Modulation of a protein-folding landscape revealed by AFM-based force spectroscopy notwithstanding instrumental limitations

Single-molecule force spectroscopy is a powerful tool for studying protein folding. Over the last decade, a key question has emerged: how are changes in intrinsic biomolecular dynamics altered by attachment to μm-scale force probes via flexible linkers? Here, we studied the folding/unfolding of α₃D using atomic force microscopy (AFM)–based force spectroscopy. α₃D offers an unusual opportunity as a prior single-molecule fluorescence resonance energy transfer (smFRET) study showed α₃D’s configurational diffusion constant within the context of Kramers theory varies with pH. The resulting pH dependence provides a test for AFM-based force spectroscopy’s ability to track intrinsic changes in protein folding dynamics. Experimentally, however, α₃D is challenging. It unfolds at low force (<15 pN) and exhibits fast-folding kinetics. We therefore used focused ion beam–modified cantilevers that combine exceptional force precision, stability, and temporal resolution to detect state occupancies as brief as 1 ms. Notably, equilibrium and nonequilibrium force spectroscopy data recapitulated the pH dependence measured using smFRET, despite differences in destabilization mechanism. We reconstructed a one-dimensional free-energy landscape from dynamic data via an inverse Weierstrass transform. At both neutral and low pH, the resulting constant-force landscapes showed minimal differences (∼0.2 to 0.5 k_BT) in transition state height. These landscapes were essentially equal to the predicted entropic barrier and symmetric. In contrast, force-dependent rates showed that the distance to the unfolding transition state increased as pH decreased and thereby contributed to the accelerated kinetics at low pH. More broadly, this precise characterization of a fast-folding, mechanically labile protein enables future AFM-based studies of subtle transitions in mechanoresponsive proteins.

Single-molecule force spectroscopy (SMFS) has been remarkably successful across broad classes of biological molecules (RNA, DNA, and proteins) (1–5). A particularly fruitful data acquisition regime probes multiple back-and-forth folding/unfolding transitions at near-equilibrium and equilibrium conditions (6–9). This methodology efficiently yields numerous transitions and therefore a wealth of kinetic data, one-dimensional (1D) free-energy landscape parameters, and even a full 1D projection of the free-energy landscape along the stretching axis (10, 11). The standard SMFS assay has the molecule of interest tethered via a flexible linker to the force probe, such as an optically trapped bead or an atomic force microscopy (AFM) cantilever (Fig. 1A). These micrometer-sized force probes are the primary measurement (x_meas) but have finite response time and are therefore coupled to, but do not precisely track, molecular dynamics (x_prot) (Fig. 1B) (12–14). Additionally, the flexible linker’s compliance modifies this coupling between the molecule and the force probe. Linkers stretched at a finite force (F) can even create an entropic barrier not present in the absence of applied force (15, 16). More generally, there is an expanding set of theoretical and experimental studies (12–30) investigating how such instrumental and assay parameters affect the underlying biomolecular dynamics and whether the measured dynamics are dominated by the instrument used to measure them.Open in a separate windowFig. 1.Probing the folding and unfolding dynamics of a globular protein by SMFS. (A) Cartoon showing a polyprotein consisting of a single copy of α₃D (blue) and two copies of NuG2 (red) stretched with an atomic force microscope. At low forces, the mechanically labile α₃D repeatedly unfolds and refolds as detected by a change in cantilever deflection. (B) A conceptual two-dimensional free-energy landscape shows the underlying protein extension (x_prot) and the experimentally measured extension (x_meas). The macroscopic force probe has finite temporal resolution, and the application of force can introduce an entropic barrier between resolved states. (C) The sum of the equilibrium folding and unfolding rates for α₃D in a strong denaturant (5 to 6 M urea) as a function of pH as determined in a prior smFRET study (37). (D) A conceptual sketch of α₃D’s 1D free-energy landscape deduced by a combination of smFRET and molecular dynamics studies based on Ref. 37. The dramatic increase in α₃D’s kinetics at low pH shown in panel C was explained as increased configurational diffusion along a smooth rather than a rough energy landscape.AFM characterization of proteins is widely used (1–5) and therefore is an important experimental regime to explore, distinct from numerous studies investigating instrumental effects on nucleic acid hairpins measured with optical traps (17, 18, 23, 24, 26, 31). Historically, limited force precision and stability coupled with the slow response of the force probe has made it challenging to perform AFM-based equilibrium and near-equilibrium studies (32) and thereby difficult to quantify the role of instrumental artifacts. Recent work using a standard gold-coated cantilever concluded that the equilibrium dynamics of the fast-folding protein gpW were dominated by the dynamics of the cantilever diffusing on a force-induced entropic barrier (29). Such results raise significant concerns about interpreting rates or landscapes measured in AFM studies of globular protein folding and thereby motivate the following question: How do variations in intrinsic protein folding dynamics manifest in AFM-based studies, particularly in an experimental regime dominated by an instrument-induced entropic barrier?Here, we address this question by directly modulating a globular protein’s underlying folding dynamics without significantly changing the height of the barrier or the free-energy difference between the states. To do so, we studied α₃D using AFM-based force spectroscopy (Fig. 1A). The dynamics and energetics of α₃D, a computationally designed, fast-folding three-helix bundle of 73 amino acids (33, 34), have been studied by traditional ensemble (33) and single-molecule fluorescence resonance energy transfer (smFRET) (35–39) assays. Equilibrium smFRET studies in chemical denaturants showed accelerated folding/unfolding kinetics as pH was reduced (35). A subsequent landmark paper (37) combined state-of-the-art smFRET and microsecond-long, all-atom molecular dynamics simulations to show that this acceleration resulted from suppression of nonnative contacts changing the local roughness of the 1D landscape (Fig. 1 C and D) rather than a change in the height or the overall shape of the barrier between states. In the context of Kramers theory (40), this roughness manifests as a change in D, the conformational diffusion coefficient along the 1D landscape. The authors concluded that most, if not all, of the 14-fold change in folding kinetics came from an increase in D. This pH-dependent change in kinetics serves as a benchmark of α₃D’s dynamics in the absence of the force probe and associated linker. In other words, we will leverage conditions known to modulate the rate of folding along the molecular coordinate (x_prot) while measuring the consequence of that change on the measured coordinate (x_meas) (Fig. 1B).While α₃D provides a conceptually attractive means to modulate intrinsic molecular dynamics, it presents significant experimental challenges. Like gpW (28, 29), α₃D unfolds at a low force (< 15 pN) by AFM standards (2, 3, 41) and exhibits even faster folding kinetics under force. Thus, spatiotemporal resolution is critical, and instrumentation limitations are expected to be even more pronounced. Force drift is also a critical issue, particularly for extended assays (>1 to 100 s) because standard gold-coated cantilevers exhibit significant force drift (42); yet, equilibrium assays of structured RNA (6) and proteins (9) are sensitive to sub-pN changes in F. We therefore used focused ion beam (FIB)–modified cantilevers (32, 43) that combine sub-pN stability over 100 s (43, 44) with a ∼13-fold improvement in spatiotemporal precision compared with the standard cantilever used in the aforementioned AFM study characterizing gpW (29). This stability in conjunction with a newly designed polyprotein construct allowed us to measure an individual α₃D unfold and fold over 5,000 times and for periods up to 1 h using both constant velocity (v) and equilibrium (v = 0) data acquisition protocols. Rates derived from both the equilibrium and dynamic data recapitulated α₃D’s pH-dependent kinetics from smFRET. However, the reconstructed 1D folding-energy landscape was consistent with the predicted entropic barrier and therefore encodes no information about α₃D’s folding landscape beyond ΔG₀, the thermodynamic stability of α₃D. Importantly, rate analysis yielded the expected asymmetric distance to the transition state from the folded and unfolded state and revealed a significant increase in the distance to the unfolding transition state as pH was lowered. These studies demonstrate that AFM-force spectroscopy can track changes in intrinsic protein dynamics with high precision, even in mechanically labile, fast-folding systems.