Concurrent Atomic Force Spectroscopy

Force-spectroscopy by Atomic Force Microscopy (AFM) is the technique of choice to measure mechanical properties of molecules, cells, tissues and materials at the nano and micro scales. However, unavoidable calibration errors of AFM probes make it cumbersome to quantify modulation of mechanics. Here, we show that concurrent AFM force measurements enable relative mechanical characterization with an accuracy that is independent of calibration uncertainty, even when averaging data from multiple, independent experiments. Compared to traditional AFM, we estimate that concurrent strategies can measure differences in protein mechanical unfolding forces with a 6-fold improvement in accuracy and a 30-fold increase in throughput. Prompted by our results, we demonstrate widely applicable orthogonal fingerprinting strategies for concurrent single-molecule nanomechanical profiling of proteins.

The development of Atomic Force Microscopy (AFM) has enabled imaging the nanoscale with 2 unprecedented length resolution, revolutionizing nanotechnology, materials science, chemistry 3 and biology [1][2][3] . AFM is based on the detection of interaction forces between a sample and a 4 microfabricated cantilever, the force probe of the technique. Traditionally, low-scanning speeds 5 have limited the reach of AFM; however, recent developments involving miniaturized 6 cantilevers have achieved imaging at video frame rates, launching the field of high-speed AFM 7 4 . The ability of AFM to measure forces at the nano and micro scales can be exploited to 8 quantify mechanical parameters such as stiffness, viscoelasticity, or adhesion forces, while 9 simultaneously imaging surface topology 2,5, 6 . Due to its force sensitivity down to picoNewtons 10 (pN), AFM-based force spectroscopy, or simply atomic force spectroscopy, can also be used to 11 examine single-molecule dynamics and ligand-receptor interactions under force [7][8][9] , of relevance 12 for cellular stiffness, mechanosensing and mechanotransduction 10-13 . 13 14 A key limitation of atomic force spectroscopy stems from uncertain calibration of the spring 15 constant ( ) of the AFM cantilever, which is needed to determine force values 14 . Different 16 calibration methods to estimate have been developed, differing in their simplicity, damage 17 to the cantilever tip, experimental compatibility and associated uncertainty. Estimates of 18 calibration uncertainty up to 25% are usually reported 15 ; however, even higher inaccuracies can 19 result from defects in individual cantilevers, and from unpredictable changes in during 20 experimentation due to material deposition, mechanical drift and wear 7,16 .

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Force calibration uncertainties in AFM lead to inaccurate quantification of mechanical 23 properties, a situation that is worsened in modes where the elusive geometry of the cantilever tip 24 is required to extract mechanical information 17 . Indeed, relative AFM studies to characterize 25 mechanical modulation of proteins, materials and cells are challenging, since they necessitate 26 multiple experiments, each one affected by different calibration errors 18,19 . As a result, there is a 27 pressing need to develop methods that can overcome inaccurate AFM force calibration 18 . The 28 traditional approach to increase statistical power is to repeat experiments, since individual 29 calibration errors are more probable to be averaged out as more experiments are included in the 30 analysis 20 . The drawback is a considerable loss of throughput of the technique. 31 32 In theory, a manner to overcome calibration errors in relative atomic force spectroscopy is to 33 measure the samples concurrently in a single experiment, using one cantilever under the same 34 calibration parameters 21 . Indeed, mechanical characterization of several proteins in a single 35 experiment has been achieved using microfluidics, on-chip protein expression and force-36 spectroscopy measurements in custom-built atomic force/total internal reflection fluorescence 37 microscopes 22,23 . However, this advanced technology is not available to most AFM users, and 38 the extent of improvement in performance by concurrent AFM remains unexplored. 39 40 Here, we use error propagation analysis and Monte Carlo simulations to examine how force 41 calibration errors impact determination of mechanical properties of proteins by atomic force 42 spectroscopy, and demonstrate the remarkable improvement that stems from concurrent 43 measurements. Unexpectedly, we find that averaging results from multiple concurrent 44 experiments retains statistical power, leading to drastically improved accuracy and throughput 45 in the determination of relative mechanical properties by AFM. Prompted by our findings, we 46 have developed orthogonal fingerprinting (OFP) as a simple and widely applicable strategy for 47 concurrent single-molecule nanomechanical profiling of proteins. 48

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Interexperimental variation of mechanical properties obtained by traditional atomic force 2 spectroscopy 3 To understand how errors in calibration of atomic force microscopes lead to inaccurate 4 determination of mechanical properties, we have measured protein mechanical stability by 5 single-molecule force-spectroscopy AFM 7 ( Figure 1A, Supplementary Figure 1). This AFM 6 mode is very well suited to examine propagation of calibration errors since protein unfolding 7 forces are obtained directly from experimental data and do not depend on further modelling or 8 approximations.

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We first measured the resistance to mechanical unfolding of the same protein in different, 11 independently calibrated atomic force spectroscopy experiments. We produced a polyprotein 12 containing eight repetitions of the C3 domain of human cardiac myosin-binding protein C forces 24 . Despite the fact that both distributions are well defined (n > 115 events), the difference 20 in their mean unfolding force (∆ ) is 19% ( Figure 1A, right  Figure 4) 7 . Figure 1B shows the 45 simulated distribution of ∆ obtained from two independent experiments in which the same 46 protein is probed (200 unfolding events per experiment). It is remarkable that two mean 47 unfolding forces obtained in different cycles can differ by more than 25% (Supplementary 48 Figure 5A). Hence, although conservative, a mere 3.6% inaccuracy in cantilever calibration can 1 explain considerably higher differences in obtained in traditional atomic force 2 spectroscopy experiments. 3 Accuracy in ∆ obtained by concurrent atomic force spectroscopy is insensitive to 4 calibration uncertainty 5 We have used our Monte Carlo simulations to estimate the accuracy in ∆ achieved by 6 concurrent measurement of the mechanical stability of two proteins. Considering equal total 7 number of events and experiments, and a 3.6% calibration uncertainty, we find that the RSD of 8 the distribution of ∆ decreases from 5.0% to 3.2% when measurements are taken 9 concurrently ( Figure 1B). RSD values are further reduced at higher number of unfolding events, 10 as expected from better definition of the distribution of unfolding forces ( Figure 1C, 11 Supplementary Figure 5B). Unexpectedly, averaging multiple concurrent experiments leads to 12 reductions in RSD, despite the fact that each individual experiment is performed under different 13 calibration parameters ( Figure 1D). Increasing the number of events or experiments also results 14 in lower RSD values when proteins are probed in traditional, separate experiments ( Figure 1  15 C,D). We find that the relative improvement in RSD achieved by concurrent over traditional 16 atomic force spectroscopy increases with the number of unfolding events per experiment, and 17 remains fairly constant at increasing number of experiments ( Figure 1E). Hence, we conclude 18 that averaging independent atomic force spectroscopy experiments in which two proteins are 19 probed concurrently retains statistical power, even if those individual experiments are affected 20 by different calibration errors.

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All our simulations in Figure 1B-E were run considering 3.6% uncertainty in force calibration, 23 which is much smaller than usually reported 7,14,15,22 . Hence, we estimated the RSD of the 24 distribution of ∆ at increasing calibration uncertainties. As expected, higher calibration 25 uncertainties lead to much increased RSD in traditional atomic force spectroscopy, whereas the 26 RSD of concurrent distributions remains insensitive to calibration uncertainty ( Figure 1F), even 27 when data from several independent experiments are averaged (Supplementary Figure 6A).

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Orthogonal fingerprinting enables concurrent mechanical characterization of proteins by 30 atomic force spectroscopy 31 Our simulation results show that under a modest 3.6% uncertainty in force, concurrent atomic 32 force spectroscopy measurements can reach the same level of accuracy in ∆ with 2-4 times 33 less experiments than the traditional approach ( Figure 1D). Furthermore, at high values of 34 calibration uncertainty, the accuracy in ∆ of concurrent measurements can be 6 times higher 35 than in the traditional approach ( Figure 1F). These remarkable improvements in throughput and 36 accuracy prompted us to design a general strategy for concurrent measurements of mechanical 37 properties of proteins that can be readily applied to any AFM-based force spectrometer.

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Having methods to identify single-molecule events is a fundamental requirement of force-40 spectroscopy AFM. In the case of mechanical characterization of proteins, this need is fulfilled 41 by the use of polyproteins, which provide molecular fingerprints that easily discriminate single-42 molecule events from spurious, non-specific interactions 26,27 (Supplementary Figure 3). As 43 exemplified in Figure 1A, mechanical unfolding of polyproteins produce repetitive events 44 whose length fingerprints the domain of interest. If two polyproteins are to be measured 45 concurrently in the same experiment, it is imperative that they have different fingerprinting 46 unfolding lengths. Here, we propose a widely applicable manner of achieving such orthogonal 47 fingerprinting (OFP) through the use of heteropolyproteins, in which marker proteins are fused 1 to the proteins of interest 28 . Since OFP identifies proteins through the unfolding length of the 2 marker domains, proteins of interest to be compared can have the same unfolding length (e.g. 3 mutant or biochemically modified proteins). To test whether heteropolyproteins can be 4 employed to achieve OFP during concurrent measurement of proteins by atomic force 5 spectroscopy, we have measured the mechanical stability of the C3 domain in different 6 polyprotein contexts. 7 8 We first followed a single-marker strategy using the heteropolyprotein (C3-L) 4 (Figure 2, 9 Supplementary Figure   and 24 nm events they contain. Our results show that a gating criterion of n(16nm) = 0 and 3 n(24nm) > 2 unambiguously identifies traces coming from (C3) 8 , whereas traces resulting from 4 (C3-L) 4 can be safely assigned when n(16nm) > 1 and 0 < n(24nm) < 5 ( Figure 2B, right). We 5 analyzed 17 such TFP experiments and obtained distributions of unfolding forces for C3 in the 6 context of both polyproteins, which we found to be very similar ( = 90. 7 and 88.4 pN for 7 the homo and the heteropolyproteins, respectively, Figure 2C, Table). We used our Monte Carlo 8 simulations to estimate the RSD associated to ∆ that is expected from the actual number of 9 experiments and events obtained ( Figure 2C, Table, Supplementary Figure 7A). 10 11 Following validation of the polyprotein gating criterion ( Figure 2B), we measured (C3) 8 and 12 (C3-L) 4 concurrently in OFP experiments. Single-molecule traces were classified according to 13 the number of 16 and 24 nm steps they contain, and sorted as coming from the (C3) 8 or (C3-L) 4 14 before analysis of unfolding data ( Figure 2D). As in the case of TFP experiments, the unfolding 15 probability distributions of C3 in the context of (C3) 8 and (C3-L) 4 are very similar ( = 96.3 16 and 93.4 pN for the homo and the heteropolyproteins, respectively, Figure 2E, Table). However, 17 only 5 OFP experiments were required to reach a lower RSD than in TFP, a 3 times higher 18 speed of data acquisition ( Figure 2C,E, Table, Supplementary Figure 7A). 19 20 Dual-marker orthogonal fingerprinting overcomes confounding protein dimerization 21 In the atomic force spectroscopy experiments reported in Figures 1 and 2, polyproteins are 22 picked up by the AFM cantilever through non-specific physisorption. Hence, experimental 23 traces can contain different number of unfolding events ( Figure 2B). Non-specific protein 24 pickup also leads to the occasional appearance of traces containing more unfolding events than 25 engineered domains in the polyprotein, an effect that results from polyprotein dimerization 29 . 26 For instance, in Figure   probability that some heterodimers are included in the gating region of (C3-L) 4 . As a result, a 1 fraction of events coming from (C3) 8 could be mistakenly assigned to (C3-L) 4 .

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In general, the extent of protein dimerization in single-molecule AFM is dependent on the 4 particular experimental conditions. Hence, heterodimerization poses a challenge to OFP, whose 5 extent may vary depending on the system to study. However, we hypothesized that difficulties 6 coming from protein dimerization could be overcome by using a second protein marker, since 7 traces originating from dimers would be fingerprinted by the presence of both marker proteins. 8 We chose the protein SUMO1 as a second marker because its unfolding length is different from 9 those ones of C3 and protein L 30 . We engineered the heteropolyprotein (C3-SUMO1) 4 and 10 pulled it in the AFM (Supplementary Figure 2). Two population of unfolding steps, at 20 nm 11 and 24 nm are detected, corresponding to the unfolding of SUMO1 and C3, respectively 12 (Supplementary Figure 3C). 13 14 Having two marker proteins enables gating criteria that are based exclusively on the presence of 1 the marker domains, in a manner that protein dimers can be identified and excluded from the 2 analysis ( Figure 3A,B, Supplementary Figure 8). According to experiments in which (C3-L) 4 3 and (C3-SUMO1) 4 are measured separately, we used the gating criterion that n(16nm) > 1 and 4 n(20nm) = 0 marks unfolding of (C3-L) 4 , and n(20nm) > 1 and n(16nm) = 0 defines unfolding 5 of (C3-SUMO1) 4 , which only misclassifies 1 out of 136 traces. Following this gating criterion, 6 we determined the distribution of unfolding forces of C3 in the context of (C3-SUMO1) 4 and 7 compared the results with C3 unfolding in the context of (C3-L) 4, both in TFP and OFP ( Figure  8 3C,D, Table). Although the of C3 in (C3-L) 4 appears to be 12% higher in TFP experiments An error propagation model to further improve performance of concurrent atomic force 16 spectroscopy 17 Our Monte Carlo simulations show that the improvement in accuracy in ∆ of concurrent 18 atomic force spectroscopy is preserved when multiple AFM experiments are averaged, and is 19 independent of calibration uncertainty ( Figure 1E,F). In apparent contradiction, we found that 20 the RSDs of the distributions of ∆ calculated for OFP concurrent datasets increase with 21 calibration uncertainty (Table)

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, 50, results in a dramatic increase of RSD especially at higher calibration 1 uncertainties ( Figure 4A). Under these unbalanced conditions, the performance of the 2 concurrent strategy diminishes drastically and the obtained RSD approaches the one obtained in 3 traditional atomic force spectroscopy ( Figure 4A).

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Since unbalanced data distributions result in poorer performance of concurrent atomic force 6 spectroscopy, we examined whether balancing datasets through data removal could result in 7 improved accuracy in ∆ . We did Monte Carlo simulations of 2 concurrent experiments in 8 which , , 50, i.e. we trimmed 100 extra events per protein so that both 9 experiments had the same number of unfolding events for both proteins. As expected, the RSD 10 of the distribution of ∆ after trimming becomes independent of the calibration uncertainty 11 ( Figure 4A). Even though having less events per experiment results per se in poorer definition 12 of distributions of unfolding forces ( Figure 1C, Supplementary Figure 5B), the RSDs of the 13 distributions of ∆ obtained using trimmed datasets become lower than in the case of the 14 more populated, but unbalanced, dataset at calibration uncertainties higher than 6% ( Figure 4A).

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Concurrent single-molecule atomic force spectroscopy datasets are expected to be unbalanced, 17 since the different proteins are picked up randomly by the AFM cantilever (Supplementary 18 Table 1). We have tested whether balancing our experimental OFP datasets also leads to 19 improved accuracy in ∆ . To this end, we have removed unfolding events so that every OFP 20 experiment verifies the balanced condition . Using Monte Carlo simulations, 21 we estimate that the RSD of the distribution of ∆ obtained from the trimmed OFP datasets 22 becomes lower than the original RSD also at calibration uncertainties higher than 6-7% 23 (Supplementary Figure 7). In the two OFP datasets analyzed, the differences between the 24 balanced and the unbalanced conditions are less prominent than in the case of artificial datasets 25 consisting of only two experiments ( Figure 4A). Indeed, we find that the extent of improvement 26 in performance by dataset trimming decreases with the number of experiments (Supplementary 27 Figure 9). Hence, we recommend that improvement in performance by balancing datasets is 28 estimated on a case-by-case basis using Monte Carlo simulations fed with actual experimental 29 data, as we have done here.
In this report, we address a main limitation of force-spectroscopy by AFM that arises from 33 uncertain calibration of cantilevers. We show, for the first time to our knowledge, that 34 concurrent measurements result in remarkable improvements in the determination of relative 35 mechanical properties by atomic force spectroscopy. We propose that concurrent AFM 36 measurements of relative mechanical properties of cells, materials and tissues can result in gains 37 in performance similar to those described here for proteins. Remarkably, concurrent strategies 38 can be achieved by adapting already available atomic force spectroscopy techniques based on 39 fluorescent labelling of cells or polymer blends 31,32 .

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Our work demonstrates that concurrent single-molecule atomic force spectroscopy outperforms 42 traditional methods in three key aspects ( Figure 5 experiments, finding a value of up to 11% 33 . However, neither of these approaches addresses 3 more fundamental assumptions of the calibration procedures, or difficult-to-detect defects in 4 individual cantilevers, which lead to higher calibration uncertainties 34 . Indeed, we propose that 5 concurrent atomic force spectroscopy strategies, in combination with further theoretical 6 developments, can be key to exploit the advantages of next generation cantilevers, which are 7 pushing the AFM into ranges of force, speed, stability and time resolution at the expense of 8 more challenging force calibration 14,[35][36][37][38][39] . It is worth mentioning that in concurrent strategies 9 where the proteins are randomly picked up and mechanically probed, changes in during 10 experimentation affect the different proteins equally leading to preserved high accuracy in 11 ∆ . 12 13 (ii) Concurrent atomic force spectroscopy shows much improved accuracy in ∆ 14 ( Figures 1E,F, 4A,B, 5). Keeping the speed of data acquisition constant at high calibration 15 uncertainties, the accuracy achieved by concurrent measurements can be 6 times higher than in 16 traditional atomic force spectroscopy (Supplementary Figure 6B). 17 18 (iii) Concurrent atomic force spectroscopy leads to high-throughput relative 19 mechanical characterization of proteins ( Figure 5). We estimate that concurrent atomic force 20 spectroscopy can obtain the data needed for the same accuracy in ∆ over 30 times faster 21 than traditional measurements at high calibration uncertainties (Supplementary Figure 6C).

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The increase in throughput and accuracy in ∆ of concurrent atomic force spectroscopy 24 come at the expense of each other. Hence, depending on the goals of a particular study, the 25 experimenter can choose to favor one or the other, or to find a balance between both. For 26 instance, in Figure 4B, we show that different gains in accuracy and throughput can be achieved 27 depending on the number of concurrent experiments carried out to compare unfolding forces of 28 two proteins. 29 30 4C). An advantage of OFP over a previous concurrent strategy based on spatial separation of 5 proteins 22,23 is that it can be readily implemented in any atomic force spectroscopy setup. In 6 addition, different fingerprinting lengths in OFP provide additional reassurance of the identity 7 of the probed proteins. In this regard, OFP is very well suited to compare mechanical properties 8 of proteins with similar unfolding lengths. Hence, OFP can define mechanical hierarchies in 9 multidomain proteins with higher accuracy, and lead to better descriptions of the mechanical 10 effects of mutations, posttranslational modifications and the chemical environment on proteins 11 and their complexes 40-45 . Indeed, our highly accurate OFP experiments show that the 12 mechanical stabilities of the C3 domain in the context of a (C3) 8 homopolyprotein, or within a 13 (C3-L) 4 or (C3-SUMO1) 4 , are very similar ( Figures 2E, 3D, Table). The fact that the 14 mechanical stability of C3 does not depend on the neighboring marker domains lends strong 15 support to the use of heteropolyproteins in force-spectroscopy AFM 28,46-48 . Another advantage 16 of OFP is that orthogonally fingerprinted proteins can be purified simultaneously 17 (Supplementary Figures 2, 10), resulting in extra savings in working time and reagents and 18 ensuring equal experimental conditions for both proteins ( Figure 5). Taking into account the full 19 experimental workflow of single-molecule atomic force spectroscopy experiments, we estimate 20 that the increase in throughput described in Figure  We envision two features of OFP that can be further optimized. Since the relative performance 1 of OFP is better at high number of events per experiment ( Figure 1E, Supplementary Text 4), 2 we propose that better improvements can be achieved by taking advantage of highly efficient 3 high-strength single-molecule tethering methods 23,29,49 . In addition, OFP strategies hold the 4 promise of further parallelization by the use of multiple marker proteins. Importantly, in those 5 cases where proteins have different unfolding lengths, concurrent single-molecule AFM 6 measurements are of immediate application leading to the increase in accuracy and throughput 7 described here 21 . Examples that could benefit from application of concurrent measurements 8 include examination of the effect of disulfide bonds, protein misfolding, multimerization, and 9 pulling geometry in the mechanical stability of proteins and their complexes 50-57 , and 10 determination of rates of force-activated chemical reactions 58  The kinetic Monte Carlo to obtain distribution of unfolding forces compares a random number 45 with the instantaneous probability of unfolding at a given force. If the unfolding probability is 46 higher than the random number, unfolding is considered to happen at that force. Instantaneous 47 probabilities of unfolding are calculated following a linear approximation 60 : 48 In Equation 3, is the number of domains that remain folded at a particular force, is the error 4 in force due to the uncertain cantilever calibration (Supplementary Text 2) and ∆ is the time 5 step of the Monte Carlo. In the simulations, we used ∆ = 10 -4 s, which ensures validity of the 6 linear approximation, since ∆ is kept under 0.05 (Supplementary Text 5). Pilot 7 simulations show that results do not vary if we use a smaller time step of 10 -5 s. 8 9 Protein production and purification 10 The cDNAs coding for the C3-L and C3-SUMO1 constructs were produced by gene synthesis 11 (NZY-Tech and Gene Art, respectively). The cDNA coding for the C3 domain was obtained by 12 PCR. cDNAs coding for polyproteins were produced following an iterative strategy of cloning 13 using BamHI, BglII and KpnI restriction enzymes, as described before 27 achieved by size-exclusion chromatography in an AKTA Pure 25L system using a Superose 6 22 Increase 10/300 GL or a Superdex 200 Increase 10/300 GL column (GE Healthcare). The 23 proteins are eluted in 10 mM Hepes, pH 7.2, 150 mM NaCl, 1 mM EDTA, which is also the 24 buffer used in atomic force spectroscopy experiments. Purity of samples was evaluated using 25 SDS-PAGE gels (a typical result is shown in Supplementary Figure 2).

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Force-spectroscopy by AFM 28 Single-molecule AFM measurements were obtained in an AFS setup (Luigs & Neumann) 29 according to established protocols 7 .We used silicon nitride MLCT-C cantilevers with a 60-nm 30 gold back side coating (Bruker), which we calibrated according to the thermal fluctuations 31 method 62 . Typical spring constant values ranged between 15 and 20 pN/nm. To run single-32 molecule AFM experiments, a small aliquot (2-10 L) of the purified protein is deposited on the 33 surface of a gold coated cover slip (Luigs & Neumann), or directly into the Hepes buffer 34 contained in the fluid chamber of the AFS. The cantilever is brought in contact to the surface for 35 1-2 s at 500-2000 pN to favor formation of single-molecule tethers. Then, the surface is 36 retracted to achieve the set point force. If a single-molecule tether is formed, the force is 37 increased linearly at 40 pN/s for 5 s while the length of the polyprotein is measured. This 38 protocol ensures full unfolding of C3, L and SUMO1 domains (Supplementary Figure 3). 39 Unfolding events are detected as increases in the length of the protein. In the initial 40 characterization of polyproteins, we analyze all traces that contain at least two events of the 41 same size, which allows to set a fingerprinting length for the domains (24 ± 1 nm for C3, 16 ± 1 42 nm for protein L, and 20 ± 1 nm for SUMO1, see Supplementary Figure 3). For the rest of the 43 analyses, we only considered traces that contain fingerprinting unfolding lengths. Unfolding 44 forces were recorded and plotted as cumulative distributions. values were obtained from 45 Gaussian fits to histograms of unfolding forces. Force inaccuracy due to laser interference was 46 lower than 40 pN in all experiments (peak-to-peak height in baseline force-extension 47 recordings) 7 . propagation of calibration errors. 20 21 Competing financial interests 22 The authors declare no competing financial interest.

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Resources 25 The code used for the Monte Carlo simulations is available as online Supplementary Material. 26 27