Segmentation and the Entropic Elasticity of Modular Proteins - The

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Biophysical Chemistry, Biomolecules, and Biomaterials; Surfactants and Membranes

Segmentation and the Entropic Elasticity of Modular Proteins Ronen Berkovich, Vicente I. Fernandez, Guillaume Stirnemann, Jessica Valle-Orero, and Julio M. Fernandez J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01925 • Publication Date (Web): 30 Jul 2018 Downloaded from http://pubs.acs.org on August 5, 2018

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The Journal of Physical Chemistry Letters

ABSTRACT. Single molecule force spectroscopy utilizes polyproteins, which are composed of tandem modular domains, to study their mechanical and structural properties. Under the application of external load, the polyproteins respond by unfolding and refolding domains to acquire the most favored extensibility. However, unlike single domain proteins, the sequential unfolding of the each domain modifies the free energy Landscape (FEL) of the polyprotein nonlinearly. Here we use force-clamp (FC) spectroscopy to measure unfolding and collapserefolding dynamics of poly-ubiquitin and poly-(I91). Their reconstructed unfolding FEL involves hundreds of kT in accumulating work performed against conformational entropy, which dwarf the ~30 kT that is typically required to overcome the free energy difference of unfolding. We speculate that the additional entropic energy caused by segmentation of the polyprotein to individual proteins plays a crucial role in defining the “shock absorber” properties of elastic proteins such as the giant muscle protein titin.

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KEYWORDS. AFM, single-molecule, force spectroscopy, proteins, free-energy landscape, entropy.


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Deformation of tandem modular proteins in response to mechanical stimuli is highly relevant to biological processes such as the regulation of mechanosensing by talin and integrin1, the modulation of muscle elasticity by titin2-3, or the remodeling of skin tissue by fibronectin and fibrillin4-5. These systems involve polyproteins that are tandem repeats of several (typically 6-12) protein domains tethered in series, and widely employed in single molecule force spectroscopy69

, as they improve statistical sampling. Upon application of a mechanical load, considerable

conformational changes take place as the individual domains undergo key unfolding transitions up to their contour lengths, resulting in protein extension going from tens up to hundreds of nanometers. Such experiments provide a framework for the study of protein mechanical and thermodynamic properties10-11 through their underlying free energy12. Indeed, the projection of its multidimensional energy landscape along the experiment reaction coordinate13, i.e. the end-toend distance x, can be obtained, leading to a coarse-grained portrayal of the protein by a 1D free energy landscape (FEL) U(x). Nonequilibrium work relations, such as the Jarzynski equality14, have enabled the direct reconstruction of the whole FEL15 from force extension measurements1618

. The corresponding reconstructed zero-force FELs of polyproteins display a large separation

between unfolding events (on the order of the unfolded protein length upon stretching), accompanied with significant free-energy changes. These patterns were associated with the work required to stretch the unfolded proteins rather than their unfolding barriers19. Recently, some of us constructed a model that predicts the effect of force on polyproteins FELs by considering the elastic extensions that follow the consecutive unfolding of individual domains/modules20-21. The multi-domain segmentation in polyproteins raises questions regarding the effect of conformational entropy on their unfolding and refolding FEL, because each individual domain unfolding leads to a dramatic increase in the conformational degrees of


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freedom21-23. Here we reconstruct the FELs of poly-I91 and poly-ubiquitin unfolding and collapsing under constant force conditions (see section 1 in SI) using a new reconstruction method. The FELs share similarities with that obtained in our previous experiments in that sense that the unfolding distances scale with the applied force via the elastic stretching, giving rise to an "accordion-like" behavior20-21. We show that this phenomenon reduces the elastic free energy stored in a polypeptide packed in a compact and segmented polyprotein conformation. Additionally, the recovered FELs exemplify the different pathways explored when polyproteins unfold at high forces and refold when removing these forces. The FEL U(x) at a given force is reconstructed using a new approach based on the integration of the chemical potential24 µ(x) = kBTln[P(x)] + U(x). Fick's law for a one-dimensional probability flux can describe the stochastic nature of this noise-driven process over a biasing potential. Generally, this can be viewed in terms of a reinjection process, and can therefore be considered stationary, i.e., P(x,t), the probability density function (PDF), can be replaced by the quasi-equilibrium PDF, P(x)

25-26

. Consequently, the diffusion flux can be written as j(x) = –

D∇x[P(x)] – P(x).(D/kBT)∇x[U(x)] = –(D/kBT).P(x).∇x[µ(x)]. Defining the flux velocity by ẋ = j/P, and integrating over both sides with respect to the position x results in –(kBT/D)∫ẋ(x)dx = µ(x) = (kBT)ln[P(x)] + U(x) , leading to (see section 2 in SI): (1)

k T U ( x) = − B D

x2

∫ x& (x )dx − k T ln[P(x )] , B

x1

where kB is Boltzmann’s constant, T the temperature and D the diffusion coefficient. x1 and x2 denote the boundary conditions of the process, and ẋ(x) is the position-dependent velocity. P(x) and ẋ are calculated directly from the experimental time-series trajectories, and allow for the estimation of the equilibrium (-kBTln[P(x)]) and nonequilibrium (-[kBT/D].∫ẋ(x)dx) contributions whose interplay eventually leads to the successful FEL reconstruction (see section 2 in the SI).


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This approach shares some similarities with the relation proposed by Vanden-Eijnden and colleagues25 used to reconstruct the FELs of collapsing poly-ubiquitin rescaled at the monomer level9. In order to understand the effect of domain segmentation, we measured the FEL of polyproteins using an Atomic Force Microscope (AFM) in the force-clamp (FC) mode. Figure 1A shows experimental traces of poly-ubiquitin stretching at 170 pN, with unfolding of each ubiquitin domain leading to step increases of 20 nm8. This phase is followed by chain collapse upon force removal, with some of the traces displaying fast collapse back to their initial lengths, while others required a longer relaxation time27-28. We reconstructed the FEL using eq. (1) at 170 pN and at zero force by separating the traces into two corresponding parts. ẋ was calculated by averaging the position local time derivatives with respect to their positions from a phase-plot (Figure 1B), and D was determined from the experiments (see sections 2 and 3 in SI). D = 835 nm2/s was obtained (see section 4 in SI), in agreement with predictions and measurements of the hydrodynamic drag forces effect on the observed dynamics9, 15, 29-30. The phase-plot and the PDF of the poly-ubiquitin at zero force are shown in Figure 1B. When force is applied, ẋ portrays the nonequilibrium transition between unfolding events through the unfolded chain elongation, while P(x) conveys the equilibrium conformations at each domain folded state (Figure 1C). The resulting FEL is shown in Figure 1E, together with that in the absence of force. Under a force of 170 pN, the obtained FEL (green) is segmented and it exhibits a peculiar pattern. In agreement with prior observations16-18, we measure unfolding energies on the order of hundreds of kBT.


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Figure 1. Free energy landscape of poly-ubiquitin. A. End-to-end traces of 20 poly-ubiquitin, all exhibiting eight unfolding events. The force protocol is shown underneath. An illustrative cartoon describes the polyprotein behavior under force is shown below. B. Phase-plot (left axis) and PDF (right axis) calculated from poly-ubiquitin collapse traces. The left axis shows the time derivatives calculated from each trace as a function of their position (light gray), whose average produces a continuous function of ẋ with x (dark gray). The right axis shows P(x) calculated from all the collapse trajectories (light blue). C. Phase-plot (left axis) and PDF (right axis) calculated from poly-ubiquitin octamers pulled at 170 pN. The calculated ẋ as a function of their position (light gray), their averages (dark gray), and P(x) (green) are plotted on the left and right axes respectively. D. Reconstructed FEL from collapse trajectories of unfolded poly-ubiquitin at zero force, calculated by eq. (1) (light blue line). The dashed (black) line shows a fit to the WLC energy model. The inset zooms on the first 60 nm of the reconstructed potential (solid light blue line), described by a Morse potential (dashed black line). E. FEL reconstructed from the measured time-series with or without force. The unfolding landscape of poly-ubiquitin at 170 pN (green) portrays an initial elastic extension followed by sequential unfolding events. Subtracting


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the perturbation (F.x) from the reconstructed collapse landscape at F = 0 (light blue) results in a curve (dark blue) that agrees with the phenomenological model described by EWLC(x) – F.x (purple).

The reconstructed FEL in the absence of force remarkably agrees with phenomenological predictions31 and measurements9 (Figure 1D). The high extension regime (60-180 nm) was fitted with a worm-like chain (WLC) expression32 EWLCl(x) = (kBT/p){(LC/4)[(1 – x/LC)–1 – 1] – x/LC + x2/(2LC)} (dashed line), leading to a contour length LC = 207 nm and a persistence length p = 2.7 nm. The high value of p does not represent the actual persistence length of the unfolded chain, and may result from the convolution of the chain and cantilever tip effects at high extensions, leading to an apparent stiffer chain. The lower extensions (< 60 nm) accounts for the collapsed (or molten globule) state28, 31, 33-36, in which native contacts began to form as the protein folds35, 37

along orthogonal reaction coordinates38-42. The collapse state potential can be fitted with a

Morse potential (inset of Figure 1D) with E0 = 35 kT, RC = 2 nm and b = 0.135 (see eq. (6) in SI). The overall FEL agrees with the observation that a highly disordered unfolded chain has to cooperatively collapse prior to the formation of a compact globular state, where monomer interactions dominate28, 31, 33, 38, 42-43. To illustrate the dramatic effect of segmentation on the FEL morphology, we subtracted the perturbation (F.x) from the reconstructed collapse landscape at F = 0 (light blue), resulting with a curve (dark blue), that agrees with the WLC predictions. Notably, segmenting the chain into eight domains reduces the total amount of work required to stretch an unsegmented chain of the same length from ~7,000 kBT to ~2,000 kBT. The collapsing FEL at zero force and the unfolding FEL at 170 pN demonstrate the differences captured within these two processes. During the


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unfolding of the proteins along the polyprotein chain, segmentation gradually reduces, until the unfolded tandem segments form a unified unsegmented long chain. This long chain cooperatively recoil and collapse with the release of the external load.

Figure 2. Time series of a single I91 octamer under a periodic force protocol. The upper panel denotes the time evolution of a single molecule, unfolding, collapsing and refolding repeatedly. The three lower panels show a superposition of different parts of the measured time-series per cycle. The protein was held at a high force for 4 s to allow the unfolding of all the domains, then collapsed at zero force for 0.5 s, followed by an unfolded pulse at 180 pN for 1 s in order to prevent folding (thus monitoring the extension of the protein), and finishing with a quench to zero force for 2.5 s (lower middle panel). In the final pulse of the cycle, after sufficient time was


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provided to refold, the polyprotein was unfolded again at 180 pN for 2.5 s and then collapsed at zero force.

To examine the generality of the segmented FEL profile, we carried out measurements on the eight-domain poly-(I91) of titin (Figure 2). Unlike the FELs shown in Figure 1E, which were calculated from an ensemble of traces, we now reconstruct the FELs from a single long trace where a single octamer was cycled between 0 and 180 pN for ~350 s to sample the different conformations resulting from domain unfolding, collapsing and stretching. By analyzing the corresponding portions of this trace, we can reconstruct for example the FELs of a chain with zero, one or two folded domains unfolding at 180 pN (Figure 3A). The energetic cost for extending a single I91 domain was measured from the net-force experienced by the molecule estimated with numerical gradient of the reconstructed FEL, dU/dx (Figure 3B). The net-force obtained from the collapse trajectories (purple), follows the WLC model with a drop at the end caused by the final collapsed state. The elastic stretching of the chain when no unfolding is observed (light blue) follows a WLC behavior with a bias of 180 pN. Traces involving one and two unfolding events (green and red respectively) display peaks at this same force, corresponding to individual domain unfolding separated by elastic stretch of the chain. The unfolding of the first (respectively, second) domain, calculated by the difference between the integrals of the light-blue and the green curve, yields an energetic cost of 576 kBT (respectively, 485 kBT). A comparable value of ~480 kBT was measured for unfolding the 3rd and 4th domains (Figures 3C, 3D). These values fall within the same order of magnitude of those reported elsewhere16-18. However, these energy differences are substantially higher than the reported unfolding barriers of ~29 kBT

44

(ubiquitin) and ~37 kBT

45

(I91), suggesting that the high


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energetic values are mostly associated with the entropic work required to stretch the unfolded chain, rather than with the unfolding barriers that are small in comparison19.

Figure 3. Unfolding free energy landscape of two different (I91)8 molecules at 180 pN. A. Reconstructed landscapes from (I91)8 time series (Figure 2). FELs of eight collapse domains (purple), and from an unstructured chains, which did not refold, of total length LC×8 (light blue) are shown. FELs reconstructed from regions of the trace with only one (green) and two (red) domains reach the same final extension. The dashed line corresponds to a profile given by EWLC(x) – F.x with LC = 186 nm, p = 0.75 nm and F = 180 pN. B. The net-force, dU/dx, obtained from the collapsing trajectories (purple), and the elastic stretching (light blue) show a WLC behavior with a separation of 180 pN. Traces with one and two unfolding events are marked in


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green and red respectively. The shaded area, estimates the energetic cost of unfolding a second domain of 485 kBT. C. FELs reconstructed from a different set of a (I91)8 time-series pulled at 175 pN (see Figure SI 6). FELs of three and four unfolding events (green and yellow respectively) are shown together with the collapse FEL (blue). The lower dotted curve is obtained by subtracting F.x from the collapsing landscape. Fitting the latter with EWLC(x) – F.x, returned LC = 213.6 nm, p = 0.26 nm and F = 175 pN. D. Numerical derivatives of the reconstructed reveal the difference in energy for unfolding the forth domain (shaded area) as 480 kBT. Note that the effective chain stiffness under stretching is lower than that of ubiquitin during collapse (p = 2.7 nm), probably because recoiling and stretching processes correspond to different regimes in the energy landscape of the chain30 that may be differently affected by the cantilever.

The general effect of segmentation was addressed in the mechanical context of sacrificial bonds46, concluding that the released entropic energy is much larger than the energy required to break sacrificial bonds. Although the discussion here revolves around protein unfolding, the same basic principle of a gradual increase in entropy stands. Therefore, we use the WLC model to estimate the entropic work of a chain with a contour length LC divided into Nf folded segments out of Ntot (each releasing a length ∆L upon unfolding), by constructing the following model (see section 6 in SI): LN f

(2) U

F Nf

Nf

L( N f

−n

)

( x, LC , p ) = ∫ FWLC (x ' , LC − N f ∆L, p )dx '+ ∑ ∫ FWLC [x ' , LC − (N f n =1 0

L( N f − n +1 )

− n )∆L, p ]dx ' −

LN f

∫ F dx ' 0

where Li is equal to the equilibrium length of the unstructured portion of the chain at this force.


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Within the WLC model framework, FWLC(x,LC,p) = (kBT/p)[0.25(1-x/LC)-2-0.25+x/LC] is the force required to extend a chain by x. The boundaries of the integrals reflect the domain length, which is being released and stretched after the unfolding of each individual domain. Consequently, eq. (2) provides an estimation of the elastic contribution to the overall FELs as a function of both, force and segmentation, neglecting the small contributions from the unfolding barriers. Plotting eq. (2) at F = 170 pN for Nf number of folded domains varying from zero to six, with ∆L = 25 nm, LC = 213 nm and p = 0.4 nm, demonstrates that the extension of a segmented chain costs hundreds of kBT (Figure 4A) and the profiles show remarkable similarity to the ones measured experimentally (Figure 1 and 3). This simple segmented elastic model is therefore able to rationalize the experimental observations, and allows for further discussion. In particular, the effect of pulling force in eq. (2) for a constant number of folded domains (Nf = 6) is shown in Figure 4B. Extrapolating this trend to zero force, the extended length of the unfolded individual domains would localize around the compact conformations measured in bulk47, where all the local barriers of each domain practically overlap the collapsed state minimum with respect to the end-to-end coordinate. Upon application of force, the sequential unfolding of each domain consequently increases the available length for the entire polypeptide while altering the free energy landscape. This rescaling “accordion” effect means that in the presence of segmentation, the perturbation cannot be simply subtracted from the unfolding energy landscape of a polyprotein at a given force to obtain the unperturbed energy landscape at zero or any other force (see section 7 in SI).


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Figure 4. Segmentation effect on the energy landscape of a polypeptide chain. A. The effect of segmentation on a chain with varying number of unfolding domains, Nf, ranging from 0 to 6 calculated by eq. (2). B. Effects of the applied force on the unfolding FELs. The FELs ware plotted for Nf = 6 tandem unfolding domains under (top to bottom) 20, 50, 90, 130 and 170 pN, demonstrating the “accordion effect”. C. Force-extension profile of a chain made up of a two polypeptides (black and green for distinction) with a total length of LC. D. Similar construction to


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the one shown in C, with the distinction of the second domain (green) being folded. Once the folded domain unfolds, the force of the system drops to some value F*, from which the chain stretches until it reaches its final extension, LC.

We now interpret the effect of segmentation on the FEL in light of a very simplified picture of conformational entropy (Figure 4C-D). In the first scenario (Figure 4C), a polypeptide made of two (independent) chains, with a total length of LCtot = LC1 + LC2, is being pulled under an external load. When collapsed, the two independent segments possess Ω1 and Ω2 degrees of freedom and thus a total of Ω1× Ω2, making the overall entropy additive: ∆Stot = ∆S1 + ∆S2, which decreases as force increases. In the second scenario (Figure 4D), segmentation is introduced by replacing the second polypeptide chain with a folded protein domain (with similar LC2 when unfolded). Under external load, initially Ω2 ~ 1 until the polypeptide fully stretches, contributing ∆Stot ≈ ∆S1 to the total entropy. Once the folded domain unfolds, entropy increases as Ω1 goes from 1 (folded) to a very high value (collapsed state), which corresponds to a much smaller force F*. In this state, each unfolded chain has Ω1(*) and Ω2(*) degrees of freedom, where Ω1(*)×Ω2(*) < Ω1×Ω2. Stretching the (now unsegmented) chain from this point close to its LCtot, will add ∆S1(*) + ∆S2(*) to the system, resulting with a total entropy change of ∆Stot = ∆S1 + ∆S1(*) + ∆S2(*). The difference between the two scenarios accounts for the hundreds of kBT measured for a domain unfolding (Figures 1C and 3). This mechanism is significantly advantageous in physiological elastic systems, where tension-driven unfolding enables further extension of the chain while maintaining its flexibility by lowering the overall energy. This feature allows segmented polymers or proteins to perform as shock absorbers under external load as well as enabling such systems to maintain their elastic function.


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In this letter, we demonstrated the full reconstruction (to scale) of unfolding and collapsing/refolding FEL of two polyproteins from FC measurements. The general behavior of both polyproteins studied deviates from the occasionally acclaimed symmetry between folding and refolding processes over the same energy landscape, which was understood using a segmented WLC model as the effect of conformational entropy. In particular, the reconstructed FELs demonstrate the effect of domain segmentation on the overall elasticity of the structure.

ASSOCIATED CONTENT Supporting Information. Detailed description of the force spectroscopy experimental methods, protein engineering materials, and summery of the physical concepts of the FEL reconstruction procedure, additional Poly-I91 measurement and entropy (WLC) based free-energy model (PDF).

AUTHOR INFORMATION Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT We would like to acknowledge Dr. Pallav Kosuri for his contribution with the second Poly-I91 measurement, Prof. Ionel Popa for his assistance with the measurements and graphics, and to


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thank Prof. Rony Granek for insightful and useful discussions, and. This work was supported by NSF (DBI-1252857) and NIH (GM116122 and HL061228) grants. R.B. is grateful to the ICORE Program of the Planning and Budgeting Committee and The Israel Science Foundation (Grant No. 152/11). G.S. acknowledges support from the "Initiative d'Excellence" program from the French State (Grant "DYNAMO", ANR-11-LABX-0011-01).

REFERENCES 1.

del Rio, A.; Perez-Jimenez, R.; Liu, R. C.; Roca-Cusachs, P.; Fernandez, J. M.; Sheetz,

M. P., Stretching Single Talin Rod Molecules Activates Vinculin Binding. Science 2009, 323 (5914), 638-641. 2.

Li, H. B.; Linke, W. A.; Oberhauser, A. F.; Carrion-Vazquez, M.; Kerkviliet, J. G.; Lu,

H.; Marszalek, P. E.; Fernandez, J. M., Reverse engineering of the giant muscle protein titin. Nature 2002, 418 (6901), 998-1002. 3.

Nedrud, J.; Labeit, S.; Gotthardt, M.; Granzier, H., Mechanics on Myocardium Deficient

in the N2B Region of Titin: The Cardiac-Unique Spring Element Improves Efficiency of the Cardiac Cycle. Biophys. J. 2011, 101 (6), 1385-1392. 4.

Baneyx, G.; Baugh, L.; Vogel, V., Fibronectin extension and unfolding within cell matrix

fibrils controlled by cytoskeletal tension. Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (8), 5139-5143. 5.

Ramirez, F.; Sakai, L. Y., Biogenesis and function of fibrillin assemblies. Cell. Tissue.

Res. 2010, 339 (1), 71-82.


17

Page 17 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6.

Rief, M.; Gautel, M.; Oesterhelt, F.; Fernandez, J. M.; Gaub, H. E., Reversible unfolding

of individual titin immunoglobulin domains by AFM. Science 1997, 276 (5315), 1109-1112. 7.

Carrion-Vazquez, M.; Marszalek, P. E.; Oberhauser, A. F.; Fernandez, J. M., Atomic

force microscopy captures length phenotypes in single proteins. Proc. Natl. Acad. Sci. U. S. A. 1999, 96 (20), 11288-11292. 8.

Fernandez, J. M.; Li, H. B., Force-clamp spectroscopy monitors the folding trajectory of

a single protein. Science 2004, 303 (5664), 1674-1678. 9.

Lannon, H.; Haghpanah, J. S.; Montclare, J. K.; Vanden-Eijnden, E.; Brujic, J., Force-

Clamp Experiments Reveal the Free-Energy Profile and Diffusion Coefficient of the Collapse of Protein Molecules. Phys. Rev. Lett. 2013, 110 (12), 128301. 10. Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G., THEORY OF PROTEIN FOLDING: The Energy Landscape Perspective. Annu. Rev. Phys. Chem. 1997, 48 (1), 545-600. 11. Wang, J.; Oliveira, R. J.; Chu, X. K.; Whitford, P. C.; Chahine, J.; Han, W.; Wang, E. K.; Onuchic, J. N.; Leite, V. B. P., Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding. Proc. Natl. Acad. Sci. U. S. A. 2012, 109 (39), 15763-15768. 12. Bryngelson, J. D.; Wolynes, P. G., Intermediates and barrier crossing in a random energy model (with applications to protein folding). J. Phys. Chem. 1989, 93 (19), 6902-6915. 13. Kawai, S.; Komatsuzaki, T., Effect of timescale on energy landscape: Distinction between free-energy landscape and potential of mean force. Phys. Rev. E. 2013, 87 (3), 030803.


18


Page 18 of 22

14. Jarzynski, C., Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 1997, 78 (14), 2690-2693. 15. Hummer, G.; Szabo, A., Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. U. S. A. 2001, 98 (7), 3658-3661. 16. Harris, N. C.; Song, Y.; Kiang, C. H., Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality. Phys. Rev. Lett. 2007, 99 (6), 068101. 17. Preiner, J.; Janovjak, H.; Rankl, C.; Knaus, H.; Cisneros, D. A.; Kedrov, A.; Kienberger, F.; Muller, D. J.; Hinterdorfer, P., Free energy of membrane protein unfolding derived from single-molecule force measurements. Biophys. J. 2007, 93 (3), 930-937. 18. Imparato, A.; Sbrana, F.; Vassalli, M., Reconstructing the free-energy landscape of a polyprotein by single-molecule experiments. EPL 2008, 82 (5), 58006. 19. Friddle, R. W., Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality - Comment. Phys. Rev. Lett. 2008, 100 (1), 019801. 20. Valle-Orero, J.; Eckels, E. C.; Stirnemann, G.; Popa, I.; Berkovich, R.; Fernandez, J. M., The elastic free energy of a tandem modular protein under force. Biochem. Biophys. Res. Commun. 2015, 460 (2), 434-438. 21. Valle-Orero, J.; Tapia-Rojo, R.; Eckels, E. C.; Rivas-Pardo, J. A.; Popa, I.; Fernández, J. M., Proteins Breaking Bad: A Free Energy Perspective. J. Phys. Chem. Lett. 2017, 8 (15), 36423647.


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22. Makarov, D. E., A Theoretical Model for the Mechanical Unfolding of Repeat Proteins. Biophys. J. 2009, 96 (6), 2160-2167. 23. Bonilla, L. L.; Carpio, A.; Prados, A., Protein unfolding and refolding as transitions through virtual states. EPL 2014, 108 (2), 28002. 24. Doi Masao , E. S. F., The Theory of Polymer Dynamics. Oxford Science Publications: 1988. 25. Zhang, Q.; Brujic, J.; Vanden-Eijnden, E., Reconstructing Free Energy Profiles from Nonequilibrium Relaxation Trajectories. J. Stat. Phys. 2011, 144 (2), 344-366. 26. Crommelin, D., Estimation of space-dependent diffusions and potential landscapes from mon-equilibrium data. J. Stat. Phys. 2012, 149 (2), 220-233. 27. Walther, K. A.; Grater, F.; Dougan, L.; Badilla, C. L.; Berne, B. J.; Fernandez, J. M., Signatures of hydrophobic collapse in extended proteins captured with force spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2007, 104 (19), 7916-7921. 28. Garcia-Manyes, S.; Dougan, L.; Badilla, C. L.; Brujic, J.; Fernandez, J. M., Direct observation of an ensemble of stable collapsed states in the mechanical folding of ubiquitin. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (26), 10534-10539. 29. Janovjak, H.; Struckmeier, J.; Muller, D. J., Hydrodynamic effects in fast AFM singlemolecule force measurements. Eur. Biophys. J. 2005, 34 (1), 91-96. 30. Berkovich, R.; Hermans, R. I.; Popa, I.; Stirnemann, G.; Garcia-Manyes, S.; Berne, B. J.; Fernandez, J. M., Rate limit of protein elastic response is tether dependent. Proc. Natl. Acad. Sci. U. S. A. 2012, 109 (36), 14416-14421.


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Page 20 of 22

31. Berkovich, R.; Garcia-Manyes, S.; Urbakh, M.; Klafter, J.; Fernandez, J. M., Collapse dynamics of single proteins extended by force. Biophys. J. 2010, 98 (11), 2692-2701. 32. Marko, J. F.; Siggia, E. D., Stretching DNA. Macromolecules 1995, 28 (26), 8759-8770. 33. Radford, S. E.; Dobson, C. M.; Evans, P. A., The folding of hen lysozyme involves partially structured intermediates and multiple pathways. Nature 1992, 358 (6384), 302-307. 34. Camacho, C. J.; Thirumalai, D., Minimum energy compact structures of random sequences of heteropolymers. Phys. Rev. Lett. 1993, 71 (15), 2505-2508. 35. Ptitsyn, O. B., Molten globule and protein folding. Adv. Protein Chem. 1995, 47, 83-229. 36. Elms, P. J.; Chodera, J. D.; Bustamante, C.; Marqusee, S., The molten globule state is unusually deformable under mechanical force. Proc. Natl. Acad. Sci. U. S. A. 2012, 109 (10), 3796-3801. 37. Chou, J. J.; Shakhnovich, E. I., A study on local-global cooperativity in protein collapse. J. Phys. Chem. B 1999, 103 (13), 2535-2542. 38. Sheinerman, F. B.; Brooks, C. L., Molecular picture of folding of a small alpha/beta protein. Proc. Natl. Acad. Sci. U. S. A. 1998, 95 (4), 1562-1567. 39. Hinczewski, M.; von Hansen, Y.; Dzubiella, J.; Netz, R. R., How the diffusivity profile reduces the arbitrariness of protein folding free energies. J. Chem. Phys. 2010, 132 (24), 245103. 40. Suzuki, Y.; Dudko, O. K., Biomolecules under mechanical stress: A simple mechanism of complex behavior. J. Chem. Phys. 2011, 134 (6), 065102.


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Page 21 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


41. Cossio, P.; Hummer, G.; Szabo, A., On artifacts in single-molecule force spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2015, 112 (46), 14248-14253. 42. Berkovich, R.; Mondal, J.; Paster, I.; Berne, B. J., Simulated Force Quench Dynamics Shows GB1 Protein Is Not a Two State Folder. J. Phys. Chem. B 2017, 121 (20), 5162-5173. 43. Gutin, A. M.; Abkevich, V. I.; Shakhnovich, E. I., Is burst hydrophobic collapse necessary for protein folding? Biochemistry 1995, 34 (9), 3066-3076. 44. Popa, I.; Fernandez, J. M.; Garcia-Manyes, S., Direct Quantification of the Attempt Frequency Determining the Mechanical Unfolding of Ubiquitin Protein. J. Biol. Chem. 2011, 286 (36), 31072-31079. 45. Carrion-Vazquez, M.; Oberhauser, A. F.; Fowler, S. B.; Marszalek, P. E.; Broedel, S. E.; Clarke, J.; Fernandez, J. M., Mechanical and chemical unfolding of a single protein: A comparison. Proc. Natl. Acad. Sci. U. S. A. 1999, 96 (7), 3694-3699. 46. Fantner, G. E.; Oroudjev, E.; Schitter, G.; Golde, L. S.; Thurner, P.; Finch, M. M.; Turner, P.; Gutsmann, T.; Morse, D. E.; Hansma, H.; Hansma, P. K., Sacrificial bonds and hidden length: Unraveling molecular mesostructures in tough materials. Biophys. J. 2006, 90 (4), 1411-1418. 47. Kohn, J. E.; Millett, I. S.; Jacob, J.; Zagrovic, B.; Dillon, T. M.; Cingel, N.; Dothager, R. S.; Seifert, S.; Thiyagarajan, P.; Sosnick, T. R.; Hasan, M. Z.; Pande, V. S.; Ruczinski, I.; Doniach, S.; Plaxco, K. W., Random-coil behavior and the dimensions of chemically unfolded proteins. Proc. Natl. Acad. Sci. U. S. A. 2004, 101 (34), 12491-12496.


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