Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation

Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation Sabyasachi Rakshit, Pritam Saha, Vishavdeep Vashisht, Ojas Singh, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3887774/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Jan, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Single-point mutations are pivotal in molecular zoology, shaping functions and influencing genetic diversity and evolution. Here we study three such genetic variants of a mechano-responsive gating-spring protein, cadherin-23, that uphold the structural integrity of the protein, but showcase distinct genotypes and phenotypes. All-atom simulations indicated marginal deviations in the transient intra-domain interactions among the variants leading to variations in the anti-cross correlated motions among constituent β-strands. In nature, the variants experience declining functions with aging at different rates. We expose these variants to constant and oscillatory forces using magnetic tweezer, and measure variations in stochastic folding dynamics. All variants exhibit multiple microstates under force. However, the protein variant with higher number of intra-domain contacts exhibits transitions among the heterogeneous microstates for larger extent of forces and persisted longer. Conversely, the protein variant with weaker inter-strand correlations exhibits greater unfolding cooperativity and faster intrinsic folding, although its folding-energy landscape is more susceptible to distortion under tension. Our study thus deciphers the molecular mechanisms underlying the variations in force-adaptations and propose a mechanical relation between genotype and phenotype. Biological sciences/Biophysics/Single-molecule biophysics Biological sciences/Biophysics/Molecular biophysics/Deformation dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Mechanical force is now well-established as a cue in developmental biology 1 . This recognition has driven efforts to comprehend how proteins engaged in mechanotransduction respond to input force-stimuli. Despite this, the utilization of mechanical properties as an evolutionary determinant remains less firmly established within the realm of molecular zoology 2 . Notably, the correlation between the magnitude of mechanical forces and protein structure can be easily drawn. β-strand-rich proteins, in physiology, are naturally selected against large mechanical forces 3 . Examples include silk proteins that surpass the extreme tensile strength of a steel 4 , muscle protein titin 5 , cadherins as gating-spring in hearing 6 – 11 , and many more. β-strands in proteins undergo strongly anticorrelated, ultrafast-frequency (in THz) breathing motions 12 , 13 . Theoretically such global motions in β-strands are quantified 14 and attributed to force-adaptation that helps proteins to regain conformations after mechanical perturbations 12 , 14 , 15 . However, the empirical effort to connect these breathing motions in β-rich proteins to force-adaptation and molecular zoology remains lacking. The most effective approach to study force-adaptation in proteins involves subjecting them to tension and examining the protein-folding funnel using single-molecule force spectroscopy 16 – 21 . Tweezer-based force probes along ultrafast atomic force spectrometers, have identified several microstates in the protein-folding funnel 16 – 18 , 20 . Theoretical models with simultaneous use of all-atom simulations have also provided the molecular resolution of the microstate structures and developed the microscopic model of protein-folding 22 – 26 . However, the search of physical parameters that correlate the force-adaptation of proteins with the microscopic protein folding model continues. Along this line, we set our objective to identify the parameters that equip proteins for diverse mechanical environments and may potentially contribute to the process of molecular evolution. We experiment with a mechanosensing protein, Cadherin-23 (Cdh23), that possesses numerous β-strand-rich extracellular domains 27 . Cdh23 is a tip-link protein that actively participates in the mechanotransduction of hearing (Fig. 1 a,b) 8 , 9 , receives force pulses of various intensities and frequencies during the lifetime of a host 28 , 29 . Notably, the protein is also one of the loci for multifactorial age-induced / noise-induced hearing loss 28 – 33 , implicating the temporal loss of protein viscoelasticity with aging and, thus the loss of sensory abilities. The overarching objective of this research is to identify parameters that equip proteins for diverse mechanical environments, necessitating force adaptation and potentially contribute to the process of molecular evolution. We used three variants of Cdh23 that reflect different hearing phenotypes in physiology. Two wildtype variants of Cdh23, S47 and V47, serve as gating-spring and mediate sustained hearing in different environments. The mutant variant, Cdh23 P47, however, reflects a detrimental effect with time and causes progressive hearing loss in mice. In short, both S47 and V47 variants are naturally selected for sustained hearing under periodic tension, while P47 is rejected. In this study, we use these three structurally near identical phenotypic and genotypic variants of Cdh23 and probe their force-adaptations directly using our laboratory-built magnetic tweezer (MT). MT enabled us to capture the microstates in the folding energy landscape under small mechanical perturbations ranging from 4 pN – 40 pN, and at a high spatial resolution of nanometres (~ 5 nm) and temporal resolution of milliseconds. Further, we devised a covalent tethering of protein variants with the glass coverslips and the magnetic beads to perform the unfolding-refolding studies at variable tensile forces repetitively and measure the stochasticity in the folding dynamics for an extended period. Moreover, here we aim to shed light into the force-adaptation of proteins to oscillatory input forces by monitoring the stochastic folding dynamics of a single protein using an effective and robust MT. Results Three variants of Cdh23 as model protein. We chose the first extracellular (EC1) domain of Cdh23 as the model protein. Cdh23 EC1 consists of nine β-strands interconnected by reverse β turns, 3 10 α-helix, and random coils (Fig. 1 c) 15 , 34 . We used three variants, Cdh23 EC1 (S47), Cdh23 EC1(V47), and Cdh23 EC1(P47), with marginally different native packing densities (Fig. 1 d, supplementary Fig. 1), long-range H-bond networks (Fig. 1 d, supplementary Fig. 1), and different anticross-correlated crankshaft types motions among β-strands 15 (supplementary Fig. 1). Cdh23 EC1(S47) is a wildtype variant conserved for a majority of the species, including Homo sapiens (Hs), whereas Cdh23 EC1 (V47) is another wildtype variant conserved in lower order vertebrates like Callorhinchus milii (fish), Gekko japonicus (reptiles), anser cygnoides domesticus (Swan goose), Alligator mississippiensis (crocodile reptile), Gallus gallus (ave) 15 . Evolutionarily these species may be in a lower order than sapiens, a majority of them possess better hearing sensitivity at a lower frequency range than humans 35 , 36 . Further, some of these lower vertebrates require hearing at low-air pressure (at high altitude for swans) or under-water pressure (for alligators) where the noise threshold is high 37 . Moreover, the evolutionary trend for proteins may not correlate with the ranks of the expressors. In line, Cdh23 EC1(V47) possesses the highest number of native contacts, long-range H-bonds, and thus most robust cross-correlated motions among β-strands 15 . The last variant is Cdh23 EC1(P47) which is a mutant-variant of Cdh23 EC1(S47) that features a progressive hearing loss (PHL) phenotype in mice 38 . PHL is an aggressive form of hearing-loss with aging where a patient suffers complete hearing loss at a very early age (less than 20 years in humans) 35 , 39 . Considering native packing, Cdh23 EC1(P47) ranks last among the three variants (Fig. 1 d, 1 e). Reportedly, V47 shows the highest resistance against thermal and chemical denaturants, whereas P47 is the least 15 . In general, serine to proline mutation isn’t unique for Cdh23, relatively abundant with phenotypes 40 . Even for mechanosensitive Titin proteins, Ser22 to Pro mutation is reported with a phenotype of cardiomyopathy 41 . Covalent tethering of proteins and MT. To monitor the responses of protein variants to small tensile forces, we force-clamped the chimeric polyprotein constructs using MT. A detailed description of the MT including hardware, resolution, instrument software and analysis software are described in the methods and supplementary Figs. 2–8. Two repeats of Cdh23 EC1 variants were recombinantly sandwiched between a trimer of I27 domain at the C-terminus and a monomeric I27 domain at the N-terminus (Fig. 2 a). I27 is the 91st Ig domain of cardiac muscle protein, titin, and is extensively used as marker in single-molecule force spectroscopy. Further, the mechanical stability of I27 is significantly higher than all three variants of Cdh23 EC1 18,19 (Supplementary Fig. 9). Trimer of I27 domains was attached to the glass-coverslip, and the I27 monomer at the N-terminus was attached to the paramagnetic bead, both covalently using sortase-mediated enzymatic stapling 42 (Methods). The assymmetry in the constructs is primarily to ease out the DNA recombinant process. For studying mechanostability, we clamped the protein variants to a range of forces for 5 minutes from a resting force of 4 pN and monitored the change in lengths ( ΔL ) from the jumps in bead positions in real-time (Supplementary Fig. 10–11). To quantitatively estimate the dwell time of steps, we performed ‘Autostepfinder’, a widely used step-finder protocol that is based on the mean standard deviation model 43 . Figure 2 depicts the typical force-clamp traces for all three variants. As anticipated from the ensemble thermal and chemical stability studies 15 , we measured the weakest force-resistance for Cdh23 P47 featuring force-induced extensions between 5 pN – 15 pN, followed by Cdh23 S47 between 13 pN − 25 pN, and strongest for Cdh23 V47 between 19 pN − 38 pN (Fig. 3 , Supplementary Fig. 11–12). Irrespective of the force-resistance, we identified numerous microstates for all the variants during unfolding-refolding transitions at small clamping forces (Supplementary Fig. 13). To characterize the microstates, we measured the length-change ( ΔL ) for each step and plotted them as distributions (Methods and Fig. 2 c, d, e supplementary Fig. 10, 13). The histograms of ΔL for all variants followed comparable trend, narrow distributions at lower forces, wide at intermediate forces reaching saturations, and finally sharp distributions at very high forces (supplementary Fig. 10). The widths of the distributions indicate the extent of reversible transitions among microstates under tension while the number of peaks in the distributions infers the number of microstates (extent of heterogeneity). It appears that the heterogeneity in microstates is consistent among all variants; nonetheless, variations in width indicate substantial differences in their capacity to withstand force reversibility. To emphasize the force-tolerance of microstates across different variants, we plotted the fraction of states or probability of states as they survive at the clamping forces (Fig. 3 ). For simplicity, we used only 3-states, a native or folded state (with 0 nm ≤ ΔL ≤ 15 nm), a complete denatured or unfolded state (45 nm ≤ ΔL , maximum x(F)) and a cluster of intermediate states (15 nm ≤ ΔL ≤ x(F)). Notably, the end-to-end extensions, x(F), with force 44 (Fig. 4 d, Supplementary Fig. 10) of all protein variants featured Worm-like chain (WLC) behaviour. x(F) defines the extent of unfolding and, thus marks the final denaturant states at the respective clamping forces (Supplementary Fig. 10–11). The probability of the states at respective force-clamps was estimated from the dwell time of each state, normalized to the total clamping time. We obtained a sigmoidal transition for the probability of folded state with force for all variants. The transitions from native to unfolded states occurred at different critical forces (F crit ), lowest for P47 (7.6 ± 0.1 pN) and largest for V47 (23.7 ± 0.2 pN). However, we noticed different widths ( ΔF ) and slopes of the transitions across variants. We highlighted these regions with light green boxes (Fig. 3 ). The green boxes marked the co-existence of all 3 states, indicating the force-range at which the protein-variants undergo reversible transitions between numerous conformational microstates. The critical force ( F crit ) of transition is a measure of force-resistance, while the width of the transitions ( ΔF ) gauges the range of force tolerance among microstates. A wider width implies greater shock-absorbing capability, force dispersion, or ductility. Considering both the critical force of transitions and the width of the distributions, we evaluated the spectrum of adaptability to external forces. Notably, the V47 variant demonstrates the highest degree of adaptability, whereas the P47 variant shows the least. Next, we mapped the probability of the open state of all three variants and fit the rise in states to linear equation, excluding the force-value points with no unfolding probability (Fig. 3 c). The slope gives quantitative estimation of protein’s unfolding cooperativity. Conceptually, a completely cooperative unfolding will show a strict two-step transition with an infinite slope, whereas the completely non-cooperative transition will have slope of 0. We obtained the slope for P47 as 0.15 ± 0.01/pN, S47 as 0.09 ± 0.01/pN, and V47 as 0.05 ± 0.01/pN, resulting the order of unfolding-cooperativity as, P47 > S47 > V47. Overall, our data from force-clamp experiments indicate that Cdh23 V47, which contains the most densely packed network of intra-domain interactions, is mechanically the most stiff yet possesses the most disseminating ability of tensile forces. We, therefore, infer that higher crankshaft or contact order transforms β-rich proteins to more ductile under tensile forces, however, without causing any permanent damage. The inter β-strand interactions serve as shock-absorber and resist elongation from mechanical inputs. Effect of intra-domain contacts in folding rates and force tolerance Contact-orders that estimate the extent of native-contacts of a protein in native state, contribute to the folding dynamics of proteins. Further, mechanoresponsive proteins undergo unfolding-folding under tension in physiology 45 – 47 . The folding dynamics of the mechanoresponsive proteins are, thus functionally important. We, therefore, set to decipher the effect of inter domain interactions of a protein in the folding and unfolding kinetics. We performed a dual-step force-clamp spectroscopy with a monomer of Cdh23 EC1 domain parsed between I27 domains as -Nterm-(I27) 3 -EC1-I27-Cterm (Fig. 5 ). The use of a monomeric domain enabled us to measure the kinetics for direct transitions from the native state to the complete denatured state and vice versa. The resting force was set to 4 pN. Subsequently, the protein variants were individually clamped at varying constant forces (19–38 pN for S47 variant, 11–19 pN for P47 variant, and 23–38 pN for V47 variant) for 30–60 seconds and monitored the survival time till complete unfolding. We excluded the extensions below 5 nm in the analysis due to the resolution limit in our measurements (Supplementary Fig. 3). After each force-clamp, we subjected the variants to a high tensile force of 38 pN for 15 seconds to ensure complete extension prior to refolding. For refolding, we clamped the proteins at low forces, 11 − 4 pN for S47 variant, 8 − 4 pN for P47 variant, and 19 − 9 pN for V47 variant, respectively. We completed the cycle by quenching the force to 4 pN. For each variant, we monitored a minimum of 25 different beads (Supplementary Table 1). The survival probabilities of the folded and unfolded states were estimated from the dwell time (Fig. 5 ). We deduced the lifetimes of folding and unfolding from the single exponential decay fit to corresponding survival probabilities (Fig. 5 b) (Supplementary Table 1) and obtained the force-induced on-rate and off-rate data (Fig. 5 d). Subsequently, the variation in rates with force were fit to Bell’s model 48 and obtained the intrinsic kinetic parameters, \({k}_{0}^{f/uf}\) (intrinsic-rate at zero force, ‘f’ represents folding and ‘uf’ refers to unfolding) and \({x}_{}^{f/uf}\) (the distance to the transition state) (Fig. 5 c,d and Supplementary Table 2). Though intrinsic fold-rates at the ‘no-force’ condition may not be physiologically relevant for force-sensors, we measured the fastest unfolding rate for P47 and the slowest for V47 (Supplementary Table 2). We measured a similar trend in the folding kinetics as well, fastest refolding for P47 (52.45 ± 32.52 s − 1 ) and the slowest for V47 (0.21 ± 0.00 s − 1 ) among the three, infering that a protein with least intra-domain interactions forms the native state fastest. The susceptibility of proteins towards force-induced unfolding(uf)-folding(f), however, depends on the distance to transition states, \({x}_{}^{f/uf}.\) \({x}_{}^{f}\) is negative in sign as folding is against the force vector (Supplementary Table 2). A higher \({x}_{}^{f}\) diminishes the folding probability under tension by increasing the barrier-height ( \({E\left(F\right)= E}_{A}- {\overrightarrow{F}.\overrightarrow{x}}_{\beta }^{f}\) ), whereas a higher \({x}_{}^{uf}\) increases the unfolding probability by reducing the potential barrier height under tension. We measured the longest \({x}_{}^{f/uf}\) for P47 ( \({x}_{}^{f}\) ~ -35.7 ± 4.1 Å and \({x}_{}^{uf}\) ~ 3.0 ± 0.2 Å) and the shortest for V47 ( \({x}_{}^{f}\) ~ -2.5 ± 0.0 Å and \({x}_{}^{uf}\) ~ 2.3 ± 0.7 Å), indicating that the mechanical tension is most vulnerable for P47 and least for V47 (Fig. 5 d). Time-dependent adaptation against fatigue while receiving repetitive force pulse We noted that the protein variants undergo stochastic transitions among microstates under constant tension. We wanted to study how do these stochastic transitions follow the oscillatory force input as we percieve from sound during hearing. Does the stochastic transitions during folding resonate with the external force pulses, allowing biomolecules to fold faster? Or do we capture, molecular fatugue, a delay in response to external frequency. Time dependent change in mechanical phenomena of a protein is generally defined as molecular-fatigue which arises from the repetitive stretch and release cycle of the protein 49 , 50 . We, therefore, exposed the protein variants to a cycle of high force and low-force (4 pN), repetitively with a periodicity of 15 seconds. The high-forces were set differently, 12.8 ± 0.1 pN for S47, 7.6 ± 0.1 pN for P47, and 23.7 ± 0.2 pN for V47, where all microstates coexisted for the respective variants (Fig. 6 a). The critical forces of unfolding and refolding are the equilibrium force obtained from the chevron plots (Fig. 5 c). We noticed two distinct unfolding patterns, direct unfolding (unfolds directly along with the initial stretch) and delayed stepwise unfolding (goes through the metastable states before complete unfolding) (Fig. 6 a). Counterintuitive to the folding-kinetics pattern, we observed the more frequent direct unfolding of P47 (20.7%) than S47 (11.3%) and V47 (6.25%), respectively. We relate the direct unfolding events with the delay in folding in the previous force-cycle, a feature of molecular fatigue. Overall, we infer that proteins with low force- adaptibility, suffer faster mechanical fatigue. More importantly, a direct unfolding relates to ‘no force-buffer’ and conveys the input mechanical signal directly, exposing the sensory organs to potential damage. Discussion All three variants; S47, P47, V47; exhibit closely aligned static structures, characterized by a predominance of β-strands with minimal distinctions in contact orders and inter β-strand interactions. Notably, the variations among these variants are remarkably localized. Specifically, while S47 and V47 are positioned at the termini of a β-strand, P47 induces a reduction in the strand length and an extension of the turn connecting two anti-parallel β-strands (refer to Fig. 1 c). It is worth emphasizing the significance of turns in β-rich proteins, serving as the foundational elements of β-strands and playing crucial roles as regulators of inter-β-strand interactions 51 , 52 . The introduction of Proline (Pro) at position 47 introduces a constrained torsion angle in the turn, resulting in comparatively weaker β-strand packing among the three variants. This, in turn, leads to a diminished anti-cross correlated crankshaft-type motion among β-strands 51 , 52 . Understanding how these seemingly trivial alterations in the protein's topology exert a substantial impact on its mechanics constitutes the primary focus of this investigation. The subsequent sections will delve into the implications of these structural variances on the overall function and dynamics of the protein variants, shedding light on the intricacies of their mechanical behaviour. We observed that all variants exhibit a number of microstates during force-clamp. However, the way these microstates respond to force varies significantly among variants. The V47 variant, characterized by strong antiparallel cross-correlated crankshaft motions 15 not only displayed the highest resistance to force but also demonstrated exceptional malleability under significant tensile forces. In contrast, the P47 variant exhibited the weakest response in this regard. Furthermore, our observations revealed that Cdh23 V47 exhibits a relatively weak response in the lower force regime, while Cdh23 P47 begins to display metastability at very low forces. We hypothesize that minimal or no response in the lower force range may help proteins filter out noise among mechanical cues, and thus Cdh23 V47 might be effective under water and up in the sky. We measured maximum force range, ΔF , where V47 variant is heterogeneous and the least for the P47 (Fig. 3 a), indicating that the V47 has enough room in conformational state space to counteract the tensile forces and avoid any irreparable damages under loud sound. We also argue that the mechanics of Cdh23 P47 mutant revealed here is likely be associated with the PHL disease phenotype and may be extrapolated to model ARHL. Interestingly, the trend in intrinsic folding rate follows the opposite pattern compared to force tolerance, with the P47 variant folding the fastest and the V47 variant folding the slowest. Weaker local interactions result in a shorter time for the protein to collapse and fold. However, it is important to note that intrinsic folding rate may not serve as the primary quality metric for mechanoresponsive proteins, as these proteins are constantly under tension. Instead, the physiologically relevant factors are the rates at which they adapt to folding and unfolding under mechanical tension. We determined that the P47 variant exhibits the longest \({x}_{}^{f}\) , suggesting that the force-induced increase in the free-energy barrier for folding is most pronounced in P47, and least in V47. Consequently, even a relatively small physiological force can significantly elevate the barrier height for P47, potentially blocking its refolding under tension. In contrast, the changes in barrier height for folding are notably less steep for S47 and V47 when compared to P47. Conversely, the trend in force-induced unfolding is the opposite. The P47 variant has the longest \({x}_{}^{uf}\) , indicating that tensile forces have the maximum impact on reducing the free-energy barrier for unfolding in P47, and the least effect in V47. As a result, P47 is most susceptible to unfolding under minimal tensile forces and may not effectively function as a mechano-protein at ambient temperature. From the repeated stretch-release activity in the force-pulse experiments, we noticed direct jumps to the unfolded state from the folded one for Cdh23 P47 more frequently than the two other variants. Although the etiology of this behaviour is not completely certain, it can be contributed to the loss of internal contacts during refolding and forming a quasi-folded closed conformation. Proteins go through the pleathrora of ridges in the folding energy landscape known as kinetic hubs and fold to native state in absense of external excitement 53 . Under oscillatory force, we experimentally show the variant with lesser intra-domain contacts shows a bias towards skipping the kinetic hubs and unfolds directly. The stochasticity of transitions among the metastable states becomes lesser in this case. We hypothesize, the wild-type protein variant which resonates with the external frequency, shows faster kinetics 54 and form native like structure during folding. Our study identifies direct transitions from these quasi-folded native like structures as a feature of proteins which are not able to resonate to the oscillatory perturbation for longer time. We also correlated the force adaptation of all three variants with unfolding cooperativity 55 . Cooperativity measures the sharpness of configurational or conformational transition 56 . Higher the cooperativity, lower is the number of kinetic traps, thus lesser chance of misfolding, however, higher is the sensitivity to mechanical perturbations 57 . Thus, P47 possessing highest cooperativity, showed the highest unfolding probability, especially during repetitive force-pulses. Conclusions Overall, our findings reveal that cooperative interactions enable proteins to undergo stochastic and reversible switches between metastable microstates under mechanical clamps. This stochasticity aids proteins in withstanding a broad range of mechanical forces and prolongs repetitive signal transduction. The study also emphasizes the diversity in the mechanics of two variants originating from species subjected to different environmental selection pressures. We conclude that the stochastic kinetics among heterogenous microstates might be an evolutionary selection trait for mechanosensing proteins. Material and methods Magnetic Tweezers Setup The tweezer is composed of a voice coil actuator (VCA, from BEI Kimco), a high-speed CMOS camera (Ximea xiQ USB 3.0 SuperSpeed), an inverted microscope (Olympus IX73), an objective piezo-scanner (P-725.xDD PIFOC) and controller (PI- E-709), and a python-based algorithm for automation and data acquisition. VCA works in closed-loop with a z-resolution of 10 µm and is controlled by Ingenia Motion Controller (PLU-1/5-48C). We use VCA as a linear actuator to move permanent magnets (Neodymium permanent ring magnets from K&J Magnetics, USA) and exert force on superparamagnetic beads (2.8 µm diameter, Fe 3 O 4 ). Beads are covalently attached to a surface via the protein to be probed. The entire setup is in the optical microscope, as shown in SI Fig. 1 . Bead movement in the z-direction under force is captured using the CMOS camera, and processed in real-time using a Python-based algorithm. The temporal z-displacement of the magnetic particle features the unfolding and refolding patterns of the probe protein under varying forces. A representative scheme and a picture of our home-built MT are shown in Figs. 2 a and supplementary Fig. 2. Command line interface-based custom written code for image capture and analysis at high FPS We plan to capture images containing beads at a very high speed, save and transfer those data to CPU, and simultaneously run image-processing algorithm to get real-time data. Alongside, we also run a visualization programme to monitor the fluctuations of beads in real time. To perform these high-end parallel computing, there are several approaches already exist. We have used multiprocessing to spawn different instances of tracking function (workers) continuously grabbing fresh frames from the queue and submitting the z-position data to another thread (recorder). This gives a significant boost in tracking fps compared to traditional sequential algorithms. We have used a 32-core (64 thread) AMD Ryzen Threadripper Pro 3975WX processor and were able to easily saturate USB bandwidth of the CMOS camera, thereby achieving the highest image acquisition rate (3.5 KHz) while performing heavy tracking computation in real time (supplementary Fig. 3). Stack collection and image processing The z-positions of the magnetic beads determine the length change of the biomolecule extension. The magnetic beads are covalently and specifically attached to the protein variants. The nonmagnetic reference beads that are used for drift corrections are fixed by physisorption to surface non-specifically. We have used a 32-core CPU system with AMD Ryzen Threadripper processor to perform image processing and real-time bead tracking. To measure the real time bead position with continuous feedback, we have built a library of images with offset in z, which is referred here as stack. To create the stack, the piezoelectric objective scanner is moved up in z-direction to 2 µm at a step size of 10 nm. During a flight between steps, 100 snap frames of the two beads are taken for future averaging and error correction to counter the miniscule changes from the instruments. A 2D FFT for each of the 100 frames at every step was computed and an average frame based on the pixel intensity matrix was calculated. After that, a region of interest (ROI) of 128x128 pixels is selected from the 10% area square box from the central point because it is the region that is most sensitive to focus change. 2D FFT helps to eliminate the x-y fluctuations coming from the beads. The ROI intensity matrix is then multiplied by a factor of 20, to distinctly differentiate the position of the frames and increase the resolution. After this library of images and their 2D FFT and ROI intensity matrix are computed, the radial profile of these images was calculated using pixel intensity value. During experiment, the z-position of the beads are determined by a correlation function, which is used to match the radial profile from the stack library (supplementary Fig. 7). Filtering methods Acquiring high speed data comes with its pros and cons. Force spectroscopy data from the real-time experiment exhibit slowly changing patterns and oscillations with abrupt transitions. Except for frequency filters, all other existing filtering methods like adjacent averaging or Savitzky-Golay filter causes loss of pattern information and thus affect the goodness of the fit. However, the Fourier transformation does not represent abrupt changes or step-like transitions efficiently. It will not be a good filtering method since it represents data as a sum of various waveforms like sine wave, etc. which are not localized in time and frequency. That is where we applied the wavelet transformation method for better fitting of steplike function and for more robust filtering. The wavelet transformation technique can decompose a data signal into several lower resolution steps in terms of both time and frequency, simultaneously. It is computationally cheap and fast. Depending on the wavelet that we choose to use to convert the data into equally spaced samples, the filtering goodness increases. For magnetic tweezer related experimental data, we use the haar wavelet because of its nature for approximating sudden step-like jumps with unfolding and refolding behaviour of proteins. Haar wavelet, a rectangular shaped waveforms with varying amplitude, is used to fit to a low frequency signal after sequentially separating high frequency noise (supplementary Fig. 8). Data analysis Step-fitting analysis for force curves from short time experiments were carried out using custom written MATLAB program (using version of MATLAB 2015b and MATLAB2021a, MATLAB2022a). However, it took more computational time in case of high fps (frame per second) data from experiment of longer period. So, to counter this problem, we used open-source resource. Auto-stepfinder, a GUI based MATLAB programme developed from the lab of Prof. Chirlmin Joo with collaboration of Cees Dekker, was used to fit the step function with the raw data. This programme also gives us an estimation of goodness of fit by providing the S-value, which is basically the ratio of sum of variance between data points and the fitted line of a counter-fit vs. existing fit. Other fitting analysis like dwell time and folding rate analysis, has been done using OriginPro software. Linear fitting, Gaussian peak fitting, kernel density plot, and single-exponential decay fitting has been done using the same software. For data visualisation as well as to highlight the three states in the force-clamp results (supplementary Fig. 11), we used our own custom written programme in Python. Force Calibration For the calibration of force using a pair of permanent neodymium-grade N52 magnets, a force ramp experiment was performed to observe the DNA B-S transition. For the sample, a 605 bp long DNA linker was cloned from λ-phage DNA (Thermo Scientific). The ends were modified with an amine group and biotin using standard PCR reaction protocol. The amplified DNA was identified in UV light (302 nm, 365 nm) and purified using the PCR clean-up protocol (Geneoid). DNA was incubated in PEG buffer with NHS-(PEG) 2 -NHS modified surface for 4 hours, and then after washing the surface it was incubated with a Streptavidin-coated bead for 20 minutes. Later after setting up the fluid chamber with TRIS blocking buffer lacking MgCl 2 and measuring the highest length of voice coil movement along the z-axis and we performed force ramp experiment to observe B-S overstretching. From the well-known magnet law modified with fitting parameters 19 we get- \(F=F\left(B-S\right)*{e}^{b(MP\left(B-S\right)-MP)}\) . We know the value of F B−S to be 65 pN. We have also found a similar step-size distribution of maltose binding protein (MBP) at similar forces and the same step-size for I27 , with respect to force (supplementary Fig. 14–15), so we have considered the fitting parameter value to be 0.9 58 . With these constants and after measuring the magnet distance for B-S overstretching, we have our final magnet law- \(F\left(MP\right)=65*{e}^{0.9(4.31-X(MP\left)\right)}\) , where X is the magnet distance. Using this equation and magnet position we can get desired clamping force between 4 pN -165 pN (supplementary Figs. 14, 16). The noise from the voice-coil actuator has also been taken into account for minute changes in the force during the experiment (supplementary Fig. 17, supplementary table 3) Specific tether identification Our chimeric construct isn’t isotropic. We have a trimer and monomer of titin domains at different ends of the Cdh23 EC1 dimer. To maximise the success of recombinant reactions during cloning, we created this anisotropic design. MT experiments are successful only when a single-tethered magnetic bead is observed and not a multitethered single bead. To address this issue, we optimised the surface preparation protocol, with varying APTES concentrations of 5–0.5%. In the protocol with low concentration of APTES, we observe the least number of multi-tether events. We can differentiate nonspecific or multitethered events by quantifying the initial entropic extension ( 20 pN) (supplementary Fig. 18). Specific events where we identify 3 or more distinct unfolding features of I27 at high force (> 100 pN) and the corresponding initial length jump shows a higher initial extension (> 50 nm), where the orientation of domains along the force directions also contributes to the initial unfolding entropic extension (supplementary Fig. 19). At very high force, the enthalpic extension contributes to overall distance and residue level entropic extension comes into play. Effct of drift on clamping force Force measurement in this magnetic tweezers has been calibrated using B-S transition. The force of the magnetic tweezers is determined by the distance between the magnet and the bead. We measured the extension due to drifting and from that distance how much the clamping force changes (supplementary Fig. 20). According to the formula for force calibration, if the baseline force drift changes from 4 pN to 5 pN, the distance will have to change by more than 0.75 mm. The bi-directional repeatability of our translation piezo is less than 20 µm (18 µm to be exact). However, because of the focal range, we limit this movement to 2 µm only. Not only that, for a limited time measurements we see the drift of about 200–300 nm which is even lesser than the whole limit of piezo movement. Therefore, the force is almost intrinsic constant with error of less than 0.001 pN. The drift observed on extension (Supplementary Fig. 20) is mainly due to the focus drift of the microscope or buffer leakage from the MT chamber. Except for instrumental drift, there are two sources of error that could change the clamping force. Firstly, the z-positional error of the objective in mounting piezo, and secondly, the linear displacement due to the vibration of the voice-coil actuator, both of which have been neglected during force-calibration measurements. Network analysis We performed the molecular dynamics simulation for all three proteins (S47, P47, and V47) using the QuickMD plugin in VMD 59 . The crystal structure solved for the S47 and P47 was taken from PDB database. But since the structural data for V47 were not available, we made the variant V47 using the structural data from WT S47 in VMD (Fig. 1 ). We used the TIP3P water system to solvate the molecules and the ions Na + and Cl − were randomly placed at the final concentration of 15 mM. We used NAMD version 2.14 60 and CHARMM36 61 force field to run the simulation. Initially, the system was minimised for 0.1 seconds and then increased the system temperature to 300K at the rate of 1 K for 600 steps. Followed by equilibration for 2 ns. Then we run the GAMD 62 , 63 for 300 ns. System pressure was maintained at 1 atm using the Noose-Hover method and long-range interactions were controlled by Particle Mesh Ewald (PME) 64 , 65 . We did the dynamic network analysis using the network view plugin into VMD 59 . A model for all three proteins was generated using a coarse-grained representation. In this model, we assign C α atom of amino acids by a node, and nodes are connected to each other within a cut-off distance of 4.5 Å for 75% of the MD trajectory. Neighbouring C α atoms were not considered for the analysis. The edge distance between two nodes is calculated from the pairwise correlation, which gives the probability of information transfer across the given edges. Edge's weight was given by the correlation coefficient, which is measured from the correlation matrix using the programme Carma 66 (supplementary Fig. 1). In network analysis, a community is defined as a group of nodes/atoms that are more connected in themselves than the other part of proteins. Thus, the community has different stability and properties depending on the interaction network. Community network analysis provides information on signal propagation throughout the proteins. Cluster analysis We characterised all transitions during continuous force clamp study and mapped those transitions in energy landscape using extension length as a proxy. The complete unfolding length of our two-domain construct is 70 nm. However, depending on the force, it can vary between 50–80 nm. Here, we have taken six clusters. C0 (0–10 nm), C1 (10–20 nm), C2 (20–30 nm), C3 (30–40 nm), C4 (40–50 nm), U (> 50 nm). First, we consider each and every step position under 10 nm and map the next step position in the cluster matrix. Since we have both unfolding and refolding and our resolution is about 5 nm, from the C0 cluster the protein can go to CO, C1, C2, C3, C4, U as an unfolding transition and can also come to C0 itself as a refolding step. Similarly, from C1, it can go C1, C2, C3, C4, U as unfolding and come back to C1 and C0 as refolding. Same way we can map the number of all transitions in all possible position in cluster and their next transition direction. The transition line with value of 0 can later be removed for the sake of visualisation and thus the hetrogeneity can be mapped using the matrix clustering process. Needless to say, the bin size can be changed depending on the resolution limit as well as the proteins transition pattern. For smaller proteins, this size can be reduced to 3–5 nm and larger or multidomain proteins can use a bin size larger than 10 nm (supplementary Fig. 21). Three-state analysis for lifetime measurement We used three-state model to quantitively measure the multiplex behaviour of our system. We have found a number of microstaes residing in the conformation landscape. To characterize the heterogeneity and simplify the quantification of this n-state behaviour, we apply state boundary and divide this conformational state space into three parts, 0–15 nm for closed state, 15–45 nm for intermediate or partially unfolded states and above 45 nm as open state. We could choose a higher number of states to characterize the folding probability, however that would introduce further complexity which does not provide any significant insight. Also, changing the boundary values will change the folding probabilites, however the pattern will remain the same. Finally, we calculate the folding probability by measuring the dwell time percentage of those three states, which basically translates to the ratio of the amount of time in each state and total time at the respective clamping forces. This experiment is performed for all three variants for a range of forces with at least a total time of 30 minutes at each force collected from 3–6 beads. Covalent attachment strategy For performing long-term robust studies using magnetic tweezers all connections were prepared covalently. 1. Surface Preparation Coverslips were kept in the plasma chamber for 30 seconds. Plasma treatment will expose the gas inside the chamber to an energy source like a microwave and make the air into a free radical, ion mixture. This will remove all organic contamination. The coverslips were then kept in piranha solution (75% H 2 SO 4 , 25% H 2 O 2 ) for 1 hour to remove all remaining traces of organic components. These surfaces were sonicated in Milli-Q water 4–5 times to remove the traces of acid. Then, it was aged with 1 M KOH solution for 2 min 67 . Again, the sonication procedure was repeated with Milli-Q water. The water was changed after each wash. These surfaces were subjected to silanization in a solution mixture of 48 ml of acetone, 0.5 %v/v (3-Aminopropyl) triethoxysilane (APTES) (0.5 ml), and 1.5 ml of Milli-Q water. It was incubated for 45 minutes. Then, they were washed with Acetone by sonicating for 5 minutes. The same process was repeated with Milli-Q water. After the last wash with acetone, the surfaces were kept in a vacuum oven at 110°C for 1 hour. This process will help expose the ends of the alkoxysilane molecules that were coated during APTES incubation. Pegylation was carried out on the surfaces with NHS-(PEG) 2 -Maleimide, mPEG-SVA or whatever modification was necessary to attach proteins and beads in the presence of PEG buffer (100 mM NaHCO 3 , 600 mM K 2 SO 4 , pH 8.3) 67 . This reaction will take 4 hours. After that, sonicate the coverslips in milli-Q for 5 minutes. Next, an incubation was performed on the surface with 100 µM tetra-glycine peptide (GGGGC) that will interact with maleimide from the PEG molecule, in SEC buffer (pH = 7.5) for 7 hours 42 . Then after washing is done, the incubation was done for the surface with protein and sortase A mixture (1 µM protein and 1–2 µM Sortase A) for 2 hours. All of these reactions are performed at room temperature. 2. Bead Preparation Two types of beads are used for performing the force spectroscopy experiments in magnetic tweezers: Magnetic beads and non-magnetic beads. Nonmagnetic beads, which were used as reference for correcting surface-related drift, were attached using adsorption for 30 minutes. However, two types of modification were done with M-270 amine-modified paramagnetic beads 7 of 2.8 µM diameter. Beads were first incubated in NHS-(PEG) 2 -NHS solution of PEG buffer for 4 hours. The PEG chemicals that were not used in the pegylation reaction were removed from the buffer to increase the efficiency and yield of the second reaction. To make a covalent bond with the protein of interest, these beads with N-hydroxysuccinimide ends were incubated in a LPETGSSC peptide solution of pH 7.5 for 7 hours. It was washed with the same buffer condition that will be used for the experiment. All of these reactions are performed at room temperature with continuous shaking. Declarations Author Contributions S.R. conceived the idea. S.R., P.S., V.V. build the MT instrument. O.S. wrote the code for image processing, filtering, and data acquisition from MT system. P.S. and V.V. designed and performed all the MT experiments. P.S. performed all the chemical modification and surface chemistry for tethering. P.S. and V.V. analysed the data. G.K.B. performed all the MD simulations. P.S. expressed and purified all the protein variants. S.G. and P.S. cloned all the chimeric constructs. S.R. and P.S. made the figures. S.R. and P.S. wrote the manuscript. Competing interests The authors declare no competing interests. Acknowledgements This work was supported by the Core Research Grant from SERB, Govt. of India. SR acknowledges and thanks Dr. Raj K. Ladher, NCBS, for generously donating the Cadherin-23 plasmid. SR acknowledges the financial support by the DBT/Wellcome Trust India Alliance and Indian Institute of Science Education and Research Mohali (IISERM) for setting up the molecular biology facilities. PS is thankful to CSIR-India for providing fellowship. 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Supplementary Files supplementaryinformation22.01.24.pdf Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation softwarepolicy.pdf Code and Software Submission Checklist reportingsummary.pdf Reporting Summary Cite Share Download PDF Status: Published Journal Publication published 25 Jan, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3887774","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":271849832,"identity":"877fe28c-8c38-4c33-85e0-229c6600a60a","order_by":0,"name":"Sabyasachi Rakshit","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYHACZgbGBgkGfmbGBjDXgIG54QCIwUZAi4RkM1wLI1FaGCQMDkC5IC14XSU/+/Bjw587LOqMjzM3f/i4Z5ucOfvBxgMMNXYMfNLYtRqcSzNO5j0jIWF2mLFNcsaz28aWPYlAhx1LZmCTOYBdCw+DMVAxRAszz4HbiRsOgLSwAZFEAnaH9bB/PvgTqMW4mbH58x+QlvMPgVr+4dbCcIbHOIEXqMUAGMjSDCAtN4C2MLbh1mJwhqfYGKhFcgbILz0Hbhsb3ADaktiXzIPHYZslf7bV8fP3H3/84ceB23IG55MPf/jwzU5OfgYOh2EHQMU8pKgfBaNgFIyCUYAKAGTfYDLq8rAaAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-8083-6857","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":true,"prefix":"","firstName":"Sabyasachi","middleName":"","lastName":"Rakshit","suffix":""},{"id":271849833,"identity":"b6d4d226-3d5d-49a4-88e6-c4eda41e6da9","order_by":1,"name":"Pritam Saha","email":"","orcid":"","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":false,"prefix":"","firstName":"Pritam","middleName":"","lastName":"Saha","suffix":""},{"id":271849834,"identity":"a723001a-6f89-44ac-b6a4-97504c306c79","order_by":2,"name":"Vishavdeep Vashisht","email":"","orcid":"","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":false,"prefix":"","firstName":"Vishavdeep","middleName":"","lastName":"Vashisht","suffix":""},{"id":271849835,"identity":"bd7de609-a34d-41ea-b11c-15efffc419a2","order_by":3,"name":"Ojas Singh","email":"","orcid":"https://orcid.org/0000-0002-2586-2542","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":false,"prefix":"","firstName":"Ojas","middleName":"","lastName":"Singh","suffix":""},{"id":271849836,"identity":"a4815dd8-d5fc-47ed-af7a-c8d6c91b7277","order_by":4,"name":"Gaurav Bhati","email":"","orcid":"","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":false,"prefix":"","firstName":"Gaurav","middleName":"","lastName":"Bhati","suffix":""},{"id":271849837,"identity":"a2e3868a-5982-43ec-b681-736e1d125f88","order_by":5,"name":"Surbhi Garg","email":"","orcid":"","institution":"Indian Institute of Science Education and Research Mohali","correspondingAuthor":false,"prefix":"","firstName":"Surbhi","middleName":"","lastName":"Garg","suffix":""}],"badges":[],"createdAt":"2024-01-22 11:23:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3887774/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3887774/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-55946-3","type":"published","date":"2025-01-25T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":50915589,"identity":"96139751-916f-474f-b978-1ef3f130040f","added_by":"auto","created_at":"2024-02-09 14:00:17","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":401937,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic depiction of all three protein variants showing differential packing density.\u0026nbsp;\u003c/strong\u003ea) Schematic depiction of a hair-cell with stereocilia in staircase pattern. b) Representation of tip-link structure between two nearest-neighbouring stereocilium, where Cadherin-23 (in blue) and Protocadherin-15 (in red) forms a trans-heterotetrametric complex. The interacting domain of Cdh-23 EC1-EC2 and Pcdh-15 EC1-EC2 is zoomed in and highlighted in ribbon structures. c) Topology diagram of Cdh-23 EC1, where b-strands, α-helices, and linkers are shown using 2D tape representation. d) Contact maps from the 300 ns MD simulations are shown for all three variants, P47 (red), S47 (black), and V47 (blue).\u0026nbsp; Green balls represent the node, and solid lines represent the edges. Reduction in the packing density is highlighted with circles. Ribbon representation of three variants of Cdh23 EC1, S47 (in black), P47 (in red), and V47 (in blue). Structures of P47 and V47 variants are modelled using alphafold 2.0. Here, H-bond between 47\u003csup\u003eth\u003c/sup\u003e amino acid and 81\u003csup\u003est\u003c/sup\u003e amino acid and 81\u003csup\u003est\u003c/sup\u003e and 94\u003csup\u003eth\u003c/sup\u003e have been marked. S47 and V47 shows H-bond with E81 with 46% and 54% occupancy, respectively, whereas in case of P47 this intra-domain contact is not formed. e) Number of contacts for all the residues of Cdh23 EC1 S47 (Black), P47 (Red), and V47 (Blue) are plotted. Differences in number of contacts among P47, S47, and V47 variants in residues near 22\u003csup\u003end\u003c/sup\u003e and 76\u003csup\u003eth\u003c/sup\u003e are highlighted in green circles.\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/2bf33450bec1678a38abc641.jpeg"},{"id":50915595,"identity":"a3dbb637-9ad8-49a9-8098-113517bc44bc","added_by":"auto","created_at":"2024-02-09 14:00:19","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":347646,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic depiction of the continuous force-clamp experiment using a Magnetic Tweezer.\u0026nbsp;\u003c/strong\u003ea) Schematics of a typical magnetic tweezer with a chimeric polyprotein. The chimeric polyprotein, the protein of interest (POI in red) sandwiched between I27 (green), is covalently attached to the coverslips and M-270 super-paramagnetic beads following sortagging chemistry. Reference beads (RB) are non-magnetic and physiosorbed to surface. b) A representative extension of Cdh23 (EC1 P47)\u003csub\u003e2\u003c/sub\u003e at a clamping force of 12 pN.\u0026nbsp; The dark grey line represents the data (collected at 580 Hz) and the red line maps the steps obtained from Autostepfinder. A number of conformations are seen between the closed and open states of the protein. (c-e) The time-trace of the protein-extension at constant clamping forces are shown for c) P47 at 13 pN, d) S47 at 20 pN, and e) V47 at 27 pN. Orange solid lines guide the steps resulted from the Autostepfinder. Each force-curve is manually segregated in three-regions: peach box represents closed/native state (15 nm from the lowest step value), sky box marks the partially unfolded states (15-45 nm extension from the lowest step value), and the yellow box segregates the open/fully unfolded states (45 nm and above from the lowest step value). The rightmost side of each force-extension curve shows the distributions of the corresponding protein-extensions using bars and black solid lines are the kernel density estimates. For (c), (d) and (e): the experiment is repeated for n = 3 beads and the extension of transitions between N↔U for a total of at least t = 900 seconds duration.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/829f7c83a9adb985ba9d5acb.jpeg"},{"id":50915596,"identity":"5d8ef0ac-4b44-446c-9e34-d5916dc1010e","added_by":"auto","created_at":"2024-02-09 14:00:19","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":253738,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEstimating heterogeneity from the protein folding probability and cooperativity. \u003c/strong\u003ea) Variations in the fraction of three states (native or closed in black, partially unfolded in red, fully unfolded, or open in blue) with clamping forces, estimated from the dwell-time analysis of force-clamp experiments, are shown for P47 (top), S47 (middle), and V47 (bottom). The green boxes qualitatively highlight the region (∆F) where all three states co-exist. For P47 ∆F was 5 pN, for S47 ∆F is 9 pN and for V47 ∆F is 17 pN. For each variant at each force, total number of beads was n=3 and total clamping time was at least t = 900 seconds. Total number of transition steps were N \u0026gt; 100. b) Probability of the closed state with clamping forces are shown for all three variants. To estimate the width of the transitions, we approximated the folded to unfolded transitions as two-state model and fit to Boltzmann equation (red line) (see Methods). We next plotted the blue solid lines, which are derivative of the fit (red line) to obtain the critical equilibrium force from the peak-position and the extent of force-tolerance from the FWHM. For P47, FWHM was 6.4 ± 0.0 pN, for S47, 8.2 ± 0.0 pN and for V47, 12.3 ± 0.0 pN c) Probability of the open state with clamping forces are shown for all three variants. The red solid lines are the linear equation fit to the transition regime to estimate the unfolding cooperativity from the slope.\u003c/p\u003e","description":"","filename":"image3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/51b82f283f4d51eb17d5e718.jpeg"},{"id":50915590,"identity":"06b6c77a-b5a3-49c3-b083-5888eba46eea","added_by":"auto","created_at":"2024-02-09 14:00:18","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":161318,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExtension (DL) of protein variants depends on clamping force. \u003c/strong\u003ea)\u003cstrong\u003e \u003c/strong\u003eSchematics of the magnetic tweezer force-clamp setup with a single unit of Cdh23 (red) sandwiched between I27 domains (green). b) From left to right, representative force-extension data of Cdh23 EC1 S47 with increasing clamping forces (from 15 pN - 38 pN). For each variant we performed n \u0026gt; 24 at every force. The inset dotted boxes highlight the unfolding pattern and the difference in the dwell time of unfolding at different forces. The variations in the thermal noise appears from different trapped beads. c) Distributions of extensions of Cdh23 EC1 S47 at varying clamping forces are shown. The red solid lines are the Kernel density estimators (KDE). Bandwidths of the kernels are estimated using Freedman-Diaconis rule (h =2\u0026nbsp;IQR(x)/n\u003csup\u003e1/3\u003c/sup\u003e, where h is the bin width, n is the number of datapoints). We monitored (n \u0026gt; 24) beads for each force for every variant (supplementary table 1). d) Single-domain unfolding contour-length is plotted at varying clamping forces for all three variants (S47 in black, P47 in red and V47 in blue). The mean-extension refers to the peak position of population of unfolding transitions in Fig 4 (c).\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/b35212bde4bf2ff90dbcf100.jpeg"},{"id":50915597,"identity":"7f7c7030-6293-46e1-a891-048adf286276","added_by":"auto","created_at":"2024-02-09 14:00:19","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":353398,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFolding dynamics of protein-variants under tensile force. \u003c/strong\u003ea) A representative time trace curve of extension of Cdh23 S47 monomer under a clamping force of 19 pN. Dwell-time and step-height are collected from the step-fitting using autostepfinder. b) Normalized survival probability of unfolding and refolding are shown here for all three variants, Cdh23 P47 (top), S47 (centre), and V47 (bottom). Red solid lines are the fit to single-exponential decay function. The total number of beads monitored for each force and for each variant is n\u0026gt;24. c) Force-induced unfolding rates (dot) and refolding rates (open box) for S47 (Black), V47 (Blue) and mutant P47 (Red) are shown in the Chevron plot. The corresponding solid lines are the fit to the Bell’s equation. The equilibrium force for S47 protein was 12.8 ± 0.1 pN, for P47 protein it was 7.6 ± 0.1 pN, and for V47 protein it was 23.7 ± 0.2 pN. d) Representative 1D potential-energy profiles for all three variants, relatively scaled according to the kinetic parameters (supplementary table 2) obtained from the Chevron plot.\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/2b0d3a3881233d1105c905d1.jpeg"},{"id":50915593,"identity":"f03606e5-b0b4-4f0d-a22b-b5aa1da49c4e","added_by":"auto","created_at":"2024-02-09 14:00:18","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":226979,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRepetitive force-pulse measurements show lesser stochasticity during unfolding for the mutant variant (P47) than WT variants (S47, V47).\u003c/strong\u003e a) The representative extensions of Cdh23 EC1 S47 from repetitive force-pulse measurements. The green shade and the red outlined box have been zoomed-in in two consecutive figures below, respectively. Bottom panel of figure (a) is shaded into three colours; red shade marks the transition of proteins to direct open state along with the initial elongation, and blue shades indicate the delayed or indirect unfolding of proteins b) 3D pie representation to show the percentage of direct unfolding (black) and delayed unfolding (red) for all three variants, S47 WT, P47 mutant, and V47 WT variant. We repeated this cycle for at least 30 times (For S47 protein N=44, P47 protein N=45, and V47 protein N=34).\u003c/p\u003e","description":"","filename":"image6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/728e906fb9af94ae78ed212b.jpeg"},{"id":74765443,"identity":"e3c4b156-b157-4eaf-88a2-d14a8f007d2b","added_by":"auto","created_at":"2025-01-26 08:06:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2963466,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/b0a129c8-2a90-457e-9f25-393931cc9c02.pdf"},{"id":50915591,"identity":"978844bf-d22e-48ce-9a99-3591cb8ef631","added_by":"auto","created_at":"2024-02-09 14:00:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":811781,"visible":true,"origin":"","legend":"\u003cp\u003eExploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation\u003c/p\u003e","description":"","filename":"supplementaryinformation22.01.24.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/716f12817bb85e75baa02dfa.pdf"},{"id":50915592,"identity":"1ff548c6-8916-4ad5-a3a3-5bb3124c2c91","added_by":"auto","created_at":"2024-02-09 14:00:18","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":542928,"visible":true,"origin":"","legend":"\u003cp\u003eCode and Software Submission Checklist\u003c/p\u003e","description":"","filename":"softwarepolicy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/4728e722929b3042045471c5.pdf"},{"id":50915594,"identity":"a868a0f0-b313-4d12-a6a4-20661f839a29","added_by":"auto","created_at":"2024-02-09 14:00:18","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":1650423,"visible":true,"origin":"","legend":"\u003cp\u003eReporting Summary\u003c/p\u003e","description":"","filename":"reportingsummary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3887774/v1/dbaf5a02eaf5855d107f5f04.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMechanical force is now well-established as a cue in developmental biology\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. This recognition has driven efforts to comprehend how proteins engaged in mechanotransduction respond to input force-stimuli. Despite this, the utilization of mechanical properties as an evolutionary determinant remains less firmly established within the realm of molecular zoology\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Notably, the correlation between the magnitude of mechanical forces and protein structure can be easily drawn. β-strand-rich proteins, in physiology, are naturally selected against large mechanical forces\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Examples include silk proteins that surpass the extreme tensile strength of a steel\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, muscle protein titin\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, cadherins as gating-spring in hearing\u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8 CR9 CR10\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, and many more. β-strands in proteins undergo strongly anticorrelated, ultrafast-frequency (in THz) breathing motions\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Theoretically such global motions in β-strands are quantified\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e and attributed to force-adaptation that helps proteins to regain conformations after mechanical perturbations\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. However, the empirical effort to connect these breathing motions in β-rich proteins to force-adaptation and molecular zoology remains lacking.\u003c/p\u003e \u003cp\u003eThe most effective approach to study force-adaptation in proteins involves subjecting them to tension and examining the protein-folding funnel using single-molecule force spectroscopy\u003csup\u003e\u003cspan additionalcitationids=\"CR17 CR18 CR19 CR20\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Tweezer-based force probes along ultrafast atomic force spectrometers, have identified several microstates in the protein-folding funnel\u003csup\u003e\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Theoretical models with simultaneous use of all-atom simulations have also provided the molecular resolution of the microstate structures and developed the microscopic model of protein-folding\u003csup\u003e\u003cspan additionalcitationids=\"CR23 CR24 CR25\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. However, the search of physical parameters that correlate the force-adaptation of proteins with the microscopic protein folding model continues. Along this line, we set our objective to identify the parameters that equip proteins for diverse mechanical environments and may potentially contribute to the process of molecular evolution. We experiment with a mechanosensing protein, Cadherin-23 (Cdh23), that possesses numerous β-strand-rich extracellular domains\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Cdh23 is a tip-link protein that actively participates in the mechanotransduction of hearing (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea,b) \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, receives force pulses of various intensities and frequencies during the lifetime of a host\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Notably, the protein is also one of the loci for multifactorial age-induced / noise-induced hearing loss\u003csup\u003e\u003cspan additionalcitationids=\"CR29 CR30 CR31 CR32\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, implicating the temporal loss of protein viscoelasticity with aging and, thus the loss of sensory abilities.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe overarching objective of this research is to identify parameters that equip proteins for diverse mechanical environments, necessitating force adaptation and potentially contribute to the process of molecular evolution. We used three variants of Cdh23 that reflect different hearing phenotypes in physiology. Two wildtype variants of Cdh23, S47 and V47, serve as gating-spring and mediate sustained hearing in different environments. The mutant variant, Cdh23 P47, however, reflects a detrimental effect with time and causes progressive hearing loss in mice. In short, both S47 and V47 variants are naturally selected for sustained hearing under periodic tension, while P47 is rejected. In this study, we use these three structurally near identical phenotypic and genotypic variants of Cdh23 and probe their force-adaptations directly using our laboratory-built magnetic tweezer (MT). MT enabled us to capture the microstates in the folding energy landscape under small mechanical perturbations ranging from 4 pN \u0026ndash; 40 pN, and at a high spatial resolution of nanometres (~\u0026thinsp;5 nm) and temporal resolution of milliseconds. Further, we devised a covalent tethering of protein variants with the glass coverslips and the magnetic beads to perform the unfolding-refolding studies at variable tensile forces repetitively and measure the stochasticity in the folding dynamics for an extended period. Moreover, here we aim to shed light into the force-adaptation of proteins to oscillatory input forces by monitoring the stochastic folding dynamics of a single protein using an effective and robust MT.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eThree variants of Cdh23 as model protein.\u003c/strong\u003e We chose the first extracellular (EC1) domain of Cdh23 as the model protein. Cdh23 EC1 consists of nine \u0026beta;-strands interconnected by reverse \u0026beta; turns, 3\u003csub\u003e10\u003c/sub\u003e \u0026alpha;-helix, and random coils (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. We used three variants, Cdh23 EC1 (S47), Cdh23 EC1(V47), and Cdh23 EC1(P47), with marginally different native packing densities (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, supplementary Fig.\u0026nbsp;1), long-range H-bond networks (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, supplementary Fig.\u0026nbsp;1), and different anticross-correlated crankshaft types motions among \u0026beta;-strands\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e (supplementary Fig.\u0026nbsp;1). Cdh23 EC1(S47) is a wildtype variant conserved for a majority of the species, including Homo sapiens (Hs), whereas Cdh23 EC1 (V47) is another wildtype variant conserved in lower order vertebrates like Callorhinchus milii (fish), Gekko japonicus (reptiles), anser cygnoides domesticus (Swan goose), Alligator mississippiensis (crocodile reptile), Gallus gallus (ave)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Evolutionarily these species may be in a lower order than sapiens, a majority of them possess better hearing sensitivity at a lower frequency range than humans\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Further, some of these lower vertebrates require hearing at low-air pressure (at high altitude for swans) or under-water pressure (for alligators) where the noise threshold is high\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. Moreover, the evolutionary trend for proteins may not correlate with the ranks of the expressors. In line, Cdh23 EC1(V47) possesses the highest number of native contacts, long-range H-bonds, and thus most robust cross-correlated motions among \u0026beta;-strands\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. The last variant is Cdh23 EC1(P47) which is a mutant-variant of Cdh23 EC1(S47) that features a progressive hearing loss (PHL) phenotype in mice\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. PHL is an aggressive form of hearing-loss with aging where a patient suffers complete hearing loss at a very early age (less than 20 years in humans)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Considering native packing, Cdh23 EC1(P47) ranks last among the three variants (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed,\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee). Reportedly, V47 shows the highest resistance against thermal and chemical denaturants, whereas P47 is the least\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. In general, serine to proline mutation isn\u0026rsquo;t unique for Cdh23, relatively abundant with phenotypes\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Even for mechanosensitive Titin proteins, Ser22 to Pro mutation is reported with a phenotype of cardiomyopathy\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCovalent tethering of proteins and MT.\u003c/strong\u003e To monitor the responses of protein variants to small tensile forces, we force-clamped the chimeric polyprotein constructs using MT. A detailed description of the MT including hardware, resolution, instrument software and analysis software are described in the methods and supplementary Figs.\u0026nbsp;2\u0026ndash;8. Two repeats of Cdh23 EC1 variants were recombinantly sandwiched between a trimer of I27 domain at the C-terminus and a monomeric I27 domain at the N-terminus (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea). I27 is the 91st Ig domain of cardiac muscle protein, titin, and is extensively used as marker in single-molecule force spectroscopy. Further, the mechanical stability of I27 is significantly higher than all three variants of Cdh23 EC1 \u003csup\u003e18,19\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;9). Trimer of I27 domains was attached to the glass-coverslip, and the I27 monomer at the N-terminus was attached to the paramagnetic bead, both covalently using sortase-mediated enzymatic stapling\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e (Methods). The assymmetry in the constructs is primarily to ease out the DNA recombinant process.\u003c/p\u003e\n\u003cp\u003eFor studying mechanostability, we clamped the protein variants to a range of forces for 5 minutes from a resting force of 4 pN and monitored the change in lengths (\u003cem\u003e\u0026Delta;L\u003c/em\u003e) from the jumps in bead positions in real-time (Supplementary Fig.\u0026nbsp;10\u0026ndash;11). To quantitatively estimate the dwell time of steps, we performed \u0026lsquo;Autostepfinder\u0026rsquo;, a widely used step-finder protocol that is based on the mean standard deviation model \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e depicts the typical force-clamp traces for all three variants. As anticipated from the ensemble thermal and chemical stability studies\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, we measured the weakest force-resistance for Cdh23 P47 featuring force-induced extensions between 5 pN \u0026ndash; 15 pN, followed by Cdh23 S47 between 13 pN \u0026minus;\u0026thinsp;25 pN, and strongest for Cdh23 V47 between 19 pN \u0026minus;\u0026thinsp;38 pN (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, Supplementary Fig.\u0026nbsp;11\u0026ndash;12). Irrespective of the force-resistance, we identified numerous microstates for all the variants during unfolding-refolding transitions at small clamping forces (Supplementary Fig.\u0026nbsp;13). To characterize the microstates, we measured the length-change (\u003cem\u003e\u0026Delta;L\u003c/em\u003e) for each step and plotted them as distributions (Methods and Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec, d, e supplementary Fig.\u0026nbsp;10, 13). The histograms of \u003cem\u003e\u0026Delta;L\u003c/em\u003e for all variants followed comparable trend, narrow distributions at lower forces, wide at intermediate forces reaching saturations, and finally sharp distributions at very high forces (supplementary Fig.\u0026nbsp;10). The widths of the distributions indicate the extent of reversible transitions among microstates under tension while the number of peaks in the distributions infers the number of microstates (extent of heterogeneity). It appears that the heterogeneity in microstates is consistent among all variants; nonetheless, variations in width indicate substantial differences in their capacity to withstand force reversibility.\u003c/p\u003e\n\u003cp\u003eTo emphasize the force-tolerance of microstates across different variants, we plotted the fraction of states or probability of states as they survive at the clamping forces (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). For simplicity, we used only 3-states, a native or folded state (with 0 nm\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003e\u0026Delta;L\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;15 nm), a complete denatured or unfolded state (45 nm\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003e\u0026Delta;L\u003c/em\u003e, maximum x(F)) and a cluster of intermediate states (15 nm\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003e\u0026Delta;L\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;x(F)). Notably, the end-to-end extensions, x(F), with force\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed, Supplementary Fig.\u0026nbsp;10) of all protein variants featured Worm-like chain (WLC) behaviour. x(F) defines the extent of unfolding and, thus marks the final denaturant states at the respective clamping forces (Supplementary Fig.\u0026nbsp;10\u0026ndash;11). The probability of the states at respective force-clamps was estimated from the dwell time of each state, normalized to the total clamping time. We obtained a sigmoidal transition for the probability of folded state with force for all variants. The transitions from native to unfolded states occurred at different critical forces \u003cem\u003e(F\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e), lowest for P47 (7.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1 pN) and largest for V47 (23.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2 pN). However, we noticed different widths (\u003cem\u003e\u0026Delta;F\u003c/em\u003e) and slopes of the transitions across variants. We highlighted these regions with light green boxes (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The green boxes marked the co-existence of all 3 states, indicating the force-range at which the protein-variants undergo reversible transitions between numerous conformational microstates. The critical force (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e) of transition is a measure of force-resistance, while the width of the transitions (\u003cem\u003e\u0026Delta;F\u003c/em\u003e) gauges the range of force tolerance among microstates. A wider width implies greater shock-absorbing capability, force dispersion, or ductility. Considering both the critical force of transitions and the width of the distributions, we evaluated the spectrum of adaptability to external forces. Notably, the V47 variant demonstrates the highest degree of adaptability, whereas the P47 variant shows the least.\u003c/p\u003e\n\u003cp\u003eNext, we mapped the probability of the open state of all three variants and fit the rise in states to linear equation, excluding the force-value points with no unfolding probability (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec). The slope gives quantitative estimation of protein\u0026rsquo;s unfolding cooperativity. Conceptually, a completely cooperative unfolding will show a strict two-step transition with an infinite slope, whereas the completely non-cooperative transition will have slope of 0. We obtained the slope for P47 as 0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01/pN, S47 as 0.09\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01/pN, and V47 as 0.05\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01/pN, resulting the order of unfolding-cooperativity as, P47\u0026thinsp;\u0026gt;\u0026thinsp;S47\u0026thinsp;\u0026gt;\u0026thinsp;V47. Overall, our data from force-clamp experiments indicate that Cdh23 V47, which contains the most densely packed network of intra-domain interactions, is mechanically the most stiff yet possesses the most disseminating ability of tensile forces. We, therefore, infer that higher crankshaft or contact order transforms \u0026beta;-rich proteins to more ductile under tensile forces, however, without causing any permanent damage. The inter \u0026beta;-strand interactions serve as shock-absorber and resist elongation from mechanical inputs.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003eEffect of intra-domain contacts in folding rates and force tolerance\u003c/h2\u003e\n\u003cp\u003eContact-orders that estimate the extent of native-contacts of a protein in native state, contribute to the folding dynamics of proteins. Further, mechanoresponsive proteins undergo unfolding-folding under tension in physiology\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The folding dynamics of the mechanoresponsive proteins are, thus functionally important. We, therefore, set to decipher the effect of inter domain interactions of a protein in the folding and unfolding kinetics.\u003c/p\u003e\n\u003cp\u003eWe performed a dual-step force-clamp spectroscopy with a monomer of Cdh23 EC1 domain parsed between I27 domains as -Nterm-(I27)\u003csub\u003e3\u003c/sub\u003e-EC1-I27-Cterm (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). The use of a monomeric domain enabled us to measure the kinetics for direct transitions from the native state to the complete denatured state and vice versa. The resting force was set to 4 pN. Subsequently, the protein variants were individually clamped at varying constant forces (19\u0026ndash;38 pN for S47 variant, 11\u0026ndash;19 pN for P47 variant, and 23\u0026ndash;38 pN for V47 variant) for 30\u0026ndash;60 seconds and monitored the survival time till complete unfolding. We excluded the extensions below 5 nm in the analysis due to the resolution limit in our measurements (Supplementary Fig.\u0026nbsp;3). After each force-clamp, we subjected the variants to a high tensile force of 38 pN for 15 seconds to ensure complete extension prior to refolding. For refolding, we clamped the proteins at low forces, 11\u0026thinsp;\u0026minus;\u0026thinsp;4 pN for S47 variant, 8\u0026thinsp;\u0026minus;\u0026thinsp;4 pN for P47 variant, and 19\u0026thinsp;\u0026minus;\u0026thinsp;9 pN for V47 variant, respectively. We completed the cycle by quenching the force to 4 pN. For each variant, we monitored a minimum of 25 different beads (Supplementary Table\u0026nbsp;1).\u003c/p\u003e\n\u003cp\u003eThe survival probabilities of the folded and unfolded states were estimated from the dwell time (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). We deduced the lifetimes of folding and unfolding from the single exponential decay fit to corresponding survival probabilities (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb) (Supplementary Table\u0026nbsp;1) and obtained the force-induced on-rate and off-rate data (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed). Subsequently, the variation in rates with force were fit to Bell\u0026rsquo;s model\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e and obtained the intrinsic kinetic parameters, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({k}_{0}^{f/uf}\\)\u003c/span\u003e\u003c/span\u003e (intrinsic-rate at zero force, \u0026lsquo;f\u0026rsquo; represents folding and \u0026lsquo;uf\u0026rsquo; refers to unfolding) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f/uf}\\)\u003c/span\u003e\u003c/span\u003e (the distance to the transition state) (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec,d and Supplementary Table\u0026nbsp;2).\u003c/p\u003e\n\u003cp\u003eThough intrinsic fold-rates at the \u0026lsquo;no-force\u0026rsquo; condition may not be physiologically relevant for force-sensors, we measured the fastest unfolding rate for P47 and the slowest for V47 (Supplementary Table\u0026nbsp;2). We measured a similar trend in the folding kinetics as well, fastest refolding for P47 (52.45\u0026thinsp;\u0026plusmn;\u0026thinsp;32.52 s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and the slowest for V47 (0.21\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00 s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) among the three, infering that a protein with least intra-domain interactions forms the native state fastest. The susceptibility of proteins towards force-induced unfolding(uf)-folding(f), however, depends on the distance to transition states, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f/uf}.\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f}\\)\u003c/span\u003e\u003c/span\u003eis negative in sign as folding is against the force vector (Supplementary Table\u0026nbsp;2). A higher \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f}\\)\u003c/span\u003e\u003c/span\u003e diminishes the folding probability under tension by increasing the barrier-height (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E\\left(F\\right)= E}_{A}- {\\overrightarrow{F}.\\overrightarrow{x}}_{\\beta }^{f}\\)\u003c/span\u003e\u003c/span\u003e), whereas a higher \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{uf}\\)\u003c/span\u003e\u003c/span\u003eincreases the unfolding probability by reducing the potential barrier height under tension. We measured the longest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f/uf}\\)\u003c/span\u003e\u003c/span\u003e for P47 (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f}\\)\u003c/span\u003e\u003c/span\u003e ~ -35.7\u0026thinsp;\u0026plusmn;\u0026thinsp;4.1 \u0026Aring; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{uf}\\)\u003c/span\u003e\u003c/span\u003e~ 3.0 \u0026plusmn; 0.2 \u0026Aring;) and the shortest for V47 (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f}\\)\u003c/span\u003e\u003c/span\u003e ~ -2.5 \u0026plusmn; 0.0 \u0026Aring; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{uf}\\)\u003c/span\u003e\u003c/span\u003e~ 2.3 \u0026plusmn; 0.7 \u0026Aring;), indicating that the mechanical tension is most vulnerable for P47 and least for V47 (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003eTime-dependent adaptation against fatigue while receiving repetitive force pulse\u003c/h2\u003e\n\u003cp\u003eWe noted that the protein variants undergo stochastic transitions among microstates under constant tension. We wanted to study how do these stochastic transitions follow the oscillatory force input as we percieve from sound during hearing. Does the stochastic transitions during folding resonate with the external force pulses, allowing biomolecules to fold faster? Or do we capture, molecular fatugue, a delay in response to external frequency. Time dependent change in mechanical phenomena of a protein is generally defined as molecular-fatigue which arises from the repetitive stretch and release cycle of the protein\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. We, therefore, exposed the protein variants to a cycle of high force and low-force (4 pN), repetitively with a periodicity of 15 seconds. The high-forces were set differently, 12.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1 pN for S47, 7.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1 pN for P47, and 23.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2 pN for V47, where all microstates coexisted for the respective variants (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea). The critical forces of unfolding and refolding are the equilibrium force obtained from the chevron plots (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec).\u003c/p\u003e\n\u003cp\u003eWe noticed two distinct unfolding patterns, direct unfolding (unfolds directly along with the initial stretch) and delayed stepwise unfolding (goes through the metastable states before complete unfolding) (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea). Counterintuitive to the folding-kinetics pattern, we observed the more frequent direct unfolding of P47 (20.7%) than S47 (11.3%) and V47 (6.25%), respectively. We relate the direct unfolding events with the delay in folding in the previous force-cycle, a feature of molecular fatigue. Overall, we infer that proteins with low force- adaptibility, suffer faster mechanical fatigue. More importantly, a direct unfolding relates to \u0026lsquo;no force-buffer\u0026rsquo; and conveys the input mechanical signal directly, exposing the sensory organs to potential damage.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eAll three variants; S47, P47, V47; exhibit closely aligned static structures, characterized by a predominance of β-strands with minimal distinctions in contact orders and inter β-strand interactions. Notably, the variations among these variants are remarkably localized. Specifically, while S47 and V47 are positioned at the termini of a β-strand, P47 induces a reduction in the strand length and an extension of the turn connecting two anti-parallel β-strands (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). It is worth emphasizing the significance of turns in β-rich proteins, serving as the foundational elements of β-strands and playing crucial roles as regulators of inter-β-strand interactions\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. The introduction of Proline (Pro) at position 47 introduces a constrained torsion angle in the turn, resulting in comparatively weaker β-strand packing among the three variants. This, in turn, leads to a diminished anti-cross correlated crankshaft-type motion among β-strands\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Understanding how these seemingly trivial alterations in the protein's topology exert a substantial impact on its mechanics constitutes the primary focus of this investigation. The subsequent sections will delve into the implications of these structural variances on the overall function and dynamics of the protein variants, shedding light on the intricacies of their mechanical behaviour.\u003c/p\u003e \u003cp\u003eWe observed that all variants exhibit a number of microstates during force-clamp. However, the way these microstates respond to force varies significantly among variants. The V47 variant, characterized by strong antiparallel cross-correlated crankshaft motions\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e not only displayed the highest resistance to force but also demonstrated exceptional malleability under significant tensile forces. In contrast, the P47 variant exhibited the weakest response in this regard. Furthermore, our observations revealed that Cdh23 V47 exhibits a relatively weak response in the lower force regime, while Cdh23 P47 begins to display metastability at very low forces. We hypothesize that minimal or no response in the lower force range may help proteins filter out noise among mechanical cues, and thus Cdh23 V47 might be effective under water and up in the sky. We measured maximum force range, \u003cem\u003eΔF\u003c/em\u003e, where V47 variant is heterogeneous and the least for the P47 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), indicating that the V47 has enough room in conformational state space to counteract the tensile forces and avoid any irreparable damages under loud sound. We also argue that the mechanics of Cdh23 P47 mutant revealed here is likely be associated with the PHL disease phenotype and may be extrapolated to model ARHL.\u003c/p\u003e \u003cp\u003eInterestingly, the trend in intrinsic folding rate follows the opposite pattern compared to force tolerance, with the P47 variant folding the fastest and the V47 variant folding the slowest. Weaker local interactions result in a shorter time for the protein to collapse and fold. However, it is important to note that intrinsic folding rate may not serve as the primary quality metric for mechanoresponsive proteins, as these proteins are constantly under tension. Instead, the physiologically relevant factors are the rates at which they adapt to folding and unfolding under mechanical tension. We determined that the P47 variant exhibits the longest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{f}\\)\u003c/span\u003e\u003c/span\u003e, suggesting that the force-induced increase in the free-energy barrier for folding is most pronounced in P47, and least in V47. Consequently, even a relatively small physiological force can significantly elevate the barrier height for P47, potentially blocking its refolding under tension. In contrast, the changes in barrier height for folding are notably less steep for S47 and V47 when compared to P47. Conversely, the trend in force-induced unfolding is the opposite. The P47 variant has the longest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{}^{uf}\\)\u003c/span\u003e\u003c/span\u003e, indicating that tensile forces have the maximum impact on reducing the free-energy barrier for unfolding in P47, and the least effect in V47. As a result, P47 is most susceptible to unfolding under minimal tensile forces and may not effectively function as a mechano-protein at ambient temperature.\u003c/p\u003e \u003cp\u003eFrom the repeated stretch-release activity in the force-pulse experiments, we noticed direct jumps to the unfolded state from the folded one for Cdh23 P47 more frequently than the two other variants. Although the etiology of this behaviour is not completely certain, it can be contributed to the loss of internal contacts during refolding and forming a quasi-folded closed conformation. Proteins go through the pleathrora of ridges in the folding energy landscape known as kinetic hubs and fold to native state in absense of external excitement\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Under oscillatory force, we experimentally show the variant with lesser intra-domain contacts shows a bias towards skipping the kinetic hubs and unfolds directly. The stochasticity of transitions among the metastable states becomes lesser in this case. We hypothesize, the wild-type protein variant which resonates with the external frequency, shows faster kinetics\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e and form native like structure during folding. Our study identifies direct transitions from these quasi-folded native like structures as a feature of proteins which are not able to resonate to the oscillatory perturbation for longer time. We also correlated the force adaptation of all three variants with unfolding cooperativity\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. Cooperativity measures the sharpness of configurational or conformational transition\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. Higher the cooperativity, lower is the number of kinetic traps, thus lesser chance of misfolding, however, higher is the sensitivity to mechanical perturbations\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. Thus, P47 possessing highest cooperativity, showed the highest unfolding probability, especially during repetitive force-pulses.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eOverall, our findings reveal that cooperative interactions enable proteins to undergo stochastic and reversible switches between metastable microstates under mechanical clamps. This stochasticity aids proteins in withstanding a broad range of mechanical forces and prolongs repetitive signal transduction. The study also emphasizes the diversity in the mechanics of two variants originating from species subjected to different environmental selection pressures. We conclude that the stochastic kinetics among heterogenous microstates might be an evolutionary selection trait for mechanosensing proteins.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eMagnetic Tweezers Setup\u003c/h2\u003e\n\u003cp\u003eThe tweezer is composed of a voice coil actuator (VCA, from BEI Kimco), a high-speed CMOS camera (Ximea xiQ USB 3.0 SuperSpeed), an inverted microscope (Olympus IX73), an objective piezo-scanner (P-725.xDD PIFOC) and controller (PI- E-709), and a python-based algorithm for automation and data acquisition. VCA works in closed-loop with a z-resolution of 10 \u0026micro;m and is controlled by Ingenia Motion Controller (PLU-1/5-48C). We use VCA as a linear actuator to move permanent magnets (Neodymium permanent ring magnets from K\u0026amp;J Magnetics, USA) and exert force on superparamagnetic beads (2.8 \u0026micro;m diameter, Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e). Beads are covalently attached to a surface via the protein to be probed. The entire setup is in the optical microscope, as shown in SI Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Bead movement in the z-direction under force is captured using the CMOS camera, and processed in real-time using a Python-based algorithm. The temporal z-displacement of the magnetic particle features the unfolding and refolding patterns of the probe protein under varying forces. A representative scheme and a picture of our home-built MT are shown in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea and supplementary Fig.\u0026nbsp;2.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch2\u003eCommand line interface-based custom written code for image capture and analysis at high FPS\u003c/h2\u003e\n\u003cp\u003eWe plan to capture images containing beads at a very high speed, save and transfer those data to CPU, and simultaneously run image-processing algorithm to get real-time data. Alongside, we also run a visualization programme to monitor the fluctuations of beads in real time. To perform these high-end parallel computing, there are several approaches already exist. We have used multiprocessing to spawn different instances of tracking function (workers) continuously grabbing fresh frames from the queue and submitting the z-position data to another thread (recorder). This gives a significant boost in tracking fps compared to traditional sequential algorithms. We have used a 32-core (64 thread) AMD Ryzen Threadripper Pro 3975WX processor and were able to easily saturate USB bandwidth of the CMOS camera, thereby achieving the highest image acquisition rate (3.5 KHz) while performing heavy tracking computation in real time (supplementary Fig.\u0026nbsp;3).\u003c/p\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n\u003ch2\u003eStack collection and image processing\u003c/h2\u003e\n\u003cp\u003eThe z-positions of the magnetic beads determine the length change of the biomolecule extension. The magnetic beads are covalently and specifically attached to the protein variants. The nonmagnetic reference beads that are used for drift corrections are fixed by physisorption to surface non-specifically. We have used a 32-core CPU system with AMD Ryzen Threadripper processor to perform image processing and real-time bead tracking. To measure the real time bead position with continuous feedback, we have built a library of images with offset in z, which is referred here as stack. To create the stack, the piezoelectric objective scanner is moved up in z-direction to 2 \u0026micro;m at a step size of 10 nm. During a flight between steps, 100 snap frames of the two beads are taken for future averaging and error correction to counter the miniscule changes from the instruments. A 2D FFT for each of the 100 frames at every step was computed and an average frame based on the pixel intensity matrix was calculated. After that, a region of interest (ROI) of 128x128 pixels is selected from the 10% area square box from the central point because it is the region that is most sensitive to focus change. 2D FFT helps to eliminate the x-y fluctuations coming from the beads. The ROI intensity matrix is then multiplied by a factor of 20, to distinctly differentiate the position of the frames and increase the resolution. After this library of images and their 2D FFT and ROI intensity matrix are computed, the radial profile of these images was calculated using pixel intensity value. During experiment, the z-position of the beads are determined by a correlation function, which is used to match the radial profile from the stack library (supplementary Fig.\u0026nbsp;7).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003eFiltering methods\u003c/h2\u003e\n\u003cp\u003eAcquiring high speed data comes with its pros and cons. Force spectroscopy data from the real-time experiment exhibit slowly changing patterns and oscillations with abrupt transitions. Except for frequency filters, all other existing filtering methods like adjacent averaging or Savitzky-Golay filter causes loss of pattern information and thus affect the goodness of the fit. However, the Fourier transformation does not represent abrupt changes or step-like transitions efficiently. It will not be a good filtering method since it represents data as a sum of various waveforms like sine wave, etc. which are not localized in time and frequency. That is where we applied the wavelet transformation method for better fitting of steplike function and for more robust filtering. The wavelet transformation technique can decompose a data signal into several lower resolution steps in terms of both time and frequency, simultaneously. It is computationally cheap and fast. Depending on the wavelet that we choose to use to convert the data into equally spaced samples, the filtering goodness increases. For magnetic tweezer related experimental data, we use the haar wavelet because of its nature for approximating sudden step-like jumps with unfolding and refolding behaviour of proteins. Haar wavelet, a rectangular shaped waveforms with varying amplitude, is used to fit to a low frequency signal after sequentially separating high frequency noise (supplementary Fig.\u0026nbsp;8).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003eData analysis\u003c/h2\u003e\n\u003cp\u003eStep-fitting analysis for force curves from short time experiments were carried out using custom written MATLAB program (using version of MATLAB 2015b and MATLAB2021a, MATLAB2022a). However, it took more computational time in case of high fps (frame per second) data from experiment of longer period. So, to counter this problem, we used open-source resource. Auto-stepfinder, a GUI based MATLAB programme developed from the lab of Prof. Chirlmin Joo with collaboration of Cees Dekker, was used to fit the step function with the raw data. This programme also gives us an estimation of goodness of fit by providing the S-value, which is basically the ratio of sum of variance between data points and the fitted line of a counter-fit vs. existing fit. Other fitting analysis like dwell time and folding rate analysis, has been done using OriginPro software. Linear fitting, Gaussian peak fitting, kernel density plot, and single-exponential decay fitting has been done using the same software. For data visualisation as well as to highlight the three states in the force-clamp results (supplementary Fig.\u0026nbsp;11), we used our own custom written programme in Python.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003eForce Calibration\u003c/h2\u003e\n\u003cp\u003eFor the calibration of force using a pair of permanent neodymium-grade N52 magnets, a force ramp experiment was performed to observe the DNA B-S transition. For the sample, a 605 bp long DNA linker was cloned from \u0026lambda;-phage DNA (Thermo Scientific). The ends were modified with an amine group and biotin using standard PCR reaction protocol. The amplified DNA was identified in UV light (302 nm, 365 nm) and purified using the PCR clean-up protocol (Geneoid). DNA was incubated in PEG buffer with NHS-(PEG)\u003csub\u003e2\u003c/sub\u003e-NHS modified surface for 4 hours, and then after washing the surface it was incubated with a Streptavidin-coated bead for 20 minutes. Later after setting up the fluid chamber with TRIS blocking buffer lacking MgCl\u003csub\u003e2\u003c/sub\u003e and measuring the highest length of voice coil movement along the z-axis and we performed force ramp experiment to observe B-S overstretching. From the well-known magnet law modified with fitting parameters\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e we get- \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F=F\\left(B-S\\right)*{e}^{b(MP\\left(B-S\\right)-MP)}\\)\u003c/span\u003e\u003c/span\u003e. We know the value of F\u003csub\u003eB\u0026minus;S\u003c/sub\u003e to be 65 pN. We have also found a similar step-size distribution of maltose binding protein (MBP) at similar forces and the same step-size for I27\u003csub\u003e,\u003c/sub\u003e with respect to force (supplementary Fig.\u0026nbsp;14\u0026ndash;15), so we have considered the fitting parameter value to be 0.9\u003csup\u003e58\u003c/sup\u003e. With these constants and after measuring the magnet distance for B-S overstretching, we have our final magnet law- \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left(MP\\right)=65*{e}^{0.9(4.31-X(MP\\left)\\right)}\\)\u003c/span\u003e\u003c/span\u003e, where X is the magnet distance. Using this equation and magnet position we can get desired clamping force between 4 pN -165 pN (supplementary Figs.\u0026nbsp;14, 16). The noise from the voice-coil actuator has also been taken into account for minute changes in the force during the experiment (supplementary Fig.\u0026nbsp;17, supplementary table 3)\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003eSpecific tether identification\u003c/h2\u003e\n\u003cp\u003eOur chimeric construct isn\u0026rsquo;t isotropic. We have a trimer and monomer of titin domains at different ends of the Cdh23 EC1 dimer. To maximise the success of recombinant reactions during cloning, we created this anisotropic design. MT experiments are successful only when a single-tethered magnetic bead is observed and not a multitethered single bead. To address this issue, we optimised the surface preparation protocol, with varying APTES concentrations of 5\u0026ndash;0.5%. In the protocol with low concentration of APTES, we observe the least number of multi-tether events. We can differentiate nonspecific or multitethered events by quantifying the initial entropic extension (\u0026lt;\u0026thinsp;20 nm) at high force (\u0026gt;\u0026thinsp;20 pN) (supplementary Fig.\u0026nbsp;18). Specific events where we identify 3 or more distinct unfolding features of I27 at high force (\u0026gt;\u0026thinsp;100 pN) and the corresponding initial length jump shows a higher initial extension (\u0026gt;\u0026thinsp;50 nm), where the orientation of domains along the force directions also contributes to the initial unfolding entropic extension (supplementary Fig.\u0026nbsp;19). At very high force, the enthalpic extension contributes to overall distance and residue level entropic extension comes into play.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003eEffct of drift on clamping force\u003c/h2\u003e\n\u003cp\u003eForce measurement in this magnetic tweezers has been calibrated using B-S transition. The force of the magnetic tweezers is determined by the distance between the magnet and the bead. We measured the extension due to drifting and from that distance how much the clamping force changes (supplementary Fig.\u0026nbsp;20). According to the formula for force calibration, if the baseline force drift changes from 4 pN to 5 pN, the distance will have to change by more than 0.75 mm. The bi-directional repeatability of our translation piezo is less than 20 \u0026micro;m (18 \u0026micro;m to be exact). However, because of the focal range, we limit this movement to 2 \u0026micro;m only. Not only that, for a limited time measurements we see the drift of about 200\u0026ndash;300 nm which is even lesser than the whole limit of piezo movement. Therefore, the force is almost intrinsic constant with error of less than 0.001 pN. The drift observed on extension (Supplementary Fig.\u0026nbsp;20) is mainly due to the focus drift of the microscope or buffer leakage from the MT chamber. Except for instrumental drift, there are two sources of error that could change the clamping force. Firstly, the z-positional error of the objective in mounting piezo, and secondly, the linear displacement due to the vibration of the voice-coil actuator, both of which have been neglected during force-calibration measurements.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003eNetwork analysis\u003c/h2\u003e\n\u003cp\u003eWe performed the molecular dynamics simulation for all three proteins (S47, P47, and V47) using the QuickMD plugin in VMD\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. The crystal structure solved for the S47 and P47 was taken from PDB database. But since the structural data for V47 were not available, we made the variant V47 using the structural data from WT S47 in VMD (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). We used the TIP3P water system to solvate the molecules and the ions Na\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e\u0026minus;\u003c/sup\u003e were randomly placed at the final concentration of 15 mM. We used NAMD version 2.14 \u003csup\u003e60\u003c/sup\u003e and CHARMM36\u003csup\u003e61\u003c/sup\u003e force field to run the simulation. Initially, the system was minimised for 0.1 seconds and then increased the system temperature to 300K at the rate of 1 K for 600 steps. Followed by equilibration for 2 ns. Then we run the GAMD\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e62\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e for 300 ns. System pressure was maintained at 1 atm using the Noose-Hover method and long-range interactions were controlled by Particle Mesh Ewald (PME)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e64\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e. We did the dynamic network analysis using the network view plugin into VMD\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. A model for all three proteins was generated using a coarse-grained representation. In this model, we assign C\u003csub\u003e\u0026alpha;\u003c/sub\u003e atom of amino acids by a node, and nodes are connected to each other within a cut-off distance of 4.5 \u0026Aring; for 75% of the MD trajectory. Neighbouring C\u003csub\u003e\u0026alpha;\u003c/sub\u003e atoms were not considered for the analysis. The edge distance between two nodes is calculated from the pairwise correlation, which gives the probability of information transfer across the given edges. Edge's weight was given by the correlation coefficient, which is measured from the correlation matrix using the programme Carma\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e66\u003c/span\u003e\u003c/sup\u003e (supplementary Fig.\u0026nbsp;1). In network analysis, a community is defined as a group of nodes/atoms that are more connected in themselves than the other part of proteins. Thus, the community has different stability and properties depending on the interaction network. Community network analysis provides information on signal propagation throughout the proteins.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n\u003ch2\u003eCluster analysis\u003c/h2\u003e\n\u003cp\u003eWe characterised all transitions during continuous force clamp study and mapped those transitions in energy landscape using extension length as a proxy. The complete unfolding length of our two-domain construct is 70 nm. However, depending on the force, it can vary between 50\u0026ndash;80 nm. Here, we have taken six clusters. C0 (0\u0026ndash;10 nm), C1 (10\u0026ndash;20 nm), C2 (20\u0026ndash;30 nm), C3 (30\u0026ndash;40 nm), C4 (40\u0026ndash;50 nm), U (\u0026gt;\u0026thinsp;50 nm). First, we consider each and every step position under 10 nm and map the next step position in the cluster matrix. Since we have both unfolding and refolding and our resolution is about 5 nm, from the C0 cluster the protein can go to CO, C1, C2, C3, C4, U as an unfolding transition and can also come to C0 itself as a refolding step. Similarly, from C1, it can go C1, C2, C3, C4, U as unfolding and come back to C1 and C0 as refolding. Same way we can map the number of all transitions in all possible position in cluster and their next transition direction. The transition line with value of 0 can later be removed for the sake of visualisation and thus the hetrogeneity can be mapped using the matrix clustering process. Needless to say, the bin size can be changed depending on the resolution limit as well as the proteins transition pattern. For smaller proteins, this size can be reduced to 3\u0026ndash;5 nm and larger or multidomain proteins can use a bin size larger than 10 nm (supplementary Fig.\u0026nbsp;21).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n\u003ch2\u003eThree-state analysis for lifetime measurement\u003c/h2\u003e\n\u003cp\u003eWe used three-state model to quantitively measure the multiplex behaviour of our system. We have found a number of microstaes residing in the conformation landscape. To characterize the heterogeneity and simplify the quantification of this n-state behaviour, we apply state boundary and divide this conformational state space into three parts, 0\u0026ndash;15 nm for closed state, 15\u0026ndash;45 nm for intermediate or partially unfolded states and above 45 nm as open state. We could choose a higher number of states to characterize the folding probability, however that would introduce further complexity which does not provide any significant insight. Also, changing the boundary values will change the folding probabilites, however the pattern will remain the same. Finally, we calculate the folding probability by measuring the dwell time percentage of those three states, which basically translates to the ratio of the amount of time in each state and total time at the respective clamping forces. This experiment is performed for all three variants for a range of forces with at least a total time of 30 minutes at each force collected from 3\u0026ndash;6 beads.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n\u003ch2\u003eCovalent attachment strategy\u003c/h2\u003e\n\u003cp\u003eFor performing long-term robust studies using magnetic tweezers all connections were prepared covalently.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\n\u003ch2\u003e1. Surface Preparation\u003c/h2\u003e\n\u003cp\u003eCoverslips were kept in the plasma chamber for 30 seconds. Plasma treatment will expose the gas inside the chamber to an energy source like a microwave and make the air into a free radical, ion mixture. This will remove all organic contamination. The coverslips were then kept in piranha solution (75% H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e, 25% H\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e) for 1 hour to remove all remaining traces of organic components. These surfaces were sonicated in Milli-Q water 4\u0026ndash;5 times to remove the traces of acid. Then, it was aged with 1 M KOH solution for 2 min\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e. Again, the sonication procedure was repeated with Milli-Q water. The water was changed after each wash. These surfaces were subjected to silanization in a solution mixture of 48 ml of acetone, 0.5 %v/v (3-Aminopropyl) triethoxysilane (APTES) (0.5 ml), and 1.5 ml of Milli-Q water. It was incubated for 45 minutes. Then, they were washed with Acetone by sonicating for 5 minutes. The same process was repeated with Milli-Q water. After the last wash with acetone, the surfaces were kept in a vacuum oven at 110\u0026deg;C for 1 hour. This process will help expose the ends of the alkoxysilane molecules that were coated during APTES incubation. Pegylation was carried out on the surfaces with NHS-(PEG)\u003csub\u003e2\u003c/sub\u003e-Maleimide, mPEG-SVA or whatever modification was necessary to attach proteins and beads in the presence of PEG buffer (100 mM NaHCO\u003csub\u003e3\u003c/sub\u003e, 600 mM K\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e, pH 8.3)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e. This reaction will take 4 hours. After that, sonicate the coverslips in milli-Q for 5 minutes. Next, an incubation was performed on the surface with 100 \u0026micro;M tetra-glycine peptide (GGGGC) that will interact with maleimide from the PEG molecule, in SEC buffer (pH\u0026thinsp;=\u0026thinsp;7.5) for 7 hours\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Then after washing is done, the incubation was done for the surface with protein and sortase A mixture (1 \u0026micro;M protein and 1\u0026ndash;2 \u0026micro;M Sortase A) for 2 hours. All of these reactions are performed at room temperature.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\n\u003ch2\u003e2. Bead Preparation\u003c/h2\u003e\n\u003cp\u003eTwo types of beads are used for performing the force spectroscopy experiments in magnetic tweezers: Magnetic beads and non-magnetic beads. Nonmagnetic beads, which were used as reference for correcting surface-related drift, were attached using adsorption for 30 minutes. However, two types of modification were done with M-270 amine-modified paramagnetic beads\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e of 2.8 \u0026micro;M diameter. Beads were first incubated in NHS-(PEG)\u003csub\u003e2\u003c/sub\u003e-NHS solution of PEG buffer for 4 hours. The PEG chemicals that were not used in the pegylation reaction were removed from the buffer to increase the efficiency and yield of the second reaction. To make a covalent bond with the protein of interest, these beads with N-hydroxysuccinimide ends were incubated in a LPETGSSC peptide solution of pH 7.5 for 7 hours. It was washed with the same buffer condition that will be used for the experiment. All of these reactions are performed at room temperature with continuous shaking.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contributions\u003c/h2\u003e\n\u003cp\u003eS.R. conceived the idea. S.R., P.S., V.V. build the MT instrument. O.S. wrote the code for image processing, filtering, and data acquisition from MT system. P.S. and V.V. designed and performed all the MT experiments. P.S. performed all the chemical modification and surface chemistry for tethering. P.S. and V.V. analysed the data. G.K.B. performed all the MD simulations. P.S. expressed and purified all the protein variants. S.G. and P.S. cloned all the chimeric constructs. S.R. and P.S. made the figures. S.R. and P.S. wrote the manuscript.\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThis work was supported by the Core Research Grant from SERB, Govt. of India.\u003c/p\u003e\n\u003cp\u003eSR acknowledges and thanks Dr. Raj K. Ladher, NCBS, for generously donating the Cadherin-23 plasmid. SR acknowledges the financial support by the DBT/Wellcome Trust India Alliance and Indian Institute of Science Education and Research Mohali (IISERM) for setting up the molecular biology facilities. PS is thankful to CSIR-India for providing fellowship. V.V., G.K.B., S.G. sincerely thank IISERM for fellowships.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWozniak, M. A. \u0026amp; Chen, C. S. Mechanotransduction in development: a growing role for contractility. \u003cem\u003eNat Rev Mol Cell Biol\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 34\u0026ndash;43 (2009).\u003c/li\u003e\n\u003cli\u003eRadin, I. \u0026amp; Haswell, E. S. Looking at mechanobiology through an evolutionary lens. \u003cem\u003eCurr Opin Plant Biol\u003c/em\u003e \u003cstrong\u003e65\u003c/strong\u003e, 102112 (2022).\u003c/li\u003e\n\u003cli\u003eXiao, S., Xiao, S. \u0026amp; Gr\u0026auml;ter, F. 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Here we study three such genetic variants of a mechano-responsive gating-spring protein, cadherin-23, that uphold the structural integrity of the protein, but showcase distinct genotypes and phenotypes. All-atom simulations indicated marginal deviations in the transient intra-domain interactions among the variants leading to variations in the anti-cross correlated motions among constituent β-strands. In nature, the variants experience declining functions with aging at different rates. We expose these variants to constant and oscillatory forces using magnetic tweezer, and measure variations in stochastic folding dynamics. All variants exhibit multiple microstates under force. However, the protein variant with higher number of intra-domain contacts exhibits transitions among the heterogeneous microstates for larger extent of forces and persisted longer. Conversely, the protein variant with weaker inter-strand correlations exhibits greater unfolding cooperativity and faster intrinsic folding, although its folding-energy landscape is more susceptible to distortion under tension. Our study thus deciphers the molecular mechanisms underlying the variations in force-adaptations and propose a mechanical relation between genotype and phenotype.\u003c/p\u003e","manuscriptTitle":"Exploring Force-Driven Stochastic Folding Dynamics in Mechano-Responsive Proteins and Implications in Phenotypic Variation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-09 14:00:11","doi":"10.21203/rs.3.rs-3887774/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a001d6fc-2d3b-403b-b08a-e8e741325178","owner":[],"postedDate":"February 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28666872,"name":"Biological sciences/Biophysics/Single-molecule biophysics"},{"id":28666873,"name":"Biological sciences/Biophysics/Molecular biophysics/Deformation dynamics"}],"tags":[],"updatedAt":"2025-01-26T08:06:23+00:00","versionOfRecord":{"articleIdentity":"rs-3887774","link":"https://doi.org/10.1038/s41467-025-55946-3","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-01-25 05:00:00","publishedOnDateReadable":"January 25th, 2025"},"versionCreatedAt":"2024-02-09 14:00:11","video":"","vorDoi":"10.1038/s41467-025-55946-3","vorDoiUrl":"https://doi.org/10.1038/s41467-025-55946-3","workflowStages":[]},"version":"v1","identity":"rs-3887774","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3887774","identity":"rs-3887774","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}