Journal of Muscle Research and Cell Motility (2005)
DOI 10.1007/s10974-005-9036-3
Ó Springer 2005
Connecting filament mechanics in the relaxed sarcomere
EKATERINA NAGORNYAK and GERALD H. POLLACK*
Department of Bioengineering, University of Washington, 357962, Seattle, WA, 98195, USA
Abstract
By examining the mechanical properties of single unactivated myofibrils it has been shown that shortening and
stretching of sarcomeres occurs in stepwise fashion, and that steps are seen also in the relaxed state (Yang et al.
(1998) Biophys J 74: 1473–1483; Blyakhman et al. (2001) Biophys J 81: 1093–1100; Nagornyak et al. (2004)
J. Muscle. Res. Cell Motil. 25: 37–43). The latter are inevitably associated with connecting filaments. Here, we
carried out measurements on single myofibrils from rabbit psoas muscle to investigate steps in unactivated specimens in more detail. Myofibrils were stretched and released in ramp-like fashion. For the single sarcomere the time
course of length change was consistently stepwise. We found that in the unactivated myofibrils, step size depended
on initial sarcomere length, diminishing progressively with increase of initial sarcomere length, whereas in the case
of activated sarcomeres, step size was consistently 2.7 nm.
Introduction
Based on the pioneering work of Professor Koscak
Maruyama, to whom this volume is dedicated, many
investigators have been inspired to explore the properties of connectin/titin. Much of this work has been
carried out using isolated connectin/titin molecules.
Here, we approach the mechanics of this protein in its
natural state: in the intact myofibril.
Recent myofibril experiments have shown that in
activated sarcomeres, shortening occurs in steps consistently on the order of 2.7 nm or integer multiples
thereof (Blyakhman et al., 1999; Yakovenko et al.,
2002). While the mechanism of active stepping remains
to be settled, stepwise behavior has also been observed
in relaxed sarcomeres. These steps have been attributed to length change of connecting filaments, for it is
only the connecting filaments that change length in the
relaxed state (Maruyama et al., 1984; Fuerst et al.,
1988; Horowits et al., 1989; Politou et al., 1995;
Improta et al., 1996).
This inference is supported by experiments on isolated titin molecules. Rief et al. (1997) reported step sizes in isolated titin molecules in the range from 25 to
30 nm, although Tskhovrebova et al. (1997) noted a
broader distribution, 5–25 nm. In experiments on single isolated myofibrils, in which thin filaments had
been functionally removed, leaving the connecting
(titin) filaments as sole agent taking up the length
change, step size was an integer multiple of 2.3 nm
(Blyakhman et al., 2001). The source of the difference
* To whom correspondence should be addressed. Phone: 206-6851880; Fax: 206-685-3300; E-mail: [email protected]
between our studies and those in isolated titin molecules is unclear, although there is some size overlap.
In the present experiments a differentially based
algorithm that could suppress noise contributions sufficiently to bring the detection limit down to subnanometer levels (Sokolov et al., 2003) was used.
With this high-resolution algorithm, we measured
steps in activated and unactivated sarcomeres both
during shortening and during imposed stretch. For
activated sarcomeres, we confirmed that step size was
invariant. For relaxed myofibrils, however, step size
was not constant: it was a function of initial sarcomere length.
Methods
Experimental apparatus
Single myofibrils were isolated and mounted in a specially constructed apparatus built around Zeiss Axiovert-35 microscope as previously described in detail
(Yang et al., 1998; Blyakhman et al., 1999) (Figure 1).
The striation pattern (Figure 1, insert) was projected
onto a 1024-element photodiode array. The array was
scanned every 50 ms (a compromise between time resolution and integration time needed to reduce noise)
to produce a trace of intensity vs. position along the
myofibril. A-bands produced positive-going signals,
I-band negative-going (Figure 1, insert). Calibration of
the photodiode array gave 8.17 pixels/lm. With sarcomere length around 2.5 lm, there were 18–20 pixels/
sarcomere.
Nagornyak et al., 2004). To identify a step it was necessary to define the pair of pauses surrounding the
step, each of which had to contain a minimum of five
consecutive sample points. The pause was taken provisionally as a region of the trace whose estimated bestfit was nominally parallel to the horizontal axis. Step
size was then computed as the vertical span between
centers of two successive best-fit line segments.
Results
Fig. 1. Schematic of apparatus. Insert: top – representative phasecontrast image of single myofibril; middle – intensity trace along
myofibril (large upward deflections represent A bands; small upward
deflections correspond to Z lines); bottom – repetitive scans of myofibril during motor-imposed length change, shown in gray scale.
Protocol
Single myofibrils were prepared from rabbit psoas
muscles (Linke et al., 1994; Nagornyak et al., 2004).
Solutions, which were used for preparation and experimentation, were previously described in detail (Nagornyak et al., 2004). All experiments were carried out
at room temperature. One end of a myofibril was attached to the tip of a glass needle; the other one was
mounted on the moving glass tip of the piezoelectric
motor, which could impose length changes on the
specimen. Experiments were carried out in relaxing or
activating solution, and a trapezoidal length change
was imposed with the aid of the motor. Motor-ramp
speeds were selected to give two nominal speeds of
sarcomere-length change: 2 nm/s and 8 nm/s. The
stretch–release protocols were carried out at moderate
length 1.8–3.3 lm for unactivated myofibrils, and at
1.6 to 2.7 lm for activated muscles. In total, 412 sarcomeres from 34 relaxed myofibrils, and 112 sarcomeres from 11 activated myofibrils were analyzed.
Figure 2 shows a representative trace of sarcomerelength vs. time in a relaxed specimen. Sarcomerelength-change traces contain multiple pause periods
during which the sarcomere-length change was close to
zero. To analyze these steps, the vertical spacing
between successive pauses was determined. Sizes
obtained from many steps were plotted as a continuous histogram. An example of the results obtained
from shortening steps is shown in Figure 3. The light
curve shows a primary peak at 2.5 nm. An additional
peak is seen at an approximate integer multiple of the
primary value (5 nm). The dark curve represents the
histogram obtained for lengthening steps. Again, two
histogram peaks are observed: a primary one at
2.5 nm and secondary one at 5 nm. The figure illustrates that the size of the shortening step is similar to
the size of lengthening step.
Experiments were also carried out to determine the
effect of ramp speed. This was done both for stretch
and for release. Figure 4 shows results for high speed
ramps (continuous line) and for low speed ramps (broken line). For the high-speed ramp, the range of sarcomere speeds was 6–11 nm/s, and for the low-speed
ramp it was 1–4 nm/s. Lower speed increased the fraction of smaller steps relative to larger ones. Otherwise,
the effect of speed was modest. Extending the range of
Sarcomere-length measurement
To detect sarcomere length, a peak-detection algorithm was developed, based on the minimum average
risk method (Sokolov et al., 2003). The algorithm
operates on repeated scans of an intensity peak, precisely quantifying peak movement between scans. The
method compares the respective A-band intensity peak
with that of the one immediately previous. From the
relative shift between two A-bands, the change of sarcomere length can be computed. Because the method
is differential, high resolution is achieved.
Step detection
Analytical details follow largely along lines already
presented (Yang et al., 1998; Blyakhman et al., 2001;
Fig. 2. Representative trace of sarcomere length change during motor-imposed trapezoid in rabbit psoas muscle. Insets show part of
the trace with representative pauses denoted.
Fig. 3. Histograms of shortening-step size (shaded line; 320 steps
from 73 traces) and lengthening-step size (dark line; 309 steps from
74 traces) in relaxed specimens. In both histograms, peaks are situated at approximate integer multiples of 2.5 nm.
speeds beyond these values was impractical because of
high noise/signal ratio on the low end, and because of
scan-time resolution on the high end.
To determine the effect of sarcomere length on step
size, histograms for four groups of initial sarcomere
length were plotted. The ISL groups were: (1) 1.8–
2.4 lm; (2) 2.4–2.7 lm; (3) 2.7–3.0 lm; (4) 3.0–3.3 lm.
For low velocity ramps (nominally 2 nm/sarc/s) and
for higher velocity ramps (nominally 8 nm/sarc/s) the
histograms show that as initial SL decreased, step size
increased. This trend is shown in Figure 5 (low velocity). All histograms show higher order peaks, which
are integer multiples of the lower order ones.
Discussion
The main finding of these studies is that minimum step
size in relaxed muscle was not constant. We found an
inverse relation between step size and initial sarcomere
length, which was revealed both for low speed and
high-speed deformations. Therefore, some feature of
Fig. 4. Histograms of step size obtained by imposing stretch ramps
at different speed. Low-velocity ramps are shown by broken line
(604 steps from 109 traces); high-velocity ramps are shown by solid
line (611 steps from 63 traces).
Fig. 5. Histograms of step size obtained during applied low-speed
ramp. Step size increases with decrease of initial sarcomere length.
(1) 604 steps from 109 traces; (2) 518 steps from 101 traces; (3) 603
steps from 109 traces; (4) 544 steps from 102 traces.
the relaxed sarcomere generates steps of variable size.
In the unactivated state the sole element mediating
shortening may be the connecting filament. Hence, the
steps must somehow reflect connecting-filament
dynamics.
Unless thick filaments changed length, it seems
inescapable that the stepwise sarcomere length changes observed here in the unactivated state imply stepwise connecting filament length changes. This
conclusion does not imply that the connecting filament is necessarily the steps’ source. The steps could
conceivably arise from thin–thick filament interaction,
which may persist even in relaxed specimens, or from
connecting filament–thin filament interaction. Some of
the experiments were carried out at lengths where
there is no thick–thin filament overlap, but the steps
were equally clear (Granzier and Pollack, 1985). Also,
stepwise dynamics of sarcomeres was found in the
experiments when the thin filament broke from the
Z-line (Yang et al., 1998; Blyakhman et al., 2001),
leaving the connecting filament itself as the sole element for force generation (Linke et al., 1994; Bartoo
et al., 1997).
Given their connecting-filament origin, the steps
have at least two possible sources. One is the folding/
unfolding of compound structures due to a state
change. Thus, the step could arise from a transition
between secondary or tertiary structural states.
Another possible mechanism is a transition within one
structural state – a progressive unfolding/folding of folded/unfolded proteins (Zocchi, 1997). One such candidate is the sevenfold beta-barrel structure of the
connecting filament’s Ig-domain (Erickson, 1994; Improta et al., 1996, 1998). Each domain contains about
90 residues. Thus, each turn is several nanometers in
length. An interesting possibility is that the 2–3-nm
increments reflect the folding-unfolding of individual
turns of the beta-barrel within one Ig-domain.
Following along this line of interpretation, if turn
lengths are not completely uniform within the beta
as, indeed, does the precise identification of the source
of these passive steps.
References
Fig. 6. Histograms of step size obtained in the activated state. Multiple peaks appear at approximate integer multiples of 2.7 nm. (1)
606 steps from 86 traces; (2) 670 steps from 78 traces; (3) 588 steps
from 74 traces.
barrel, then a series of different step sizes will be elicited during folding/unfolding. Especially if unfolding
of different turns occurs at different tensions (Rief
et al., 1999), then an SL dependence of step size might
be envisioned. Thus, within one beta-barrel weaker
turns will unfold at lower tension level; at higher tension (larger SL) the weakest turns will already have
stretched (unfolded), and the remaining steps would
arise from unfolding of the stiffer (stronger) turns. The
results showed smaller steps for larger SL. This might
then imply that the turns that unfold at shorter SL are
the longer ones, while those that unfold later, at longer SL, are the shorter ones. This is a speculation that
warrants followup.
Potential artifacts
Measurements of sarcomere-length change at high resolution are subject to various potential sources of artifact. To check for artifact, many controls have been
carried out (Yang et al., 1998; Blyakhman et al., 1999,
2001), and all have been negative for artifact. As an
additional control, we examined the influence of initial
SL on step size in activated specimens (see Figure 6),
and found that SL-dependence observed for relaxed
myofibrils apparently does not arise in the case of activated muscle. For all histograms the primary peak was
seen at 2.68–2.71 nm, with additional peaks at integer
multiples of this quantal value. Also the influence of
noise was tested, by eliminating records in which peakto-peak noise during the pause exceeded 2 nm. Results
were similar.
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sarcomere length in unactivated mammalian sarcomeres occur in steps, which apparently reflect the
mechanical properties of connectin filaments. Unlike
the case in activated sarcomeres, where step size is
invariant, step size in relaxed sarcomeres is inversely
proportional to initial sarcomere length. The reason
for this dependence awaits further experimentation –
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