α-Actinin/titin interaction: A dynamic and mechanicallystable cluster of bonds in the muscle Z-diskMarco Grisona, Ulrich Merkela, Julius Kostanb, Kristina Djinovi�c-Carugob,c, and Matthias Riefa,d,1

aPhysik Department E22, Technische Universität München, 85748 Garching, Germany; bDepartment of Structural and Computational Biology, Max F. PerutzLaboratories, University of Vienna, A-1030 Vienna, Austria; cDepartment of Biochemistry, Faculty of Chemistry and Chemical Technology, University ofLjubljana, SI-1000 Ljubljana, Slovenia; and dMunich Center for Integrated Protein Science, 81377 Munich, Germany

Edited by James A. Spudich, Stanford University School of Medicine, Stanford, CA, and approved December 16, 2016 (received for review August 2, 2016)

Stable anchoring of titin within the muscle Z-disk is essential forpreserving muscle integrity during passive stretching. One of themain candidates for anchoring titin in the Z-disk is the actin cross-linker α-actinin. The calmodulin-like domain of α-actinin binds tothe Z-repeats of titin. However, the mechanical and kinetic prop-erties of this important interaction are still unknown. Here, we usea dual-beam optical tweezers assay to study the mechanics of thisinteraction at the single-molecule level. A single interaction ofα-actinin and titin turns out to be surprisingly weak if force isapplied. Depending on the direction of force application, the un-binding forces can more than triple. Our results suggest a modelwhere multiple α-actinin/Z-repeat interactions cooperate to en-sure long-term stable titin anchoring while allowing the individualcomponents to exchange dynamically.

α-actinin | titin Z-repeats | Z-disk mechanics | optical tweezers

Muscle is the tissue that is constantly subjected to high me-chanical loads. Whereas thick and thin filaments are re-

sponsible for active force production, the passive elasticity ofmuscle is dominated by titin/connectin filaments (1). Hence,under passive stretching conditions the integrity of muscle relieson titin’s being firmly anchored within the sarcomere, preventingthe interdigitated muscle filaments from falling apart (Fig. 1A).Whereas titin is firmly attached to thick filaments in the A-bandand the M-line (2–6), it is much less clear how stable anchoring isachieved in the Z-disk, where adjacent sarcomeres overlap. Thesuperstable titin/telethonin interaction within the Z-disk wasconsidered important for titin anchoring (7–9), but knockoutmutants later showed that it is not essential for muscle integrity(10–12). Apart from a direct interaction between actin filamentsand titin at the Z-disk edge (13), the most prominent candidatefor the anchoring of titin within the Z-disk is its interaction withα-actinin (Fig. 1B) (6, 12, 14).Four isoforms of human α-actinin have been identified: the

calcium-insensitive muscle isoforms 2 and 3, which cross-linkactin filaments in sarcomere-delimiting Z-disk complexes, andcalcium-sensitive nonmuscle isoforms 1 and 4. α-Actinin is anantiparallel homodimer whose most prominent task is cross-linking actin filaments of neighboring sarcomeres in the Z-disk(Fig. 1B; reviewed in ref. 14). In each subunit, a flexible regioncalled the neck separates the actin binding domain (ABD) fromfour spectrin-like repeats (SR) forming the rod region (Fig. 1Band Fig. S1). The rod regions of the two subunits interact andprovide a rigid spacer between the actin filaments. At the otherend of each subunit a calmodulin-like domain (CaMD) formedby two pairs of EF-hands (EF1-2 and EF3-4) is able to bind aZ-disk region of titin formed by the so-called Z-repeats (15–17).The current model for α-actinin 2 dynamic regulation suggeststhat EF3-4 hands of one subunit bind to the neck region of thejuxtaposed subunit, thus not being available for the interactionwith titin Z-repeats (Fig. S1) (18, 19). Upon activation of α-actininin the Z-disk by phosphatidylinositol 4,5-biphosphate (PIP2), EF3-4is released from the neck and binding of titin can be achieved in thisopen conformation of α-actinin.

In humans, the isoforms of titin exhibit four to seven Z-repeats(15, 16, 20). The structure of the EF3-4 hands complex with titinZ-repeat 7 shows the bound Z-repeat in an α-helical confor-mation (21). In solution assays, binding affinities of variousZ-repeats to EF3-4 were determined to lie in the micromolarrange (22). Micromolar affinity points only to a moderatelystable interaction, the kinetics of which are unknown. This raisesthe question of how such a relatively weak interaction canachieve the task of firmly anchoring titin within the Z-disk evenunder applied mechanical loads. To answer this question, we setout to investigate the mechanical as well as kinetic stability ofthis interaction directly in a single-molecule mechanical experi-ment. We provide evidence that the concerted action of severalα-actinin/Z-repeat bonds can establish long-term mechanicallystable anchoring, whereas the individual bonds can break andreform on the second timescale.

ResultsInteraction Between α-Actinin and Titin Z-Repeat 7 (PullA-T7 Geometry).To probe the mechanical strength of the interaction betweenα-actinin and titin Z-repeat 7 (T7), we prepared a construct where23 residues of T7 (21) were fused to the C terminus of EF3-4 of theCaMD of α-actinin 2 via a 4 × (GGS) linker. To apply load to thisfusion construct we tethered dsDNA linkers to cysteine residues atthe termini (Fig. 1C) that could be attached to 1-μm-sized beads inthe optical tweezers. For details on the assay see Materials andMethods and SI Materials and Methods. Note that in this constructthe force propagates through both the α-actinin EF3-4 domain andthe T7 peptide, mimicking how force propagates in the Z-disk (Fig.1B). We therefore called this construct PullA-T7.

Significance

Muscle is the tissue in our body experiencing most extrememechanical forces. The mechanism of active force generationhas been investigated for more than 50 y and is fairly wellunderstood. However, despite its physiological significance, itis still unknown what mechanical linkages hold together themuscle machinery under passive stretching forces. In this pa-per, we show with direct mechanical single-molecule mea-surements that an array of titin/α-actinin bonds composes adynamic network that can provide stable anchoring, main-taining the integrity of the muscle Z-disk even under load. Thisdynamic network explains how components of the Z-disk areable to rapidly rearrange and, at the same time, form a long-term stable mechanical structure.

Author contributions: M.G., K.D.-C., and M.R. designed research; M.G. performed re-search; U.M. and J.K. contributed new reagents/analytic tools; M.G. and M.R. analyzeddata; and M.G., K.D.-C., and M.R. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: mrief@ph.tum.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1612681114/-/DCSupplemental.

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When force is applied to PullA-T7, unbinding/unfoldingtransitions occur already at surprisingly low forces, as shown inFig. 1D. At the low pulling speed of 10 nm/s, only transitionsbetween the fully folded/peptide-bound state and the unfolded/peptide-unbound state can be observed. This conclusion is cor-roborated by worm-like chain (WLC) fits revealing a contourlength increase of 34 ± 1 (SEM) nm, which corresponds to bothdetachment of the peptide (assuming that it is unstructured afterunbinding) as well as unfolding of the EF3-4.To reveal more details of the force-induced unbinding/unfold-

ing kinetics, we performed a series of time traces, measuring forcefluctuations while keeping the distance between the two trapcenters fixed (passive-mode assay with preload around 3–5 pN). Atime trace excerpt of 5 s is shown in Fig. 1E, together with aschematic of the expected unbinding/unfolding pathway. Closeinspection of the time traces revealed short dwells (green spikes;see also the zoom in Fig. 1E) in addition to the folded/bound(purple, hereafter named FB) and unfolded/unbound state (red,UU). This third state is consistent with a conformation whereα-actinin is folded and T7 unbound (green, FU), because it alsoshows up in a mutant without ligand, where we only pull on EF3-4(PullA construct; details in Fig. S2 and SI Materials and Methods).

We used a hidden Markov model (HMM) algorithm (23) toidentify the transitions between this three-state system on theunfiltered traces. From the dwell-time distributions we calculatedtransition rates assuming the transition network shown in Fig. 1Ewith the FU state as an obligatory on-pathway intermediate. Fig.1F shows force-dependent folding (red) and unfolding (green)rates of EF3-4, and Fig. 1G shows binding (green) and unbinding(purple) rates of T7. A detailed discussion about the extraction ofthe unbinding rates of T7 in Fig. 1G is presented in Figs. S3 andS4. The force dependence of the unbinding rate is weak, as can beseen by an increase of only one order of magnitude within about10 pN of force. This weak force coupling is a consequence of thetransition state’s being close (2 nm) to the bound state. We find thatthe unbinding rate of T7 at zero force is 0.6 ± 0.1/s (Table 1).Force-dependent population probabilities (Fig. 1H) allow the

extraction of free-energy differences between the three statesusing a model (fitting curve) (24) explained in SI Materials andMethods. We find that the UU state has a free-energy differenceof 0.5 kBT with respect to the FU state, and 4.7 kBT to the FBstate (Table 1).The measurements shown so far, using the PullA-T7 construct,

do not allow the measurement of solution binding rates or the

A

B

C

D

E

F

I

G H

Fig. 1. Interaction between α-actinin EF3-4 and titin Z-repeat 7 in PullA-T7 geometry. (A) Schematic of the sarcomere organization under stretching con-ditions, showing titin elongation. (B) Arrangement of actin, titin, telethonin, and α-actinin within the Z-disk. (C) Schematic of the dual-beam optical tweezersexperimental setup with a fusion construct [Protein Data Bank (PDB) ID code 1h8h]. Yellow dots mark cysteine residues, here and elsewhere. (D) Force-extension trace obtained by moving the beads apart at a constant velocity, here for the PullA-T7 fusion construct. Gray dots are full bandwidth data, andblack dots are smoothed data. Dotted lines are WLC fits (SI Materials and Methods). (E) Passive-mode time trace of 5 s at an average force of 3.7 pN. Gray dotsare full-bandwidth data, on which HMM analysis was performed assuming the kinetic network on the right. For clarity, smoothed data are colored, based onHMM-assigned states. (Top Right) Zoom of 1 s, where full-bandwidth data are colored and smoothed data are in black. (F) Force-dependent transition ratesfrom UU to FU (red) and from FU to UU (green). Solid lines are fits that allow extrapolation to zero-force rates (SI Materials and Methods). (G) Same fortransition rates from FB to FU (purple) and from FU to FB (green). (H) Population probability of the three states as a function of force, and fits as described in SIMaterials and Methods. (I) Competition assay performed by addition of T7 in solution to evaluate the dissociation constant. A passive-mode sample trace of5 s shows that the solution binding event (cyan) has the same force (and contour length) as the FU state but can be identified by the different lifetime.

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dissociation constant, because the T7 peptide is tethered to theEF3-4 domain. To this end, we used a competition assay withfree T7 peptide in solution as described in ref. 25. Adding the T7peptide (650–698) to the solution now establishes a competitionbetween the tethered and the solution peptides (Fig. 1I). Apartfrom the three states already discussed above, a new long-livedstate (cyan) arises at a contour length identical to the green state(see the contour length vs. dwell-time scatter plot in Fig. S5B). Inthis state, a peptide from solution has bound, thus blocking the

rebinding of the tethered peptide and stabilizing the foldedconformation of EF3-4. Because no force is applied to the freepeptide, it will only dissociate at rates similar to the force-free case.Indeed, from the dwell times of the cyan states, we find a zero forceoff-rate koff = 1.3 ± 0.5/s, within a factor of two from the extrapo-lated zero force value of the purple branch in Fig. 1G. We esti-mated the pseudo first-order on-rate of the peptide to kon = 17 ± 6/sby summing up the total time the molecule spends in the green statebetween two subsequent cyan events (see also SI Materials and

Table 1. Energetic and kinetic binding parameters of different target peptides

Peptide Sequence fused to EF3-4 ΔG0, kBT KD, μM kF=0on , 1=s kF=0

off , 1=s

T7 654_GKKAEAVATVVAAVDQARVREPR_676 4.7* 4.3 ± 2.1† 302 ± 17 0.64 ± 0.06T1 422_ADKSAAVATVVAAVDMARVREPV_444 5.9* 1.3 ± 1.1‡ 509 ± 97 0.46 ± 0.05T3 518_GTEKAFVPKVVISAAKAKEQET_539 3.5* 14 ± 11‡ 158 ± 13 11 ± 10T2 472_EAEKIAVSKVVVAADKAKEQELK_494 <0.5§ > 287‡ — —

T5 562_ETRKTVVPKVIVATPKVKEQDLV_584 <0.5§ > 287‡ — —

Neck 259_AEQAETAANRIVKVLAVNQENERLME_284 0.7* 235 ± 160‡ 137 ± 6 40 ± 13

Bold amino acids in the peptide sequences mark key hydrophobic binding positions of the α-helix, alignedfollowing refs. 19, 21, and 22. Complete sequences of the constructs are given in SI Materials and Methods. Themost relevant error in ΔG0 comes from the force calibration, and it is estimated to be about 10%. The zero-forceextrapolated rate constants are obtained from the fits in Fig. 1G (T7), Fig. S6 (T1 and T3), and Fig. S8 (neck). Thezero-force rates errors, here and elsewhere, are SD.*From the population probability vs. force plot obtained from passive-mode traces.†From the competition assay.‡From Eq. 2.§The folding free-energy of the EF3-4 (0.5 kBT) sets a thereshold for the detection of the binding events.

A B C

Fig. 2. Interaction of α-actinin EF3-4 with different titin Z-repeats, with the same pulling geometry and the same color coding as in Fig. 1. (A–C) Interactionwith T1 in A, T3 in B, and T5 in C. Upper row: constant-velocity traces with fits (dashed lines) as in Fig. 1. The contour length increases for T1 and T3 are inagreement with the 34 ± 1 nm found for the PullA-T7 construct and expected from length measurements on the PDB structure. For T5, the dashed line is not afit (forces are below resolution) but marks the expected contour length of the FB state to guide the eye. Middle row: 5-s passive-mode time traces. Similartraces in competition assay with T7 in solution are shown in Fig. S7, to confirm that the FU state can also bind T7 as in Fig. 1I. Bottom row: populationprobability plots of UU and FB states as a function of force. Solid lines are a global fit to the data and dotted gray lines are fits to data from the pullA-T7construct, for comparison (Fig. 1H).

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Methods and Fig. S5A). The dissociation constant KD, with 52 μMof T7 was estimated to 4 ± 2 μM, using the relation

KD =koffkon

  ½Psolution�. [1]

Interaction of EF3-4 with Other Target Peptides. In a second set ofexperiments, we measured the mechanical strength of other titinZ-repeats with the α-actinin 2 C-terminal EF3-4 domain, fusingtogether the proteins in analogy with the PullA-T7 construct(Table 1). For comparison with T7, we investigated T1 (Fig. 2A),T2, T3 (Fig. 2B), and T5 (Fig. 2C). We could measure bindingfor repeats T1 and T3, but T2 and T5 showed no detectablebinding. Constant-velocity traces (top row) depict unbinding/unfolding forces for the T1 fusion construct similar to T7,whereas T3 forces are lower. This result is confirmed by passive-mode traces (middle row), where the lifetimes of the peptide-bound state are much longer for T1 than for T3 (T5 data re-semble those of the PullA construct in Fig. S2, where no peptideis tethered). In analogy with Fig. 1 F–H, we analyzed both theprobability (bottom row) as well as the dwell time distributions ofpassive-mode traces. Force-dependent kinetics were estimated(Fig. S6) and zero-force rates kF=0on (FU to FB) and kF=0off (FB toFU) extracted (Table 1).The general behavior of the T1 and T3 constructs under force

is similar to that observed for T7, as shown in the lower row ofFig. 2. The force-probability plot is slightly shifted toward higherforces for T1, and to lower forces for T3. This is related to ahigher free energy ΔG0 =G0

UU −G0FB for T1 and a lower for T3.

Table 1 summarizes both energetic as well as kinetic parametersof the different tethered titin Z-repeats.Because we directly measured the solution affinity of T7 in the

competition assay described above, KD values for the otherpeptides can now directly be obtained from the free-energyvalues measured for the tethered peptides. We designed theconstructs to have the same effective concentration of the teth-ered peptides, by using the same linker length of PullA-T7 (fordetails see SI Materials and Methods). For each repeat Ti, we cantherefore relate the measured binding/folding free energy ΔG0

Tidirectly to its dissociation constant KTi

D using

ΔG0Ti −ΔG0

T7 = ln

KT7D

KTiD

!. [2]

Finally, we investigated the interaction of EF3-4 with the neckregion of α-actinin 2 (G258–M283), which is crucial for the reg-ulation of α-actinin during sarcomere assembly and regulation(18, 19). Not only is the neck region unstructured in absence of asubstrate (18, 19), but also no interaction of the peptide lackingthe neighboring domains was ever observed. Our data (Fig. S8 andTable 1) show that in the fusion construct the neck peptide bindsEF3-4, albeit with very low affinity. A detailed discussion of theseexperiments is presented in SI Materials and Methods.

PullT7 Geometry. Although the tethered constructs (e.g., PullA-T7) used in the above experiments allow precise characterizationof the unbinding rates, they may not precisely mimic the waythose molecules refold/rebind in the Z-disk. In our experiments,owing to the direct tethering of T7 and EF3-4, the latter issubjected to load even after the bond has broken, leading torapid unfolding of the domain. In muscle, after unbinding of T7,EF3-4 will not be under load and, hence, will not experienceforced unfolding (Fig. 1B). The low midpoint force we measurefor the PullA-T7 construct (3.5 pN, Fig. 1H) results from thedifficulties of unfolded EF3-4 to refold under force, as can be

seen from Fig. 1E, where the bound state is populated only abouthalf of the time.To avoid forced unfolding of EF3-4 and getting more realistic

rebinding kinetics, we designed a new construct, PullT7, wherethe points of force application are changed, such that force isonly applied to the tethered peptide (Fig. 3A, Inset). Constant-velocity curves (Fig. 3A) already show a notable increase in theforces required to stretch and unbind the tethered peptide fromthe EF3-4 domain. Detectable unbinding events start at 8 pNand reach as high as 18 pN. Also, in passive-mode experiments(Fig. 3B) binding/unbinding forces are higher. Force-dependentpopulation probabilities (Fig. 3D) show the midpoint for theunbinding force at 13 pN, whereas the associated free energiesare similar to the ones measured in the PullA-T7 construct.

A

B

C D

E

Fig. 3. Interaction between α-actinin EF3-4 and titin Z-repeat 7 in PullT7geometry. (A) Constant-velocity trace at 10 nm/s and schematic of the pull-ing geometry. The contour length increase obtained from the fits is 4.3 ± 0.5(SEM) nm, in agreement with the expected stretching of the peptide helix.(B) Passive-mode trace, with the same color coding as in Fig.1. (C) Transitionrates from FU to FB (green, on-rates) and from FB to FU (purple, off-rates).From fits (solid lines), we extracted an off-rate at zero-force of 0.6 ± 0.3/s andan on-rate of 216 ± 106/s. (D) Population probability plot. From fits (solidlines), a free energy difference between FU and FB of 5.8 kBT was extracted.(E) Competition assay with 10 μM of T7 in solution. As described for Fig. 1I, weextracted a KD of 8 ± 4 μM from this data. Because in the absence of force theEF3-4 domain can still unfold (FU to UU rates in Fig. 1F), a correction of thekinetic parameters is necessary (SI Materials and Methods).

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Furthermore, binding/unbinding kinetics in this geometry (Fig.3C) extrapolate to zero-force values similar to those of thePullA-T7 construct (Fig. 1G). A competition assay with T7 so-lution peptide similar to the one of Fig. 1I yields identical so-lution binding and unbinding kinetics (Fig. 3E).

DiscussionInteraction Between α-Actinin and Titin Z-Repeat 7. Generally,proteins responsible for muscle mechanics and stability havebeen shown to be very stable either mechanically or thermody-namically. Titin Ig-domains unfold at forces around 200 pN (26,27) and the titin/telethonin interaction has been reported as oneof the most stable noncovalent bonds (∼800 pN) (9). Hence, itmay come as a surprise that in the PullA-T7 geometry we findthat the mechanical stability of the titin Z-repeat/α-actinin in-teraction involves protein structures that tolerate only a fewpiconewtons of force before they detach or unfold. EF3-4 with-out peptide bound already unfolds at around 1 pN (Fig. 1F).Even when the peptide is bound, the complex unbinds with amidpoint force of 3.5 pN (Fig. 1H). The relatively low mechan-ical stability we find for the complex is in agreement with themoderate dissociation constants reported in the literature (KD =0.1–0.25 μM) (18, 22). Our competition assay (Fig. 1I) yields ahigher KD value (4 μM), which may be explained by differentexperimental conditions. It is important to note that the KDvalues we measure for Z-repeats 1 and 3 (discussed below andshown in Table 1) are also consistently higher than those reportedin the literature; however, relative stabilities agree very wellwith literature. Our single-molecule competition experimentalso provides direct force-free measurements of the kinetics ofthe α-actinin/T7 repeat bond, and we find that the dynamics ofthis bond are surprisingly high with an average lifetime of 0.7 ±0.3 s (Fig. 1I).From the model shown in Fig. 1B it becomes obvious that, in

the Z-disk, forces resulting from sarcomere length increase willstretch titin and propagates through α-actinin, like in the probedPullA-T7 geometry, which we consider therefore a good modelfor the force-dependent unbinding kinetics in muscle (FB-to-FUtransition; Fig. 1G). Nonetheless, the midpoint force we measurefor the PullA-T7 construct (3.5 pN) is within the physiologicalrange of forces acting on a single titin molecule, estimated to be0–5 pN in a number of studies (27–29). The low measured forcesin the PullA-T7 construct can be ascribed to the fact that EF3-4readily unfolds after unbinding of T7, whereas this will not happenif titin and α-actinin are not tethered, as is the case in muscle.The PullT7 construct resolves this problem because force is

applied only across the Z-repeat 7 (Fig. 3). Hence, this constructbetter mimics the rebinding kinetics (FU-to-FB transition), be-cause the EF3-4 domain is not kept under force after unbindingof T7. Note that in PullT7 the unbinding kinetics are identicalwithin errors to the kinetics of the PullA-T7 construct (Fig. 1Gvs. Fig. 3C). Hence, force-dependent binding and unbindingkinetics measured with PullT7 are likely similar to those occur-ring in muscle. The midpoint force in PullT7 (Fig. 3D) now shiftsfrom 3.5 to 13 pN, showing that the α-actinin/T7 bond can, in-deed, resist forces considered physiologically relevant (27–29).The higher forces for this pulling direction are a consequence ofthe shorter difference in extension between the bound and theunbound conformations (4 nm of contour length, vs. 34 nm forthe PullA-T7 construct, including unfolding of EF3-4): Atequilibrium, interaction free energies can be related to the forcemultiplied by the elongation and the much shorter elongation inthe PullT7 construct leads to a higher midpoint unbinding force.

Interaction with Other Titin Z-Repeats. The number of Z-repeatsfound in titin depends on the isoform and ranges between twoand seven across all species (20), with repeats T1 and T7 beingalways present. Joseph et al. (22) assessed affinities of all repeats

to α-actinin and found measurable affinities to α-actinin 2 for T1,T3, and T7. Consistent with those earlier results, we observed nobinding of T2 and T5, and we measured similar affinities for T1(KD = 1 μM) and T7 (KD = 4 μM) and lower for T3 (KD = 14 μM;Table 1). Although Joseph et al. (22) found T1 to be a slightlyweaker binder, it is rather more stable in our experiments (Fig.2A). The differences in affinities are also reflected in the binding/unbinding rates (Fig. S6). Whereas the differences in on-rates aresmall among the constructs, we observe significant difference inoff-rates between the strongly binding peptides T1 and T7 vs. theweakly binding peptide T3. Overall, the kinetic data suggest thateven the strongest Z-repeat/α-actinin bonds can last no longerthan a few seconds in the absence of force.

Sarcomeric Z-Disk Model. Our single-molecule data indicate that,for a single α-actinin/Z-repeat bond, the unbinding rates in theabsence of load are faster than 2 s. How can this be reconciledwith a long-term stable arrangement of the Z-disk? Apparently,a single bond cannot provide enough long-term stability for theα-actinin/titin arrangement. The picture, however, changes if wetake into account that, in the Z-disk, there is more than oneα-actinin/Z-repeat interaction for each titin molecule. Lutherand Squire (30) have estimated, from the 19-nm α-actininspacing found in electron microscopy studies, that every otherZ-repeat can bind α-actinin in the Z-disk. Hence, if seven repeatsare present, up to four α-actinins will bind to the same titinmolecule simultaneously. Under load, titin will remain anchoredin the Z-disk as long as at least one Z-repeat interacts withα-actinin at any given time. Additionally, interaction of the Zqregion, which flanks Z-repeats, with α-actinin rod further con-tributes to stabilization of the titin/α-actinin interaction (17). Toassess the overall anchoring stability we therefore have to takeinto account the avidity effect originating from those multipleinteractions (Fig. 4).Avidity (31) is a concept originally proposed for antibodies

where, in an early phase of the immune response, low-affinityantibody fragments are combined in pentamers (IgM), thus in-creasing the number of interaction sites from 2 to 10. Individualinteraction free energies add up owing to the increased valency.In a similar way, the increased number of α-actinin/Z-repeat

bonds will increase the overall strength of titin anchoring. For anestimate of lifetimes, it is important to note that α-actinin inmuscle is also bound to actin, keeping each α-actinin close to itsZ-repeat, even if it has transiently detached. Hence, we believethe fast on-rates we measure for our fusion constructs are goodmodels for the on-rates in the muscle. Each interaction of thethree we identified in this study (T1, T3, and T7) has an off-ratebetween 0.5/s and 10/s and a rebinding rate of 150–500/s (Table1). For simplicity, we assume an equal off-rate of 1/s and an on-rate of 100/s of each interaction for the following estimate. Atzero force, the probability for each interaction’s being unbound

Fig. 4. Mechanical and kinetic model of titin anchoring within the Z-disk.α-Actinin spacing allows the binding of one actin cross-linker every two titinZ-repeats. The measured titin Z-repeats T1, T3, and T7 have unbinding ratesat zero load in the range of 0.5–10/s, whereas the binding rates are in therange of 100–500/s. Fast rebinding is ensured by the additional anchoring ofα-actinin to the actin filaments. This picture holds up to forces of severalpiconewtons (physiological range), ensuring long-term stability.

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is the ratio between on- and off-rate (i.e., 10−2). Starting fromtwo Z-repeats only, once per second the first Z-repeat de-taches. Before the rebinding takes place, the probability thatthe second also detaches is 10−2, meaning that on average it takes102 attempts (100 s) until both Z-repeats are contemporary de-tached and titin is released from the anchoring. With three re-peats, the average lifetime of the cluster would accordingly be1 s ×  104 = 10,000 s. This simple estimate shows that many dy-namic bonds, when acting together, can lead to a long-term stableanchor. Even under a mechanical load of 5 pN, the probability offinding a single Z-repeat bound (Fig. 3D), as well as the unbindingrate (Fig. 3C), would not change significantly, and even underthose conditions the Z-disk would remain stable. The concertedeffort of many bonds reconciles the apparently contradictory find-ings of a long-term stable Z-disk (half-life of titin ≈14 h) (32) and afast exchange of its individual components (half-lives of α-actininand other Z-disk proteins <1 min) (19, 33), as has been measuredin various fluorescence recovery after photobleaching studies.It is interesting to note that also the interaction of filamin to

the von Willebrand receptor GP1b involves such dynamic bondswhich, in combination with a cluster of interaction sites, result inlong-term stability (25). Dynamic bonds in combination withavidity providing long-term stability may be a common motif forall situations where a mechanically stable connection has to bemaintained while still providing reorganization, flexibility, anddynamics of the components involved.

Materials and MethodsAll protein constructs were prepared using standard recombinant techniques.The amino acid sequences, as well as the experimental procedures, arepresented in SI Materials and Methods.

The experiments were carried out using custom-built dual-beam opticaltweezers, with a design similar to the one described in ref. 34, but using twosteerable traps, one by means of acousto-optic deflectors (AODs) (AA OptoElectronic) and the other by a two-axis piezoelectric mirror tip/tilt actuator(Mad City Labs). Constant-velocity traces were obtained by tilting the piezomirror, and the AODs were used for the jump assays (SI Materials andMethods), because of the higher steering speed.

The stiffness and sensitivity of both traps were calibrated using a standardmethod (35) with back focal plane detection. Data acquisition was carriedout at a sampling rate of 150 kHz, averaged to 30 kHz before recording.After cross-talk correction for cross-polarization between the two traps (36),the signal of the two traps was averaged to improve the signal-to-noise ratio.

ACKNOWLEDGMENTS. We thank Matthias Gautel, Andrea Ghisleni, andEuripedes de Almeida Ribeiro for helpful discussions; Maik Veelders fortechnical assistance; and Katarzyna Tych and Markus Jahn for commentson the manuscript. This work was supported by Marie Curie InitialTraining Network MUZIC Grant 238423; Austrian Science Fund ProjectsI525, I1593, P22276, and P19060; Federal Ministry of Economy, Family andYouth through the initiative, “Laura Bassi Centres of Expertise” (K.D.C.);Center of Optimized Structural Studies Grant 253275 (to J.K.); the Univer-sity of Vienna; and Deutsche Forschungsgemeinschaft Grant FOR 1352 P8(to M.R.).

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