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The Elasticity of Single Titin Molecules Using a Two-Bead Optical Tweezers Assay

Mark C. Leake , David Wilson ^*, Mathias Gautel  and Robert M. Simmons ^*

^* Medical Research Council Muscle and Cell Motility Unit, Randall Centre for Molecular Mechanisms of Cell Function, King's College London, London SE1 1UL, United Kingdom; and Department of Physical Biochemistry, Max-Planck-Institut für molekulare Physiologie, 44202 Dortmund, Germany

Correspondence: Address reprint requests to Robert M. Simmons, Randall Centre, King's College London, New Hunt's House, Guy's Campus, London SE1 1UL, UK. Tel.: 44-1672-562281; E-mail: robert.simmons{at}tiscali.co.uk.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Titin is responsible for the passive elasticity of the muscle sarcomere. The mechanical properties of skeletal and cardiac muscle titin were characterized in single molecules using a novel dual optical tweezers assay. Antibody pairs were attached to beads and used to select the whole molecule, I-band, A-band, a tandem-immunoglobulin (Ig) segment, and the PEVK region. A construct from the PEVK region expressing >25% of the full-length skeletal muscle isoform was chemically conjugated to beads and similarly characterized. By elucidating the elasticity of the different regions, we showed directly for the first time, to our knowledge, that two entropic components act in series in the skeletal muscle titin I-band (confirming previous speculations), one associated with tandem-immunoglobulin domains and the other with the PEVK region, with persistence lengths of 2.9 nm and 0.76 nm, respectively (150 mM ionic strength, 22°C). Novel findings were: the persistence length of the PEVK component rose (0.4–2.7 nm) with an increase in ionic strength (15–300 mM) and fell (3.0–0.3 nm) with a temperature increase (10–60°C); stress-relaxation in 10–12-nm steps was observed in the PEVK construct and hysteresis in the native PEVK region. The region may not be a pure random coil, as previously thought, but contains structured elements, possibly with hydrophobic interactions.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The giant muscle protein titin (connectin), molecular mass 3 MDa (Wang et al., 1979), is responsible for the major part of the passive elasticity of vertebrate muscle (Wang and Greaser, 1985; Trombitas et al., 1991; Granzier and Irving, 1995). It extends across the entire half-sarcomere from the Z-disk at its N-terminus to the M-line at its C-terminus. Under normal conditions the A-band region is firmly associated with the myosin thick filament and is considered to be inextensible, but the I-band section is free to elongate and therefore constitutes the physiologically relevant portion (Fürst et al., 1988; Whiting et al., 1989; Trombitas et al., 1991).

In recent years, the mechanical characteristics of titin have been determined in a number of preparations: in myofibrils or single cells, where most of the elasticity derives from titin and in which fluorescence-labeled or gold-labeled antibodies to specific titin epitopes have been used to apportion stretch between different regions of the molecule (Trombitas et al., 1993; Linke et al., 1996, 1998a; Gautel and Goulding, 1996; Gautel et al., 1996a; Granzier et al., 1996), and in single molecules or expressed fragments, using optical tweezers or atomic force microscopy (AFM) techniques (Kellermayer et al., 1997; Rief et al., 1997; Tskhovrebova et al., 1997). Measurements relating to polymer properties are also available from light scattering measurements (Higuchi et al., 1993), NMR (Fraternali and Pastore, 1999), and electron microscopy (EM) (Tskhovrebova and Trinick, 2001).

The I-band region of skeletal muscle titin has a sequence consisting mainly of 43–96 immunoglobulin (Ig) domains (Labeit et al., 1992; Labeit and Kolmerer, 1995) and a specialized elastic PEVK region, so-called because it is rich in proline, glutamate, valine, and lysine residues. At a low force, the main contribution to the compliance of titin comes from the nonlinear, entropic elasticity of the random chain of Ig domains (Tskhovrebova et al., 1997; Linke et al., 1998b). As the molecule is stretched the end-to-end distance increases as the chain is straightened, and force rises. At greater stretch, the Ig chain becomes stiffer and the PEVK region then contributes more to compliance. In experiments on isolated whole titin molecules, the A-band region (composed mainly of 123 Ig and 48 Fn) domains also comes into play.

A third component of elasticity may be supplied by unfolded I-band Ig domains: these domains unfold upon stretch at a rate that depends on force and rate of stretch (Evans and Ritchie, 1999). Once unfolded, most domains do not refold until the force is reduced to near zero (Kellermayer et al., 1997; Rief et al., 1997; Tskhovrebova et al., 1997; Carrion-Vazquez et al., 1999). Unfolding appears to explain much of the stress relaxation shown by stretched passive muscle (Minajeva et al., 2001), but its exact role is unclear. Unfolding may constitute a mechanism for resetting stiffness when a muscle is extended to a new mean length (Tskhovrebova and Trinick, 2000); or it may provide a safety mechanism to prevent damage from a force overload (Rief et al., 1997;Tskhovrebova et al., 1997); or a fraction of the Ig domains may remain more or less permanently unfolded and contribute additional compliance (Kellermayer et al., 1997), though recent data suggests that the unfolding pathway of most titin I-band domains will not result in unfolding at physiological forces (Williams et al., 2003). These mechanisms are not mutually exclusive.

Two polymer models, the worm-like chain (WLC) and the freely jointed chain (FJC), can be used to describe these sources of elasticity. These random chain, entropic models are characterized by the extended length of the chain, the contour length (L_c), and the functional segment length, which is the persistence length (L_p) in the worm-like chain model and the Kühn length (L_k) in the freely jointed chain model. In principle, a multiple component polymer having serially distinct chains of different segment length can be characterized from mechanical measurements, provided the difference between the segment lengths is sufficiently great. Two types of elastic component have proved to be of interest: i), the chain of Ig (and Fn) domains, where structural NMR data (Fraternali and Pastore, 1999) have shown the length of a single Ig domain is 4.5 nm. If the domains are linked in tandem via a universal joint with no steric hindrance then L_k should be 4.5 nm and L_p 2.2 nm; and ii), unfolded or random coil structures, where the minimal segment length is the extended residue repeat of 0.36 nm, where L_k should be 0.36 nm and L_p 0.18 nm, if there is no hindrance to rotation.

Tskhovrebova et al. (1997) fitted force-extension curves of the whole rabbit longissimus dorsi muscle titin molecule with a two-component polymer model. The components were identified with a chain comprising the PEVK region (here referred to as chain I) and the chain of Ig/Fn domains (chain II): for chain I, the value of L_p, 0.15 nm, was close to the value expected for a random, unhindered polypeptide chain, and the value of L_c, 416 nm, was close to the predicted extended length of the PEVK region. Similarly for chain II, L_p at 4.6 nm was close to the value expected from the repeat distance of Ig and Fn domains, and L_c at 1020 nm coincided with the value expected from sequence information for the total length of Ig/Fn domains.

For the whole molecule, fitted with a single component model, a further laser-tweezers study gave values of 1.5–2.0 nm (Kellermayer et al., 1997, 1998, both using rabbit longissimus dorsi muscle titin), consistent with the two-component fit by Tskhovrebova et al. (1997) in that a single component approximation to a two-component system will generate an effective persistence length that is a weighted average of the persistence lengths of the two-component system and thus a value intermediate between the two. However, a recent study on a cardiac muscle PEVK construct gave L_p values with a range from 0.4 to 2.5 nm (Li et al., 2002, using a concatemer of human cardiac PEVK and the human Ig domain I27, (I27-PEVK)₃), with a similar range of persistence lengths observed using recombinant soleus muscle PEVK molecules (Labeit et al., 2003), much higher than the estimate of Tskhovrebova et al. (1997) for the putative native PEVK domain, also to be compared with an estimate of 2.0 nm for the PEVK region from Trombitas et al. (1998) using human soleus muscle fibers. There is also the possibility that unfolded Ig domains contribute to the lower L_p component, but AFM mechanical studies have given L_p values of 0.4–0.8 nm or unfolded Ig/Fn domains either in whole titin or an expressed region containing tandem Ig repeats (Rief et al., 1997, using constructs of human I91–93 and I91–98; Rief et al., 1998, using constructs of human I91–98, I112–118, and A60–65; Carrion-Vazquez et al., 1999, using concatemers of I27, (I27)₈, and (I27)₁₂).

In addition, electron microscopy (Tskhovrebova and Trinick, 2001, using rabbit longissimus dorsi muscle titin) and dynamic light scattering (Higuchi et al., 1993, using rabbit longissimus dorsi muscle titin) of the whole molecule have suggested L_p values for the whole titin molecule of 13.5 and 15.0 nm, respectively, far greater than any of the other single molecule estimates, though consistent with an estimate of 15.0 nm for the tandem-Ig region from immunoelectron microscopy of stretched human soleus muscle fibers (Trombitas et al., 1998). Data from single myofibril stretches have also been fitted by a broad range of persistence lengths, typically with a mean of 0.6 nm for the PEVK region, with the suggestion of an additional enthalpic component to the elasticity (Linke et al., 1998a, using rat psoas myofibrils) and as much as 42 nm for the tandem Ig region (Linke et al., 1998b, using rat psoas myofibrils).

One difficulty in obtaining clear results in mechanical studies is that, without special precautions, purified titin is likely to be a mixture of isoforms of different lengths and may also be multimeric (Tskhovrebova and Trinick, 1997, using rabbit longissimus dorsi muscle titin). There are several isoforms, generated from a series of exon-skipping events of a single gene (Freiburg et al., 2000). The full-length isoform is expressed in soleus and diaphragm, with the shortest isoform expressed in cardiac muscle that has 53 fewer IgI domains and a much shorter PEVK region of 186 residues compared to 2181 in soleus, accounting for its greater intrinsic stiffness. Oligomers of titin, with up to five chains connected, form the bulk of purified titin when it is eluted from a gel filtration column. The effect of multiple attachments in supposedly single molecule experiments is to give a low apparent value of L_p, and this could help to explain the low value for the PEVK domain obtained by Tskhovrebova et al. (1997).

Using an improved two-bead laser-tweezers method, we have reinvestigated the elastic properties of skeletal muscle titin, employing a range of antibodies raised against specific epitopes to attach beads to locations along the molecule. We used skeletal muscle titin purified from a single fast muscle (longissimus dorsi) to restrict the number of isoforms present, and we used a fraction that was shown by EM to be almost exclusively monomeric. Using a protocol designed to reduce the number of multiple and nonspecific attachments, we derived polymer fits to force-extension curves for the whole molecule, the A-band region, the I-band region, and two subdivisions of the I-band, the PEVK region and a short tandem Ig region. Only in the I-band region and the whole molecule was it necessary to use a two-component model: chain I with a low value of L_p (0.5–0.8 nm) and chain II with a high value (3.0–3.6 nm). The tandem Ig/Fn regions (the A-band and tandem Ig region) and the PEVK region could each be fitted with a single component model, with L_p values similar to those found for chain I and chain II, respectively. In addition, chain I was not found in cardiac muscle titin, in which the PEVK region is greatly truncated. In the case of skeletal muscle titin, chain I is therefore very likely to derive from the (large) PEVK region.

The value of the short L_p component (chain I) depended on ionic strength, and we investigated this dependence more thoroughly together with the temperature dependence in the native PEVK region and in a construct comprising about one-quarter of the native PEVK sequence. Stepwise lengthening was detected with stretch, particularly with the PEVK construct, tentatively suggesting that there are regions in the PEVK domain corresponding to short structures that reversibly unfold and refold with stretch and release. These may correspond to the repeated charged regions of PEVK identified from the sequence (Greaser, 2001) and shown by NMR to have homology to a polyproline-II left-handed helix coil (Ma et al., 2001).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Preparation of titin
Skeletal muscle titin was prepared from the longissimus dorsi muscle of New Zealand white rabbit, Orycytolagus cuniculus, using the method of Trinick et al. (1984) with minor modifications. At the end of the procedure, the crude extract of titin was pumped through a large pore gel filtration column (5 cm diameter x 1 m length, Sepharose 4B-CL, Sigma-Aldrich, St. Louis, MO), collecting 80 fractions of 4.0 ml, monitoring A₂₈₀. Low-angle rotary-shadowed specimens of various fractions dialysed into buffer E (Table 1), dried and viewed by electron microscopy, showed that the first titin fractions eluted were highly oligomeric in nature, consisting of perhaps as many as five monomers, decreasing to two with the peak of the A₂₈₀ signal; subsequent fractions were found to be largely monomeric and uniform in terms of measured molecular contour length until later fractions where shorter components emerge. Titin remained stable for over 4 months when stored at –20°C in 50% glycerol.

PEVK construct preparation and sequence
A fragment of skeletal titin encompassing residues 5594–6143 of skeletal titin (European Molecular Biology Laboratory X90569, Heidelberg, Germany) was subcloned into a modified pET vector, introducing a C- and N-terminal cysteine, and referred to as PEVK1. PEVK1 was expressed in Escherichia coli at 15°C, purified by nickel-chelating chromatography by use of an N-terminal His⁶-tag followed by anion-exchange chromatography on a monoQ column (Amersham-Pharmacia, Buckinghamshire, UK). The His⁶-tag was cleaved off using TEV protease essentially as described (Young et al., 1998). The PEVK fragment was found to be stable at 4°C for several weeks in the presence of protease inhibitors (as above) and for several months at –20°C in 50% glycerol.

Bead preparation for native titin
For native titin, several antibodies with well-defined epitopes, mostly sequence assigned, were used to cross-link the protein to latex beads, 2.0-µm diameter polystyrene beads derivatized with aldehyde-sulfate groups (Interfacial Dynamics, Portland, OR), using the method of Tskhovrebova et al. (1997) with minor modifications. If fluorescent beads were required, 1 µM rhodamine isothiocyanate (RITC) was incubated before the final wash and incubation with bovine serum albumin (BSA). Stored at 4°C, the antibody-labeled beads remained viable, in terms of ability to bind to titin, for 2–3 months. The binding of titin followed the method of Kellermayer et al. (1997). The surface density of titin could be controlled by varying the concentration in the incubation mixture.

Tethering via sulfo-SMCC
The titin construct, PEVK1, was engineered to have a free sulphydryl group on each terminus. The entire length of titin PEVK contains no cysteine residues, allowing therefore end-specific thiol-directed attachment. The terminal sulphydryl groups were used to tether to amine-coated polystyrene latex beads via the water-soluble maleimide N-hydroxy-succinimide heterobifunctional cross-linker, sulfo-succinimidyl 4-(N-maleimidomethyl) cyclohexane-1-carboxylate (Sulfo-SMCC; Pierce Chemical, Rockford, IL), to constrain the entire length of the construct between two beads.

The protocol used was modified from the method of the manufacturer (Pierce Chemical, "Instructions: NHS-Esters Crosslinkers", 9/1997). A quantity of 1.0 ml 0.5-mg/ml suspension of 2.1-µm diameter polystyrene latex beads derivatized with aliphatic amine groups (Interfacial Dynamics) was spun down and the pellet resuspended in 50 µl 1-mg/ml solution Sulfo-SMCC in buffer C, the incubation allowed to proceed for 1 h at room temperature (if fluorescent beads were required, 5 µl 1 µM RITC in buffer C was added and left to incubate for a further 5 min at room temperature), and 10 µl 200 mM buffer D was added to quench the NHS-ester conjugation, incubating for a further 5 min. The beads were then washed, spun down, and resuspended in 100 µl buffer B.

To coat the SMCC-beads in the construct, 100 µl beads were first spun down and the pellet resuspended in 50 µl 2-mM solution of ß-mercaptoethanol, incubating for 30 min at room temperature to preblock 80% of the active maleimide sites. The beads were then washed, spun down, and resuspended in 50 µl 0.2 nM PEVK1, incubating overnight on an agitator at 4°C. After a final wash and spin, the beads were resuspended in 80 µl buffer C.

Immunofluorescence
Immunofluorescence studies on antititin antibodies were performed on single relaxed myofibrils prepared from rabbit longissimus dorsi muscle by a modification of a technique developed for rabbit psoas muscle (Linke et al., 1997). Photomicrographs taken under fluorescence and phase contrast were scanned, and image analysis was performed using the shareware package Scion Image. Intensity profiles were obtained across an 8–10 sarcomere length of myofibril mean averaging across a 20-pixel width at each point on the length axis. The profile corresponded to an equally spaced Gaussian intensity doublet across each Z-disk. The whole intensity profile was fitted with Gaussians using a least-squares routine written in Matlab to obtain the doublet separation. At separations of less than 50 nm, two Gaussians could no longer be resolved.

The measured loci of the epitopes are listed in Table 2, and are shown in comparison to their positions predicted from the sequence for soleus muscle, supposing a titin molecule to be fully extended. In deriving the predicted values, it was assumed that the N-terminus of titin begins at the center of the Z-disk (Gautel et al., 1996b). Lengths were assumed as follows: 4.4 nm for IgI- and Fn3-like domains (Pfuhl et al., 1995), 15 nm for each Z-repeat lattice spacing (Young et al., 1998), and 0.36 nm for individual amino acid residues in a random-coil configuration.

Surface plasmon resonance on a stationary phase of titin and a mobile phase of free-flowing anti-N2-A gave a spontaneous dissociation rate of 2.5 x 10^–3 s^–1. Assuming a width of activation potential for the dissociation transition of 0.4 nm (Schwesinger et al., 2000) and modeling the most probable dissociation force by the formulation of Evans and Ritchie (1997) suggested a most likely force at which dissociation occurs of 80–95 pN for the rates of loading used in the dynamic stretch protocol (20–200 pN s^–1). This was in excess of the maximal force applied in the optical tweezers experiments.

Optical tweezers
The single bead technique used previously in this laboratory for full-length titin (Tskhovrebova et al., 1997) requires a very large geometric correction at the shorter lengths needed in this study; so instead we used a two-bead system (Leake et al., 2003), similar in approach to Kellermayer et al. (1997). In the bulk of the experiments a 2-W near infrared laser (Nd:YLF 1.047 µm TFR, Spectra Physics, Mountain View, CA) was used. Two independent single-beam gradient traps were used, similar to the design of Simmons et al. (1996) except where stated.

The objective was mounted on a piezoelectric transducer (PZT) focusing device (Physik Instrumente, Karlsruhe, Germany), which allowed submicron precision movement over a range of 0–0.35 mm. Movement of one trap (trap 1) was effected by a pair of acousto-optic modulators (AOM; Isle Optics, Taunton, UK), using negative feedback to act as a tensiometer (Simmons et al., 1996). The other trap (trap 2) was positioned by two galvanometer-driven mirrors (Cambridge Technology, Cambridge, MA). The galvanometer system was chosen as it provided the large extensions needed for the whole titin molecule experiments. The position of the two trapped beads was monitored by splitting and focusing the brightfield image onto two separate 1-mm diameter quadrant photodiode detectors, QD1 and QD2. The quadrant detectors had a bandwidth of 15 kHz. The overlap between the images and also the overlap between the laser beams of the two beads had to be minimized. This was in part achieved by using 2-µm diameter beads, though corrections were necessary. Photodiode sensitivity was optimized by focusing the bead image to a dark outer ring with a lighter center, with the outer diameter of the dark ring roughly 20% larger than that of the quadrant detector.

Trap stiffness was routinely measured by a method utilizing Stokes' Law, which was found to be in satisfactory agreement with methods employing the measured Brownian motion of the trapped bead and the corner frequency of the power spectral density (Svoboda and Block, 1994).

The discrimination between bead types in these two-bead experiments was made possible by making one of the sets of beads fluorescent with RITC and observing the fluorescence image with a separate charge-coupled device (CCD) camera.

Formation of tethers
For most experiments, the beads were injected into a simple flow cell, constructed from a glass microscope slide and a glass coverslip, with a volume of 35 µl. One bead was trapped in trap 1 (tensiometer), and the tether was stretched by moving trap 2 holding the other bead, similar to the protocol of Leake et al. (2003).

The best method for producing a tethered bead pair was to tap together heterogeneous pairs (Kellermayer et al., 1997). A low frequency triangle wave of typically 1 Hz was applied to the x axis galvanometer (where x is the direction along the axis between the beads), large enough for the beads to touch at maximal displacement of bead 2.

An advantage of this approach was that it directly generated a calibration function for QD2 in the presence of bead 1. At a small separation of the beads, the Airy disk of bead 1 was detected by QD2, resulting in an effective reduction of the sensitivity of QD2 to movements of bead 2 by as much as 30%; a calibration for QD2 in the presence of bead 1 was obtained for each bead pair studied, using a polynomial fit as for QD1. The response was linear for a bead separation of up to 300 nm and had a practical range of 600 nm. For greater separations, a larger split photodiode detector was employed. This had the disadvantage that sensitivity was fourfold lower, but the advantage that the correction needed for bead image overlap was negligible.

Depending upon the range of surface densities of titin and antibody (or PEVK construct and SMCC) employed, the time taken for tether formation could be as low as a few seconds and as high as 15 min. The likelihood of multiple tether formation is obviously higher the greater the surface density, and, as addressed later, a compromise value was chosen that would give a mean tether formation time of at least 5 min.

Sustained contact, where a bead pair is held in contact for anything from a few seconds to several minutes, and then pulled apart, was found to produce an unacceptably high proportion both of very stiffly tethered beads where a gap could still be discerned between the two, consistent with multiple tether formation, and of bead pairs where no gap could be observed even at the highest trapping forces achievable of 150 pN, probably due to adhesion between the latex of the beads, despite blocking with bovine serum albumin.

Applied stretches
For triangle wave stretches, the molecule was extended at 1 Hz, starting with a small amplitude oscillation, usually less than 50 nm, and subsequently at increased stationary bead-bead separation by offsetting the x direction galvanometer (along the axis between the beads) until the beads just touched at the extremity of the oscillation as before. The highest force that could be obtained was 150 pN, but the practical limit was 80 pN at which the position of the trapped beads became unstable.

For square wave stretches, bead 1 was held in a position feedback-clamp, and bead 2 oscillated with a square wave. The frequency was 0.05–5 Hz, and the amplitude was adjusted as for triangle waves.

Data acquisition and analysis
Data were acquired continuously at a sample rate of 1 kHz, with retrospective low-pass filtering using a first-order Butterworth filter with a frequency cutoff of 100 Hz. Force-extension data were fitted with both one- and multiorder-component freely jointed chain (Florey, 1969) and worm-like chain (Marko and Siggia, 1995) models, including the presence of enthalpic components and higher order improvements to the worm-like chain model, using routines written in Matlab that applied a Nelder-Mead downhill-simplex minimization algorithm (Nelder and Mead, 1965). Different models within each same data set were compared on a pairwise basis by applying a Student's t-test between each relevant goodness-of-fit factor to test if a statistically significant improvement in fitting had occurred at a confidence level of P < 0.01. The equations used and details of the fitting and statistical methods are given in the Supplementary Material.

Antibody experiments
In preliminary experiments, no marked differences were found depending on which one of a pair of antibody-labeled beads was precomplexed with titin or which bead of a pair was held in the fixed-position trap. The identical procedure was, however, followed for each bead pair within a set of experiments: the titin was always preincubated with the bead carrying the antibody to the epitope nearer to the M-line.

Tethers fell into two distinct populations: short-lived tethers (roughly two-thirds of the total number) that lasted for less than 10 stretch-release cycles before breaking and long-lived tethers that lasted for the duration of the stretch experiment (typically at least 5 min) without breaking.

The experiments were performed at room temperature, 22°C, in a 10-mM HEPES buffer, pH 7.2, with total ionic strength in most experiments of either 150 or 300 mM formed by addition of sodium chloride. It was not possible to change the solution while maintaining trapping, so the different ionic strengths were tested in separate experiments.

Controlling flow-cell temperature
In experiments in which the temperature of the flow cell was varied, the temperature control was achieved by applying a thermal gradient across the glass surfaces driven from a pair of 40-W Peltier units in thermal contact with the objective. To reduce heat loss, there was an air gap between the condenser and the flow cell. The flow cell itself consisted of two coverslips supported by a Perspex spacer on the microscope stage.

A feedback system was employed between a thermocouple embedded in the aluminium cuff encasing the objective and the Peltier units. The calibration of temperature was performed by heating waxes of calibrated melting point inside the chamber. The flow-cell temperature could be varied between 10°C and 60°C and settled to ±1°C of the equilibrium temperature within 1 min of a change in command temperature. The presence of the laser-trap was found to increase the temperature in the vicinity of the focal waist by 2°C, consistent with previous findings (Kuo, 1998).

There was no significant change in magnification with temperature, but there was a change in the height of the bead above the coverslip. This was manifest in an alteration in the focus of the bead image at the level of the detectors resulting in a different sensitivity. It was rectified by refocusing through z movement of the objective and recalibrating the detectors by oscillating the beads (tethered together) with a piezoelectric transducer-controlled mirror.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Force-extension experiment protocol and data fitting
In all the experiments on native titin, the molecule was attached to two beads, each labeled with an antibody to a different epitope. The procedure used (described in detail in the Materials and Methods section) was to introduce the two sets of beads into a flow cell, one of the sets of beads carrying a fluorescent marker. One bead from each set was trapped, and the two beads held apart. One of these beads was then moved using a triangular wave of 1–2 Hz so as to tap the second bead at one extreme of its motion. When an attachment (tether) had formed, the bead and trap positions were recorded while the triangular wave movement was continued or an alternative mechanical perturbation applied. The procedure used in the PEVK construct experiments was similar, except that the construct was chemically cross-linked to the beads (see Materials and Methods).

Fitting the data with all models described (Supplementary Materials) produced some results common to all data sets:

1. Worm-like chain fits of a given order n were always better than freely jointed chain fits of the same order (consequently only the worm-like chain results are given).
   
2. The addition of a small enthalpic component (elastic modulus K in the range 600–900 pN) improved some of the fits (P = 0.1–0.2) but never at the prescribed level of confidence of P < 0.01 (we therefore modeled the elasticity for all regions of titin as having a pure entropic basis, at least in the first place).
   
3. Higher order corrections to the pure entropic worm-like chain model made some improvement to most of the fits (again in the range P = 0.1–0.2) but not at the prescribed level of confidence of P < 0.01.
   
4. The highest order n of worm-like chains in series within any data set that improved the fit at a confidence level P < 0.01 was 2 and was only found for titin segments that included both the PEVK region and the tandem-Ig domains.
   
5. With further components added to a pure single worm-like chain model, there was found to be some evidence for systematic deviation for the whole skeletal muscle titin data sets possibly due to fitting of intrinsic noise as opposed to underlying signal (Supplementary Material). Also, there was some evidence for systematic deviations in the fitted parameters of multiorder worm-like chain models for data sets in which a single chain fit was adequate, which were consistent with applying the same fitting algorithms to theoretically generated noisy single worm-like chain force-extension data.
   

Position of antibodies
The loci of the known epitopes of the antibodies used are shown diagrammatically in Fig. 1. As these antibodies were not raised against the source of titin used in our experiments, rabbit longissimus dorsi, we checked the positions of binding sites in the sarcomere in myofibrils from this muscle using immunofluorescence (Materials and Methods). The results are shown in Table 2 together with the positions expected from sequence information. There is reasonable agreement between the two.

View larger version (25K): [in this window] [in a new window]   FIGURE 1  Schematic diagram of the two native titin isoforms used of (A) bovine cardiac, consisting predominantly of the N2-B isoform, and (B) rabbit longissimus dorsi. The epitopes for the antibodies used in this study have been marked with arrows. The number of residues in the PEVK region of the longissimus dorsi region has not been determined to date, though it is known to be less than that of the full-length isoform as expressed in soleus muscle (2181 aa). The results (C) from immunofluorescence labeling of rabbit longissimus dorsi muscle myofibrils (full results are given in Table 2) are superimposed on a ruler to be compared with B. Error bars are set at one standard deviation from the mean (•).

Experiments on the skeletal (rabbit longissimus dorsi) muscle isoform employed antibody pairs chosen to select the following regions: the whole of the titin molecule from the Z-disk to M-line regions (for both the skeletal and cardiac isoforms), the A-band region, the I-band region, a tandem Ig domain region from the I-band, and the PEVK region. For each region, separate experiments were performed at ionic strength 150 mM and 300 mM. The results for the whole skeletal muscle titin molecule are given in some detail to illustrate the methods used, and the results for the other regions and for cardiac titin are presented more briefly.

Whole titin
The antibody pair used (T12-AB5) selects the whole of the molecule except for a region 60 nm from the Z-disk. All force-extension curves were fitted with multicomponent freely jointed and worm-like chain models, both with and without enthalpic contribution (Supplementary Material). As shown in Fig. 2, the fits were qualititatively similar whichever model was used, though in both cases two components produced a better fit to the data than one component with a WLC model giving better fits than that of a freely jointed chain. This was the case for both of the two regions (whole molecule and I-band) of the molecule for which two chains in series were needed to fit the data, but for regions of the molecule for which a single chain sufficed (PEVK region, tandem-Ig region, and A-band), the data were better fitted by the WLC model, and for this reason (and for the sake of brevity) only the WLC-based analysis is presented here.

View larger version (28K): [in this window] [in a new window]   FIGURE 2  Force-extension relation for the whole titin molecule and polymer model fits. Force-extension curves at (A) 150 and (B) 300 mM ionic strength (red) with polymer fits of single freely jointed chain (green), single worm-like chain (magenta), and double worm-like chain (black). (C) Force residuals for the fits of A. (D) Force residuals for the fits of B.

The time-averaged force-extension curves derived for 56 bead pairs are shown in Fig. 3. Because no data were excluded, Fig. 3 includes both short-lived (5–10 s) and long-lived (5–20 min) tethers. The fits by one- and two-component worm-like chain models are compiled in Fig. 4, by plotting 1/L_p versus L_c. It is noticeable in both figures that the curves for long-lived tethers lie to one extreme of the length distribution, corresponding to long contour lengths. Supposing that the preincubated titin is specifically bound to the antibody on the bead via the epitope at the M-line, short-lived tethers are bound to the other bead nonspecifically, apparently at random along the length of the molecule.

View larger version (32K): [in this window] [in a new window]   FIGURE 3  Complete data sets for time-averaged force-extension relations for the whole molecule at 150 and 300 mM ionic strength. Short-lived tethers (shaded) lasted less than 10 s before detachment. Long-lived tethers (solid) lasted at least 5 min of continuous stretch-release cycles before the experiment was terminated.

View larger version (20K): [in this window] [in a new window]   FIGURE 4  Plots of 1/Lp versus Lc for the whole molecule at 150 and 300 mM ionic strength. (Upper row) Single worm-like chain fits, short-lived tethers (), and long-lived tethers (). (Lower row) Double worm-like chain fits, short-lived tethers ( and for chain I and II, respectively), and long-lived tethers (+ and x for chain I and II, respectively).

As regards the values of L_p and L_c for long-lived tethers, the values for the two components found in this study are similar but not identical in magnitude to those reported by Tskhovrebova et al. (1997). The short persistence length component (chain I) was identified by Tskhovrebova et al. with the PEVK region, and the experimental and theoretical values of L_c are in reasonable agreement (Tables 3 and 4). The value of L_p of 0.50 nm is roughly equivalent to an L_k of 1.0 nm, or to a chain segment length of 1.0/0.38 = 2.6 amino acid residues, consistent with a polypeptide chain with some degree of hindered rotation. The long persistence length component (chain II) with a value of L_c of 966 nm is to be identified with the chain of Ig/Fn domains for the whole molecule, with a value of L_p of 3 nm and a segment length of 6 nm, corresponding to flexibility over a stretch of 1–2 neighboring domains.

Chain I was sensitive to ionic strength, with the value of L_p changing from 0.50 nm at 150 mM to 1.7 nm at 300 mM (Table 4), whereas chain II was not affected by ionic strength.

A-band region
The antibody pair used was anti-I105-AB5. This demarks a region consisted of the entire A-band component plus a small 13 Ig/Fn domain segment of the I-band (Table 2 and Fig. 1). The results of single WLC modeling are shown in Fig. 5, upper left panel. At first sight it is surprising that the curves for short-lived tethers lie to the low L_c side of the curves for long-lived tethers: titin was precomplexed with the M-line antibody (AB5), and thus there is no apparent reason why short-lived (nonspecific) tethers should not have spanned the entire length of the molecule. However, there are few full-length short-lived tethers in any of the experiments, implying that the Z-line end of the molecule is either not as accessible as the rest of the molecule or that it was often truncated (Nave et al., 1989).

View larger version (17K): [in this window] [in a new window]   FIGURE 5  Plots of 1/Lp versus Lc for double WLC fits for A-band, tandem Ig's, and I-band at 150 mM and 300 mM ionic strength. Short-lived tethers () and long-lived tethers () for A-band region anti-I105-AB5 (top row), tandem Ig region anti-I84–86-anti-I105, (middle row), and I-band region T12-anti-I105 (bottom row).

I-band region
The I-band region was selected by using the T12 and anti-I105 antibodies, the anti-I105 antibody mapping 50–60 nm on the N-terminal side of the A/I junction (Fig. 1 and Table 2). The I-band region force-extension data were best fitted by a two-component model, with values of L_p similar to those found for the two components of the whole molecule, and with values of L_c of 507 and 374 nm for chains I and II, respectively (Table 5 and Fig. 5). Only the short persistence length component was sensitive to ionic strength. It follows that chain I lies within the I-band region. Most curves exhibited little obvious signs of hysteresis, similar to the whole skeletal muscle titin stretch data, with only one tether in the 150-mM data set and two in the 300-mM data set showing some small transient hysteresis that lasted less than 10 consecutive stretch-release cycles.

PEVK region
Antibodies anti-N2-A and anti-I84–86 were used to select the PEVK region (Fig. 1 and Table 2). The steady-state force-extension curves of long-lived tethers were fitted adequately by a single worm-like chain model (Table 6). The persistence length (0.91 nm) and contour length (533 nm) show that this corresponds to chain I of the whole molecule, and as expected L_p is sensitive to ionic strength. Thus chain I corresponds to the PEVK region. More detailed results on the dependence of the polymer parameters on ionic strength and on temperature are given below.

View larger version (17K): [in this window] [in a new window]   FIGURE 6  Plots of 1/Lp versus Lc for single WLC fits for the native PEVK region, the PEVK construct, and for the whole molecule of cardiac muscle titin at 150 and 300 mM ionic strength. Short-lived tethers () and long-lived tethers (), for the native PEVK region N2-A to anti-I84-86 (top row), 550-aa PEVK construct (middle row), and whole bovine cardiac titin region T12-AB5 (bottom row).

The contour lengths obtained from the fits are plotted against the extended lengths predicted from sequence information of the soleus muscle titin isoform in Fig. 7. There is reasonable agreement between most of the experimental values of L_c and the predicted values, though there is some deviation especially for the highest contour lengths, consistent with the presence of fewer Ig domains and a shorter PEVK region in longissimus dorsi compared to the soleus sequence. The simplest interpretation of these results is that over the range of forces examined, the elastic properties of skeletal muscle titin can be described by two chains in series, one (chain I) deriving from the PEVK region and the other (chain II) from the chain of Ig/Fn domains. Only the PEVK region is affected by ionic strength.

View larger version (14K): [in this window] [in a new window]   FIGURE 7  Comparison of total contour length from WLC fits with contour length predicted from the soleus muscle titin isoform sequence. (Vertical bars) Total range of fitted contour lengths. (Horizontal bars) Error of 10% of the predicted contour length from the sequence. (Solid line) Theoretical 1:1 plot. Ranges of contour length rather than errors are plotted as the preparation used may have contained a number of isoforms of different length; the error in contour length is included as a guide to the distribution of length.

Force-extension relation of PEVK region: ionic strength, temperature, and pH dependence
As the PEVK region showed a marked dependence on ionic strength, we investigated the dependence in more detail, and we also measured the effect of change of temperature. We attempted to do these experiments on both the native PEVK region and the PEVK construct, but experiments on the former were limited to the effect of ionic strength, as the antibody binding became too weak with substantial increase of temperature. The effect of changing pH was also investigated, though problems associated with weakening of tether binding restricted the range to only 1–2-pH units, and no significant changes in elasticity over this range were detected.

Ionic strength
The force-extension relation was measured as a function of ionic strength over the range 15–300 mM. Fitting the force-extension curve of long-lived tethers with a WLC model resulted in the relation of L_p and L_c to ionic strength shown in Fig. 8 A. The upper pair of curves is for the PEVK construct and the lower pair for native PEVK. Both show little or no systematic change in L_c but a marked dependence of L_p on ionic strength. As the Debye-Hückel electrostatic screening effect depends on the inverse of the square root of ionic strength, the data are replotted on a log-log scale in Fig. 8 B. This reveals that the dependence on ionic strength is 1.4 and 1.8 power for native and construct PEVK, respectively, much higher than is expected from screening effects alone. The extrapolation of L_p to zero ionic strength gives a value of 0.2 nm, close to the expected value of a fully flexible polypeptide chain. If the variation in persistence length with ionic strength has its origin in Debye-Hückel screening, the power dependence implies a complex effect, possibly involving hydrophobic effects (see Discussion).

View larger version (32K): [in this window] [in a new window]   FIGURE 8  (A) Dependence of persistence length (Lp) and contour length (Lc) on ionic strength for PEVK construct (upper pair of plots) and native PEVK region (lower pair of plots) for long-lived tethers. Error bars are one SE of the mean. (B) Double logarithmic plots of Lp against ionic strength, with regression lines; (upper) PEVK construct; (lower) native PEVK region. Effect of temperature on force-extension relation of PEVK construct (for long-lived tethers): (C) Variation in force-extension relation with temperature for the same tether and (D) dependence of contour length (top) and persistence length (bottom) on temperature from single WLC fits. Data points connected by a line represent a single tether. • are the mean values of the parameters after binning of all data over a 10°C range; error bars are one standard deviation from this mean.

In an entropic model (worm-like chain or freely jointed chain), force at a fixed extension should be proportional to the absolute temperature, and thus it should vary by 60/270 = 25% over the range studied, whereas the relation is clearly much steeper. It appears that the construct adopts a more compact form as the temperature is raised (lower L_p), with part of the molecule no longer compliant (lower L_c) over the range of forces applied.

Hysteresis in the PEVK region
Transient hysteresis in long-lived tethers was observed in the nonaveraged force-extension curves for the PEVK component, both in the native PEVK region and the PEVK construct, principally within the first 10 stretch-release cycles and then rarely for subsequent cycles. Hysteresis implies the presence of stress relaxation, and in many records there was direct evidence for stepwise stress relaxation, though the lack of significant hysteresis in the whole skeletal muscle titin and I-band data sets seems possibly to contradict this result as is discussed later (Discussion).

PEVK construct
Two successive stretch-release cycles from the start of an experiment are shown in the record of Fig. 9 A taken at an ionic strength of 15 mM for a long-lived tether. This particular record was selected as it showed the greatest number of lengthening steps. The force-extension plots (Fig. 9 B) show stepwise lengthening, visibly with 7–9 steps. Chung-Kennedy edge detection (Chung and Kennedy, 1991) was performed on the data using a threshold t-statistic of 8 (Supplementary Material), and the raw step lengths were measured for those steps found to be statistically significant. The distribution of step lengths lumps together steps that occurred at different levels of force, and because of the nonlinearity of force-extension relation, the step lengths need to be standardized. This can be achieved by fitting theoretical polymer curves to the force-extension relation of Fig. 9 in between steps (Rief et al., 1997) and then using differences between the resulting contour lengths (Supplementary Material). The results are shown overlaid on the force-extension data of Fig. 9 B, and a plot of 1/L_p versus L_c is shown in Fig. 9 C.

View larger version (17K): [in this window] [in a new window]   FIGURE 9  Stepwise lengthening from triangle wave stretches of the PEVK construct for long-lived tethers. (A) Force and extension records and the Chung-Kennedy t-statistic output. For clarity, only two consecutive stretch-release cycles are shown (solid and shaded, respectively). Arrows mark the position of detected steps. (B) The equivalent force-extension relation for each cycle in A. Single WLC fits are overlaid on each interstep region of the force-extension relation. (C) Plot of 1/Lp versus 1/Lc for the fits in B. Ionic strength was 15 mM.

The distribution of the amplitude of steps in contour length during both stretch and release half-cycles for long-lived tethers is shown in Fig. 10 A. Three positive extension peaks are resolved, which can be fitted by a series of Gaussian curves based on multiples of an 10–12-nm basic step; if the whole set is fitted by an integral multiple of a basic step, its value is 11.1 nm. There are a few negative-going (i.e., increasing force) steps as well as the predominantly positive-going steps. The negative-going steps occurred at forces less than 20 pN; although too few in number to justify Gaussian fitting, there appear to be peaks at –10 and –20 nm. Autocorrelation analysis (Supplementary Material) on this histogram and that for square wave stretches (Fig. 10 D) suggested a periodicity of 12.3 nm, which agreed reasonably well with the observed peak spacing. The modal value occurs at 24 nm, double the basic step. This could arise from a number of reasons: 1), the Chung-Kennedy detector might miss many of the single steps; 2), the real basic step might be 24 nm, but there were a number of instances of double tethers, where the effect of a step in one molecule is halved; and 3), there might be cooperativity between the units (modules) underlying the steps, for example the lengthening of one module might destabilize a neighboring module. Experiments using square wave stretches (next section) suggest that the first explanation is the correct one.

View larger version (40K): [in this window] [in a new window]   FIGURE 10  (A) Distribution of lengthening step size for triangle wave stretches of PEVK construct for long-lived tethers from eight bead pairs after Chung-Kennedy edge detection (20-ms window size and a t-statistic detection threshold of 8), using 5-nm bins. A total of 193 steps were detected, 27 negative extension steps and 166 positive extension steps. Fits for a three-Gaussian unconstrained fit for positive steps are shown (shaded) with the individual Gaussians (solid); Gaussian widths shown above each peak. Imposing the constraint that each peak should be an integer multiple of a unitary value produced a slightly worse fit with a unitary peak of 11.1 nm. Statistical tests confirmed that the Gaussian peaks were real and distinct at a confidence level P < 0.01. Square wave stretches on the PEVK construct for long-lived tethers: (B) force and extension records and (C, top) expansion of data from B, and (bottom) t-statistic output of Chung-Kennedy edge detection routine, window size of 20 ms with t-statistic threshold for step acceptance set at 8. (Arrows) Position of detected steps. (D) Distribution of the lengthening step size for square wave stretches on PEVK construct for long-lived tethers (26 bead pairs, window size of 20 ms, and t-statistic threshold of 8; bin size is 5 nm) distribution of contour length step size binned in 5-nm intervals. Unconstrained three-Gaussian fit (shaded) and the individual Gaussians (solid). Constraining the peaks to be integer multiples of a unitary value led to a slightly worse fit with a unitary peak of 10.5 nm. Vertical errors on the histograms bars are 3%.

The lengthening process might be explained by the breaking of multiple tethers, since L_p increases, but since L_c clearly also changes this seems unlikely (additional counterarguments are given in the Discussion). This is because the apparent persistence length of n parallel tethers is equal to L_p/n, and as each tether breaks, there is an increase in apparent persistence length by L_p(1/(n – 1) – 1/n) but no change in L_c. Whether the later lengthening process is due to unfolding of structural modules or to stepwise desorption of the molecule from the surface is dealt with in the Discussion.

Stepwise stress relaxation was observed more clearly when square wave stretches were applied (Fig. 10, B and C). Tethers were generated using the same tapping protocol and, as with triangle wave stretches, bead 1 held in positional feedback whereas the other bead was moved by applying a square wave of frequency 1–2 Hz to the galvanometer mirrors of trap 2 such that the force on the PEVK tether would be zero for half a cycle and nonzero for the other half, the value of which was determined by the chosen amplitude of the square wave.

There was a single peak in the raw extension step at 7–8 nm, but no values for negative extension-steps; however, the minimal force applied in these experiments was 25 pN, larger than the maximal force at which negative-going steps were seen in triangle wave experiments. As in the triangle wave experiments, it was necessary to standardize steps by correcting for the differing force at which they occurred, by estimating the change in contour length at each step. This was less straightforward than for triangle wave experiments since there is no interstep stretch of the force-extension relation to fit. However, WLC fits to the triangle wave stretch data can be compiled into a look-up table for contour and persistence lengths corresponding to points on the force-extension plane, allowing the equivalent contour and persistence lengths for square wave stretch data to be predicted after appropriate extrapolation. The result is shown in Fig. 10 D.

Unlike the result from triangle wave stretches, the modal value of step size is the same as the basic step size of 12 nm. A possible explanation is that in all cases the two adjacent Chung-Kennedy detection windows run parallel to the time vector and not parallel to the vector of mean slope of extension with respect to time, unless a square wave stretch is employed. For triangle wave stretches, the molecule stiffens with increasing time and so the difference in mean extension values between adjacent detection windows either side of a true step event is lower than is the case for square wave stretches, hence lowering the likelihood for detecting small events. Thus more of the basic step events are missed for triangle wave stretches compared to square wave stretches.

Native PEVK
Stress relaxation was also observed for stretches on long-lived tethers of the native longissimus dorsi muscle titin PEVK region, using the antibody bead-conjugation technique to select the region bounded by the anti-N2-A and anti-I84–86 epitopes. The hysteresis between stretch and release half-cycles, which occurred only for the first 10 cycles, was more dramatic than