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Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers

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Science  16 May 1997:
Vol. 276, Issue 5315, pp. 1112-1116
DOI: 10.1126/science.276.5315.1112

Abstract

Titin, a giant filamentous polypeptide, is believed to play a fundamental role in maintaining sarcomeric structural integrity and developing what is known as passive force in muscle. Measurements of the force required to stretch a single molecule revealed that titin behaves as a highly nonlinear entropic spring. The molecule unfolds in a high-force transition beginning at 20 to 30 piconewtons and refolds in a low-force transition at ∼2.5 piconewtons. A fraction of the molecule (5 to 40 percent) remains permanently unfolded, behaving as a wormlike chain with a persistence length (a measure of the chain’s bending rigidity) of 20 angstroms. Force hysteresis arises from a difference between the unfolding and refolding kinetics of the molecule relative to the stretch and release rates in the experiments, respectively. Scaling the molecular data up to sarcomeric dimensions reproduced many features of the passive force versus extension curve of muscle fibers.

Passive force develops when a relaxed muscle is stretched; this force is responsible for restoring muscle length after release, and it is required for maintaining the structural integrity of the sarcomere in actively contracting muscle (1). Titin (2), a giant 3.5-MD protein, spans the half-sarcomere, from the Z line to the M line (3) (Fig.1A). Because titin is anchored both to the Z line and to the thick filaments of the A band, passive force while the sarcomere is stretched is probably generated by extension of the I-band segment of the molecule (4, 5). It has been suggested (6, 7) that the elasticity of titin derives from the reversible unfolding of the linear array of ∼300 immunoglobulin C2 (Ig) and fibronectin type III (FNIII) domains (8) that make up the molecule. In addition, a unique proline (P)-, glutamate (E)-, valine (V)-, and lysine (K)-rich (PEVK) domain recently identified in titin (9) has been hypothesized to form a semistable region that operates as a low-stiffness spring (9).

Figure 1

(A) Diagram of the location of titin and the binding sites of the antibodies to titin (T12 and T51) and myomesin in the half-sarcomere. (B) Titin molecules were stretched between two beads by moving the micropipette away from the optical trap. The bead in the optical trap (bead at left) was coated with antibody T12, and the other bead was held by a micropipette and bound to the M line end of titin. The end-to-end length (z) was measured as previously described (11), and the force on the trapped bead was measured by detecting the change in the light momentum (deflection) as it left the trap (11). Use of a coaxial dual-beam optical trap permitted high-force manipulation (∼70 pN) far from cover glass surfaces (100 μm) with minimal light power input (100 mW).

Here, we stretched titin by attaching each of its ends to a different latex bead (10), one of which was held by a movable micropipette and the other was trapped in force-measuring laser tweezers (11) (Fig. 1B). The micropipette was then moved at a constant rate while the force generated in the molecule was continuously monitored. When a maximum predetermined force (f max) was reached, the process was reversed to obtain the release half-cycle. The force versus extension (fversus z) curves from these experiments (Fig. 2) illustrate several characteristics of the data. (i) The end-to-end distance (z) at which the common f maxis reached varies considerably, probably as a result of a variation in the location of the bead attachments in titin. (ii) Many molecules were extended far beyond the ∼1-μm contour length of native titin (12). (iii) Normalizing the curves to the same length scale reveals that the force generated for a given fractional extension (the ratio of z to the contour length, L) also varies from experiment to experiment, probably reflecting different numbers of titin molecules within the tethers. (iv) All curves show hysteresis.

Figure 2

Ensemble of f versus zcurves for three titin tethers. The directions of data acquisition are indicated by arrows. Stretch and release rates were ∼90 nm/s.

To identify single-molecule tethers and determine their length, we segregated the data into classes by comparing them with the predictions of two entropic elasticity models: the freely jointed chain [FJC (13)] and the wormlike chain [WLC (14)] models. The FJC model did not describe the data, but the WLC model fit the stretch data at low to moderate forces and the release data at moderate to high forces (15). The WLC model describes the chain as a deformable continuum (rod) of persistence lengthA, which is a measure of the chain’s bending rigidity. For a WLC, z is related to the external force (f) byfA/k B T =z/L + 1/4(1 –z/L)2 – 1/4, wherek B is the Boltzmann constant and T is absolute temperature (16). The end-to-end length (z) of a WLC approaches its contour length (L) asf −1/2. The contour lengths of the tethers were thus estimated by plotting the data as f −1/2versus z and extrapolating to infinite force (16) (Fig. 3A). A histogram of the release contour lengths obtained in this way showed a bimodal distribution with peaks at ∼1.5 and ∼4 μm (15), reflecting the presence of two titin sizes in our preparations [T1 and the difference fragment (Fig. 1A)]. However, there is a discrepancy between the calculated 10-μm contour length for a fully unfolded titin molecule (17) and the observed contour-length peak at ∼4 μm. Possibly the molecules were never fully unfolded and extended under the forces used (18).

Figure 3

(A) Thef 1/2 versus z plots for the stretch (red) and release (blue) of a triple-titin tether at a rate of 64 nm/s. A linear fit to the force data at high extension is extrapolated to the z axis to obtain the contour length (L) and to the force to obtain the effective persistence length (A). Dotted lines from left to right are WLC curves for A = 4, 6, 8, and 10 Å for the stretch data, andA = 6, 8, 10, and 12 Å for the release data. (B) Histogram of effective persistence lengths showing a multimodal distribution where peaks correspond to various numbers of parallel titin molecules (indicated as numbers above the peaks). The peak at the largest persistence length (∼20 Å) was assigned to the single titin molecule. (Inset) Thef versus z curves (release data) for a triple-titin tether and a single titin molecule. Contour lengths for the two tethers were comparable (4.2 μm for the triple titin and 4 μm for the single).

In the f −1/2 versus zplot, the extrapolated force-axis intercept of a curve at high extension indicates the persistence length of a molecule by the relation A =kBT/4F [whereF is force at the intercept (Fig. 3A)]. When multiple molecules are present in a tether, this intercept (the apparent persistence length of the tether) is divided proportionately. The frequency of apparent persistence lengths for 302 releases of 45 tethers is shown in Fig. 3B. The distribution is multimodal with peaks corresponding to single, double, and triple parallel strands of the molecule. Accordingly, the persistence length of the single, unfolded molecule is ∼20 Å. For a given extension, proportionally greater amounts of force were generated when multiple strands of titin were subjected to the stretch-release cycle than when only a single molecule was present (Fig. 3B, inset).

The f −1/2 versus z plots revealed that titin does not behave as a WLC throughout the entire stretch-release cycle: Its behavior deviates from that of a WLC at high force during stretch and at low force during release, indicating the onset of structural transitions (Fig. 3A). Because in most experiments the stretch and the release transitions occurred at extensions larger than the contour length of the extended but native titin, these transitions must involve force-induced unfolding and refolding in the molecule. Accordingly, we propose the following model to rationalize these observations: (i) At the beginning of stretch, a variable fraction of the molecule, 5 to 40%, is already unfolded (19). In this early part of the stretch curve (WLC region 1 in Fig. 3A, and from points a to c in Fig. 4A), the molecule behaves as a WLC whose properties are dominated by this pre-unfolded fraction. Consistent with this model,L stretch (Fig. 3A) is more than twice as long as the contour length of the native molecule, and the persistence length associated with this part of the curve (20 Å) is about one-seventh that estimated for native titin (20). The pre-unfolded fraction may contain the PEVK domain, although in most cases it exceeds the length attributable to this domain (19). (ii) As titin is stretched to high force (20 to 30 pN), transitions begin to occur in the molecule (onset of stretch transition in Fig. 3A, and point c in Fig. 4A) that convert part of the folded fraction into unfolded protein. As titin is further stretched, mechanical denaturation (unfolding) of additional Ig- and FNIII-type domains in the molecule takes place, a process that may not be completed when the maximum force allowed by the instrument, f max, is reached (stretch transition in Fig. 3A, and points c to d in Fig. 4A). Thus, the contour length of the fully denatured titin was never observed in our experiments. (iii) Upon release of the unfolded titin, the molecule does not refold in the initial ∼15 s of the release part of the cycle but behaves instead as a WLC (points d to e in Fig. 4A) with the properties of an unfolded polypeptide (persistence length ∼20 Å). (iv) Only when the molecule is allowed to shorten down to about one-half of its release contour length (L release) does refolding begin to take place, which is seen as a transition in both the f versusz curve (from points e to b in Fig. 4A) and in thef −1/2 versus z plots (release transition, Fig. 3A). In this region, much of the shortening occurs around 2.5 pN as the data cross various WLC curves corresponding to different persistence lengths. The release transition marks the refolding of the Ig and FNIII domains. (v) As titin shortens below ∼40% of its release contour length, the refolding ceases and the force drops (points b to a in Fig. 4), and the molecule again behaves as a WLC with a shortened contour length (L stretch, Fig. 3A).

Figure 4

(A) The f versus extension curve normalized to a single titin molecule (from a double-molecule tether), highlighting the points at the beginning and at the end of the transitions. Both stretch (red) and release (blue) had a rate of ∼60 nm/s. (Inset) Curves off versus z for experiments where the stretch or the release of titin was stopped short of entering the stretch or release transition (points c and e, respectively). (B) Effect of repetitive cycles of stretch and release in the absence of chemical denaturant. Shown here are the second (A, red), third (B, green), and fifth (C, blue) cycles in a series taken at a rate of 65 nm/s.

In this model, the f versus z curves display hysteresis because the rate at which the molecule is stretched or released exceeds the rate of unfolding and refolding of the molecule at equilibrium at that extension. If our stretch-release experiment had been done more slowly, the stretch and release portions of the force curve would have converged toward a single intermediate curve representing the true equilibrium denaturation-renaturation force. The unfolding and refolding rates under force are much lower than those rates in the presence of strong chemical denaturants (21), suggesting that titin’s domains must pass through kinetic folding intermediates with high activation energies (E a), and that pulling a domain does relatively little to lower those energies. During unfolding, such intermediate states might not increase the axial end-to-end length of a domain significantly and therefore might be accessible only through the generation of force perpendicular to the pulling direction (by thermal fluctuations). Thus, an axial force would do little to speed up the denaturation. Tension in the chain must be increased above its folding-unfolding equilibrium value to access these states at the experimental rate. During renaturation under external force, intermediate states are required that would shorten the unfolded domains axially. Tension in the denatured chain will raise the energy of these states, which now stand as barriers (activation states) to renaturation. Therefore, to access these states at the experimental rate, the tension in the chain must be lowered below its equilibrium value. A simulation based on this model reproduces the hysteresis and other features seen in the f versus z curves of Fig. 4 (22).

In support of our model, stopping short of the transition in either direction abolished hysteresis. Thus, it was possible to stretch and release the molecule reversibly between points b and c, and also between points d and e in Fig. 4 (Fig. 4A, inset). By comparison, hysteresis was reestablished when either transition was allowed to occur, either in part or to completion. As a further test of this model, titin was stretched in the presence of the chemical denaturant guanidinium-HCl (GuCl) at a concentration of 1.6 M (6). Upon addition of GuCl, the molecule exhibited one normal stretch half-cycle but failed to refold on the release half-cycle, so the first stretch-release cycle showed force hysteresis. In the next cycle, hysteresis almost completely disappeared, and the stretch curve approached the release curve, indicating that the release data indeed represents the elastic behavior of an unfolded polypeptide.

Repetitive cycles of stretch and release alone also led to the progressive denaturation of titin. During this process the stretch and release transitions shortened, and the stretch curve moved progressively toward the release curve (Fig. 4B). Thus, it appears that after each stretch-release cycle an increasing fraction of the unfolded titin failed to refold. Such a “wearing out” of titin may be caused by the randomization of proline isomer forms in the Ig and FNIII domains (23).

The force measured for a single titin molecule can be scaled up by the number of titin molecules in the sarcomere to test the hypothesis that titin is solely responsible for the passive elastic response of muscle. Assuming six titins per thick filament per half-sarcomere (4), the calculated curves of passive force per muscle cross-sectional area as a function of sarcomere length can be obtained. The calculated curve is very similar in shape and magnitude to that obtained experimentally for a single skeletal muscle fiber in which caldesmon had been used to block the weak acto-myosin interaction (24) (Fig. 5). This agreement validates the previous conclusion (24) that titin is the main determinant of the passive force response of muscle. In addition, this analysis indicates that the hysteresis observed in stretch-release experiments in relaxed muscle results from the combined folding-unfolding kinetics of many independent titin molecules (Fig. 5, inset).

Figure 5

Calculated passive force per cross-sectional area of skeletal muscle as a function of sarcomere length, scaled up from single-titin data (stretch rate, 65 nm/s, open circles). The scaled-up curve is compared with one obtained for a rabbit m. psoas fiber (estimated stretch rate, 3.3 nm/s, filled squares). Titin density per muscle cross-sectional area was assumed to be 2.8 × 1015/m2 (4, 20). Sarcomere lengths for the scaled-up data were obtained from lengths associated with the fractional extension of the elastic I band segment of titin (26), thereby disregarding any difference between the contour length of the I band segment and that of the titin molecules used in the experiments. (Inset) Curves off −1/2 versus sarcomere length for the psoas muscle fiber data, showing similar features to those of single titin molecules (Fig. 3A).

It has been argued (6, 7) that domain unfolding-refolding is likely to be involved in the role of titin as an elastic element in muscle physiology. However, if parts of the molecule unfold and refold each time a muscle is stretched and released, an amount of energy equal to the area inside the hysteresis curve would be wasted as heat. We suggest, rather, that the pre-unfolded fraction of titin functions as an efficient (reversible) entropic spring in muscle. Then the purpose of the slow “wearing out” of titin with recent folding-refolding transitions (Fig. 4B) might be to increase the length of the molecule’s pre-unfolded region; the longer the pre-unfolded region, the longer also is the range of motion over which the force curve is reversible (regions a to c in Fig. 4A), thereby minimizing subsequent hysteresis and keeping efficiency high. By pre-unfolding just as much titin as necessary, the maximum of the range of efficient elastic response in muscle may be adjusted. Regulating the range of the efficient elastic response in muscle through titin unfolding and refolding may serve as an adaptive mechanism during the repetitive mechanical loading of skeletal or cardiac muscle.

  • * These authors contributed equally to this work.

  • Present address: Central Laboratory, University Medical School of Pecs, Hungary.

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