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. 2024 Mar 7;146(11):7266–7273. doi: 10.1021/jacs.3c10923

Unraveling the Dual-Stretch-Mode Impact on Tension Gauge Tethers’ Mechanical Stability

Jingzhun Liu ‡, Jie Yan †,‡,§,*
PMCID: PMC10959107  PMID: 38451494

Abstract

graphic file with name ja3c10923_0005.jpg

Tension gauge tethers (TGTs), short DNA segments serving as extracellular tension sensors, are instrumental in assessing the tension dynamics in mechanotransduction. These TGTs feature an initial shear-stretch region and an unzip-stretch region. Despite their utility, no theoretical model has been available to estimate their tension-dependent lifetimes [τ(f)], restricting insights from cellular mechanotransduction experiments. We have now formulated a concise expression for τ(f) of TGTs, accommodating contributions from both stretch regions. Our model uncovers a tension-dependent energy barrier shift occurring when tension surpasses a switching force of approximately 13 pN for the recently developed TGTs, greatly influencing τ(f) profiles. Experimental data from several TGTs validated our model. The calibrated expression can predict τ(f) of TGTs at 37 °C based on their sequences with minor fold changes, supporting future applications of TGTs.

Introduction

Tension gauge tethers (TGTs) are short segments of double-stranded DNA (dsDNA) that irreversibly dissociate in response to tension. TGTs were initially developed as sensors to measure tension levels transmitted across tension-bearing extracellular receptors, such as integrin, cadherin, and T-cell receptors.1−11 In these applications, a TGT is incorporated into a tension-transmission pathway via two attachment points on the TGT, which consists of a total of N base pairs. The first point, P1, is located at the end of one single-stranded DNA (ssDNA), and the second point, P2, is situated on the opposite strand, at the Mth base pair position relative to the P1 end (Figure 1a). Therefore, the stretching geometry of a TGT with a specific sequence is entirely defined by N and M, and it is henceforth denoted as M/N-TGT (Figure 1b).

Figure 1.

Figure 1

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Illustration of TGTs and the transition pathway for the tension-dependent strand dissociation pathway. (a) P1 (red) and P2 (green) are two force attaching points on a TGT with a total length of N bp that divide it into two regions: Rs (black) and Ru (gray) under shear- and unzip-stretching geometries, respectively. A TGT is named as M/N-TGT where M is the base pair distance between P1 and P2. (b) Typical design of TGTs with P2 at different positions (from top to bottom: left-end, middle, and right-end) on a DNA strand, named as 21/21-bp, 11/21-bp, and 1/21-bp TGT. (c) Tension-dependent strand dissociation pathway of a TGT via strand peeling from the P1 end.

A TGT can be divided into two distinct regions: Rs, which exists between P1 and P2 under a shear-stretching geometry, and Ru, which exists after P2 under an unzip-stretching geometry (as shown in Figure 1a). The strand dissociation of a TGT, which depends on the tension, follows a lowest-energy kinetic pathway. This pathway involves the sequential breakage of base pairs from the P1 end until the strands are fully dissociated (as shown in Figure 1c). The transition state can be indicated by the number of base pairs (n) between the fork (Figure 1c, red arrows) and P1. It is clear that there is a switch in stretching geometry when the fork passes n = M – 1.

Our current understanding of the mechanical stability of TGTs remains incomplete. The original description of mechanical stability has been based on the tension tolerance, Ttol, which is the tension required to dissociate a TGT with a given average lifetime of 2 s as per the studies by Wang and Ha.1 Recent research underscores the significance of comprehending the tension-dependent lifetime, τ(f),12 which offers a comprehensive understanding of the mechanical stability of TGTs. Despite its importance, no theoretical model has been available to estimate τ(f) for TGTs based on their sequences and stretching geometry, restricting insights from cellular mechanotransduction experiments.

In this study, we utilized Kramers’ kinetic theory to derive a general expression for the TGTs’ τ(f), which has a single model parameter, the effective diffusion coefficient D of DNA fork migration (depicted by red arrows in Figure 1c) during the transition. Our expression depends on the tension-dependent, one-dimensional energy landscape, which is influenced by various factors, including the DNA sequence, the entropic elasticity of both dsDNA and ssDNA, and the stretching geometries involved.

Results

Piecewise Linear Energy Landscape of TGTs

The process of strand dissociation of a TGT can be understood by considering the random movement of the fork position with the rates of base pair opening (forward) and formation (backward) depending on the tension. The energy required to open the ith base pair from the P1 end can be expressed as

graphic file with name ja3c10923_m001.jpg 1

here xss(f) and xds(f) are the extension of 1-nt ssDNA and 1-bp dsDNA under a stretching force f, respectively, which are calculated based on the worm-like chain polymer model with a bending persistent length of 0.7 nm for ssDNA13,14 and 50 nm for dsDNA15 using the Marko–Siggia formula.16 εi represents the energy cost to open the base pair at zero tension, which is evaluated in the work using the Santa Lucia nearest-neighbor base pair energy data.17 The force–extension curve of ssDNA, as modeled by the worm-like chain polymer model, fails at forces below approximately 8 pN.14,18 Additionally, the base pair energy data from Santa Lucia represent the free-energy difference between the base-paired state and disrupted state. In this disrupted state, the conformation of the released nucleotide steps differs from that under mechanical stretching. Therefore, an empirical energy shift is likely needed to be introduced to Δgi(F) compensating for such inaccuracies [refer to subsection “Single-Molecule Quantification of τ(f) for Several TGTs” and Supporting Information I].

We calculated tension-dependent energy landscapes for several commonly used TGTs with a given sequence, N, and M (see Figure 2). For forces below a threshold of fuc ∼ 13 pN, the energy profile monotonically increases with the number of opened base pairs until the second-last base pair in the TGT is ruptured. Note that the threshold tension fuc ∼ 13 pN is critical because it represents the tension at which the opening and closing rates of a base pair are equal under the unzip-stretch geometry. However, at higher forces, the energy profile is nonmonotonic, with a maximum at the base pair position n = M – 1. Our analysis suggests a tension-dependent shift in the energy barrier.

Figure 2.

Figure 2

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Tension-dependent energy landscape Inline graphic of a series of 21-bp TGTs with different stretching geometries (5′-GTGTCGTGCCTCCGTGCTGTG-3′): (a) 21/21-TGT in shear-stretch mode, (b) 11/21-TGT in dual-stretch mode, and (c) 1/21-TGT in unzip-stretch mode. The transition distance, the x-axis, is indicated by the fork position n. The tension-dependent energy landscapes of these TGTs are plotted over a wide force range. (d) Illustration of the simplified energy landscapes of the 11/21-TGT with 10 bp in shear-stretch mode and 11 bp in unzip-stretch mode.

In Figure 2a–c, various TGTs exhibit a similar increasing trend under tension levels below the threshold force due to a continuous increase in aggregated energy. In contrast, at forces higher than the threshold, the energy landscape profile becomes nonmonotonic, with a barrier located at n = M – 1. This is because within this force range, the energy required to break each base pair is positive in the shear-stretch region and negative in the unzip-stretch region (refer to Supporting Information II).

It can be seen from Figure 2 that for TGTs with the sequence 5′-GTGTCGTGCCTCCGTGCTGTG-3′ (N = 21), at a given tension, the energy landscape can be approximated by a piecewise linear function

graphic file with name ja3c10923_m002.jpg 2

here δ is a force-independent transition coordinate, chosen to be the number of dissociated base pairs during the transition. The energy landscape is composed of two straight lines with different slopes, each defined by four geometric parameters. The first set of parameters, δ1 and ΔG1, describes the number of dissociated base pairs and energy difference between the fully hybridized state (n = 1) and the state at the fork position n = M – 1. The second set of parameters, δ2 and ΔG2, describes the corresponding differences between the fully hybridized state (n = 1) and the rupture of the second-last base pair (n = N – 1) which breaks the stacking energy of the last base pair step (as shown in Figure 2d).

The four parameters are not independent variables; rather, they are directly derived from the values of M, N, and the tension- and sequence-dependent base pair energy data Δgi. Specifically, they are calculated as follows: δ1 = M – 1, δ2 = N – 1, Inline graphic, and Inline graphic. The slopes of the two lines are determined by the corresponding parameters: Inline graphic and Inline graphic, respectively.

Analytical Expression of τ(f) for TGTs

We examine τ(f) of a TGT based on the energy landscape (eq 2) within the framework of Kramers’ kinetic theory.19 Following the derivation reported previously,20,21 it can be shown that (Supporting Information III)

graphic file with name ja3c10923_m007.jpg 3

here β = 1/kBT, where kB is the Boltzmann constant and T is the temperature. The single model parameter D is the effective diffusion coefficient for fork migration during the transition process. The above formula has assumed sufficiently high value ΔG1 to meet the pre-equilibration condition imposed by the Kramers’ kinetic theoretical framework.19

At tensions much greater than Fuc, ΔG1 ≫ ΔG2 and so Inline graphic, indicating that the lifetime is determined by the barrier ΔG1. On the contrary, at tensions much smaller than Fuc, ΔG1 ≪ ΔG2 and so Inline graphic, indicating that the lifetime is determined by ΔG2. The result indicates a switch of the energy barrier from ΔG1 to ΔG2 when the tension decreases from above to below fuc.

Single-Molecule Quantification of τ(f) for Several TGTs

To evaluate the predictive capabilities of the model for dual-stretch-mode TGTs containing both shear-stretch and unzip-stretch regions at various forces, we conducted experiments for five TGTs, 11/11-TGT, 11/16-TGT, 11/21-TGT, 15/21-TGT, and 20/21-TGT (Figure 3a). Comprehensive details regarding the single-molecule experiment are presented in the Experimental Section in Supporting Information IV. The first three TGTs share the same shear-stretch region but differ in the length of their unzip-stretch regions, while the last three TGTs have the same overall length but feature different separations of shear-stretch and unzip-stretch regions (Figure 3b). A flexible ssDNA loop is incorporated to facilitate repeated measurements on the same tethered TGT, enabling the reformation of a dissociated TGT at low forces without impacting its tension-dependent lifetime.

Figure 3.

Figure 3

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Single-molecule quantification of τ(f) of five different TGTs and the prediction of τ(f) of currently widely utilized TGTs (N = 21). (a) Schematic of the designed DNA detector tethered between a glass surface and a superparamagnetic bead. The TGT is stretched through a thiol anchored on the glass surface and a biotin linked to a 576-bp DNA handle attached on the superparamagnetic bead. (b) Stretching geometry of our examined TGTs with varying lengths in unzip- or shear-stretch regions. (c) τ(f) of 11/11-, 11/16-, 11/21-, 15/21-, and 20/21-TGTs. The solid lines represent the best-fitting curves for the quantified data points, while the dashed lines depict the τ(f) values predicted by the average of the five best-fitting parameters D, obtained from the five TGTs. (d) Predicted τ(f) of seven widely utilized TGTs in the cellular experiment (N = 21).

For each TGT, the average lifetimes were determined by analyzing at least 30 force–jump cycles for each target tension using data from three individual detectors. One exception is the data point obtained at 9 pN for the 11/21 TGT, where only nine data points were obtained from a single tether due to the long lifetime at this force. As the tension increases, the lifetime of all these TGTs decreases, indicating that they become less stable under higher tension. As depicted in Figure 3c (solid lines), the model can reasonably fit the data obtained from all the TGTs, with fitting values of D over a range from 1.6 × 107 to 1.0 × 108 s–1, by introducing a small constant energy correction σ = 0.45 kBT to account for any inaccuracy in tension-dependent base pair energy, which serves as an empirical parameter that enables a reasonable fit of the expression (eq 3) to the experimental data. While the factors underlying this energy correction are unclear, several possible causes are discussed in Supporting Information I. Using an average value of approximately D = 5.7 × 107 s–1, the predicted τ(f) agrees reasonably well with all the individually fitted profiles of these experimentally quantified TGTs (Figure 3c, dash lines with corresponding colors).

As the contour length of a dsDNA base pair is lds = 0.34 nm, the effective diffusion coefficient D can be converted to D′ = lds2·D with the unit of nm2·s–1. The value of D′ is over the range from 1.9 × 106 to 1.2 × 107 nm2·s–1, which is similar to the magnitude reported in previous studies.22,23

Collectively, these findings indicate that the model (eq 3) can be applied to various TGTs with differing lengths, diverse stretch region-to-unzip region ratios, and both lower (f < fuc) and higher (f > fuc) forces. Although the fork diffusion constant D fitting values vary among TGTs, the fold differences remain within 1 order of magnitude. These disparities in the fitting values of D can be attributed to inaccuracies in estimating tension-dependent base pair energies (Supporting Information I).

By utilizing the average value of D, we were able to estimate τ(f) for seven 21-bp TGTs that were investigated in previous cell experiments1−4,8,10,11 (as depicted in Figure 3d). The calculation is detailed in Supporting Information V. The plot reveals highly different tension-dependent lifetime profiles due to the different positions of P2. When P2 is located near the middle of the DNA segment, the profile shows a clear change of slope slightly above the value of fuc ≈ 13 pN. Since the highly diverse τ(f) profiles result from changes in P2 that alter the lengths of the shear-stretch and unzip-stretch regions, this strongly suggests differential contributions from both regions to the tension-dependent lifetime of TGTs.

Overall, the findings suggest that, at high forces (f > fuc), the transition rate is primarily influenced by the energy barrier’s height at position M – 1. Additionally, the unzip-stretch region has a marginal impact on the transition rate at forces slightly higher than fuc. At lower forces (f < fuc), both the shear- and unzip-stretch regions contribute to the tension-dependent lifetime τ(f). The significantly increased lifetime in the lower force range is a direct result of the higher energy cost of breaking each base pair, the switched energy barrier, and the longer diffusion distance. Further details on the differential contributions from shear- and unzip-stretch regions at low or high force regions are provided in Supporting Information VI and VII.

Rupture Tension and Lifetime Distributions of Widely Utilized TGTs

TGTs offer comprehensive insights into the mechanical responses of mechanosensing systems and tension-transmission interactions in supramolecular linkages. Beyond their originally proposed role as tension-threshold sensors, requiring a lifetime of a few seconds, TGTs can serve a dual function during dynamic stretching processes. Specifically, TGTs can indicate whether the applied tension surpasses the threshold needed to activate key mechanosensing proteins and whether the duration of this tension is sufficient for the activated proteins to facilitate downstream mechanotransduction processes.

To substantiate this, Figure 4 displays the distributions of rupture forces (expressed as Inline graphic,20Figure 4a) and lifetimes (Inline graphic, Figure 4b) of seven commonly used TGTs subjected to linearly increasing forces with various loading rates Inline graphic. For the 1/21-, 4/21-, and 7/21-TGTs, their lifetimes exhibit a rapid decrease with tension, yielding a “sharp distribution” of rupture force and lifetime at pN/s loading rates. In contrast, TGTs that contain a longer shear-stretch region showcase a slower decrease in lifetimes with tension, resulting in a “wider distribution” of rupture force and lifetime. At a given loading rate, TGTs exhibiting a sharp distribution can indicate the threshold of the tension level and tension duration, whereas TGTs with a wide distribution can provide only a confidence range for the tension level and tension duration.

Figure 4.

Figure 4

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Rupture force distributions (a) and the lifetime distributions (b) of seven widely utilized TGTs (N = 21) with different force increasing rates derived from the predicted τ(f) of these TGTs shown in Figure 3d. From the top to the bottom panel, the increasing rates are r = 10, 4, and 1 pN/s, respectively.

Consider 11/21-TGT and 15/21-TGT as examples: While both have been demonstrated to support cell adhesion spreading, cells spread on the 15/21-TGT surface exhibit greater spreading and focal adhesion areas than those on the 11/21-TGT.11Figure 4a reveals that at loading rates of >1 pN/s, both TGTs rupture at forces >10 pN, a magnitude exceeding the activation forces required for talin mechanosensing domains via mechanical unfolding.12,24 Furthermore, Figure 4b demonstrates that the lifetime of 15/21-TGT is significantly longer than that of 11/21-TGT at identical loading rates. This potentially allows for an extended duration of downstream mechanotransduction processes, offering a plausible mechanism to explain the distinct cell adhesion behaviors observed on surfaces coated with these specific TGTs.

Discussions and Conclusions

In summary, through the analysis of the energy landscape of dual-stretch-mode TGTs and the application of Kramers’ kinetic theory, we have derived a simple analytical expression, τ(f), for which the fork diffusion constant serves as a model parameter. The energy parameters, ΔG1 and ΔG2, are calculated from the DNA sequences using the Santa Lucia nearest-neighbor base pair energy data and the force–extension curves of the ds and ssDNA. The expression was calibrated at a temperature of 37 °C, which aligns with the conditions of most cell experiments. The calibrated expression yielded a range of fork diffusion constants between 1.6 × 107 and 1.0 × 108 s–1 for five different TGTs with varying lengths and shear-to-unzip base pair ratios. Using the average of the diffusion coefficient, the expression can predict τ(f) with reasonable accuracy solely based on the sequence and the stretching geometry of TGTs, facilitating their use in cell mechanotransduction studies conducted at 37 °C.

In our theoretical treatment, we divide the energy landscape into two regions: a shear-stretch region and an unzip-stretch region. This division is not solely based on the alignment of the force direction and the tangent of the dsDNA, whether they are nearly parallel (shear-stretch) or nearly perpendicular (unzip-stretch) to each other. It also takes into account whether one (shear-stretch) or two (unzip-stretch) nucleoside steps are under force after a base pair is disrupted, which is a significant force-dependent factor in base pair energy. When the strand-peeling fork approaches P2 within a distance of approximately 2 nm in the shear-stretch region, even though the force direction no longer aligns precisely with the dsDNA tangent, one nucleotide step remains under force, while the other is not, after the base pair is ruptured. Therefore, the nonideal alignment of the force direction and the dsDNA tangent, which could cause a small shift in the force-dependent dsDNA base pair energy, should not have a significant impact on the results.

Short dsDNA segments under shear-stretch geometry have been theoretically investigated.25,26 Analyzing the static micromechanics, a critical rupture force fc was predicted, above which short dsDNA becomes mechanically unstable. fc increases with the dsDNA length and saturates when the dsDNA is sufficiently long. This prediction was subsequently explored experimentally in a single-molecule manipulation study, wherein the critical rupture force of a short dsDNA segment was measured during incremental force increases of 2 pN per second. The study observed a monotonically increasing fc, which saturates at approximately 60 pN for lengths significantly exceeding 25 bp.27 A similar trend was observed in a simulation study using the oxDNA software based on a coarse-grained DNA model.28−30 Crucially, this simulation offered comprehensive insights into the kinetics of the rupture transition across a force-dependent energy barrier.29 Consistent with previous findings, our analytical expression (eq 3) predicts an increasing fc over a 1 s observation window as a function of dsDNA length, which plateaus at around 55 pN when the length significantly exceeds 25 bp (Supporting Information VIII). The lower saturating force observed in our study, compared to previous single-molecule studies,27 is attributed to the higher temperature (37 °C) used in our study.

The dual-stretch-mode TGTs feature a considerable lifespan at zero tension due to their ample length, which prevents spontaneous dissociation, and display a tension-dependent lifespan across a broad tension spectrum. This characteristic holds promise for a variety of applications. In addition to shedding light on the time scales involved in specific mechanotransduction processes at cell–matrix adhesions,1−8 cell–cell adherence junctions,9 and mechanical activation of T-cells,10,31 they may also be applied to study the tension duration of various mechanically sensitive membrane receptors, such as adhesion GPCRs32,33 and tethered ion channels.34 Moreover, the potential of dual-stretch-mode TGTs to significantly augment the utility of TGTs as mechanical instruments in DNA nanotechnology and bioengineering is considerable. For instance, they can act as hydrogel cross-linkers to modulate stiffness and elasticity.35,36 Their prolonged stability at zero tension is beneficial for preserving hydrogel integrity over extended rest periods, while their tunable-tension-dependent lifespan can be leveraged to deliberately design hydrogels with adjustable yielding strengths. The development of a theoretical model for τ(f) of dual-stretch-mode TGTs, which predicts τ(f) based on sequence and stretching geometry, offers a strategic framework for the design of dual-stretch-mode TGTs tailored to specific applications.

There are a few limitations to the application of the tension-dependent lifetime expression, which is currently calibrated for a specific experimental condition: 37 °C, 150 mM NaCl, and pH 7.4. When this expression is used to assess the mechanical stability of TGTs under different conditions, such as varying temperatures and salt concentrations, it will be necessary to recalibrate the parameters for the corresponding conditions. Additionally, even with the inclusion of an energy shift to account for inaccuracies in the force-dependent free energy required to disrupt a base pair, the calibrated expression is not applicable at forces lower than 8 pN, where complex intramolecular interactions occur and significant deviations from the behavior of a worm-like-chain polymer become evident.14,18

Acknowledgments

The research was funded by the Singapore Ministry of Education Academic Research Funds Tier 2 (MOE-T2EP50220-0015, MOE-T2EP50123-0008), the Singapore Ministry of Education Academic Research Fund Tier 3 (MOET32021-0003), and the Ministry of Education under the Research Centres of Excellence programme.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c10923.

  • Experimental Section (including single-molecule constructs, single-molecule manipulation, and tension-jump assay), deviation for the analytical expression of tension-dependent lifetime of TGTs, energy cost for DNA base pair disruption under different stretching geometries, the energy correction σ introduced for model fitting, differential contributions from shear- and unzip-stretch regions at high and low force ranges, the length dependence of the critical rupture force of short dsDNA under shear-stretch geometry, and the code for calculating tension-dependent lifetime of TGTs (PDF)

The authors declare no competing financial interest.

Supplementary Material

ja3c10923_si_001.pdf (549.6KB, pdf)

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