Molecular Fluctuations as a Ruler of Force-Induced Protein Conformations

Abstract

Molecular fluctuations directly reflect the underlying energy landscape. Variance analysis examines protein dynamics in several biochemistry-driven approaches, yet measurement of probe-independent fluctuations in proteins exposed to mechanical forces remains only accessible through steered molecular dynamics simulations. Using single molecule magnetic tweezers, here we conduct variance analysis to show that individual unfolding and refolding transitions occurring in dynamic equilibrium in a single protein under force are hallmarked by a change in the protein's end-to-end fluctuations, revealing a change in protein stiffness. By unfolding and refolding three structurally distinct proteins under a wide range of constant forces, we demonstrate that the associated change in protein compliance to reach force-induced thermodynamically stable states scales with the protein's contour length increment, in agreement with the sequence-independent freely jointed chain model of polymer physics. Our findings will help elucidate the conformational dynamics of proteins exposed to mechanical force at high resolution which are of central importance in mechanosensing and mechanotransduction.

Keywords: energy landscape; protein fluctuations; protein folding; protein nanomechanics; protein stiffness; single molecule magnetic tweezers.

FIG. 1. The effect of force on the free energy landscape of protein (un)folding.

Using the example of protein L, in the absence of force (grey line), there is one minimum, corresponding to the folded state (blue). When a low force is applied, a broad local minimum corresponding to an unfolded state emerges (yellow). At a certain, coexistence force (red), the protein will equally likely be found in folded and unfolded states. As force increases, the unfolded minimum becomes narrower, eventually becoming the global minimum (green).

FIG. 2. A step-wise change in protein compliance fingerprints mechanical unfolding/refolding of a single PL monomer under force.

(A) Schematic illustration of PL (PDB: 1HZ6) construct being stretched in a magnetic tweezers set-up. (B) Raw extension-time measurement of a protein L monomer hopping in equilibrium between the folded and unfolded states. The (Ig32)₂-PL-(Ig32)₂ construct is initially pulled at 38 pN, which extends and unfolds the PL monomer. After 60 s, the force is quenched down to 8.1 pN for 60 minutes. During this time the PL monomer stochastically hops between the folded and unfolded states in steps of Δ<x> = 10.3 ± 0.3 nm. A final pulse at a high force (38 pN) value triggers the (re)unfolding of the PL monomer. (C) Result of flattening the protein extension data during the 8.1pN pulse to remove slow drift effects, clearly highlighting 13 individual (un)folding transitions. (D) Compliance of (C) (calculated over a 3-second moving window), showing step-wise changes (Δc = 0.86 ± 0.09 nm/pN) concomitant to the PL individual unfolding and refolding events.

FIG. 3. The change in compliance in a PL₈ polyprotein is additive and recapitulates that of an individual domain.

(A) Illustration of the PL₈ construct being pulled in the MT set-up. (B) Typical (un)folding hopping trajectory of PL₈ under force. Following a force-quench protocol, a high force pulse (49 pN) is first applied, to trigger the unfolding of each individual domain within the polyprotein chain (red asterisks), hallmarked by changes in extension of 17.2 nm. The force was subsequently dropped down to 8.1 pN (resulting in an initial decrease in extension) and held for 50 minutes. During this period of time, the PL₈ polyprotein dynamically hops between well-defined states separated by Δ<x> = 10.7 ± 0.1 nm. (C) Segment flattening and colour-based assignment of the number of unfolded domains allows for clearer visualisation of the step-wise hopping dynamics. (D) The average compliance (n = 131 (un)folding events) can be calculated for a given number of unfolded domains. Linear fit (weighted by the total observation time at each level) to the data yields a gradient of 0.81 ± 0.15 (R ² = 0.983), corresponding to the change in compliance of an individual domain.

FIG. 4. Correlating force-dependent extension and compliance changes upon mechanical (un)folding through the FJC model of polymer elasticity.

(A) Cyclic unfolding and refolding trajectories allow probing the change in protein stiffness upon PL unfolding at varying high forces. Using a force quench protocol, the protein is initially held at a seemingly low force (1.8 pN) for 30 seconds to ensure correct refolding. The force is then increased to a higher constant force value in each cycle (namely 21.9, 16.7, 12.7, and 9.7 pN) for 5 minutes, which triggers in each case the unfolding of the PL monomer (marked by a step-wise increase in length). (B) Similar cyclic force-quench protocol to capture the change in protein compliance upon mechanical refolding at low forces. Before each cycle, the force is first kept low (1.8 pN) for 30 seconds to reach the protein’s native state. Subsequently, in each cycle the protein is unfolded at high force (49.2 pN) for 40 seconds, before the force is successively quenched at low forces, namely 6.2 pN (5 min), 5.7 pN (4 min), 5.2 pN (3 min), 4.7 pN (2 min) and 4.3 pN (1 min), respectively. When held at such low force values, the protein stochastically refolds back to the native state, as evidenced by the step-wise reduction in length. While the folded state dominates at these forces, some hopping back to an unfolded state is observed. (C) Representative unfolding (left) and folding (right) events occurring at high (21.9 pN) and low (5.7 pN) forces respectively (corresponding to the green dashed box in (A) and the yellow dashed box in (B), respectively). High force unfolding is hallmarked by a large increase in average extension but a small increase in compliance, conversely low force folding is hallmarked by a small decrease in average extension but a large decrease in compliance. (D) Plot of (absolute) compliance change against (absolute) extension change combining low (yellow), hopping (red), and high (green) force experiments, clearly showing that, upon PL un/folding, an inverse correlation between its changes in extension and compliance is measured. Data points for monomers (circles) correspond to the mean ± s.e. of 9–17 events occurring at each force, data for the PL₈ octamer (square) is taken from Fig. 3D. Combined, this data show very good agreement with the FJC model (grey dashed line) with Kuhn length b = 1.1 nm, k _B T = 4.04 pN nm, and ΔL = 18.6 nm.

FIG. 5. Direct observation of the change in end-to-end fluctuations upon individual talin and nesprin unfolding/refolding events.

(A) Illustration of the [(Spy0128)₂-TalinR3_IVVI] construct being pulled in the MT set-up (PDB: 2L7A). (B) (Left) Raw, unfiltered extension-time data corresponding to the stretching of individual talin R3 IVVI monomer at a constant force of 8.35 pN for 200 seconds. During this time, the protein monomer undergoes multiple unfolding and refolding transitions. (Right) Zoom in on the hopping section, showing 84 consecutive unfolding(red)/refolding(blue) transitions concomitant to an average change in extension of Δ<x> = 22.2 ± 0.2 nm, and an average change in compliance between the folded and unfolded states of Δc = 1.24 ± 0.14 nm/pN. Averaging over 5 such cycles gives Δ<x> = 22.2 ± 0.1 nm and Δc = 1.28 ± 0.08 nm/pN. (C) Illustration of the [Ig27-SR73]₄ construct being pulled in the MT set-up (lacking crystal structure, here we display the similar SR16 (PDB: 1U4Q). (D) Typical individual (unfiltered) folding trajectory under a force quench. The force is first increased from 10.6 pN to 37.5 pN over the course of 30 s (corresponding to the linear movement of magnet position by 1.4 mm over this time), resulting in the sequential step-wise unfolding of the four SR73 domains of nesprin (green asterisks). Note that, within this force range, the mechanically rigid Ig27 domains in the construct do not unfold. The force is then quenched down to 7.4 pN for 30 seconds, triggering the collapse and refolding of nesprin. At such a low (<F _0.5) force value, refolding is relatively slow, such that the staircase-like pattern that mirrors that of unfolding can be captured. The force is subsequently ramped up again (test pulse) back to 37.5 pN, to probe that all the individual SR73 domains (green asterisks) had effectively refolded during the force-quench. (E) Zoom (yellow square) on the initial folding section of (B), where the four SR73 domains of nesprin refold sequentially, marked by a step-wise reduction of the protein extension by Δ<x> = 17.1 ± 0.5 nm. The refolding of each individual domain occurs concomitant to a reduction in the end-to-end fluctuations of the protein construct. (F) Plotting the compliance against the number of unfolded domains measured in (C) allows calculation of the change in compliance per domain, Δc/domain = 2.30 ± 0.59 nm/pN. Averaging over 10 such folding trajectories with four SR73 nesprin unfolded domains gives Δ<x> = 16.8 ± 0.2 nm and Δc/domain = 1.99 ± 0.12 nm/pN. (G) Plotting normalised compliance change (Δc/β bΔL) against normalised extension change (Δx/ΔL) crucially reveals that the observed behaviour is protein independent, showing quantitative agreement with a master curve of the FJC model.