding of a given structural segment depends upon the particular insertase. For example, YidC promotes random reinsertion whereas SecYEG promotes sequential reinsertion. Panels A–D reprinted from Ref. 189. Copyright 2017, American Chemical Society. Panel E reprinted from Ref. 190. Copyright 2019, AAAS.

This strategy of inferring details of interactions between a target protein and an insertase through insertase-dependent changes in unfolding or refolding behavior has been applied to several other $\alpha$-helical membrane-protein systems. These have included studies of the interaction of bacteriophage Pf3 coat protein with YidC,²²⁷ polytopic melibiose permease MelB with YidC,²²⁸ and human glucose transporter GLUT3 with the ER membrane protein complex (EMC).¹⁶¹ The latter study was performed using a magnetic-tweezer force-jump assay that resolved a number of GLUT3 folding intermediates and observed changes in their folding probability based on GLUT3-EMC interactions.¹⁶¹ Laskowski et al. similarly localized coat protein-YidC interaction to particular amino acids through complementary molecular dynamics simulations and introduction of targeted mutations.²²⁷

Using related methods in the $\beta$-barrel membrane protein FhuA, Thoma et al. investigated the role of periplasmic chaperones Skp and SurA.²¹³ Using SMFS to probe refolding after mechanical unfolding, they found that both chaperones prevented FhuA misfolding by stabilizing it in a dynamic, unfolded state. However, the chaperones employed different mechanisms, as indicated by complementary NMR measurements. Skp preserved FhuA in a compact “fluid globule,” whereas SurA enabled sequential insertion of β-hairpins into the membrane. The SMFS measurements demonstrated that SurA allowed FhuA to insert β-hairpins in a stepwise manner until the complete β-barrel formed, reducing the chaperone-polypeptide interaction surface as folding proceeded. This work supports a picture in which $\beta$-barrel membrane proteins are successfully folded through interations with both a chaperone that prevents misfolding and an insertase that promotes bilayer insertion.

4.5. Mechanism of topology formation

The mechanism by which membrane proteins establish and maintain their topology (i.e., up/down orientation of helices in the bilayer) remains incompletely understood despite its fundamental importance to protein function. Statistical analysis of membrane protein sequences revealed that positively charged residues are preferentially located in cytoplasmic loops, leading to the formulation of the “positive-inside” rule as a key determinant of topology.^229–233 This was later refined into the “charge-balance” rule to account for interactions between charged residues in interhelical loops and anionic lipid headgroups as a function of bilayer charge and local headgroup pK_a.^234–236 The charge-balance rule successfully predicts topology in many cases and can explain phenomena like the phosphatidylethanolamine (PE)-dependent topological changes observed in the LacY model system, which exists in a mixed ensemble of topologies. However, the detailed energetics underlying these effects have not been quantitatively measured and the mechanism is unclear.

SMFS studies could offer new insight into understanding the mechanism of topology formation. Serdiuk et al. showed that the two topologies of LacY have distinguishable force spectra and that the relative frequency of observing these spectra changes depending on lipid bilayer composition, similar to how conformational switching in DtpA is induced by the presence of a ligand.^{7, 8} They also explored the effects of a conformationally restricted mutant and of galactosidase sugar binding on LacY.¹⁰³ They performed refolding experiments in the presence of YidC and SecYEG that could inform the biological folding pathway (Fig. 13),^{189, 190} although some biochemical studies suggest that topology formation is an equilibrium phenomenon independent of folding pathway.²³⁷ While none of these studies probed thermodynamically reversible refolding that would directly yield energetic information, they establish SMFS studies of LacY as a plausible avenue for understanding topology formation. Similarly informative could be SMFS studies of EmrE, a protein that can change topology due to a single-charge mutation.²³⁸

5. ENERGETICS

While there are challenges in assigning biological meaning to locations of intermediates and properties of barriers along the mechanical unfolding pathway of a membrane protein (Sec. 4.1), the relative free energies ($\Delta G$) of the intermediates do have direct biological interpretability. Because free energy is a thermodynamic state function, it is path independent. Thus, the equilibrium work done to mechanically unfold a section of the protein can be interpreted as the intrinsic thermodynamic stability of that section. Changes in these free energies due to amino-acid mutation, ligand binding, lipid effects, etc. ($\Delta \Delta G$) are similarly amenable to direct biological interpretation.

Interpretation of these energies requires that the starting and ending states of the thermodynamic process are precisely defined. As shown in Fig. 14, there is some subtlety in comparing different energetics methods. For example, consider the unfolded state. In biology, this could refer to any number of conditions depending on context, including dissociated helices in the bilayer or a random-coil amino-acid chain in the cytoplasm. In an orthogonal-pulling SMFS experiment, the protein is stretched and extracted from the membrane. In a chemical-denaturation measurement, the helices remain within the detergent micelle with tertiary structure—and some secondary structure—disrupted. In a parallel-pulling SMFS experiment, losses of tertiary and secondary structure sometimes occur as separate steps.

FIGURE 14.

Energy differences relevant to the biological pathway of membrane-protein folding (A) or the idealized two-stage model (B) can be measured in a variety of unfolding assays (C) including orthogonal-pulling SMFS, parallel-pulling SMFS, chemical denaturation, and steric trapping. The mechanically unfolded state after correction for work done on the unfolded amino acid chain (braces) ideally corresponds to the fully unfolded random-coil state of the native protein and the chemically denatured or sterically trapped states ideally correspond to the native protein with helices dissociated in the membrane. Depending on the assay, parallel-pulling MT experiments are sometimes sensitive to a helix-dissociated “zigzag” stage or a state where helices are extracted from the bilayer but still interact with it.

The following subsections discuss measurements that have employed advances in assay design and instrumentation to record reversible, equilibrium membrane-protein SMFS data and extract energetics. In each case, it is possible to precisely locate the start and end states of the measurement in Fig. 14 and to apply biophysically justified corrections to relate the measured quantity to the underlying biological system of interest.

5.1. Free energy of unfolding

If a membrane-protein system is probed by SMFS, the observation of reversible equilibrium between states (e.g., Fig. 2D) indicates that the arguments of Sec. 2.3 can be applied to quantify a total free-energy difference between those states ($\Delta G_u^{\text{raw}}$ of Fig. 14), which includes the work done to stretch polymer linkers and, in an AFM experiment, to bend the cantilever. Since the elasticity of the stretched, unfolded amino-acid chain is well understood using the WLC model ($\Delta G_{\text{WLC}}$ of Fig. 14) and the elasticity of the cantilever is described by Hooke’s law, both can be subtracted to yield the unfolding free energy associated with disrupting tertiary and secondary structure and transferring the protein out of the bilayer ($\Delta G_u$). Strategies for implementing such measuremetnts have included (I.) using AFM cantilevers with fast time response to observe rapid unfolding/refolding transitions of small portions of proteins in the context of their intact interactions with the rest of the structure;⁷⁰ (II.) using highly stable MT assays to record the slow unfolding/refolding kinetics of an entire (de-novo designed) protein;⁴⁶ or (III.) using parallel-pulling MT to monitor helix association/dissociation in the bilayer.^{49, 239}

To date, orthogonal-pulling AFM-based SMFS energetics measurements have focused on the bacteriorhodopsin model system because it is easy to work with and because it admits comparison with bulk chemical-denaturation results. Yu et al. demonstrated that site-specific application of force to the C-terminal tail of bR resulted in equilibrium unfolding and refolding of an eight-amino-acid region up to Lys²¹⁶, which is the attachment site of the retinal cofactor.¹³⁹ Subsequent work analyzed this equilibrium behavior using a kinetics analysis, the Crooks fluctuation theorem, and the inverse-Boltzmann method to obtain $\Delta G_u$ for the region in question (Fig. 2).⁷⁰ Values of 16.4 ± 0.5, 20.0 ± 1.3, and 15.8 ± 0.6 kcal/mol were obtained for the three methods, respectively, after correcting for work done to bend the cantilever and stretch the unfolded amino-acid chain. Taking the kinetics value as an example, this corresponds to a folding free energy of 2.1 kcal/mol per $\alpha$-helical amino acid. This value represents the free-energy difference between an initial state in which these amino acids are folded into their native positions in the bilayer and a final state in which the helical structure is disrupted, the tertiary contacts are broken, and the residues are transferred into water.

Whereas short lifetimes in states necessitate high-time-resolution methods to observe equilibrium behavior in bR, slow kinetics of the de-novo designed scTMHC2 protein required the exceptional force stability of MT in order to obtain equilibrium data. Figure 8B shows nine hours of equilibrium data at 12 pN that can be directly analyzed by the inverse-Boltzmann method to obtain the free-energy difference between native and fully unfolded, stretched state at 12 pN ($\Delta G_u^{F,\text{raw}}$).⁴⁶ Although not carried out by Kim et al., this analysis can be extended to give the zero-force $\Delta G_u$ between states by adding the effect of tilting the energy landscape and subtracting the work done to stretch the unfolded amino-acid chain:

$$\Delta G_u=\Delta G_u^{F,\text{raw}}+F\Delta X-{\int }_0^{X\left(F\right)}{F}_{WLC}\left(X^{\prime }\right)d{X}^{\prime },$$ (10)

where $F_{WLC}\left(X\right)$ is the Marko-Siggia WLC interpolation formula³⁸ and $\Delta X$ is the extension change upon unfolding at 12 pN. This gives an overall $\Delta G_u=30.5$ kcal/mol, which is 0.20 kcal/mol per $\alpha$-helical amino acid. Unlike for bR, the helices of this designed protein extend beyond the membrane.¹⁰⁶ Those residues are included in this calculation, but it should be remembered that they likely do not have the substantial hydrophobic contribution of those folded into the bilayer. This $\Delta G_u$ value can be compared with the bR measurements, since both involve a transition from a protein folded in the bilayer to one with secondary and tertiary structure disrupted and the residues transferred into water. The value of $\Delta G_u$ per amino acid is about tenfold smaller than that for helix G of bR, consistent with an equilibrium unfolding force of ~12 pN for scTMHC2 versus ~100 pN for the bR region in question. Even when one considers the scTMHC2 $\Delta G_u$ on a per-transmembrane-amino-acid basis, the 0.4 kcal/mol per amino acid value is still fivefold smaller than for bR. It remains an open question why these two proteins—one naturally occurring and the other designed, but both stabilized by the same basic interactions—would exhibit such disparate thermodynamic stabilities. The overall $\Delta G_u$ of GlpG, although measured using non-equilibrium methods, falls in between these values (Table 1). The scTMHC2 $\Delta G_u=30.5$ kcal/mol value obtained from equilibrium analysis is significantly larger than the value of 7.8 kcal/mol determined from kinetic analysis in an earlier work (the same analysis was separately applied to GlpG).^{37, 106}

TABLE 1.

Equilibrium free-energy measurements of membrane proteins

	$\Delta G_u$ of bR per $\alpha$-helical amino acid (kcal/mol/aa)	$\Delta \Delta G$ of bR mutant noted (kcal/mol)	$\Delta G_u$ of scTMHC2 per $\alpha$-helical amino acid (kcal/mol/aa)	$\Delta G_u$ of GlpG per $\alpha$-helical amino acid (kcal/mol/aa)
Equilibrium SMFS	2.1 ± 0.170 (helix G)	−2.3 ± 0.641 (L223A) −2.4 ± 0.641 (V217A)	0.20a	0.0849 (to zig-zag state)
Nonequilibrium SMFS	1.3 ± 0.181 (A-E) 2.5 ± 0.2139 (A-G) 5.4 ± 0.5139 (F-G)			0.649 (full)
Steric trapping	0.0615			0.05241
SDS denaturation	0.1515	−2.1 ± 0.124 (L223A) −1.1 ± 0.226 (V217A)		0.08241

^aCalculated from Kim et al.⁴⁶ Fig. 6E using inverse-Boltzmann argument, adding the effect of tilting the energy landscape to zero force (+$FX$), and subtracting the work done to stretch the 153 aa unfolded protein to 12 pN. The total $\Delta G_u$ is 30.5 kcal/mol.

Under optimized conditions, Choi et al. showed that MT experiments can observe equilibrium transitions between a zig-zag state of dissociated helices and several intermediates of partial helix association in GlpG.⁴⁹ Equilibrium data (e.g., Fig. 10B) are amenable to direct energetic analysis, although Choi et al. instead report $\Delta G$ values obtained from a kinetics analysis. The resulting value of 9.0 kcal/mol for GlpG corresponds to 0.08 kcal/mol per $\alpha$-helical amino acid. This value cannot be compared with the above bR and scTMHC2 results, since it represents a difference between the (nearly) fully folded structure and the zig-zag state of dissociated helices. It is thus a measurement only of the energetics of tertiary structure, without contributions from breaking backbone hydrogen bonds or transferring residues into water.

Energetic results of equilibrium SMFS studies can be compared to results from bulk biochemical experiments, all of which have different sensitivities to the various interactions stabilizing the folded structure. The classic experiment is reversible chemical denaturation, in which addition of SDS disrupts the protein’s tertiary structure and some of its secondary structure. Biologically relevant results must be extrapolated to the zero denaturant condition. More recent steric-trapping studies do not involve this extrapolation.¹⁵ In bR, the two methods disagree by a factor of three (Table 1). On a per-$\alpha$-helical-amino-acid basis, both results are dramatically smaller than the AFM-based SMFS value. For example, the average unfolding free energy of the eight amino acids studied by equilibrium SMFS is 35-fold larger than the steric-trapping result. This discrepancy represents a difference in the thermodynamic states being studied. While, like in the SMFS, the initial state of the steric trapping is the protein folded into a hydrophobic environment (micelle or bicelle), the final state involves dissociation of the helix tertiary contacts but no breaking of the helix hydrogen bonds and no transfer of residues into water (Fig. 14).²⁴⁰ This is similar to the final state of MT-based measurements of unfolding into the zig-zag state of GlpG. And, in fact, these $\Delta G_u$ values per $\alpha$-helical amino acid are of the same order of magnitude as the GlpG steric-trapping values (Table 1).

Efforts have been made to measure $\Delta G_u$ of the entire bR protein (beyond the first eight amino acids) through analysis of non-equilibrium data using results derived from the Jarzynski equality (Eq. 1). Preiner et al. carried out such an analysis using the weighted histogram method, Heenan et al. later carried out a similar analysis using the more-robust inverse Weierstrass transform, and Yu et al. extended the analysis to treat all seven of bR’s helices.^{80, 81, 139} This analysis yielded $\Delta G_u=2.5$ kcal/mol per $\alpha$-helical amino acid for all of bR and, specifically, $\Delta G_u=5.4$ kcal/mol per $\alpha$-helical amino acid in helices G and F. The latter is expected to be higher, since fully unfolding these helices involves extracting the retinal cofactor; the value drops to 3.1 kcal/mol per $\alpha$-helical amino acid when retinal is chemically removed.¹³⁹ Results obtained by methods based on the Jarzynski equality must be treated cautiously, however: the further they are from equilibrium, the more data is required for them to converge to the equilibrium value (Sec. 2.1).^{76, 79–81} Since bR does not refold after being completely mechanically unfolded, the system is likely very far from equilibrium. Anomalous behavior is seen, for example, in a higher $\Delta G_u$ measured for bR’s helix A than for helices E and D (~66 kcal/mol vs. ~37 kcal/mol),⁸¹ even though the unfolding of the latter involves the breaking of more hydrogen bonds, the transfer of more hydrophobic residues into water, and the disruption of more intact tertiary interactions with the rest of the structure. Non-equilibrium analysis has also been applied to GlpG, with a Jarzynski analysis⁴⁹ yielding $\Delta G_u=0.6$ kcal/mol per $\alpha$-helical amino acid for full unfolding to a polypeptide state—of order-of-magnitude equivalence to bR and scTMHC2 values to the polypeptide state—and a novel analysis based on a master-equation formalism³⁷ yielding the much smaller 0.03 kcal/mol per $\alpha$-helical amino acid.

5.2. Mutant-induced free-energy changes

Single amino acid mutations provide a powerful approach for investigating the energetic contributions of specific residues to membrane protein stability. Measurements of the change in unfolding free energy caused by point mutations $\left(\Delta \Delta G_{\text{mutant}}\right)$ can isolate the contribution of individual side chains to the thermodynamic stability of the protein. Such measurements have been made for at least 85 residues in the bR model system using chemical-denaturation experiments.^{13, 19–25, 242} However, like for $\Delta G_u$ measurements, it has not been possible to extend such measurements to most other systems because they do not refold reversibly in denaturant. SMFS methods have been used to probe the effect of mutations on unfolding intermediates and, via DFS, unfolding energy barriers under non-equilibrium conditions.^{59, 90, 92, 151, 159, 183}

Perkins and I demonstrated the ability to make equilibrium $\Delta \Delta G_{\text{mutant}}$ measurements using SMFS.⁴¹ We continued to work in the bR model system to allow comparison to the chemical-denaturation results, although these methods are expected to be applicable to a broader array of membrane proteins. The measurements require only reversible local refolding of the region of interest, rather than the reversible global refolding needed in chemical denaturation. Furthermore, the SMFS approach is able to localize specific structural transitions affected by mutations, either proximate to the mutation site or non-locally elsewhere in the structure. Two mutants previously characterized in the SDS denaturation experiments of Curnow et al.²⁴ occur in the eight-amino-acid region of equilibrium folding seen in Fig. 2. The Leu²²³ residue faces in towards the core of bR and thus its $\Delta \Delta G$ is expected to be dominated by tertiary helix-helix interactions (Fig. 15A, magenta). The Val²¹⁷ residue faces out towards the lipid environment and its $\Delta \Delta G$ is thus expected to have a protein-lipid contribution (Fig. 15A, purple). Chemical-denaturation experiments were expected to be poorly sensitive to such a protein-lipid contribution, since the SDS-denatured state is still detergent solvated (Fig. 14).

FIGURE 15.

SMFS measurement of mutant-induced free-energy changes ($\Delta \Delta G_{\text{mutant}}$) in bacteriorhodopsin. (A) Location of mutants in bR crystal structure²⁴³ with helix G shown as coil and helices A-E shown in space-filling representation. (B,C) Rate maps of wild type (solid lines) and mutant (dashed/dotted lines) bR for $I_G^0\leftrightarrow I_G^1$ (B) and $I_G^1\leftrightarrow I_G^2$ (C) transitions. Reprinted from Ref. 41, which was published under the CC BY-NC-ND license. Copyright 2021, Jacobson and Perkins.

For the L223A mutation, we measured $\Delta \Delta G=-2.3\pm 0.6$ kcal/mol, all attributed to the unfolding of the first five amino acids (i.e., the region containing the mutation).⁴¹ This value quantitatively agreed with previous SDS denaturation measurements (−2.1 ± 0.1 kcal/mol) despite the substantial difference in $\Delta G_u$ between the two techniques (Table 1).²⁴ Such agreement suggests that internal tertiary interactions within the protein core are similarly measured by both techniques. Kinetic analysis revealed that L223A primarily increased the unfolding rate (a 35-fold increase at 100 pN versus only a 2-fold increase in folding rate). This indicates that the mutation predominantly destabilizes the folded state, which is consistent with the removal of favorable van der Waals packing interactions within the protein core (Fig. 15B,C, dashed lines).

In contrast, the V217A mutation, which faces outward toward the lipid environment, showed more complex energetic consequences. Here we measured $\Delta \Delta G=-2.4\pm 0.6$ kcal/mol, which was 2.2-fold larger than the value obtained from chemical denaturation (−1.1 ± 0.2 kcal/mol).^{24, 41} This disparity was attributed to two factors. About 0.7 kcal/mol of the 1.3 kcal/mol total difference could be attributed to differences in secondary structure. The SDS-denatured state retains approximately 60% of its α-helical structure (likely including Val²¹⁷, which is located in the middle of the bilayer) whereas the SMFS experiment fully disrupts secondary structure (Fig. 14). While the energetics of secondary-structure formation primarily involve backbone hydrogen bonds, the side chains also play a role, which can be estimated using the Pace-Scholtz helix propensity scale.²¹⁶ The remaining 0.6 kcal/mol of difference can be attributed to protein-lipid interactions. V217 interacts generally with the hydrophobic environment of the bilayer and, specifically, with a crystallographically resolved squalene lipid.²⁴³ Chemical denaturation assays are not sensitive to these interactions, since native lipid species are not present and the folded and unfolded states are both detergent solubilized (Fig. 14). Differing sensitivities to lipid interactions could be further quantified by making SMFS measurements in detergent, as demonstrated in proof-of-concept $\beta$-barrel experiments.²⁴⁴ Interestingly, V217A caused a shift in the unfolding intermediate—with unfolding now occurring in two four-amino acid steps rather than the five-and-three pattern observed in wild-type bR—and caused a concerted destabilization of the first transition ($\Delta \Delta G_{01}=-4.6\pm 0.5$ kcal/mol) and stabilization of the second transition ($\Delta \Delta G_{12}=+2.2\pm 0.3$ kcal/mol). This suggested a nonlocal effect of the mutation (Fig. 15B,C, dotted lines).

5.3. Ligand-induced free-energy changes

SMFS approaches can also be used to quantify how ligand binding or modification alters membrane protein energetics. Separate from traditional measurements of ligand binding affinity, SMFS studies can report on the underlying change in thermodynamic stability $\left(\Delta \Delta G_{\text{ligand}}\right)$ of the membrane protein or portion of the membrane protein. This informs how membrane proteins respond to their chemical environment and how ligand binding induces conformational changes that drive biological functions. Nascent measurements of $\Delta \Delta G_{\text{ligand}}$ build on extensive SMFS measurements that have observed changes in unfolding intermediates and DFS-derived parameters as a function of ligand or ion interactions.^{7, 63, 66, 68, 95, 97, 98, 100, 102–105, 139, 152, 245, 246}

Unlike for many membrane proteins, the ligand-induced change in bR is not brought about by ligand binding but rather by photoisomerization of a covalently bound ligand. Absorption of light causes the retinal cofactor to transition from the all-trans to 13-cis,15-anti configuration, leading to further conformational changes that result in the cytoplasmic end of helix F being displaced up to ~1 nm away from helix G (Fig. 16A).^247–249 This displacement breaks native tertiary contacts and destabilizes the eight-amino-acid region of equilibrium folding behavior discussed in prior sections.

FIGURE 16.

Measurement of a light-induced ligand conformational change in bacteriorhodopsin. (A) bR photocycle and associated movement of helix F with respect to helix G in the open phase.²⁴⁹ Cyan region is the portion of helix G reversibly refolded in equilibrium SMFS measurements. (B) AFM-based SMFS assay incorporating a 540-nm pulsed light source in the substrate to controllably induce photoactivation. (C) Light pulse (green arrow) shifts the three-state unfolding equilibrium for tens of ms. Histograms of state occupancy during photoactivated (purple) and non-photoactivated (gray) states are amenable to inverse Boltzmann analysis to obtain free energy landscapes in each phase, from which $\Delta \Delta G_{\text{open}}$ may be directly read out without correction. Reprinted from Ref. 145, which was published under the CC BY-NC-ND license. Copyright 2024, Jacobson and Perkins.

To detect the light-induced change in stability of this region in the photoactivated “open” phase $\left(\Delta \Delta G_{\text{open}}\right)$, Perkins and I observed the three-state folding/unfolding equilibrium of the terminal 8-amino-acid region of bR’s G-helix as in Figs. 2 and 15, but now used a light emitting diode beneath the sample substrate to apply precisely timed 200-μs pulses of 540-nm light to induce photoisomerization (Fig. 16B).¹⁴⁵ Upon photoactivation, we observed two distinct behaviors: in ~60% of photoactivation events, the 8-amino-acid region was destabilized as expected. Using the inverse Boltzmann method to analyze the equilibrium data, we obtained energy landscapes of this region of bR in the open and closed phases, finding that $\Delta \Delta G_{\text{open}}=3.4\pm 0.3$ kcal/mol (Fig. 16C). Because the open and closed states are observed in the same singe-molecule record—separated in time—it is possible to directly read off $\Delta \Delta G_{\text{open}}$ without making corrections for the work done on the cantilever and the linkers, which are strictly the same in both states. Importantly, the lifetime of the destabilized state (38 ± 3 ms at pH 7.8) matched previous measurements of bR’s open phase from a high-speed AFM imaging study,²⁵⁰ confirming that the observed energetic change corresponded to a biologically relevant conformational state. In the remaining ~40% of events, we observed a stabilizing effect with longer lifetime that may be a previously undetected alternate pathway or an artifact of the SMFS assay.¹⁴⁵

5.4. Biological significance

While they constitute a promising new approach to understanding membrane-protein thermodynamics, inspection of Table 1 reveals that the energetics measurement techniques discussed above have so far been employed only in studies of a limited number of model systems. Bacteriorhodopsin was studied, for example, because of the possibility of comparing with existing chemical-denaturation results—bR is one of the small number of $\alpha$-helical membrane proteins for which reversible chemical denaturation is possible.^{24, 35} The biological relevance of these results is that they demonstrate the feasibility of a class of experiments than can now be used to probe not just the classic model systems that are amenable to chemical denaturation, but a much larger universe of membrane proteins. Mutations, in particular, represent a classic biochemical strategy for understanding the activity and stability of a protein. By performing single-amino-acid mutation studies similar to those demonstrated in bR, one can explore the contributions of those amino acids to thermodynamic stability independent of other effects, like modulation of ligand binding affinity or function. This is illustrated most clearly in trying to understand the effect of a disease-causing mutation, which could enact its deleterious effect through relative destabilization of the folded state, disruption of a binding site, or interaction with cellular quality control machinery.³⁵ Only with a robust means of measuring membrane-protein thermodynamic stability can these possibilities be distinguished.

6. PROTEIN-PROTEIN INTERACTIONS

Membrane proteins rarely function in isolation, instead engaging in complex networks of interactions with other membrane proteins, soluble proteins, and membrane-associated proteins that regulate their folding, trafficking, stability, and function. To understand the details of these interactions requires energetics measurements of further sophistication, either measuring the free energy associated with the protein-protein binding reaction or the change in thermodynamic stability of one protein or the other upon binding. Site-specific attachment chemistry can make such experiments tractable, since specifically labeled proteins can be addressed from a membrane containing multiple species. SMFS studies have begun to provide insights into protein-protein interactions through their impact on the unfolding force-extension curve and refolding rate in non-equilibrium measurements. Systems studied have included chaperone-assisted folding, translocon-mediated insertion (as discussed in Sec. 4.4), higher-order complex formation, and, recently, the kinetics and energetics of dimerization in a designed protein.

Early SMFS work on membrane protein-protein interactions explored the strengths of interactions in multimers and receptor-ligand systems. These studies included measurement of bacteriorhodopsin stability in dimers/trimers versus in monomers,¹⁴² of subunit interaction strength in light-harvesting complex 2 (LHC2),¹⁸⁰ and of sensory rhodopsin II stability in the presence and absence of the transducer protein HtrII.^{245, 246} In the bacteriorhodopsin and sensory rhodopsin work, the experimental readout was the unfolding force of a given structural segment under particular pulling conditions. A higher unfolding force is correlated with greater stability. For example, the average unfolding force of helices E and D of bR in the trimer is 151 ± 29 pN, compared with 98 ± 34 pN in the monomer. Thus the replacement of protein-lipid interactions in the monomer with protein-protein interactions in the trimer presumably has a net stabilizing effect, although the correlation between the non-equilibrium unfolding force and an equilibrium free-energy change is not linear. In the case of LHC2, Liu et al. pulled on a chain of subunits and observed the average extension change before final rupture; i.e., they measured how many LHC2 subunits could be pulled out of the membrane before one of the subunit-subunit interactions broke. The exponential decay in the histogram of extension change is related to the binding free energy of the subunits under the strong assumption of reversibility. SMFS studies have also been applied to measure interactions of peripheral membrane proteins with the bilayer.^{53, 54, 251}

Recent MT studies have used the designed two-helix homodimer-forming protein TMHC2 to study the pathway and energetics of dimer formation in the bilayer.²³⁹ scTMHC2, discussed in Sec. 5, was a fusion of two TMHC2 monomers. In this study, the two monomers were linked by a ~100 amino-acid elastin-like peptide, which allowed the monomers to dissociate under high force while staying close enough together to re-dimerize at lower force (Fig 17A). This re-dimerization occurred in steps, indicating that, like folding, the process can occur through multiple metastable intermediates. Coarse-grained MD simulations suggest that this re-dimerization occurs along the predominant force-free pathway. At certain forces, the dimerization showed reversible transitions between the monomer, intermediates, and dimer states (Fig. 17B), from which Sadongo et al. extracted transition rate maps (Fig. 17C) and, using Bell-model analysis, the energetics of the dimerization process (Fig. 17D). The reported value of 12.8 $k_{B}T$ (7.6 kcal/mol) is 25% of the $\Delta G_u$ estimated for the total unfolding of the four-helix fusion scTMHC2 (30.5 kcal/mol, see Sec. 5.1). This is surprising, since dimer formation is expected to engage two helix-helix interfaces, leaving the remaining 75% of scTMHC2’s unfolding free energy to account for the other two helix-helix interactions as well as the entire energetics of disrupting its secondary structure. Recall that, in both bR and GlpG, the free energy of secondary-structure formation is an order of magnitude or more stronger than that of tertiary structure formation (as estimated by comparing SMFS and steric-trapping $\Delta G_u$ results, Table 1). This work, which establishes a powerful SMFS assay for probing protein-protein interactions, can now be used in further work to investigate this apparent discrepancy between the strengths of inter- and intra-molecular helix-helix interactions and to begin studying dimerization of naturally occurring membrane proteins.

FIGURE 17.

MT-based SMFS assay to probe intermediates and energetics of membrane-protein dimerization.²³⁹ (A) Two two-helix monomers are separated in a bicelle by force but remain tethered by an elastin-like peptide, allowing subsequent re-dimerization. (B) At 6.0 pN, reversible equilibrium transitions are observed between the monomer state (M), two partially dimerized intermediates (I1, I2), and the full dimer (D). (C) Analysis of transitions at different forces allows construction of rate maps like this for the $M\rightleftharpoons I1$ transition. (D) Bell-model and further thermodynamic analysis allows reconstruction the underlying energy landscape of dimerization, characterized by a total free energy of dimerization of −12.8 $k_{B}T$ (−7.6 kcal/mol). Adapted from Ref. 239, which was published under the CC BY-NC-ND license. Copyright 2025, Sadongo et al.

Many SMFS studies of protein-protein interactions have focused specifically on interactions with chaperones, translocons, and insertases.^{161, 188, 190, 213, 227, 228} While membrane proteins are generally thought to adopt folded states at thermodynamic free-energy minima, their interactions with these helper molecules open a folding pathway to these minima on accessible timescales. The insights gleaned from these studies relevant to membrane-protein folding were discussed in Sec. 4.4. In general, they consist of a variation on the refolding study of Fig. 12: a target protein is partially or fully unfolded and then refolded either in bare bilayer or in the presence of an insertase. By analyzing which regions are most prone to refold, conclusions can be drawn about the residues participating in the protein-protein interaction and about whether that interaction promotes folding, misfolding, or maintenance of the unfolded state. Although such studies do not directly measure the energetic strengths of these interactions, additional details of the interactions can be gleaned from complementary experiments. For example, Laskowski et al. precisely characterized the interaction between bacteriophage Pf3 coat protein and the insertase YidC by combining measurements of the lifetime of the protein-protein interaction under tension with molecular dynamics simulations and targeted mutations in the interaction region of interest.²²⁷ This study also used DFS to report a free energy of the protein-protein interaction under the strong assumption of a particular pre-exponential attempt frequency.

Beyond protein-protein interactions, membrane proteins are frequently modified with polysaccharides that form the glycocalyx: a carbohydrate-rich layer on cell surfaces. These glycans can modulate protein stability, mediate cell-cell recognition, and influence protein-lipid interactions. While some SMFS studies have probed the mechanical properties of cell-surface polysaccharides and protein interactions with the bacterial peptidoglycan,^{150, 252–254} there is room to apply many of the techniques discussed above to these systems.

7. OUTLOOK

Over 25 years, SMFS experiments have emerged as a thermodynamically rigorous way of studying membrane-protein folding and interactions. Measurements have been applied to a variety of systems: $\alpha$-helical and $\beta$-barrel, eukaryotic and prokaryotic, and in native and synthetic bilayers. Many studies have revealed increasing details of the mechanical unfolding pathway, including the locations of intermediates and the barriers separating them. Studies have also used force as an assay of refolding. They have correlated many of these results with ligand-binding, lipid-interaction, and mutant effects. These studies have laid an increasingly sophisticated technological foundation.

The field of membrane-protein SMFS has now matured to the point where our primary interest is in asking questions of direct biological, physiological, and biophysical relevance. For example, we can go beyond mechanical unfolding studies where the attachment point, pulling direction, and chemical environment were chosen for experimental feasibility and instead design assays that address the conditions of folding in a biological context. We glimpse this in studies performed over the past ~10 years involving site-specific attachment chemistry, pulling in the plane of the bilayer, and refolding in the context of insertases. Verily, though, we remain a long way from being able to make quantitative predictions of the strengths of specific interactions within a protein in real energy units, from knowing the degree of energetic stabilization conferred on the nascent protein by the translocon, and from understanding the mechanism of biological membrane protein folding and topology formation in all of its physical-chemical detail. These questions represent the coming payoff of this field.

Many questions remain open to study via SMFS experiments of increasing technological and biochemical sophistication. In the area of membrane-protein folding, we seek a comprehensive quantitative understanding of strengths of interactions stabilizing the folded state, including those within the protein, with ligands, and with the bilayer. We then want to understand how all of this is modulated by interactions with the translocon or BAM complex, with chaperones, etc. SMFS measurements, especially of equilibrium energetics, can be combined with other biophysical assays to elucidate the mechanisms of these interactions and to understand, for example, why topology is established in agreement with the positive-inside rule. Similar mechanistic questions can be asked about the myriad functional interactions occurring between membrane protein species, for example in the ERAD pathway, during membrane fusion and vesicle trafficking, in protein-protein allostery, and in the assembly of macromolecular complexes. In addition to fundamental problems in membrane-protein folding, SMFS experiments are also poised to address practical questions in biology and medicine, for example by exploring the effects of disease-causing mutations on all of the above.

There also remain avenues for further technical advancement in SMFS experiments. Time resolution, discussed extensively in Sec. 3.1, remains an issue. While the most advanced AFM-based assays can now reliably detect a large number of short-lived intermediates, simulations suggest there may be even shorter-lived intermediates still being lost below the cantilever’s response time.²⁰² Transition paths between states, which have been directly observed in DNA hairpin constructs and contain the most concrete information about the transition-state barrier, remain too fast to resolve in membrane proteins.²⁵⁵ Still-smaller cantilevers would be expected to have even faster response times, although they begin to be too small to reflect a diffraction-limited detection laser; piezoelectric cantilevers could offer an alternative.²⁵⁶ In many cases, there is significant room for improvement in the time resolution of MT experiments by using a high-frame-rate camera that fully samples the bead’s time response.¹³⁷ Building on data-analysis approaches that have grown with this field,^{155, 184} machine learning could offer new strategies for triaging and processing the thousands of force-extension curves collected in a typical experiment.

A particularly fruitful collaboration in pursuing these goals will be with researchers doing computer simulations. While thermodynamically well-defined, SMFS studies have an inherently low information content. The behavior of the membrane protein, with hundreds of degrees of freedom, is projected onto a single axis of force application. Steered molecular dynamics simulations that reproduce SMFS results allow observation of conformational details in those many other degrees of freedom. MD simulations can facilitate additional interpretation of SMFS experiments while SMFS results can ground MD simulations in empirical observation.

LIST OF ABBREVIATIONS AND VARIABLES

Abbreviations:

AFM

atomic force microscopy

AD

Allan deviation

$\beta$2AR

$\beta$2-adrenergic receptor

bR

bacteriorhodopsin

DFS

dynamic force spectroscopy

DGK

diacylglycerol kinase

EMC

ER membrane protein complex

ER

endoplasmic reticulum

ERAD

ER-associated degradation

FIB

focused ion beam

GPCR

G-protein coupled receptor

LacY

lactose permease

MD

molecular dynamics

MT

magnetic tweezers

PEG

polyethylene glycol

PSD

power spectral density

scTMHC2

single-chain transmembrane helical protein 2 (de-novo designed protein)

SDS

sodium dodecyl sulfate

SMFS

single-molecule force spectroscopy

WLC

wormlike chain

Variables:

$A$

attempt frequency (pre-exponential factor)

$\beta$

hydrodynamic drag coefficient

$d$

cantilever deflection

$\eta$

dynamic viscosity

$f$

frequency

$\Delta f$

frequency bandwidth

$F$

force

$F_{1/2}$

force at which folding and unfolding rates are equal (coexistence force)

$F_{\text{mp}}$

most-probable unfolding force

$F_{\text{WLC}}$

polymer elastic force from wormlike chain model

$\delta F$

force noise

$\Delta G_{2°}$

free energy associated with helix formation and insertion (in idealized two-stage model of membrane-protein folding)

$\Delta G_{3°}$

free energy associated with helix association (in idealized two-stage model of membrane-protein folding)

$\Delta G_{\text{helix}}$

free energy change associated with formation of helices at the bilayer interface from a stretched amino-acid chain

$\Delta G_{\text{insert}}$

free energy change associated with helices at the bilayer interface partially entering the bilayer to form a “zigzag” state

$\Delta G_u$

free energy of unfolding

$\Delta G_u^{\text{raw}}$

a free energy change obtained directly from analysis of SMFS data without correction for factors such as linker or force-probe elasticity

$\Delta G_u^{\text{SDS}}$

free energy changed measured in a chemical denaturation experiment (see Sec. 1 for discussion of folded and denatured state identities)

$\Delta G_u^{‡}$

activation free energy (barrier height)

$\Delta G_{\text{WLC}}$

work done on the molecular linker during an unfolding transition (linker elasticity modeled as WLC)

$\Delta G_{\text{zigzag}}$

free energy change associated with helices in a partially bilayer-spanning zigzag configuration adopting the fully folded structure

$\Delta \Delta G$

change in $\Delta G_u$ upon perturbation to the molecule, including by mutation, ligand binding, or ligand isomerization

$k_0$

zero-force unfolding rate

$k_B$

Boltzmann’s constant

$k_{\text{eff}}$

effective stiffness

$k_{\text{linker}}$

stiffness of molecular linker

$k_s$

cantilever spring consant

$L_c$

contour length (in WLC model)

$l_p$

persistence length (in WLC model)

$P_X$

probability density of observing molecule at given extension $X$

$r$

loading rate ($dF/dt$)

$T$

temperature

$t_{\text{bin}}$

timescale of Allan deviation calculation

$\tau$

response time

$W$

work

$X$

molecular extension

$\Delta X^{‡}$

distance to transition state

$Z$

cantilever height (see Fig. 1A)

Biography

David R. Jacobson is assistant professor of Chemistry at Clemson University. His lab uses AFM-based single molecule force spectroscopy to study membrane-protein folding and energetics. As a postdoctoral researcher with Tom Perkins at JILA, he worked on developing SMFS methods for measuring membrane-protein energetics in the bacteriorhodopsin model system. He completed his Ph.D. in Physics at the University of California Santa Barbara under Omar Saleh and his B.A. in Physics and Biochemistry at the University of Pennsylvania.